Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3

Percentage Accurate: 68.0% → 84.6%

Time: 27.1s

Alternatives: 43

Speedup: 0.3×

Specification

Math

\[\begin{array}{l} \\ x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (+ x (/ (* (- y x) (- z t)) (- a t))))

C

double code(double x, double y, double z, double t, double a) {
	return x + (((y - x) * (z - t)) / (a - t));
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + (((y - x) * (z - t)) / (a - t))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + (((y - x) * (z - t)) / (a - t));
}

Python

def code(x, y, z, t, a):
	return x + (((y - x) * (z - t)) / (a - t))

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + (((y - x) * (z - t)) / (a - t));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 68.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (+ x (/ (* (- y x) (- z t)) (- a t))))

C

double code(double x, double y, double z, double t, double a) {
	return x + (((y - x) * (z - t)) / (a - t));
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + (((y - x) * (z - t)) / (a - t))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + (((y - x) * (z - t)) / (a - t));
}

Python

def code(x, y, z, t, a):
	return x + (((y - x) * (z - t)) / (a - t))

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + (((y - x) * (z - t)) / (a - t));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 84.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+68}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+173}:\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+220}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+287}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot a - \left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;y - x \cdot \frac{a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.9e+68)
   (+ y (* (/ (- y x) t) (- a z)))
   (if (<= t 1.2e+173)
     (fma (- z t) (/ (- y x) (- a t)) x)
     (if (<= t 2.8e+220)
       (+ y (* (- y x) (/ (- a z) t)))
       (if (<= t 4.6e+287)
         (+ y (/ (- (* (- y x) a) (* (- y x) z)) t))
         (- y (* x (/ a t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.9e+68) {
		tmp = y + (((y - x) / t) * (a - z));
	} else if (t <= 1.2e+173) {
		tmp = fma((z - t), ((y - x) / (a - t)), x);
	} else if (t <= 2.8e+220) {
		tmp = y + ((y - x) * ((a - z) / t));
	} else if (t <= 4.6e+287) {
		tmp = y + ((((y - x) * a) - ((y - x) * z)) / t);
	} else {
		tmp = y - (x * (a / t));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.9e+68)
		tmp = Float64(y + Float64(Float64(Float64(y - x) / t) * Float64(a - z)));
	elseif (t <= 1.2e+173)
		tmp = fma(Float64(z - t), Float64(Float64(y - x) / Float64(a - t)), x);
	elseif (t <= 2.8e+220)
		tmp = Float64(y + Float64(Float64(y - x) * Float64(Float64(a - z) / t)));
	elseif (t <= 4.6e+287)
		tmp = Float64(y + Float64(Float64(Float64(Float64(y - x) * a) - Float64(Float64(y - x) * z)) / t));
	else
		tmp = Float64(y - Float64(x * Float64(a / t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.9e+68], N[(y + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.2e+173], N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t, 2.8e+220], N[(y + N[(N[(y - x), $MachinePrecision] * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.6e+287], N[(y + N[(N[(N[(N[(y - x), $MachinePrecision] * a), $MachinePrecision] - N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(y - N[(x * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.90000000000000011e68

   1. Initial program 41.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 62.2%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 62.2%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 62.2%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 62.2%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 62.2%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 62.2%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 62.2%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 73.8%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 87.7%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 87.7%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 87.7%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]

   if -2.90000000000000011e68 < t < 1.2e173

   1. Initial program 83.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 80.3%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. +-commutative 80.3%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. +-commutative 80.3%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{a - t} + 1\right)} \]

      3. distribute-lft-in 80.3%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \color{blue}{\left(x \cdot \left(-1 \cdot \frac{z - t}{a - t}\right) + x \cdot 1\right)} \]

      4. mul-1-neg 80.3%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(x \cdot \color{blue}{\left(-\frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      5. distribute-rgt-neg-in 80.3%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{\left(-x \cdot \frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      6. associate-/l* 80.9%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\left(-\color{blue}{\frac{x \cdot \left(z - t\right)}{a - t}}\right) + x \cdot 1\right) \]

      7. mul-1-neg 80.9%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} + x \cdot 1\right) \]

      8. *-rgt-identity 80.9%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \color{blue}{x}\right) \]

      9. associate-+l+ 80.2%

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(z - t\right)}{a - t} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) + x} \]

   5. Simplified 92.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)} \]

   if 1.2e173 < t < 2.8000000000000001e220

   1. Initial program 12.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 52.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. +-commutative 52.2%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. +-commutative 52.2%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{a - t} + 1\right)} \]

      3. distribute-lft-in 52.2%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \color{blue}{\left(x \cdot \left(-1 \cdot \frac{z - t}{a - t}\right) + x \cdot 1\right)} \]

      4. mul-1-neg 52.2%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(x \cdot \color{blue}{\left(-\frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      5. distribute-rgt-neg-in 52.2%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{\left(-x \cdot \frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      6. associate-/l* 12.1%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\left(-\color{blue}{\frac{x \cdot \left(z - t\right)}{a - t}}\right) + x \cdot 1\right) \]

      7. mul-1-neg 12.1%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} + x \cdot 1\right) \]

      8. *-rgt-identity 12.1%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \color{blue}{x}\right) \]

      9. associate-+l+ 12.1%

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(z - t\right)}{a - t} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) + x} \]

   5. Simplified 41.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)} \]

   6. Taylor expanded in t around inf 80.0%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   7. Step-by-step derivation

      1. cancel-sign-sub-inv 80.0%

         \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) + \left(--1\right) \cdot \frac{a \cdot \left(y - x\right)}{t}} \]

      2. mul-1-neg 80.0%

         \[\leadsto \left(y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right)}{t}\right)}\right) + \left(--1\right) \cdot \frac{a \cdot \left(y - x\right)}{t} \]

      3. sub-neg 80.0%

         \[\leadsto \color{blue}{\left(y - \frac{z \cdot \left(y - x\right)}{t}\right)} + \left(--1\right) \cdot \frac{a \cdot \left(y - x\right)}{t} \]

      4. metadata-eval 80.0%

         \[\leadsto \left(y - \frac{z \cdot \left(y - x\right)}{t}\right) + \color{blue}{1} \cdot \frac{a \cdot \left(y - x\right)}{t} \]

      5. *-lft-identity 80.0%

         \[\leadsto \left(y - \frac{z \cdot \left(y - x\right)}{t}\right) + \color{blue}{\frac{a \cdot \left(y - x\right)}{t}} \]

      6. *-commutative 80.0%

         \[\leadsto \left(y - \frac{z \cdot \left(y - x\right)}{t}\right) + \frac{\color{blue}{\left(y - x\right) \cdot a}}{t} \]

      7. associate-+l- 80.0%

         \[\leadsto \color{blue}{y - \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{\left(y - x\right) \cdot a}{t}\right)} \]

      8. div-sub 80.0%

         \[\leadsto y - \color{blue}{\frac{z \cdot \left(y - x\right) - \left(y - x\right) \cdot a}{t}} \]

      9. *-commutative 80.0%

         \[\leadsto y - \frac{z \cdot \left(y - x\right) - \color{blue}{a \cdot \left(y - x\right)}}{t} \]

      10. distribute-rgt-out-- 80.7%

          \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

      11. associate-*r/ 90.9%

          \[\leadsto y - \color{blue}{\left(y - x\right) \cdot \frac{z - a}{t}} \]

   8. Simplified 90.9%

      \[\leadsto \color{blue}{y - \left(y - x\right) \cdot \frac{z - a}{t}} \]

   if 2.8000000000000001e220 < t < 4.60000000000000028e287

   1. Initial program 25.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around -inf 94.9%

      \[\leadsto \color{blue}{y + -1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

   if 4.60000000000000028e287 < t

   1. Initial program 7.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 68.3%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 68.3%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 68.3%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 68.3%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 68.3%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 68.3%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 68.3%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 83.1%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 84.8%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 84.8%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 84.8%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]
   6. Step-by-step derivation

      1. *-commutative 84.8%

         \[\leadsto y - \color{blue}{\left(z - a\right) \cdot \frac{y - x}{t}} \]

      2. clear-num 84.8%

         \[\leadsto y - \left(z - a\right) \cdot \color{blue}{\frac{1}{\frac{t}{y - x}}} \]

      3. un-div-inv 84.8%

         \[\leadsto y - \color{blue}{\frac{z - a}{\frac{t}{y - x}}} \]

   7. Applied egg-rr 84.8%

      \[\leadsto y - \color{blue}{\frac{z - a}{\frac{t}{y - x}}} \]

   8. Taylor expanded in y around 0 99.7%

      \[\leadsto y - \color{blue}{-1 \cdot \frac{x \cdot \left(z - a\right)}{t}} \]
   9. Step-by-step derivation

      1. mul-1-neg 99.7%

         \[\leadsto y - \color{blue}{\left(-\frac{x \cdot \left(z - a\right)}{t}\right)} \]

      2. associate-/l* 100.0%

         \[\leadsto y - \left(-\color{blue}{x \cdot \frac{z - a}{t}}\right) \]

   10. Simplified 100.0%

       \[\leadsto y - \color{blue}{\left(-x \cdot \frac{z - a}{t}\right)} \]

   11. Taylor expanded in z around 0 99.7%

       \[\leadsto \color{blue}{y + -1 \cdot \frac{a \cdot x}{t}} \]
   12. Step-by-step derivation

       1. mul-1-neg 99.7%

          \[\leadsto y + \color{blue}{\left(-\frac{a \cdot x}{t}\right)} \]

       2. *-commutative 99.7%

          \[\leadsto y + \left(-\frac{\color{blue}{x \cdot a}}{t}\right) \]

       3. associate-*r/ 100.0%

          \[\leadsto y + \left(-\color{blue}{x \cdot \frac{a}{t}}\right) \]

       4. unsub-neg 100.0%

          \[\leadsto \color{blue}{y - x \cdot \frac{a}{t}} \]

   13. Simplified 100.0%

       \[\leadsto \color{blue}{y - x \cdot \frac{a}{t}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+68}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+173}:\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+220}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+287}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot a - \left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;y - x \cdot \frac{a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 86.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.05 \cdot 10^{+63}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;t \leq -400:\\ \;\;\;\;x \cdot \left(\left(1 + \frac{t}{a - t}\right) + \left(\frac{y \cdot \left(z - t\right)}{x \cdot \left(a - t\right)} + \frac{z}{t - a}\right)\right)\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-272}:\\ \;\;\;\;x + \frac{-1}{\frac{a - t}{\left(y - x\right) \cdot \left(t - z\right)}}\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{+173}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.05e+63)
   (+ y (* (/ (- y x) t) (- a z)))
   (if (<= t -400.0)
     (*
      x
      (+
       (+ 1.0 (/ t (- a t)))
       (+ (/ (* y (- z t)) (* x (- a t))) (/ z (- t a)))))
     (if (<= t 1.2e-272)
       (+ x (/ -1.0 (/ (- a t) (* (- y x) (- t z)))))
       (if (<= t 1.22e+173)
         (fma (- y x) (/ (- z t) (- a t)) x)
         (+ y (* (- y x) (/ (- a z) t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.05e+63) {
		tmp = y + (((y - x) / t) * (a - z));
	} else if (t <= -400.0) {
		tmp = x * ((1.0 + (t / (a - t))) + (((y * (z - t)) / (x * (a - t))) + (z / (t - a))));
	} else if (t <= 1.2e-272) {
		tmp = x + (-1.0 / ((a - t) / ((y - x) * (t - z))));
	} else if (t <= 1.22e+173) {
		tmp = fma((y - x), ((z - t) / (a - t)), x);
	} else {
		tmp = y + ((y - x) * ((a - z) / t));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.05e+63)
		tmp = Float64(y + Float64(Float64(Float64(y - x) / t) * Float64(a - z)));
	elseif (t <= -400.0)
		tmp = Float64(x * Float64(Float64(1.0 + Float64(t / Float64(a - t))) + Float64(Float64(Float64(y * Float64(z - t)) / Float64(x * Float64(a - t))) + Float64(z / Float64(t - a)))));
	elseif (t <= 1.2e-272)
		tmp = Float64(x + Float64(-1.0 / Float64(Float64(a - t) / Float64(Float64(y - x) * Float64(t - z)))));
	elseif (t <= 1.22e+173)
		tmp = fma(Float64(y - x), Float64(Float64(z - t) / Float64(a - t)), x);
	else
		tmp = Float64(y + Float64(Float64(y - x) * Float64(Float64(a - z) / t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.05e+63], N[(y + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -400.0], N[(x * N[(N[(1.0 + N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(x * N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.2e-272], N[(x + N[(-1.0 / N[(N[(a - t), $MachinePrecision] / N[(N[(y - x), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.22e+173], N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(y + N[(N[(y - x), $MachinePrecision] * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -3.04999999999999984e63

   1. Initial program 43.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 63.7%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 63.7%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 63.7%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 63.7%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 63.7%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 63.7%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 63.7%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 74.8%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 88.2%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 88.2%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 88.2%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]

   if -3.04999999999999984e63 < t < -400

   1. Initial program 80.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around -inf 99.5%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(\left(-1 \cdot \frac{y \cdot \left(z - t\right)}{x \cdot \left(a - t\right)} + \frac{z}{a - t}\right) - \left(1 + \frac{t}{a - t}\right)\right)\right)} \]

   if -400 < t < 1.19999999999999995e-272

   1. Initial program 91.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 91.1%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{a - t}{\left(y - x\right) \cdot \left(z - t\right)}}} \]

      2. inv-pow 91.1%

         \[\leadsto x + \color{blue}{{\left(\frac{a - t}{\left(y - x\right) \cdot \left(z - t\right)}\right)}^{-1}} \]

      3. *-commutative 91.1%

         \[\leadsto x + {\left(\frac{a - t}{\color{blue}{\left(z - t\right) \cdot \left(y - x\right)}}\right)}^{-1} \]

      4. associate-/r* 88.9%

         \[\leadsto x + {\color{blue}{\left(\frac{\frac{a - t}{z - t}}{y - x}\right)}}^{-1} \]

   4. Applied egg-rr 88.9%

      \[\leadsto x + \color{blue}{{\left(\frac{\frac{a - t}{z - t}}{y - x}\right)}^{-1}} \]
   5. Step-by-step derivation

      1. unpow-1 88.9%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{a - t}{z - t}}{y - x}}} \]

      2. associate-/l/ 91.1%

         \[\leadsto x + \frac{1}{\color{blue}{\frac{a - t}{\left(y - x\right) \cdot \left(z - t\right)}}} \]

      3. *-commutative 91.1%

         \[\leadsto x + \frac{1}{\frac{a - t}{\color{blue}{\left(z - t\right) \cdot \left(y - x\right)}}} \]

   6. Simplified 91.1%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{a - t}{\left(z - t\right) \cdot \left(y - x\right)}}} \]

   if 1.19999999999999995e-272 < t < 1.22e173

   1. Initial program 76.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 76.1%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-/l* 93.5%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. fma-define 93.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]

   3. Simplified 93.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]
   4. Add Preprocessing

   if 1.22e173 < t

   1. Initial program 18.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 44.5%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. +-commutative 44.5%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. +-commutative 44.5%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{a - t} + 1\right)} \]

      3. distribute-lft-in 44.5%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \color{blue}{\left(x \cdot \left(-1 \cdot \frac{z - t}{a - t}\right) + x \cdot 1\right)} \]

      4. mul-1-neg 44.5%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(x \cdot \color{blue}{\left(-\frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      5. distribute-rgt-neg-in 44.5%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{\left(-x \cdot \frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      6. associate-/l* 21.0%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\left(-\color{blue}{\frac{x \cdot \left(z - t\right)}{a - t}}\right) + x \cdot 1\right) \]

      7. mul-1-neg 21.0%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} + x \cdot 1\right) \]

      8. *-rgt-identity 21.0%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \color{blue}{x}\right) \]

      9. associate-+l+ 18.4%

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(z - t\right)}{a - t} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) + x} \]

   5. Simplified 48.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)} \]

   6. Taylor expanded in t around inf 85.8%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   7. Step-by-step derivation

      1. cancel-sign-sub-inv 85.8%

         \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) + \left(--1\right) \cdot \frac{a \cdot \left(y - x\right)}{t}} \]

      2. mul-1-neg 85.8%

         \[\leadsto \left(y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right)}{t}\right)}\right) + \left(--1\right) \cdot \frac{a \cdot \left(y - x\right)}{t} \]

      3. sub-neg 85.8%

         \[\leadsto \color{blue}{\left(y - \frac{z \cdot \left(y - x\right)}{t}\right)} + \left(--1\right) \cdot \frac{a \cdot \left(y - x\right)}{t} \]

      4. metadata-eval 85.8%

         \[\leadsto \left(y - \frac{z \cdot \left(y - x\right)}{t}\right) + \color{blue}{1} \cdot \frac{a \cdot \left(y - x\right)}{t} \]

      5. *-lft-identity 85.8%

         \[\leadsto \left(y - \frac{z \cdot \left(y - x\right)}{t}\right) + \color{blue}{\frac{a \cdot \left(y - x\right)}{t}} \]

      6. *-commutative 85.8%

         \[\leadsto \left(y - \frac{z \cdot \left(y - x\right)}{t}\right) + \frac{\color{blue}{\left(y - x\right) \cdot a}}{t} \]

      7. associate-+l- 85.8%

         \[\leadsto \color{blue}{y - \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{\left(y - x\right) \cdot a}{t}\right)} \]

      8. div-sub 85.8%

         \[\leadsto y - \color{blue}{\frac{z \cdot \left(y - x\right) - \left(y - x\right) \cdot a}{t}} \]

      9. *-commutative 85.8%

         \[\leadsto y - \frac{z \cdot \left(y - x\right) - \color{blue}{a \cdot \left(y - x\right)}}{t} \]

      10. distribute-rgt-out-- 86.0%

          \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

      11. associate-*r/ 91.3%

          \[\leadsto y - \color{blue}{\left(y - x\right) \cdot \frac{z - a}{t}} \]

   8. Simplified 91.3%

      \[\leadsto \color{blue}{y - \left(y - x\right) \cdot \frac{z - a}{t}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.05 \cdot 10^{+63}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;t \leq -400:\\ \;\;\;\;x \cdot \left(\left(1 + \frac{t}{a - t}\right) + \left(\frac{y \cdot \left(z - t\right)}{x \cdot \left(a - t\right)} + \frac{z}{t - a}\right)\right)\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-272}:\\ \;\;\;\;x + \frac{-1}{\frac{a - t}{\left(y - x\right) \cdot \left(t - z\right)}}\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{+173}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \frac{y - x}{t} \cdot \left(a - z\right)\\ t_2 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-69}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z + t \cdot \left(x - y\right)}{a - t}\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t\_2 \leq 10^{+259}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* (/ (- y x) t) (- a z))))
        (t_2 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -2e-69)
       (+ x (/ (+ (* (- y x) z) (* t (- x y))) (- a t)))
       (if (<= t_2 0.0)
         (+ y (* (- y x) (/ (- a z) t)))
         (if (<= t_2 1e+259) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (((y - x) / t) * (a - z));
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -2e-69) {
		tmp = x + ((((y - x) * z) + (t * (x - y))) / (a - t));
	} else if (t_2 <= 0.0) {
		tmp = y + ((y - x) * ((a - z) / t));
	} else if (t_2 <= 1e+259) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (((y - x) / t) * (a - z));
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -2e-69) {
		tmp = x + ((((y - x) * z) + (t * (x - y))) / (a - t));
	} else if (t_2 <= 0.0) {
		tmp = y + ((y - x) * ((a - z) / t));
	} else if (t_2 <= 1e+259) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + (((y - x) / t) * (a - z))
	t_2 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -2e-69:
		tmp = x + ((((y - x) * z) + (t * (x - y))) / (a - t))
	elif t_2 <= 0.0:
		tmp = y + ((y - x) * ((a - z) / t))
	elif t_2 <= 1e+259:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(Float64(Float64(y - x) / t) * Float64(a - z)))
	t_2 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -2e-69)
		tmp = Float64(x + Float64(Float64(Float64(Float64(y - x) * z) + Float64(t * Float64(x - y))) / Float64(a - t)));
	elseif (t_2 <= 0.0)
		tmp = Float64(y + Float64(Float64(y - x) * Float64(Float64(a - z) / t)));
	elseif (t_2 <= 1e+259)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + (((y - x) / t) * (a - z));
	t_2 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -2e-69)
		tmp = x + ((((y - x) * z) + (t * (x - y))) / (a - t));
	elseif (t_2 <= 0.0)
		tmp = y + ((y - x) * ((a - z) / t));
	elseif (t_2 <= 1e+259)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -2e-69], N[(x + N[(N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] + N[(t * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 0.0], N[(y + N[(N[(y - x), $MachinePrecision] * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+259], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -inf.0 or 9.999999999999999e258 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 40.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 53.8%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 53.8%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 53.8%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 56.6%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 56.6%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 56.6%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 53.8%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 64.3%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 65.2%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 75.5%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 75.5%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -1.9999999999999999e-69

   1. Initial program 99.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg 99.6%

         \[\leadsto x + \frac{\left(y - x\right) \cdot \color{blue}{\left(z + \left(-t\right)\right)}}{a - t} \]

      2. distribute-lft-in 99.7%

         \[\leadsto x + \frac{\color{blue}{\left(y - x\right) \cdot z + \left(y - x\right) \cdot \left(-t\right)}}{a - t} \]

   4. Applied egg-rr 99.7%

      \[\leadsto x + \frac{\color{blue}{\left(y - x\right) \cdot z + \left(y - x\right) \cdot \left(-t\right)}}{a - t} \]

   if -1.9999999999999999e-69 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 34.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 47.6%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. +-commutative 47.6%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. +-commutative 47.6%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{a - t} + 1\right)} \]

      3. distribute-lft-in 47.7%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \color{blue}{\left(x \cdot \left(-1 \cdot \frac{z - t}{a - t}\right) + x \cdot 1\right)} \]

      4. mul-1-neg 47.7%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(x \cdot \color{blue}{\left(-\frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      5. distribute-rgt-neg-in 47.7%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{\left(-x \cdot \frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      6. associate-/l* 43.7%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\left(-\color{blue}{\frac{x \cdot \left(z - t\right)}{a - t}}\right) + x \cdot 1\right) \]

      7. mul-1-neg 43.7%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} + x \cdot 1\right) \]

      8. *-rgt-identity 43.7%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \color{blue}{x}\right) \]

      9. associate-+l+ 34.0%

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(z - t\right)}{a - t} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) + x} \]

   5. Simplified 32.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)} \]

   6. Taylor expanded in t around inf 83.2%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   7. Step-by-step derivation

      1. cancel-sign-sub-inv 83.2%

         \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) + \left(--1\right) \cdot \frac{a \cdot \left(y - x\right)}{t}} \]

      2. mul-1-neg 83.2%

         \[\leadsto \left(y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right)}{t}\right)}\right) + \left(--1\right) \cdot \frac{a \cdot \left(y - x\right)}{t} \]

      3. sub-neg 83.2%

         \[\leadsto \color{blue}{\left(y - \frac{z \cdot \left(y - x\right)}{t}\right)} + \left(--1\right) \cdot \frac{a \cdot \left(y - x\right)}{t} \]

      4. metadata-eval 83.2%

         \[\leadsto \left(y - \frac{z \cdot \left(y - x\right)}{t}\right) + \color{blue}{1} \cdot \frac{a \cdot \left(y - x\right)}{t} \]

      5. *-lft-identity 83.2%

         \[\leadsto \left(y - \frac{z \cdot \left(y - x\right)}{t}\right) + \color{blue}{\frac{a \cdot \left(y - x\right)}{t}} \]

      6. *-commutative 83.2%

         \[\leadsto \left(y - \frac{z \cdot \left(y - x\right)}{t}\right) + \frac{\color{blue}{\left(y - x\right) \cdot a}}{t} \]

      7. associate-+l- 83.2%

         \[\leadsto \color{blue}{y - \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{\left(y - x\right) \cdot a}{t}\right)} \]

      8. div-sub 83.2%

         \[\leadsto y - \color{blue}{\frac{z \cdot \left(y - x\right) - \left(y - x\right) \cdot a}{t}} \]

      9. *-commutative 83.2%

         \[\leadsto y - \frac{z \cdot \left(y - x\right) - \color{blue}{a \cdot \left(y - x\right)}}{t} \]

      10. distribute-rgt-out-- 83.2%

          \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

      11. associate-*r/ 83.2%

          \[\leadsto y - \color{blue}{\left(y - x\right) \cdot \frac{z - a}{t}} \]

   8. Simplified 83.2%

      \[\leadsto \color{blue}{y - \left(y - x\right) \cdot \frac{z - a}{t}} \]

   if 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 9.999999999999999e258

   1. Initial program 96.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing
3. Recombined 4 regimes into one program.

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -\infty:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -2 \cdot 10^{-69}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z + t \cdot \left(x - y\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 10^{+259}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \frac{y - x}{t} \cdot \left(a - z\right)\\ t_2 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-69}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t\_2 \leq 10^{+259}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* (/ (- y x) t) (- a z))))
        (t_2 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -2e-69)
       t_2
       (if (<= t_2 0.0)
         (+ y (* (- y x) (/ (- a z) t)))
         (if (<= t_2 1e+259) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (((y - x) / t) * (a - z));
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -2e-69) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y + ((y - x) * ((a - z) / t));
	} else if (t_2 <= 1e+259) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (((y - x) / t) * (a - z));
	double t_2 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -2e-69) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y + ((y - x) * ((a - z) / t));
	} else if (t_2 <= 1e+259) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + (((y - x) / t) * (a - z))
	t_2 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -2e-69:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = y + ((y - x) * ((a - z) / t))
	elif t_2 <= 1e+259:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(Float64(Float64(y - x) / t) * Float64(a - z)))
	t_2 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -2e-69)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(y + Float64(Float64(y - x) * Float64(Float64(a - z) / t)));
	elseif (t_2 <= 1e+259)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + (((y - x) / t) * (a - z));
	t_2 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -2e-69)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = y + ((y - x) * ((a - z) / t));
	elseif (t_2 <= 1e+259)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -2e-69], t$95$2, If[LessEqual[t$95$2, 0.0], N[(y + N[(N[(y - x), $MachinePrecision] * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+259], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -inf.0 or 9.999999999999999e258 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 40.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 53.8%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 53.8%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 53.8%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 56.6%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 56.6%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 56.6%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 53.8%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 64.3%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 65.2%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 75.5%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 75.5%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -1.9999999999999999e-69 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 9.999999999999999e258

   1. Initial program 98.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   if -1.9999999999999999e-69 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 34.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 47.6%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. +-commutative 47.6%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. +-commutative 47.6%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{a - t} + 1\right)} \]

      3. distribute-lft-in 47.7%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \color{blue}{\left(x \cdot \left(-1 \cdot \frac{z - t}{a - t}\right) + x \cdot 1\right)} \]

      4. mul-1-neg 47.7%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(x \cdot \color{blue}{\left(-\frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      5. distribute-rgt-neg-in 47.7%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{\left(-x \cdot \frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      6. associate-/l* 43.7%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\left(-\color{blue}{\frac{x \cdot \left(z - t\right)}{a - t}}\right) + x \cdot 1\right) \]

      7. mul-1-neg 43.7%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} + x \cdot 1\right) \]

      8. *-rgt-identity 43.7%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \color{blue}{x}\right) \]

      9. associate-+l+ 34.0%

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(z - t\right)}{a - t} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) + x} \]

   5. Simplified 32.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)} \]

   6. Taylor expanded in t around inf 83.2%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   7. Step-by-step derivation

      1. cancel-sign-sub-inv 83.2%

         \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) + \left(--1\right) \cdot \frac{a \cdot \left(y - x\right)}{t}} \]

      2. mul-1-neg 83.2%

         \[\leadsto \left(y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right)}{t}\right)}\right) + \left(--1\right) \cdot \frac{a \cdot \left(y - x\right)}{t} \]

      3. sub-neg 83.2%

         \[\leadsto \color{blue}{\left(y - \frac{z \cdot \left(y - x\right)}{t}\right)} + \left(--1\right) \cdot \frac{a \cdot \left(y - x\right)}{t} \]

      4. metadata-eval 83.2%

         \[\leadsto \left(y - \frac{z \cdot \left(y - x\right)}{t}\right) + \color{blue}{1} \cdot \frac{a \cdot \left(y - x\right)}{t} \]

      5. *-lft-identity 83.2%

         \[\leadsto \left(y - \frac{z \cdot \left(y - x\right)}{t}\right) + \color{blue}{\frac{a \cdot \left(y - x\right)}{t}} \]

      6. *-commutative 83.2%

         \[\leadsto \left(y - \frac{z \cdot \left(y - x\right)}{t}\right) + \frac{\color{blue}{\left(y - x\right) \cdot a}}{t} \]

      7. associate-+l- 83.2%

         \[\leadsto \color{blue}{y - \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{\left(y - x\right) \cdot a}{t}\right)} \]

      8. div-sub 83.2%

         \[\leadsto y - \color{blue}{\frac{z \cdot \left(y - x\right) - \left(y - x\right) \cdot a}{t}} \]

      9. *-commutative 83.2%

         \[\leadsto y - \frac{z \cdot \left(y - x\right) - \color{blue}{a \cdot \left(y - x\right)}}{t} \]

      10. distribute-rgt-out-- 83.2%

          \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

      11. associate-*r/ 83.2%

          \[\leadsto y - \color{blue}{\left(y - x\right) \cdot \frac{z - a}{t}} \]

   8. Simplified 83.2%

      \[\leadsto \color{blue}{y - \left(y - x\right) \cdot \frac{z - a}{t}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -\infty:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -2 \cdot 10^{-69}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 10^{+259}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 64.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y - x}{a - t}\\ t_2 := y \cdot \frac{z - t}{a - t}\\ t_3 := x + z \cdot \frac{y - x}{a}\\ \mathbf{if}\;t \leq -8.8 \cdot 10^{-11}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.02 \cdot 10^{-93}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-152}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-208}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-208}:\\ \;\;\;\;y \cdot \frac{t}{-a}\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-246}:\\ \;\;\;\;x - \frac{x \cdot z}{a}\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-253}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-283}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-61}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 56000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 50000000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+79}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+114}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+178}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ (- y x) (- a t))))
        (t_2 (* y (/ (- z t) (- a t))))
        (t_3 (+ x (* z (/ (- y x) a)))))
   (if (<= t -8.8e-11)
     t_2
     (if (<= t -1.02e-93)
       t_1
       (if (<= t -1.6e-152)
         t_3
         (if (<= t -1.05e-208)
           (+ x (/ (* (- y x) z) a))
           (if (<= t -1e-208)
             (* y (/ t (- a)))
             (if (<= t -1.9e-246)
               (- x (/ (* x z) a))
               (if (<= t -1.2e-253)
                 t_1
                 (if (<= t -7e-283)
                   (+ x (/ (- y x) (/ a z)))
                   (if (<= t 1.4e-61)
                     t_3
                     (if (<= t 56000.0)
                       t_2
                       (if (<= t 50000000000000.0)
                         x
                         (if (<= t 1.35e+79)
                           t_2
                           (if (<= t 6e+114)
                             (+ x (* t (/ y (- t a))))
                             (if (<= t 7.5e+178)
                               t_2
                               (+ y (* (- y x) (/ a t)))))))))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((y - x) / (a - t));
	double t_2 = y * ((z - t) / (a - t));
	double t_3 = x + (z * ((y - x) / a));
	double tmp;
	if (t <= -8.8e-11) {
		tmp = t_2;
	} else if (t <= -1.02e-93) {
		tmp = t_1;
	} else if (t <= -1.6e-152) {
		tmp = t_3;
	} else if (t <= -1.05e-208) {
		tmp = x + (((y - x) * z) / a);
	} else if (t <= -1e-208) {
		tmp = y * (t / -a);
	} else if (t <= -1.9e-246) {
		tmp = x - ((x * z) / a);
	} else if (t <= -1.2e-253) {
		tmp = t_1;
	} else if (t <= -7e-283) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 1.4e-61) {
		tmp = t_3;
	} else if (t <= 56000.0) {
		tmp = t_2;
	} else if (t <= 50000000000000.0) {
		tmp = x;
	} else if (t <= 1.35e+79) {
		tmp = t_2;
	} else if (t <= 6e+114) {
		tmp = x + (t * (y / (t - a)));
	} else if (t <= 7.5e+178) {
		tmp = t_2;
	} else {
		tmp = y + ((y - x) * (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = z * ((y - x) / (a - t))
    t_2 = y * ((z - t) / (a - t))
    t_3 = x + (z * ((y - x) / a))
    if (t <= (-8.8d-11)) then
        tmp = t_2
    else if (t <= (-1.02d-93)) then
        tmp = t_1
    else if (t <= (-1.6d-152)) then
        tmp = t_3
    else if (t <= (-1.05d-208)) then
        tmp = x + (((y - x) * z) / a)
    else if (t <= (-1d-208)) then
        tmp = y * (t / -a)
    else if (t <= (-1.9d-246)) then
        tmp = x - ((x * z) / a)
    else if (t <= (-1.2d-253)) then
        tmp = t_1
    else if (t <= (-7d-283)) then
        tmp = x + ((y - x) / (a / z))
    else if (t <= 1.4d-61) then
        tmp = t_3
    else if (t <= 56000.0d0) then
        tmp = t_2
    else if (t <= 50000000000000.0d0) then
        tmp = x
    else if (t <= 1.35d+79) then
        tmp = t_2
    else if (t <= 6d+114) then
        tmp = x + (t * (y / (t - a)))
    else if (t <= 7.5d+178) then
        tmp = t_2
    else
        tmp = y + ((y - x) * (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((y - x) / (a - t));
	double t_2 = y * ((z - t) / (a - t));
	double t_3 = x + (z * ((y - x) / a));
	double tmp;
	if (t <= -8.8e-11) {
		tmp = t_2;
	} else if (t <= -1.02e-93) {
		tmp = t_1;
	} else if (t <= -1.6e-152) {
		tmp = t_3;
	} else if (t <= -1.05e-208) {
		tmp = x + (((y - x) * z) / a);
	} else if (t <= -1e-208) {
		tmp = y * (t / -a);
	} else if (t <= -1.9e-246) {
		tmp = x - ((x * z) / a);
	} else if (t <= -1.2e-253) {
		tmp = t_1;
	} else if (t <= -7e-283) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 1.4e-61) {
		tmp = t_3;
	} else if (t <= 56000.0) {
		tmp = t_2;
	} else if (t <= 50000000000000.0) {
		tmp = x;
	} else if (t <= 1.35e+79) {
		tmp = t_2;
	} else if (t <= 6e+114) {
		tmp = x + (t * (y / (t - a)));
	} else if (t <= 7.5e+178) {
		tmp = t_2;
	} else {
		tmp = y + ((y - x) * (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * ((y - x) / (a - t))
	t_2 = y * ((z - t) / (a - t))
	t_3 = x + (z * ((y - x) / a))
	tmp = 0
	if t <= -8.8e-11:
		tmp = t_2
	elif t <= -1.02e-93:
		tmp = t_1
	elif t <= -1.6e-152:
		tmp = t_3
	elif t <= -1.05e-208:
		tmp = x + (((y - x) * z) / a)
	elif t <= -1e-208:
		tmp = y * (t / -a)
	elif t <= -1.9e-246:
		tmp = x - ((x * z) / a)
	elif t <= -1.2e-253:
		tmp = t_1
	elif t <= -7e-283:
		tmp = x + ((y - x) / (a / z))
	elif t <= 1.4e-61:
		tmp = t_3
	elif t <= 56000.0:
		tmp = t_2
	elif t <= 50000000000000.0:
		tmp = x
	elif t <= 1.35e+79:
		tmp = t_2
	elif t <= 6e+114:
		tmp = x + (t * (y / (t - a)))
	elif t <= 7.5e+178:
		tmp = t_2
	else:
		tmp = y + ((y - x) * (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(Float64(y - x) / Float64(a - t)))
	t_2 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_3 = Float64(x + Float64(z * Float64(Float64(y - x) / a)))
	tmp = 0.0
	if (t <= -8.8e-11)
		tmp = t_2;
	elseif (t <= -1.02e-93)
		tmp = t_1;
	elseif (t <= -1.6e-152)
		tmp = t_3;
	elseif (t <= -1.05e-208)
		tmp = Float64(x + Float64(Float64(Float64(y - x) * z) / a));
	elseif (t <= -1e-208)
		tmp = Float64(y * Float64(t / Float64(-a)));
	elseif (t <= -1.9e-246)
		tmp = Float64(x - Float64(Float64(x * z) / a));
	elseif (t <= -1.2e-253)
		tmp = t_1;
	elseif (t <= -7e-283)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	elseif (t <= 1.4e-61)
		tmp = t_3;
	elseif (t <= 56000.0)
		tmp = t_2;
	elseif (t <= 50000000000000.0)
		tmp = x;
	elseif (t <= 1.35e+79)
		tmp = t_2;
	elseif (t <= 6e+114)
		tmp = Float64(x + Float64(t * Float64(y / Float64(t - a))));
	elseif (t <= 7.5e+178)
		tmp = t_2;
	else
		tmp = Float64(y + Float64(Float64(y - x) * Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * ((y - x) / (a - t));
	t_2 = y * ((z - t) / (a - t));
	t_3 = x + (z * ((y - x) / a));
	tmp = 0.0;
	if (t <= -8.8e-11)
		tmp = t_2;
	elseif (t <= -1.02e-93)
		tmp = t_1;
	elseif (t <= -1.6e-152)
		tmp = t_3;
	elseif (t <= -1.05e-208)
		tmp = x + (((y - x) * z) / a);
	elseif (t <= -1e-208)
		tmp = y * (t / -a);
	elseif (t <= -1.9e-246)
		tmp = x - ((x * z) / a);
	elseif (t <= -1.2e-253)
		tmp = t_1;
	elseif (t <= -7e-283)
		tmp = x + ((y - x) / (a / z));
	elseif (t <= 1.4e-61)
		tmp = t_3;
	elseif (t <= 56000.0)
		tmp = t_2;
	elseif (t <= 50000000000000.0)
		tmp = x;
	elseif (t <= 1.35e+79)
		tmp = t_2;
	elseif (t <= 6e+114)
		tmp = x + (t * (y / (t - a)));
	elseif (t <= 7.5e+178)
		tmp = t_2;
	else
		tmp = y + ((y - x) * (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.8e-11], t$95$2, If[LessEqual[t, -1.02e-93], t$95$1, If[LessEqual[t, -1.6e-152], t$95$3, If[LessEqual[t, -1.05e-208], N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1e-208], N[(y * N[(t / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.9e-246], N[(x - N[(N[(x * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.2e-253], t$95$1, If[LessEqual[t, -7e-283], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.4e-61], t$95$3, If[LessEqual[t, 56000.0], t$95$2, If[LessEqual[t, 50000000000000.0], x, If[LessEqual[t, 1.35e+79], t$95$2, If[LessEqual[t, 6e+114], N[(x + N[(t * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.5e+178], t$95$2, N[(y + N[(N[(y - x), $MachinePrecision] * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if t < -8.8000000000000006e-11 or 1.4000000000000001e-61 < t < 56000 or 5e13 < t < 1.35e79 or 6.0000000000000001e114 < t < 7.4999999999999995e178

   1. Initial program 55.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 64.6%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. +-commutative 64.6%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. +-commutative 64.6%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{a - t} + 1\right)} \]

      3. distribute-lft-in 64.6%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \color{blue}{\left(x \cdot \left(-1 \cdot \frac{z - t}{a - t}\right) + x \cdot 1\right)} \]

      4. mul-1-neg 64.6%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(x \cdot \color{blue}{\left(-\frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      5. distribute-rgt-neg-in 64.6%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{\left(-x \cdot \frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      6. associate-/l* 56.5%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\left(-\color{blue}{\frac{x \cdot \left(z - t\right)}{a - t}}\right) + x \cdot 1\right) \]

      7. mul-1-neg 56.5%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} + x \cdot 1\right) \]

      8. *-rgt-identity 56.5%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \color{blue}{x}\right) \]

      9. associate-+l+ 54.4%

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(z - t\right)}{a - t} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) + x} \]

   5. Simplified 77.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)} \]

   6. Taylor expanded in y around inf 66.3%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 66.3%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

   8. Simplified 66.3%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   if -8.8000000000000006e-11 < t < -1.02e-93 or -1.89999999999999988e-246 < t < -1.20000000000000005e-253

   1. Initial program 86.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 81.9%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. +-commutative 81.9%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. +-commutative 81.9%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{a - t} + 1\right)} \]

      3. distribute-lft-in 82.0%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \color{blue}{\left(x \cdot \left(-1 \cdot \frac{z - t}{a - t}\right) + x \cdot 1\right)} \]

      4. mul-1-neg 82.0%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(x \cdot \color{blue}{\left(-\frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      5. distribute-rgt-neg-in 82.0%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{\left(-x \cdot \frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      6. associate-/l* 86.2%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\left(-\color{blue}{\frac{x \cdot \left(z - t\right)}{a - t}}\right) + x \cdot 1\right) \]

      7. mul-1-neg 86.2%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} + x \cdot 1\right) \]

      8. *-rgt-identity 86.2%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \color{blue}{x}\right) \]

      9. associate-+l+ 86.3%

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(z - t\right)}{a - t} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) + x} \]

   5. Simplified 95.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)} \]

   6. Taylor expanded in z around inf 81.9%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 81.9%

         \[\leadsto z \cdot \color{blue}{\frac{y - x}{a - t}} \]

   8. Simplified 81.9%

      \[\leadsto \color{blue}{z \cdot \frac{y - x}{a - t}} \]

   if -1.02e-93 < t < -1.60000000000000006e-152 or -6.9999999999999997e-283 < t < 1.4000000000000001e-61

   1. Initial program 89.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 78.3%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* 85.5%

         \[\leadsto x + \color{blue}{z \cdot \frac{y - x}{a}} \]

   5. Simplified 85.5%

      \[\leadsto x + \color{blue}{z \cdot \frac{y - x}{a}} \]

   if -1.60000000000000006e-152 < t < -1.05000000000000006e-208

   1. Initial program 99.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 68.5%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]

   if -1.05000000000000006e-208 < t < -1.0000000000000001e-208

   1. Initial program 98.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 98.4%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   5. Simplified 100.0%

      \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]
   6. Step-by-step derivation

      1. clear-num 100.0%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

      2. inv-pow 100.0%

         \[\leadsto x + y \cdot \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}} \]

   7. Applied egg-rr 100.0%

      \[\leadsto x + y \cdot \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}} \]
   8. Step-by-step derivation

      1. unpow-1 100.0%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

   9. Simplified 100.0%

      \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

   10. Taylor expanded in z around 0 98.4%

       \[\leadsto \color{blue}{x + -1 \cdot \frac{t \cdot y}{a - t}} \]
   11. Step-by-step derivation

       1. mul-1-neg 98.4%

          \[\leadsto x + \color{blue}{\left(-\frac{t \cdot y}{a - t}\right)} \]

       2. unsub-neg 98.4%

          \[\leadsto \color{blue}{x - \frac{t \cdot y}{a - t}} \]

       3. associate-/l* 98.4%

          \[\leadsto x - \color{blue}{t \cdot \frac{y}{a - t}} \]

   12. Simplified 98.4%

       \[\leadsto \color{blue}{x - t \cdot \frac{y}{a - t}} \]

   13. Taylor expanded in t around 0 98.4%

       \[\leadsto x - \color{blue}{\frac{t \cdot y}{a}} \]
   14. Step-by-step derivation

       1. associate-/l* 98.4%

          \[\leadsto x - \color{blue}{t \cdot \frac{y}{a}} \]

   15. Simplified 98.4%

       \[\leadsto x - \color{blue}{t \cdot \frac{y}{a}} \]

   16. Taylor expanded in x around 0 98.4%

       \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot y}{a}} \]
   17. Step-by-step derivation

       1. mul-1-neg 98.4%

          \[\leadsto \color{blue}{-\frac{t \cdot y}{a}} \]

       2. *-commutative 98.4%

          \[\leadsto -\frac{\color{blue}{y \cdot t}}{a} \]

       3. distribute-frac-neg2 98.4%

          \[\leadsto \color{blue}{\frac{y \cdot t}{-a}} \]

       4. associate-/l* 100.0%

          \[\leadsto \color{blue}{y \cdot \frac{t}{-a}} \]

   18. Simplified 100.0%

       \[\leadsto \color{blue}{y \cdot \frac{t}{-a}} \]

   if -1.0000000000000001e-208 < t < -1.89999999999999988e-246

   1. Initial program 99.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 71.4%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]

   4. Taylor expanded in y around 0 86.0%

      \[\leadsto x + \frac{\color{blue}{-1 \cdot \left(x \cdot z\right)}}{a} \]
   5. Step-by-step derivation

      1. mul-1-neg 86.0%

         \[\leadsto x + \frac{\color{blue}{-x \cdot z}}{a} \]

      2. distribute-lft-neg-out 86.0%

         \[\leadsto x + \frac{\color{blue}{\left(-x\right) \cdot z}}{a} \]

      3. *-commutative 86.0%

         \[\leadsto x + \frac{\color{blue}{z \cdot \left(-x\right)}}{a} \]

   6. Simplified 86.0%

      \[\leadsto x + \frac{\color{blue}{z \cdot \left(-x\right)}}{a} \]

   if -1.20000000000000005e-253 < t < -6.9999999999999997e-283

   1. Initial program 87.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 87.1%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]
   4. Step-by-step derivation

      1. clear-num 87.1%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{a}{z \cdot \left(y - x\right)}}} \]

      2. inv-pow 87.1%

         \[\leadsto x + \color{blue}{{\left(\frac{a}{z \cdot \left(y - x\right)}\right)}^{-1}} \]

   5. Applied egg-rr 87.1%

      \[\leadsto x + \color{blue}{{\left(\frac{a}{z \cdot \left(y - x\right)}\right)}^{-1}} \]
   6. Step-by-step derivation

      1. unpow-1 87.1%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{a}{z \cdot \left(y - x\right)}}} \]

      2. associate-/r* 100.0%

         \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{a}{z}}{y - x}}} \]

   7. Simplified 100.0%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{a}{z}}{y - x}}} \]
   8. Step-by-step derivation

      1. clear-num 100.0%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a}{z}}} \]

      2. add-cube-cbrt 99.2%

         \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \sqrt[3]{y - x}}}{\frac{a}{z}} \]

      3. *-un-lft-identity 99.2%

         \[\leadsto x + \frac{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \sqrt[3]{y - x}}{\color{blue}{1 \cdot \frac{a}{z}}} \]

      4. times-frac 99.1%

         \[\leadsto x + \color{blue}{\frac{\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}}{1} \cdot \frac{\sqrt[3]{y - x}}{\frac{a}{z}}} \]

      5. pow2 99.1%

         \[\leadsto x + \frac{\color{blue}{{\left(\sqrt[3]{y - x}\right)}^{2}}}{1} \cdot \frac{\sqrt[3]{y - x}}{\frac{a}{z}} \]

   9. Applied egg-rr 99.1%

      \[\leadsto x + \color{blue}{\frac{{\left(\sqrt[3]{y - x}\right)}^{2}}{1} \cdot \frac{\sqrt[3]{y - x}}{\frac{a}{z}}} \]
   10. Step-by-step derivation

       1. /-rgt-identity 99.1%

          \[\leadsto x + \color{blue}{{\left(\sqrt[3]{y - x}\right)}^{2}} \cdot \frac{\sqrt[3]{y - x}}{\frac{a}{z}} \]

       2. associate-*r/ 99.2%

          \[\leadsto x + \color{blue}{\frac{{\left(\sqrt[3]{y - x}\right)}^{2} \cdot \sqrt[3]{y - x}}{\frac{a}{z}}} \]

       3. unpow2 99.2%

          \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right)} \cdot \sqrt[3]{y - x}}{\frac{a}{z}} \]

       4. rem-3cbrt-lft 100.0%

          \[\leadsto x + \frac{\color{blue}{y - x}}{\frac{a}{z}} \]

   11. Simplified 100.0%

       \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a}{z}}} \]

   if 56000 < t < 5e13

   1. Initial program 100.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 100.0%

      \[\leadsto \color{blue}{x} \]

   if 1.35e79 < t < 6.0000000000000001e114

   1. Initial program 44.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 42.8%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. associate-/l* 79.7%

         \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   5. Simplified 79.7%

      \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]
   6. Step-by-step derivation

      1. clear-num 80.1%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

      2. inv-pow 80.1%

         \[\leadsto x + y \cdot \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}} \]

   7. Applied egg-rr 80.1%

      \[\leadsto x + y \cdot \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}} \]
   8. Step-by-step derivation

      1. unpow-1 80.1%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

   9. Simplified 80.1%

      \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

   10. Taylor expanded in z around 0 42.8%

       \[\leadsto \color{blue}{x + -1 \cdot \frac{t \cdot y}{a - t}} \]
   11. Step-by-step derivation

       1. mul-1-neg 42.8%

          \[\leadsto x + \color{blue}{\left(-\frac{t \cdot y}{a - t}\right)} \]

       2. unsub-neg 42.8%

          \[\leadsto \color{blue}{x - \frac{t \cdot y}{a - t}} \]

       3. associate-/l* 79.7%

          \[\leadsto x - \color{blue}{t \cdot \frac{y}{a - t}} \]

   12. Simplified 79.7%

       \[\leadsto \color{blue}{x - t \cdot \frac{y}{a - t}} \]

   if 7.4999999999999995e178 < t

   1. Initial program 18.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 85.8%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 85.8%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 85.8%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 85.8%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 85.8%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 85.8%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 85.8%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 85.7%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 89.2%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 89.2%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 89.2%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]

   6. Taylor expanded in z around 0 82.9%

      \[\leadsto \color{blue}{y - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   7. Step-by-step derivation

      1. cancel-sign-sub-inv 82.9%

         \[\leadsto \color{blue}{y + \left(--1\right) \cdot \frac{a \cdot \left(y - x\right)}{t}} \]

      2. metadata-eval 82.9%

         \[\leadsto y + \color{blue}{1} \cdot \frac{a \cdot \left(y - x\right)}{t} \]

      3. *-lft-identity 82.9%

         \[\leadsto y + \color{blue}{\frac{a \cdot \left(y - x\right)}{t}} \]

      4. *-commutative 82.9%

         \[\leadsto y + \frac{\color{blue}{\left(y - x\right) \cdot a}}{t} \]

      5. associate-/l* 88.3%

         \[\leadsto y + \color{blue}{\left(y - x\right) \cdot \frac{a}{t}} \]

   8. Simplified 88.3%

      \[\leadsto \color{blue}{y + \left(y - x\right) \cdot \frac{a}{t}} \]
3. Recombined 10 regimes into one program.

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.8 \cdot 10^{-11}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -1.02 \cdot 10^{-93}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-152}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-208}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-208}:\\ \;\;\;\;y \cdot \frac{t}{-a}\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-246}:\\ \;\;\;\;x - \frac{x \cdot z}{a}\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-253}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-283}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-61}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 56000:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 50000000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+79}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+114}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+178}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 62.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := \frac{z}{\frac{a - t}{y - x}}\\ t_3 := x + t \cdot \frac{y}{t - a}\\ \mathbf{if}\;t \leq -3.8 \cdot 10^{+164}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{+26}:\\ \;\;\;\;y - \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{elif}\;t \leq -2.75 \cdot 10^{+14}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-103}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-173}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{-192}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3.6 \cdot 10^{-208}:\\ \;\;\;\;x + \frac{-1}{\frac{a}{x \cdot z}}\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-265}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-67}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 56000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 540000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+116}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t))))
        (t_2 (/ z (/ (- a t) (- y x))))
        (t_3 (+ x (* t (/ y (- t a))))))
   (if (<= t -3.8e+164)
     (/ y (/ (- a t) (- z t)))
     (if (<= t -1.35e+26)
       (- y (/ (* (- y x) z) t))
       (if (<= t -2.75e+14)
         t_3
         (if (<= t -4e-103)
           t_2
           (if (<= t -3e-173)
             (+ x (/ (- y x) (/ a z)))
             (if (<= t -3.3e-192)
               t_2
               (if (<= t -3.6e-208)
                 (+ x (/ -1.0 (/ a (* x z))))
                 (if (<= t -3.1e-265)
                   t_2
                   (if (<= t 1.9e-67)
                     (+ x (* z (/ (- y x) a)))
                     (if (<= t 56000.0)
                       t_1
                       (if (<= t 540000000000.0)
                         x
                         (if (<= t 8e+79)
                           t_1
                           (if (<= t 3.3e+116)
                             t_3
                             (+ y (* (- y x) (/ a t))))))))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = z / ((a - t) / (y - x));
	double t_3 = x + (t * (y / (t - a)));
	double tmp;
	if (t <= -3.8e+164) {
		tmp = y / ((a - t) / (z - t));
	} else if (t <= -1.35e+26) {
		tmp = y - (((y - x) * z) / t);
	} else if (t <= -2.75e+14) {
		tmp = t_3;
	} else if (t <= -4e-103) {
		tmp = t_2;
	} else if (t <= -3e-173) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= -3.3e-192) {
		tmp = t_2;
	} else if (t <= -3.6e-208) {
		tmp = x + (-1.0 / (a / (x * z)));
	} else if (t <= -3.1e-265) {
		tmp = t_2;
	} else if (t <= 1.9e-67) {
		tmp = x + (z * ((y - x) / a));
	} else if (t <= 56000.0) {
		tmp = t_1;
	} else if (t <= 540000000000.0) {
		tmp = x;
	} else if (t <= 8e+79) {
		tmp = t_1;
	} else if (t <= 3.3e+116) {
		tmp = t_3;
	} else {
		tmp = y + ((y - x) * (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    t_2 = z / ((a - t) / (y - x))
    t_3 = x + (t * (y / (t - a)))
    if (t <= (-3.8d+164)) then
        tmp = y / ((a - t) / (z - t))
    else if (t <= (-1.35d+26)) then
        tmp = y - (((y - x) * z) / t)
    else if (t <= (-2.75d+14)) then
        tmp = t_3
    else if (t <= (-4d-103)) then
        tmp = t_2
    else if (t <= (-3d-173)) then
        tmp = x + ((y - x) / (a / z))
    else if (t <= (-3.3d-192)) then
        tmp = t_2
    else if (t <= (-3.6d-208)) then
        tmp = x + ((-1.0d0) / (a / (x * z)))
    else if (t <= (-3.1d-265)) then
        tmp = t_2
    else if (t <= 1.9d-67) then
        tmp = x + (z * ((y - x) / a))
    else if (t <= 56000.0d0) then
        tmp = t_1
    else if (t <= 540000000000.0d0) then
        tmp = x
    else if (t <= 8d+79) then
        tmp = t_1
    else if (t <= 3.3d+116) then
        tmp = t_3
    else
        tmp = y + ((y - x) * (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = z / ((a - t) / (y - x));
	double t_3 = x + (t * (y / (t - a)));
	double tmp;
	if (t <= -3.8e+164) {
		tmp = y / ((a - t) / (z - t));
	} else if (t <= -1.35e+26) {
		tmp = y - (((y - x) * z) / t);
	} else if (t <= -2.75e+14) {
		tmp = t_3;
	} else if (t <= -4e-103) {
		tmp = t_2;
	} else if (t <= -3e-173) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= -3.3e-192) {
		tmp = t_2;
	} else if (t <= -3.6e-208) {
		tmp = x + (-1.0 / (a / (x * z)));
	} else if (t <= -3.1e-265) {
		tmp = t_2;
	} else if (t <= 1.9e-67) {
		tmp = x + (z * ((y - x) / a));
	} else if (t <= 56000.0) {
		tmp = t_1;
	} else if (t <= 540000000000.0) {
		tmp = x;
	} else if (t <= 8e+79) {
		tmp = t_1;
	} else if (t <= 3.3e+116) {
		tmp = t_3;
	} else {
		tmp = y + ((y - x) * (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = z / ((a - t) / (y - x))
	t_3 = x + (t * (y / (t - a)))
	tmp = 0
	if t <= -3.8e+164:
		tmp = y / ((a - t) / (z - t))
	elif t <= -1.35e+26:
		tmp = y - (((y - x) * z) / t)
	elif t <= -2.75e+14:
		tmp = t_3
	elif t <= -4e-103:
		tmp = t_2
	elif t <= -3e-173:
		tmp = x + ((y - x) / (a / z))
	elif t <= -3.3e-192:
		tmp = t_2
	elif t <= -3.6e-208:
		tmp = x + (-1.0 / (a / (x * z)))
	elif t <= -3.1e-265:
		tmp = t_2
	elif t <= 1.9e-67:
		tmp = x + (z * ((y - x) / a))
	elif t <= 56000.0:
		tmp = t_1
	elif t <= 540000000000.0:
		tmp = x
	elif t <= 8e+79:
		tmp = t_1
	elif t <= 3.3e+116:
		tmp = t_3
	else:
		tmp = y + ((y - x) * (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(z / Float64(Float64(a - t) / Float64(y - x)))
	t_3 = Float64(x + Float64(t * Float64(y / Float64(t - a))))
	tmp = 0.0
	if (t <= -3.8e+164)
		tmp = Float64(y / Float64(Float64(a - t) / Float64(z - t)));
	elseif (t <= -1.35e+26)
		tmp = Float64(y - Float64(Float64(Float64(y - x) * z) / t));
	elseif (t <= -2.75e+14)
		tmp = t_3;
	elseif (t <= -4e-103)
		tmp = t_2;
	elseif (t <= -3e-173)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	elseif (t <= -3.3e-192)
		tmp = t_2;
	elseif (t <= -3.6e-208)
		tmp = Float64(x + Float64(-1.0 / Float64(a / Float64(x * z))));
	elseif (t <= -3.1e-265)
		tmp = t_2;
	elseif (t <= 1.9e-67)
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / a)));
	elseif (t <= 56000.0)
		tmp = t_1;
	elseif (t <= 540000000000.0)
		tmp = x;
	elseif (t <= 8e+79)
		tmp = t_1;
	elseif (t <= 3.3e+116)
		tmp = t_3;
	else
		tmp = Float64(y + Float64(Float64(y - x) * Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = z / ((a - t) / (y - x));
	t_3 = x + (t * (y / (t - a)));
	tmp = 0.0;
	if (t <= -3.8e+164)
		tmp = y / ((a - t) / (z - t));
	elseif (t <= -1.35e+26)
		tmp = y - (((y - x) * z) / t);
	elseif (t <= -2.75e+14)
		tmp = t_3;
	elseif (t <= -4e-103)
		tmp = t_2;
	elseif (t <= -3e-173)
		tmp = x + ((y - x) / (a / z));
	elseif (t <= -3.3e-192)
		tmp = t_2;
	elseif (t <= -3.6e-208)
		tmp = x + (-1.0 / (a / (x * z)));
	elseif (t <= -3.1e-265)
		tmp = t_2;
	elseif (t <= 1.9e-67)
		tmp = x + (z * ((y - x) / a));
	elseif (t <= 56000.0)
		tmp = t_1;
	elseif (t <= 540000000000.0)
		tmp = x;
	elseif (t <= 8e+79)
		tmp = t_1;
	elseif (t <= 3.3e+116)
		tmp = t_3;
	else
		tmp = y + ((y - x) * (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z / N[(N[(a - t), $MachinePrecision] / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(t * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.8e+164], N[(y / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.35e+26], N[(y - N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.75e+14], t$95$3, If[LessEqual[t, -4e-103], t$95$2, If[LessEqual[t, -3e-173], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.3e-192], t$95$2, If[LessEqual[t, -3.6e-208], N[(x + N[(-1.0 / N[(a / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.1e-265], t$95$2, If[LessEqual[t, 1.9e-67], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 56000.0], t$95$1, If[LessEqual[t, 540000000000.0], x, If[LessEqual[t, 8e+79], t$95$1, If[LessEqual[t, 3.3e+116], t$95$3, N[(y + N[(N[(y - x), $MachinePrecision] * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if t < -3.80000000000000021e164

   1. Initial program 29.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 47.3%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. +-commutative 47.3%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. +-commutative 47.3%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{a - t} + 1\right)} \]

      3. distribute-lft-in 47.3%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \color{blue}{\left(x \cdot \left(-1 \cdot \frac{z - t}{a - t}\right) + x \cdot 1\right)} \]

      4. mul-1-neg 47.3%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(x \cdot \color{blue}{\left(-\frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      5. distribute-rgt-neg-in 47.3%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{\left(-x \cdot \frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      6. associate-/l* 29.1%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\left(-\color{blue}{\frac{x \cdot \left(z - t\right)}{a - t}}\right) + x \cdot 1\right) \]

      7. mul-1-neg 29.1%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} + x \cdot 1\right) \]

      8. *-rgt-identity 29.1%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \color{blue}{x}\right) \]

      9. associate-+l+ 29.1%

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(z - t\right)}{a - t} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) + x} \]

   5. Simplified 71.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)} \]

   6. Taylor expanded in y around inf 81.0%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 81.0%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

   8. Simplified 81.0%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]
   9. Step-by-step derivation

      1. clear-num 69.0%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

      2. un-div-inv 69.0%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

   10. Applied egg-rr 81.1%

       \[\leadsto \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

   if -3.80000000000000021e164 < t < -1.35e26

   1. Initial program 64.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 77.4%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 77.4%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 77.4%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 77.4%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 77.4%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 77.4%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 77.4%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 80.7%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 80.6%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 80.6%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 80.6%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]

   6. Taylor expanded in z around inf 67.9%

      \[\leadsto y - \color{blue}{\frac{z \cdot \left(y - x\right)}{t}} \]

   if -1.35e26 < t < -2.75e14 or 7.99999999999999974e79 < t < 3.2999999999999998e116

   1. Initial program 45.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 59.1%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. associate-/l* 85.5%

         \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   5. Simplified 85.5%

      \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]
   6. Step-by-step derivation

      1. clear-num 85.8%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

      2. inv-pow 85.8%

         \[\leadsto x + y \cdot \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}} \]

   7. Applied egg-rr 85.8%

      \[\leadsto x + y \cdot \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}} \]
   8. Step-by-step derivation

      1. unpow-1 85.8%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

   9. Simplified 85.8%

      \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

   10. Taylor expanded in z around 0 59.1%

       \[\leadsto \color{blue}{x + -1 \cdot \frac{t \cdot y}{a - t}} \]
   11. Step-by-step derivation

       1. mul-1-neg 59.1%

          \[\leadsto x + \color{blue}{\left(-\frac{t \cdot y}{a - t}\right)} \]

       2. unsub-neg 59.1%

          \[\leadsto \color{blue}{x - \frac{t \cdot y}{a - t}} \]

       3. associate-/l* 85.5%

          \[\leadsto x - \color{blue}{t \cdot \frac{y}{a - t}} \]

   12. Simplified 85.5%

       \[\leadsto \color{blue}{x - t \cdot \frac{y}{a - t}} \]

   if -2.75e14 < t < -3.99999999999999983e-103 or -3.0000000000000001e-173 < t < -3.29999999999999989e-192 or -3.5999999999999998e-208 < t < -3.09999999999999988e-265

   1. Initial program 88.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 84.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. +-commutative 84.2%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. +-commutative 84.2%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{a - t} + 1\right)} \]

      3. distribute-lft-in 84.3%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \color{blue}{\left(x \cdot \left(-1 \cdot \frac{z - t}{a - t}\right) + x \cdot 1\right)} \]

      4. mul-1-neg 84.3%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(x \cdot \color{blue}{\left(-\frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      5. distribute-rgt-neg-in 84.3%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{\left(-x \cdot \frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      6. associate-/l* 86.1%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\left(-\color{blue}{\frac{x \cdot \left(z - t\right)}{a - t}}\right) + x \cdot 1\right) \]

      7. mul-1-neg 86.1%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} + x \cdot 1\right) \]

      8. *-rgt-identity 86.1%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \color{blue}{x}\right) \]

      9. associate-+l+ 86.1%

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(z - t\right)}{a - t} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) + x} \]

   5. Simplified 93.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)} \]

   6. Taylor expanded in z around inf 66.8%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 69.1%

         \[\leadsto z \cdot \color{blue}{\frac{y - x}{a - t}} \]

   8. Simplified 69.1%

      \[\leadsto \color{blue}{z \cdot \frac{y - x}{a - t}} \]
   9. Step-by-step derivation

      1. clear-num 69.0%

         \[\leadsto z \cdot \color{blue}{\frac{1}{\frac{a - t}{y - x}}} \]

      2. un-div-inv 71.2%

         \[\leadsto \color{blue}{\frac{z}{\frac{a - t}{y - x}}} \]

   10. Applied egg-rr 71.2%

       \[\leadsto \color{blue}{\frac{z}{\frac{a - t}{y - x}}} \]

   if -3.99999999999999983e-103 < t < -3.0000000000000001e-173

   1. Initial program 87.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 61.6%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]
   4. Step-by-step derivation

      1. clear-num 61.6%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{a}{z \cdot \left(y - x\right)}}} \]

      2. inv-pow 61.6%

         \[\leadsto x + \color{blue}{{\left(\frac{a}{z \cdot \left(y - x\right)}\right)}^{-1}} \]

   5. Applied egg-rr 61.6%

      \[\leadsto x + \color{blue}{{\left(\frac{a}{z \cdot \left(y - x\right)}\right)}^{-1}} \]
   6. Step-by-step derivation

      1. unpow-1 61.6%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{a}{z \cdot \left(y - x\right)}}} \]

      2. associate-/r* 67.9%

         \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{a}{z}}{y - x}}} \]

   7. Simplified 67.9%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{a}{z}}{y - x}}} \]
   8. Step-by-step derivation

      1. clear-num 67.9%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a}{z}}} \]

      2. add-cube-cbrt 67.5%

         \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \sqrt[3]{y - x}}}{\frac{a}{z}} \]

      3. *-un-lft-identity 67.5%

         \[\leadsto x + \frac{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \sqrt[3]{y - x}}{\color{blue}{1 \cdot \frac{a}{z}}} \]

      4. times-frac 67.4%

         \[\leadsto x + \color{blue}{\frac{\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}}{1} \cdot \frac{\sqrt[3]{y - x}}{\frac{a}{z}}} \]

      5. pow2 67.4%

         \[\leadsto x + \frac{\color{blue}{{\left(\sqrt[3]{y - x}\right)}^{2}}}{1} \cdot \frac{\sqrt[3]{y - x}}{\frac{a}{z}} \]

   9. Applied egg-rr 67.4%

      \[\leadsto x + \color{blue}{\frac{{\left(\sqrt[3]{y - x}\right)}^{2}}{1} \cdot \frac{\sqrt[3]{y - x}}{\frac{a}{z}}} \]
   10. Step-by-step derivation

       1. /-rgt-identity 67.4%

          \[\leadsto x + \color{blue}{{\left(\sqrt[3]{y - x}\right)}^{2}} \cdot \frac{\sqrt[3]{y - x}}{\frac{a}{z}} \]

       2. associate-*r/ 67.5%

          \[\leadsto x + \color{blue}{\frac{{\left(\sqrt[3]{y - x}\right)}^{2} \cdot \sqrt[3]{y - x}}{\frac{a}{z}}} \]

       3. unpow2 67.5%

          \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right)} \cdot \sqrt[3]{y - x}}{\frac{a}{z}} \]

       4. rem-3cbrt-lft 67.9%

          \[\leadsto x + \frac{\color{blue}{y - x}}{\frac{a}{z}} \]

   11. Simplified 67.9%

       \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a}{z}}} \]

   if -3.29999999999999989e-192 < t < -3.5999999999999998e-208

   1. Initial program 99.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 99.6%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]
   4. Step-by-step derivation

      1. clear-num 100.0%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{a}{z \cdot \left(y - x\right)}}} \]

      2. inv-pow 100.0%

         \[\leadsto x + \color{blue}{{\left(\frac{a}{z \cdot \left(y - x\right)}\right)}^{-1}} \]

   5. Applied egg-rr 100.0%

      \[\leadsto x + \color{blue}{{\left(\frac{a}{z \cdot \left(y - x\right)}\right)}^{-1}} \]
   6. Step-by-step derivation

      1. unpow-1 100.0%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{a}{z \cdot \left(y - x\right)}}} \]

      2. associate-/r* 76.2%

         \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{a}{z}}{y - x}}} \]

   7. Simplified 76.2%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{a}{z}}{y - x}}} \]

   8. Taylor expanded in y around 0 100.0%

      \[\leadsto x + \frac{1}{\color{blue}{-1 \cdot \frac{a}{x \cdot z}}} \]
   9. Step-by-step derivation

      1. mul-1-neg 100.0%

         \[\leadsto x + \frac{1}{\color{blue}{-\frac{a}{x \cdot z}}} \]

      2. distribute-neg-frac2 100.0%

         \[\leadsto x + \frac{1}{\color{blue}{\frac{a}{-x \cdot z}}} \]

      3. *-commutative 100.0%

         \[\leadsto x + \frac{1}{\frac{a}{-\color{blue}{z \cdot x}}} \]

      4. distribute-rgt-neg-out 100.0%

         \[\leadsto x + \frac{1}{\frac{a}{\color{blue}{z \cdot \left(-x\right)}}} \]

   10. Simplified 100.0%

       \[\leadsto x + \frac{1}{\color{blue}{\frac{a}{z \cdot \left(-x\right)}}} \]

   if -3.09999999999999988e-265 < t < 1.89999999999999994e-67

   1. Initial program 91.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 83.6%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* 88.6%

         \[\leadsto x + \color{blue}{z \cdot \frac{y - x}{a}} \]

   5. Simplified 88.6%

      \[\leadsto x + \color{blue}{z \cdot \frac{y - x}{a}} \]

   if 1.89999999999999994e-67 < t < 56000 or 5.4e11 < t < 7.99999999999999974e79

   1. Initial program 68.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 69.6%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. +-commutative 69.6%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. +-commutative 69.6%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{a - t} + 1\right)} \]

      3. distribute-lft-in 69.6%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \color{blue}{\left(x \cdot \left(-1 \cdot \frac{z - t}{a - t}\right) + x \cdot 1\right)} \]

      4. mul-1-neg 69.6%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(x \cdot \color{blue}{\left(-\frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      5. distribute-rgt-neg-in 69.6%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{\left(-x \cdot \frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      6. associate-/l* 69.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\left(-\color{blue}{\frac{x \cdot \left(z - t\right)}{a - t}}\right) + x \cdot 1\right) \]

      7. mul-1-neg 69.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} + x \cdot 1\right) \]

      8. *-rgt-identity 69.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \color{blue}{x}\right) \]

      9. associate-+l+ 68.9%

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(z - t\right)}{a - t} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) + x} \]

   5. Simplified 83.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)} \]

   6. Taylor expanded in y around inf 66.0%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 66.0%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

   8. Simplified 66.0%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   if 56000 < t < 5.4e11

   1. Initial program 100.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 100.0%

      \[\leadsto \color{blue}{x} \]

   if 3.2999999999999998e116 < t

   1. Initial program 24.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 77.5%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 77.5%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 77.5%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 77.5%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 77.5%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 77.5%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 77.5%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 83.5%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 86.3%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 86.3%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 86.3%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]

   6. Taylor expanded in z around 0 74.8%

      \[\leadsto \color{blue}{y - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   7. Step-by-step derivation

      1. cancel-sign-sub-inv 74.8%

         \[\leadsto \color{blue}{y + \left(--1\right) \cdot \frac{a \cdot \left(y - x\right)}{t}} \]

      2. metadata-eval 74.8%

         \[\leadsto y + \color{blue}{1} \cdot \frac{a \cdot \left(y - x\right)}{t} \]

      3. *-lft-identity 74.8%

         \[\leadsto y + \color{blue}{\frac{a \cdot \left(y - x\right)}{t}} \]

      4. *-commutative 74.8%

         \[\leadsto y + \frac{\color{blue}{\left(y - x\right) \cdot a}}{t} \]

      5. associate-/l* 79.0%

         \[\leadsto y + \color{blue}{\left(y - x\right) \cdot \frac{a}{t}} \]

   8. Simplified 79.0%

      \[\leadsto \color{blue}{y + \left(y - x\right) \cdot \frac{a}{t}} \]
3. Recombined 10 regimes into one program.

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+164}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{+26}:\\ \;\;\;\;y - \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{elif}\;t \leq -2.75 \cdot 10^{+14}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-103}:\\ \;\;\;\;\frac{z}{\frac{a - t}{y - x}}\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-173}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{-192}:\\ \;\;\;\;\frac{z}{\frac{a - t}{y - x}}\\ \mathbf{elif}\;t \leq -3.6 \cdot 10^{-208}:\\ \;\;\;\;x + \frac{-1}{\frac{a}{x \cdot z}}\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-265}:\\ \;\;\;\;\frac{z}{\frac{a - t}{y - x}}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-67}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 56000:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 540000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+79}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+116}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 62.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{\frac{a - t}{y - x}}\\ t_2 := x + t \cdot \frac{y}{t - a}\\ t_3 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -1.42 \cdot 10^{+159}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;t \leq -7 \cdot 10^{+26}:\\ \;\;\;\;y - \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{elif}\;t \leq -1050000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -6.6 \cdot 10^{-103}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.75 \cdot 10^{-173}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-193}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-207}:\\ \;\;\;\;x - \frac{x \cdot z}{a}\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-265}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-64}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 56000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 235000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+80}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 1.14 \cdot 10^{+117}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ z (/ (- a t) (- y x))))
        (t_2 (+ x (* t (/ y (- t a)))))
        (t_3 (* y (/ (- z t) (- a t)))))
   (if (<= t -1.42e+159)
     (/ y (/ (- a t) (- z t)))
     (if (<= t -7e+26)
       (- y (/ (* (- y x) z) t))
       (if (<= t -1050000000000.0)
         t_2
         (if (<= t -6.6e-103)
           t_1
           (if (<= t -2.75e-173)
             (+ x (/ (- y x) (/ a z)))
             (if (<= t -3.5e-193)
               t_1
               (if (<= t -3.4e-207)
                 (- x (/ (* x z) a))
                 (if (<= t -3.1e-265)
                   t_1
                   (if (<= t 3.6e-64)
                     (+ x (* z (/ (- y x) a)))
                     (if (<= t 56000.0)
                       t_3
                       (if (<= t 235000000000.0)
                         x
                         (if (<= t 1.2e+80)
                           t_3
                           (if (<= t 1.14e+117)
                             t_2
                             (+ y (* (- y x) (/ a t))))))))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z / ((a - t) / (y - x));
	double t_2 = x + (t * (y / (t - a)));
	double t_3 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -1.42e+159) {
		tmp = y / ((a - t) / (z - t));
	} else if (t <= -7e+26) {
		tmp = y - (((y - x) * z) / t);
	} else if (t <= -1050000000000.0) {
		tmp = t_2;
	} else if (t <= -6.6e-103) {
		tmp = t_1;
	} else if (t <= -2.75e-173) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= -3.5e-193) {
		tmp = t_1;
	} else if (t <= -3.4e-207) {
		tmp = x - ((x * z) / a);
	} else if (t <= -3.1e-265) {
		tmp = t_1;
	} else if (t <= 3.6e-64) {
		tmp = x + (z * ((y - x) / a));
	} else if (t <= 56000.0) {
		tmp = t_3;
	} else if (t <= 235000000000.0) {
		tmp = x;
	} else if (t <= 1.2e+80) {
		tmp = t_3;
	} else if (t <= 1.14e+117) {
		tmp = t_2;
	} else {
		tmp = y + ((y - x) * (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = z / ((a - t) / (y - x))
    t_2 = x + (t * (y / (t - a)))
    t_3 = y * ((z - t) / (a - t))
    if (t <= (-1.42d+159)) then
        tmp = y / ((a - t) / (z - t))
    else if (t <= (-7d+26)) then
        tmp = y - (((y - x) * z) / t)
    else if (t <= (-1050000000000.0d0)) then
        tmp = t_2
    else if (t <= (-6.6d-103)) then
        tmp = t_1
    else if (t <= (-2.75d-173)) then
        tmp = x + ((y - x) / (a / z))
    else if (t <= (-3.5d-193)) then
        tmp = t_1
    else if (t <= (-3.4d-207)) then
        tmp = x - ((x * z) / a)
    else if (t <= (-3.1d-265)) then
        tmp = t_1
    else if (t <= 3.6d-64) then
        tmp = x + (z * ((y - x) / a))
    else if (t <= 56000.0d0) then
        tmp = t_3
    else if (t <= 235000000000.0d0) then
        tmp = x
    else if (t <= 1.2d+80) then
        tmp = t_3
    else if (t <= 1.14d+117) then
        tmp = t_2
    else
        tmp = y + ((y - x) * (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = z / ((a - t) / (y - x));
	double t_2 = x + (t * (y / (t - a)));
	double t_3 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -1.42e+159) {
		tmp = y / ((a - t) / (z - t));
	} else if (t <= -7e+26) {
		tmp = y - (((y - x) * z) / t);
	} else if (t <= -1050000000000.0) {
		tmp = t_2;
	} else if (t <= -6.6e-103) {
		tmp = t_1;
	} else if (t <= -2.75e-173) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= -3.5e-193) {
		tmp = t_1;
	} else if (t <= -3.4e-207) {
		tmp = x - ((x * z) / a);
	} else if (t <= -3.1e-265) {
		tmp = t_1;
	} else if (t <= 3.6e-64) {
		tmp = x + (z * ((y - x) / a));
	} else if (t <= 56000.0) {
		tmp = t_3;
	} else if (t <= 235000000000.0) {
		tmp = x;
	} else if (t <= 1.2e+80) {
		tmp = t_3;
	} else if (t <= 1.14e+117) {
		tmp = t_2;
	} else {
		tmp = y + ((y - x) * (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z / ((a - t) / (y - x))
	t_2 = x + (t * (y / (t - a)))
	t_3 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -1.42e+159:
		tmp = y / ((a - t) / (z - t))
	elif t <= -7e+26:
		tmp = y - (((y - x) * z) / t)
	elif t <= -1050000000000.0:
		tmp = t_2
	elif t <= -6.6e-103:
		tmp = t_1
	elif t <= -2.75e-173:
		tmp = x + ((y - x) / (a / z))
	elif t <= -3.5e-193:
		tmp = t_1
	elif t <= -3.4e-207:
		tmp = x - ((x * z) / a)
	elif t <= -3.1e-265:
		tmp = t_1
	elif t <= 3.6e-64:
		tmp = x + (z * ((y - x) / a))
	elif t <= 56000.0:
		tmp = t_3
	elif t <= 235000000000.0:
		tmp = x
	elif t <= 1.2e+80:
		tmp = t_3
	elif t <= 1.14e+117:
		tmp = t_2
	else:
		tmp = y + ((y - x) * (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z / Float64(Float64(a - t) / Float64(y - x)))
	t_2 = Float64(x + Float64(t * Float64(y / Float64(t - a))))
	t_3 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -1.42e+159)
		tmp = Float64(y / Float64(Float64(a - t) / Float64(z - t)));
	elseif (t <= -7e+26)
		tmp = Float64(y - Float64(Float64(Float64(y - x) * z) / t));
	elseif (t <= -1050000000000.0)
		tmp = t_2;
	elseif (t <= -6.6e-103)
		tmp = t_1;
	elseif (t <= -2.75e-173)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	elseif (t <= -3.5e-193)
		tmp = t_1;
	elseif (t <= -3.4e-207)
		tmp = Float64(x - Float64(Float64(x * z) / a));
	elseif (t <= -3.1e-265)
		tmp = t_1;
	elseif (t <= 3.6e-64)
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / a)));
	elseif (t <= 56000.0)
		tmp = t_3;
	elseif (t <= 235000000000.0)
		tmp = x;
	elseif (t <= 1.2e+80)
		tmp = t_3;
	elseif (t <= 1.14e+117)
		tmp = t_2;
	else
		tmp = Float64(y + Float64(Float64(y - x) * Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z / ((a - t) / (y - x));
	t_2 = x + (t * (y / (t - a)));
	t_3 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t <= -1.42e+159)
		tmp = y / ((a - t) / (z - t));
	elseif (t <= -7e+26)
		tmp = y - (((y - x) * z) / t);
	elseif (t <= -1050000000000.0)
		tmp = t_2;
	elseif (t <= -6.6e-103)
		tmp = t_1;
	elseif (t <= -2.75e-173)
		tmp = x + ((y - x) / (a / z));
	elseif (t <= -3.5e-193)
		tmp = t_1;
	elseif (t <= -3.4e-207)
		tmp = x - ((x * z) / a);
	elseif (t <= -3.1e-265)
		tmp = t_1;
	elseif (t <= 3.6e-64)
		tmp = x + (z * ((y - x) / a));
	elseif (t <= 56000.0)
		tmp = t_3;
	elseif (t <= 235000000000.0)
		tmp = x;
	elseif (t <= 1.2e+80)
		tmp = t_3;
	elseif (t <= 1.14e+117)
		tmp = t_2;
	else
		tmp = y + ((y - x) * (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z / N[(N[(a - t), $MachinePrecision] / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.42e+159], N[(y / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -7e+26], N[(y - N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1050000000000.0], t$95$2, If[LessEqual[t, -6.6e-103], t$95$1, If[LessEqual[t, -2.75e-173], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.5e-193], t$95$1, If[LessEqual[t, -3.4e-207], N[(x - N[(N[(x * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.1e-265], t$95$1, If[LessEqual[t, 3.6e-64], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 56000.0], t$95$3, If[LessEqual[t, 235000000000.0], x, If[LessEqual[t, 1.2e+80], t$95$3, If[LessEqual[t, 1.14e+117], t$95$2, N[(y + N[(N[(y - x), $MachinePrecision] * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 10 regimes

2. if t < -1.4199999999999999e159

   1. Initial program 29.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 47.3%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. +-commutative 47.3%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. +-commutative 47.3%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{a - t} + 1\right)} \]

      3. distribute-lft-in 47.3%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \color{blue}{\left(x \cdot \left(-1 \cdot \frac{z - t}{a - t}\right) + x \cdot 1\right)} \]

      4. mul-1-neg 47.3%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(x \cdot \color{blue}{\left(-\frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      5. distribute-rgt-neg-in 47.3%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{\left(-x \cdot \frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      6. associate-/l* 29.1%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\left(-\color{blue}{\frac{x \cdot \left(z - t\right)}{a - t}}\right) + x \cdot 1\right) \]

      7. mul-1-neg 29.1%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} + x \cdot 1\right) \]

      8. *-rgt-identity 29.1%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \color{blue}{x}\right) \]

      9. associate-+l+ 29.1%

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(z - t\right)}{a - t} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) + x} \]

   5. Simplified 71.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)} \]

   6. Taylor expanded in y around inf 81.0%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 81.0%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

   8. Simplified 81.0%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]
   9. Step-by-step derivation

      1. clear-num 69.0%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

      2. un-div-inv 69.0%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

   10. Applied egg-rr 81.1%

       \[\leadsto \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

   if -1.4199999999999999e159 < t < -6.9999999999999998e26

   1. Initial program 64.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 77.4%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 77.4%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 77.4%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 77.4%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 77.4%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 77.4%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 77.4%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 80.7%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 80.6%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 80.6%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 80.6%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]

   6. Taylor expanded in z around inf 67.9%

      \[\leadsto y - \color{blue}{\frac{z \cdot \left(y - x\right)}{t}} \]

   if -6.9999999999999998e26 < t < -1.05e12 or 1.1999999999999999e80 < t < 1.13999999999999997e117

   1. Initial program 45.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 59.1%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. associate-/l* 85.5%

         \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   5. Simplified 85.5%

      \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]
   6. Step-by-step derivation

      1. clear-num 85.8%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

      2. inv-pow 85.8%

         \[\leadsto x + y \cdot \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}} \]

   7. Applied egg-rr 85.8%

      \[\leadsto x + y \cdot \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}} \]
   8. Step-by-step derivation

      1. unpow-1 85.8%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

   9. Simplified 85.8%

      \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

   10. Taylor expanded in z around 0 59.1%

       \[\leadsto \color{blue}{x + -1 \cdot \frac{t \cdot y}{a - t}} \]
   11. Step-by-step derivation

       1. mul-1-neg 59.1%

          \[\leadsto x + \color{blue}{\left(-\frac{t \cdot y}{a - t}\right)} \]

       2. unsub-neg 59.1%

          \[\leadsto \color{blue}{x - \frac{t \cdot y}{a - t}} \]

       3. associate-/l* 85.5%

          \[\leadsto x - \color{blue}{t \cdot \frac{y}{a - t}} \]

   12. Simplified 85.5%

       \[\leadsto \color{blue}{x - t \cdot \frac{y}{a - t}} \]

   if -1.05e12 < t < -6.59999999999999979e-103 or -2.75000000000000011e-173 < t < -3.50000000000000005e-193 or -3.39999999999999999e-207 < t < -3.09999999999999988e-265

   1. Initial program 88.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 84.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. +-commutative 84.2%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. +-commutative 84.2%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{a - t} + 1\right)} \]

      3. distribute-lft-in 84.3%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \color{blue}{\left(x \cdot \left(-1 \cdot \frac{z - t}{a - t}\right) + x \cdot 1\right)} \]

      4. mul-1-neg 84.3%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(x \cdot \color{blue}{\left(-\frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      5. distribute-rgt-neg-in 84.3%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{\left(-x \cdot \frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      6. associate-/l* 86.1%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\left(-\color{blue}{\frac{x \cdot \left(z - t\right)}{a - t}}\right) + x \cdot 1\right) \]

      7. mul-1-neg 86.1%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} + x \cdot 1\right) \]

      8. *-rgt-identity 86.1%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \color{blue}{x}\right) \]

      9. associate-+l+ 86.1%

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(z - t\right)}{a - t} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) + x} \]

   5. Simplified 93.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)} \]

   6. Taylor expanded in z around inf 66.8%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 69.1%

         \[\leadsto z \cdot \color{blue}{\frac{y - x}{a - t}} \]

   8. Simplified 69.1%

      \[\leadsto \color{blue}{z \cdot \frac{y - x}{a - t}} \]
   9. Step-by-step derivation

      1. clear-num 69.0%

         \[\leadsto z \cdot \color{blue}{\frac{1}{\frac{a - t}{y - x}}} \]

      2. un-div-inv 71.2%

         \[\leadsto \color{blue}{\frac{z}{\frac{a - t}{y - x}}} \]

   10. Applied egg-rr 71.2%

       \[\leadsto \color{blue}{\frac{z}{\frac{a - t}{y - x}}} \]

   if -6.59999999999999979e-103 < t < -2.75000000000000011e-173

   1. Initial program 87.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 61.6%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]
   4. Step-by-step derivation

      1. clear-num 61.6%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{a}{z \cdot \left(y - x\right)}}} \]

      2. inv-pow 61.6%

         \[\leadsto x + \color{blue}{{\left(\frac{a}{z \cdot \left(y - x\right)}\right)}^{-1}} \]

   5. Applied egg-rr 61.6%

      \[\leadsto x + \color{blue}{{\left(\frac{a}{z \cdot \left(y - x\right)}\right)}^{-1}} \]
   6. Step-by-step derivation

      1. unpow-1 61.6%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{a}{z \cdot \left(y - x\right)}}} \]

      2. associate-/r* 67.9%

         \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{a}{z}}{y - x}}} \]

   7. Simplified 67.9%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{a}{z}}{y - x}}} \]
   8. Step-by-step derivation

      1. clear-num 67.9%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a}{z}}} \]

      2. add-cube-cbrt 67.5%

         \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \sqrt[3]{y - x}}}{\frac{a}{z}} \]

      3. *-un-lft-identity 67.5%

         \[\leadsto x + \frac{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \sqrt[3]{y - x}}{\color{blue}{1 \cdot \frac{a}{z}}} \]

      4. times-frac 67.4%

         \[\leadsto x + \color{blue}{\frac{\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}}{1} \cdot \frac{\sqrt[3]{y - x}}{\frac{a}{z}}} \]

      5. pow2 67.4%

         \[\leadsto x + \frac{\color{blue}{{\left(\sqrt[3]{y - x}\right)}^{2}}}{1} \cdot \frac{\sqrt[3]{y - x}}{\frac{a}{z}} \]

   9. Applied egg-rr 67.4%

      \[\leadsto x + \color{blue}{\frac{{\left(\sqrt[3]{y - x}\right)}^{2}}{1} \cdot \frac{\sqrt[3]{y - x}}{\frac{a}{z}}} \]
   10. Step-by-step derivation

       1. /-rgt-identity 67.4%

          \[\leadsto x + \color{blue}{{\left(\sqrt[3]{y - x}\right)}^{2}} \cdot \frac{\sqrt[3]{y - x}}{\frac{a}{z}} \]

       2. associate-*r/ 67.5%

          \[\leadsto x + \color{blue}{\frac{{\left(\sqrt[3]{y - x}\right)}^{2} \cdot \sqrt[3]{y - x}}{\frac{a}{z}}} \]

       3. unpow2 67.5%

          \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right)} \cdot \sqrt[3]{y - x}}{\frac{a}{z}} \]

       4. rem-3cbrt-lft 67.9%

          \[\leadsto x + \frac{\color{blue}{y - x}}{\frac{a}{z}} \]

   11. Simplified 67.9%

       \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a}{z}}} \]

   if -3.50000000000000005e-193 < t < -3.39999999999999999e-207

   1. Initial program 99.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 99.6%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]

   4. Taylor expanded in y around 0 99.6%

      \[\leadsto x + \frac{\color{blue}{-1 \cdot \left(x \cdot z\right)}}{a} \]
   5. Step-by-step derivation

      1. mul-1-neg 99.6%

         \[\leadsto x + \frac{\color{blue}{-x \cdot z}}{a} \]

      2. distribute-lft-neg-out 99.6%

         \[\leadsto x + \frac{\color{blue}{\left(-x\right) \cdot z}}{a} \]

      3. *-commutative 99.6%

         \[\leadsto x + \frac{\color{blue}{z \cdot \left(-x\right)}}{a} \]

   6. Simplified 99.6%

      \[\leadsto x + \frac{\color{blue}{z \cdot \left(-x\right)}}{a} \]

   if -3.09999999999999988e-265 < t < 3.5999999999999998e-64

   1. Initial program 91.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 83.6%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* 88.6%

         \[\leadsto x + \color{blue}{z \cdot \frac{y - x}{a}} \]

   5. Simplified 88.6%

      \[\leadsto x + \color{blue}{z \cdot \frac{y - x}{a}} \]

   if 3.5999999999999998e-64 < t < 56000 or 2.35e11 < t < 1.1999999999999999e80

   1. Initial program 68.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 69.6%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. +-commutative 69.6%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. +-commutative 69.6%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{a - t} + 1\right)} \]

      3. distribute-lft-in 69.6%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \color{blue}{\left(x \cdot \left(-1 \cdot \frac{z - t}{a - t}\right) + x \cdot 1\right)} \]

      4. mul-1-neg 69.6%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(x \cdot \color{blue}{\left(-\frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      5. distribute-rgt-neg-in 69.6%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{\left(-x \cdot \frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      6. associate-/l* 69.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\left(-\color{blue}{\frac{x \cdot \left(z - t\right)}{a - t}}\right) + x \cdot 1\right) \]

      7. mul-1-neg 69.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} + x \cdot 1\right) \]

      8. *-rgt-identity 69.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \color{blue}{x}\right) \]

      9. associate-+l+ 68.9%

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(z - t\right)}{a - t} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) + x} \]

   5. Simplified 83.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)} \]

   6. Taylor expanded in y around inf 66.0%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 66.0%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

   8. Simplified 66.0%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   if 56000 < t < 2.35e11

   1. Initial program 100.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 100.0%

      \[\leadsto \color{blue}{x} \]

   if 1.13999999999999997e117 < t

   1. Initial program 24.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 77.5%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 77.5%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 77.5%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 77.5%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 77.5%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 77.5%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 77.5%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 83.5%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 86.3%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 86.3%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 86.3%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]

   6. Taylor expanded in z around 0 74.8%

      \[\leadsto \color{blue}{y - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   7. Step-by-step derivation

      1. cancel-sign-sub-inv 74.8%

         \[\leadsto \color{blue}{y + \left(--1\right) \cdot \frac{a \cdot \left(y - x\right)}{t}} \]

      2. metadata-eval 74.8%

         \[\leadsto y + \color{blue}{1} \cdot \frac{a \cdot \left(y - x\right)}{t} \]

      3. *-lft-identity 74.8%

         \[\leadsto y + \color{blue}{\frac{a \cdot \left(y - x\right)}{t}} \]

      4. *-commutative 74.8%

         \[\leadsto y + \frac{\color{blue}{\left(y - x\right) \cdot a}}{t} \]

      5. associate-/l* 79.0%

         \[\leadsto y + \color{blue}{\left(y - x\right) \cdot \frac{a}{t}} \]

   8. Simplified 79.0%

      \[\leadsto \color{blue}{y + \left(y - x\right) \cdot \frac{a}{t}} \]
3. Recombined 10 regimes into one program.

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.42 \cdot 10^{+159}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;t \leq -7 \cdot 10^{+26}:\\ \;\;\;\;y - \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{elif}\;t \leq -1050000000000:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \mathbf{elif}\;t \leq -6.6 \cdot 10^{-103}:\\ \;\;\;\;\frac{z}{\frac{a - t}{y - x}}\\ \mathbf{elif}\;t \leq -2.75 \cdot 10^{-173}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-193}:\\ \;\;\;\;\frac{z}{\frac{a - t}{y - x}}\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-207}:\\ \;\;\;\;x - \frac{x \cdot z}{a}\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-265}:\\ \;\;\;\;\frac{z}{\frac{a - t}{y - x}}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-64}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 56000:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 235000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+80}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 1.14 \cdot 10^{+117}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y - x}{a}\\ t_2 := \frac{z}{\frac{a - t}{y - x}}\\ t_3 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -1.7 \cdot 10^{-26}:\\ \;\;\;\;y + \frac{z - a}{\frac{t}{x}}\\ \mathbf{elif}\;t \leq -1.95 \cdot 10^{-52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.52 \cdot 10^{-92}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-155}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-208}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-212}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-253}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-291}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 56000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 235000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+77}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot \frac{z - a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ (- y x) a))))
        (t_2 (/ z (/ (- a t) (- y x))))
        (t_3 (* y (/ (- z t) (- a t)))))
   (if (<= t -1.7e-26)
     (+ y (/ (- z a) (/ t x)))
     (if (<= t -1.95e-52)
       t_1
       (if (<= t -1.52e-92)
         t_2
         (if (<= t -9.5e-155)
           t_1
           (if (<= t -1.05e-208)
             (+ x (/ (* (- y x) z) a))
             (if (<= t -4.6e-212)
               (+ x (* t (/ y (- t a))))
               (if (<= t -1.2e-253)
                 t_2
                 (if (<= t -5e-291)
                   (+ x (/ (- y x) (/ a z)))
                   (if (<= t 6e-63)
                     t_1
                     (if (<= t 56000.0)
                       t_3
                       (if (<= t 235000000000.0)
                         x
                         (if (<= t 6.8e+77)
                           t_3
                           (+ y (* x (/ (- z a) t)))))))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * ((y - x) / a));
	double t_2 = z / ((a - t) / (y - x));
	double t_3 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -1.7e-26) {
		tmp = y + ((z - a) / (t / x));
	} else if (t <= -1.95e-52) {
		tmp = t_1;
	} else if (t <= -1.52e-92) {
		tmp = t_2;
	} else if (t <= -9.5e-155) {
		tmp = t_1;
	} else if (t <= -1.05e-208) {
		tmp = x + (((y - x) * z) / a);
	} else if (t <= -4.6e-212) {
		tmp = x + (t * (y / (t - a)));
	} else if (t <= -1.2e-253) {
		tmp = t_2;
	} else if (t <= -5e-291) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 6e-63) {
		tmp = t_1;
	} else if (t <= 56000.0) {
		tmp = t_3;
	} else if (t <= 235000000000.0) {
		tmp = x;
	} else if (t <= 6.8e+77) {
		tmp = t_3;
	} else {
		tmp = y + (x * ((z - a) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + (z * ((y - x) / a))
    t_2 = z / ((a - t) / (y - x))
    t_3 = y * ((z - t) / (a - t))
    if (t <= (-1.7d-26)) then
        tmp = y + ((z - a) / (t / x))
    else if (t <= (-1.95d-52)) then
        tmp = t_1
    else if (t <= (-1.52d-92)) then
        tmp = t_2
    else if (t <= (-9.5d-155)) then
        tmp = t_1
    else if (t <= (-1.05d-208)) then
        tmp = x + (((y - x) * z) / a)
    else if (t <= (-4.6d-212)) then
        tmp = x + (t * (y / (t - a)))
    else if (t <= (-1.2d-253)) then
        tmp = t_2
    else if (t <= (-5d-291)) then
        tmp = x + ((y - x) / (a / z))
    else if (t <= 6d-63) then
        tmp = t_1
    else if (t <= 56000.0d0) then
        tmp = t_3
    else if (t <= 235000000000.0d0) then
        tmp = x
    else if (t <= 6.8d+77) then
        tmp = t_3
    else
        tmp = y + (x * ((z - a) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * ((y - x) / a));
	double t_2 = z / ((a - t) / (y - x));
	double t_3 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -1.7e-26) {
		tmp = y + ((z - a) / (t / x));
	} else if (t <= -1.95e-52) {
		tmp = t_1;
	} else if (t <= -1.52e-92) {
		tmp = t_2;
	} else if (t <= -9.5e-155) {
		tmp = t_1;
	} else if (t <= -1.05e-208) {
		tmp = x + (((y - x) * z) / a);
	} else if (t <= -4.6e-212) {
		tmp = x + (t * (y / (t - a)));
	} else if (t <= -1.2e-253) {
		tmp = t_2;
	} else if (t <= -5e-291) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 6e-63) {
		tmp = t_1;
	} else if (t <= 56000.0) {
		tmp = t_3;
	} else if (t <= 235000000000.0) {
		tmp = x;
	} else if (t <= 6.8e+77) {
		tmp = t_3;
	} else {
		tmp = y + (x * ((z - a) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * ((y - x) / a))
	t_2 = z / ((a - t) / (y - x))
	t_3 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -1.7e-26:
		tmp = y + ((z - a) / (t / x))
	elif t <= -1.95e-52:
		tmp = t_1
	elif t <= -1.52e-92:
		tmp = t_2
	elif t <= -9.5e-155:
		tmp = t_1
	elif t <= -1.05e-208:
		tmp = x + (((y - x) * z) / a)
	elif t <= -4.6e-212:
		tmp = x + (t * (y / (t - a)))
	elif t <= -1.2e-253:
		tmp = t_2
	elif t <= -5e-291:
		tmp = x + ((y - x) / (a / z))
	elif t <= 6e-63:
		tmp = t_1
	elif t <= 56000.0:
		tmp = t_3
	elif t <= 235000000000.0:
		tmp = x
	elif t <= 6.8e+77:
		tmp = t_3
	else:
		tmp = y + (x * ((z - a) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(Float64(y - x) / a)))
	t_2 = Float64(z / Float64(Float64(a - t) / Float64(y - x)))
	t_3 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -1.7e-26)
		tmp = Float64(y + Float64(Float64(z - a) / Float64(t / x)));
	elseif (t <= -1.95e-52)
		tmp = t_1;
	elseif (t <= -1.52e-92)
		tmp = t_2;
	elseif (t <= -9.5e-155)
		tmp = t_1;
	elseif (t <= -1.05e-208)
		tmp = Float64(x + Float64(Float64(Float64(y - x) * z) / a));
	elseif (t <= -4.6e-212)
		tmp = Float64(x + Float64(t * Float64(y / Float64(t - a))));
	elseif (t <= -1.2e-253)
		tmp = t_2;
	elseif (t <= -5e-291)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	elseif (t <= 6e-63)
		tmp = t_1;
	elseif (t <= 56000.0)
		tmp = t_3;
	elseif (t <= 235000000000.0)
		tmp = x;
	elseif (t <= 6.8e+77)
		tmp = t_3;
	else
		tmp = Float64(y + Float64(x * Float64(Float64(z - a) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * ((y - x) / a));
	t_2 = z / ((a - t) / (y - x));
	t_3 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t <= -1.7e-26)
		tmp = y + ((z - a) / (t / x));
	elseif (t <= -1.95e-52)
		tmp = t_1;
	elseif (t <= -1.52e-92)
		tmp = t_2;
	elseif (t <= -9.5e-155)
		tmp = t_1;
	elseif (t <= -1.05e-208)
		tmp = x + (((y - x) * z) / a);
	elseif (t <= -4.6e-212)
		tmp = x + (t * (y / (t - a)));
	elseif (t <= -1.2e-253)
		tmp = t_2;
	elseif (t <= -5e-291)
		tmp = x + ((y - x) / (a / z));
	elseif (t <= 6e-63)
		tmp = t_1;
	elseif (t <= 56000.0)
		tmp = t_3;
	elseif (t <= 235000000000.0)
		tmp = x;
	elseif (t <= 6.8e+77)
		tmp = t_3;
	else
		tmp = y + (x * ((z - a) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z / N[(N[(a - t), $MachinePrecision] / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.7e-26], N[(y + N[(N[(z - a), $MachinePrecision] / N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.95e-52], t$95$1, If[LessEqual[t, -1.52e-92], t$95$2, If[LessEqual[t, -9.5e-155], t$95$1, If[LessEqual[t, -1.05e-208], N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.6e-212], N[(x + N[(t * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.2e-253], t$95$2, If[LessEqual[t, -5e-291], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e-63], t$95$1, If[LessEqual[t, 56000.0], t$95$3, If[LessEqual[t, 235000000000.0], x, If[LessEqual[t, 6.8e+77], t$95$3, N[(y + N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if t < -1.70000000000000007e-26

   1. Initial program 52.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 63.1%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 63.1%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 63.1%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 63.1%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 63.1%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 63.1%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 63.1%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 71.8%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 82.1%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 82.1%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 82.1%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]
   6. Step-by-step derivation

      1. *-commutative 82.1%

         \[\leadsto y - \color{blue}{\left(z - a\right) \cdot \frac{y - x}{t}} \]

      2. clear-num 82.0%

         \[\leadsto y - \left(z - a\right) \cdot \color{blue}{\frac{1}{\frac{t}{y - x}}} \]

      3. un-div-inv 82.1%

         \[\leadsto y - \color{blue}{\frac{z - a}{\frac{t}{y - x}}} \]

   7. Applied egg-rr 82.1%

      \[\leadsto y - \color{blue}{\frac{z - a}{\frac{t}{y - x}}} \]

   8. Taylor expanded in y around 0 72.1%

      \[\leadsto y - \frac{z - a}{\color{blue}{-1 \cdot \frac{t}{x}}} \]
   9. Step-by-step derivation

      1. associate-*r/ 72.1%

         \[\leadsto y - \frac{z - a}{\color{blue}{\frac{-1 \cdot t}{x}}} \]

      2. mul-1-neg 72.1%

         \[\leadsto y - \frac{z - a}{\frac{\color{blue}{-t}}{x}} \]

   10. Simplified 72.1%

       \[\leadsto y - \frac{z - a}{\color{blue}{\frac{-t}{x}}} \]

   if -1.70000000000000007e-26 < t < -1.95000000000000009e-52 or -1.52e-92 < t < -9.50000000000000024e-155 or -5.0000000000000003e-291 < t < 5.99999999999999959e-63

   1. Initial program 89.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 77.2%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* 85.1%

         \[\leadsto x + \color{blue}{z \cdot \frac{y - x}{a}} \]

   5. Simplified 85.1%

      \[\leadsto x + \color{blue}{z \cdot \frac{y - x}{a}} \]

   if -1.95000000000000009e-52 < t < -1.52e-92 or -4.6000000000000002e-212 < t < -1.20000000000000005e-253

   1. Initial program 89.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 84.6%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. +-commutative 84.6%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. +-commutative 84.6%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{a - t} + 1\right)} \]

      3. distribute-lft-in 84.6%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \color{blue}{\left(x \cdot \left(-1 \cdot \frac{z - t}{a - t}\right) + x \cdot 1\right)} \]

      4. mul-1-neg 84.6%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(x \cdot \color{blue}{\left(-\frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      5. distribute-rgt-neg-in 84.6%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{\left(-x \cdot \frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      6. associate-/l* 89.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\left(-\color{blue}{\frac{x \cdot \left(z - t\right)}{a - t}}\right) + x \cdot 1\right) \]

      7. mul-1-neg 89.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} + x \cdot 1\right) \]

      8. *-rgt-identity 89.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \color{blue}{x}\right) \]

      9. associate-+l+ 89.4%

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(z - t\right)}{a - t} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) + x} \]

   5. Simplified 94.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)} \]

   6. Taylor expanded in z around inf 79.0%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 79.0%

         \[\leadsto z \cdot \color{blue}{\frac{y - x}{a - t}} \]

   8. Simplified 79.0%

      \[\leadsto \color{blue}{z \cdot \frac{y - x}{a - t}} \]
   9. Step-by-step derivation

      1. clear-num 79.0%

         \[\leadsto z \cdot \color{blue}{\frac{1}{\frac{a - t}{y - x}}} \]

      2. un-div-inv 79.1%

         \[\leadsto \color{blue}{\frac{z}{\frac{a - t}{y - x}}} \]

   10. Applied egg-rr 79.1%

       \[\leadsto \color{blue}{\frac{z}{\frac{a - t}{y - x}}} \]

   if -9.50000000000000024e-155 < t < -1.05000000000000006e-208

   1. Initial program 99.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 68.5%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]

   if -1.05000000000000006e-208 < t < -4.6000000000000002e-212

   1. Initial program 99.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 99.5%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   5. Simplified 100.0%

      \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]
   6. Step-by-step derivation

      1. clear-num 100.0%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

      2. inv-pow 100.0%

         \[\leadsto x + y \cdot \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}} \]

   7. Applied egg-rr 100.0%

      \[\leadsto x + y \cdot \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}} \]
   8. Step-by-step derivation

      1. unpow-1 100.0%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

   9. Simplified 100.0%

      \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

   10. Taylor expanded in z around 0 68.6%

       \[\leadsto \color{blue}{x + -1 \cdot \frac{t \cdot y}{a - t}} \]
   11. Step-by-step derivation

       1. mul-1-neg 68.6%

          \[\leadsto x + \color{blue}{\left(-\frac{t \cdot y}{a - t}\right)} \]

       2. unsub-neg 68.6%

          \[\leadsto \color{blue}{x - \frac{t \cdot y}{a - t}} \]

       3. associate-/l* 99.5%

          \[\leadsto x - \color{blue}{t \cdot \frac{y}{a - t}} \]

   12. Simplified 99.5%

       \[\leadsto \color{blue}{x - t \cdot \frac{y}{a - t}} \]

   if -1.20000000000000005e-253 < t < -5.0000000000000003e-291

   1. Initial program 88.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 88.7%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]
   4. Step-by-step derivation

      1. clear-num 88.7%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{a}{z \cdot \left(y - x\right)}}} \]

      2. inv-pow 88.7%

         \[\leadsto x + \color{blue}{{\left(\frac{a}{z \cdot \left(y - x\right)}\right)}^{-1}} \]

   5. Applied egg-rr 88.7%

      \[\leadsto x + \color{blue}{{\left(\frac{a}{z \cdot \left(y - x\right)}\right)}^{-1}} \]
   6. Step-by-step derivation

      1. unpow-1 88.7%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{a}{z \cdot \left(y - x\right)}}} \]

      2. associate-/r* 100.0%

         \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{a}{z}}{y - x}}} \]

   7. Simplified 100.0%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{a}{z}}{y - x}}} \]
   8. Step-by-step derivation

      1. clear-num 100.0%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a}{z}}} \]

      2. add-cube-cbrt 99.3%

         \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \sqrt[3]{y - x}}}{\frac{a}{z}} \]

      3. *-un-lft-identity 99.3%

         \[\leadsto x + \frac{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \sqrt[3]{y - x}}{\color{blue}{1 \cdot \frac{a}{z}}} \]

      4. times-frac 99.2%

         \[\leadsto x + \color{blue}{\frac{\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}}{1} \cdot \frac{\sqrt[3]{y - x}}{\frac{a}{z}}} \]

      5. pow2 99.2%

         \[\leadsto x + \frac{\color{blue}{{\left(\sqrt[3]{y - x}\right)}^{2}}}{1} \cdot \frac{\sqrt[3]{y - x}}{\frac{a}{z}} \]

   9. Applied egg-rr 99.2%

      \[\leadsto x + \color{blue}{\frac{{\left(\sqrt[3]{y - x}\right)}^{2}}{1} \cdot \frac{\sqrt[3]{y - x}}{\frac{a}{z}}} \]
   10. Step-by-step derivation

       1. /-rgt-identity 99.2%

          \[\leadsto x + \color{blue}{{\left(\sqrt[3]{y - x}\right)}^{2}} \cdot \frac{\sqrt[3]{y - x}}{\frac{a}{z}} \]

       2. associate-*r/ 99.3%

          \[\leadsto x + \color{blue}{\frac{{\left(\sqrt[3]{y - x}\right)}^{2} \cdot \sqrt[3]{y - x}}{\frac{a}{z}}} \]

       3. unpow2 99.3%

          \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right)} \cdot \sqrt[3]{y - x}}{\frac{a}{z}} \]

       4. rem-3cbrt-lft 100.0%

          \[\leadsto x + \frac{\color{blue}{y - x}}{\frac{a}{z}} \]

   11. Simplified 100.0%

       \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a}{z}}} \]

   if 5.99999999999999959e-63 < t < 56000 or 2.35e11 < t < 6.79999999999999993e77

   1. Initial program 68.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 69.6%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. +-commutative 69.6%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. +-commutative 69.6%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{a - t} + 1\right)} \]

      3. distribute-lft-in 69.6%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \color{blue}{\left(x \cdot \left(-1 \cdot \frac{z - t}{a - t}\right) + x \cdot 1\right)} \]

      4. mul-1-neg 69.6%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(x \cdot \color{blue}{\left(-\frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      5. distribute-rgt-neg-in 69.6%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{\left(-x \cdot \frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      6. associate-/l* 69.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\left(-\color{blue}{\frac{x \cdot \left(z - t\right)}{a - t}}\right) + x \cdot 1\right) \]

      7. mul-1-neg 69.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} + x \cdot 1\right) \]

      8. *-rgt-identity 69.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \color{blue}{x}\right) \]

      9. associate-+l+ 68.9%

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(z - t\right)}{a - t} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) + x} \]

   5. Simplified 83.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)} \]

   6. Taylor expanded in y around inf 66.0%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 66.0%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

   8. Simplified 66.0%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   if 56000 < t < 2.35e11

   1. Initial program 100.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 100.0%

      \[\leadsto \color{blue}{x} \]

   if 6.79999999999999993e77 < t

   1. Initial program 26.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 73.7%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 73.7%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 73.7%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 73.7%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 73.7%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 73.7%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 73.7%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 81.1%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 83.6%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 83.6%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 83.6%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]
   6. Step-by-step derivation

      1. *-commutative 83.6%

         \[\leadsto y - \color{blue}{\left(z - a\right) \cdot \frac{y - x}{t}} \]

      2. clear-num 83.6%

         \[\leadsto y - \left(z - a\right) \cdot \color{blue}{\frac{1}{\frac{t}{y - x}}} \]

      3. un-div-inv 83.5%

         \[\leadsto y - \color{blue}{\frac{z - a}{\frac{t}{y - x}}} \]

   7. Applied egg-rr 83.5%

      \[\leadsto y - \color{blue}{\frac{z - a}{\frac{t}{y - x}}} \]

   8. Taylor expanded in y around 0 79.1%

      \[\leadsto y - \color{blue}{-1 \cdot \frac{x \cdot \left(z - a\right)}{t}} \]
   9. Step-by-step derivation

      1. mul-1-neg 79.1%

         \[\leadsto y - \color{blue}{\left(-\frac{x \cdot \left(z - a\right)}{t}\right)} \]

      2. associate-/l* 80.7%

         \[\leadsto y - \left(-\color{blue}{x \cdot \frac{z - a}{t}}\right) \]

   10. Simplified 80.7%

       \[\leadsto y - \color{blue}{\left(-x \cdot \frac{z - a}{t}\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{-26}:\\ \;\;\;\;y + \frac{z - a}{\frac{t}{x}}\\ \mathbf{elif}\;t \leq -1.95 \cdot 10^{-52}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq -1.52 \cdot 10^{-92}:\\ \;\;\;\;\frac{z}{\frac{a - t}{y - x}}\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-155}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-208}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-212}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-253}:\\ \;\;\;\;\frac{z}{\frac{a - t}{y - x}}\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-291}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-63}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 56000:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 235000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+77}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot \frac{z - a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 63.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y - x}{a - t}\\ t_2 := y \cdot \frac{z - t}{a - t}\\ t_3 := x + z \cdot \frac{y - x}{a}\\ \mathbf{if}\;t \leq -6.3 \cdot 10^{-15}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-154}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-208}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-208}:\\ \;\;\;\;y \cdot \frac{t}{-a}\\ \mathbf{elif}\;t \leq -9.4 \cdot 10^{-244}:\\ \;\;\;\;x - \frac{x \cdot z}{a}\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-253}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-283}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-63}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 49000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 235000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{+79}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ (- y x) (- a t))))
        (t_2 (* y (/ (- z t) (- a t))))
        (t_3 (+ x (* z (/ (- y x) a)))))
   (if (<= t -6.3e-15)
     t_2
     (if (<= t -1.7e-92)
       t_1
       (if (<= t -4.2e-154)
         t_3
         (if (<= t -1.05e-208)
           (+ x (/ (* (- y x) z) a))
           (if (<= t -1e-208)
             (* y (/ t (- a)))
             (if (<= t -9.4e-244)
               (- x (/ (* x z) a))
               (if (<= t -1.2e-253)
                 t_1
                 (if (<= t -9.2e-283)
                   (+ x (/ (- y x) (/ a z)))
                   (if (<= t 7e-63)
                     t_3
                     (if (<= t 49000.0)
                       t_2
                       (if (<= t 235000000000.0)
                         x
                         (if (<= t 9.8e+79)
                           t_2
                           (+ y (* (- y x) (/ a t)))))))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((y - x) / (a - t));
	double t_2 = y * ((z - t) / (a - t));
	double t_3 = x + (z * ((y - x) / a));
	double tmp;
	if (t <= -6.3e-15) {
		tmp = t_2;
	} else if (t <= -1.7e-92) {
		tmp = t_1;
	} else if (t <= -4.2e-154) {
		tmp = t_3;
	} else if (t <= -1.05e-208) {
		tmp = x + (((y - x) * z) / a);
	} else if (t <= -1e-208) {
		tmp = y * (t / -a);
	} else if (t <= -9.4e-244) {
		tmp = x - ((x * z) / a);
	} else if (t <= -1.2e-253) {
		tmp = t_1;
	} else if (t <= -9.2e-283) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 7e-63) {
		tmp = t_3;
	} else if (t <= 49000.0) {
		tmp = t_2;
	} else if (t <= 235000000000.0) {
		tmp = x;
	} else if (t <= 9.8e+79) {
		tmp = t_2;
	} else {
		tmp = y + ((y - x) * (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = z * ((y - x) / (a - t))
    t_2 = y * ((z - t) / (a - t))
    t_3 = x + (z * ((y - x) / a))
    if (t <= (-6.3d-15)) then
        tmp = t_2
    else if (t <= (-1.7d-92)) then
        tmp = t_1
    else if (t <= (-4.2d-154)) then
        tmp = t_3
    else if (t <= (-1.05d-208)) then
        tmp = x + (((y - x) * z) / a)
    else if (t <= (-1d-208)) then
        tmp = y * (t / -a)
    else if (t <= (-9.4d-244)) then
        tmp = x - ((x * z) / a)
    else if (t <= (-1.2d-253)) then
        tmp = t_1
    else if (t <= (-9.2d-283)) then
        tmp = x + ((y - x) / (a / z))
    else if (t <= 7d-63) then
        tmp = t_3
    else if (t <= 49000.0d0) then
        tmp = t_2
    else if (t <= 235000000000.0d0) then
        tmp = x
    else if (t <= 9.8d+79) then
        tmp = t_2
    else
        tmp = y + ((y - x) * (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((y - x) / (a - t));
	double t_2 = y * ((z - t) / (a - t));
	double t_3 = x + (z * ((y - x) / a));
	double tmp;
	if (t <= -6.3e-15) {
		tmp = t_2;
	} else if (t <= -1.7e-92) {
		tmp = t_1;
	} else if (t <= -4.2e-154) {
		tmp = t_3;
	} else if (t <= -1.05e-208) {
		tmp = x + (((y - x) * z) / a);
	} else if (t <= -1e-208) {
		tmp = y * (t / -a);
	} else if (t <= -9.4e-244) {
		tmp = x - ((x * z) / a);
	} else if (t <= -1.2e-253) {
		tmp = t_1;
	} else if (t <= -9.2e-283) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 7e-63) {
		tmp = t_3;
	} else if (t <= 49000.0) {
		tmp = t_2;
	} else if (t <= 235000000000.0) {
		tmp = x;
	} else if (t <= 9.8e+79) {
		tmp = t_2;
	} else {
		tmp = y + ((y - x) * (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * ((y - x) / (a - t))
	t_2 = y * ((z - t) / (a - t))
	t_3 = x + (z * ((y - x) / a))
	tmp = 0
	if t <= -6.3e-15:
		tmp = t_2
	elif t <= -1.7e-92:
		tmp = t_1
	elif t <= -4.2e-154:
		tmp = t_3
	elif t <= -1.05e-208:
		tmp = x + (((y - x) * z) / a)
	elif t <= -1e-208:
		tmp = y * (t / -a)
	elif t <= -9.4e-244:
		tmp = x - ((x * z) / a)
	elif t <= -1.2e-253:
		tmp = t_1
	elif t <= -9.2e-283:
		tmp = x + ((y - x) / (a / z))
	elif t <= 7e-63:
		tmp = t_3
	elif t <= 49000.0:
		tmp = t_2
	elif t <= 235000000000.0:
		tmp = x
	elif t <= 9.8e+79:
		tmp = t_2
	else:
		tmp = y + ((y - x) * (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(Float64(y - x) / Float64(a - t)))
	t_2 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_3 = Float64(x + Float64(z * Float64(Float64(y - x) / a)))
	tmp = 0.0
	if (t <= -6.3e-15)
		tmp = t_2;
	elseif (t <= -1.7e-92)
		tmp = t_1;
	elseif (t <= -4.2e-154)
		tmp = t_3;
	elseif (t <= -1.05e-208)
		tmp = Float64(x + Float64(Float64(Float64(y - x) * z) / a));
	elseif (t <= -1e-208)
		tmp = Float64(y * Float64(t / Float64(-a)));
	elseif (t <= -9.4e-244)
		tmp = Float64(x - Float64(Float64(x * z) / a));
	elseif (t <= -1.2e-253)
		tmp = t_1;
	elseif (t <= -9.2e-283)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	elseif (t <= 7e-63)
		tmp = t_3;
	elseif (t <= 49000.0)
		tmp = t_2;
	elseif (t <= 235000000000.0)
		tmp = x;
	elseif (t <= 9.8e+79)
		tmp = t_2;
	else
		tmp = Float64(y + Float64(Float64(y - x) * Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * ((y - x) / (a - t));
	t_2 = y * ((z - t) / (a - t));
	t_3 = x + (z * ((y - x) / a));
	tmp = 0.0;
	if (t <= -6.3e-15)
		tmp = t_2;
	elseif (t <= -1.7e-92)
		tmp = t_1;
	elseif (t <= -4.2e-154)
		tmp = t_3;
	elseif (t <= -1.05e-208)
		tmp = x + (((y - x) * z) / a);
	elseif (t <= -1e-208)
		tmp = y * (t / -a);
	elseif (t <= -9.4e-244)
		tmp = x - ((x * z) / a);
	elseif (t <= -1.2e-253)
		tmp = t_1;
	elseif (t <= -9.2e-283)
		tmp = x + ((y - x) / (a / z));
	elseif (t <= 7e-63)
		tmp = t_3;
	elseif (t <= 49000.0)
		tmp = t_2;
	elseif (t <= 235000000000.0)
		tmp = x;
	elseif (t <= 9.8e+79)
		tmp = t_2;
	else
		tmp = y + ((y - x) * (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.3e-15], t$95$2, If[LessEqual[t, -1.7e-92], t$95$1, If[LessEqual[t, -4.2e-154], t$95$3, If[LessEqual[t, -1.05e-208], N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1e-208], N[(y * N[(t / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -9.4e-244], N[(x - N[(N[(x * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.2e-253], t$95$1, If[LessEqual[t, -9.2e-283], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e-63], t$95$3, If[LessEqual[t, 49000.0], t$95$2, If[LessEqual[t, 235000000000.0], x, If[LessEqual[t, 9.8e+79], t$95$2, N[(y + N[(N[(y - x), $MachinePrecision] * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if t < -6.29999999999999982e-15 or 7.00000000000000006e-63 < t < 49000 or 2.35e11 < t < 9.7999999999999997e79

   1. Initial program 56.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 65.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. +-commutative 65.2%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. +-commutative 65.2%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{a - t} + 1\right)} \]

      3. distribute-lft-in 65.2%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \color{blue}{\left(x \cdot \left(-1 \cdot \frac{z - t}{a - t}\right) + x \cdot 1\right)} \]

      4. mul-1-neg 65.2%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(x \cdot \color{blue}{\left(-\frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      5. distribute-rgt-neg-in 65.2%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{\left(-x \cdot \frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      6. associate-/l* 57.3%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\left(-\color{blue}{\frac{x \cdot \left(z - t\right)}{a - t}}\right) + x \cdot 1\right) \]

      7. mul-1-neg 57.3%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} + x \cdot 1\right) \]

      8. *-rgt-identity 57.3%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \color{blue}{x}\right) \]

      9. associate-+l+ 55.1%

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(z - t\right)}{a - t} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) + x} \]

   5. Simplified 76.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)} \]

   6. Taylor expanded in y around inf 65.5%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 65.5%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

   8. Simplified 65.5%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   if -6.29999999999999982e-15 < t < -1.7000000000000001e-92 or -9.3999999999999997e-244 < t < -1.20000000000000005e-253

   1. Initial program 86.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 81.9%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. +-commutative 81.9%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. +-commutative 81.9%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{a - t} + 1\right)} \]

      3. distribute-lft-in 82.0%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \color{blue}{\left(x \cdot \left(-1 \cdot \frac{z - t}{a - t}\right) + x \cdot 1\right)} \]

      4. mul-1-neg 82.0%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(x \cdot \color{blue}{\left(-\frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      5. distribute-rgt-neg-in 82.0%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{\left(-x \cdot \frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      6. associate-/l* 86.2%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\left(-\color{blue}{\frac{x \cdot \left(z - t\right)}{a - t}}\right) + x \cdot 1\right) \]

      7. mul-1-neg 86.2%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} + x \cdot 1\right) \]

      8. *-rgt-identity 86.2%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \color{blue}{x}\right) \]

      9. associate-+l+ 86.3%

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(z - t\right)}{a - t} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) + x} \]

   5. Simplified 95.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)} \]

   6. Taylor expanded in z around inf 81.9%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 81.9%

         \[\leadsto z \cdot \color{blue}{\frac{y - x}{a - t}} \]

   8. Simplified 81.9%

      \[\leadsto \color{blue}{z \cdot \frac{y - x}{a - t}} \]

   if -1.7000000000000001e-92 < t < -4.19999999999999969e-154 or -9.1999999999999996e-283 < t < 7.00000000000000006e-63

   1. Initial program 89.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 78.3%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* 85.5%

         \[\leadsto x + \color{blue}{z \cdot \frac{y - x}{a}} \]

   5. Simplified 85.5%

      \[\leadsto x + \color{blue}{z \cdot \frac{y - x}{a}} \]

   if -4.19999999999999969e-154 < t < -1.05000000000000006e-208

   1. Initial program 99.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 68.5%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]

   if -1.05000000000000006e-208 < t < -1.0000000000000001e-208

   1. Initial program 98.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 98.4%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   5. Simplified 100.0%

      \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]
   6. Step-by-step derivation

      1. clear-num 100.0%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

      2. inv-pow 100.0%

         \[\leadsto x + y \cdot \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}} \]

   7. Applied egg-rr 100.0%

      \[\leadsto x + y \cdot \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}} \]
   8. Step-by-step derivation

      1. unpow-1 100.0%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

   9. Simplified 100.0%

      \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

   10. Taylor expanded in z around 0 98.4%

       \[\leadsto \color{blue}{x + -1 \cdot \frac{t \cdot y}{a - t}} \]
   11. Step-by-step derivation

       1. mul-1-neg 98.4%

          \[\leadsto x + \color{blue}{\left(-\frac{t \cdot y}{a - t}\right)} \]

       2. unsub-neg 98.4%

          \[\leadsto \color{blue}{x - \frac{t \cdot y}{a - t}} \]

       3. associate-/l* 98.4%

          \[\leadsto x - \color{blue}{t \cdot \frac{y}{a - t}} \]

   12. Simplified 98.4%

       \[\leadsto \color{blue}{x - t \cdot \frac{y}{a - t}} \]

   13. Taylor expanded in t around 0 98.4%

       \[\leadsto x - \color{blue}{\frac{t \cdot y}{a}} \]
   14. Step-by-step derivation

       1. associate-/l* 98.4%

          \[\leadsto x - \color{blue}{t \cdot \frac{y}{a}} \]

   15. Simplified 98.4%

       \[\leadsto x - \color{blue}{t \cdot \frac{y}{a}} \]

   16. Taylor expanded in x around 0 98.4%

       \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot y}{a}} \]
   17. Step-by-step derivation

       1. mul-1-neg 98.4%

          \[\leadsto \color{blue}{-\frac{t \cdot y}{a}} \]

       2. *-commutative 98.4%

          \[\leadsto -\frac{\color{blue}{y \cdot t}}{a} \]

       3. distribute-frac-neg2 98.4%

          \[\leadsto \color{blue}{\frac{y \cdot t}{-a}} \]

       4. associate-/l* 100.0%

          \[\leadsto \color{blue}{y \cdot \frac{t}{-a}} \]

   18. Simplified 100.0%

       \[\leadsto \color{blue}{y \cdot \frac{t}{-a}} \]

   if -1.0000000000000001e-208 < t < -9.3999999999999997e-244

   1. Initial program 99.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 71.4%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]

   4. Taylor expanded in y around 0 86.0%

      \[\leadsto x + \frac{\color{blue}{-1 \cdot \left(x \cdot z\right)}}{a} \]
   5. Step-by-step derivation

      1. mul-1-neg 86.0%

         \[\leadsto x + \frac{\color{blue}{-x \cdot z}}{a} \]

      2. distribute-lft-neg-out 86.0%

         \[\leadsto x + \frac{\color{blue}{\left(-x\right) \cdot z}}{a} \]

      3. *-commutative 86.0%

         \[\leadsto x + \frac{\color{blue}{z \cdot \left(-x\right)}}{a} \]

   6. Simplified 86.0%

      \[\leadsto x + \frac{\color{blue}{z \cdot \left(-x\right)}}{a} \]

   if -1.20000000000000005e-253 < t < -9.1999999999999996e-283

   1. Initial program 87.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 87.1%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]
   4. Step-by-step derivation

      1. clear-num 87.1%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{a}{z \cdot \left(y - x\right)}}} \]

      2. inv-pow 87.1%

         \[\leadsto x + \color{blue}{{\left(\frac{a}{z \cdot \left(y - x\right)}\right)}^{-1}} \]

   5. Applied egg-rr 87.1%

      \[\leadsto x + \color{blue}{{\left(\frac{a}{z \cdot \left(y - x\right)}\right)}^{-1}} \]
   6. Step-by-step derivation

      1. unpow-1 87.1%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{a}{z \cdot \left(y - x\right)}}} \]

      2. associate-/r* 100.0%

         \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{a}{z}}{y - x}}} \]

   7. Simplified 100.0%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{a}{z}}{y - x}}} \]
   8. Step-by-step derivation

      1. clear-num 100.0%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a}{z}}} \]

      2. add-cube-cbrt 99.2%

         \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \sqrt[3]{y - x}}}{\frac{a}{z}} \]

      3. *-un-lft-identity 99.2%

         \[\leadsto x + \frac{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \sqrt[3]{y - x}}{\color{blue}{1 \cdot \frac{a}{z}}} \]

      4. times-frac 99.1%

         \[\leadsto x + \color{blue}{\frac{\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}}{1} \cdot \frac{\sqrt[3]{y - x}}{\frac{a}{z}}} \]

      5. pow2 99.1%

         \[\leadsto x + \frac{\color{blue}{{\left(\sqrt[3]{y - x}\right)}^{2}}}{1} \cdot \frac{\sqrt[3]{y - x}}{\frac{a}{z}} \]

   9. Applied egg-rr 99.1%

      \[\leadsto x + \color{blue}{\frac{{\left(\sqrt[3]{y - x}\right)}^{2}}{1} \cdot \frac{\sqrt[3]{y - x}}{\frac{a}{z}}} \]
   10. Step-by-step derivation

       1. /-rgt-identity 99.1%

          \[\leadsto x + \color{blue}{{\left(\sqrt[3]{y - x}\right)}^{2}} \cdot \frac{\sqrt[3]{y - x}}{\frac{a}{z}} \]

       2. associate-*r/ 99.2%

          \[\leadsto x + \color{blue}{\frac{{\left(\sqrt[3]{y - x}\right)}^{2} \cdot \sqrt[3]{y - x}}{\frac{a}{z}}} \]

       3. unpow2 99.2%

          \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right)} \cdot \sqrt[3]{y - x}}{\frac{a}{z}} \]

       4. rem-3cbrt-lft 100.0%

          \[\leadsto x + \frac{\color{blue}{y - x}}{\frac{a}{z}} \]

   11. Simplified 100.0%

       \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a}{z}}} \]

   if 49000 < t < 2.35e11

   1. Initial program 100.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 100.0%

      \[\leadsto \color{blue}{x} \]

   if 9.7999999999999997e79 < t

   1. Initial program 26.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 73.7%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 73.7%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 73.7%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 73.7%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 73.7%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 73.7%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 73.7%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 81.1%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 83.6%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 83.6%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 83.6%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]

   6. Taylor expanded in z around 0 71.2%

      \[\leadsto \color{blue}{y - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   7. Step-by-step derivation

      1. cancel-sign-sub-inv 71.2%

         \[\leadsto \color{blue}{y + \left(--1\right) \cdot \frac{a \cdot \left(y - x\right)}{t}} \]

      2. metadata-eval 71.2%

         \[\leadsto y + \color{blue}{1} \cdot \frac{a \cdot \left(y - x\right)}{t} \]

      3. *-lft-identity 71.2%

         \[\leadsto y + \color{blue}{\frac{a \cdot \left(y - x\right)}{t}} \]

      4. *-commutative 71.2%

         \[\leadsto y + \frac{\color{blue}{\left(y - x\right) \cdot a}}{t} \]

      5. associate-/l* 75.0%

         \[\leadsto y + \color{blue}{\left(y - x\right) \cdot \frac{a}{t}} \]

   8. Simplified 75.0%

      \[\leadsto \color{blue}{y + \left(y - x\right) \cdot \frac{a}{t}} \]
3. Recombined 9 regimes into one program.

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.3 \cdot 10^{-15}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-92}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-154}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-208}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-208}:\\ \;\;\;\;y \cdot \frac{t}{-a}\\ \mathbf{elif}\;t \leq -9.4 \cdot 10^{-244}:\\ \;\;\;\;x - \frac{x \cdot z}{a}\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-253}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-283}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-63}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 49000:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 235000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{+79}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 63.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y - x}{a - t}\\ t_2 := y \cdot \frac{z - t}{a - t}\\ t_3 := x + z \cdot \frac{y - x}{a}\\ \mathbf{if}\;t \leq -1.65 \cdot 10^{-13}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-93}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-148}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-208}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-208}:\\ \;\;\;\;y \cdot \frac{t}{-a}\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-243}:\\ \;\;\;\;x - \frac{x \cdot z}{a}\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-253}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-284}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-64}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 56000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 240000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{+80}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;y - x \cdot \frac{a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ (- y x) (- a t))))
        (t_2 (* y (/ (- z t) (- a t))))
        (t_3 (+ x (* z (/ (- y x) a)))))
   (if (<= t -1.65e-13)
     t_2
     (if (<= t -4.4e-93)
       t_1
       (if (<= t -2.6e-148)
         t_3
         (if (<= t -1.05e-208)
           (+ x (/ (* (- y x) z) a))
           (if (<= t -1e-208)
             (* y (/ t (- a)))
             (if (<= t -1.5e-243)
               (- x (/ (* x z) a))
               (if (<= t -1.2e-253)
                 t_1
                 (if (<= t -4.6e-284)
                   (+ x (/ (- y x) (/ a z)))
                   (if (<= t 6.2e-64)
                     t_3
                     (if (<= t 56000.0)
                       t_2
                       (if (<= t 240000000000.0)
                         x
                         (if (<= t 1.12e+80)
                           t_2
                           (- y (* x (/ a t)))))))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((y - x) / (a - t));
	double t_2 = y * ((z - t) / (a - t));
	double t_3 = x + (z * ((y - x) / a));
	double tmp;
	if (t <= -1.65e-13) {
		tmp = t_2;
	} else if (t <= -4.4e-93) {
		tmp = t_1;
	} else if (t <= -2.6e-148) {
		tmp = t_3;
	} else if (t <= -1.05e-208) {
		tmp = x + (((y - x) * z) / a);
	} else if (t <= -1e-208) {
		tmp = y * (t / -a);
	} else if (t <= -1.5e-243) {
		tmp = x - ((x * z) / a);
	} else if (t <= -1.2e-253) {
		tmp = t_1;
	} else if (t <= -4.6e-284) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 6.2e-64) {
		tmp = t_3;
	} else if (t <= 56000.0) {
		tmp = t_2;
	} else if (t <= 240000000000.0) {
		tmp = x;
	} else if (t <= 1.12e+80) {
		tmp = t_2;
	} else {
		tmp = y - (x * (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = z * ((y - x) / (a - t))
    t_2 = y * ((z - t) / (a - t))
    t_3 = x + (z * ((y - x) / a))
    if (t <= (-1.65d-13)) then
        tmp = t_2
    else if (t <= (-4.4d-93)) then
        tmp = t_1
    else if (t <= (-2.6d-148)) then
        tmp = t_3
    else if (t <= (-1.05d-208)) then
        tmp = x + (((y - x) * z) / a)
    else if (t <= (-1d-208)) then
        tmp = y * (t / -a)
    else if (t <= (-1.5d-243)) then
        tmp = x - ((x * z) / a)
    else if (t <= (-1.2d-253)) then
        tmp = t_1
    else if (t <= (-4.6d-284)) then
        tmp = x + ((y - x) / (a / z))
    else if (t <= 6.2d-64) then
        tmp = t_3
    else if (t <= 56000.0d0) then
        tmp = t_2
    else if (t <= 240000000000.0d0) then
        tmp = x
    else if (t <= 1.12d+80) then
        tmp = t_2
    else
        tmp = y - (x * (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((y - x) / (a - t));
	double t_2 = y * ((z - t) / (a - t));
	double t_3 = x + (z * ((y - x) / a));
	double tmp;
	if (t <= -1.65e-13) {
		tmp = t_2;
	} else if (t <= -4.4e-93) {
		tmp = t_1;
	} else if (t <= -2.6e-148) {
		tmp = t_3;
	} else if (t <= -1.05e-208) {
		tmp = x + (((y - x) * z) / a);
	} else if (t <= -1e-208) {
		tmp = y * (t / -a);
	} else if (t <= -1.5e-243) {
		tmp = x - ((x * z) / a);
	} else if (t <= -1.2e-253) {
		tmp = t_1;
	} else if (t <= -4.6e-284) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 6.2e-64) {
		tmp = t_3;
	} else if (t <= 56000.0) {
		tmp = t_2;
	} else if (t <= 240000000000.0) {
		tmp = x;
	} else if (t <= 1.12e+80) {
		tmp = t_2;
	} else {
		tmp = y - (x * (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * ((y - x) / (a - t))
	t_2 = y * ((z - t) / (a - t))
	t_3 = x + (z * ((y - x) / a))
	tmp = 0
	if t <= -1.65e-13:
		tmp = t_2
	elif t <= -4.4e-93:
		tmp = t_1
	elif t <= -2.6e-148:
		tmp = t_3
	elif t <= -1.05e-208:
		tmp = x + (((y - x) * z) / a)
	elif t <= -1e-208:
		tmp = y * (t / -a)
	elif t <= -1.5e-243:
		tmp = x - ((x * z) / a)
	elif t <= -1.2e-253:
		tmp = t_1
	elif t <= -4.6e-284:
		tmp = x + ((y - x) / (a / z))
	elif t <= 6.2e-64:
		tmp = t_3
	elif t <= 56000.0:
		tmp = t_2
	elif t <= 240000000000.0:
		tmp = x
	elif t <= 1.12e+80:
		tmp = t_2
	else:
		tmp = y - (x * (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(Float64(y - x) / Float64(a - t)))
	t_2 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_3 = Float64(x + Float64(z * Float64(Float64(y - x) / a)))
	tmp = 0.0
	if (t <= -1.65e-13)
		tmp = t_2;
	elseif (t <= -4.4e-93)
		tmp = t_1;
	elseif (t <= -2.6e-148)
		tmp = t_3;
	elseif (t <= -1.05e-208)
		tmp = Float64(x + Float64(Float64(Float64(y - x) * z) / a));
	elseif (t <= -1e-208)
		tmp = Float64(y * Float64(t / Float64(-a)));
	elseif (t <= -1.5e-243)
		tmp = Float64(x - Float64(Float64(x * z) / a));
	elseif (t <= -1.2e-253)
		tmp = t_1;
	elseif (t <= -4.6e-284)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	elseif (t <= 6.2e-64)
		tmp = t_3;
	elseif (t <= 56000.0)
		tmp = t_2;
	elseif (t <= 240000000000.0)
		tmp = x;
	elseif (t <= 1.12e+80)
		tmp = t_2;
	else
		tmp = Float64(y - Float64(x * Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * ((y - x) / (a - t));
	t_2 = y * ((z - t) / (a - t));
	t_3 = x + (z * ((y - x) / a));
	tmp = 0.0;
	if (t <= -1.65e-13)
		tmp = t_2;
	elseif (t <= -4.4e-93)
		tmp = t_1;
	elseif (t <= -2.6e-148)
		tmp = t_3;
	elseif (t <= -1.05e-208)
		tmp = x + (((y - x) * z) / a);
	elseif (t <= -1e-208)
		tmp = y * (t / -a);
	elseif (t <= -1.5e-243)
		tmp = x - ((x * z) / a);
	elseif (t <= -1.2e-253)
		tmp = t_1;
	elseif (t <= -4.6e-284)
		tmp = x + ((y - x) / (a / z));
	elseif (t <= 6.2e-64)
		tmp = t_3;
	elseif (t <= 56000.0)
		tmp = t_2;
	elseif (t <= 240000000000.0)
		tmp = x;
	elseif (t <= 1.12e+80)
		tmp = t_2;
	else
		tmp = y - (x * (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.65e-13], t$95$2, If[LessEqual[t, -4.4e-93], t$95$1, If[LessEqual[t, -2.6e-148], t$95$3, If[LessEqual[t, -1.05e-208], N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1e-208], N[(y * N[(t / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.5e-243], N[(x - N[(N[(x * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.2e-253], t$95$1, If[LessEqual[t, -4.6e-284], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.2e-64], t$95$3, If[LessEqual[t, 56000.0], t$95$2, If[LessEqual[t, 240000000000.0], x, If[LessEqual[t, 1.12e+80], t$95$2, N[(y - N[(x * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if t < -1.65e-13 or 6.20000000000000049e-64 < t < 56000 or 2.4e11 < t < 1.12e80

   1. Initial program 56.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 65.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. +-commutative 65.2%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. +-commutative 65.2%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{a - t} + 1\right)} \]

      3. distribute-lft-in 65.2%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \color{blue}{\left(x \cdot \left(-1 \cdot \frac{z - t}{a - t}\right) + x \cdot 1\right)} \]

      4. mul-1-neg 65.2%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(x \cdot \color{blue}{\left(-\frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      5. distribute-rgt-neg-in 65.2%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{\left(-x \cdot \frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      6. associate-/l* 57.3%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\left(-\color{blue}{\frac{x \cdot \left(z - t\right)}{a - t}}\right) + x \cdot 1\right) \]

      7. mul-1-neg 57.3%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} + x \cdot 1\right) \]

      8. *-rgt-identity 57.3%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \color{blue}{x}\right) \]

      9. associate-+l+ 55.1%

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(z - t\right)}{a - t} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) + x} \]

   5. Simplified 76.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)} \]

   6. Taylor expanded in y around inf 65.5%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 65.5%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

   8. Simplified 65.5%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   if -1.65e-13 < t < -4.39999999999999991e-93 or -1.5000000000000001e-243 < t < -1.20000000000000005e-253

   1. Initial program 86.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 81.9%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. +-commutative 81.9%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. +-commutative 81.9%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{a - t} + 1\right)} \]

      3. distribute-lft-in 82.0%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \color{blue}{\left(x \cdot \left(-1 \cdot \frac{z - t}{a - t}\right) + x \cdot 1\right)} \]

      4. mul-1-neg 82.0%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(x \cdot \color{blue}{\left(-\frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      5. distribute-rgt-neg-in 82.0%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{\left(-x \cdot \frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      6. associate-/l* 86.2%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\left(-\color{blue}{\frac{x \cdot \left(z - t\right)}{a - t}}\right) + x \cdot 1\right) \]

      7. mul-1-neg 86.2%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} + x \cdot 1\right) \]

      8. *-rgt-identity 86.2%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \color{blue}{x}\right) \]

      9. associate-+l+ 86.3%

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(z - t\right)}{a - t} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) + x} \]

   5. Simplified 95.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)} \]

   6. Taylor expanded in z around inf 81.9%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 81.9%

         \[\leadsto z \cdot \color{blue}{\frac{y - x}{a - t}} \]

   8. Simplified 81.9%

      \[\leadsto \color{blue}{z \cdot \frac{y - x}{a - t}} \]

   if -4.39999999999999991e-93 < t < -2.60000000000000008e-148 or -4.6e-284 < t < 6.20000000000000049e-64

   1. Initial program 89.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 78.3%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* 85.5%

         \[\leadsto x + \color{blue}{z \cdot \frac{y - x}{a}} \]

   5. Simplified 85.5%

      \[\leadsto x + \color{blue}{z \cdot \frac{y - x}{a}} \]

   if -2.60000000000000008e-148 < t < -1.05000000000000006e-208

   1. Initial program 99.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 68.5%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]

   if -1.05000000000000006e-208 < t < -1.0000000000000001e-208

   1. Initial program 98.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 98.4%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   5. Simplified 100.0%

      \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]
   6. Step-by-step derivation

      1. clear-num 100.0%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

      2. inv-pow 100.0%

         \[\leadsto x + y \cdot \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}} \]

   7. Applied egg-rr 100.0%

      \[\leadsto x + y \cdot \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}} \]
   8. Step-by-step derivation

      1. unpow-1 100.0%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

   9. Simplified 100.0%

      \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

   10. Taylor expanded in z around 0 98.4%

       \[\leadsto \color{blue}{x + -1 \cdot \frac{t \cdot y}{a - t}} \]
   11. Step-by-step derivation

       1. mul-1-neg 98.4%

          \[\leadsto x + \color{blue}{\left(-\frac{t \cdot y}{a - t}\right)} \]

       2. unsub-neg 98.4%

          \[\leadsto \color{blue}{x - \frac{t \cdot y}{a - t}} \]

       3. associate-/l* 98.4%

          \[\leadsto x - \color{blue}{t \cdot \frac{y}{a - t}} \]

   12. Simplified 98.4%

       \[\leadsto \color{blue}{x - t \cdot \frac{y}{a - t}} \]

   13. Taylor expanded in t around 0 98.4%

       \[\leadsto x - \color{blue}{\frac{t \cdot y}{a}} \]
   14. Step-by-step derivation

       1. associate-/l* 98.4%

          \[\leadsto x - \color{blue}{t \cdot \frac{y}{a}} \]

   15. Simplified 98.4%

       \[\leadsto x - \color{blue}{t \cdot \frac{y}{a}} \]

   16. Taylor expanded in x around 0 98.4%

       \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot y}{a}} \]
   17. Step-by-step derivation

       1. mul-1-neg 98.4%

          \[\leadsto \color{blue}{-\frac{t \cdot y}{a}} \]

       2. *-commutative 98.4%

          \[\leadsto -\frac{\color{blue}{y \cdot t}}{a} \]

       3. distribute-frac-neg2 98.4%

          \[\leadsto \color{blue}{\frac{y \cdot t}{-a}} \]

       4. associate-/l* 100.0%

          \[\leadsto \color{blue}{y \cdot \frac{t}{-a}} \]

   18. Simplified 100.0%

       \[\leadsto \color{blue}{y \cdot \frac{t}{-a}} \]

   if -1.0000000000000001e-208 < t < -1.5000000000000001e-243

   1. Initial program 99.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 71.4%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]

   4. Taylor expanded in y around 0 86.0%

      \[\leadsto x + \frac{\color{blue}{-1 \cdot \left(x \cdot z\right)}}{a} \]
   5. Step-by-step derivation

      1. mul-1-neg 86.0%

         \[\leadsto x + \frac{\color{blue}{-x \cdot z}}{a} \]

      2. distribute-lft-neg-out 86.0%

         \[\leadsto x + \frac{\color{blue}{\left(-x\right) \cdot z}}{a} \]

      3. *-commutative 86.0%

         \[\leadsto x + \frac{\color{blue}{z \cdot \left(-x\right)}}{a} \]

   6. Simplified 86.0%

      \[\leadsto x + \frac{\color{blue}{z \cdot \left(-x\right)}}{a} \]

   if -1.20000000000000005e-253 < t < -4.6e-284

   1. Initial program 87.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 87.1%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]
   4. Step-by-step derivation

      1. clear-num 87.1%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{a}{z \cdot \left(y - x\right)}}} \]

      2. inv-pow 87.1%

         \[\leadsto x + \color{blue}{{\left(\frac{a}{z \cdot \left(y - x\right)}\right)}^{-1}} \]

   5. Applied egg-rr 87.1%

      \[\leadsto x + \color{blue}{{\left(\frac{a}{z \cdot \left(y - x\right)}\right)}^{-1}} \]
   6. Step-by-step derivation

      1. unpow-1 87.1%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{a}{z \cdot \left(y - x\right)}}} \]

      2. associate-/r* 100.0%

         \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{a}{z}}{y - x}}} \]

   7. Simplified 100.0%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{a}{z}}{y - x}}} \]
   8. Step-by-step derivation

      1. clear-num 100.0%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a}{z}}} \]

      2. add-cube-cbrt 99.2%

         \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \sqrt[3]{y - x}}}{\frac{a}{z}} \]

      3. *-un-lft-identity 99.2%

         \[\leadsto x + \frac{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \sqrt[3]{y - x}}{\color{blue}{1 \cdot \frac{a}{z}}} \]

      4. times-frac 99.1%

         \[\leadsto x + \color{blue}{\frac{\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}}{1} \cdot \frac{\sqrt[3]{y - x}}{\frac{a}{z}}} \]

      5. pow2 99.1%

         \[\leadsto x + \frac{\color{blue}{{\left(\sqrt[3]{y - x}\right)}^{2}}}{1} \cdot \frac{\sqrt[3]{y - x}}{\frac{a}{z}} \]

   9. Applied egg-rr 99.1%

      \[\leadsto x + \color{blue}{\frac{{\left(\sqrt[3]{y - x}\right)}^{2}}{1} \cdot \frac{\sqrt[3]{y - x}}{\frac{a}{z}}} \]
   10. Step-by-step derivation

       1. /-rgt-identity 99.1%

          \[\leadsto x + \color{blue}{{\left(\sqrt[3]{y - x}\right)}^{2}} \cdot \frac{\sqrt[3]{y - x}}{\frac{a}{z}} \]

       2. associate-*r/ 99.2%

          \[\leadsto x + \color{blue}{\frac{{\left(\sqrt[3]{y - x}\right)}^{2} \cdot \sqrt[3]{y - x}}{\frac{a}{z}}} \]

       3. unpow2 99.2%

          \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right)} \cdot \sqrt[3]{y - x}}{\frac{a}{z}} \]

       4. rem-3cbrt-lft 100.0%

          \[\leadsto x + \frac{\color{blue}{y - x}}{\frac{a}{z}} \]

   11. Simplified 100.0%

       \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a}{z}}} \]

   if 56000 < t < 2.4e11

   1. Initial program 100.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 100.0%

      \[\leadsto \color{blue}{x} \]

   if 1.12e80 < t

   1. Initial program 26.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 73.7%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 73.7%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 73.7%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 73.7%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 73.7%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 73.7%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 73.7%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 81.1%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 83.6%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 83.6%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 83.6%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]
   6. Step-by-step derivation

      1. *-commutative 83.6%

         \[\leadsto y - \color{blue}{\left(z - a\right) \cdot \frac{y - x}{t}} \]

      2. clear-num 83.6%

         \[\leadsto y - \left(z - a\right) \cdot \color{blue}{\frac{1}{\frac{t}{y - x}}} \]

      3. un-div-inv 83.5%

         \[\leadsto y - \color{blue}{\frac{z - a}{\frac{t}{y - x}}} \]

   7. Applied egg-rr 83.5%

      \[\leadsto y - \color{blue}{\frac{z - a}{\frac{t}{y - x}}} \]

   8. Taylor expanded in y around 0 79.1%

      \[\leadsto y - \color{blue}{-1 \cdot \frac{x \cdot \left(z - a\right)}{t}} \]
   9. Step-by-step derivation

      1. mul-1-neg 79.1%

         \[\leadsto y - \color{blue}{\left(-\frac{x \cdot \left(z - a\right)}{t}\right)} \]

      2. associate-/l* 80.7%

         \[\leadsto y - \left(-\color{blue}{x \cdot \frac{z - a}{t}}\right) \]

   10. Simplified 80.7%

       \[\leadsto y - \color{blue}{\left(-x \cdot \frac{z - a}{t}\right)} \]

   11. Taylor expanded in z around 0 75.0%

       \[\leadsto \color{blue}{y + -1 \cdot \frac{a \cdot x}{t}} \]
   12. Step-by-step derivation

       1. mul-1-neg 75.0%

          \[\leadsto y + \color{blue}{\left(-\frac{a \cdot x}{t}\right)} \]

       2. *-commutative 75.0%

          \[\leadsto y + \left(-\frac{\color{blue}{x \cdot a}}{t}\right) \]

       3. associate-*r/ 74.6%

          \[\leadsto y + \left(-\color{blue}{x \cdot \frac{a}{t}}\right) \]

       4. unsub-neg 74.6%

          \[\leadsto \color{blue}{y - x \cdot \frac{a}{t}} \]

   13. Simplified 74.6%

       \[\leadsto \color{blue}{y - x \cdot \frac{a}{t}} \]
3. Recombined 9 regimes into one program.

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{-13}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-93}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-148}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-208}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-208}:\\ \;\;\;\;y \cdot \frac{t}{-a}\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-243}:\\ \;\;\;\;x - \frac{x \cdot z}{a}\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-253}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-284}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-64}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 56000:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 240000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{+80}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y - x \cdot \frac{a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot z}{a}\\ t_2 := z \cdot \frac{y - x}{a - t}\\ t_3 := y \cdot \frac{z - t}{a - t}\\ t_4 := x + z \cdot \frac{y - x}{a}\\ \mathbf{if}\;t \leq -7.6 \cdot 10^{-20}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-93}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-155}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-208}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-208}:\\ \;\;\;\;y \cdot \frac{t}{-a}\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-246}:\\ \;\;\;\;x - \frac{x \cdot z}{a}\\ \mathbf{elif}\;t \leq -1.02 \cdot 10^{-254}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-286}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-67}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t \leq 56000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 230000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+80}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;y - x \cdot \frac{a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) z) a)))
        (t_2 (* z (/ (- y x) (- a t))))
        (t_3 (* y (/ (- z t) (- a t))))
        (t_4 (+ x (* z (/ (- y x) a)))))
   (if (<= t -7.6e-20)
     t_3
     (if (<= t -6.2e-93)
       t_2
       (if (<= t -7e-155)
         t_4
         (if (<= t -1.05e-208)
           t_1
           (if (<= t -1e-208)
             (* y (/ t (- a)))
             (if (<= t -2.7e-246)
               (- x (/ (* x z) a))
               (if (<= t -1.02e-254)
                 t_2
                 (if (<= t -5e-286)
                   t_1
                   (if (<= t 3.4e-67)
                     t_4
                     (if (<= t 56000.0)
                       t_3
                       (if (<= t 230000000000.0)
                         x
                         (if (<= t 1.25e+80)
                           t_3
                           (- y (* x (/ a t)))))))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * z) / a);
	double t_2 = z * ((y - x) / (a - t));
	double t_3 = y * ((z - t) / (a - t));
	double t_4 = x + (z * ((y - x) / a));
	double tmp;
	if (t <= -7.6e-20) {
		tmp = t_3;
	} else if (t <= -6.2e-93) {
		tmp = t_2;
	} else if (t <= -7e-155) {
		tmp = t_4;
	} else if (t <= -1.05e-208) {
		tmp = t_1;
	} else if (t <= -1e-208) {
		tmp = y * (t / -a);
	} else if (t <= -2.7e-246) {
		tmp = x - ((x * z) / a);
	} else if (t <= -1.02e-254) {
		tmp = t_2;
	} else if (t <= -5e-286) {
		tmp = t_1;
	} else if (t <= 3.4e-67) {
		tmp = t_4;
	} else if (t <= 56000.0) {
		tmp = t_3;
	} else if (t <= 230000000000.0) {
		tmp = x;
	} else if (t <= 1.25e+80) {
		tmp = t_3;
	} else {
		tmp = y - (x * (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = x + (((y - x) * z) / a)
    t_2 = z * ((y - x) / (a - t))
    t_3 = y * ((z - t) / (a - t))
    t_4 = x + (z * ((y - x) / a))
    if (t <= (-7.6d-20)) then
        tmp = t_3
    else if (t <= (-6.2d-93)) then
        tmp = t_2
    else if (t <= (-7d-155)) then
        tmp = t_4
    else if (t <= (-1.05d-208)) then
        tmp = t_1
    else if (t <= (-1d-208)) then
        tmp = y * (t / -a)
    else if (t <= (-2.7d-246)) then
        tmp = x - ((x * z) / a)
    else if (t <= (-1.02d-254)) then
        tmp = t_2
    else if (t <= (-5d-286)) then
        tmp = t_1
    else if (t <= 3.4d-67) then
        tmp = t_4
    else if (t <= 56000.0d0) then
        tmp = t_3
    else if (t <= 230000000000.0d0) then
        tmp = x
    else if (t <= 1.25d+80) then
        tmp = t_3
    else
        tmp = y - (x * (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * z) / a);
	double t_2 = z * ((y - x) / (a - t));
	double t_3 = y * ((z - t) / (a - t));
	double t_4 = x + (z * ((y - x) / a));
	double tmp;
	if (t <= -7.6e-20) {
		tmp = t_3;
	} else if (t <= -6.2e-93) {
		tmp = t_2;
	} else if (t <= -7e-155) {
		tmp = t_4;
	} else if (t <= -1.05e-208) {
		tmp = t_1;
	} else if (t <= -1e-208) {
		tmp = y * (t / -a);
	} else if (t <= -2.7e-246) {
		tmp = x - ((x * z) / a);
	} else if (t <= -1.02e-254) {
		tmp = t_2;
	} else if (t <= -5e-286) {
		tmp = t_1;
	} else if (t <= 3.4e-67) {
		tmp = t_4;
	} else if (t <= 56000.0) {
		tmp = t_3;
	} else if (t <= 230000000000.0) {
		tmp = x;
	} else if (t <= 1.25e+80) {
		tmp = t_3;
	} else {
		tmp = y - (x * (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) * z) / a)
	t_2 = z * ((y - x) / (a - t))
	t_3 = y * ((z - t) / (a - t))
	t_4 = x + (z * ((y - x) / a))
	tmp = 0
	if t <= -7.6e-20:
		tmp = t_3
	elif t <= -6.2e-93:
		tmp = t_2
	elif t <= -7e-155:
		tmp = t_4
	elif t <= -1.05e-208:
		tmp = t_1
	elif t <= -1e-208:
		tmp = y * (t / -a)
	elif t <= -2.7e-246:
		tmp = x - ((x * z) / a)
	elif t <= -1.02e-254:
		tmp = t_2
	elif t <= -5e-286:
		tmp = t_1
	elif t <= 3.4e-67:
		tmp = t_4
	elif t <= 56000.0:
		tmp = t_3
	elif t <= 230000000000.0:
		tmp = x
	elif t <= 1.25e+80:
		tmp = t_3
	else:
		tmp = y - (x * (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * z) / a))
	t_2 = Float64(z * Float64(Float64(y - x) / Float64(a - t)))
	t_3 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_4 = Float64(x + Float64(z * Float64(Float64(y - x) / a)))
	tmp = 0.0
	if (t <= -7.6e-20)
		tmp = t_3;
	elseif (t <= -6.2e-93)
		tmp = t_2;
	elseif (t <= -7e-155)
		tmp = t_4;
	elseif (t <= -1.05e-208)
		tmp = t_1;
	elseif (t <= -1e-208)
		tmp = Float64(y * Float64(t / Float64(-a)));
	elseif (t <= -2.7e-246)
		tmp = Float64(x - Float64(Float64(x * z) / a));
	elseif (t <= -1.02e-254)
		tmp = t_2;
	elseif (t <= -5e-286)
		tmp = t_1;
	elseif (t <= 3.4e-67)
		tmp = t_4;
	elseif (t <= 56000.0)
		tmp = t_3;
	elseif (t <= 230000000000.0)
		tmp = x;
	elseif (t <= 1.25e+80)
		tmp = t_3;
	else
		tmp = Float64(y - Float64(x * Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) * z) / a);
	t_2 = z * ((y - x) / (a - t));
	t_3 = y * ((z - t) / (a - t));
	t_4 = x + (z * ((y - x) / a));
	tmp = 0.0;
	if (t <= -7.6e-20)
		tmp = t_3;
	elseif (t <= -6.2e-93)
		tmp = t_2;
	elseif (t <= -7e-155)
		tmp = t_4;
	elseif (t <= -1.05e-208)
		tmp = t_1;
	elseif (t <= -1e-208)
		tmp = y * (t / -a);
	elseif (t <= -2.7e-246)
		tmp = x - ((x * z) / a);
	elseif (t <= -1.02e-254)
		tmp = t_2;
	elseif (t <= -5e-286)
		tmp = t_1;
	elseif (t <= 3.4e-67)
		tmp = t_4;
	elseif (t <= 56000.0)
		tmp = t_3;
	elseif (t <= 230000000000.0)
		tmp = x;
	elseif (t <= 1.25e+80)
		tmp = t_3;
	else
		tmp = y - (x * (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.6e-20], t$95$3, If[LessEqual[t, -6.2e-93], t$95$2, If[LessEqual[t, -7e-155], t$95$4, If[LessEqual[t, -1.05e-208], t$95$1, If[LessEqual[t, -1e-208], N[(y * N[(t / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.7e-246], N[(x - N[(N[(x * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.02e-254], t$95$2, If[LessEqual[t, -5e-286], t$95$1, If[LessEqual[t, 3.4e-67], t$95$4, If[LessEqual[t, 56000.0], t$95$3, If[LessEqual[t, 230000000000.0], x, If[LessEqual[t, 1.25e+80], t$95$3, N[(y - N[(x * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if t < -7.5999999999999995e-20 or 3.4000000000000001e-67 < t < 56000 or 2.3e11 < t < 1.2499999999999999e80

   1. Initial program 56.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 65.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. +-commutative 65.2%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. +-commutative 65.2%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{a - t} + 1\right)} \]

      3. distribute-lft-in 65.2%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \color{blue}{\left(x \cdot \left(-1 \cdot \frac{z - t}{a - t}\right) + x \cdot 1\right)} \]

      4. mul-1-neg 65.2%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(x \cdot \color{blue}{\left(-\frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      5. distribute-rgt-neg-in 65.2%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{\left(-x \cdot \frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      6. associate-/l* 57.3%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\left(-\color{blue}{\frac{x \cdot \left(z - t\right)}{a - t}}\right) + x \cdot 1\right) \]

      7. mul-1-neg 57.3%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} + x \cdot 1\right) \]

      8. *-rgt-identity 57.3%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \color{blue}{x}\right) \]

      9. associate-+l+ 55.1%

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(z - t\right)}{a - t} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) + x} \]

   5. Simplified 76.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)} \]

   6. Taylor expanded in y around inf 65.5%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 65.5%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

   8. Simplified 65.5%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   if -7.5999999999999995e-20 < t < -6.19999999999999999e-93 or -2.6999999999999999e-246 < t < -1.0200000000000001e-254

   1. Initial program 83.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 78.4%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. +-commutative 78.4%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. +-commutative 78.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{a - t} + 1\right)} \]

      3. distribute-lft-in 78.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \color{blue}{\left(x \cdot \left(-1 \cdot \frac{z - t}{a - t}\right) + x \cdot 1\right)} \]

      4. mul-1-neg 78.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(x \cdot \color{blue}{\left(-\frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      5. distribute-rgt-neg-in 78.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{\left(-x \cdot \frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      6. associate-/l* 82.5%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\left(-\color{blue}{\frac{x \cdot \left(z - t\right)}{a - t}}\right) + x \cdot 1\right) \]

      7. mul-1-neg 82.5%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} + x \cdot 1\right) \]

      8. *-rgt-identity 82.5%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \color{blue}{x}\right) \]

      9. associate-+l+ 82.5%

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(z - t\right)}{a - t} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) + x} \]

   5. Simplified 95.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)} \]

   6. Taylor expanded in z around inf 82.7%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 82.7%

         \[\leadsto z \cdot \color{blue}{\frac{y - x}{a - t}} \]

   8. Simplified 82.7%

      \[\leadsto \color{blue}{z \cdot \frac{y - x}{a - t}} \]

   if -6.19999999999999999e-93 < t < -7.00000000000000031e-155 or -5.00000000000000037e-286 < t < 3.4000000000000001e-67

   1. Initial program 89.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 78.3%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* 85.5%

         \[\leadsto x + \color{blue}{z \cdot \frac{y - x}{a}} \]

   5. Simplified 85.5%

      \[\leadsto x + \color{blue}{z \cdot \frac{y - x}{a}} \]

   if -7.00000000000000031e-155 < t < -1.05000000000000006e-208 or -1.0200000000000001e-254 < t < -5.00000000000000037e-286

   1. Initial program 99.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 78.9%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]

   if -1.05000000000000006e-208 < t < -1.0000000000000001e-208

   1. Initial program 98.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 98.4%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   5. Simplified 100.0%

      \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]
   6. Step-by-step derivation

      1. clear-num 100.0%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

      2. inv-pow 100.0%

         \[\leadsto x + y \cdot \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}} \]

   7. Applied egg-rr 100.0%

      \[\leadsto x + y \cdot \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}} \]
   8. Step-by-step derivation

      1. unpow-1 100.0%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

   9. Simplified 100.0%

      \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

   10. Taylor expanded in z around 0 98.4%

       \[\leadsto \color{blue}{x + -1 \cdot \frac{t \cdot y}{a - t}} \]
   11. Step-by-step derivation

       1. mul-1-neg 98.4%

          \[\leadsto x + \color{blue}{\left(-\frac{t \cdot y}{a - t}\right)} \]

       2. unsub-neg 98.4%

          \[\leadsto \color{blue}{x - \frac{t \cdot y}{a - t}} \]

       3. associate-/l* 98.4%

          \[\leadsto x - \color{blue}{t \cdot \frac{y}{a - t}} \]

   12. Simplified 98.4%

       \[\leadsto \color{blue}{x - t \cdot \frac{y}{a - t}} \]

   13. Taylor expanded in t around 0 98.4%

       \[\leadsto x - \color{blue}{\frac{t \cdot y}{a}} \]
   14. Step-by-step derivation

       1. associate-/l* 98.4%

          \[\leadsto x - \color{blue}{t \cdot \frac{y}{a}} \]

   15. Simplified 98.4%

       \[\leadsto x - \color{blue}{t \cdot \frac{y}{a}} \]

   16. Taylor expanded in x around 0 98.4%

       \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot y}{a}} \]
   17. Step-by-step derivation

       1. mul-1-neg 98.4%

          \[\leadsto \color{blue}{-\frac{t \cdot y}{a}} \]

       2. *-commutative 98.4%

          \[\leadsto -\frac{\color{blue}{y \cdot t}}{a} \]

       3. distribute-frac-neg2 98.4%

          \[\leadsto \color{blue}{\frac{y \cdot t}{-a}} \]

       4. associate-/l* 100.0%

          \[\leadsto \color{blue}{y \cdot \frac{t}{-a}} \]

   18. Simplified 100.0%

       \[\leadsto \color{blue}{y \cdot \frac{t}{-a}} \]

   if -1.0000000000000001e-208 < t < -2.6999999999999999e-246

   1. Initial program 99.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 71.4%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]

   4. Taylor expanded in y around 0 86.0%

      \[\leadsto x + \frac{\color{blue}{-1 \cdot \left(x \cdot z\right)}}{a} \]
   5. Step-by-step derivation

      1. mul-1-neg 86.0%

         \[\leadsto x + \frac{\color{blue}{-x \cdot z}}{a} \]

      2. distribute-lft-neg-out 86.0%

         \[\leadsto x + \frac{\color{blue}{\left(-x\right) \cdot z}}{a} \]

      3. *-commutative 86.0%

         \[\leadsto x + \frac{\color{blue}{z \cdot \left(-x\right)}}{a} \]

   6. Simplified 86.0%

      \[\leadsto x + \frac{\color{blue}{z \cdot \left(-x\right)}}{a} \]

   if 56000 < t < 2.3e11

   1. Initial program 100.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 100.0%

      \[\leadsto \color{blue}{x} \]

   if 1.2499999999999999e80 < t

   1. Initial program 26.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 73.7%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 73.7%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 73.7%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 73.7%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 73.7%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 73.7%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 73.7%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 81.1%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 83.6%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 83.6%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 83.6%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]
   6. Step-by-step derivation

      1. *-commutative 83.6%

         \[\leadsto y - \color{blue}{\left(z - a\right) \cdot \frac{y - x}{t}} \]

      2. clear-num 83.6%

         \[\leadsto y - \left(z - a\right) \cdot \color{blue}{\frac{1}{\frac{t}{y - x}}} \]

      3. un-div-inv 83.5%

         \[\leadsto y - \color{blue}{\frac{z - a}{\frac{t}{y - x}}} \]

   7. Applied egg-rr 83.5%

      \[\leadsto y - \color{blue}{\frac{z - a}{\frac{t}{y - x}}} \]

   8. Taylor expanded in y around 0 79.1%

      \[\leadsto y - \color{blue}{-1 \cdot \frac{x \cdot \left(z - a\right)}{t}} \]
   9. Step-by-step derivation

      1. mul-1-neg 79.1%

         \[\leadsto y - \color{blue}{\left(-\frac{x \cdot \left(z - a\right)}{t}\right)} \]

      2. associate-/l* 80.7%

         \[\leadsto y - \left(-\color{blue}{x \cdot \frac{z - a}{t}}\right) \]

   10. Simplified 80.7%

       \[\leadsto y - \color{blue}{\left(-x \cdot \frac{z - a}{t}\right)} \]

   11. Taylor expanded in z around 0 75.0%

       \[\leadsto \color{blue}{y + -1 \cdot \frac{a \cdot x}{t}} \]
   12. Step-by-step derivation

       1. mul-1-neg 75.0%

          \[\leadsto y + \color{blue}{\left(-\frac{a \cdot x}{t}\right)} \]

       2. *-commutative 75.0%

          \[\leadsto y + \left(-\frac{\color{blue}{x \cdot a}}{t}\right) \]

       3. associate-*r/ 74.6%

          \[\leadsto y + \left(-\color{blue}{x \cdot \frac{a}{t}}\right) \]

       4. unsub-neg 74.6%

          \[\leadsto \color{blue}{y - x \cdot \frac{a}{t}} \]

   13. Simplified 74.6%

       \[\leadsto \color{blue}{y - x \cdot \frac{a}{t}} \]
3. Recombined 8 regimes into one program.

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.6 \cdot 10^{-20}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-93}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-155}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-208}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-208}:\\ \;\;\;\;y \cdot \frac{t}{-a}\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-246}:\\ \;\;\;\;x - \frac{x \cdot z}{a}\\ \mathbf{elif}\;t \leq -1.02 \cdot 10^{-254}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-286}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-67}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 56000:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 230000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+80}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y - x \cdot \frac{a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 46.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ t_2 := z \cdot \frac{x - y}{t}\\ \mathbf{if}\;t \leq -4.2 \cdot 10^{+219}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{+155}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{+121}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{+84}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-9}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.02 \cdot 10^{-11}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{a}{t}\\ \mathbf{elif}\;t \leq -3.9 \cdot 10^{-53}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{-274}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-245}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+79}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))) (t_2 (* z (/ (- x y) t))))
   (if (<= t -4.2e+219)
     y
     (if (<= t -2.8e+155)
       t_2
       (if (<= t -3.5e+121)
         y
         (if (<= t -3.1e+84)
           t_2
           (if (<= t -1.9e+33)
             (* x (/ (- z a) t))
             (if (<= t -1.7e-9)
               t_2
               (if (<= t -1.02e-11)
                 (* (- y x) (/ a t))
                 (if (<= t -3.9e-53)
                   (* y (/ (- z t) a))
                   (if (<= t 2.05e-274)
                     t_1
                     (if (<= t 5.8e-245)
                       (* z (/ (- y x) a))
                       (if (<= t 9e+14)
                         t_1
                         (if (<= t 1.6e+79) (* y (/ z (- a t))) y))))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double t_2 = z * ((x - y) / t);
	double tmp;
	if (t <= -4.2e+219) {
		tmp = y;
	} else if (t <= -2.8e+155) {
		tmp = t_2;
	} else if (t <= -3.5e+121) {
		tmp = y;
	} else if (t <= -3.1e+84) {
		tmp = t_2;
	} else if (t <= -1.9e+33) {
		tmp = x * ((z - a) / t);
	} else if (t <= -1.7e-9) {
		tmp = t_2;
	} else if (t <= -1.02e-11) {
		tmp = (y - x) * (a / t);
	} else if (t <= -3.9e-53) {
		tmp = y * ((z - t) / a);
	} else if (t <= 2.05e-274) {
		tmp = t_1;
	} else if (t <= 5.8e-245) {
		tmp = z * ((y - x) / a);
	} else if (t <= 9e+14) {
		tmp = t_1;
	} else if (t <= 1.6e+79) {
		tmp = y * (z / (a - t));
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    t_2 = z * ((x - y) / t)
    if (t <= (-4.2d+219)) then
        tmp = y
    else if (t <= (-2.8d+155)) then
        tmp = t_2
    else if (t <= (-3.5d+121)) then
        tmp = y
    else if (t <= (-3.1d+84)) then
        tmp = t_2
    else if (t <= (-1.9d+33)) then
        tmp = x * ((z - a) / t)
    else if (t <= (-1.7d-9)) then
        tmp = t_2
    else if (t <= (-1.02d-11)) then
        tmp = (y - x) * (a / t)
    else if (t <= (-3.9d-53)) then
        tmp = y * ((z - t) / a)
    else if (t <= 2.05d-274) then
        tmp = t_1
    else if (t <= 5.8d-245) then
        tmp = z * ((y - x) / a)
    else if (t <= 9d+14) then
        tmp = t_1
    else if (t <= 1.6d+79) then
        tmp = y * (z / (a - t))
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double t_2 = z * ((x - y) / t);
	double tmp;
	if (t <= -4.2e+219) {
		tmp = y;
	} else if (t <= -2.8e+155) {
		tmp = t_2;
	} else if (t <= -3.5e+121) {
		tmp = y;
	} else if (t <= -3.1e+84) {
		tmp = t_2;
	} else if (t <= -1.9e+33) {
		tmp = x * ((z - a) / t);
	} else if (t <= -1.7e-9) {
		tmp = t_2;
	} else if (t <= -1.02e-11) {
		tmp = (y - x) * (a / t);
	} else if (t <= -3.9e-53) {
		tmp = y * ((z - t) / a);
	} else if (t <= 2.05e-274) {
		tmp = t_1;
	} else if (t <= 5.8e-245) {
		tmp = z * ((y - x) / a);
	} else if (t <= 9e+14) {
		tmp = t_1;
	} else if (t <= 1.6e+79) {
		tmp = y * (z / (a - t));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	t_2 = z * ((x - y) / t)
	tmp = 0
	if t <= -4.2e+219:
		tmp = y
	elif t <= -2.8e+155:
		tmp = t_2
	elif t <= -3.5e+121:
		tmp = y
	elif t <= -3.1e+84:
		tmp = t_2
	elif t <= -1.9e+33:
		tmp = x * ((z - a) / t)
	elif t <= -1.7e-9:
		tmp = t_2
	elif t <= -1.02e-11:
		tmp = (y - x) * (a / t)
	elif t <= -3.9e-53:
		tmp = y * ((z - t) / a)
	elif t <= 2.05e-274:
		tmp = t_1
	elif t <= 5.8e-245:
		tmp = z * ((y - x) / a)
	elif t <= 9e+14:
		tmp = t_1
	elif t <= 1.6e+79:
		tmp = y * (z / (a - t))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	t_2 = Float64(z * Float64(Float64(x - y) / t))
	tmp = 0.0
	if (t <= -4.2e+219)
		tmp = y;
	elseif (t <= -2.8e+155)
		tmp = t_2;
	elseif (t <= -3.5e+121)
		tmp = y;
	elseif (t <= -3.1e+84)
		tmp = t_2;
	elseif (t <= -1.9e+33)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (t <= -1.7e-9)
		tmp = t_2;
	elseif (t <= -1.02e-11)
		tmp = Float64(Float64(y - x) * Float64(a / t));
	elseif (t <= -3.9e-53)
		tmp = Float64(y * Float64(Float64(z - t) / a));
	elseif (t <= 2.05e-274)
		tmp = t_1;
	elseif (t <= 5.8e-245)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	elseif (t <= 9e+14)
		tmp = t_1;
	elseif (t <= 1.6e+79)
		tmp = Float64(y * Float64(z / Float64(a - t)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	t_2 = z * ((x - y) / t);
	tmp = 0.0;
	if (t <= -4.2e+219)
		tmp = y;
	elseif (t <= -2.8e+155)
		tmp = t_2;
	elseif (t <= -3.5e+121)
		tmp = y;
	elseif (t <= -3.1e+84)
		tmp = t_2;
	elseif (t <= -1.9e+33)
		tmp = x * ((z - a) / t);
	elseif (t <= -1.7e-9)
		tmp = t_2;
	elseif (t <= -1.02e-11)
		tmp = (y - x) * (a / t);
	elseif (t <= -3.9e-53)
		tmp = y * ((z - t) / a);
	elseif (t <= 2.05e-274)
		tmp = t_1;
	elseif (t <= 5.8e-245)
		tmp = z * ((y - x) / a);
	elseif (t <= 9e+14)
		tmp = t_1;
	elseif (t <= 1.6e+79)
		tmp = y * (z / (a - t));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.2e+219], y, If[LessEqual[t, -2.8e+155], t$95$2, If[LessEqual[t, -3.5e+121], y, If[LessEqual[t, -3.1e+84], t$95$2, If[LessEqual[t, -1.9e+33], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.7e-9], t$95$2, If[LessEqual[t, -1.02e-11], N[(N[(y - x), $MachinePrecision] * N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.9e-53], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.05e-274], t$95$1, If[LessEqual[t, 5.8e-245], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9e+14], t$95$1, If[LessEqual[t, 1.6e+79], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if t < -4.19999999999999976e219 or -2.80000000000000016e155 < t < -3.5e121 or 1.60000000000000001e79 < t

   1. Initial program 32.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 67.4%

      \[\leadsto \color{blue}{y} \]

   if -4.19999999999999976e219 < t < -2.80000000000000016e155 or -3.5e121 < t < -3.10000000000000003e84 or -1.90000000000000001e33 < t < -1.6999999999999999e-9

   1. Initial program 57.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 56.0%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 56.0%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 56.0%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 56.0%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 56.0%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 56.0%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 56.0%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 69.0%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 75.9%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 75.9%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 75.9%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]

   6. Taylor expanded in z around inf 60.2%

      \[\leadsto \color{blue}{z \cdot \left(\frac{x}{t} - \frac{y}{t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 60.2%

         \[\leadsto z \cdot \color{blue}{\frac{x - y}{t}} \]

   8. Simplified 60.2%

      \[\leadsto \color{blue}{z \cdot \frac{x - y}{t}} \]

   if -3.10000000000000003e84 < t < -1.90000000000000001e33

   1. Initial program 58.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 73.7%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 73.7%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 73.7%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 73.7%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 73.7%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 73.7%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 73.7%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 73.7%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 73.5%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 73.5%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 73.5%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]

   6. Taylor expanded in y around 0 46.0%

      \[\leadsto \color{blue}{\frac{x \cdot \left(z - a\right)}{t}} \]
   7. Step-by-step derivation

      1. associate-/l* 45.7%

         \[\leadsto \color{blue}{x \cdot \frac{z - a}{t}} \]

   8. Simplified 45.7%

      \[\leadsto \color{blue}{x \cdot \frac{z - a}{t}} \]

   if -1.6999999999999999e-9 < t < -1.01999999999999994e-11

   1. Initial program 51.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 100.0%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 100.0%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 100.0%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 100.0%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 100.0%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 100.0%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 100.0%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 100.0%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 99.2%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 99.2%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 99.2%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]

   6. Taylor expanded in a around inf 54.0%

      \[\leadsto \color{blue}{\frac{a \cdot \left(y - x\right)}{t}} \]
   7. Step-by-step derivation

      1. *-commutative 54.0%

         \[\leadsto \frac{\color{blue}{\left(y - x\right) \cdot a}}{t} \]

      2. associate-/l* 54.0%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{a}{t}} \]

   8. Simplified 54.0%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{a}{t}} \]

   if -1.01999999999999994e-11 < t < -3.9000000000000002e-53

   1. Initial program 89.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 88.0%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. +-commutative 88.0%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. +-commutative 88.0%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{a - t} + 1\right)} \]

      3. distribute-lft-in 88.2%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \color{blue}{\left(x \cdot \left(-1 \cdot \frac{z - t}{a - t}\right) + x \cdot 1\right)} \]

      4. mul-1-neg 88.2%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(x \cdot \color{blue}{\left(-\frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      5. distribute-rgt-neg-in 88.2%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{\left(-x \cdot \frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      6. associate-/l* 88.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\left(-\color{blue}{\frac{x \cdot \left(z - t\right)}{a - t}}\right) + x \cdot 1\right) \]

      7. mul-1-neg 88.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} + x \cdot 1\right) \]

      8. *-rgt-identity 88.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \color{blue}{x}\right) \]

      9. associate-+l+ 88.4%

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(z - t\right)}{a - t} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) + x} \]

   5. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)} \]

   6. Taylor expanded in y around inf 43.5%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 43.5%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

   8. Simplified 43.5%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   9. Taylor expanded in a around inf 55.7%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a}} \]
   10. Step-by-step derivation

       1. associate-/l* 55.9%

          \[\leadsto \color{blue}{y \cdot \frac{z - t}{a}} \]

   11. Simplified 55.9%

       \[\leadsto \color{blue}{y \cdot \frac{z - t}{a}} \]

   if -3.9000000000000002e-53 < t < 2.04999999999999994e-274 or 5.7999999999999999e-245 < t < 9e14

   1. Initial program 88.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 64.8%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]

   4. Taylor expanded in x around inf 54.1%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z}{a}\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 54.1%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{z}{a}\right)}\right) \]

      2. unsub-neg 54.1%

         \[\leadsto x \cdot \color{blue}{\left(1 - \frac{z}{a}\right)} \]

   6. Simplified 54.1%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{a}\right)} \]

   if 2.04999999999999994e-274 < t < 5.7999999999999999e-245

   1. Initial program 99.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 99.6%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]

   4. Taylor expanded in z around inf 88.2%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a} - \frac{x}{a}\right)} \]
   5. Step-by-step derivation

      1. div-sub 88.2%

         \[\leadsto z \cdot \color{blue}{\frac{y - x}{a}} \]

      2. associate-*r/ 88.4%

         \[\leadsto \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]

      3. *-commutative 88.4%

         \[\leadsto \frac{\color{blue}{\left(y - x\right) \cdot z}}{a} \]

      4. associate-*r/ 76.9%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z}{a}} \]

      5. *-commutative 76.9%

         \[\leadsto \color{blue}{\frac{z}{a} \cdot \left(y - x\right)} \]

   6. Simplified 76.9%

      \[\leadsto \color{blue}{\frac{z}{a} \cdot \left(y - x\right)} \]
   7. Step-by-step derivation

      1. *-commutative 76.9%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z}{a}} \]

      2. clear-num 76.5%

         \[\leadsto \left(y - x\right) \cdot \color{blue}{\frac{1}{\frac{a}{z}}} \]

      3. un-div-inv 76.7%

         \[\leadsto \color{blue}{\frac{y - x}{\frac{a}{z}}} \]

   8. Applied egg-rr 76.7%

      \[\leadsto \color{blue}{\frac{y - x}{\frac{a}{z}}} \]
   9. Step-by-step derivation

      1. associate-/r/ 88.2%

         \[\leadsto \color{blue}{\frac{y - x}{a} \cdot z} \]

   10. Simplified 88.2%

       \[\leadsto \color{blue}{\frac{y - x}{a} \cdot z} \]

   if 9e14 < t < 1.60000000000000001e79

   1. Initial program 61.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 62.1%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. +-commutative 62.1%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. +-commutative 62.1%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{a - t} + 1\right)} \]

      3. distribute-lft-in 62.1%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \color{blue}{\left(x \cdot \left(-1 \cdot \frac{z - t}{a - t}\right) + x \cdot 1\right)} \]

      4. mul-1-neg 62.1%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(x \cdot \color{blue}{\left(-\frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      5. distribute-rgt-neg-in 62.1%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{\left(-x \cdot \frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      6. associate-/l* 61.9%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\left(-\color{blue}{\frac{x \cdot \left(z - t\right)}{a - t}}\right) + x \cdot 1\right) \]

      7. mul-1-neg 61.9%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} + x \cdot 1\right) \]

      8. *-rgt-identity 61.9%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \color{blue}{x}\right) \]

      9. associate-+l+ 61.9%

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(z - t\right)}{a - t} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) + x} \]

   5. Simplified 81.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)} \]

   6. Taylor expanded in y around inf 73.5%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 73.5%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

   8. Simplified 73.5%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   9. Taylor expanded in z around inf 33.3%

      \[\leadsto \color{blue}{\frac{y \cdot z}{a - t}} \]
   10. Step-by-step derivation

       1. associate-/l* 51.6%

          \[\leadsto \color{blue}{y \cdot \frac{z}{a - t}} \]

   11. Simplified 51.6%

       \[\leadsto \color{blue}{y \cdot \frac{z}{a - t}} \]
3. Recombined 8 regimes into one program.

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+219}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{+155}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{+121}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{+84}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-9}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq -1.02 \cdot 10^{-11}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{a}{t}\\ \mathbf{elif}\;t \leq -3.9 \cdot 10^{-53}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{-274}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-245}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+79}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 66.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y - x}{a}\\ t_2 := y + x \cdot \frac{z - a}{t}\\ t_3 := \frac{z}{\frac{a - t}{y - x}}\\ t_4 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -2.5 \cdot 10^{-23}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-103}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{-173}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-222}:\\ \;\;\;\;x + \frac{-1}{\frac{a}{x \cdot z}}\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-255}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{-290}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 56000:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t \leq 420000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+152}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ (- y x) a))))
        (t_2 (+ y (* x (/ (- z a) t))))
        (t_3 (/ z (/ (- a t) (- y x))))
        (t_4 (* y (/ (- z t) (- a t)))))
   (if (<= t -2.5e-23)
     t_2
     (if (<= t -1.05e-52)
       t_1
       (if (<= t -6.2e-103)
         t_3
         (if (<= t -5.6e-173)
           (+ x (/ y (/ (- a t) z)))
           (if (<= t -4.4e-222)
             (+ x (/ -1.0 (/ a (* x z))))
             (if (<= t -4e-255)
               t_3
               (if (<= t -4.1e-290)
                 (+ x (/ (- y x) (/ a z)))
                 (if (<= t 1.4e-66)
                   t_1
                   (if (<= t 56000.0)
                     t_4
                     (if (<= t 420000000000.0)
                       x
                       (if (<= t 2.6e+152) t_4 t_2)))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * ((y - x) / a));
	double t_2 = y + (x * ((z - a) / t));
	double t_3 = z / ((a - t) / (y - x));
	double t_4 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -2.5e-23) {
		tmp = t_2;
	} else if (t <= -1.05e-52) {
		tmp = t_1;
	} else if (t <= -6.2e-103) {
		tmp = t_3;
	} else if (t <= -5.6e-173) {
		tmp = x + (y / ((a - t) / z));
	} else if (t <= -4.4e-222) {
		tmp = x + (-1.0 / (a / (x * z)));
	} else if (t <= -4e-255) {
		tmp = t_3;
	} else if (t <= -4.1e-290) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 1.4e-66) {
		tmp = t_1;
	} else if (t <= 56000.0) {
		tmp = t_4;
	} else if (t <= 420000000000.0) {
		tmp = x;
	} else if (t <= 2.6e+152) {
		tmp = t_4;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = x + (z * ((y - x) / a))
    t_2 = y + (x * ((z - a) / t))
    t_3 = z / ((a - t) / (y - x))
    t_4 = y * ((z - t) / (a - t))
    if (t <= (-2.5d-23)) then
        tmp = t_2
    else if (t <= (-1.05d-52)) then
        tmp = t_1
    else if (t <= (-6.2d-103)) then
        tmp = t_3
    else if (t <= (-5.6d-173)) then
        tmp = x + (y / ((a - t) / z))
    else if (t <= (-4.4d-222)) then
        tmp = x + ((-1.0d0) / (a / (x * z)))
    else if (t <= (-4d-255)) then
        tmp = t_3
    else if (t <= (-4.1d-290)) then
        tmp = x + ((y - x) / (a / z))
    else if (t <= 1.4d-66) then
        tmp = t_1
    else if (t <= 56000.0d0) then
        tmp = t_4
    else if (t <= 420000000000.0d0) then
        tmp = x
    else if (t <= 2.6d+152) then
        tmp = t_4
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * ((y - x) / a));
	double t_2 = y + (x * ((z - a) / t));
	double t_3 = z / ((a - t) / (y - x));
	double t_4 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -2.5e-23) {
		tmp = t_2;
	} else if (t <= -1.05e-52) {
		tmp = t_1;
	} else if (t <= -6.2e-103) {
		tmp = t_3;
	} else if (t <= -5.6e-173) {
		tmp = x + (y / ((a - t) / z));
	} else if (t <= -4.4e-222) {
		tmp = x + (-1.0 / (a / (x * z)));
	} else if (t <= -4e-255) {
		tmp = t_3;
	} else if (t <= -4.1e-290) {
		tmp = x + ((y - x) / (a / z));
	} else if (t <= 1.4e-66) {
		tmp = t_1;
	} else if (t <= 56000.0) {
		tmp = t_4;
	} else if (t <= 420000000000.0) {
		tmp = x;
	} else if (t <= 2.6e+152) {
		tmp = t_4;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * ((y - x) / a))
	t_2 = y + (x * ((z - a) / t))
	t_3 = z / ((a - t) / (y - x))
	t_4 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -2.5e-23:
		tmp = t_2
	elif t <= -1.05e-52:
		tmp = t_1
	elif t <= -6.2e-103:
		tmp = t_3
	elif t <= -5.6e-173:
		tmp = x + (y / ((a - t) / z))
	elif t <= -4.4e-222:
		tmp = x + (-1.0 / (a / (x * z)))
	elif t <= -4e-255:
		tmp = t_3
	elif t <= -4.1e-290:
		tmp = x + ((y - x) / (a / z))
	elif t <= 1.4e-66:
		tmp = t_1
	elif t <= 56000.0:
		tmp = t_4
	elif t <= 420000000000.0:
		tmp = x
	elif t <= 2.6e+152:
		tmp = t_4
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(Float64(y - x) / a)))
	t_2 = Float64(y + Float64(x * Float64(Float64(z - a) / t)))
	t_3 = Float64(z / Float64(Float64(a - t) / Float64(y - x)))
	t_4 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -2.5e-23)
		tmp = t_2;
	elseif (t <= -1.05e-52)
		tmp = t_1;
	elseif (t <= -6.2e-103)
		tmp = t_3;
	elseif (t <= -5.6e-173)
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / z)));
	elseif (t <= -4.4e-222)
		tmp = Float64(x + Float64(-1.0 / Float64(a / Float64(x * z))));
	elseif (t <= -4e-255)
		tmp = t_3;
	elseif (t <= -4.1e-290)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(a / z)));
	elseif (t <= 1.4e-66)
		tmp = t_1;
	elseif (t <= 56000.0)
		tmp = t_4;
	elseif (t <= 420000000000.0)
		tmp = x;
	elseif (t <= 2.6e+152)
		tmp = t_4;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * ((y - x) / a));
	t_2 = y + (x * ((z - a) / t));
	t_3 = z / ((a - t) / (y - x));
	t_4 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t <= -2.5e-23)
		tmp = t_2;
	elseif (t <= -1.05e-52)
		tmp = t_1;
	elseif (t <= -6.2e-103)
		tmp = t_3;
	elseif (t <= -5.6e-173)
		tmp = x + (y / ((a - t) / z));
	elseif (t <= -4.4e-222)
		tmp = x + (-1.0 / (a / (x * z)));
	elseif (t <= -4e-255)
		tmp = t_3;
	elseif (t <= -4.1e-290)
		tmp = x + ((y - x) / (a / z));
	elseif (t <= 1.4e-66)
		tmp = t_1;
	elseif (t <= 56000.0)
		tmp = t_4;
	elseif (t <= 420000000000.0)
		tmp = x;
	elseif (t <= 2.6e+152)
		tmp = t_4;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z / N[(N[(a - t), $MachinePrecision] / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.5e-23], t$95$2, If[LessEqual[t, -1.05e-52], t$95$1, If[LessEqual[t, -6.2e-103], t$95$3, If[LessEqual[t, -5.6e-173], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.4e-222], N[(x + N[(-1.0 / N[(a / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4e-255], t$95$3, If[LessEqual[t, -4.1e-290], N[(x + N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.4e-66], t$95$1, If[LessEqual[t, 56000.0], t$95$4, If[LessEqual[t, 420000000000.0], x, If[LessEqual[t, 2.6e+152], t$95$4, t$95$2]]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if t < -2.5000000000000001e-23 or 2.6000000000000001e152 < t

   1. Initial program 41.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 68.9%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 68.9%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 68.9%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 68.9%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 68.9%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 68.9%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 68.9%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 75.3%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 83.0%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 83.0%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 83.0%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]
   6. Step-by-step derivation

      1. *-commutative 83.0%

         \[\leadsto y - \color{blue}{\left(z - a\right) \cdot \frac{y - x}{t}} \]

      2. clear-num 83.0%

         \[\leadsto y - \left(z - a\right) \cdot \color{blue}{\frac{1}{\frac{t}{y - x}}} \]

      3. un-div-inv 83.0%

         \[\leadsto y - \color{blue}{\frac{z - a}{\frac{t}{y - x}}} \]

   7. Applied egg-rr 83.0%

      \[\leadsto y - \color{blue}{\frac{z - a}{\frac{t}{y - x}}} \]

   8. Taylor expanded in y around 0 72.6%

      \[\leadsto y - \color{blue}{-1 \cdot \frac{x \cdot \left(z - a\right)}{t}} \]
   9. Step-by-step derivation

      1. mul-1-neg 72.6%

         \[\leadsto y - \color{blue}{\left(-\frac{x \cdot \left(z - a\right)}{t}\right)} \]

      2. associate-/l* 76.1%

         \[\leadsto y - \left(-\color{blue}{x \cdot \frac{z - a}{t}}\right) \]

   10. Simplified 76.1%

       \[\leadsto y - \color{blue}{\left(-x \cdot \frac{z - a}{t}\right)} \]

   if -2.5000000000000001e-23 < t < -1.0499999999999999e-52 or -4.1000000000000003e-290 < t < 1.4e-66

   1. Initial program 90.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 80.6%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* 88.5%

         \[\leadsto x + \color{blue}{z \cdot \frac{y - x}{a}} \]

   5. Simplified 88.5%

      \[\leadsto x + \color{blue}{z \cdot \frac{y - x}{a}} \]

   if -1.0499999999999999e-52 < t < -6.2000000000000003e-103 or -4.4e-222 < t < -4e-255

   1. Initial program 85.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 80.3%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. +-commutative 80.3%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. +-commutative 80.3%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{a - t} + 1\right)} \]

      3. distribute-lft-in 80.3%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \color{blue}{\left(x \cdot \left(-1 \cdot \frac{z - t}{a - t}\right) + x \cdot 1\right)} \]

      4. mul-1-neg 80.3%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(x \cdot \color{blue}{\left(-\frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      5. distribute-rgt-neg-in 80.3%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{\left(-x \cdot \frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      6. associate-/l* 84.9%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\left(-\color{blue}{\frac{x \cdot \left(z - t\right)}{a - t}}\right) + x \cdot 1\right) \]

      7. mul-1-neg 84.9%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} + x \cdot 1\right) \]

      8. *-rgt-identity 84.9%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \color{blue}{x}\right) \]

      9. associate-+l+ 85.0%

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(z - t\right)}{a - t} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) + x} \]

   5. Simplified 94.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)} \]

   6. Taylor expanded in z around inf 85.0%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 85.0%

         \[\leadsto z \cdot \color{blue}{\frac{y - x}{a - t}} \]

   8. Simplified 85.0%

      \[\leadsto \color{blue}{z \cdot \frac{y - x}{a - t}} \]
   9. Step-by-step derivation

      1. clear-num 85.0%

         \[\leadsto z \cdot \color{blue}{\frac{1}{\frac{a - t}{y - x}}} \]

      2. un-div-inv 85.1%

         \[\leadsto \color{blue}{\frac{z}{\frac{a - t}{y - x}}} \]

   10. Applied egg-rr 85.1%

       \[\leadsto \color{blue}{\frac{z}{\frac{a - t}{y - x}}} \]

   if -6.2000000000000003e-103 < t < -5.5999999999999998e-173

   1. Initial program 86.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 60.7%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. associate-/l* 67.7%

         \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   5. Simplified 67.7%

      \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]
   6. Step-by-step derivation

      1. clear-num 67.8%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

      2. un-div-inv 67.9%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

   7. Applied egg-rr 67.9%

      \[\leadsto x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

   8. Taylor expanded in z around inf 67.9%

      \[\leadsto x + \frac{y}{\color{blue}{\frac{a - t}{z}}} \]

   if -5.5999999999999998e-173 < t < -4.4e-222

   1. Initial program 99.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 63.2%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]
   4. Step-by-step derivation

      1. clear-num 63.3%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{a}{z \cdot \left(y - x\right)}}} \]

      2. inv-pow 63.3%

         \[\leadsto x + \color{blue}{{\left(\frac{a}{z \cdot \left(y - x\right)}\right)}^{-1}} \]

   5. Applied egg-rr 63.3%

      \[\leadsto x + \color{blue}{{\left(\frac{a}{z \cdot \left(y - x\right)}\right)}^{-1}} \]
   6. Step-by-step derivation

      1. unpow-1 63.3%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{a}{z \cdot \left(y - x\right)}}} \]

      2. associate-/r* 56.0%

         \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{a}{z}}{y - x}}} \]

   7. Simplified 56.0%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{a}{z}}{y - x}}} \]

   8. Taylor expanded in y around 0 70.9%

      \[\leadsto x + \frac{1}{\color{blue}{-1 \cdot \frac{a}{x \cdot z}}} \]
   9. Step-by-step derivation

      1. mul-1-neg 70.9%

         \[\leadsto x + \frac{1}{\color{blue}{-\frac{a}{x \cdot z}}} \]

      2. distribute-neg-frac2 70.9%

         \[\leadsto x + \frac{1}{\color{blue}{\frac{a}{-x \cdot z}}} \]

      3. *-commutative 70.9%

         \[\leadsto x + \frac{1}{\frac{a}{-\color{blue}{z \cdot x}}} \]

      4. distribute-rgt-neg-out 70.9%

         \[\leadsto x + \frac{1}{\frac{a}{\color{blue}{z \cdot \left(-x\right)}}} \]

   10. Simplified 70.9%

       \[\leadsto x + \frac{1}{\color{blue}{\frac{a}{z \cdot \left(-x\right)}}} \]

   if -4e-255 < t < -4.1000000000000003e-290

   1. Initial program 99.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 99.8%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]
   4. Step-by-step derivation

      1. clear-num 99.8%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{a}{z \cdot \left(y - x\right)}}} \]

      2. inv-pow 99.8%

         \[\leadsto x + \color{blue}{{\left(\frac{a}{z \cdot \left(y - x\right)}\right)}^{-1}} \]

   5. Applied egg-rr 99.8%

      \[\leadsto x + \color{blue}{{\left(\frac{a}{z \cdot \left(y - x\right)}\right)}^{-1}} \]
   6. Step-by-step derivation

      1. unpow-1 99.8%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{a}{z \cdot \left(y - x\right)}}} \]

      2. associate-/r* 100.0%

         \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{a}{z}}{y - x}}} \]

   7. Simplified 100.0%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{a}{z}}{y - x}}} \]
   8. Step-by-step derivation

      1. clear-num 100.0%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a}{z}}} \]

      2. add-cube-cbrt 99.4%

         \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \sqrt[3]{y - x}}}{\frac{a}{z}} \]

      3. *-un-lft-identity 99.4%

         \[\leadsto x + \frac{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right) \cdot \sqrt[3]{y - x}}{\color{blue}{1 \cdot \frac{a}{z}}} \]

      4. times-frac 99.3%

         \[\leadsto x + \color{blue}{\frac{\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}}{1} \cdot \frac{\sqrt[3]{y - x}}{\frac{a}{z}}} \]

      5. pow2 99.3%

         \[\leadsto x + \frac{\color{blue}{{\left(\sqrt[3]{y - x}\right)}^{2}}}{1} \cdot \frac{\sqrt[3]{y - x}}{\frac{a}{z}} \]

   9. Applied egg-rr 99.3%

      \[\leadsto x + \color{blue}{\frac{{\left(\sqrt[3]{y - x}\right)}^{2}}{1} \cdot \frac{\sqrt[3]{y - x}}{\frac{a}{z}}} \]
   10. Step-by-step derivation

       1. /-rgt-identity 99.3%

          \[\leadsto x + \color{blue}{{\left(\sqrt[3]{y - x}\right)}^{2}} \cdot \frac{\sqrt[3]{y - x}}{\frac{a}{z}} \]

       2. associate-*r/ 99.4%

          \[\leadsto x + \color{blue}{\frac{{\left(\sqrt[3]{y - x}\right)}^{2} \cdot \sqrt[3]{y - x}}{\frac{a}{z}}} \]

       3. unpow2 99.4%

          \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{y - x} \cdot \sqrt[3]{y - x}\right)} \cdot \sqrt[3]{y - x}}{\frac{a}{z}} \]

       4. rem-3cbrt-lft 100.0%

          \[\leadsto x + \frac{\color{blue}{y - x}}{\frac{a}{z}} \]

   11. Simplified 100.0%

       \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a}{z}}} \]

   if 1.4e-66 < t < 56000 or 4.2e11 < t < 2.6000000000000001e152

   1. Initial program 60.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 62.4%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. +-commutative 62.4%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. +-commutative 62.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{a - t} + 1\right)} \]

      3. distribute-lft-in 62.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \color{blue}{\left(x \cdot \left(-1 \cdot \frac{z - t}{a - t}\right) + x \cdot 1\right)} \]

      4. mul-1-neg 62.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(x \cdot \color{blue}{\left(-\frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      5. distribute-rgt-neg-in 62.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{\left(-x \cdot \frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      6. associate-/l* 60.6%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\left(-\color{blue}{\frac{x \cdot \left(z - t\right)}{a - t}}\right) + x \cdot 1\right) \]

      7. mul-1-neg 60.6%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} + x \cdot 1\right) \]

      8. *-rgt-identity 60.6%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \color{blue}{x}\right) \]

      9. associate-+l+ 60.2%

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(z - t\right)}{a - t} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) + x} \]

   5. Simplified 85.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)} \]

   6. Taylor expanded in y around inf 71.0%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 71.0%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

   8. Simplified 71.0%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   if 56000 < t < 4.2e11

   1. Initial program 100.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 100.0%

      \[\leadsto \color{blue}{x} \]
3. Recombined 8 regimes into one program.

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{-23}:\\ \;\;\;\;y + x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-52}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-103}:\\ \;\;\;\;\frac{z}{\frac{a - t}{y - x}}\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{-173}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-222}:\\ \;\;\;\;x + \frac{-1}{\frac{a}{x \cdot z}}\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-255}:\\ \;\;\;\;\frac{z}{\frac{a - t}{y - x}}\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{-290}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-66}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 56000:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 420000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+152}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot \frac{z - a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 56.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := z \cdot \frac{y - x}{a - t}\\ t_3 := y - x \cdot \frac{a}{t}\\ \mathbf{if}\;z \leq -1.16 \cdot 10^{+218}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-173}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-226}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-309}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-296}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-290}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-193}:\\ \;\;\;\;x - \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+235} \lor \neg \left(z \leq 5.4 \cdot 10^{+262}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t))))
        (t_2 (* z (/ (- y x) (- a t))))
        (t_3 (- y (* x (/ a t)))))
   (if (<= z -1.16e+218)
     t_2
     (if (<= z -4.2e-173)
       t_1
       (if (<= z -1.4e-226)
         (+ y x)
         (if (<= z -7e-309)
           t_3
           (if (<= z 6.2e-296)
             x
             (if (<= z 1.15e-290)
               t_3
               (if (<= z 2.15e-193)
                 (- x (/ t (/ a y)))
                 (if (<= z 4e-7)
                   t_1
                   (if (or (<= z 2.6e+235) (not (<= z 5.4e+262)))
                     t_2
                     (* x (- 1.0 (/ z a))))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = z * ((y - x) / (a - t));
	double t_3 = y - (x * (a / t));
	double tmp;
	if (z <= -1.16e+218) {
		tmp = t_2;
	} else if (z <= -4.2e-173) {
		tmp = t_1;
	} else if (z <= -1.4e-226) {
		tmp = y + x;
	} else if (z <= -7e-309) {
		tmp = t_3;
	} else if (z <= 6.2e-296) {
		tmp = x;
	} else if (z <= 1.15e-290) {
		tmp = t_3;
	} else if (z <= 2.15e-193) {
		tmp = x - (t / (a / y));
	} else if (z <= 4e-7) {
		tmp = t_1;
	} else if ((z <= 2.6e+235) || !(z <= 5.4e+262)) {
		tmp = t_2;
	} else {
		tmp = x * (1.0 - (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    t_2 = z * ((y - x) / (a - t))
    t_3 = y - (x * (a / t))
    if (z <= (-1.16d+218)) then
        tmp = t_2
    else if (z <= (-4.2d-173)) then
        tmp = t_1
    else if (z <= (-1.4d-226)) then
        tmp = y + x
    else if (z <= (-7d-309)) then
        tmp = t_3
    else if (z <= 6.2d-296) then
        tmp = x
    else if (z <= 1.15d-290) then
        tmp = t_3
    else if (z <= 2.15d-193) then
        tmp = x - (t / (a / y))
    else if (z <= 4d-7) then
        tmp = t_1
    else if ((z <= 2.6d+235) .or. (.not. (z <= 5.4d+262))) then
        tmp = t_2
    else
        tmp = x * (1.0d0 - (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = z * ((y - x) / (a - t));
	double t_3 = y - (x * (a / t));
	double tmp;
	if (z <= -1.16e+218) {
		tmp = t_2;
	} else if (z <= -4.2e-173) {
		tmp = t_1;
	} else if (z <= -1.4e-226) {
		tmp = y + x;
	} else if (z <= -7e-309) {
		tmp = t_3;
	} else if (z <= 6.2e-296) {
		tmp = x;
	} else if (z <= 1.15e-290) {
		tmp = t_3;
	} else if (z <= 2.15e-193) {
		tmp = x - (t / (a / y));
	} else if (z <= 4e-7) {
		tmp = t_1;
	} else if ((z <= 2.6e+235) || !(z <= 5.4e+262)) {
		tmp = t_2;
	} else {
		tmp = x * (1.0 - (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = z * ((y - x) / (a - t))
	t_3 = y - (x * (a / t))
	tmp = 0
	if z <= -1.16e+218:
		tmp = t_2
	elif z <= -4.2e-173:
		tmp = t_1
	elif z <= -1.4e-226:
		tmp = y + x
	elif z <= -7e-309:
		tmp = t_3
	elif z <= 6.2e-296:
		tmp = x
	elif z <= 1.15e-290:
		tmp = t_3
	elif z <= 2.15e-193:
		tmp = x - (t / (a / y))
	elif z <= 4e-7:
		tmp = t_1
	elif (z <= 2.6e+235) or not (z <= 5.4e+262):
		tmp = t_2
	else:
		tmp = x * (1.0 - (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(z * Float64(Float64(y - x) / Float64(a - t)))
	t_3 = Float64(y - Float64(x * Float64(a / t)))
	tmp = 0.0
	if (z <= -1.16e+218)
		tmp = t_2;
	elseif (z <= -4.2e-173)
		tmp = t_1;
	elseif (z <= -1.4e-226)
		tmp = Float64(y + x);
	elseif (z <= -7e-309)
		tmp = t_3;
	elseif (z <= 6.2e-296)
		tmp = x;
	elseif (z <= 1.15e-290)
		tmp = t_3;
	elseif (z <= 2.15e-193)
		tmp = Float64(x - Float64(t / Float64(a / y)));
	elseif (z <= 4e-7)
		tmp = t_1;
	elseif ((z <= 2.6e+235) || !(z <= 5.4e+262))
		tmp = t_2;
	else
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = z * ((y - x) / (a - t));
	t_3 = y - (x * (a / t));
	tmp = 0.0;
	if (z <= -1.16e+218)
		tmp = t_2;
	elseif (z <= -4.2e-173)
		tmp = t_1;
	elseif (z <= -1.4e-226)
		tmp = y + x;
	elseif (z <= -7e-309)
		tmp = t_3;
	elseif (z <= 6.2e-296)
		tmp = x;
	elseif (z <= 1.15e-290)
		tmp = t_3;
	elseif (z <= 2.15e-193)
		tmp = x - (t / (a / y));
	elseif (z <= 4e-7)
		tmp = t_1;
	elseif ((z <= 2.6e+235) || ~((z <= 5.4e+262)))
		tmp = t_2;
	else
		tmp = x * (1.0 - (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y - N[(x * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.16e+218], t$95$2, If[LessEqual[z, -4.2e-173], t$95$1, If[LessEqual[z, -1.4e-226], N[(y + x), $MachinePrecision], If[LessEqual[z, -7e-309], t$95$3, If[LessEqual[z, 6.2e-296], x, If[LessEqual[z, 1.15e-290], t$95$3, If[LessEqual[z, 2.15e-193], N[(x - N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4e-7], t$95$1, If[Or[LessEqual[z, 2.6e+235], N[Not[LessEqual[z, 5.4e+262]], $MachinePrecision]], t$95$2, N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if z < -1.15999999999999994e218 or 3.9999999999999998e-7 < z < 2.5999999999999998e235 or 5.4000000000000002e262 < z

   1. Initial program 70.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 59.4%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. +-commutative 59.4%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. +-commutative 59.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{a - t} + 1\right)} \]

      3. distribute-lft-in 59.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \color{blue}{\left(x \cdot \left(-1 \cdot \frac{z - t}{a - t}\right) + x \cdot 1\right)} \]

      4. mul-1-neg 59.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(x \cdot \color{blue}{\left(-\frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      5. distribute-rgt-neg-in 59.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{\left(-x \cdot \frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      6. associate-/l* 63.0%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\left(-\color{blue}{\frac{x \cdot \left(z - t\right)}{a - t}}\right) + x \cdot 1\right) \]

      7. mul-1-neg 63.0%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} + x \cdot 1\right) \]

      8. *-rgt-identity 63.0%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \color{blue}{x}\right) \]

      9. associate-+l+ 63.0%

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(z - t\right)}{a - t} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) + x} \]

   5. Simplified 95.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)} \]

   6. Taylor expanded in z around inf 81.3%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 82.6%

         \[\leadsto z \cdot \color{blue}{\frac{y - x}{a - t}} \]

   8. Simplified 82.6%

      \[\leadsto \color{blue}{z \cdot \frac{y - x}{a - t}} \]

   if -1.15999999999999994e218 < z < -4.20000000000000003e-173 or 2.1500000000000001e-193 < z < 3.9999999999999998e-7

   1. Initial program 67.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 76.9%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. +-commutative 76.9%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. +-commutative 76.9%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{a - t} + 1\right)} \]

      3. distribute-lft-in 76.9%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \color{blue}{\left(x \cdot \left(-1 \cdot \frac{z - t}{a - t}\right) + x \cdot 1\right)} \]

      4. mul-1-neg 76.9%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(x \cdot \color{blue}{\left(-\frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      5. distribute-rgt-neg-in 76.9%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{\left(-x \cdot \frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      6. associate-/l* 68.9%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\left(-\color{blue}{\frac{x \cdot \left(z - t\right)}{a - t}}\right) + x \cdot 1\right) \]

      7. mul-1-neg 68.9%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} + x \cdot 1\right) \]

      8. *-rgt-identity 68.9%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \color{blue}{x}\right) \]

      9. associate-+l+ 66.5%

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(z - t\right)}{a - t} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) + x} \]

   5. Simplified 77.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)} \]

   6. Taylor expanded in y around inf 62.4%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 62.4%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

   8. Simplified 62.4%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   if -4.20000000000000003e-173 < z < -1.40000000000000004e-226

   1. Initial program 72.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 70.1%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. associate-/l* 82.2%

         \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   5. Simplified 82.2%

      \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   6. Taylor expanded in t around inf 68.3%

      \[\leadsto \color{blue}{x + y} \]

   if -1.40000000000000004e-226 < z < -6.9999999999999984e-309 or 6.2000000000000004e-296 < z < 1.15e-290

   1. Initial program 25.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 77.1%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 77.1%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 77.1%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 77.1%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 77.1%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 77.1%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 77.1%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 77.1%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 88.2%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 88.2%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 88.2%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]
   6. Step-by-step derivation

      1. *-commutative 88.2%

         \[\leadsto y - \color{blue}{\left(z - a\right) \cdot \frac{y - x}{t}} \]

      2. clear-num 88.3%

         \[\leadsto y - \left(z - a\right) \cdot \color{blue}{\frac{1}{\frac{t}{y - x}}} \]

      3. un-div-inv 88.4%

         \[\leadsto y - \color{blue}{\frac{z - a}{\frac{t}{y - x}}} \]

   7. Applied egg-rr 88.4%

      \[\leadsto y - \color{blue}{\frac{z - a}{\frac{t}{y - x}}} \]

   8. Taylor expanded in y around 0 77.1%

      \[\leadsto y - \color{blue}{-1 \cdot \frac{x \cdot \left(z - a\right)}{t}} \]
   9. Step-by-step derivation

      1. mul-1-neg 77.1%

         \[\leadsto y - \color{blue}{\left(-\frac{x \cdot \left(z - a\right)}{t}\right)} \]

      2. associate-/l* 82.8%

         \[\leadsto y - \left(-\color{blue}{x \cdot \frac{z - a}{t}}\right) \]

   10. Simplified 82.8%

       \[\leadsto y - \color{blue}{\left(-x \cdot \frac{z - a}{t}\right)} \]

   11. Taylor expanded in z around 0 71.5%

       \[\leadsto \color{blue}{y + -1 \cdot \frac{a \cdot x}{t}} \]
   12. Step-by-step derivation

       1. mul-1-neg 71.5%

          \[\leadsto y + \color{blue}{\left(-\frac{a \cdot x}{t}\right)} \]

       2. *-commutative 71.5%

          \[\leadsto y + \left(-\frac{\color{blue}{x \cdot a}}{t}\right) \]

       3. associate-*r/ 82.8%

          \[\leadsto y + \left(-\color{blue}{x \cdot \frac{a}{t}}\right) \]

       4. unsub-neg 82.8%

          \[\leadsto \color{blue}{y - x \cdot \frac{a}{t}} \]

   13. Simplified 82.8%

       \[\leadsto \color{blue}{y - x \cdot \frac{a}{t}} \]

   if -6.9999999999999984e-309 < z < 6.2000000000000004e-296

   1. Initial program 80.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 100.0%

      \[\leadsto \color{blue}{x} \]

   if 1.15e-290 < z < 2.1500000000000001e-193

   1. Initial program 72.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 68.9%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. associate-/l* 77.5%

         \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   5. Simplified 77.5%

      \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]
   6. Step-by-step derivation

      1. clear-num 77.7%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

      2. inv-pow 77.7%

         \[\leadsto x + y \cdot \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}} \]

   7. Applied egg-rr 77.7%

      \[\leadsto x + y \cdot \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}} \]
   8. Step-by-step derivation

      1. unpow-1 77.7%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

   9. Simplified 77.7%

      \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

   10. Taylor expanded in z around 0 68.9%

       \[\leadsto \color{blue}{x + -1 \cdot \frac{t \cdot y}{a - t}} \]
   11. Step-by-step derivation

       1. mul-1-neg 68.9%

          \[\leadsto x + \color{blue}{\left(-\frac{t \cdot y}{a - t}\right)} \]

       2. unsub-neg 68.9%

          \[\leadsto \color{blue}{x - \frac{t \cdot y}{a - t}} \]

       3. associate-/l* 77.4%

          \[\leadsto x - \color{blue}{t \cdot \frac{y}{a - t}} \]

   12. Simplified 77.4%

       \[\leadsto \color{blue}{x - t \cdot \frac{y}{a - t}} \]

   13. Taylor expanded in t around 0 59.1%

       \[\leadsto x - \color{blue}{\frac{t \cdot y}{a}} \]
   14. Step-by-step derivation

       1. associate-/l* 59.1%

          \[\leadsto x - \color{blue}{t \cdot \frac{y}{a}} \]

   15. Simplified 59.1%

       \[\leadsto x - \color{blue}{t \cdot \frac{y}{a}} \]
   16. Step-by-step derivation

       1. clear-num 59.1%

          \[\leadsto x - t \cdot \color{blue}{\frac{1}{\frac{a}{y}}} \]

       2. un-div-inv 59.1%

          \[\leadsto x - \color{blue}{\frac{t}{\frac{a}{y}}} \]

   17. Applied egg-rr 59.1%

       \[\leadsto x - \color{blue}{\frac{t}{\frac{a}{y}}} \]

   if 2.5999999999999998e235 < z < 5.4000000000000002e262

   1. Initial program 81.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 81.7%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]

   4. Taylor expanded in x around inf 82.1%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z}{a}\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 82.1%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{z}{a}\right)}\right) \]

      2. unsub-neg 82.1%

         \[\leadsto x \cdot \color{blue}{\left(1 - \frac{z}{a}\right)} \]

   6. Simplified 82.1%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{a}\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{+218}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-173}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-226}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-309}:\\ \;\;\;\;y - x \cdot \frac{a}{t}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-296}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-290}:\\ \;\;\;\;y - x \cdot \frac{a}{t}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-193}:\\ \;\;\;\;x - \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-7}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+235} \lor \neg \left(z \leq 5.4 \cdot 10^{+262}\right):\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 63.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y - x}{a - t}\\ t_2 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -1.45 \cdot 10^{-13}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-81}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{-173}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-208}:\\ \;\;\;\;x - \frac{x \cdot z}{a}\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-211}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq -1.02 \cdot 10^{-254}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-62}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 56000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 240000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+171}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;y - x \cdot \frac{a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ (- y x) (- a t)))) (t_2 (* y (/ (- z t) (- a t)))))
   (if (<= t -1.45e-13)
     t_2
     (if (<= t -6.2e-81)
       t_1
       (if (<= t -5.6e-173)
         (+ x (/ y (/ (- a t) z)))
         (if (<= t -2.1e-208)
           (- x (/ (* x z) a))
           (if (<= t -9.2e-211)
             (- x (* t (/ y a)))
             (if (<= t -1.02e-254)
               t_1
               (if (<= t 3.6e-62)
                 (+ x (* z (/ (- y x) a)))
                 (if (<= t 56000.0)
                   t_2
                   (if (<= t 240000000000.0)
                     x
                     (if (<= t 6.2e+171) t_2 (- y (* x (/ a t)))))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((y - x) / (a - t));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -1.45e-13) {
		tmp = t_2;
	} else if (t <= -6.2e-81) {
		tmp = t_1;
	} else if (t <= -5.6e-173) {
		tmp = x + (y / ((a - t) / z));
	} else if (t <= -2.1e-208) {
		tmp = x - ((x * z) / a);
	} else if (t <= -9.2e-211) {
		tmp = x - (t * (y / a));
	} else if (t <= -1.02e-254) {
		tmp = t_1;
	} else if (t <= 3.6e-62) {
		tmp = x + (z * ((y - x) / a));
	} else if (t <= 56000.0) {
		tmp = t_2;
	} else if (t <= 240000000000.0) {
		tmp = x;
	} else if (t <= 6.2e+171) {
		tmp = t_2;
	} else {
		tmp = y - (x * (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * ((y - x) / (a - t))
    t_2 = y * ((z - t) / (a - t))
    if (t <= (-1.45d-13)) then
        tmp = t_2
    else if (t <= (-6.2d-81)) then
        tmp = t_1
    else if (t <= (-5.6d-173)) then
        tmp = x + (y / ((a - t) / z))
    else if (t <= (-2.1d-208)) then
        tmp = x - ((x * z) / a)
    else if (t <= (-9.2d-211)) then
        tmp = x - (t * (y / a))
    else if (t <= (-1.02d-254)) then
        tmp = t_1
    else if (t <= 3.6d-62) then
        tmp = x + (z * ((y - x) / a))
    else if (t <= 56000.0d0) then
        tmp = t_2
    else if (t <= 240000000000.0d0) then
        tmp = x
    else if (t <= 6.2d+171) then
        tmp = t_2
    else
        tmp = y - (x * (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((y - x) / (a - t));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -1.45e-13) {
		tmp = t_2;
	} else if (t <= -6.2e-81) {
		tmp = t_1;
	} else if (t <= -5.6e-173) {
		tmp = x + (y / ((a - t) / z));
	} else if (t <= -2.1e-208) {
		tmp = x - ((x * z) / a);
	} else if (t <= -9.2e-211) {
		tmp = x - (t * (y / a));
	} else if (t <= -1.02e-254) {
		tmp = t_1;
	} else if (t <= 3.6e-62) {
		tmp = x + (z * ((y - x) / a));
	} else if (t <= 56000.0) {
		tmp = t_2;
	} else if (t <= 240000000000.0) {
		tmp = x;
	} else if (t <= 6.2e+171) {
		tmp = t_2;
	} else {
		tmp = y - (x * (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * ((y - x) / (a - t))
	t_2 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -1.45e-13:
		tmp = t_2
	elif t <= -6.2e-81:
		tmp = t_1
	elif t <= -5.6e-173:
		tmp = x + (y / ((a - t) / z))
	elif t <= -2.1e-208:
		tmp = x - ((x * z) / a)
	elif t <= -9.2e-211:
		tmp = x - (t * (y / a))
	elif t <= -1.02e-254:
		tmp = t_1
	elif t <= 3.6e-62:
		tmp = x + (z * ((y - x) / a))
	elif t <= 56000.0:
		tmp = t_2
	elif t <= 240000000000.0:
		tmp = x
	elif t <= 6.2e+171:
		tmp = t_2
	else:
		tmp = y - (x * (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(Float64(y - x) / Float64(a - t)))
	t_2 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -1.45e-13)
		tmp = t_2;
	elseif (t <= -6.2e-81)
		tmp = t_1;
	elseif (t <= -5.6e-173)
		tmp = Float64(x + Float64(y / Float64(Float64(a - t) / z)));
	elseif (t <= -2.1e-208)
		tmp = Float64(x - Float64(Float64(x * z) / a));
	elseif (t <= -9.2e-211)
		tmp = Float64(x - Float64(t * Float64(y / a)));
	elseif (t <= -1.02e-254)
		tmp = t_1;
	elseif (t <= 3.6e-62)
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / a)));
	elseif (t <= 56000.0)
		tmp = t_2;
	elseif (t <= 240000000000.0)
		tmp = x;
	elseif (t <= 6.2e+171)
		tmp = t_2;
	else
		tmp = Float64(y - Float64(x * Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * ((y - x) / (a - t));
	t_2 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t <= -1.45e-13)
		tmp = t_2;
	elseif (t <= -6.2e-81)
		tmp = t_1;
	elseif (t <= -5.6e-173)
		tmp = x + (y / ((a - t) / z));
	elseif (t <= -2.1e-208)
		tmp = x - ((x * z) / a);
	elseif (t <= -9.2e-211)
		tmp = x - (t * (y / a));
	elseif (t <= -1.02e-254)
		tmp = t_1;
	elseif (t <= 3.6e-62)
		tmp = x + (z * ((y - x) / a));
	elseif (t <= 56000.0)
		tmp = t_2;
	elseif (t <= 240000000000.0)
		tmp = x;
	elseif (t <= 6.2e+171)
		tmp = t_2;
	else
		tmp = y - (x * (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.45e-13], t$95$2, If[LessEqual[t, -6.2e-81], t$95$1, If[LessEqual[t, -5.6e-173], N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.1e-208], N[(x - N[(N[(x * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -9.2e-211], N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.02e-254], t$95$1, If[LessEqual[t, 3.6e-62], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 56000.0], t$95$2, If[LessEqual[t, 240000000000.0], x, If[LessEqual[t, 6.2e+171], t$95$2, N[(y - N[(x * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if t < -1.4499999999999999e-13 or 3.6e-62 < t < 56000 or 2.4e11 < t < 6.1999999999999998e171

   1. Initial program 54.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 63.9%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. +-commutative 63.9%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. +-commutative 63.9%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{a - t} + 1\right)} \]

      3. distribute-lft-in 63.9%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \color{blue}{\left(x \cdot \left(-1 \cdot \frac{z - t}{a - t}\right) + x \cdot 1\right)} \]

      4. mul-1-neg 63.9%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(x \cdot \color{blue}{\left(-\frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      5. distribute-rgt-neg-in 63.9%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{\left(-x \cdot \frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      6. associate-/l* 55.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\left(-\color{blue}{\frac{x \cdot \left(z - t\right)}{a - t}}\right) + x \cdot 1\right) \]

      7. mul-1-neg 55.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} + x \cdot 1\right) \]

      8. *-rgt-identity 55.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \color{blue}{x}\right) \]

      9. associate-+l+ 53.5%

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(z - t\right)}{a - t} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) + x} \]

   5. Simplified 78.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)} \]

   6. Taylor expanded in y around inf 67.0%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 67.0%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

   8. Simplified 67.0%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   if -1.4499999999999999e-13 < t < -6.19999999999999976e-81 or -9.19999999999999953e-211 < t < -1.0200000000000001e-254

   1. Initial program 84.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 76.1%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. +-commutative 76.1%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. +-commutative 76.1%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{a - t} + 1\right)} \]

      3. distribute-lft-in 76.2%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \color{blue}{\left(x \cdot \left(-1 \cdot \frac{z - t}{a - t}\right) + x \cdot 1\right)} \]

      4. mul-1-neg 76.2%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(x \cdot \color{blue}{\left(-\frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      5. distribute-rgt-neg-in 76.2%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{\left(-x \cdot \frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      6. associate-/l* 79.9%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\left(-\color{blue}{\frac{x \cdot \left(z - t\right)}{a - t}}\right) + x \cdot 1\right) \]

      7. mul-1-neg 79.9%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} + x \cdot 1\right) \]

      8. *-rgt-identity 79.9%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \color{blue}{x}\right) \]

      9. associate-+l+ 79.9%

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(z - t\right)}{a - t} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) + x} \]

   5. Simplified 95.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)} \]

   6. Taylor expanded in z around inf 72.3%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 76.3%

         \[\leadsto z \cdot \color{blue}{\frac{y - x}{a - t}} \]

   8. Simplified 76.3%

      \[\leadsto \color{blue}{z \cdot \frac{y - x}{a - t}} \]

   if -6.19999999999999976e-81 < t < -5.5999999999999998e-173

   1. Initial program 89.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 65.6%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. associate-/l* 70.8%

         \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   5. Simplified 70.8%

      \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]
   6. Step-by-step derivation

      1. clear-num 70.8%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

      2. un-div-inv 70.8%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

   7. Applied egg-rr 70.8%

      \[\leadsto x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

   8. Taylor expanded in z around inf 70.8%

      \[\leadsto x + \frac{y}{\color{blue}{\frac{a - t}{z}}} \]

   if -5.5999999999999998e-173 < t < -2.10000000000000012e-208

   1. Initial program 99.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 68.1%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]

   4. Taylor expanded in y around 0 68.7%

      \[\leadsto x + \frac{\color{blue}{-1 \cdot \left(x \cdot z\right)}}{a} \]
   5. Step-by-step derivation

      1. mul-1-neg 68.7%

         \[\leadsto x + \frac{\color{blue}{-x \cdot z}}{a} \]

      2. distribute-lft-neg-out 68.7%

         \[\leadsto x + \frac{\color{blue}{\left(-x\right) \cdot z}}{a} \]

      3. *-commutative 68.7%

         \[\leadsto x + \frac{\color{blue}{z \cdot \left(-x\right)}}{a} \]

   6. Simplified 68.7%

      \[\leadsto x + \frac{\color{blue}{z \cdot \left(-x\right)}}{a} \]

   if -2.10000000000000012e-208 < t < -9.19999999999999953e-211

   1. Initial program 99.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 99.2%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   5. Simplified 100.0%

      \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]
   6. Step-by-step derivation

      1. clear-num 100.0%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

      2. inv-pow 100.0%

         \[\leadsto x + y \cdot \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}} \]

   7. Applied egg-rr 100.0%

      \[\leadsto x + y \cdot \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}} \]
   8. Step-by-step derivation

      1. unpow-1 100.0%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

   9. Simplified 100.0%

      \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

   10. Taylor expanded in z around 0 99.2%

       \[\leadsto \color{blue}{x + -1 \cdot \frac{t \cdot y}{a - t}} \]
   11. Step-by-step derivation

       1. mul-1-neg 99.2%

          \[\leadsto x + \color{blue}{\left(-\frac{t \cdot y}{a - t}\right)} \]

       2. unsub-neg 99.2%

          \[\leadsto \color{blue}{x - \frac{t \cdot y}{a - t}} \]

       3. associate-/l* 99.2%

          \[\leadsto x - \color{blue}{t \cdot \frac{y}{a - t}} \]

   12. Simplified 99.2%

       \[\leadsto \color{blue}{x - t \cdot \frac{y}{a - t}} \]

   13. Taylor expanded in t around 0 99.2%

       \[\leadsto x - \color{blue}{\frac{t \cdot y}{a}} \]
   14. Step-by-step derivation

       1. associate-/l* 99.2%

          \[\leadsto x - \color{blue}{t \cdot \frac{y}{a}} \]

   15. Simplified 99.2%

       \[\leadsto x - \color{blue}{t \cdot \frac{y}{a}} \]

   if -1.0200000000000001e-254 < t < 3.6e-62

   1. Initial program 92.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 84.1%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* 89.0%

         \[\leadsto x + \color{blue}{z \cdot \frac{y - x}{a}} \]

   5. Simplified 89.0%

      \[\leadsto x + \color{blue}{z \cdot \frac{y - x}{a}} \]

   if 56000 < t < 2.4e11

   1. Initial program 100.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 100.0%

      \[\leadsto \color{blue}{x} \]

   if 6.1999999999999998e171 < t

   1. Initial program 20.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 83.4%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 83.4%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 83.4%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 83.4%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 83.4%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 83.4%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 83.4%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 83.3%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 86.7%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 86.7%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 86.7%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]
   6. Step-by-step derivation

      1. *-commutative 86.7%

         \[\leadsto y - \color{blue}{\left(z - a\right) \cdot \frac{y - x}{t}} \]

      2. clear-num 86.7%

         \[\leadsto y - \left(z - a\right) \cdot \color{blue}{\frac{1}{\frac{t}{y - x}}} \]

      3. un-div-inv 86.7%

         \[\leadsto y - \color{blue}{\frac{z - a}{\frac{t}{y - x}}} \]

   7. Applied egg-rr 86.7%

      \[\leadsto y - \color{blue}{\frac{z - a}{\frac{t}{y - x}}} \]

   8. Taylor expanded in y around 0 91.1%

      \[\leadsto y - \color{blue}{-1 \cdot \frac{x \cdot \left(z - a\right)}{t}} \]
   9. Step-by-step derivation

      1. mul-1-neg 91.1%

         \[\leadsto y - \color{blue}{\left(-\frac{x \cdot \left(z - a\right)}{t}\right)} \]

      2. associate-/l* 87.9%

         \[\leadsto y - \left(-\color{blue}{x \cdot \frac{z - a}{t}}\right) \]

   10. Simplified 87.9%

       \[\leadsto y - \color{blue}{\left(-x \cdot \frac{z - a}{t}\right)} \]

   11. Taylor expanded in z around 0 85.8%

       \[\leadsto \color{blue}{y + -1 \cdot \frac{a \cdot x}{t}} \]
   12. Step-by-step derivation

       1. mul-1-neg 85.8%

          \[\leadsto y + \color{blue}{\left(-\frac{a \cdot x}{t}\right)} \]

       2. *-commutative 85.8%

          \[\leadsto y + \left(-\frac{\color{blue}{x \cdot a}}{t}\right) \]

       3. associate-*r/ 85.2%

          \[\leadsto y + \left(-\color{blue}{x \cdot \frac{a}{t}}\right) \]

       4. unsub-neg 85.2%

          \[\leadsto \color{blue}{y - x \cdot \frac{a}{t}} \]

   13. Simplified 85.2%

       \[\leadsto \color{blue}{y - x \cdot \frac{a}{t}} \]
3. Recombined 8 regimes into one program.

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{-13}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-81}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{-173}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z}}\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-208}:\\ \;\;\;\;x - \frac{x \cdot z}{a}\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-211}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq -1.02 \cdot 10^{-254}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-62}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 56000:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 240000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+171}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y - x \cdot \frac{a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 46.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{x - y}{t}\\ \mathbf{if}\;t \leq -3.7 \cdot 10^{+219}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{+156}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -7.8 \cdot 10^{+120}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{+81}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-16}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{a}{t}\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-62}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 1.04 \cdot 10^{+77}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ (- x y) t))))
   (if (<= t -3.7e+219)
     y
     (if (<= t -2.15e+156)
       t_1
       (if (<= t -7.8e+120)
         y
         (if (<= t -3.5e+81)
           t_1
           (if (<= t -1.7e+33)
             (* x (/ (- z a) t))
             (if (<= t -1.7e-9)
               t_1
               (if (<= t -6.2e-16)
                 (* (- y x) (/ a t))
                 (if (<= t -2e-62)
                   (* y (/ (- z t) a))
                   (if (<= t 1.6e+14)
                     (* x (- 1.0 (/ z a)))
                     (if (<= t 1.04e+77) (* y (/ z (- a t))) y))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((x - y) / t);
	double tmp;
	if (t <= -3.7e+219) {
		tmp = y;
	} else if (t <= -2.15e+156) {
		tmp = t_1;
	} else if (t <= -7.8e+120) {
		tmp = y;
	} else if (t <= -3.5e+81) {
		tmp = t_1;
	} else if (t <= -1.7e+33) {
		tmp = x * ((z - a) / t);
	} else if (t <= -1.7e-9) {
		tmp = t_1;
	} else if (t <= -6.2e-16) {
		tmp = (y - x) * (a / t);
	} else if (t <= -2e-62) {
		tmp = y * ((z - t) / a);
	} else if (t <= 1.6e+14) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 1.04e+77) {
		tmp = y * (z / (a - t));
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * ((x - y) / t)
    if (t <= (-3.7d+219)) then
        tmp = y
    else if (t <= (-2.15d+156)) then
        tmp = t_1
    else if (t <= (-7.8d+120)) then
        tmp = y
    else if (t <= (-3.5d+81)) then
        tmp = t_1
    else if (t <= (-1.7d+33)) then
        tmp = x * ((z - a) / t)
    else if (t <= (-1.7d-9)) then
        tmp = t_1
    else if (t <= (-6.2d-16)) then
        tmp = (y - x) * (a / t)
    else if (t <= (-2d-62)) then
        tmp = y * ((z - t) / a)
    else if (t <= 1.6d+14) then
        tmp = x * (1.0d0 - (z / a))
    else if (t <= 1.04d+77) then
        tmp = y * (z / (a - t))
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((x - y) / t);
	double tmp;
	if (t <= -3.7e+219) {
		tmp = y;
	} else if (t <= -2.15e+156) {
		tmp = t_1;
	} else if (t <= -7.8e+120) {
		tmp = y;
	} else if (t <= -3.5e+81) {
		tmp = t_1;
	} else if (t <= -1.7e+33) {
		tmp = x * ((z - a) / t);
	} else if (t <= -1.7e-9) {
		tmp = t_1;
	} else if (t <= -6.2e-16) {
		tmp = (y - x) * (a / t);
	} else if (t <= -2e-62) {
		tmp = y * ((z - t) / a);
	} else if (t <= 1.6e+14) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 1.04e+77) {
		tmp = y * (z / (a - t));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * ((x - y) / t)
	tmp = 0
	if t <= -3.7e+219:
		tmp = y
	elif t <= -2.15e+156:
		tmp = t_1
	elif t <= -7.8e+120:
		tmp = y
	elif t <= -3.5e+81:
		tmp = t_1
	elif t <= -1.7e+33:
		tmp = x * ((z - a) / t)
	elif t <= -1.7e-9:
		tmp = t_1
	elif t <= -6.2e-16:
		tmp = (y - x) * (a / t)
	elif t <= -2e-62:
		tmp = y * ((z - t) / a)
	elif t <= 1.6e+14:
		tmp = x * (1.0 - (z / a))
	elif t <= 1.04e+77:
		tmp = y * (z / (a - t))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(Float64(x - y) / t))
	tmp = 0.0
	if (t <= -3.7e+219)
		tmp = y;
	elseif (t <= -2.15e+156)
		tmp = t_1;
	elseif (t <= -7.8e+120)
		tmp = y;
	elseif (t <= -3.5e+81)
		tmp = t_1;
	elseif (t <= -1.7e+33)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (t <= -1.7e-9)
		tmp = t_1;
	elseif (t <= -6.2e-16)
		tmp = Float64(Float64(y - x) * Float64(a / t));
	elseif (t <= -2e-62)
		tmp = Float64(y * Float64(Float64(z - t) / a));
	elseif (t <= 1.6e+14)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (t <= 1.04e+77)
		tmp = Float64(y * Float64(z / Float64(a - t)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * ((x - y) / t);
	tmp = 0.0;
	if (t <= -3.7e+219)
		tmp = y;
	elseif (t <= -2.15e+156)
		tmp = t_1;
	elseif (t <= -7.8e+120)
		tmp = y;
	elseif (t <= -3.5e+81)
		tmp = t_1;
	elseif (t <= -1.7e+33)
		tmp = x * ((z - a) / t);
	elseif (t <= -1.7e-9)
		tmp = t_1;
	elseif (t <= -6.2e-16)
		tmp = (y - x) * (a / t);
	elseif (t <= -2e-62)
		tmp = y * ((z - t) / a);
	elseif (t <= 1.6e+14)
		tmp = x * (1.0 - (z / a));
	elseif (t <= 1.04e+77)
		tmp = y * (z / (a - t));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.7e+219], y, If[LessEqual[t, -2.15e+156], t$95$1, If[LessEqual[t, -7.8e+120], y, If[LessEqual[t, -3.5e+81], t$95$1, If[LessEqual[t, -1.7e+33], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.7e-9], t$95$1, If[LessEqual[t, -6.2e-16], N[(N[(y - x), $MachinePrecision] * N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2e-62], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.6e+14], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.04e+77], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -3.7e219 or -2.14999999999999993e156 < t < -7.7999999999999997e120 or 1.04e77 < t

   1. Initial program 32.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 67.4%

      \[\leadsto \color{blue}{y} \]

   if -3.7e219 < t < -2.14999999999999993e156 or -7.7999999999999997e120 < t < -3.5e81 or -1.7e33 < t < -1.6999999999999999e-9

   1. Initial program 57.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 56.0%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 56.0%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 56.0%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 56.0%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 56.0%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 56.0%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 56.0%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 69.0%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 75.9%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 75.9%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 75.9%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]

   6. Taylor expanded in z around inf 60.2%

      \[\leadsto \color{blue}{z \cdot \left(\frac{x}{t} - \frac{y}{t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 60.2%

         \[\leadsto z \cdot \color{blue}{\frac{x - y}{t}} \]

   8. Simplified 60.2%

      \[\leadsto \color{blue}{z \cdot \frac{x - y}{t}} \]

   if -3.5e81 < t < -1.7e33

   1. Initial program 58.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 73.7%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 73.7%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 73.7%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 73.7%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 73.7%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 73.7%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 73.7%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 73.7%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 73.5%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 73.5%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 73.5%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]

   6. Taylor expanded in y around 0 46.0%

      \[\leadsto \color{blue}{\frac{x \cdot \left(z - a\right)}{t}} \]
   7. Step-by-step derivation

      1. associate-/l* 45.7%

         \[\leadsto \color{blue}{x \cdot \frac{z - a}{t}} \]

   8. Simplified 45.7%

      \[\leadsto \color{blue}{x \cdot \frac{z - a}{t}} \]

   if -1.6999999999999999e-9 < t < -6.2000000000000002e-16

   1. Initial program 51.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 100.0%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 100.0%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 100.0%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 100.0%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 100.0%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 100.0%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 100.0%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 100.0%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 99.2%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 99.2%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 99.2%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]

   6. Taylor expanded in a around inf 54.0%

      \[\leadsto \color{blue}{\frac{a \cdot \left(y - x\right)}{t}} \]
   7. Step-by-step derivation

      1. *-commutative 54.0%

         \[\leadsto \frac{\color{blue}{\left(y - x\right) \cdot a}}{t} \]

      2. associate-/l* 54.0%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{a}{t}} \]

   8. Simplified 54.0%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{a}{t}} \]

   if -6.2000000000000002e-16 < t < -2.0000000000000001e-62

   1. Initial program 89.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 88.0%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. +-commutative 88.0%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. +-commutative 88.0%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{a - t} + 1\right)} \]

      3. distribute-lft-in 88.2%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \color{blue}{\left(x \cdot \left(-1 \cdot \frac{z - t}{a - t}\right) + x \cdot 1\right)} \]

      4. mul-1-neg 88.2%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(x \cdot \color{blue}{\left(-\frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      5. distribute-rgt-neg-in 88.2%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{\left(-x \cdot \frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      6. associate-/l* 88.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\left(-\color{blue}{\frac{x \cdot \left(z - t\right)}{a - t}}\right) + x \cdot 1\right) \]

      7. mul-1-neg 88.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} + x \cdot 1\right) \]

      8. *-rgt-identity 88.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \color{blue}{x}\right) \]

      9. associate-+l+ 88.4%

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(z - t\right)}{a - t} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) + x} \]

   5. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)} \]

   6. Taylor expanded in y around inf 43.5%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 43.5%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

   8. Simplified 43.5%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   9. Taylor expanded in a around inf 55.7%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a}} \]
   10. Step-by-step derivation

       1. associate-/l* 55.9%

          \[\leadsto \color{blue}{y \cdot \frac{z - t}{a}} \]

   11. Simplified 55.9%

       \[\leadsto \color{blue}{y \cdot \frac{z - t}{a}} \]

   if -2.0000000000000001e-62 < t < 1.6e14

   1. Initial program 88.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 67.1%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]

   4. Taylor expanded in x around inf 52.3%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z}{a}\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 52.3%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{z}{a}\right)}\right) \]

      2. unsub-neg 52.3%

         \[\leadsto x \cdot \color{blue}{\left(1 - \frac{z}{a}\right)} \]

   6. Simplified 52.3%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{a}\right)} \]

   if 1.6e14 < t < 1.04e77

   1. Initial program 61.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 62.1%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. +-commutative 62.1%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. +-commutative 62.1%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{a - t} + 1\right)} \]

      3. distribute-lft-in 62.1%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \color{blue}{\left(x \cdot \left(-1 \cdot \frac{z - t}{a - t}\right) + x \cdot 1\right)} \]

      4. mul-1-neg 62.1%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(x \cdot \color{blue}{\left(-\frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      5. distribute-rgt-neg-in 62.1%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{\left(-x \cdot \frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      6. associate-/l* 61.9%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\left(-\color{blue}{\frac{x \cdot \left(z - t\right)}{a - t}}\right) + x \cdot 1\right) \]

      7. mul-1-neg 61.9%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} + x \cdot 1\right) \]

      8. *-rgt-identity 61.9%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \color{blue}{x}\right) \]

      9. associate-+l+ 61.9%

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(z - t\right)}{a - t} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) + x} \]

   5. Simplified 81.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)} \]

   6. Taylor expanded in y around inf 73.5%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 73.5%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

   8. Simplified 73.5%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   9. Taylor expanded in z around inf 33.3%

      \[\leadsto \color{blue}{\frac{y \cdot z}{a - t}} \]
   10. Step-by-step derivation

       1. associate-/l* 51.6%

          \[\leadsto \color{blue}{y \cdot \frac{z}{a - t}} \]

   11. Simplified 51.6%

       \[\leadsto \color{blue}{y \cdot \frac{z}{a - t}} \]
3. Recombined 7 regimes into one program.
4. Add Preprocessing

Alternative 17: 46.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{x - y}{t}\\ \mathbf{if}\;t \leq -3.7 \cdot 10^{+219}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{+156}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{+123}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -4.7 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-11}:\\ \;\;\;\;\frac{y - x}{t} \cdot a\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-54}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 15000000000000:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{+76}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ (- x y) t))))
   (if (<= t -3.7e+219)
     y
     (if (<= t -2.4e+156)
       t_1
       (if (<= t -1.8e+123)
         y
         (if (<= t -4.7e+82)
           t_1
           (if (<= t -1.65e+33)
             (* x (/ (- z a) t))
             (if (<= t -5e-9)
               t_1
               (if (<= t -6.5e-11)
                 (* (/ (- y x) t) a)
                 (if (<= t -3.4e-54)
                   (* y (/ (- z t) a))
                   (if (<= t 15000000000000.0)
                     (* x (- 1.0 (/ z a)))
                     (if (<= t 8.6e+76) (* y (/ z (- a t))) y))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((x - y) / t);
	double tmp;
	if (t <= -3.7e+219) {
		tmp = y;
	} else if (t <= -2.4e+156) {
		tmp = t_1;
	} else if (t <= -1.8e+123) {
		tmp = y;
	} else if (t <= -4.7e+82) {
		tmp = t_1;
	} else if (t <= -1.65e+33) {
		tmp = x * ((z - a) / t);
	} else if (t <= -5e-9) {
		tmp = t_1;
	} else if (t <= -6.5e-11) {
		tmp = ((y - x) / t) * a;
	} else if (t <= -3.4e-54) {
		tmp = y * ((z - t) / a);
	} else if (t <= 15000000000000.0) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 8.6e+76) {
		tmp = y * (z / (a - t));
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * ((x - y) / t)
    if (t <= (-3.7d+219)) then
        tmp = y
    else if (t <= (-2.4d+156)) then
        tmp = t_1
    else if (t <= (-1.8d+123)) then
        tmp = y
    else if (t <= (-4.7d+82)) then
        tmp = t_1
    else if (t <= (-1.65d+33)) then
        tmp = x * ((z - a) / t)
    else if (t <= (-5d-9)) then
        tmp = t_1
    else if (t <= (-6.5d-11)) then
        tmp = ((y - x) / t) * a
    else if (t <= (-3.4d-54)) then
        tmp = y * ((z - t) / a)
    else if (t <= 15000000000000.0d0) then
        tmp = x * (1.0d0 - (z / a))
    else if (t <= 8.6d+76) then
        tmp = y * (z / (a - t))
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((x - y) / t);
	double tmp;
	if (t <= -3.7e+219) {
		tmp = y;
	} else if (t <= -2.4e+156) {
		tmp = t_1;
	} else if (t <= -1.8e+123) {
		tmp = y;
	} else if (t <= -4.7e+82) {
		tmp = t_1;
	} else if (t <= -1.65e+33) {
		tmp = x * ((z - a) / t);
	} else if (t <= -5e-9) {
		tmp = t_1;
	} else if (t <= -6.5e-11) {
		tmp = ((y - x) / t) * a;
	} else if (t <= -3.4e-54) {
		tmp = y * ((z - t) / a);
	} else if (t <= 15000000000000.0) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 8.6e+76) {
		tmp = y * (z / (a - t));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * ((x - y) / t)
	tmp = 0
	if t <= -3.7e+219:
		tmp = y
	elif t <= -2.4e+156:
		tmp = t_1
	elif t <= -1.8e+123:
		tmp = y
	elif t <= -4.7e+82:
		tmp = t_1
	elif t <= -1.65e+33:
		tmp = x * ((z - a) / t)
	elif t <= -5e-9:
		tmp = t_1
	elif t <= -6.5e-11:
		tmp = ((y - x) / t) * a
	elif t <= -3.4e-54:
		tmp = y * ((z - t) / a)
	elif t <= 15000000000000.0:
		tmp = x * (1.0 - (z / a))
	elif t <= 8.6e+76:
		tmp = y * (z / (a - t))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(Float64(x - y) / t))
	tmp = 0.0
	if (t <= -3.7e+219)
		tmp = y;
	elseif (t <= -2.4e+156)
		tmp = t_1;
	elseif (t <= -1.8e+123)
		tmp = y;
	elseif (t <= -4.7e+82)
		tmp = t_1;
	elseif (t <= -1.65e+33)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (t <= -5e-9)
		tmp = t_1;
	elseif (t <= -6.5e-11)
		tmp = Float64(Float64(Float64(y - x) / t) * a);
	elseif (t <= -3.4e-54)
		tmp = Float64(y * Float64(Float64(z - t) / a));
	elseif (t <= 15000000000000.0)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (t <= 8.6e+76)
		tmp = Float64(y * Float64(z / Float64(a - t)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * ((x - y) / t);
	tmp = 0.0;
	if (t <= -3.7e+219)
		tmp = y;
	elseif (t <= -2.4e+156)
		tmp = t_1;
	elseif (t <= -1.8e+123)
		tmp = y;
	elseif (t <= -4.7e+82)
		tmp = t_1;
	elseif (t <= -1.65e+33)
		tmp = x * ((z - a) / t);
	elseif (t <= -5e-9)
		tmp = t_1;
	elseif (t <= -6.5e-11)
		tmp = ((y - x) / t) * a;
	elseif (t <= -3.4e-54)
		tmp = y * ((z - t) / a);
	elseif (t <= 15000000000000.0)
		tmp = x * (1.0 - (z / a));
	elseif (t <= 8.6e+76)
		tmp = y * (z / (a - t));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.7e+219], y, If[LessEqual[t, -2.4e+156], t$95$1, If[LessEqual[t, -1.8e+123], y, If[LessEqual[t, -4.7e+82], t$95$1, If[LessEqual[t, -1.65e+33], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5e-9], t$95$1, If[LessEqual[t, -6.5e-11], N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[t, -3.4e-54], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 15000000000000.0], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.6e+76], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -3.7e219 or -2.4000000000000001e156 < t < -1.79999999999999999e123 or 8.59999999999999957e76 < t

   1. Initial program 32.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 67.4%

      \[\leadsto \color{blue}{y} \]

   if -3.7e219 < t < -2.4000000000000001e156 or -1.79999999999999999e123 < t < -4.7e82 or -1.64999999999999988e33 < t < -5.0000000000000001e-9

   1. Initial program 57.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 56.0%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 56.0%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 56.0%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 56.0%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 56.0%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 56.0%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 56.0%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 69.0%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 75.9%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 75.9%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 75.9%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]

   6. Taylor expanded in z around inf 60.2%

      \[\leadsto \color{blue}{z \cdot \left(\frac{x}{t} - \frac{y}{t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 60.2%

         \[\leadsto z \cdot \color{blue}{\frac{x - y}{t}} \]

   8. Simplified 60.2%

      \[\leadsto \color{blue}{z \cdot \frac{x - y}{t}} \]

   if -4.7e82 < t < -1.64999999999999988e33

   1. Initial program 58.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 73.7%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 73.7%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 73.7%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 73.7%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 73.7%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 73.7%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 73.7%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 73.7%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 73.5%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 73.5%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 73.5%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]

   6. Taylor expanded in y around 0 46.0%

      \[\leadsto \color{blue}{\frac{x \cdot \left(z - a\right)}{t}} \]
   7. Step-by-step derivation

      1. associate-/l* 45.7%

         \[\leadsto \color{blue}{x \cdot \frac{z - a}{t}} \]

   8. Simplified 45.7%

      \[\leadsto \color{blue}{x \cdot \frac{z - a}{t}} \]

   if -5.0000000000000001e-9 < t < -6.49999999999999953e-11

   1. Initial program 51.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 100.0%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 100.0%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 100.0%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 100.0%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 100.0%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 100.0%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 100.0%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 100.0%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 99.2%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 99.2%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 99.2%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]
   6. Step-by-step derivation

      1. *-commutative 99.2%

         \[\leadsto y - \color{blue}{\left(z - a\right) \cdot \frac{y - x}{t}} \]

      2. clear-num 99.2%

         \[\leadsto y - \left(z - a\right) \cdot \color{blue}{\frac{1}{\frac{t}{y - x}}} \]

      3. un-div-inv 100.0%

         \[\leadsto y - \color{blue}{\frac{z - a}{\frac{t}{y - x}}} \]

   7. Applied egg-rr 100.0%

      \[\leadsto y - \color{blue}{\frac{z - a}{\frac{t}{y - x}}} \]

   8. Taylor expanded in a around inf 54.0%

      \[\leadsto \color{blue}{\frac{a \cdot \left(y - x\right)}{t}} \]
   9. Step-by-step derivation

      1. associate-/l* 53.3%

         \[\leadsto \color{blue}{a \cdot \frac{y - x}{t}} \]

   10. Simplified 53.3%

       \[\leadsto \color{blue}{a \cdot \frac{y - x}{t}} \]

   if -6.49999999999999953e-11 < t < -3.39999999999999987e-54

   1. Initial program 89.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 88.0%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. +-commutative 88.0%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. +-commutative 88.0%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{a - t} + 1\right)} \]

      3. distribute-lft-in 88.2%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \color{blue}{\left(x \cdot \left(-1 \cdot \frac{z - t}{a - t}\right) + x \cdot 1\right)} \]

      4. mul-1-neg 88.2%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(x \cdot \color{blue}{\left(-\frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      5. distribute-rgt-neg-in 88.2%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{\left(-x \cdot \frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      6. associate-/l* 88.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\left(-\color{blue}{\frac{x \cdot \left(z - t\right)}{a - t}}\right) + x \cdot 1\right) \]

      7. mul-1-neg 88.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} + x \cdot 1\right) \]

      8. *-rgt-identity 88.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \color{blue}{x}\right) \]

      9. associate-+l+ 88.4%

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(z - t\right)}{a - t} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) + x} \]

   5. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)} \]

   6. Taylor expanded in y around inf 43.5%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 43.5%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

   8. Simplified 43.5%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   9. Taylor expanded in a around inf 55.7%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a}} \]
   10. Step-by-step derivation

       1. associate-/l* 55.9%

          \[\leadsto \color{blue}{y \cdot \frac{z - t}{a}} \]

   11. Simplified 55.9%

       \[\leadsto \color{blue}{y \cdot \frac{z - t}{a}} \]

   if -3.39999999999999987e-54 < t < 1.5e13

   1. Initial program 88.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 67.1%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]

   4. Taylor expanded in x around inf 52.3%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z}{a}\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 52.3%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{z}{a}\right)}\right) \]

      2. unsub-neg 52.3%

         \[\leadsto x \cdot \color{blue}{\left(1 - \frac{z}{a}\right)} \]

   6. Simplified 52.3%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{a}\right)} \]

   if 1.5e13 < t < 8.59999999999999957e76

   1. Initial program 61.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 62.1%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. +-commutative 62.1%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. +-commutative 62.1%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{a - t} + 1\right)} \]

      3. distribute-lft-in 62.1%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \color{blue}{\left(x \cdot \left(-1 \cdot \frac{z - t}{a - t}\right) + x \cdot 1\right)} \]

      4. mul-1-neg 62.1%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(x \cdot \color{blue}{\left(-\frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      5. distribute-rgt-neg-in 62.1%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{\left(-x \cdot \frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      6. associate-/l* 61.9%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\left(-\color{blue}{\frac{x \cdot \left(z - t\right)}{a - t}}\right) + x \cdot 1\right) \]

      7. mul-1-neg 61.9%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} + x \cdot 1\right) \]

      8. *-rgt-identity 61.9%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \color{blue}{x}\right) \]

      9. associate-+l+ 61.9%

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(z - t\right)}{a - t} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) + x} \]

   5. Simplified 81.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)} \]

   6. Taylor expanded in y around inf 73.5%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 73.5%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

   8. Simplified 73.5%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   9. Taylor expanded in z around inf 33.3%

      \[\leadsto \color{blue}{\frac{y \cdot z}{a - t}} \]
   10. Step-by-step derivation

       1. associate-/l* 51.6%

          \[\leadsto \color{blue}{y \cdot \frac{z}{a - t}} \]

   11. Simplified 51.6%

       \[\leadsto \color{blue}{y \cdot \frac{z}{a - t}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{+219}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{+156}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{+123}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -4.7 \cdot 10^{+82}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-9}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-11}:\\ \;\;\;\;\frac{y - x}{t} \cdot a\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-54}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 15000000000000:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{+76}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 79.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y - x}{a - t}\\ t_2 := y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{if}\;t \leq -4.5 \cdot 10^{+30}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.02 \cdot 10^{-51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-70}:\\ \;\;\;\;x + y \cdot \frac{-1}{\frac{a}{t - z}}\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-208}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-208}:\\ \;\;\;\;y \cdot \frac{t}{-a}\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-269}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-273}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.26 \cdot 10^{+48}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ (- y x) (- a t)))))
        (t_2 (+ y (* (- y x) (/ (- a z) t)))))
   (if (<= t -4.5e+30)
     t_2
     (if (<= t -1.02e-51)
       t_1
       (if (<= t -7e-70)
         (+ x (* y (/ -1.0 (/ a (- t z)))))
         (if (<= t -1.05e-208)
           t_1
           (if (<= t -1e-208)
             (* y (/ t (- a)))
             (if (<= t -1.4e-269)
               t_1
               (if (<= t 3.1e-273)
                 (+ x (/ (* (- y x) z) a))
                 (if (<= t 3.5e-82)
                   t_1
                   (if (<= t 1.26e+48)
                     (+ x (* y (/ (- z t) (- a t))))
                     t_2)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * ((y - x) / (a - t)));
	double t_2 = y + ((y - x) * ((a - z) / t));
	double tmp;
	if (t <= -4.5e+30) {
		tmp = t_2;
	} else if (t <= -1.02e-51) {
		tmp = t_1;
	} else if (t <= -7e-70) {
		tmp = x + (y * (-1.0 / (a / (t - z))));
	} else if (t <= -1.05e-208) {
		tmp = t_1;
	} else if (t <= -1e-208) {
		tmp = y * (t / -a);
	} else if (t <= -1.4e-269) {
		tmp = t_1;
	} else if (t <= 3.1e-273) {
		tmp = x + (((y - x) * z) / a);
	} else if (t <= 3.5e-82) {
		tmp = t_1;
	} else if (t <= 1.26e+48) {
		tmp = x + (y * ((z - t) / (a - t)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z * ((y - x) / (a - t)))
    t_2 = y + ((y - x) * ((a - z) / t))
    if (t <= (-4.5d+30)) then
        tmp = t_2
    else if (t <= (-1.02d-51)) then
        tmp = t_1
    else if (t <= (-7d-70)) then
        tmp = x + (y * ((-1.0d0) / (a / (t - z))))
    else if (t <= (-1.05d-208)) then
        tmp = t_1
    else if (t <= (-1d-208)) then
        tmp = y * (t / -a)
    else if (t <= (-1.4d-269)) then
        tmp = t_1
    else if (t <= 3.1d-273) then
        tmp = x + (((y - x) * z) / a)
    else if (t <= 3.5d-82) then
        tmp = t_1
    else if (t <= 1.26d+48) then
        tmp = x + (y * ((z - t) / (a - t)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * ((y - x) / (a - t)));
	double t_2 = y + ((y - x) * ((a - z) / t));
	double tmp;
	if (t <= -4.5e+30) {
		tmp = t_2;
	} else if (t <= -1.02e-51) {
		tmp = t_1;
	} else if (t <= -7e-70) {
		tmp = x + (y * (-1.0 / (a / (t - z))));
	} else if (t <= -1.05e-208) {
		tmp = t_1;
	} else if (t <= -1e-208) {
		tmp = y * (t / -a);
	} else if (t <= -1.4e-269) {
		tmp = t_1;
	} else if (t <= 3.1e-273) {
		tmp = x + (((y - x) * z) / a);
	} else if (t <= 3.5e-82) {
		tmp = t_1;
	} else if (t <= 1.26e+48) {
		tmp = x + (y * ((z - t) / (a - t)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * ((y - x) / (a - t)))
	t_2 = y + ((y - x) * ((a - z) / t))
	tmp = 0
	if t <= -4.5e+30:
		tmp = t_2
	elif t <= -1.02e-51:
		tmp = t_1
	elif t <= -7e-70:
		tmp = x + (y * (-1.0 / (a / (t - z))))
	elif t <= -1.05e-208:
		tmp = t_1
	elif t <= -1e-208:
		tmp = y * (t / -a)
	elif t <= -1.4e-269:
		tmp = t_1
	elif t <= 3.1e-273:
		tmp = x + (((y - x) * z) / a)
	elif t <= 3.5e-82:
		tmp = t_1
	elif t <= 1.26e+48:
		tmp = x + (y * ((z - t) / (a - t)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(Float64(y - x) / Float64(a - t))))
	t_2 = Float64(y + Float64(Float64(y - x) * Float64(Float64(a - z) / t)))
	tmp = 0.0
	if (t <= -4.5e+30)
		tmp = t_2;
	elseif (t <= -1.02e-51)
		tmp = t_1;
	elseif (t <= -7e-70)
		tmp = Float64(x + Float64(y * Float64(-1.0 / Float64(a / Float64(t - z)))));
	elseif (t <= -1.05e-208)
		tmp = t_1;
	elseif (t <= -1e-208)
		tmp = Float64(y * Float64(t / Float64(-a)));
	elseif (t <= -1.4e-269)
		tmp = t_1;
	elseif (t <= 3.1e-273)
		tmp = Float64(x + Float64(Float64(Float64(y - x) * z) / a));
	elseif (t <= 3.5e-82)
		tmp = t_1;
	elseif (t <= 1.26e+48)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * ((y - x) / (a - t)));
	t_2 = y + ((y - x) * ((a - z) / t));
	tmp = 0.0;
	if (t <= -4.5e+30)
		tmp = t_2;
	elseif (t <= -1.02e-51)
		tmp = t_1;
	elseif (t <= -7e-70)
		tmp = x + (y * (-1.0 / (a / (t - z))));
	elseif (t <= -1.05e-208)
		tmp = t_1;
	elseif (t <= -1e-208)
		tmp = y * (t / -a);
	elseif (t <= -1.4e-269)
		tmp = t_1;
	elseif (t <= 3.1e-273)
		tmp = x + (((y - x) * z) / a);
	elseif (t <= 3.5e-82)
		tmp = t_1;
	elseif (t <= 1.26e+48)
		tmp = x + (y * ((z - t) / (a - t)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(N[(y - x), $MachinePrecision] * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.5e+30], t$95$2, If[LessEqual[t, -1.02e-51], t$95$1, If[LessEqual[t, -7e-70], N[(x + N[(y * N[(-1.0 / N[(a / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.05e-208], t$95$1, If[LessEqual[t, -1e-208], N[(y * N[(t / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.4e-269], t$95$1, If[LessEqual[t, 3.1e-273], N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.5e-82], t$95$1, If[LessEqual[t, 1.26e+48], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -4.49999999999999995e30 or 1.26000000000000001e48 < t

   1. Initial program 38.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 53.7%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. +-commutative 53.7%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. +-commutative 53.7%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{a - t} + 1\right)} \]

      3. distribute-lft-in 53.7%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \color{blue}{\left(x \cdot \left(-1 \cdot \frac{z - t}{a - t}\right) + x \cdot 1\right)} \]

      4. mul-1-neg 53.7%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(x \cdot \color{blue}{\left(-\frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      5. distribute-rgt-neg-in 53.7%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{\left(-x \cdot \frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      6. associate-/l* 39.5%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\left(-\color{blue}{\frac{x \cdot \left(z - t\right)}{a - t}}\right) + x \cdot 1\right) \]

      7. mul-1-neg 39.5%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} + x \cdot 1\right) \]

      8. *-rgt-identity 39.5%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \color{blue}{x}\right) \]

      9. associate-+l+ 36.9%

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(z - t\right)}{a - t} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) + x} \]

   5. Simplified 66.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)} \]

   6. Taylor expanded in t around inf 68.9%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   7. Step-by-step derivation

      1. cancel-sign-sub-inv 68.9%

         \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) + \left(--1\right) \cdot \frac{a \cdot \left(y - x\right)}{t}} \]

      2. mul-1-neg 68.9%

         \[\leadsto \left(y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right)}{t}\right)}\right) + \left(--1\right) \cdot \frac{a \cdot \left(y - x\right)}{t} \]

      3. sub-neg 68.9%

         \[\leadsto \color{blue}{\left(y - \frac{z \cdot \left(y - x\right)}{t}\right)} + \left(--1\right) \cdot \frac{a \cdot \left(y - x\right)}{t} \]

      4. metadata-eval 68.9%

         \[\leadsto \left(y - \frac{z \cdot \left(y - x\right)}{t}\right) + \color{blue}{1} \cdot \frac{a \cdot \left(y - x\right)}{t} \]

      5. *-lft-identity 68.9%

         \[\leadsto \left(y - \frac{z \cdot \left(y - x\right)}{t}\right) + \color{blue}{\frac{a \cdot \left(y - x\right)}{t}} \]

      6. *-commutative 68.9%

         \[\leadsto \left(y - \frac{z \cdot \left(y - x\right)}{t}\right) + \frac{\color{blue}{\left(y - x\right) \cdot a}}{t} \]

      7. associate-+l- 68.9%

         \[\leadsto \color{blue}{y - \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{\left(y - x\right) \cdot a}{t}\right)} \]

      8. div-sub 68.9%

         \[\leadsto y - \color{blue}{\frac{z \cdot \left(y - x\right) - \left(y - x\right) \cdot a}{t}} \]

      9. *-commutative 68.9%

         \[\leadsto y - \frac{z \cdot \left(y - x\right) - \color{blue}{a \cdot \left(y - x\right)}}{t} \]

      10. distribute-rgt-out-- 69.2%

          \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

      11. associate-*r/ 85.0%

          \[\leadsto y - \color{blue}{\left(y - x\right) \cdot \frac{z - a}{t}} \]

   8. Simplified 85.0%

      \[\leadsto \color{blue}{y - \left(y - x\right) \cdot \frac{z - a}{t}} \]

   if -4.49999999999999995e30 < t < -1.01999999999999998e-51 or -6.99999999999999949e-70 < t < -1.05000000000000006e-208 or -1.0000000000000001e-208 < t < -1.39999999999999997e-269 or 3.09999999999999988e-273 < t < 3.4999999999999999e-82

   1. Initial program 88.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 82.8%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a - t}} \]
   4. Step-by-step derivation

      1. associate-/l* 88.6%

         \[\leadsto x + \color{blue}{z \cdot \frac{y - x}{a - t}} \]

   5. Simplified 88.6%

      \[\leadsto x + \color{blue}{z \cdot \frac{y - x}{a - t}} \]

   if -1.01999999999999998e-51 < t < -6.99999999999999949e-70

   1. Initial program 80.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 76.9%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. associate-/l* 95.9%

         \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   5. Simplified 95.9%

      \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]
   6. Step-by-step derivation

      1. clear-num 95.9%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

      2. inv-pow 95.9%

         \[\leadsto x + y \cdot \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}} \]

   7. Applied egg-rr 95.9%

      \[\leadsto x + y \cdot \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}} \]
   8. Step-by-step derivation

      1. unpow-1 95.9%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

   9. Simplified 95.9%

      \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

   10. Taylor expanded in a around inf 95.9%

       \[\leadsto x + y \cdot \frac{1}{\color{blue}{\frac{a}{z - t}}} \]

   if -1.05000000000000006e-208 < t < -1.0000000000000001e-208

   1. Initial program 98.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 98.4%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   5. Simplified 100.0%

      \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]
   6. Step-by-step derivation

      1. clear-num 100.0%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

      2. inv-pow 100.0%

         \[\leadsto x + y \cdot \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}} \]

   7. Applied egg-rr 100.0%

      \[\leadsto x + y \cdot \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}} \]
   8. Step-by-step derivation

      1. unpow-1 100.0%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

   9. Simplified 100.0%

      \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

   10. Taylor expanded in z around 0 98.4%

       \[\leadsto \color{blue}{x + -1 \cdot \frac{t \cdot y}{a - t}} \]
   11. Step-by-step derivation

       1. mul-1-neg 98.4%

          \[\leadsto x + \color{blue}{\left(-\frac{t \cdot y}{a - t}\right)} \]

       2. unsub-neg 98.4%

          \[\leadsto \color{blue}{x - \frac{t \cdot y}{a - t}} \]

       3. associate-/l* 98.4%

          \[\leadsto x - \color{blue}{t \cdot \frac{y}{a - t}} \]

   12. Simplified 98.4%

       \[\leadsto \color{blue}{x - t \cdot \frac{y}{a - t}} \]

   13. Taylor expanded in t around 0 98.4%

       \[\leadsto x - \color{blue}{\frac{t \cdot y}{a}} \]
   14. Step-by-step derivation

       1. associate-/l* 98.4%

          \[\leadsto x - \color{blue}{t \cdot \frac{y}{a}} \]

   15. Simplified 98.4%

       \[\leadsto x - \color{blue}{t \cdot \frac{y}{a}} \]

   16. Taylor expanded in x around 0 98.4%

       \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot y}{a}} \]
   17. Step-by-step derivation

       1. mul-1-neg 98.4%

          \[\leadsto \color{blue}{-\frac{t \cdot y}{a}} \]

       2. *-commutative 98.4%

          \[\leadsto -\frac{\color{blue}{y \cdot t}}{a} \]

       3. distribute-frac-neg2 98.4%

          \[\leadsto \color{blue}{\frac{y \cdot t}{-a}} \]

       4. associate-/l* 100.0%

          \[\leadsto \color{blue}{y \cdot \frac{t}{-a}} \]

   18. Simplified 100.0%

       \[\leadsto \color{blue}{y \cdot \frac{t}{-a}} \]

   if -1.39999999999999997e-269 < t < 3.09999999999999988e-273

   1. Initial program 100.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 100.0%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]

   if 3.4999999999999999e-82 < t < 1.26000000000000001e48

   1. Initial program 80.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 69.4%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. associate-/l* 77.0%

         \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   5. Simplified 77.0%

      \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+30}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t \leq -1.02 \cdot 10^{-51}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-70}:\\ \;\;\;\;x + y \cdot \frac{-1}{\frac{a}{t - z}}\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-208}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-208}:\\ \;\;\;\;y \cdot \frac{t}{-a}\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-269}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-273}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-82}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 1.26 \cdot 10^{+48}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 64.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y}{t - a}\\ t_2 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -3.7 \cdot 10^{+158}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{+25}:\\ \;\;\;\;y - \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{elif}\;t \leq -1 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-103}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-61}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 30000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 420000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+77}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{+116}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ y (- t a))))) (t_2 (* y (/ (- z t) (- a t)))))
   (if (<= t -3.7e+158)
     (/ y (/ (- a t) (- z t)))
     (if (<= t -5.2e+25)
       (- y (/ (* (- y x) z) t))
       (if (<= t -1e+14)
         t_1
         (if (<= t -6e-103)
           (* z (/ (- y x) (- a t)))
           (if (<= t 1.35e-61)
             (+ x (* z (/ (- y x) a)))
             (if (<= t 30000.0)
               t_2
               (if (<= t 420000000000.0)
                 x
                 (if (<= t 6e+77)
                   t_2
                   (if (<= t 1.12e+116)
                     t_1
                     (+ y (* (- y x) (/ a t))))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / (t - a)));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -3.7e+158) {
		tmp = y / ((a - t) / (z - t));
	} else if (t <= -5.2e+25) {
		tmp = y - (((y - x) * z) / t);
	} else if (t <= -1e+14) {
		tmp = t_1;
	} else if (t <= -6e-103) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 1.35e-61) {
		tmp = x + (z * ((y - x) / a));
	} else if (t <= 30000.0) {
		tmp = t_2;
	} else if (t <= 420000000000.0) {
		tmp = x;
	} else if (t <= 6e+77) {
		tmp = t_2;
	} else if (t <= 1.12e+116) {
		tmp = t_1;
	} else {
		tmp = y + ((y - x) * (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (t * (y / (t - a)))
    t_2 = y * ((z - t) / (a - t))
    if (t <= (-3.7d+158)) then
        tmp = y / ((a - t) / (z - t))
    else if (t <= (-5.2d+25)) then
        tmp = y - (((y - x) * z) / t)
    else if (t <= (-1d+14)) then
        tmp = t_1
    else if (t <= (-6d-103)) then
        tmp = z * ((y - x) / (a - t))
    else if (t <= 1.35d-61) then
        tmp = x + (z * ((y - x) / a))
    else if (t <= 30000.0d0) then
        tmp = t_2
    else if (t <= 420000000000.0d0) then
        tmp = x
    else if (t <= 6d+77) then
        tmp = t_2
    else if (t <= 1.12d+116) then
        tmp = t_1
    else
        tmp = y + ((y - x) * (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / (t - a)));
	double t_2 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -3.7e+158) {
		tmp = y / ((a - t) / (z - t));
	} else if (t <= -5.2e+25) {
		tmp = y - (((y - x) * z) / t);
	} else if (t <= -1e+14) {
		tmp = t_1;
	} else if (t <= -6e-103) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 1.35e-61) {
		tmp = x + (z * ((y - x) / a));
	} else if (t <= 30000.0) {
		tmp = t_2;
	} else if (t <= 420000000000.0) {
		tmp = x;
	} else if (t <= 6e+77) {
		tmp = t_2;
	} else if (t <= 1.12e+116) {
		tmp = t_1;
	} else {
		tmp = y + ((y - x) * (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * (y / (t - a)))
	t_2 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -3.7e+158:
		tmp = y / ((a - t) / (z - t))
	elif t <= -5.2e+25:
		tmp = y - (((y - x) * z) / t)
	elif t <= -1e+14:
		tmp = t_1
	elif t <= -6e-103:
		tmp = z * ((y - x) / (a - t))
	elif t <= 1.35e-61:
		tmp = x + (z * ((y - x) / a))
	elif t <= 30000.0:
		tmp = t_2
	elif t <= 420000000000.0:
		tmp = x
	elif t <= 6e+77:
		tmp = t_2
	elif t <= 1.12e+116:
		tmp = t_1
	else:
		tmp = y + ((y - x) * (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(y / Float64(t - a))))
	t_2 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -3.7e+158)
		tmp = Float64(y / Float64(Float64(a - t) / Float64(z - t)));
	elseif (t <= -5.2e+25)
		tmp = Float64(y - Float64(Float64(Float64(y - x) * z) / t));
	elseif (t <= -1e+14)
		tmp = t_1;
	elseif (t <= -6e-103)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (t <= 1.35e-61)
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / a)));
	elseif (t <= 30000.0)
		tmp = t_2;
	elseif (t <= 420000000000.0)
		tmp = x;
	elseif (t <= 6e+77)
		tmp = t_2;
	elseif (t <= 1.12e+116)
		tmp = t_1;
	else
		tmp = Float64(y + Float64(Float64(y - x) * Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * (y / (t - a)));
	t_2 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t <= -3.7e+158)
		tmp = y / ((a - t) / (z - t));
	elseif (t <= -5.2e+25)
		tmp = y - (((y - x) * z) / t);
	elseif (t <= -1e+14)
		tmp = t_1;
	elseif (t <= -6e-103)
		tmp = z * ((y - x) / (a - t));
	elseif (t <= 1.35e-61)
		tmp = x + (z * ((y - x) / a));
	elseif (t <= 30000.0)
		tmp = t_2;
	elseif (t <= 420000000000.0)
		tmp = x;
	elseif (t <= 6e+77)
		tmp = t_2;
	elseif (t <= 1.12e+116)
		tmp = t_1;
	else
		tmp = y + ((y - x) * (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.7e+158], N[(y / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.2e+25], N[(y - N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1e+14], t$95$1, If[LessEqual[t, -6e-103], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e-61], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 30000.0], t$95$2, If[LessEqual[t, 420000000000.0], x, If[LessEqual[t, 6e+77], t$95$2, If[LessEqual[t, 1.12e+116], t$95$1, N[(y + N[(N[(y - x), $MachinePrecision] * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if t < -3.70000000000000011e158

   1. Initial program 29.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 47.3%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. +-commutative 47.3%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. +-commutative 47.3%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{a - t} + 1\right)} \]

      3. distribute-lft-in 47.3%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \color{blue}{\left(x \cdot \left(-1 \cdot \frac{z - t}{a - t}\right) + x \cdot 1\right)} \]

      4. mul-1-neg 47.3%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(x \cdot \color{blue}{\left(-\frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      5. distribute-rgt-neg-in 47.3%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{\left(-x \cdot \frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      6. associate-/l* 29.1%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\left(-\color{blue}{\frac{x \cdot \left(z - t\right)}{a - t}}\right) + x \cdot 1\right) \]

      7. mul-1-neg 29.1%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} + x \cdot 1\right) \]

      8. *-rgt-identity 29.1%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \color{blue}{x}\right) \]

      9. associate-+l+ 29.1%

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(z - t\right)}{a - t} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) + x} \]

   5. Simplified 71.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)} \]

   6. Taylor expanded in y around inf 81.0%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 81.0%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

   8. Simplified 81.0%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]
   9. Step-by-step derivation

      1. clear-num 69.0%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

      2. un-div-inv 69.0%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

   10. Applied egg-rr 81.1%

       \[\leadsto \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

   if -3.70000000000000011e158 < t < -5.1999999999999997e25

   1. Initial program 64.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 77.4%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 77.4%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 77.4%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 77.4%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 77.4%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 77.4%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 77.4%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 80.7%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 80.6%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 80.6%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 80.6%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]

   6. Taylor expanded in z around inf 67.9%

      \[\leadsto y - \color{blue}{\frac{z \cdot \left(y - x\right)}{t}} \]

   if -5.1999999999999997e25 < t < -1e14 or 5.9999999999999996e77 < t < 1.12e116

   1. Initial program 45.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 59.1%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. associate-/l* 85.5%

         \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   5. Simplified 85.5%

      \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]
   6. Step-by-step derivation

      1. clear-num 85.8%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

      2. inv-pow 85.8%

         \[\leadsto x + y \cdot \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}} \]

   7. Applied egg-rr 85.8%

      \[\leadsto x + y \cdot \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}} \]
   8. Step-by-step derivation

      1. unpow-1 85.8%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

   9. Simplified 85.8%

      \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

   10. Taylor expanded in z around 0 59.1%

       \[\leadsto \color{blue}{x + -1 \cdot \frac{t \cdot y}{a - t}} \]
   11. Step-by-step derivation

       1. mul-1-neg 59.1%

          \[\leadsto x + \color{blue}{\left(-\frac{t \cdot y}{a - t}\right)} \]

       2. unsub-neg 59.1%

          \[\leadsto \color{blue}{x - \frac{t \cdot y}{a - t}} \]

       3. associate-/l* 85.5%

          \[\leadsto x - \color{blue}{t \cdot \frac{y}{a - t}} \]

   12. Simplified 85.5%

       \[\leadsto \color{blue}{x - t \cdot \frac{y}{a - t}} \]

   if -1e14 < t < -6e-103

   1. Initial program 84.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 84.6%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. +-commutative 84.6%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. +-commutative 84.6%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{a - t} + 1\right)} \]

      3. distribute-lft-in 84.7%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \color{blue}{\left(x \cdot \left(-1 \cdot \frac{z - t}{a - t}\right) + x \cdot 1\right)} \]

      4. mul-1-neg 84.7%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(x \cdot \color{blue}{\left(-\frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      5. distribute-rgt-neg-in 84.7%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{\left(-x \cdot \frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      6. associate-/l* 84.1%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\left(-\color{blue}{\frac{x \cdot \left(z - t\right)}{a - t}}\right) + x \cdot 1\right) \]

      7. mul-1-neg 84.1%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} + x \cdot 1\right) \]

      8. *-rgt-identity 84.1%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \color{blue}{x}\right) \]

      9. associate-+l+ 84.2%

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(z - t\right)}{a - t} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) + x} \]

   5. Simplified 92.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)} \]

   6. Taylor expanded in z around inf 68.9%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 68.9%

         \[\leadsto z \cdot \color{blue}{\frac{y - x}{a - t}} \]

   8. Simplified 68.9%

      \[\leadsto \color{blue}{z \cdot \frac{y - x}{a - t}} \]

   if -6e-103 < t < 1.34999999999999997e-61

   1. Initial program 91.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 74.1%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* 78.1%

         \[\leadsto x + \color{blue}{z \cdot \frac{y - x}{a}} \]

   5. Simplified 78.1%

      \[\leadsto x + \color{blue}{z \cdot \frac{y - x}{a}} \]

   if 1.34999999999999997e-61 < t < 3e4 or 4.2e11 < t < 5.9999999999999996e77

   1. Initial program 68.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 69.6%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. +-commutative 69.6%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. +-commutative 69.6%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{a - t} + 1\right)} \]

      3. distribute-lft-in 69.6%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \color{blue}{\left(x \cdot \left(-1 \cdot \frac{z - t}{a - t}\right) + x \cdot 1\right)} \]

      4. mul-1-neg 69.6%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(x \cdot \color{blue}{\left(-\frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      5. distribute-rgt-neg-in 69.6%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{\left(-x \cdot \frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      6. associate-/l* 69.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\left(-\color{blue}{\frac{x \cdot \left(z - t\right)}{a - t}}\right) + x \cdot 1\right) \]

      7. mul-1-neg 69.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} + x \cdot 1\right) \]

      8. *-rgt-identity 69.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \color{blue}{x}\right) \]

      9. associate-+l+ 68.9%

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(z - t\right)}{a - t} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) + x} \]

   5. Simplified 83.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)} \]

   6. Taylor expanded in y around inf 66.0%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 66.0%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

   8. Simplified 66.0%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   if 3e4 < t < 4.2e11

   1. Initial program 100.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 100.0%

      \[\leadsto \color{blue}{x} \]

   if 1.12e116 < t

   1. Initial program 24.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 77.5%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 77.5%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 77.5%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 77.5%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 77.5%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 77.5%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 77.5%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 83.5%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 86.3%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 86.3%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 86.3%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]

   6. Taylor expanded in z around 0 74.8%

      \[\leadsto \color{blue}{y - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   7. Step-by-step derivation

      1. cancel-sign-sub-inv 74.8%

         \[\leadsto \color{blue}{y + \left(--1\right) \cdot \frac{a \cdot \left(y - x\right)}{t}} \]

      2. metadata-eval 74.8%

         \[\leadsto y + \color{blue}{1} \cdot \frac{a \cdot \left(y - x\right)}{t} \]

      3. *-lft-identity 74.8%

         \[\leadsto y + \color{blue}{\frac{a \cdot \left(y - x\right)}{t}} \]

      4. *-commutative 74.8%

         \[\leadsto y + \frac{\color{blue}{\left(y - x\right) \cdot a}}{t} \]

      5. associate-/l* 79.0%

         \[\leadsto y + \color{blue}{\left(y - x\right) \cdot \frac{a}{t}} \]

   8. Simplified 79.0%

      \[\leadsto \color{blue}{y + \left(y - x\right) \cdot \frac{a}{t}} \]
3. Recombined 8 regimes into one program.

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{+158}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{+25}:\\ \;\;\;\;y - \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{elif}\;t \leq -1 \cdot 10^{+14}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-103}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-61}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 30000:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 420000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+77}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{+116}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 64.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x + t \cdot \frac{y}{t - a}\\ \mathbf{if}\;t \leq -1.5 \cdot 10^{+159}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{+26}:\\ \;\;\;\;y - \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{elif}\;t \leq -66000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-103}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-64}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 49000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2500000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+116}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))) (t_2 (+ x (* t (/ y (- t a))))))
   (if (<= t -1.5e+159)
     t_1
     (if (<= t -1.25e+26)
       (- y (/ (* (- y x) z) t))
       (if (<= t -66000000000.0)
         t_2
         (if (<= t -7.5e-103)
           (* z (/ (- y x) (- a t)))
           (if (<= t 1.5e-64)
             (+ x (* z (/ (- y x) a)))
             (if (<= t 49000.0)
               t_1
               (if (<= t 2500000000000.0)
                 x
                 (if (<= t 4.4e+78)
                   t_1
                   (if (<= t 4.2e+116) t_2 (+ y (* (- y x) (/ a t))))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + (t * (y / (t - a)));
	double tmp;
	if (t <= -1.5e+159) {
		tmp = t_1;
	} else if (t <= -1.25e+26) {
		tmp = y - (((y - x) * z) / t);
	} else if (t <= -66000000000.0) {
		tmp = t_2;
	} else if (t <= -7.5e-103) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 1.5e-64) {
		tmp = x + (z * ((y - x) / a));
	} else if (t <= 49000.0) {
		tmp = t_1;
	} else if (t <= 2500000000000.0) {
		tmp = x;
	} else if (t <= 4.4e+78) {
		tmp = t_1;
	} else if (t <= 4.2e+116) {
		tmp = t_2;
	} else {
		tmp = y + ((y - x) * (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    t_2 = x + (t * (y / (t - a)))
    if (t <= (-1.5d+159)) then
        tmp = t_1
    else if (t <= (-1.25d+26)) then
        tmp = y - (((y - x) * z) / t)
    else if (t <= (-66000000000.0d0)) then
        tmp = t_2
    else if (t <= (-7.5d-103)) then
        tmp = z * ((y - x) / (a - t))
    else if (t <= 1.5d-64) then
        tmp = x + (z * ((y - x) / a))
    else if (t <= 49000.0d0) then
        tmp = t_1
    else if (t <= 2500000000000.0d0) then
        tmp = x
    else if (t <= 4.4d+78) then
        tmp = t_1
    else if (t <= 4.2d+116) then
        tmp = t_2
    else
        tmp = y + ((y - x) * (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + (t * (y / (t - a)));
	double tmp;
	if (t <= -1.5e+159) {
		tmp = t_1;
	} else if (t <= -1.25e+26) {
		tmp = y - (((y - x) * z) / t);
	} else if (t <= -66000000000.0) {
		tmp = t_2;
	} else if (t <= -7.5e-103) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= 1.5e-64) {
		tmp = x + (z * ((y - x) / a));
	} else if (t <= 49000.0) {
		tmp = t_1;
	} else if (t <= 2500000000000.0) {
		tmp = x;
	} else if (t <= 4.4e+78) {
		tmp = t_1;
	} else if (t <= 4.2e+116) {
		tmp = t_2;
	} else {
		tmp = y + ((y - x) * (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = x + (t * (y / (t - a)))
	tmp = 0
	if t <= -1.5e+159:
		tmp = t_1
	elif t <= -1.25e+26:
		tmp = y - (((y - x) * z) / t)
	elif t <= -66000000000.0:
		tmp = t_2
	elif t <= -7.5e-103:
		tmp = z * ((y - x) / (a - t))
	elif t <= 1.5e-64:
		tmp = x + (z * ((y - x) / a))
	elif t <= 49000.0:
		tmp = t_1
	elif t <= 2500000000000.0:
		tmp = x
	elif t <= 4.4e+78:
		tmp = t_1
	elif t <= 4.2e+116:
		tmp = t_2
	else:
		tmp = y + ((y - x) * (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(x + Float64(t * Float64(y / Float64(t - a))))
	tmp = 0.0
	if (t <= -1.5e+159)
		tmp = t_1;
	elseif (t <= -1.25e+26)
		tmp = Float64(y - Float64(Float64(Float64(y - x) * z) / t));
	elseif (t <= -66000000000.0)
		tmp = t_2;
	elseif (t <= -7.5e-103)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (t <= 1.5e-64)
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / a)));
	elseif (t <= 49000.0)
		tmp = t_1;
	elseif (t <= 2500000000000.0)
		tmp = x;
	elseif (t <= 4.4e+78)
		tmp = t_1;
	elseif (t <= 4.2e+116)
		tmp = t_2;
	else
		tmp = Float64(y + Float64(Float64(y - x) * Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = x + (t * (y / (t - a)));
	tmp = 0.0;
	if (t <= -1.5e+159)
		tmp = t_1;
	elseif (t <= -1.25e+26)
		tmp = y - (((y - x) * z) / t);
	elseif (t <= -66000000000.0)
		tmp = t_2;
	elseif (t <= -7.5e-103)
		tmp = z * ((y - x) / (a - t));
	elseif (t <= 1.5e-64)
		tmp = x + (z * ((y - x) / a));
	elseif (t <= 49000.0)
		tmp = t_1;
	elseif (t <= 2500000000000.0)
		tmp = x;
	elseif (t <= 4.4e+78)
		tmp = t_1;
	elseif (t <= 4.2e+116)
		tmp = t_2;
	else
		tmp = y + ((y - x) * (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.5e+159], t$95$1, If[LessEqual[t, -1.25e+26], N[(y - N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -66000000000.0], t$95$2, If[LessEqual[t, -7.5e-103], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.5e-64], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 49000.0], t$95$1, If[LessEqual[t, 2500000000000.0], x, If[LessEqual[t, 4.4e+78], t$95$1, If[LessEqual[t, 4.2e+116], t$95$2, N[(y + N[(N[(y - x), $MachinePrecision] * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -1.5000000000000001e159 or 1.5e-64 < t < 49000 or 2.5e12 < t < 4.40000000000000028e78

   1. Initial program 48.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 58.0%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. +-commutative 58.0%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. +-commutative 58.0%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{a - t} + 1\right)} \]

      3. distribute-lft-in 58.0%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \color{blue}{\left(x \cdot \left(-1 \cdot \frac{z - t}{a - t}\right) + x \cdot 1\right)} \]

      4. mul-1-neg 58.0%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(x \cdot \color{blue}{\left(-\frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      5. distribute-rgt-neg-in 58.0%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{\left(-x \cdot \frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      6. associate-/l* 48.5%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\left(-\color{blue}{\frac{x \cdot \left(z - t\right)}{a - t}}\right) + x \cdot 1\right) \]

      7. mul-1-neg 48.5%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} + x \cdot 1\right) \]

      8. *-rgt-identity 48.5%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \color{blue}{x}\right) \]

      9. associate-+l+ 48.2%

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(z - t\right)}{a - t} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) + x} \]

   5. Simplified 77.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)} \]

   6. Taylor expanded in y around inf 73.8%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 73.8%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

   8. Simplified 73.8%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   if -1.5000000000000001e159 < t < -1.25e26

   1. Initial program 64.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 77.4%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 77.4%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 77.4%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 77.4%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 77.4%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 77.4%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 77.4%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 80.7%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 80.6%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 80.6%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 80.6%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]

   6. Taylor expanded in z around inf 67.9%

      \[\leadsto y - \color{blue}{\frac{z \cdot \left(y - x\right)}{t}} \]

   if -1.25e26 < t < -6.6e10 or 4.40000000000000028e78 < t < 4.2000000000000002e116

   1. Initial program 45.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 59.1%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. associate-/l* 85.5%

         \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   5. Simplified 85.5%

      \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]
   6. Step-by-step derivation

      1. clear-num 85.8%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

      2. inv-pow 85.8%

         \[\leadsto x + y \cdot \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}} \]

   7. Applied egg-rr 85.8%

      \[\leadsto x + y \cdot \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}} \]
   8. Step-by-step derivation

      1. unpow-1 85.8%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

   9. Simplified 85.8%

      \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

   10. Taylor expanded in z around 0 59.1%

       \[\leadsto \color{blue}{x + -1 \cdot \frac{t \cdot y}{a - t}} \]
   11. Step-by-step derivation

       1. mul-1-neg 59.1%

          \[\leadsto x + \color{blue}{\left(-\frac{t \cdot y}{a - t}\right)} \]

       2. unsub-neg 59.1%

          \[\leadsto \color{blue}{x - \frac{t \cdot y}{a - t}} \]

       3. associate-/l* 85.5%

          \[\leadsto x - \color{blue}{t \cdot \frac{y}{a - t}} \]

   12. Simplified 85.5%

       \[\leadsto \color{blue}{x - t \cdot \frac{y}{a - t}} \]

   if -6.6e10 < t < -7.5e-103

   1. Initial program 84.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 84.6%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. +-commutative 84.6%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. +-commutative 84.6%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{a - t} + 1\right)} \]

      3. distribute-lft-in 84.7%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \color{blue}{\left(x \cdot \left(-1 \cdot \frac{z - t}{a - t}\right) + x \cdot 1\right)} \]

      4. mul-1-neg 84.7%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(x \cdot \color{blue}{\left(-\frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      5. distribute-rgt-neg-in 84.7%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{\left(-x \cdot \frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      6. associate-/l* 84.1%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\left(-\color{blue}{\frac{x \cdot \left(z - t\right)}{a - t}}\right) + x \cdot 1\right) \]

      7. mul-1-neg 84.1%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} + x \cdot 1\right) \]

      8. *-rgt-identity 84.1%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \color{blue}{x}\right) \]

      9. associate-+l+ 84.2%

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(z - t\right)}{a - t} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) + x} \]

   5. Simplified 92.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)} \]

   6. Taylor expanded in z around inf 68.9%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 68.9%

         \[\leadsto z \cdot \color{blue}{\frac{y - x}{a - t}} \]

   8. Simplified 68.9%

      \[\leadsto \color{blue}{z \cdot \frac{y - x}{a - t}} \]

   if -7.5e-103 < t < 1.5e-64

   1. Initial program 91.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 74.1%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* 78.1%

         \[\leadsto x + \color{blue}{z \cdot \frac{y - x}{a}} \]

   5. Simplified 78.1%

      \[\leadsto x + \color{blue}{z \cdot \frac{y - x}{a}} \]

   if 49000 < t < 2.5e12

   1. Initial program 100.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 100.0%

      \[\leadsto \color{blue}{x} \]

   if 4.2000000000000002e116 < t

   1. Initial program 24.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 77.5%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 77.5%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 77.5%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 77.5%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 77.5%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 77.5%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 77.5%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 83.5%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 86.3%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 86.3%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 86.3%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]

   6. Taylor expanded in z around 0 74.8%

      \[\leadsto \color{blue}{y - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   7. Step-by-step derivation

      1. cancel-sign-sub-inv 74.8%

         \[\leadsto \color{blue}{y + \left(--1\right) \cdot \frac{a \cdot \left(y - x\right)}{t}} \]

      2. metadata-eval 74.8%

         \[\leadsto y + \color{blue}{1} \cdot \frac{a \cdot \left(y - x\right)}{t} \]

      3. *-lft-identity 74.8%

         \[\leadsto y + \color{blue}{\frac{a \cdot \left(y - x\right)}{t}} \]

      4. *-commutative 74.8%

         \[\leadsto y + \frac{\color{blue}{\left(y - x\right) \cdot a}}{t} \]

      5. associate-/l* 79.0%

         \[\leadsto y + \color{blue}{\left(y - x\right) \cdot \frac{a}{t}} \]

   8. Simplified 79.0%

      \[\leadsto \color{blue}{y + \left(y - x\right) \cdot \frac{a}{t}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+159}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{+26}:\\ \;\;\;\;y - \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{elif}\;t \leq -66000000000:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-103}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-64}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 49000:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 2500000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+78}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+116}:\\ \;\;\;\;x + t \cdot \frac{y}{t - a}\\ \mathbf{else}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 63.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x + z \cdot \frac{y - x}{a}\\ \mathbf{if}\;t \leq -2.15 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-93}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-155}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -4.9 \cdot 10^{-224}:\\ \;\;\;\;x - \frac{x \cdot z}{a}\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{-227}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-62}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 56000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 750000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{+122}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y - x \cdot \frac{a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))) (t_2 (+ x (* z (/ (- y x) a)))))
   (if (<= t -2.15e-17)
     t_1
     (if (<= t -9.2e-93)
       (* z (/ (- y x) (- a t)))
       (if (<= t -6.5e-155)
         t_2
         (if (<= t -4.9e-224)
           (- x (/ (* x z) a))
           (if (<= t -2.3e-227)
             (* y (/ z (- a t)))
             (if (<= t 6.2e-62)
               t_2
               (if (<= t 56000.0)
                 t_1
                 (if (<= t 750000000000.0)
                   x
                   (if (<= t 2.65e+122) t_1 (- y (* x (/ a t))))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + (z * ((y - x) / a));
	double tmp;
	if (t <= -2.15e-17) {
		tmp = t_1;
	} else if (t <= -9.2e-93) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= -6.5e-155) {
		tmp = t_2;
	} else if (t <= -4.9e-224) {
		tmp = x - ((x * z) / a);
	} else if (t <= -2.3e-227) {
		tmp = y * (z / (a - t));
	} else if (t <= 6.2e-62) {
		tmp = t_2;
	} else if (t <= 56000.0) {
		tmp = t_1;
	} else if (t <= 750000000000.0) {
		tmp = x;
	} else if (t <= 2.65e+122) {
		tmp = t_1;
	} else {
		tmp = y - (x * (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    t_2 = x + (z * ((y - x) / a))
    if (t <= (-2.15d-17)) then
        tmp = t_1
    else if (t <= (-9.2d-93)) then
        tmp = z * ((y - x) / (a - t))
    else if (t <= (-6.5d-155)) then
        tmp = t_2
    else if (t <= (-4.9d-224)) then
        tmp = x - ((x * z) / a)
    else if (t <= (-2.3d-227)) then
        tmp = y * (z / (a - t))
    else if (t <= 6.2d-62) then
        tmp = t_2
    else if (t <= 56000.0d0) then
        tmp = t_1
    else if (t <= 750000000000.0d0) then
        tmp = x
    else if (t <= 2.65d+122) then
        tmp = t_1
    else
        tmp = y - (x * (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + (z * ((y - x) / a));
	double tmp;
	if (t <= -2.15e-17) {
		tmp = t_1;
	} else if (t <= -9.2e-93) {
		tmp = z * ((y - x) / (a - t));
	} else if (t <= -6.5e-155) {
		tmp = t_2;
	} else if (t <= -4.9e-224) {
		tmp = x - ((x * z) / a);
	} else if (t <= -2.3e-227) {
		tmp = y * (z / (a - t));
	} else if (t <= 6.2e-62) {
		tmp = t_2;
	} else if (t <= 56000.0) {
		tmp = t_1;
	} else if (t <= 750000000000.0) {
		tmp = x;
	} else if (t <= 2.65e+122) {
		tmp = t_1;
	} else {
		tmp = y - (x * (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = x + (z * ((y - x) / a))
	tmp = 0
	if t <= -2.15e-17:
		tmp = t_1
	elif t <= -9.2e-93:
		tmp = z * ((y - x) / (a - t))
	elif t <= -6.5e-155:
		tmp = t_2
	elif t <= -4.9e-224:
		tmp = x - ((x * z) / a)
	elif t <= -2.3e-227:
		tmp = y * (z / (a - t))
	elif t <= 6.2e-62:
		tmp = t_2
	elif t <= 56000.0:
		tmp = t_1
	elif t <= 750000000000.0:
		tmp = x
	elif t <= 2.65e+122:
		tmp = t_1
	else:
		tmp = y - (x * (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(x + Float64(z * Float64(Float64(y - x) / a)))
	tmp = 0.0
	if (t <= -2.15e-17)
		tmp = t_1;
	elseif (t <= -9.2e-93)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (t <= -6.5e-155)
		tmp = t_2;
	elseif (t <= -4.9e-224)
		tmp = Float64(x - Float64(Float64(x * z) / a));
	elseif (t <= -2.3e-227)
		tmp = Float64(y * Float64(z / Float64(a - t)));
	elseif (t <= 6.2e-62)
		tmp = t_2;
	elseif (t <= 56000.0)
		tmp = t_1;
	elseif (t <= 750000000000.0)
		tmp = x;
	elseif (t <= 2.65e+122)
		tmp = t_1;
	else
		tmp = Float64(y - Float64(x * Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = x + (z * ((y - x) / a));
	tmp = 0.0;
	if (t <= -2.15e-17)
		tmp = t_1;
	elseif (t <= -9.2e-93)
		tmp = z * ((y - x) / (a - t));
	elseif (t <= -6.5e-155)
		tmp = t_2;
	elseif (t <= -4.9e-224)
		tmp = x - ((x * z) / a);
	elseif (t <= -2.3e-227)
		tmp = y * (z / (a - t));
	elseif (t <= 6.2e-62)
		tmp = t_2;
	elseif (t <= 56000.0)
		tmp = t_1;
	elseif (t <= 750000000000.0)
		tmp = x;
	elseif (t <= 2.65e+122)
		tmp = t_1;
	else
		tmp = y - (x * (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.15e-17], t$95$1, If[LessEqual[t, -9.2e-93], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6.5e-155], t$95$2, If[LessEqual[t, -4.9e-224], N[(x - N[(N[(x * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.3e-227], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.2e-62], t$95$2, If[LessEqual[t, 56000.0], t$95$1, If[LessEqual[t, 750000000000.0], x, If[LessEqual[t, 2.65e+122], t$95$1, N[(y - N[(x * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -2.15000000000000012e-17 or 6.1999999999999999e-62 < t < 56000 or 7.5e11 < t < 2.65e122

   1. Initial program 55.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 64.1%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. +-commutative 64.1%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. +-commutative 64.1%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{a - t} + 1\right)} \]

      3. distribute-lft-in 64.1%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \color{blue}{\left(x \cdot \left(-1 \cdot \frac{z - t}{a - t}\right) + x \cdot 1\right)} \]

      4. mul-1-neg 64.1%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(x \cdot \color{blue}{\left(-\frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      5. distribute-rgt-neg-in 64.1%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{\left(-x \cdot \frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      6. associate-/l* 56.1%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\left(-\color{blue}{\frac{x \cdot \left(z - t\right)}{a - t}}\right) + x \cdot 1\right) \]

      7. mul-1-neg 56.1%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} + x \cdot 1\right) \]

      8. *-rgt-identity 56.1%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \color{blue}{x}\right) \]

      9. associate-+l+ 54.0%

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(z - t\right)}{a - t} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) + x} \]

   5. Simplified 77.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)} \]

   6. Taylor expanded in y around inf 66.0%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 66.0%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

   8. Simplified 66.0%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   if -2.15000000000000012e-17 < t < -9.1999999999999993e-93

   1. Initial program 83.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 83.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. +-commutative 83.2%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. +-commutative 83.2%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{a - t} + 1\right)} \]

      3. distribute-lft-in 83.2%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \color{blue}{\left(x \cdot \left(-1 \cdot \frac{z - t}{a - t}\right) + x \cdot 1\right)} \]

      4. mul-1-neg 83.2%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(x \cdot \color{blue}{\left(-\frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      5. distribute-rgt-neg-in 83.2%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{\left(-x \cdot \frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      6. associate-/l* 83.3%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\left(-\color{blue}{\frac{x \cdot \left(z - t\right)}{a - t}}\right) + x \cdot 1\right) \]

      7. mul-1-neg 83.3%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} + x \cdot 1\right) \]

      8. *-rgt-identity 83.3%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \color{blue}{x}\right) \]

      9. associate-+l+ 83.4%

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(z - t\right)}{a - t} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) + x} \]

   5. Simplified 94.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)} \]

   6. Taylor expanded in z around inf 78.0%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 78.0%

         \[\leadsto z \cdot \color{blue}{\frac{y - x}{a - t}} \]

   8. Simplified 78.0%

      \[\leadsto \color{blue}{z \cdot \frac{y - x}{a - t}} \]

   if -9.1999999999999993e-93 < t < -6.5e-155 or -2.30000000000000012e-227 < t < 6.1999999999999999e-62

   1. Initial program 90.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 77.2%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* 83.2%

         \[\leadsto x + \color{blue}{z \cdot \frac{y - x}{a}} \]

   5. Simplified 83.2%

      \[\leadsto x + \color{blue}{z \cdot \frac{y - x}{a}} \]

   if -6.5e-155 < t < -4.8999999999999996e-224

   1. Initial program 99.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 64.4%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]

   4. Taylor expanded in y around 0 64.7%

      \[\leadsto x + \frac{\color{blue}{-1 \cdot \left(x \cdot z\right)}}{a} \]
   5. Step-by-step derivation

      1. mul-1-neg 64.7%

         \[\leadsto x + \frac{\color{blue}{-x \cdot z}}{a} \]

      2. distribute-lft-neg-out 64.7%

         \[\leadsto x + \frac{\color{blue}{\left(-x\right) \cdot z}}{a} \]

      3. *-commutative 64.7%

         \[\leadsto x + \frac{\color{blue}{z \cdot \left(-x\right)}}{a} \]

   6. Simplified 64.7%

      \[\leadsto x + \frac{\color{blue}{z \cdot \left(-x\right)}}{a} \]

   if -4.8999999999999996e-224 < t < -2.30000000000000012e-227

   1. Initial program 98.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 98.4%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. +-commutative 98.4%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. +-commutative 98.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{a - t} + 1\right)} \]

      3. distribute-lft-in 98.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \color{blue}{\left(x \cdot \left(-1 \cdot \frac{z - t}{a - t}\right) + x \cdot 1\right)} \]

      4. mul-1-neg 98.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(x \cdot \color{blue}{\left(-\frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      5. distribute-rgt-neg-in 98.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{\left(-x \cdot \frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      6. associate-/l* 98.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\left(-\color{blue}{\frac{x \cdot \left(z - t\right)}{a - t}}\right) + x \cdot 1\right) \]

      7. mul-1-neg 98.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} + x \cdot 1\right) \]

      8. *-rgt-identity 98.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \color{blue}{x}\right) \]

      9. associate-+l+ 98.4%

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(z - t\right)}{a - t} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) + x} \]

   5. Simplified 98.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)} \]

   6. Taylor expanded in y around inf 98.4%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 98.4%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

   8. Simplified 98.4%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   9. Taylor expanded in z around inf 98.4%

      \[\leadsto \color{blue}{\frac{y \cdot z}{a - t}} \]
   10. Step-by-step derivation

       1. associate-/l* 98.4%

          \[\leadsto \color{blue}{y \cdot \frac{z}{a - t}} \]

   11. Simplified 98.4%

       \[\leadsto \color{blue}{y \cdot \frac{z}{a - t}} \]

   if 56000 < t < 7.5e11

   1. Initial program 100.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 100.0%

      \[\leadsto \color{blue}{x} \]

   if 2.65e122 < t

   1. Initial program 25.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 76.9%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 76.9%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 76.9%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 76.9%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 76.9%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 76.9%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 76.9%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 83.2%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 86.0%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 86.0%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 86.0%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]
   6. Step-by-step derivation

      1. *-commutative 86.0%

         \[\leadsto y - \color{blue}{\left(z - a\right) \cdot \frac{y - x}{t}} \]

      2. clear-num 86.0%

         \[\leadsto y - \left(z - a\right) \cdot \color{blue}{\frac{1}{\frac{t}{y - x}}} \]

      3. un-div-inv 85.9%

         \[\leadsto y - \color{blue}{\frac{z - a}{\frac{t}{y - x}}} \]

   7. Applied egg-rr 85.9%

      \[\leadsto y - \color{blue}{\frac{z - a}{\frac{t}{y - x}}} \]

   8. Taylor expanded in y around 0 83.0%

      \[\leadsto y - \color{blue}{-1 \cdot \frac{x \cdot \left(z - a\right)}{t}} \]
   9. Step-by-step derivation

      1. mul-1-neg 83.0%

         \[\leadsto y - \color{blue}{\left(-\frac{x \cdot \left(z - a\right)}{t}\right)} \]

      2. associate-/l* 82.6%

         \[\leadsto y - \left(-\color{blue}{x \cdot \frac{z - a}{t}}\right) \]

   10. Simplified 82.6%

       \[\leadsto y - \color{blue}{\left(-x \cdot \frac{z - a}{t}\right)} \]

   11. Taylor expanded in z around 0 78.5%

       \[\leadsto \color{blue}{y + -1 \cdot \frac{a \cdot x}{t}} \]
   12. Step-by-step derivation

       1. mul-1-neg 78.5%

          \[\leadsto y + \color{blue}{\left(-\frac{a \cdot x}{t}\right)} \]

       2. *-commutative 78.5%

          \[\leadsto y + \left(-\frac{\color{blue}{x \cdot a}}{t}\right) \]

       3. associate-*r/ 78.0%

          \[\leadsto y + \left(-\color{blue}{x \cdot \frac{a}{t}}\right) \]

       4. unsub-neg 78.0%

          \[\leadsto \color{blue}{y - x \cdot \frac{a}{t}} \]

   13. Simplified 78.0%

       \[\leadsto \color{blue}{y - x \cdot \frac{a}{t}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{-17}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-93}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-155}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq -4.9 \cdot 10^{-224}:\\ \;\;\;\;x - \frac{x \cdot z}{a}\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{-227}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-62}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 56000:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 750000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{+122}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y - x \cdot \frac{a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 49.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{x - y}{t}\\ \mathbf{if}\;t \leq -3.7 \cdot 10^{+219}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{+156}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{+121}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{+81}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -0.043:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{-173}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-253}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-80}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ (- x y) t))))
   (if (<= t -3.7e+219)
     y
     (if (<= t -2.4e+156)
       t_1
       (if (<= t -2.3e+121)
         y
         (if (<= t -5.2e+81)
           t_1
           (if (<= t -2.7e+33)
             (* x (/ (- z a) t))
             (if (<= t -0.043)
               t_1
               (if (<= t -5.6e-173)
                 (+ x (/ y (/ a z)))
                 (if (<= t -4.2e-253)
                   (* x (- 1.0 (/ z a)))
                   (if (<= t 1.05e-80) (+ x (* y (/ z a))) y)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((x - y) / t);
	double tmp;
	if (t <= -3.7e+219) {
		tmp = y;
	} else if (t <= -2.4e+156) {
		tmp = t_1;
	} else if (t <= -2.3e+121) {
		tmp = y;
	} else if (t <= -5.2e+81) {
		tmp = t_1;
	} else if (t <= -2.7e+33) {
		tmp = x * ((z - a) / t);
	} else if (t <= -0.043) {
		tmp = t_1;
	} else if (t <= -5.6e-173) {
		tmp = x + (y / (a / z));
	} else if (t <= -4.2e-253) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 1.05e-80) {
		tmp = x + (y * (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * ((x - y) / t)
    if (t <= (-3.7d+219)) then
        tmp = y
    else if (t <= (-2.4d+156)) then
        tmp = t_1
    else if (t <= (-2.3d+121)) then
        tmp = y
    else if (t <= (-5.2d+81)) then
        tmp = t_1
    else if (t <= (-2.7d+33)) then
        tmp = x * ((z - a) / t)
    else if (t <= (-0.043d0)) then
        tmp = t_1
    else if (t <= (-5.6d-173)) then
        tmp = x + (y / (a / z))
    else if (t <= (-4.2d-253)) then
        tmp = x * (1.0d0 - (z / a))
    else if (t <= 1.05d-80) then
        tmp = x + (y * (z / a))
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((x - y) / t);
	double tmp;
	if (t <= -3.7e+219) {
		tmp = y;
	} else if (t <= -2.4e+156) {
		tmp = t_1;
	} else if (t <= -2.3e+121) {
		tmp = y;
	} else if (t <= -5.2e+81) {
		tmp = t_1;
	} else if (t <= -2.7e+33) {
		tmp = x * ((z - a) / t);
	} else if (t <= -0.043) {
		tmp = t_1;
	} else if (t <= -5.6e-173) {
		tmp = x + (y / (a / z));
	} else if (t <= -4.2e-253) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 1.05e-80) {
		tmp = x + (y * (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * ((x - y) / t)
	tmp = 0
	if t <= -3.7e+219:
		tmp = y
	elif t <= -2.4e+156:
		tmp = t_1
	elif t <= -2.3e+121:
		tmp = y
	elif t <= -5.2e+81:
		tmp = t_1
	elif t <= -2.7e+33:
		tmp = x * ((z - a) / t)
	elif t <= -0.043:
		tmp = t_1
	elif t <= -5.6e-173:
		tmp = x + (y / (a / z))
	elif t <= -4.2e-253:
		tmp = x * (1.0 - (z / a))
	elif t <= 1.05e-80:
		tmp = x + (y * (z / a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(Float64(x - y) / t))
	tmp = 0.0
	if (t <= -3.7e+219)
		tmp = y;
	elseif (t <= -2.4e+156)
		tmp = t_1;
	elseif (t <= -2.3e+121)
		tmp = y;
	elseif (t <= -5.2e+81)
		tmp = t_1;
	elseif (t <= -2.7e+33)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (t <= -0.043)
		tmp = t_1;
	elseif (t <= -5.6e-173)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= -4.2e-253)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (t <= 1.05e-80)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * ((x - y) / t);
	tmp = 0.0;
	if (t <= -3.7e+219)
		tmp = y;
	elseif (t <= -2.4e+156)
		tmp = t_1;
	elseif (t <= -2.3e+121)
		tmp = y;
	elseif (t <= -5.2e+81)
		tmp = t_1;
	elseif (t <= -2.7e+33)
		tmp = x * ((z - a) / t);
	elseif (t <= -0.043)
		tmp = t_1;
	elseif (t <= -5.6e-173)
		tmp = x + (y / (a / z));
	elseif (t <= -4.2e-253)
		tmp = x * (1.0 - (z / a));
	elseif (t <= 1.05e-80)
		tmp = x + (y * (z / a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.7e+219], y, If[LessEqual[t, -2.4e+156], t$95$1, If[LessEqual[t, -2.3e+121], y, If[LessEqual[t, -5.2e+81], t$95$1, If[LessEqual[t, -2.7e+33], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -0.043], t$95$1, If[LessEqual[t, -5.6e-173], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.2e-253], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.05e-80], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -3.7e219 or -2.4000000000000001e156 < t < -2.2999999999999999e121 or 1.05000000000000001e-80 < t

   1. Initial program 44.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 56.1%

      \[\leadsto \color{blue}{y} \]

   if -3.7e219 < t < -2.4000000000000001e156 or -2.2999999999999999e121 < t < -5.19999999999999984e81 or -2.69999999999999991e33 < t < -0.042999999999999997

   1. Initial program 55.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 57.9%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 57.9%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 57.9%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 57.9%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 57.9%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 57.9%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 57.9%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 71.4%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 78.5%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 78.5%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 78.5%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]

   6. Taylor expanded in z around inf 61.9%

      \[\leadsto \color{blue}{z \cdot \left(\frac{x}{t} - \frac{y}{t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 61.9%

         \[\leadsto z \cdot \color{blue}{\frac{x - y}{t}} \]

   8. Simplified 61.9%

      \[\leadsto \color{blue}{z \cdot \frac{x - y}{t}} \]

   if -5.19999999999999984e81 < t < -2.69999999999999991e33

   1. Initial program 58.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 73.7%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 73.7%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 73.7%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 73.7%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 73.7%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 73.7%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 73.7%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 73.7%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 73.5%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 73.5%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 73.5%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]

   6. Taylor expanded in y around 0 46.0%

      \[\leadsto \color{blue}{\frac{x \cdot \left(z - a\right)}{t}} \]
   7. Step-by-step derivation

      1. associate-/l* 45.7%

         \[\leadsto \color{blue}{x \cdot \frac{z - a}{t}} \]

   8. Simplified 45.7%

      \[\leadsto \color{blue}{x \cdot \frac{z - a}{t}} \]

   if -0.042999999999999997 < t < -5.5999999999999998e-173

   1. Initial program 83.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 62.0%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. associate-/l* 67.4%

         \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   5. Simplified 67.4%

      \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]
   6. Step-by-step derivation

      1. clear-num 67.4%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

      2. un-div-inv 67.4%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

   7. Applied egg-rr 67.4%

      \[\leadsto x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

   8. Taylor expanded in t around 0 55.7%

      \[\leadsto x + \frac{y}{\color{blue}{\frac{a}{z}}} \]

   if -5.5999999999999998e-173 < t < -4.1999999999999998e-253

   1. Initial program 99.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 61.0%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]

   4. Taylor expanded in x around inf 56.5%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z}{a}\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 56.5%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{z}{a}\right)}\right) \]

      2. unsub-neg 56.5%

         \[\leadsto x \cdot \color{blue}{\left(1 - \frac{z}{a}\right)} \]

   6. Simplified 56.5%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{a}\right)} \]

   if -4.1999999999999998e-253 < t < 1.05000000000000001e-80

   1. Initial program 90.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 76.0%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. associate-/l* 76.0%

         \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   5. Simplified 76.0%

      \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   6. Taylor expanded in t around 0 69.5%

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{a}} \]
   7. Step-by-step derivation

      1. associate-/l* 69.5%

         \[\leadsto x + \color{blue}{y \cdot \frac{z}{a}} \]

   8. Simplified 69.5%

      \[\leadsto x + \color{blue}{y \cdot \frac{z}{a}} \]
3. Recombined 6 regimes into one program.
4. Add Preprocessing

Alternative 23: 48.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{a}\\ t_2 := z \cdot \frac{x - y}{t}\\ \mathbf{if}\;t \leq -3.7 \cdot 10^{+219}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{+156}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{+121}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{+82}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -0.0305:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-172}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-253}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-87}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z a)))) (t_2 (* z (/ (- x y) t))))
   (if (<= t -3.7e+219)
     y
     (if (<= t -1.85e+156)
       t_2
       (if (<= t -1.8e+121)
         y
         (if (<= t -1.15e+82)
           t_2
           (if (<= t -3e+33)
             (* x (/ (- z a) t))
             (if (<= t -0.0305)
               t_2
               (if (<= t -1.9e-172)
                 t_1
                 (if (<= t -4.2e-253)
                   (* x (- 1.0 (/ z a)))
                   (if (<= t 6e-87) t_1 y)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / a));
	double t_2 = z * ((x - y) / t);
	double tmp;
	if (t <= -3.7e+219) {
		tmp = y;
	} else if (t <= -1.85e+156) {
		tmp = t_2;
	} else if (t <= -1.8e+121) {
		tmp = y;
	} else if (t <= -1.15e+82) {
		tmp = t_2;
	} else if (t <= -3e+33) {
		tmp = x * ((z - a) / t);
	} else if (t <= -0.0305) {
		tmp = t_2;
	} else if (t <= -1.9e-172) {
		tmp = t_1;
	} else if (t <= -4.2e-253) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 6e-87) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (y * (z / a))
    t_2 = z * ((x - y) / t)
    if (t <= (-3.7d+219)) then
        tmp = y
    else if (t <= (-1.85d+156)) then
        tmp = t_2
    else if (t <= (-1.8d+121)) then
        tmp = y
    else if (t <= (-1.15d+82)) then
        tmp = t_2
    else if (t <= (-3d+33)) then
        tmp = x * ((z - a) / t)
    else if (t <= (-0.0305d0)) then
        tmp = t_2
    else if (t <= (-1.9d-172)) then
        tmp = t_1
    else if (t <= (-4.2d-253)) then
        tmp = x * (1.0d0 - (z / a))
    else if (t <= 6d-87) then
        tmp = t_1
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / a));
	double t_2 = z * ((x - y) / t);
	double tmp;
	if (t <= -3.7e+219) {
		tmp = y;
	} else if (t <= -1.85e+156) {
		tmp = t_2;
	} else if (t <= -1.8e+121) {
		tmp = y;
	} else if (t <= -1.15e+82) {
		tmp = t_2;
	} else if (t <= -3e+33) {
		tmp = x * ((z - a) / t);
	} else if (t <= -0.0305) {
		tmp = t_2;
	} else if (t <= -1.9e-172) {
		tmp = t_1;
	} else if (t <= -4.2e-253) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 6e-87) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (z / a))
	t_2 = z * ((x - y) / t)
	tmp = 0
	if t <= -3.7e+219:
		tmp = y
	elif t <= -1.85e+156:
		tmp = t_2
	elif t <= -1.8e+121:
		tmp = y
	elif t <= -1.15e+82:
		tmp = t_2
	elif t <= -3e+33:
		tmp = x * ((z - a) / t)
	elif t <= -0.0305:
		tmp = t_2
	elif t <= -1.9e-172:
		tmp = t_1
	elif t <= -4.2e-253:
		tmp = x * (1.0 - (z / a))
	elif t <= 6e-87:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(z / a)))
	t_2 = Float64(z * Float64(Float64(x - y) / t))
	tmp = 0.0
	if (t <= -3.7e+219)
		tmp = y;
	elseif (t <= -1.85e+156)
		tmp = t_2;
	elseif (t <= -1.8e+121)
		tmp = y;
	elseif (t <= -1.15e+82)
		tmp = t_2;
	elseif (t <= -3e+33)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (t <= -0.0305)
		tmp = t_2;
	elseif (t <= -1.9e-172)
		tmp = t_1;
	elseif (t <= -4.2e-253)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (t <= 6e-87)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (z / a));
	t_2 = z * ((x - y) / t);
	tmp = 0.0;
	if (t <= -3.7e+219)
		tmp = y;
	elseif (t <= -1.85e+156)
		tmp = t_2;
	elseif (t <= -1.8e+121)
		tmp = y;
	elseif (t <= -1.15e+82)
		tmp = t_2;
	elseif (t <= -3e+33)
		tmp = x * ((z - a) / t);
	elseif (t <= -0.0305)
		tmp = t_2;
	elseif (t <= -1.9e-172)
		tmp = t_1;
	elseif (t <= -4.2e-253)
		tmp = x * (1.0 - (z / a));
	elseif (t <= 6e-87)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.7e+219], y, If[LessEqual[t, -1.85e+156], t$95$2, If[LessEqual[t, -1.8e+121], y, If[LessEqual[t, -1.15e+82], t$95$2, If[LessEqual[t, -3e+33], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -0.0305], t$95$2, If[LessEqual[t, -1.9e-172], t$95$1, If[LessEqual[t, -4.2e-253], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e-87], t$95$1, y]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -3.7e219 or -1.85000000000000001e156 < t < -1.79999999999999991e121 or 6.00000000000000033e-87 < t

   1. Initial program 44.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 55.1%

      \[\leadsto \color{blue}{y} \]

   if -3.7e219 < t < -1.85000000000000001e156 or -1.79999999999999991e121 < t < -1.14999999999999994e82 or -2.99999999999999984e33 < t < -0.030499999999999999

   1. Initial program 55.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 57.9%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 57.9%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 57.9%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 57.9%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 57.9%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 57.9%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 57.9%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 71.4%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 78.5%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 78.5%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 78.5%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]

   6. Taylor expanded in z around inf 61.9%

      \[\leadsto \color{blue}{z \cdot \left(\frac{x}{t} - \frac{y}{t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 61.9%

         \[\leadsto z \cdot \color{blue}{\frac{x - y}{t}} \]

   8. Simplified 61.9%

      \[\leadsto \color{blue}{z \cdot \frac{x - y}{t}} \]

   if -1.14999999999999994e82 < t < -2.99999999999999984e33

   1. Initial program 58.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 73.7%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 73.7%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 73.7%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 73.7%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 73.7%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 73.7%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 73.7%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 73.7%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 73.5%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 73.5%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 73.5%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]

   6. Taylor expanded in y around 0 46.0%

      \[\leadsto \color{blue}{\frac{x \cdot \left(z - a\right)}{t}} \]
   7. Step-by-step derivation

      1. associate-/l* 45.7%

         \[\leadsto \color{blue}{x \cdot \frac{z - a}{t}} \]

   8. Simplified 45.7%

      \[\leadsto \color{blue}{x \cdot \frac{z - a}{t}} \]

   if -0.030499999999999999 < t < -1.89999999999999993e-172 or -4.1999999999999998e-253 < t < 6.00000000000000033e-87

   1. Initial program 88.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 72.1%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. associate-/l* 74.1%

         \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   5. Simplified 74.1%

      \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   6. Taylor expanded in t around 0 63.5%

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{a}} \]
   7. Step-by-step derivation

      1. associate-/l* 65.5%

         \[\leadsto x + \color{blue}{y \cdot \frac{z}{a}} \]

   8. Simplified 65.5%

      \[\leadsto x + \color{blue}{y \cdot \frac{z}{a}} \]

   if -1.89999999999999993e-172 < t < -4.1999999999999998e-253

   1. Initial program 99.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 61.0%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]

   4. Taylor expanded in x around inf 56.5%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z}{a}\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 56.5%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{z}{a}\right)}\right) \]

      2. unsub-neg 56.5%

         \[\leadsto x \cdot \color{blue}{\left(1 - \frac{z}{a}\right)} \]

   6. Simplified 56.5%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{a}\right)} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 24: 71.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{\frac{a - t}{y - x}}\\ t_2 := x + y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -4.8 \cdot 10^{+27}:\\ \;\;\;\;y + \frac{z - a}{\frac{t}{x}}\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-9}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-11}:\\ \;\;\;\;y - x \cdot \frac{a}{t}\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-236}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.45 \cdot 10^{-265}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-272}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+174}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot \frac{z - a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ z (/ (- a t) (- y x)))) (t_2 (+ x (* y (/ (- z t) (- a t))))))
   (if (<= t -4.8e+27)
     (+ y (/ (- z a) (/ t x)))
     (if (<= t -1.7e-9)
       t_2
       (if (<= t -9.5e-11)
         (- y (* x (/ a t)))
         (if (<= t -1e-51)
           t_1
           (if (<= t -1.05e-236)
             t_2
             (if (<= t -2.45e-265)
               t_1
               (if (<= t 6.5e-272)
                 (+ x (/ (* (- y x) z) a))
                 (if (<= t 3.5e+174) t_2 (+ y (* x (/ (- z a) t)))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z / ((a - t) / (y - x));
	double t_2 = x + (y * ((z - t) / (a - t)));
	double tmp;
	if (t <= -4.8e+27) {
		tmp = y + ((z - a) / (t / x));
	} else if (t <= -1.7e-9) {
		tmp = t_2;
	} else if (t <= -9.5e-11) {
		tmp = y - (x * (a / t));
	} else if (t <= -1e-51) {
		tmp = t_1;
	} else if (t <= -1.05e-236) {
		tmp = t_2;
	} else if (t <= -2.45e-265) {
		tmp = t_1;
	} else if (t <= 6.5e-272) {
		tmp = x + (((y - x) * z) / a);
	} else if (t <= 3.5e+174) {
		tmp = t_2;
	} else {
		tmp = y + (x * ((z - a) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z / ((a - t) / (y - x))
    t_2 = x + (y * ((z - t) / (a - t)))
    if (t <= (-4.8d+27)) then
        tmp = y + ((z - a) / (t / x))
    else if (t <= (-1.7d-9)) then
        tmp = t_2
    else if (t <= (-9.5d-11)) then
        tmp = y - (x * (a / t))
    else if (t <= (-1d-51)) then
        tmp = t_1
    else if (t <= (-1.05d-236)) then
        tmp = t_2
    else if (t <= (-2.45d-265)) then
        tmp = t_1
    else if (t <= 6.5d-272) then
        tmp = x + (((y - x) * z) / a)
    else if (t <= 3.5d+174) then
        tmp = t_2
    else
        tmp = y + (x * ((z - a) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = z / ((a - t) / (y - x));
	double t_2 = x + (y * ((z - t) / (a - t)));
	double tmp;
	if (t <= -4.8e+27) {
		tmp = y + ((z - a) / (t / x));
	} else if (t <= -1.7e-9) {
		tmp = t_2;
	} else if (t <= -9.5e-11) {
		tmp = y - (x * (a / t));
	} else if (t <= -1e-51) {
		tmp = t_1;
	} else if (t <= -1.05e-236) {
		tmp = t_2;
	} else if (t <= -2.45e-265) {
		tmp = t_1;
	} else if (t <= 6.5e-272) {
		tmp = x + (((y - x) * z) / a);
	} else if (t <= 3.5e+174) {
		tmp = t_2;
	} else {
		tmp = y + (x * ((z - a) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z / ((a - t) / (y - x))
	t_2 = x + (y * ((z - t) / (a - t)))
	tmp = 0
	if t <= -4.8e+27:
		tmp = y + ((z - a) / (t / x))
	elif t <= -1.7e-9:
		tmp = t_2
	elif t <= -9.5e-11:
		tmp = y - (x * (a / t))
	elif t <= -1e-51:
		tmp = t_1
	elif t <= -1.05e-236:
		tmp = t_2
	elif t <= -2.45e-265:
		tmp = t_1
	elif t <= 6.5e-272:
		tmp = x + (((y - x) * z) / a)
	elif t <= 3.5e+174:
		tmp = t_2
	else:
		tmp = y + (x * ((z - a) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z / Float64(Float64(a - t) / Float64(y - x)))
	t_2 = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (t <= -4.8e+27)
		tmp = Float64(y + Float64(Float64(z - a) / Float64(t / x)));
	elseif (t <= -1.7e-9)
		tmp = t_2;
	elseif (t <= -9.5e-11)
		tmp = Float64(y - Float64(x * Float64(a / t)));
	elseif (t <= -1e-51)
		tmp = t_1;
	elseif (t <= -1.05e-236)
		tmp = t_2;
	elseif (t <= -2.45e-265)
		tmp = t_1;
	elseif (t <= 6.5e-272)
		tmp = Float64(x + Float64(Float64(Float64(y - x) * z) / a));
	elseif (t <= 3.5e+174)
		tmp = t_2;
	else
		tmp = Float64(y + Float64(x * Float64(Float64(z - a) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z / ((a - t) / (y - x));
	t_2 = x + (y * ((z - t) / (a - t)));
	tmp = 0.0;
	if (t <= -4.8e+27)
		tmp = y + ((z - a) / (t / x));
	elseif (t <= -1.7e-9)
		tmp = t_2;
	elseif (t <= -9.5e-11)
		tmp = y - (x * (a / t));
	elseif (t <= -1e-51)
		tmp = t_1;
	elseif (t <= -1.05e-236)
		tmp = t_2;
	elseif (t <= -2.45e-265)
		tmp = t_1;
	elseif (t <= 6.5e-272)
		tmp = x + (((y - x) * z) / a);
	elseif (t <= 3.5e+174)
		tmp = t_2;
	else
		tmp = y + (x * ((z - a) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z / N[(N[(a - t), $MachinePrecision] / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.8e+27], N[(y + N[(N[(z - a), $MachinePrecision] / N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.7e-9], t$95$2, If[LessEqual[t, -9.5e-11], N[(y - N[(x * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1e-51], t$95$1, If[LessEqual[t, -1.05e-236], t$95$2, If[LessEqual[t, -2.45e-265], t$95$1, If[LessEqual[t, 6.5e-272], N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.5e+174], t$95$2, N[(y + N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -4.79999999999999995e27

   1. Initial program 48.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 64.3%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 64.3%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 64.3%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 64.3%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 64.3%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 64.3%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 64.3%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 74.3%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 86.2%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 86.2%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 86.2%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]
   6. Step-by-step derivation

      1. *-commutative 86.2%

         \[\leadsto y - \color{blue}{\left(z - a\right) \cdot \frac{y - x}{t}} \]

      2. clear-num 86.2%

         \[\leadsto y - \left(z - a\right) \cdot \color{blue}{\frac{1}{\frac{t}{y - x}}} \]

      3. un-div-inv 86.2%

         \[\leadsto y - \color{blue}{\frac{z - a}{\frac{t}{y - x}}} \]

   7. Applied egg-rr 86.2%

      \[\leadsto y - \color{blue}{\frac{z - a}{\frac{t}{y - x}}} \]

   8. Taylor expanded in y around 0 76.2%

      \[\leadsto y - \frac{z - a}{\color{blue}{-1 \cdot \frac{t}{x}}} \]
   9. Step-by-step derivation

      1. associate-*r/ 76.2%

         \[\leadsto y - \frac{z - a}{\color{blue}{\frac{-1 \cdot t}{x}}} \]

      2. mul-1-neg 76.2%

         \[\leadsto y - \frac{z - a}{\frac{\color{blue}{-t}}{x}} \]

   10. Simplified 76.2%

       \[\leadsto y - \frac{z - a}{\color{blue}{\frac{-t}{x}}} \]

   if -4.79999999999999995e27 < t < -1.6999999999999999e-9 or -1e-51 < t < -1.04999999999999989e-236 or 6.5e-272 < t < 3.5000000000000001e174

   1. Initial program 80.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 67.1%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. associate-/l* 76.3%

         \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   5. Simplified 76.3%

      \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   if -1.6999999999999999e-9 < t < -9.49999999999999951e-11

   1. Initial program 51.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 100.0%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 100.0%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 100.0%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 100.0%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 100.0%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 100.0%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 100.0%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 100.0%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 99.2%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 99.2%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 99.2%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]
   6. Step-by-step derivation

      1. *-commutative 99.2%

         \[\leadsto y - \color{blue}{\left(z - a\right) \cdot \frac{y - x}{t}} \]

      2. clear-num 99.2%

         \[\leadsto y - \left(z - a\right) \cdot \color{blue}{\frac{1}{\frac{t}{y - x}}} \]

      3. un-div-inv 100.0%

         \[\leadsto y - \color{blue}{\frac{z - a}{\frac{t}{y - x}}} \]

   7. Applied egg-rr 100.0%

      \[\leadsto y - \color{blue}{\frac{z - a}{\frac{t}{y - x}}} \]

   8. Taylor expanded in y around 0 100.0%

      \[\leadsto y - \color{blue}{-1 \cdot \frac{x \cdot \left(z - a\right)}{t}} \]
   9. Step-by-step derivation

      1. mul-1-neg 100.0%

         \[\leadsto y - \color{blue}{\left(-\frac{x \cdot \left(z - a\right)}{t}\right)} \]

      2. associate-/l* 100.0%

         \[\leadsto y - \left(-\color{blue}{x \cdot \frac{z - a}{t}}\right) \]

   10. Simplified 100.0%

       \[\leadsto y - \color{blue}{\left(-x \cdot \frac{z - a}{t}\right)} \]

   11. Taylor expanded in z around 0 100.0%

       \[\leadsto \color{blue}{y + -1 \cdot \frac{a \cdot x}{t}} \]
   12. Step-by-step derivation

       1. mul-1-neg 100.0%

          \[\leadsto y + \color{blue}{\left(-\frac{a \cdot x}{t}\right)} \]

       2. *-commutative 100.0%

          \[\leadsto y + \left(-\frac{\color{blue}{x \cdot a}}{t}\right) \]

       3. associate-*r/ 100.0%

          \[\leadsto y + \left(-\color{blue}{x \cdot \frac{a}{t}}\right) \]

       4. unsub-neg 100.0%

          \[\leadsto \color{blue}{y - x \cdot \frac{a}{t}} \]

   13. Simplified 100.0%

       \[\leadsto \color{blue}{y - x \cdot \frac{a}{t}} \]

   if -9.49999999999999951e-11 < t < -1e-51 or -1.04999999999999989e-236 < t < -2.45e-265

   1. Initial program 88.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 81.0%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. +-commutative 81.0%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. +-commutative 81.0%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{a - t} + 1\right)} \]

      3. distribute-lft-in 81.0%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \color{blue}{\left(x \cdot \left(-1 \cdot \frac{z - t}{a - t}\right) + x \cdot 1\right)} \]

      4. mul-1-neg 81.0%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(x \cdot \color{blue}{\left(-\frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      5. distribute-rgt-neg-in 81.0%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{\left(-x \cdot \frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      6. associate-/l* 86.8%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\left(-\color{blue}{\frac{x \cdot \left(z - t\right)}{a - t}}\right) + x \cdot 1\right) \]

      7. mul-1-neg 86.8%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} + x \cdot 1\right) \]

      8. *-rgt-identity 86.8%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \color{blue}{x}\right) \]

      9. associate-+l+ 86.8%

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(z - t\right)}{a - t} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) + x} \]

   5. Simplified 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)} \]

   6. Taylor expanded in z around inf 93.6%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 93.6%

         \[\leadsto z \cdot \color{blue}{\frac{y - x}{a - t}} \]

   8. Simplified 93.6%

      \[\leadsto \color{blue}{z \cdot \frac{y - x}{a - t}} \]
   9. Step-by-step derivation

      1. clear-num 93.4%

         \[\leadsto z \cdot \color{blue}{\frac{1}{\frac{a - t}{y - x}}} \]

      2. un-div-inv 93.9%

         \[\leadsto \color{blue}{\frac{z}{\frac{a - t}{y - x}}} \]

   10. Applied egg-rr 93.9%

       \[\leadsto \color{blue}{\frac{z}{\frac{a - t}{y - x}}} \]

   if -2.45e-265 < t < 6.5e-272

   1. Initial program 100.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 100.0%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]

   if 3.5000000000000001e174 < t

   1. Initial program 18.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 85.8%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 85.8%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 85.8%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 85.8%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 85.8%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 85.8%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 85.8%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 85.7%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 89.2%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 89.2%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 89.2%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]
   6. Step-by-step derivation

      1. *-commutative 89.2%

         \[\leadsto y - \color{blue}{\left(z - a\right) \cdot \frac{y - x}{t}} \]

      2. clear-num 89.2%

         \[\leadsto y - \left(z - a\right) \cdot \color{blue}{\frac{1}{\frac{t}{y - x}}} \]

      3. un-div-inv 89.2%

         \[\leadsto y - \color{blue}{\frac{z - a}{\frac{t}{y - x}}} \]

   7. Applied egg-rr 89.2%

      \[\leadsto y - \color{blue}{\frac{z - a}{\frac{t}{y - x}}} \]

   8. Taylor expanded in y around 0 93.7%

      \[\leadsto y - \color{blue}{-1 \cdot \frac{x \cdot \left(z - a\right)}{t}} \]
   9. Step-by-step derivation

      1. mul-1-neg 93.7%

         \[\leadsto y - \color{blue}{\left(-\frac{x \cdot \left(z - a\right)}{t}\right)} \]

      2. associate-/l* 90.4%

         \[\leadsto y - \left(-\color{blue}{x \cdot \frac{z - a}{t}}\right) \]

   10. Simplified 90.4%

       \[\leadsto y - \color{blue}{\left(-x \cdot \frac{z - a}{t}\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+27}:\\ \;\;\;\;y + \frac{z - a}{\frac{t}{x}}\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-9}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-11}:\\ \;\;\;\;y - x \cdot \frac{a}{t}\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-51}:\\ \;\;\;\;\frac{z}{\frac{a - t}{y - x}}\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-236}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -2.45 \cdot 10^{-265}:\\ \;\;\;\;\frac{z}{\frac{a - t}{y - x}}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-272}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+174}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot \frac{z - a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 79.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y - x}{a - t}\\ \mathbf{if}\;t \leq -2.15 \cdot 10^{+30}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{-80}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-274}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-273}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{elif}\;t \leq 10^{-80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+47}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ (- y x) (- a t))))))
   (if (<= t -2.15e+30)
     (+ y (* (/ (- y x) t) (- a z)))
     (if (<= t -3.8e-80)
       t_1
       (if (<= t -3.7e-80)
         (* z (/ x t))
         (if (<= t -6.5e-274)
           t_1
           (if (<= t 5e-273)
             (+ x (/ (* (- y x) z) a))
             (if (<= t 1e-80)
               t_1
               (if (<= t 6.5e+47)
                 (+ x (* y (/ (- z t) (- a t))))
                 (+ y (* (- y x) (/ (- a z) t))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * ((y - x) / (a - t)));
	double tmp;
	if (t <= -2.15e+30) {
		tmp = y + (((y - x) / t) * (a - z));
	} else if (t <= -3.8e-80) {
		tmp = t_1;
	} else if (t <= -3.7e-80) {
		tmp = z * (x / t);
	} else if (t <= -6.5e-274) {
		tmp = t_1;
	} else if (t <= 5e-273) {
		tmp = x + (((y - x) * z) / a);
	} else if (t <= 1e-80) {
		tmp = t_1;
	} else if (t <= 6.5e+47) {
		tmp = x + (y * ((z - t) / (a - t)));
	} else {
		tmp = y + ((y - x) * ((a - z) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z * ((y - x) / (a - t)))
    if (t <= (-2.15d+30)) then
        tmp = y + (((y - x) / t) * (a - z))
    else if (t <= (-3.8d-80)) then
        tmp = t_1
    else if (t <= (-3.7d-80)) then
        tmp = z * (x / t)
    else if (t <= (-6.5d-274)) then
        tmp = t_1
    else if (t <= 5d-273) then
        tmp = x + (((y - x) * z) / a)
    else if (t <= 1d-80) then
        tmp = t_1
    else if (t <= 6.5d+47) then
        tmp = x + (y * ((z - t) / (a - t)))
    else
        tmp = y + ((y - x) * ((a - z) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * ((y - x) / (a - t)));
	double tmp;
	if (t <= -2.15e+30) {
		tmp = y + (((y - x) / t) * (a - z));
	} else if (t <= -3.8e-80) {
		tmp = t_1;
	} else if (t <= -3.7e-80) {
		tmp = z * (x / t);
	} else if (t <= -6.5e-274) {
		tmp = t_1;
	} else if (t <= 5e-273) {
		tmp = x + (((y - x) * z) / a);
	} else if (t <= 1e-80) {
		tmp = t_1;
	} else if (t <= 6.5e+47) {
		tmp = x + (y * ((z - t) / (a - t)));
	} else {
		tmp = y + ((y - x) * ((a - z) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * ((y - x) / (a - t)))
	tmp = 0
	if t <= -2.15e+30:
		tmp = y + (((y - x) / t) * (a - z))
	elif t <= -3.8e-80:
		tmp = t_1
	elif t <= -3.7e-80:
		tmp = z * (x / t)
	elif t <= -6.5e-274:
		tmp = t_1
	elif t <= 5e-273:
		tmp = x + (((y - x) * z) / a)
	elif t <= 1e-80:
		tmp = t_1
	elif t <= 6.5e+47:
		tmp = x + (y * ((z - t) / (a - t)))
	else:
		tmp = y + ((y - x) * ((a - z) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(Float64(y - x) / Float64(a - t))))
	tmp = 0.0
	if (t <= -2.15e+30)
		tmp = Float64(y + Float64(Float64(Float64(y - x) / t) * Float64(a - z)));
	elseif (t <= -3.8e-80)
		tmp = t_1;
	elseif (t <= -3.7e-80)
		tmp = Float64(z * Float64(x / t));
	elseif (t <= -6.5e-274)
		tmp = t_1;
	elseif (t <= 5e-273)
		tmp = Float64(x + Float64(Float64(Float64(y - x) * z) / a));
	elseif (t <= 1e-80)
		tmp = t_1;
	elseif (t <= 6.5e+47)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))));
	else
		tmp = Float64(y + Float64(Float64(y - x) * Float64(Float64(a - z) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * ((y - x) / (a - t)));
	tmp = 0.0;
	if (t <= -2.15e+30)
		tmp = y + (((y - x) / t) * (a - z));
	elseif (t <= -3.8e-80)
		tmp = t_1;
	elseif (t <= -3.7e-80)
		tmp = z * (x / t);
	elseif (t <= -6.5e-274)
		tmp = t_1;
	elseif (t <= 5e-273)
		tmp = x + (((y - x) * z) / a);
	elseif (t <= 1e-80)
		tmp = t_1;
	elseif (t <= 6.5e+47)
		tmp = x + (y * ((z - t) / (a - t)));
	else
		tmp = y + ((y - x) * ((a - z) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.15e+30], N[(y + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.8e-80], t$95$1, If[LessEqual[t, -3.7e-80], N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6.5e-274], t$95$1, If[LessEqual[t, 5e-273], N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e-80], t$95$1, If[LessEqual[t, 6.5e+47], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(y - x), $MachinePrecision] * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -2.15e30

   1. Initial program 47.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 63.6%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 63.6%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 63.6%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 63.6%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 63.6%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 63.6%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 63.6%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 73.8%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 85.9%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 85.9%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 85.9%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]

   if -2.15e30 < t < -3.79999999999999967e-80 or -3.70000000000000033e-80 < t < -6.49999999999999959e-274 or 4.99999999999999965e-273 < t < 9.99999999999999961e-81

   1. Initial program 88.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 81.6%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a - t}} \]
   4. Step-by-step derivation

      1. associate-/l* 88.0%

         \[\leadsto x + \color{blue}{z \cdot \frac{y - x}{a - t}} \]

   5. Simplified 88.0%

      \[\leadsto x + \color{blue}{z \cdot \frac{y - x}{a - t}} \]

   if -3.79999999999999967e-80 < t < -3.70000000000000033e-80

   1. Initial program 3.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 100.0%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 100.0%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 100.0%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 100.0%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 100.0%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 100.0%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 100.0%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 100.0%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 100.0%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 100.0%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 100.0%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]

   6. Taylor expanded in z around inf 100.0%

      \[\leadsto \color{blue}{z \cdot \left(\frac{x}{t} - \frac{y}{t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 100.0%

         \[\leadsto z \cdot \color{blue}{\frac{x - y}{t}} \]

   8. Simplified 100.0%

      \[\leadsto \color{blue}{z \cdot \frac{x - y}{t}} \]

   9. Taylor expanded in x around inf 100.0%

      \[\leadsto z \cdot \color{blue}{\frac{x}{t}} \]

   if -6.49999999999999959e-274 < t < 4.99999999999999965e-273

   1. Initial program 100.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 100.0%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]

   if 9.99999999999999961e-81 < t < 6.49999999999999988e47

   1. Initial program 80.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 69.4%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. associate-/l* 77.0%

         \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   5. Simplified 77.0%

      \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   if 6.49999999999999988e47 < t

   1. Initial program 28.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 47.9%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. +-commutative 47.9%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. +-commutative 47.9%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{a - t} + 1\right)} \]

      3. distribute-lft-in 47.9%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \color{blue}{\left(x \cdot \left(-1 \cdot \frac{z - t}{a - t}\right) + x \cdot 1\right)} \]

      4. mul-1-neg 47.9%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(x \cdot \color{blue}{\left(-\frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      5. distribute-rgt-neg-in 47.9%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{\left(-x \cdot \frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      6. associate-/l* 29.8%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\left(-\color{blue}{\frac{x \cdot \left(z - t\right)}{a - t}}\right) + x \cdot 1\right) \]

      7. mul-1-neg 29.8%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} + x \cdot 1\right) \]

      8. *-rgt-identity 29.8%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \color{blue}{x}\right) \]

      9. associate-+l+ 28.2%

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(z - t\right)}{a - t} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) + x} \]

   5. Simplified 61.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)} \]

   6. Taylor expanded in t around inf 74.6%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   7. Step-by-step derivation

      1. cancel-sign-sub-inv 74.6%

         \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) + \left(--1\right) \cdot \frac{a \cdot \left(y - x\right)}{t}} \]

      2. mul-1-neg 74.6%

         \[\leadsto \left(y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right)}{t}\right)}\right) + \left(--1\right) \cdot \frac{a \cdot \left(y - x\right)}{t} \]

      3. sub-neg 74.6%

         \[\leadsto \color{blue}{\left(y - \frac{z \cdot \left(y - x\right)}{t}\right)} + \left(--1\right) \cdot \frac{a \cdot \left(y - x\right)}{t} \]

      4. metadata-eval 74.6%

         \[\leadsto \left(y - \frac{z \cdot \left(y - x\right)}{t}\right) + \color{blue}{1} \cdot \frac{a \cdot \left(y - x\right)}{t} \]

      5. *-lft-identity 74.6%

         \[\leadsto \left(y - \frac{z \cdot \left(y - x\right)}{t}\right) + \color{blue}{\frac{a \cdot \left(y - x\right)}{t}} \]

      6. *-commutative 74.6%

         \[\leadsto \left(y - \frac{z \cdot \left(y - x\right)}{t}\right) + \frac{\color{blue}{\left(y - x\right) \cdot a}}{t} \]

      7. associate-+l- 74.6%

         \[\leadsto \color{blue}{y - \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{\left(y - x\right) \cdot a}{t}\right)} \]

      8. div-sub 74.6%

         \[\leadsto y - \color{blue}{\frac{z \cdot \left(y - x\right) - \left(y - x\right) \cdot a}{t}} \]

      9. *-commutative 74.6%

         \[\leadsto y - \frac{z \cdot \left(y - x\right) - \color{blue}{a \cdot \left(y - x\right)}}{t} \]

      10. distribute-rgt-out-- 74.7%

          \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

      11. associate-*r/ 85.6%

          \[\leadsto y - \color{blue}{\left(y - x\right) \cdot \frac{z - a}{t}} \]

   8. Simplified 85.6%

      \[\leadsto \color{blue}{y - \left(y - x\right) \cdot \frac{z - a}{t}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{+30}:\\ \;\;\;\;y + \frac{y - x}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-80}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{-80}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-274}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-273}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{elif}\;t \leq 10^{-80}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+47}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 76.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z - t}{a - t}\\ t_2 := y + \frac{z - a}{\frac{t}{x}}\\ \mathbf{if}\;t \leq -8.6 \cdot 10^{+29}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-9}:\\ \;\;\;\;x \cdot \frac{a}{-t}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-82}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+87}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 10^{+177}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot \frac{z - a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ (- z t) (- a t))))) (t_2 (+ y (/ (- z a) (/ t x)))))
   (if (<= t -8.6e+29)
     t_2
     (if (<= t -1.7e-9)
       t_1
       (if (<= t -1.65e-9)
         (* x (/ a (- t)))
         (if (<= t 1.75e-82)
           (+ x (* z (/ (- y x) (- a t))))
           (if (<= t 1.4e+48)
             t_1
             (if (<= t 1.6e+87)
               t_2
               (if (<= t 1e+177) t_1 (+ y (* x (/ (- z a) t))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / (a - t)));
	double t_2 = y + ((z - a) / (t / x));
	double tmp;
	if (t <= -8.6e+29) {
		tmp = t_2;
	} else if (t <= -1.7e-9) {
		tmp = t_1;
	} else if (t <= -1.65e-9) {
		tmp = x * (a / -t);
	} else if (t <= 1.75e-82) {
		tmp = x + (z * ((y - x) / (a - t)));
	} else if (t <= 1.4e+48) {
		tmp = t_1;
	} else if (t <= 1.6e+87) {
		tmp = t_2;
	} else if (t <= 1e+177) {
		tmp = t_1;
	} else {
		tmp = y + (x * ((z - a) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (y * ((z - t) / (a - t)))
    t_2 = y + ((z - a) / (t / x))
    if (t <= (-8.6d+29)) then
        tmp = t_2
    else if (t <= (-1.7d-9)) then
        tmp = t_1
    else if (t <= (-1.65d-9)) then
        tmp = x * (a / -t)
    else if (t <= 1.75d-82) then
        tmp = x + (z * ((y - x) / (a - t)))
    else if (t <= 1.4d+48) then
        tmp = t_1
    else if (t <= 1.6d+87) then
        tmp = t_2
    else if (t <= 1d+177) then
        tmp = t_1
    else
        tmp = y + (x * ((z - a) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / (a - t)));
	double t_2 = y + ((z - a) / (t / x));
	double tmp;
	if (t <= -8.6e+29) {
		tmp = t_2;
	} else if (t <= -1.7e-9) {
		tmp = t_1;
	} else if (t <= -1.65e-9) {
		tmp = x * (a / -t);
	} else if (t <= 1.75e-82) {
		tmp = x + (z * ((y - x) / (a - t)));
	} else if (t <= 1.4e+48) {
		tmp = t_1;
	} else if (t <= 1.6e+87) {
		tmp = t_2;
	} else if (t <= 1e+177) {
		tmp = t_1;
	} else {
		tmp = y + (x * ((z - a) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * ((z - t) / (a - t)))
	t_2 = y + ((z - a) / (t / x))
	tmp = 0
	if t <= -8.6e+29:
		tmp = t_2
	elif t <= -1.7e-9:
		tmp = t_1
	elif t <= -1.65e-9:
		tmp = x * (a / -t)
	elif t <= 1.75e-82:
		tmp = x + (z * ((y - x) / (a - t)))
	elif t <= 1.4e+48:
		tmp = t_1
	elif t <= 1.6e+87:
		tmp = t_2
	elif t <= 1e+177:
		tmp = t_1
	else:
		tmp = y + (x * ((z - a) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))))
	t_2 = Float64(y + Float64(Float64(z - a) / Float64(t / x)))
	tmp = 0.0
	if (t <= -8.6e+29)
		tmp = t_2;
	elseif (t <= -1.7e-9)
		tmp = t_1;
	elseif (t <= -1.65e-9)
		tmp = Float64(x * Float64(a / Float64(-t)));
	elseif (t <= 1.75e-82)
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / Float64(a - t))));
	elseif (t <= 1.4e+48)
		tmp = t_1;
	elseif (t <= 1.6e+87)
		tmp = t_2;
	elseif (t <= 1e+177)
		tmp = t_1;
	else
		tmp = Float64(y + Float64(x * Float64(Float64(z - a) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * ((z - t) / (a - t)));
	t_2 = y + ((z - a) / (t / x));
	tmp = 0.0;
	if (t <= -8.6e+29)
		tmp = t_2;
	elseif (t <= -1.7e-9)
		tmp = t_1;
	elseif (t <= -1.65e-9)
		tmp = x * (a / -t);
	elseif (t <= 1.75e-82)
		tmp = x + (z * ((y - x) / (a - t)));
	elseif (t <= 1.4e+48)
		tmp = t_1;
	elseif (t <= 1.6e+87)
		tmp = t_2;
	elseif (t <= 1e+177)
		tmp = t_1;
	else
		tmp = y + (x * ((z - a) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(N[(z - a), $MachinePrecision] / N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.6e+29], t$95$2, If[LessEqual[t, -1.7e-9], t$95$1, If[LessEqual[t, -1.65e-9], N[(x * N[(a / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.75e-82], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.4e+48], t$95$1, If[LessEqual[t, 1.6e+87], t$95$2, If[LessEqual[t, 1e+177], t$95$1, N[(y + N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -8.6000000000000006e29 or 1.40000000000000006e48 < t < 1.6e87

   1. Initial program 47.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 65.9%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 65.9%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 65.9%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 65.9%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 65.9%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 65.9%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 65.9%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 77.4%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 87.9%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 87.9%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 87.9%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]
   6. Step-by-step derivation

      1. *-commutative 87.9%

         \[\leadsto y - \color{blue}{\left(z - a\right) \cdot \frac{y - x}{t}} \]

      2. clear-num 87.8%

         \[\leadsto y - \left(z - a\right) \cdot \color{blue}{\frac{1}{\frac{t}{y - x}}} \]

      3. un-div-inv 87.9%

         \[\leadsto y - \color{blue}{\frac{z - a}{\frac{t}{y - x}}} \]

   7. Applied egg-rr 87.9%

      \[\leadsto y - \color{blue}{\frac{z - a}{\frac{t}{y - x}}} \]

   8. Taylor expanded in y around 0 76.1%

      \[\leadsto y - \frac{z - a}{\color{blue}{-1 \cdot \frac{t}{x}}} \]
   9. Step-by-step derivation

      1. associate-*r/ 76.1%

         \[\leadsto y - \frac{z - a}{\color{blue}{\frac{-1 \cdot t}{x}}} \]

      2. mul-1-neg 76.1%

         \[\leadsto y - \frac{z - a}{\frac{\color{blue}{-t}}{x}} \]

   10. Simplified 76.1%

       \[\leadsto y - \frac{z - a}{\color{blue}{\frac{-t}{x}}} \]

   if -8.6000000000000006e29 < t < -1.6999999999999999e-9 or 1.7499999999999999e-82 < t < 1.40000000000000006e48 or 1.6e87 < t < 1e177

   1. Initial program 72.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 65.9%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. associate-/l* 81.1%

         \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   5. Simplified 81.1%

      \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   if -1.6999999999999999e-9 < t < -1.65000000000000009e-9

   1. Initial program 3.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 100.0%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 100.0%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 100.0%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 100.0%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 100.0%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 100.0%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 100.0%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 100.0%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 98.4%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 98.4%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 98.4%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]

   6. Taylor expanded in y around 0 100.0%

      \[\leadsto \color{blue}{\frac{x \cdot \left(z - a\right)}{t}} \]

   7. Taylor expanded in z around 0 100.0%

      \[\leadsto \frac{\color{blue}{-1 \cdot \left(a \cdot x\right)}}{t} \]
   8. Step-by-step derivation

      1. mul-1-neg 100.0%

         \[\leadsto \frac{\color{blue}{-a \cdot x}}{t} \]

      2. distribute-rgt-neg-in 100.0%

         \[\leadsto \frac{\color{blue}{a \cdot \left(-x\right)}}{t} \]

   9. Simplified 100.0%

      \[\leadsto \frac{\color{blue}{a \cdot \left(-x\right)}}{t} \]
   10. Step-by-step derivation

       1. *-commutative 100.0%

          \[\leadsto \frac{\color{blue}{\left(-x\right) \cdot a}}{t} \]

       2. associate-/l* 100.0%

          \[\leadsto \color{blue}{\left(-x\right) \cdot \frac{a}{t}} \]

       3. add-sqr-sqrt 0.0%

          \[\leadsto \color{blue}{\left(\sqrt{-x} \cdot \sqrt{-x}\right)} \cdot \frac{a}{t} \]

       4. sqrt-unprod 1.6%

          \[\leadsto \color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}} \cdot \frac{a}{t} \]

       5. sqr-neg 1.6%

          \[\leadsto \sqrt{\color{blue}{x \cdot x}} \cdot \frac{a}{t} \]

       6. sqrt-unprod 1.6%

          \[\leadsto \color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)} \cdot \frac{a}{t} \]

       7. add-sqr-sqrt 1.6%

          \[\leadsto \color{blue}{x} \cdot \frac{a}{t} \]

   11. Applied egg-rr 1.6%

       \[\leadsto \color{blue}{x \cdot \frac{a}{t}} \]
   12. Step-by-step derivation

       1. frac-2neg 1.6%

          \[\leadsto x \cdot \color{blue}{\frac{-a}{-t}} \]

       2. associate-*r/ 1.6%

          \[\leadsto \color{blue}{\frac{x \cdot \left(-a\right)}{-t}} \]

       3. add-sqr-sqrt 1.6%

          \[\leadsto \frac{x \cdot \left(-a\right)}{\color{blue}{\sqrt{-t} \cdot \sqrt{-t}}} \]

       4. sqrt-unprod 1.6%

          \[\leadsto \frac{x \cdot \left(-a\right)}{\color{blue}{\sqrt{\left(-t\right) \cdot \left(-t\right)}}} \]

       5. sqr-neg 1.6%

          \[\leadsto \frac{x \cdot \left(-a\right)}{\sqrt{\color{blue}{t \cdot t}}} \]

       6. sqrt-unprod 0.0%

          \[\leadsto \frac{x \cdot \left(-a\right)}{\color{blue}{\sqrt{t} \cdot \sqrt{t}}} \]

       7. add-sqr-sqrt 100.0%

          \[\leadsto \frac{x \cdot \left(-a\right)}{\color{blue}{t}} \]

   13. Applied egg-rr 100.0%

       \[\leadsto \color{blue}{\frac{x \cdot \left(-a\right)}{t}} \]
   14. Step-by-step derivation

       1. associate-/l* 100.0%

          \[\leadsto \color{blue}{x \cdot \frac{-a}{t}} \]

   15. Simplified 100.0%

       \[\leadsto \color{blue}{x \cdot \frac{-a}{t}} \]

   if -1.65000000000000009e-9 < t < 1.7499999999999999e-82

   1. Initial program 90.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 85.7%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a - t}} \]
   4. Step-by-step derivation

      1. associate-/l* 89.9%

         \[\leadsto x + \color{blue}{z \cdot \frac{y - x}{a - t}} \]

   5. Simplified 89.9%

      \[\leadsto x + \color{blue}{z \cdot \frac{y - x}{a - t}} \]

   if 1e177 < t

   1. Initial program 18.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 85.8%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 85.8%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 85.8%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 85.8%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 85.8%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 85.8%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 85.8%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 85.7%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 89.2%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 89.2%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 89.2%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]
   6. Step-by-step derivation

      1. *-commutative 89.2%

         \[\leadsto y - \color{blue}{\left(z - a\right) \cdot \frac{y - x}{t}} \]

      2. clear-num 89.2%

         \[\leadsto y - \left(z - a\right) \cdot \color{blue}{\frac{1}{\frac{t}{y - x}}} \]

      3. un-div-inv 89.2%

         \[\leadsto y - \color{blue}{\frac{z - a}{\frac{t}{y - x}}} \]

   7. Applied egg-rr 89.2%

      \[\leadsto y - \color{blue}{\frac{z - a}{\frac{t}{y - x}}} \]

   8. Taylor expanded in y around 0 93.7%

      \[\leadsto y - \color{blue}{-1 \cdot \frac{x \cdot \left(z - a\right)}{t}} \]
   9. Step-by-step derivation

      1. mul-1-neg 93.7%

         \[\leadsto y - \color{blue}{\left(-\frac{x \cdot \left(z - a\right)}{t}\right)} \]

      2. associate-/l* 90.4%

         \[\leadsto y - \left(-\color{blue}{x \cdot \frac{z - a}{t}}\right) \]

   10. Simplified 90.4%

       \[\leadsto y - \color{blue}{\left(-x \cdot \frac{z - a}{t}\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{+29}:\\ \;\;\;\;y + \frac{z - a}{\frac{t}{x}}\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-9}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-9}:\\ \;\;\;\;x \cdot \frac{a}{-t}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-82}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+48}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+87}:\\ \;\;\;\;y + \frac{z - a}{\frac{t}{x}}\\ \mathbf{elif}\;t \leq 10^{+177}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot \frac{z - a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 32.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+121}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-52}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-195}:\\ \;\;\;\;\frac{x \cdot z}{t}\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-254}:\\ \;\;\;\;t \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-281}:\\ \;\;\;\;x \cdot \frac{z}{-a}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-173}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-79}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -5.5e+121)
   y
   (if (<= t -5.5e-52)
     (* z (/ x t))
     (if (<= t -2.1e-195)
       (/ (* x z) t)
       (if (<= t -1.35e-254)
         (* t (/ x t))
         (if (<= t -8e-281)
           (* x (/ z (- a)))
           (if (<= t 3e-173) x (if (<= t 9e-79) (* t (/ (- y) a)) y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.5e+121) {
		tmp = y;
	} else if (t <= -5.5e-52) {
		tmp = z * (x / t);
	} else if (t <= -2.1e-195) {
		tmp = (x * z) / t;
	} else if (t <= -1.35e-254) {
		tmp = t * (x / t);
	} else if (t <= -8e-281) {
		tmp = x * (z / -a);
	} else if (t <= 3e-173) {
		tmp = x;
	} else if (t <= 9e-79) {
		tmp = t * (-y / a);
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-5.5d+121)) then
        tmp = y
    else if (t <= (-5.5d-52)) then
        tmp = z * (x / t)
    else if (t <= (-2.1d-195)) then
        tmp = (x * z) / t
    else if (t <= (-1.35d-254)) then
        tmp = t * (x / t)
    else if (t <= (-8d-281)) then
        tmp = x * (z / -a)
    else if (t <= 3d-173) then
        tmp = x
    else if (t <= 9d-79) then
        tmp = t * (-y / a)
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.5e+121) {
		tmp = y;
	} else if (t <= -5.5e-52) {
		tmp = z * (x / t);
	} else if (t <= -2.1e-195) {
		tmp = (x * z) / t;
	} else if (t <= -1.35e-254) {
		tmp = t * (x / t);
	} else if (t <= -8e-281) {
		tmp = x * (z / -a);
	} else if (t <= 3e-173) {
		tmp = x;
	} else if (t <= 9e-79) {
		tmp = t * (-y / a);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -5.5e+121:
		tmp = y
	elif t <= -5.5e-52:
		tmp = z * (x / t)
	elif t <= -2.1e-195:
		tmp = (x * z) / t
	elif t <= -1.35e-254:
		tmp = t * (x / t)
	elif t <= -8e-281:
		tmp = x * (z / -a)
	elif t <= 3e-173:
		tmp = x
	elif t <= 9e-79:
		tmp = t * (-y / a)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -5.5e+121)
		tmp = y;
	elseif (t <= -5.5e-52)
		tmp = Float64(z * Float64(x / t));
	elseif (t <= -2.1e-195)
		tmp = Float64(Float64(x * z) / t);
	elseif (t <= -1.35e-254)
		tmp = Float64(t * Float64(x / t));
	elseif (t <= -8e-281)
		tmp = Float64(x * Float64(z / Float64(-a)));
	elseif (t <= 3e-173)
		tmp = x;
	elseif (t <= 9e-79)
		tmp = Float64(t * Float64(Float64(-y) / a));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -5.5e+121)
		tmp = y;
	elseif (t <= -5.5e-52)
		tmp = z * (x / t);
	elseif (t <= -2.1e-195)
		tmp = (x * z) / t;
	elseif (t <= -1.35e-254)
		tmp = t * (x / t);
	elseif (t <= -8e-281)
		tmp = x * (z / -a);
	elseif (t <= 3e-173)
		tmp = x;
	elseif (t <= 9e-79)
		tmp = t * (-y / a);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -5.5e+121], y, If[LessEqual[t, -5.5e-52], N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.1e-195], N[(N[(x * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, -1.35e-254], N[(t * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -8e-281], N[(x * N[(z / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3e-173], x, If[LessEqual[t, 9e-79], N[(t * N[((-y) / a), $MachinePrecision]), $MachinePrecision], y]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -5.4999999999999998e121 or 9.0000000000000006e-79 < t

   1. Initial program 43.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 52.8%

      \[\leadsto \color{blue}{y} \]

   if -5.4999999999999998e121 < t < -5.5e-52

   1. Initial program 69.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 64.0%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 64.0%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 64.0%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 64.0%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 64.0%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 64.0%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 64.0%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 66.8%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 63.9%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 66.7%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 66.7%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]

   6. Taylor expanded in z around inf 42.3%

      \[\leadsto \color{blue}{z \cdot \left(\frac{x}{t} - \frac{y}{t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 42.3%

         \[\leadsto z \cdot \color{blue}{\frac{x - y}{t}} \]

   8. Simplified 42.3%

      \[\leadsto \color{blue}{z \cdot \frac{x - y}{t}} \]

   9. Taylor expanded in x around inf 31.3%

      \[\leadsto z \cdot \color{blue}{\frac{x}{t}} \]

   if -5.5e-52 < t < -2.1e-195

   1. Initial program 87.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 42.6%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 42.6%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 42.6%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 45.7%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 45.7%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 45.7%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 42.6%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 36.3%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 32.9%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 39.8%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 39.8%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]

   6. Taylor expanded in y around 0 34.3%

      \[\leadsto \color{blue}{\frac{x \cdot \left(z - a\right)}{t}} \]

   7. Taylor expanded in z around inf 34.2%

      \[\leadsto \frac{\color{blue}{x \cdot z}}{t} \]
   8. Step-by-step derivation

      1. *-commutative 34.2%

         \[\leadsto \frac{\color{blue}{z \cdot x}}{t} \]

   9. Simplified 34.2%

      \[\leadsto \frac{\color{blue}{z \cdot x}}{t} \]

   if -2.1e-195 < t < -1.35000000000000003e-254

   1. Initial program 99.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 80.3%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. associate-/l* 74.4%

         \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   5. Simplified 74.4%

      \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]
   6. Step-by-step derivation

      1. clear-num 74.4%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

      2. inv-pow 74.4%

         \[\leadsto x + y \cdot \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}} \]

   7. Applied egg-rr 74.4%

      \[\leadsto x + y \cdot \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}} \]
   8. Step-by-step derivation

      1. unpow-1 74.4%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

   9. Simplified 74.4%

      \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

   10. Taylor expanded in z around 0 42.1%

       \[\leadsto \color{blue}{x + -1 \cdot \frac{t \cdot y}{a - t}} \]
   11. Step-by-step derivation

       1. mul-1-neg 42.1%

          \[\leadsto x + \color{blue}{\left(-\frac{t \cdot y}{a - t}\right)} \]

       2. unsub-neg 42.1%

          \[\leadsto \color{blue}{x - \frac{t \cdot y}{a - t}} \]

       3. associate-/l* 48.4%

          \[\leadsto x - \color{blue}{t \cdot \frac{y}{a - t}} \]

   12. Simplified 48.4%

       \[\leadsto \color{blue}{x - t \cdot \frac{y}{a - t}} \]

   13. Taylor expanded in t around 0 42.0%

       \[\leadsto x - \color{blue}{\frac{t \cdot y}{a}} \]
   14. Step-by-step derivation

       1. associate-/l* 42.0%

          \[\leadsto x - \color{blue}{t \cdot \frac{y}{a}} \]

   15. Simplified 42.0%

       \[\leadsto x - \color{blue}{t \cdot \frac{y}{a}} \]

   16. Taylor expanded in t around inf 54.5%

       \[\leadsto \color{blue}{t \cdot \left(\frac{x}{t} - \frac{y}{a}\right)} \]

   17. Taylor expanded in x around inf 54.6%

       \[\leadsto t \cdot \color{blue}{\frac{x}{t}} \]

   if -1.35000000000000003e-254 < t < -8.0000000000000001e-281

   1. Initial program 85.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 85.0%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]

   4. Taylor expanded in z around inf 70.6%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a} - \frac{x}{a}\right)} \]
   5. Step-by-step derivation

      1. div-sub 70.6%

         \[\leadsto z \cdot \color{blue}{\frac{y - x}{a}} \]

      2. associate-*r/ 70.7%

         \[\leadsto \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]

      3. *-commutative 70.7%

         \[\leadsto \frac{\color{blue}{\left(y - x\right) \cdot z}}{a} \]

      4. associate-*r/ 85.2%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z}{a}} \]

      5. *-commutative 85.2%

         \[\leadsto \color{blue}{\frac{z}{a} \cdot \left(y - x\right)} \]

   6. Simplified 85.2%

      \[\leadsto \color{blue}{\frac{z}{a} \cdot \left(y - x\right)} \]

   7. Taylor expanded in y around 0 54.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot z}{a}} \]
   8. Step-by-step derivation

      1. mul-1-neg 54.0%

         \[\leadsto \color{blue}{-\frac{x \cdot z}{a}} \]

      2. associate-/l* 68.6%

         \[\leadsto -\color{blue}{x \cdot \frac{z}{a}} \]

      3. distribute-lft-neg-out 68.6%

         \[\leadsto \color{blue}{\left(-x\right) \cdot \frac{z}{a}} \]

      4. *-commutative 68.6%

         \[\leadsto \color{blue}{\frac{z}{a} \cdot \left(-x\right)} \]

   9. Simplified 68.6%

      \[\leadsto \color{blue}{\frac{z}{a} \cdot \left(-x\right)} \]

   if -8.0000000000000001e-281 < t < 3.0000000000000001e-173

   1. Initial program 92.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 54.0%

      \[\leadsto \color{blue}{x} \]

   if 3.0000000000000001e-173 < t < 9.0000000000000006e-79

   1. Initial program 88.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 64.6%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. associate-/l* 70.5%

         \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   5. Simplified 70.5%

      \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]
   6. Step-by-step derivation

      1. clear-num 70.5%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

      2. inv-pow 70.5%

         \[\leadsto x + y \cdot \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}} \]

   7. Applied egg-rr 70.5%

      \[\leadsto x + y \cdot \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}} \]
   8. Step-by-step derivation

      1. unpow-1 70.5%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

   9. Simplified 70.5%

      \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

   10. Taylor expanded in z around 0 33.7%

       \[\leadsto \color{blue}{x + -1 \cdot \frac{t \cdot y}{a - t}} \]
   11. Step-by-step derivation

       1. mul-1-neg 33.7%

          \[\leadsto x + \color{blue}{\left(-\frac{t \cdot y}{a - t}\right)} \]

       2. unsub-neg 33.7%

          \[\leadsto \color{blue}{x - \frac{t \cdot y}{a - t}} \]

       3. associate-/l* 39.6%

          \[\leadsto x - \color{blue}{t \cdot \frac{y}{a - t}} \]

   12. Simplified 39.6%

       \[\leadsto \color{blue}{x - t \cdot \frac{y}{a - t}} \]

   13. Taylor expanded in t around 0 40.0%

       \[\leadsto x - \color{blue}{\frac{t \cdot y}{a}} \]
   14. Step-by-step derivation

       1. associate-/l* 51.7%

          \[\leadsto x - \color{blue}{t \cdot \frac{y}{a}} \]

   15. Simplified 51.7%

       \[\leadsto x - \color{blue}{t \cdot \frac{y}{a}} \]

   16. Taylor expanded in x around 0 27.9%

       \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot y}{a}} \]
   17. Step-by-step derivation

       1. associate-/l* 39.6%

          \[\leadsto -1 \cdot \color{blue}{\left(t \cdot \frac{y}{a}\right)} \]

       2. associate-*r* 39.6%

          \[\leadsto \color{blue}{\left(-1 \cdot t\right) \cdot \frac{y}{a}} \]

       3. neg-mul-1 39.6%

          \[\leadsto \color{blue}{\left(-t\right)} \cdot \frac{y}{a} \]

       4. *-commutative 39.6%

          \[\leadsto \color{blue}{\frac{y}{a} \cdot \left(-t\right)} \]

   18. Simplified 39.6%

       \[\leadsto \color{blue}{\frac{y}{a} \cdot \left(-t\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+121}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-52}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-195}:\\ \;\;\;\;\frac{x \cdot z}{t}\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-254}:\\ \;\;\;\;t \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-281}:\\ \;\;\;\;x \cdot \frac{z}{-a}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-173}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-79}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 35.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{x}{t}\\ \mathbf{if}\;t \leq -4.2 \cdot 10^{+120}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-197}:\\ \;\;\;\;\frac{x \cdot z}{t}\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-253}:\\ \;\;\;\;t \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{+34}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+50}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+86}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ x t))))
   (if (<= t -4.2e+120)
     y
     (if (<= t -6.2e-52)
       t_1
       (if (<= t -1.8e-197)
         (/ (* x z) t)
         (if (<= t -1.15e-253)
           (* t (/ x t))
           (if (<= t 1.16e+34)
             x
             (if (<= t 1.7e+50) (* y (/ z a)) (if (<= t 2.2e+86) t_1 y)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (x / t);
	double tmp;
	if (t <= -4.2e+120) {
		tmp = y;
	} else if (t <= -6.2e-52) {
		tmp = t_1;
	} else if (t <= -1.8e-197) {
		tmp = (x * z) / t;
	} else if (t <= -1.15e-253) {
		tmp = t * (x / t);
	} else if (t <= 1.16e+34) {
		tmp = x;
	} else if (t <= 1.7e+50) {
		tmp = y * (z / a);
	} else if (t <= 2.2e+86) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (x / t)
    if (t <= (-4.2d+120)) then
        tmp = y
    else if (t <= (-6.2d-52)) then
        tmp = t_1
    else if (t <= (-1.8d-197)) then
        tmp = (x * z) / t
    else if (t <= (-1.15d-253)) then
        tmp = t * (x / t)
    else if (t <= 1.16d+34) then
        tmp = x
    else if (t <= 1.7d+50) then
        tmp = y * (z / a)
    else if (t <= 2.2d+86) then
        tmp = t_1
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (x / t);
	double tmp;
	if (t <= -4.2e+120) {
		tmp = y;
	} else if (t <= -6.2e-52) {
		tmp = t_1;
	} else if (t <= -1.8e-197) {
		tmp = (x * z) / t;
	} else if (t <= -1.15e-253) {
		tmp = t * (x / t);
	} else if (t <= 1.16e+34) {
		tmp = x;
	} else if (t <= 1.7e+50) {
		tmp = y * (z / a);
	} else if (t <= 2.2e+86) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * (x / t)
	tmp = 0
	if t <= -4.2e+120:
		tmp = y
	elif t <= -6.2e-52:
		tmp = t_1
	elif t <= -1.8e-197:
		tmp = (x * z) / t
	elif t <= -1.15e-253:
		tmp = t * (x / t)
	elif t <= 1.16e+34:
		tmp = x
	elif t <= 1.7e+50:
		tmp = y * (z / a)
	elif t <= 2.2e+86:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(x / t))
	tmp = 0.0
	if (t <= -4.2e+120)
		tmp = y;
	elseif (t <= -6.2e-52)
		tmp = t_1;
	elseif (t <= -1.8e-197)
		tmp = Float64(Float64(x * z) / t);
	elseif (t <= -1.15e-253)
		tmp = Float64(t * Float64(x / t));
	elseif (t <= 1.16e+34)
		tmp = x;
	elseif (t <= 1.7e+50)
		tmp = Float64(y * Float64(z / a));
	elseif (t <= 2.2e+86)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * (x / t);
	tmp = 0.0;
	if (t <= -4.2e+120)
		tmp = y;
	elseif (t <= -6.2e-52)
		tmp = t_1;
	elseif (t <= -1.8e-197)
		tmp = (x * z) / t;
	elseif (t <= -1.15e-253)
		tmp = t * (x / t);
	elseif (t <= 1.16e+34)
		tmp = x;
	elseif (t <= 1.7e+50)
		tmp = y * (z / a);
	elseif (t <= 2.2e+86)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.2e+120], y, If[LessEqual[t, -6.2e-52], t$95$1, If[LessEqual[t, -1.8e-197], N[(N[(x * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, -1.15e-253], N[(t * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.16e+34], x, If[LessEqual[t, 1.7e+50], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.2e+86], t$95$1, y]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -4.2000000000000001e120 or 2.20000000000000003e86 < t

   1. Initial program 33.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 61.3%

      \[\leadsto \color{blue}{y} \]

   if -4.2000000000000001e120 < t < -6.1999999999999998e-52 or 1.6999999999999999e50 < t < 2.20000000000000003e86

   1. Initial program 62.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 64.8%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 64.8%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 64.8%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 64.8%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 64.8%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 64.8%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 64.8%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 71.7%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 69.1%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 71.6%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 71.6%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]

   6. Taylor expanded in z around inf 46.1%

      \[\leadsto \color{blue}{z \cdot \left(\frac{x}{t} - \frac{y}{t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 46.1%

         \[\leadsto z \cdot \color{blue}{\frac{x - y}{t}} \]

   8. Simplified 46.1%

      \[\leadsto \color{blue}{z \cdot \frac{x - y}{t}} \]

   9. Taylor expanded in x around inf 32.0%

      \[\leadsto z \cdot \color{blue}{\frac{x}{t}} \]

   if -6.1999999999999998e-52 < t < -1.7999999999999999e-197

   1. Initial program 87.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 42.6%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 42.6%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 42.6%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 45.7%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 45.7%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 45.7%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 42.6%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 36.3%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 32.9%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 39.8%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 39.8%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]

   6. Taylor expanded in y around 0 34.3%

      \[\leadsto \color{blue}{\frac{x \cdot \left(z - a\right)}{t}} \]

   7. Taylor expanded in z around inf 34.2%

      \[\leadsto \frac{\color{blue}{x \cdot z}}{t} \]
   8. Step-by-step derivation

      1. *-commutative 34.2%

         \[\leadsto \frac{\color{blue}{z \cdot x}}{t} \]

   9. Simplified 34.2%

      \[\leadsto \frac{\color{blue}{z \cdot x}}{t} \]

   if -1.7999999999999999e-197 < t < -1.15e-253

   1. Initial program 99.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 80.3%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. associate-/l* 74.4%

         \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   5. Simplified 74.4%

      \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]
   6. Step-by-step derivation

      1. clear-num 74.4%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

      2. inv-pow 74.4%

         \[\leadsto x + y \cdot \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}} \]

   7. Applied egg-rr 74.4%

      \[\leadsto x + y \cdot \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}} \]
   8. Step-by-step derivation

      1. unpow-1 74.4%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

   9. Simplified 74.4%

      \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

   10. Taylor expanded in z around 0 42.1%

       \[\leadsto \color{blue}{x + -1 \cdot \frac{t \cdot y}{a - t}} \]
   11. Step-by-step derivation

       1. mul-1-neg 42.1%

          \[\leadsto x + \color{blue}{\left(-\frac{t \cdot y}{a - t}\right)} \]

       2. unsub-neg 42.1%

          \[\leadsto \color{blue}{x - \frac{t \cdot y}{a - t}} \]

       3. associate-/l* 48.4%

          \[\leadsto x - \color{blue}{t \cdot \frac{y}{a - t}} \]

   12. Simplified 48.4%

       \[\leadsto \color{blue}{x - t \cdot \frac{y}{a - t}} \]

   13. Taylor expanded in t around 0 42.0%

       \[\leadsto x - \color{blue}{\frac{t \cdot y}{a}} \]
   14. Step-by-step derivation

       1. associate-/l* 42.0%

          \[\leadsto x - \color{blue}{t \cdot \frac{y}{a}} \]

   15. Simplified 42.0%

       \[\leadsto x - \color{blue}{t \cdot \frac{y}{a}} \]

   16. Taylor expanded in t around inf 54.5%

       \[\leadsto \color{blue}{t \cdot \left(\frac{x}{t} - \frac{y}{a}\right)} \]

   17. Taylor expanded in x around inf 54.6%

       \[\leadsto t \cdot \color{blue}{\frac{x}{t}} \]

   if -1.15e-253 < t < 1.1600000000000001e34

   1. Initial program 88.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 37.9%

      \[\leadsto \color{blue}{x} \]

   if 1.1600000000000001e34 < t < 1.6999999999999999e50

   1. Initial program 76.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 76.7%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. +-commutative 76.7%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. +-commutative 76.7%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{a - t} + 1\right)} \]

      3. distribute-lft-in 76.7%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \color{blue}{\left(x \cdot \left(-1 \cdot \frac{z - t}{a - t}\right) + x \cdot 1\right)} \]

      4. mul-1-neg 76.7%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(x \cdot \color{blue}{\left(-\frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      5. distribute-rgt-neg-in 76.7%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{\left(-x \cdot \frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      6. associate-/l* 76.7%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\left(-\color{blue}{\frac{x \cdot \left(z - t\right)}{a - t}}\right) + x \cdot 1\right) \]

      7. mul-1-neg 76.7%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} + x \cdot 1\right) \]

      8. *-rgt-identity 76.7%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \color{blue}{x}\right) \]

      9. associate-+l+ 76.7%

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(z - t\right)}{a - t} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) + x} \]

   5. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)} \]

   6. Taylor expanded in y around inf 82.7%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 82.7%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

   8. Simplified 82.7%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   9. Taylor expanded in t around 0 28.5%

      \[\leadsto \color{blue}{\frac{y \cdot z}{a}} \]
   10. Step-by-step derivation

       1. associate-/l* 54.6%

          \[\leadsto x + \color{blue}{y \cdot \frac{z}{a}} \]

   11. Simplified 51.9%

       \[\leadsto \color{blue}{y \cdot \frac{z}{a}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+120}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-52}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-197}:\\ \;\;\;\;\frac{x \cdot z}{t}\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-253}:\\ \;\;\;\;t \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{+34}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+50}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+86}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 56.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;x \leq -1.25 \cdot 10^{+186}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.85 \cdot 10^{-80}:\\ \;\;\;\;x - \frac{t \cdot y}{a}\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+37}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+102}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))) (t_2 (* x (- 1.0 (/ z a)))))
   (if (<= x -1.25e+186)
     t_2
     (if (<= x -1.9e-20)
       t_1
       (if (<= x -1.85e-80)
         (- x (/ (* t y) a))
         (if (<= x 8.2e-17)
           t_1
           (if (<= x 5.2e+37)
             t_2
             (if (<= x 1.15e+102) t_1 (+ y (* x (/ z t)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x * (1.0 - (z / a));
	double tmp;
	if (x <= -1.25e+186) {
		tmp = t_2;
	} else if (x <= -1.9e-20) {
		tmp = t_1;
	} else if (x <= -1.85e-80) {
		tmp = x - ((t * y) / a);
	} else if (x <= 8.2e-17) {
		tmp = t_1;
	} else if (x <= 5.2e+37) {
		tmp = t_2;
	} else if (x <= 1.15e+102) {
		tmp = t_1;
	} else {
		tmp = y + (x * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    t_2 = x * (1.0d0 - (z / a))
    if (x <= (-1.25d+186)) then
        tmp = t_2
    else if (x <= (-1.9d-20)) then
        tmp = t_1
    else if (x <= (-1.85d-80)) then
        tmp = x - ((t * y) / a)
    else if (x <= 8.2d-17) then
        tmp = t_1
    else if (x <= 5.2d+37) then
        tmp = t_2
    else if (x <= 1.15d+102) then
        tmp = t_1
    else
        tmp = y + (x * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x * (1.0 - (z / a));
	double tmp;
	if (x <= -1.25e+186) {
		tmp = t_2;
	} else if (x <= -1.9e-20) {
		tmp = t_1;
	} else if (x <= -1.85e-80) {
		tmp = x - ((t * y) / a);
	} else if (x <= 8.2e-17) {
		tmp = t_1;
	} else if (x <= 5.2e+37) {
		tmp = t_2;
	} else if (x <= 1.15e+102) {
		tmp = t_1;
	} else {
		tmp = y + (x * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = x * (1.0 - (z / a))
	tmp = 0
	if x <= -1.25e+186:
		tmp = t_2
	elif x <= -1.9e-20:
		tmp = t_1
	elif x <= -1.85e-80:
		tmp = x - ((t * y) / a)
	elif x <= 8.2e-17:
		tmp = t_1
	elif x <= 5.2e+37:
		tmp = t_2
	elif x <= 1.15e+102:
		tmp = t_1
	else:
		tmp = y + (x * (z / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (x <= -1.25e+186)
		tmp = t_2;
	elseif (x <= -1.9e-20)
		tmp = t_1;
	elseif (x <= -1.85e-80)
		tmp = Float64(x - Float64(Float64(t * y) / a));
	elseif (x <= 8.2e-17)
		tmp = t_1;
	elseif (x <= 5.2e+37)
		tmp = t_2;
	elseif (x <= 1.15e+102)
		tmp = t_1;
	else
		tmp = Float64(y + Float64(x * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (x <= -1.25e+186)
		tmp = t_2;
	elseif (x <= -1.9e-20)
		tmp = t_1;
	elseif (x <= -1.85e-80)
		tmp = x - ((t * y) / a);
	elseif (x <= 8.2e-17)
		tmp = t_1;
	elseif (x <= 5.2e+37)
		tmp = t_2;
	elseif (x <= 1.15e+102)
		tmp = t_1;
	else
		tmp = y + (x * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.25e+186], t$95$2, If[LessEqual[x, -1.9e-20], t$95$1, If[LessEqual[x, -1.85e-80], N[(x - N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.2e-17], t$95$1, If[LessEqual[x, 5.2e+37], t$95$2, If[LessEqual[x, 1.15e+102], t$95$1, N[(y + N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.24999999999999988e186 or 8.2000000000000001e-17 < x < 5.1999999999999998e37

   1. Initial program 67.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 51.6%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]

   4. Taylor expanded in x around inf 57.1%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z}{a}\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 57.1%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{z}{a}\right)}\right) \]

      2. unsub-neg 57.1%

         \[\leadsto x \cdot \color{blue}{\left(1 - \frac{z}{a}\right)} \]

   6. Simplified 57.1%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{a}\right)} \]

   if -1.24999999999999988e186 < x < -1.8999999999999999e-20 or -1.85000000000000016e-80 < x < 8.2000000000000001e-17 or 5.1999999999999998e37 < x < 1.1499999999999999e102

   1. Initial program 67.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 70.0%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. +-commutative 70.0%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. +-commutative 70.0%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{a - t} + 1\right)} \]

      3. distribute-lft-in 70.0%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \color{blue}{\left(x \cdot \left(-1 \cdot \frac{z - t}{a - t}\right) + x \cdot 1\right)} \]

      4. mul-1-neg 70.0%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(x \cdot \color{blue}{\left(-\frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      5. distribute-rgt-neg-in 70.0%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{\left(-x \cdot \frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      6. associate-/l* 68.1%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\left(-\color{blue}{\frac{x \cdot \left(z - t\right)}{a - t}}\right) + x \cdot 1\right) \]

      7. mul-1-neg 68.1%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} + x \cdot 1\right) \]

      8. *-rgt-identity 68.1%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \color{blue}{x}\right) \]

      9. associate-+l+ 66.4%

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(z - t\right)}{a - t} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) + x} \]

   5. Simplified 84.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)} \]

   6. Taylor expanded in y around inf 71.7%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 71.7%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

   8. Simplified 71.7%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   if -1.8999999999999999e-20 < x < -1.85000000000000016e-80

   1. Initial program 93.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 78.0%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. associate-/l* 84.9%

         \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   5. Simplified 84.9%

      \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]
   6. Step-by-step derivation

      1. clear-num 84.9%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

      2. inv-pow 84.9%

         \[\leadsto x + y \cdot \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}} \]

   7. Applied egg-rr 84.9%

      \[\leadsto x + y \cdot \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}} \]
   8. Step-by-step derivation

      1. unpow-1 84.9%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

   9. Simplified 84.9%

      \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

   10. Taylor expanded in z around 0 56.8%

       \[\leadsto \color{blue}{x + -1 \cdot \frac{t \cdot y}{a - t}} \]
   11. Step-by-step derivation

       1. mul-1-neg 56.8%

          \[\leadsto x + \color{blue}{\left(-\frac{t \cdot y}{a - t}\right)} \]

       2. unsub-neg 56.8%

          \[\leadsto \color{blue}{x - \frac{t \cdot y}{a - t}} \]

       3. associate-/l* 63.2%

          \[\leadsto x - \color{blue}{t \cdot \frac{y}{a - t}} \]

   12. Simplified 63.2%

       \[\leadsto \color{blue}{x - t \cdot \frac{y}{a - t}} \]

   13. Taylor expanded in t around 0 56.2%

       \[\leadsto x - \color{blue}{\frac{t \cdot y}{a}} \]

   if 1.1499999999999999e102 < x

   1. Initial program 51.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 49.6%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 49.6%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 49.6%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 52.2%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 52.2%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 52.2%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 49.6%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 52.0%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 48.7%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 57.0%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 57.0%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]
   6. Step-by-step derivation

      1. *-commutative 57.0%

         \[\leadsto y - \color{blue}{\left(z - a\right) \cdot \frac{y - x}{t}} \]

      2. clear-num 57.0%

         \[\leadsto y - \left(z - a\right) \cdot \color{blue}{\frac{1}{\frac{t}{y - x}}} \]

      3. un-div-inv 57.0%

         \[\leadsto y - \color{blue}{\frac{z - a}{\frac{t}{y - x}}} \]

   7. Applied egg-rr 57.0%

      \[\leadsto y - \color{blue}{\frac{z - a}{\frac{t}{y - x}}} \]

   8. Taylor expanded in y around 0 55.0%

      \[\leadsto y - \color{blue}{-1 \cdot \frac{x \cdot \left(z - a\right)}{t}} \]
   9. Step-by-step derivation

      1. mul-1-neg 55.0%

         \[\leadsto y - \color{blue}{\left(-\frac{x \cdot \left(z - a\right)}{t}\right)} \]

      2. associate-/l* 60.6%

         \[\leadsto y - \left(-\color{blue}{x \cdot \frac{z - a}{t}}\right) \]

   10. Simplified 60.6%

       \[\leadsto y - \color{blue}{\left(-x \cdot \frac{z - a}{t}\right)} \]

   11. Taylor expanded in a around 0 47.7%

       \[\leadsto \color{blue}{y + \frac{x \cdot z}{t}} \]
   12. Step-by-step derivation

       1. +-commutative 47.7%

          \[\leadsto \color{blue}{\frac{x \cdot z}{t} + y} \]

       2. associate-/l* 52.4%

          \[\leadsto \color{blue}{x \cdot \frac{z}{t}} + y \]

   13. Simplified 52.4%

       \[\leadsto \color{blue}{x \cdot \frac{z}{t} + y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+186}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-20}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;x \leq -1.85 \cdot 10^{-80}:\\ \;\;\;\;x - \frac{t \cdot y}{a}\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-17}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+37}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+102}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 55.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{-25}:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-155}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-227}:\\ \;\;\;\;x - \frac{x \cdot z}{a}\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-253}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-62}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+86}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;y - x \cdot \frac{a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.2e-25)
   (+ y (* x (/ z t)))
   (if (<= t -7.5e-155)
     (+ x (/ y (/ a z)))
     (if (<= t -2.7e-227)
       (- x (/ (* x z) a))
       (if (<= t -1.2e-253)
         (* z (/ (- x y) t))
         (if (<= t 7e-62)
           (+ x (* y (/ z a)))
           (if (<= t 3.8e+86) (* y (/ (- t z) t)) (- y (* x (/ a t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.2e-25) {
		tmp = y + (x * (z / t));
	} else if (t <= -7.5e-155) {
		tmp = x + (y / (a / z));
	} else if (t <= -2.7e-227) {
		tmp = x - ((x * z) / a);
	} else if (t <= -1.2e-253) {
		tmp = z * ((x - y) / t);
	} else if (t <= 7e-62) {
		tmp = x + (y * (z / a));
	} else if (t <= 3.8e+86) {
		tmp = y * ((t - z) / t);
	} else {
		tmp = y - (x * (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.2d-25)) then
        tmp = y + (x * (z / t))
    else if (t <= (-7.5d-155)) then
        tmp = x + (y / (a / z))
    else if (t <= (-2.7d-227)) then
        tmp = x - ((x * z) / a)
    else if (t <= (-1.2d-253)) then
        tmp = z * ((x - y) / t)
    else if (t <= 7d-62) then
        tmp = x + (y * (z / a))
    else if (t <= 3.8d+86) then
        tmp = y * ((t - z) / t)
    else
        tmp = y - (x * (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.2e-25) {
		tmp = y + (x * (z / t));
	} else if (t <= -7.5e-155) {
		tmp = x + (y / (a / z));
	} else if (t <= -2.7e-227) {
		tmp = x - ((x * z) / a);
	} else if (t <= -1.2e-253) {
		tmp = z * ((x - y) / t);
	} else if (t <= 7e-62) {
		tmp = x + (y * (z / a));
	} else if (t <= 3.8e+86) {
		tmp = y * ((t - z) / t);
	} else {
		tmp = y - (x * (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.2e-25:
		tmp = y + (x * (z / t))
	elif t <= -7.5e-155:
		tmp = x + (y / (a / z))
	elif t <= -2.7e-227:
		tmp = x - ((x * z) / a)
	elif t <= -1.2e-253:
		tmp = z * ((x - y) / t)
	elif t <= 7e-62:
		tmp = x + (y * (z / a))
	elif t <= 3.8e+86:
		tmp = y * ((t - z) / t)
	else:
		tmp = y - (x * (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.2e-25)
		tmp = Float64(y + Float64(x * Float64(z / t)));
	elseif (t <= -7.5e-155)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= -2.7e-227)
		tmp = Float64(x - Float64(Float64(x * z) / a));
	elseif (t <= -1.2e-253)
		tmp = Float64(z * Float64(Float64(x - y) / t));
	elseif (t <= 7e-62)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (t <= 3.8e+86)
		tmp = Float64(y * Float64(Float64(t - z) / t));
	else
		tmp = Float64(y - Float64(x * Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.2e-25)
		tmp = y + (x * (z / t));
	elseif (t <= -7.5e-155)
		tmp = x + (y / (a / z));
	elseif (t <= -2.7e-227)
		tmp = x - ((x * z) / a);
	elseif (t <= -1.2e-253)
		tmp = z * ((x - y) / t);
	elseif (t <= 7e-62)
		tmp = x + (y * (z / a));
	elseif (t <= 3.8e+86)
		tmp = y * ((t - z) / t);
	else
		tmp = y - (x * (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.2e-25], N[(y + N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -7.5e-155], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.7e-227], N[(x - N[(N[(x * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.2e-253], N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e-62], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.8e+86], N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(y - N[(x * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -2.2000000000000002e-25

   1. Initial program 52.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 63.1%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 63.1%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 63.1%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 63.1%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 63.1%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 63.1%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 63.1%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 71.8%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 82.1%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 82.1%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 82.1%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]
   6. Step-by-step derivation

      1. *-commutative 82.1%

         \[\leadsto y - \color{blue}{\left(z - a\right) \cdot \frac{y - x}{t}} \]

      2. clear-num 82.0%

         \[\leadsto y - \left(z - a\right) \cdot \color{blue}{\frac{1}{\frac{t}{y - x}}} \]

      3. un-div-inv 82.1%

         \[\leadsto y - \color{blue}{\frac{z - a}{\frac{t}{y - x}}} \]

   7. Applied egg-rr 82.1%

      \[\leadsto y - \color{blue}{\frac{z - a}{\frac{t}{y - x}}} \]

   8. Taylor expanded in y around 0 64.9%

      \[\leadsto y - \color{blue}{-1 \cdot \frac{x \cdot \left(z - a\right)}{t}} \]
   9. Step-by-step derivation

      1. mul-1-neg 64.9%

         \[\leadsto y - \color{blue}{\left(-\frac{x \cdot \left(z - a\right)}{t}\right)} \]

      2. associate-/l* 70.7%

         \[\leadsto y - \left(-\color{blue}{x \cdot \frac{z - a}{t}}\right) \]

   10. Simplified 70.7%

       \[\leadsto y - \color{blue}{\left(-x \cdot \frac{z - a}{t}\right)} \]

   11. Taylor expanded in a around 0 57.7%

       \[\leadsto \color{blue}{y + \frac{x \cdot z}{t}} \]
   12. Step-by-step derivation

       1. +-commutative 57.7%

          \[\leadsto \color{blue}{\frac{x \cdot z}{t} + y} \]

       2. associate-/l* 60.6%

          \[\leadsto \color{blue}{x \cdot \frac{z}{t}} + y \]

   13. Simplified 60.6%

       \[\leadsto \color{blue}{x \cdot \frac{z}{t} + y} \]

   if -2.2000000000000002e-25 < t < -7.5000000000000006e-155

   1. Initial program 83.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 62.9%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. associate-/l* 69.6%

         \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   5. Simplified 69.6%

      \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]
   6. Step-by-step derivation

      1. clear-num 69.5%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

      2. un-div-inv 69.5%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

   7. Applied egg-rr 69.5%

      \[\leadsto x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

   8. Taylor expanded in t around 0 57.6%

      \[\leadsto x + \frac{y}{\color{blue}{\frac{a}{z}}} \]

   if -7.5000000000000006e-155 < t < -2.7e-227

   1. Initial program 99.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 64.4%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]

   4. Taylor expanded in y around 0 64.7%

      \[\leadsto x + \frac{\color{blue}{-1 \cdot \left(x \cdot z\right)}}{a} \]
   5. Step-by-step derivation

      1. mul-1-neg 64.7%

         \[\leadsto x + \frac{\color{blue}{-x \cdot z}}{a} \]

      2. distribute-lft-neg-out 64.7%

         \[\leadsto x + \frac{\color{blue}{\left(-x\right) \cdot z}}{a} \]

      3. *-commutative 64.7%

         \[\leadsto x + \frac{\color{blue}{z \cdot \left(-x\right)}}{a} \]

   6. Simplified 64.7%

      \[\leadsto x + \frac{\color{blue}{z \cdot \left(-x\right)}}{a} \]

   if -2.7e-227 < t < -1.20000000000000005e-253

   1. Initial program 99.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 62.2%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 62.2%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 62.2%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 62.2%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 62.2%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 62.2%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 62.2%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 62.2%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 35.9%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 62.2%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 62.2%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]

   6. Taylor expanded in z around inf 62.0%

      \[\leadsto \color{blue}{z \cdot \left(\frac{x}{t} - \frac{y}{t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 62.0%

         \[\leadsto z \cdot \color{blue}{\frac{x - y}{t}} \]

   8. Simplified 62.0%

      \[\leadsto \color{blue}{z \cdot \frac{x - y}{t}} \]

   if -1.20000000000000005e-253 < t < 7.0000000000000003e-62

   1. Initial program 90.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 75.1%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. associate-/l* 75.1%

         \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   5. Simplified 75.1%

      \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   6. Taylor expanded in t around 0 68.9%

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{a}} \]
   7. Step-by-step derivation

      1. associate-/l* 69.0%

         \[\leadsto x + \color{blue}{y \cdot \frac{z}{a}} \]

   8. Simplified 69.0%

      \[\leadsto x + \color{blue}{y \cdot \frac{z}{a}} \]

   if 7.0000000000000003e-62 < t < 3.79999999999999978e86

   1. Initial program 66.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 69.4%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. +-commutative 69.4%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. +-commutative 69.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{a - t} + 1\right)} \]

      3. distribute-lft-in 69.5%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \color{blue}{\left(x \cdot \left(-1 \cdot \frac{z - t}{a - t}\right) + x \cdot 1\right)} \]

      4. mul-1-neg 69.5%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(x \cdot \color{blue}{\left(-\frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      5. distribute-rgt-neg-in 69.5%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{\left(-x \cdot \frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      6. associate-/l* 67.2%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\left(-\color{blue}{\frac{x \cdot \left(z - t\right)}{a - t}}\right) + x \cdot 1\right) \]

      7. mul-1-neg 67.2%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} + x \cdot 1\right) \]

      8. *-rgt-identity 67.2%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \color{blue}{x}\right) \]

      9. associate-+l+ 66.7%

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(z - t\right)}{a - t} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) + x} \]

   5. Simplified 84.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)} \]

   6. Taylor expanded in y around inf 60.7%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 60.7%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

   8. Simplified 60.7%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   9. Taylor expanded in a around 0 47.0%

      \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{t}\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 47.0%

          \[\leadsto y \cdot \color{blue}{\left(-\frac{z - t}{t}\right)} \]

   11. Simplified 47.0%

       \[\leadsto y \cdot \color{blue}{\left(-\frac{z - t}{t}\right)} \]

   if 3.79999999999999978e86 < t

   1. Initial program 27.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 74.6%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 74.6%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 74.6%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 74.6%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 74.6%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 74.6%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 74.6%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 80.3%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 82.9%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 82.9%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 82.9%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]
   6. Step-by-step derivation

      1. *-commutative 82.9%

         \[\leadsto y - \color{blue}{\left(z - a\right) \cdot \frac{y - x}{t}} \]

      2. clear-num 82.9%

         \[\leadsto y - \left(z - a\right) \cdot \color{blue}{\frac{1}{\frac{t}{y - x}}} \]

      3. un-div-inv 82.8%

         \[\leadsto y - \color{blue}{\frac{z - a}{\frac{t}{y - x}}} \]

   7. Applied egg-rr 82.8%

      \[\leadsto y - \color{blue}{\frac{z - a}{\frac{t}{y - x}}} \]

   8. Taylor expanded in y around 0 80.2%

      \[\leadsto y - \color{blue}{-1 \cdot \frac{x \cdot \left(z - a\right)}{t}} \]
   9. Step-by-step derivation

      1. mul-1-neg 80.2%

         \[\leadsto y - \color{blue}{\left(-\frac{x \cdot \left(z - a\right)}{t}\right)} \]

      2. associate-/l* 79.9%

         \[\leadsto y - \left(-\color{blue}{x \cdot \frac{z - a}{t}}\right) \]

   10. Simplified 79.9%

       \[\leadsto y - \color{blue}{\left(-x \cdot \frac{z - a}{t}\right)} \]

   11. Taylor expanded in z around 0 76.1%

       \[\leadsto \color{blue}{y + -1 \cdot \frac{a \cdot x}{t}} \]
   12. Step-by-step derivation

       1. mul-1-neg 76.1%

          \[\leadsto y + \color{blue}{\left(-\frac{a \cdot x}{t}\right)} \]

       2. *-commutative 76.1%

          \[\leadsto y + \left(-\frac{\color{blue}{x \cdot a}}{t}\right) \]

       3. associate-*r/ 75.6%

          \[\leadsto y + \left(-\color{blue}{x \cdot \frac{a}{t}}\right) \]

       4. unsub-neg 75.6%

          \[\leadsto \color{blue}{y - x \cdot \frac{a}{t}} \]

   13. Simplified 75.6%

       \[\leadsto \color{blue}{y - x \cdot \frac{a}{t}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{-25}:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-155}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-227}:\\ \;\;\;\;x - \frac{x \cdot z}{a}\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-253}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-62}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+86}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;y - x \cdot \frac{a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 31: 35.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{a}\\ \mathbf{if}\;t \leq -9.8 \cdot 10^{+100}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-131}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-282}:\\ \;\;\;\;t \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-246}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-165}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z a))))
   (if (<= t -9.8e+100)
     y
     (if (<= t -4e-131)
       (* x (/ z t))
       (if (<= t 9.5e-282)
         (* t (/ x t))
         (if (<= t 6.8e-246)
           t_1
           (if (<= t 2.2e-165)
             x
             (if (<= t 1.2e-46) t_1 (if (<= t 2.1e-14) x y)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / a);
	double tmp;
	if (t <= -9.8e+100) {
		tmp = y;
	} else if (t <= -4e-131) {
		tmp = x * (z / t);
	} else if (t <= 9.5e-282) {
		tmp = t * (x / t);
	} else if (t <= 6.8e-246) {
		tmp = t_1;
	} else if (t <= 2.2e-165) {
		tmp = x;
	} else if (t <= 1.2e-46) {
		tmp = t_1;
	} else if (t <= 2.1e-14) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (z / a)
    if (t <= (-9.8d+100)) then
        tmp = y
    else if (t <= (-4d-131)) then
        tmp = x * (z / t)
    else if (t <= 9.5d-282) then
        tmp = t * (x / t)
    else if (t <= 6.8d-246) then
        tmp = t_1
    else if (t <= 2.2d-165) then
        tmp = x
    else if (t <= 1.2d-46) then
        tmp = t_1
    else if (t <= 2.1d-14) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / a);
	double tmp;
	if (t <= -9.8e+100) {
		tmp = y;
	} else if (t <= -4e-131) {
		tmp = x * (z / t);
	} else if (t <= 9.5e-282) {
		tmp = t * (x / t);
	} else if (t <= 6.8e-246) {
		tmp = t_1;
	} else if (t <= 2.2e-165) {
		tmp = x;
	} else if (t <= 1.2e-46) {
		tmp = t_1;
	} else if (t <= 2.1e-14) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / a)
	tmp = 0
	if t <= -9.8e+100:
		tmp = y
	elif t <= -4e-131:
		tmp = x * (z / t)
	elif t <= 9.5e-282:
		tmp = t * (x / t)
	elif t <= 6.8e-246:
		tmp = t_1
	elif t <= 2.2e-165:
		tmp = x
	elif t <= 1.2e-46:
		tmp = t_1
	elif t <= 2.1e-14:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / a))
	tmp = 0.0
	if (t <= -9.8e+100)
		tmp = y;
	elseif (t <= -4e-131)
		tmp = Float64(x * Float64(z / t));
	elseif (t <= 9.5e-282)
		tmp = Float64(t * Float64(x / t));
	elseif (t <= 6.8e-246)
		tmp = t_1;
	elseif (t <= 2.2e-165)
		tmp = x;
	elseif (t <= 1.2e-46)
		tmp = t_1;
	elseif (t <= 2.1e-14)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / a);
	tmp = 0.0;
	if (t <= -9.8e+100)
		tmp = y;
	elseif (t <= -4e-131)
		tmp = x * (z / t);
	elseif (t <= 9.5e-282)
		tmp = t * (x / t);
	elseif (t <= 6.8e-246)
		tmp = t_1;
	elseif (t <= 2.2e-165)
		tmp = x;
	elseif (t <= 1.2e-46)
		tmp = t_1;
	elseif (t <= 2.1e-14)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.8e+100], y, If[LessEqual[t, -4e-131], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.5e-282], N[(t * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.8e-246], t$95$1, If[LessEqual[t, 2.2e-165], x, If[LessEqual[t, 1.2e-46], t$95$1, If[LessEqual[t, 2.1e-14], x, y]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -9.79999999999999934e100 or 2.0999999999999999e-14 < t

   1. Initial program 37.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 55.9%

      \[\leadsto \color{blue}{y} \]

   if -9.79999999999999934e100 < t < -3.9999999999999999e-131

   1. Initial program 79.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 55.1%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 55.1%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 55.1%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 55.1%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 55.1%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 55.1%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 55.1%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 53.2%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 51.1%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 53.1%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 53.1%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]

   6. Taylor expanded in y around 0 33.7%

      \[\leadsto \color{blue}{\frac{x \cdot \left(z - a\right)}{t}} \]

   7. Taylor expanded in z around inf 27.9%

      \[\leadsto \color{blue}{\frac{x \cdot z}{t}} \]
   8. Step-by-step derivation

      1. associate-/l* 29.8%

         \[\leadsto \color{blue}{x \cdot \frac{z}{t}} \]

   9. Simplified 29.8%

      \[\leadsto \color{blue}{x \cdot \frac{z}{t}} \]

   if -3.9999999999999999e-131 < t < 9.49999999999999941e-282

   1. Initial program 95.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 67.4%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. associate-/l* 67.5%

         \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   5. Simplified 67.5%

      \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]
   6. Step-by-step derivation

      1. clear-num 67.6%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

      2. inv-pow 67.6%

         \[\leadsto x + y \cdot \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}} \]

   7. Applied egg-rr 67.6%

      \[\leadsto x + y \cdot \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}} \]
   8. Step-by-step derivation

      1. unpow-1 67.6%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

   9. Simplified 67.6%

      \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

   10. Taylor expanded in z around 0 40.5%

       \[\leadsto \color{blue}{x + -1 \cdot \frac{t \cdot y}{a - t}} \]
   11. Step-by-step derivation

       1. mul-1-neg 40.5%

          \[\leadsto x + \color{blue}{\left(-\frac{t \cdot y}{a - t}\right)} \]

       2. unsub-neg 40.5%

          \[\leadsto \color{blue}{x - \frac{t \cdot y}{a - t}} \]

       3. associate-/l* 42.4%

          \[\leadsto x - \color{blue}{t \cdot \frac{y}{a - t}} \]

   12. Simplified 42.4%

       \[\leadsto \color{blue}{x - t \cdot \frac{y}{a - t}} \]

   13. Taylor expanded in t around 0 40.6%

       \[\leadsto x - \color{blue}{\frac{t \cdot y}{a}} \]
   14. Step-by-step derivation

       1. associate-/l* 40.5%

          \[\leadsto x - \color{blue}{t \cdot \frac{y}{a}} \]

   15. Simplified 40.5%

       \[\leadsto x - \color{blue}{t \cdot \frac{y}{a}} \]

   16. Taylor expanded in t around inf 40.6%

       \[\leadsto \color{blue}{t \cdot \left(\frac{x}{t} - \frac{y}{a}\right)} \]

   17. Taylor expanded in x around inf 40.4%

       \[\leadsto t \cdot \color{blue}{\frac{x}{t}} \]

   if 9.49999999999999941e-282 < t < 6.8000000000000003e-246 or 2.1999999999999999e-165 < t < 1.20000000000000007e-46

   1. Initial program 86.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 75.7%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. +-commutative 75.7%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. +-commutative 75.7%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{a - t} + 1\right)} \]

      3. distribute-lft-in 75.7%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \color{blue}{\left(x \cdot \left(-1 \cdot \frac{z - t}{a - t}\right) + x \cdot 1\right)} \]

      4. mul-1-neg 75.7%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(x \cdot \color{blue}{\left(-\frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      5. distribute-rgt-neg-in 75.7%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{\left(-x \cdot \frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      6. associate-/l* 79.3%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\left(-\color{blue}{\frac{x \cdot \left(z - t\right)}{a - t}}\right) + x \cdot 1\right) \]

      7. mul-1-neg 79.3%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} + x \cdot 1\right) \]

      8. *-rgt-identity 79.3%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \color{blue}{x}\right) \]

      9. associate-+l+ 79.4%

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(z - t\right)}{a - t} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) + x} \]

   5. Simplified 92.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)} \]

   6. Taylor expanded in y around inf 58.7%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 58.7%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

   8. Simplified 58.7%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   9. Taylor expanded in t around 0 35.0%

      \[\leadsto \color{blue}{\frac{y \cdot z}{a}} \]
   10. Step-by-step derivation

       1. associate-/l* 49.0%

          \[\leadsto x + \color{blue}{y \cdot \frac{z}{a}} \]

   11. Simplified 38.5%

       \[\leadsto \color{blue}{y \cdot \frac{z}{a}} \]

   if 6.8000000000000003e-246 < t < 2.1999999999999999e-165 or 1.20000000000000007e-46 < t < 2.0999999999999999e-14

   1. Initial program 85.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 60.3%

      \[\leadsto \color{blue}{x} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 32: 37.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z}{t}\\ \mathbf{if}\;t \leq -5.7 \cdot 10^{+100}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -4.15 \cdot 10^{-131}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -7.4 \cdot 10^{-164}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{-191}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.62 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 18000:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 3800000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ z t))))
   (if (<= t -5.7e+100)
     y
     (if (<= t -4.15e-131)
       t_1
       (if (<= t -7.4e-164)
         x
         (if (<= t -2.3e-191)
           t_1
           (if (<= t 1.62e-9)
             x
             (if (<= t 18000.0) y (if (<= t 3800000000.0) x y)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (z / t);
	double tmp;
	if (t <= -5.7e+100) {
		tmp = y;
	} else if (t <= -4.15e-131) {
		tmp = t_1;
	} else if (t <= -7.4e-164) {
		tmp = x;
	} else if (t <= -2.3e-191) {
		tmp = t_1;
	} else if (t <= 1.62e-9) {
		tmp = x;
	} else if (t <= 18000.0) {
		tmp = y;
	} else if (t <= 3800000000.0) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (z / t)
    if (t <= (-5.7d+100)) then
        tmp = y
    else if (t <= (-4.15d-131)) then
        tmp = t_1
    else if (t <= (-7.4d-164)) then
        tmp = x
    else if (t <= (-2.3d-191)) then
        tmp = t_1
    else if (t <= 1.62d-9) then
        tmp = x
    else if (t <= 18000.0d0) then
        tmp = y
    else if (t <= 3800000000.0d0) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (z / t);
	double tmp;
	if (t <= -5.7e+100) {
		tmp = y;
	} else if (t <= -4.15e-131) {
		tmp = t_1;
	} else if (t <= -7.4e-164) {
		tmp = x;
	} else if (t <= -2.3e-191) {
		tmp = t_1;
	} else if (t <= 1.62e-9) {
		tmp = x;
	} else if (t <= 18000.0) {
		tmp = y;
	} else if (t <= 3800000000.0) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (z / t)
	tmp = 0
	if t <= -5.7e+100:
		tmp = y
	elif t <= -4.15e-131:
		tmp = t_1
	elif t <= -7.4e-164:
		tmp = x
	elif t <= -2.3e-191:
		tmp = t_1
	elif t <= 1.62e-9:
		tmp = x
	elif t <= 18000.0:
		tmp = y
	elif t <= 3800000000.0:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(z / t))
	tmp = 0.0
	if (t <= -5.7e+100)
		tmp = y;
	elseif (t <= -4.15e-131)
		tmp = t_1;
	elseif (t <= -7.4e-164)
		tmp = x;
	elseif (t <= -2.3e-191)
		tmp = t_1;
	elseif (t <= 1.62e-9)
		tmp = x;
	elseif (t <= 18000.0)
		tmp = y;
	elseif (t <= 3800000000.0)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (z / t);
	tmp = 0.0;
	if (t <= -5.7e+100)
		tmp = y;
	elseif (t <= -4.15e-131)
		tmp = t_1;
	elseif (t <= -7.4e-164)
		tmp = x;
	elseif (t <= -2.3e-191)
		tmp = t_1;
	elseif (t <= 1.62e-9)
		tmp = x;
	elseif (t <= 18000.0)
		tmp = y;
	elseif (t <= 3800000000.0)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.7e+100], y, If[LessEqual[t, -4.15e-131], t$95$1, If[LessEqual[t, -7.4e-164], x, If[LessEqual[t, -2.3e-191], t$95$1, If[LessEqual[t, 1.62e-9], x, If[LessEqual[t, 18000.0], y, If[LessEqual[t, 3800000000.0], x, y]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.69999999999999984e100 or 1.61999999999999999e-9 < t < 18000 or 3.8e9 < t

   1. Initial program 37.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 56.4%

      \[\leadsto \color{blue}{y} \]

   if -5.69999999999999984e100 < t < -4.14999999999999982e-131 or -7.3999999999999998e-164 < t < -2.30000000000000011e-191

   1. Initial program 81.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 55.2%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 55.2%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 55.2%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 55.2%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 55.2%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 55.2%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 55.2%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 51.8%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 47.8%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 51.7%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 51.7%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]

   6. Taylor expanded in y around 0 34.4%

      \[\leadsto \color{blue}{\frac{x \cdot \left(z - a\right)}{t}} \]

   7. Taylor expanded in z around inf 28.8%

      \[\leadsto \color{blue}{\frac{x \cdot z}{t}} \]
   8. Step-by-step derivation

      1. associate-/l* 30.5%

         \[\leadsto \color{blue}{x \cdot \frac{z}{t}} \]

   9. Simplified 30.5%

      \[\leadsto \color{blue}{x \cdot \frac{z}{t}} \]

   if -4.14999999999999982e-131 < t < -7.3999999999999998e-164 or -2.30000000000000011e-191 < t < 1.61999999999999999e-9 or 18000 < t < 3.8e9

   1. Initial program 90.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 40.0%

      \[\leadsto \color{blue}{x} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 33: 33.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{+121}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{-52}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-194}:\\ \;\;\;\;\frac{x \cdot z}{t}\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-243}:\\ \;\;\;\;t \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-173}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-76}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -5.4e+121)
   y
   (if (<= t -5.6e-52)
     (* z (/ x t))
     (if (<= t -7.5e-194)
       (/ (* x z) t)
       (if (<= t -1.8e-243)
         (* t (/ x t))
         (if (<= t 3e-173) x (if (<= t 9.5e-76) (* t (/ (- y) a)) y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.4e+121) {
		tmp = y;
	} else if (t <= -5.6e-52) {
		tmp = z * (x / t);
	} else if (t <= -7.5e-194) {
		tmp = (x * z) / t;
	} else if (t <= -1.8e-243) {
		tmp = t * (x / t);
	} else if (t <= 3e-173) {
		tmp = x;
	} else if (t <= 9.5e-76) {
		tmp = t * (-y / a);
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-5.4d+121)) then
        tmp = y
    else if (t <= (-5.6d-52)) then
        tmp = z * (x / t)
    else if (t <= (-7.5d-194)) then
        tmp = (x * z) / t
    else if (t <= (-1.8d-243)) then
        tmp = t * (x / t)
    else if (t <= 3d-173) then
        tmp = x
    else if (t <= 9.5d-76) then
        tmp = t * (-y / a)
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.4e+121) {
		tmp = y;
	} else if (t <= -5.6e-52) {
		tmp = z * (x / t);
	} else if (t <= -7.5e-194) {
		tmp = (x * z) / t;
	} else if (t <= -1.8e-243) {
		tmp = t * (x / t);
	} else if (t <= 3e-173) {
		tmp = x;
	} else if (t <= 9.5e-76) {
		tmp = t * (-y / a);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -5.4e+121:
		tmp = y
	elif t <= -5.6e-52:
		tmp = z * (x / t)
	elif t <= -7.5e-194:
		tmp = (x * z) / t
	elif t <= -1.8e-243:
		tmp = t * (x / t)
	elif t <= 3e-173:
		tmp = x
	elif t <= 9.5e-76:
		tmp = t * (-y / a)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -5.4e+121)
		tmp = y;
	elseif (t <= -5.6e-52)
		tmp = Float64(z * Float64(x / t));
	elseif (t <= -7.5e-194)
		tmp = Float64(Float64(x * z) / t);
	elseif (t <= -1.8e-243)
		tmp = Float64(t * Float64(x / t));
	elseif (t <= 3e-173)
		tmp = x;
	elseif (t <= 9.5e-76)
		tmp = Float64(t * Float64(Float64(-y) / a));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -5.4e+121)
		tmp = y;
	elseif (t <= -5.6e-52)
		tmp = z * (x / t);
	elseif (t <= -7.5e-194)
		tmp = (x * z) / t;
	elseif (t <= -1.8e-243)
		tmp = t * (x / t);
	elseif (t <= 3e-173)
		tmp = x;
	elseif (t <= 9.5e-76)
		tmp = t * (-y / a);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -5.4e+121], y, If[LessEqual[t, -5.6e-52], N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -7.5e-194], N[(N[(x * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, -1.8e-243], N[(t * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3e-173], x, If[LessEqual[t, 9.5e-76], N[(t * N[((-y) / a), $MachinePrecision]), $MachinePrecision], y]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -5.4000000000000004e121 or 9.49999999999999984e-76 < t

   1. Initial program 43.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 52.8%

      \[\leadsto \color{blue}{y} \]

   if -5.4000000000000004e121 < t < -5.59999999999999989e-52

   1. Initial program 69.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 64.0%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 64.0%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 64.0%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 64.0%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 64.0%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 64.0%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 64.0%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 66.8%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 63.9%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 66.7%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 66.7%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]

   6. Taylor expanded in z around inf 42.3%

      \[\leadsto \color{blue}{z \cdot \left(\frac{x}{t} - \frac{y}{t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 42.3%

         \[\leadsto z \cdot \color{blue}{\frac{x - y}{t}} \]

   8. Simplified 42.3%

      \[\leadsto \color{blue}{z \cdot \frac{x - y}{t}} \]

   9. Taylor expanded in x around inf 31.3%

      \[\leadsto z \cdot \color{blue}{\frac{x}{t}} \]

   if -5.59999999999999989e-52 < t < -7.4999999999999998e-194

   1. Initial program 87.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 42.6%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 42.6%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 42.6%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 45.7%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 45.7%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 45.7%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 42.6%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 36.3%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 32.9%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 39.8%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 39.8%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]

   6. Taylor expanded in y around 0 34.3%

      \[\leadsto \color{blue}{\frac{x \cdot \left(z - a\right)}{t}} \]

   7. Taylor expanded in z around inf 34.2%

      \[\leadsto \frac{\color{blue}{x \cdot z}}{t} \]
   8. Step-by-step derivation

      1. *-commutative 34.2%

         \[\leadsto \frac{\color{blue}{z \cdot x}}{t} \]

   9. Simplified 34.2%

      \[\leadsto \frac{\color{blue}{z \cdot x}}{t} \]

   if -7.4999999999999998e-194 < t < -1.8000000000000001e-243

   1. Initial program 99.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 73.4%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. associate-/l* 73.5%

         \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   5. Simplified 73.5%

      \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]
   6. Step-by-step derivation

      1. clear-num 73.5%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

      2. inv-pow 73.5%

         \[\leadsto x + y \cdot \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}} \]

   7. Applied egg-rr 73.5%

      \[\leadsto x + y \cdot \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}} \]
   8. Step-by-step derivation

      1. unpow-1 73.5%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

   9. Simplified 73.5%

      \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

   10. Taylor expanded in z around 0 55.9%

       \[\leadsto \color{blue}{x + -1 \cdot \frac{t \cdot y}{a - t}} \]
   11. Step-by-step derivation

       1. mul-1-neg 55.9%

          \[\leadsto x + \color{blue}{\left(-\frac{t \cdot y}{a - t}\right)} \]

       2. unsub-neg 55.9%

          \[\leadsto \color{blue}{x - \frac{t \cdot y}{a - t}} \]

       3. associate-/l* 64.3%

          \[\leadsto x - \color{blue}{t \cdot \frac{y}{a - t}} \]

   12. Simplified 64.3%

       \[\leadsto \color{blue}{x - t \cdot \frac{y}{a - t}} \]

   13. Taylor expanded in t around 0 55.8%

       \[\leadsto x - \color{blue}{\frac{t \cdot y}{a}} \]
   14. Step-by-step derivation

       1. associate-/l* 55.8%

          \[\leadsto x - \color{blue}{t \cdot \frac{y}{a}} \]

   15. Simplified 55.8%

       \[\leadsto x - \color{blue}{t \cdot \frac{y}{a}} \]

   16. Taylor expanded in t around inf 55.7%

       \[\leadsto \color{blue}{t \cdot \left(\frac{x}{t} - \frac{y}{a}\right)} \]

   17. Taylor expanded in x around inf 55.7%

       \[\leadsto t \cdot \color{blue}{\frac{x}{t}} \]

   if -1.8000000000000001e-243 < t < 3.0000000000000001e-173

   1. Initial program 91.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 45.6%

      \[\leadsto \color{blue}{x} \]

   if 3.0000000000000001e-173 < t < 9.49999999999999984e-76

   1. Initial program 88.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 64.6%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. associate-/l* 70.5%

         \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   5. Simplified 70.5%

      \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]
   6. Step-by-step derivation

      1. clear-num 70.5%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

      2. inv-pow 70.5%

         \[\leadsto x + y \cdot \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}} \]

   7. Applied egg-rr 70.5%

      \[\leadsto x + y \cdot \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}} \]
   8. Step-by-step derivation

      1. unpow-1 70.5%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

   9. Simplified 70.5%

      \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

   10. Taylor expanded in z around 0 33.7%

       \[\leadsto \color{blue}{x + -1 \cdot \frac{t \cdot y}{a - t}} \]
   11. Step-by-step derivation

       1. mul-1-neg 33.7%

          \[\leadsto x + \color{blue}{\left(-\frac{t \cdot y}{a - t}\right)} \]

       2. unsub-neg 33.7%

          \[\leadsto \color{blue}{x - \frac{t \cdot y}{a - t}} \]

       3. associate-/l* 39.6%

          \[\leadsto x - \color{blue}{t \cdot \frac{y}{a - t}} \]

   12. Simplified 39.6%

       \[\leadsto \color{blue}{x - t \cdot \frac{y}{a - t}} \]

   13. Taylor expanded in t around 0 40.0%

       \[\leadsto x - \color{blue}{\frac{t \cdot y}{a}} \]
   14. Step-by-step derivation

       1. associate-/l* 51.7%

          \[\leadsto x - \color{blue}{t \cdot \frac{y}{a}} \]

   15. Simplified 51.7%

       \[\leadsto x - \color{blue}{t \cdot \frac{y}{a}} \]

   16. Taylor expanded in x around 0 27.9%

       \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot y}{a}} \]
   17. Step-by-step derivation

       1. associate-/l* 39.6%

          \[\leadsto -1 \cdot \color{blue}{\left(t \cdot \frac{y}{a}\right)} \]

       2. associate-*r* 39.6%

          \[\leadsto \color{blue}{\left(-1 \cdot t\right) \cdot \frac{y}{a}} \]

       3. neg-mul-1 39.6%

          \[\leadsto \color{blue}{\left(-t\right)} \cdot \frac{y}{a} \]

       4. *-commutative 39.6%

          \[\leadsto \color{blue}{\frac{y}{a} \cdot \left(-t\right)} \]

   18. Simplified 39.6%

       \[\leadsto \color{blue}{\frac{y}{a} \cdot \left(-t\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 45.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{+121}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{-52}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-194}:\\ \;\;\;\;\frac{x \cdot z}{t}\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-243}:\\ \;\;\;\;t \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-173}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-76}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 34: 54.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;t \leq -4.2 \cdot 10^{-21}:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-155}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-281}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-246}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-87}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y - x \cdot \frac{a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a z)))))
   (if (<= t -4.2e-21)
     (+ y (* x (/ z t)))
     (if (<= t -9e-155)
       t_1
       (if (<= t -8e-281)
         (* x (- 1.0 (/ z a)))
         (if (<= t 4e-246)
           (+ x (/ (* y z) a))
           (if (<= t 6e-87) t_1 (- y (* x (/ a t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / z));
	double tmp;
	if (t <= -4.2e-21) {
		tmp = y + (x * (z / t));
	} else if (t <= -9e-155) {
		tmp = t_1;
	} else if (t <= -8e-281) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 4e-246) {
		tmp = x + ((y * z) / a);
	} else if (t <= 6e-87) {
		tmp = t_1;
	} else {
		tmp = y - (x * (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y / (a / z))
    if (t <= (-4.2d-21)) then
        tmp = y + (x * (z / t))
    else if (t <= (-9d-155)) then
        tmp = t_1
    else if (t <= (-8d-281)) then
        tmp = x * (1.0d0 - (z / a))
    else if (t <= 4d-246) then
        tmp = x + ((y * z) / a)
    else if (t <= 6d-87) then
        tmp = t_1
    else
        tmp = y - (x * (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / z));
	double tmp;
	if (t <= -4.2e-21) {
		tmp = y + (x * (z / t));
	} else if (t <= -9e-155) {
		tmp = t_1;
	} else if (t <= -8e-281) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 4e-246) {
		tmp = x + ((y * z) / a);
	} else if (t <= 6e-87) {
		tmp = t_1;
	} else {
		tmp = y - (x * (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / z))
	tmp = 0
	if t <= -4.2e-21:
		tmp = y + (x * (z / t))
	elif t <= -9e-155:
		tmp = t_1
	elif t <= -8e-281:
		tmp = x * (1.0 - (z / a))
	elif t <= 4e-246:
		tmp = x + ((y * z) / a)
	elif t <= 6e-87:
		tmp = t_1
	else:
		tmp = y - (x * (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / z)))
	tmp = 0.0
	if (t <= -4.2e-21)
		tmp = Float64(y + Float64(x * Float64(z / t)));
	elseif (t <= -9e-155)
		tmp = t_1;
	elseif (t <= -8e-281)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (t <= 4e-246)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	elseif (t <= 6e-87)
		tmp = t_1;
	else
		tmp = Float64(y - Float64(x * Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / z));
	tmp = 0.0;
	if (t <= -4.2e-21)
		tmp = y + (x * (z / t));
	elseif (t <= -9e-155)
		tmp = t_1;
	elseif (t <= -8e-281)
		tmp = x * (1.0 - (z / a));
	elseif (t <= 4e-246)
		tmp = x + ((y * z) / a);
	elseif (t <= 6e-87)
		tmp = t_1;
	else
		tmp = y - (x * (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.2e-21], N[(y + N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -9e-155], t$95$1, If[LessEqual[t, -8e-281], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e-246], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e-87], t$95$1, N[(y - N[(x * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -4.20000000000000025e-21

   1. Initial program 52.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 63.1%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 63.1%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 63.1%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 63.1%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 63.1%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 63.1%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 63.1%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 71.8%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 82.1%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 82.1%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 82.1%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]
   6. Step-by-step derivation

      1. *-commutative 82.1%

         \[\leadsto y - \color{blue}{\left(z - a\right) \cdot \frac{y - x}{t}} \]

      2. clear-num 82.0%

         \[\leadsto y - \left(z - a\right) \cdot \color{blue}{\frac{1}{\frac{t}{y - x}}} \]

      3. un-div-inv 82.1%

         \[\leadsto y - \color{blue}{\frac{z - a}{\frac{t}{y - x}}} \]

   7. Applied egg-rr 82.1%

      \[\leadsto y - \color{blue}{\frac{z - a}{\frac{t}{y - x}}} \]

   8. Taylor expanded in y around 0 64.9%

      \[\leadsto y - \color{blue}{-1 \cdot \frac{x \cdot \left(z - a\right)}{t}} \]
   9. Step-by-step derivation

      1. mul-1-neg 64.9%

         \[\leadsto y - \color{blue}{\left(-\frac{x \cdot \left(z - a\right)}{t}\right)} \]

      2. associate-/l* 70.7%

         \[\leadsto y - \left(-\color{blue}{x \cdot \frac{z - a}{t}}\right) \]

   10. Simplified 70.7%

       \[\leadsto y - \color{blue}{\left(-x \cdot \frac{z - a}{t}\right)} \]

   11. Taylor expanded in a around 0 57.7%

       \[\leadsto \color{blue}{y + \frac{x \cdot z}{t}} \]
   12. Step-by-step derivation

       1. +-commutative 57.7%

          \[\leadsto \color{blue}{\frac{x \cdot z}{t} + y} \]

       2. associate-/l* 60.6%

          \[\leadsto \color{blue}{x \cdot \frac{z}{t}} + y \]

   13. Simplified 60.6%

       \[\leadsto \color{blue}{x \cdot \frac{z}{t} + y} \]

   if -4.20000000000000025e-21 < t < -9.0000000000000007e-155 or 3.99999999999999982e-246 < t < 6.00000000000000033e-87

   1. Initial program 85.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 72.5%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. associate-/l* 77.3%

         \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   5. Simplified 77.3%

      \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]
   6. Step-by-step derivation

      1. clear-num 77.3%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

      2. un-div-inv 77.3%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

   7. Applied egg-rr 77.3%

      \[\leadsto x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

   8. Taylor expanded in t around 0 66.8%

      \[\leadsto x + \frac{y}{\color{blue}{\frac{a}{z}}} \]

   if -9.0000000000000007e-155 < t < -8.0000000000000001e-281

   1. Initial program 96.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 64.6%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]

   4. Taylor expanded in x around inf 58.1%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z}{a}\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 58.1%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{z}{a}\right)}\right) \]

      2. unsub-neg 58.1%

         \[\leadsto x \cdot \color{blue}{\left(1 - \frac{z}{a}\right)} \]

   6. Simplified 58.1%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{a}\right)} \]

   if -8.0000000000000001e-281 < t < 3.99999999999999982e-246

   1. Initial program 99.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 79.9%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. associate-/l* 75.3%

         \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   5. Simplified 75.3%

      \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   6. Taylor expanded in t around 0 79.9%

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{a}} \]

   if 6.00000000000000033e-87 < t

   1. Initial program 45.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 67.6%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 67.6%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 67.6%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 67.6%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 67.6%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 67.6%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 67.6%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 73.1%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 74.5%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 74.5%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 74.5%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]
   6. Step-by-step derivation

      1. *-commutative 74.5%

         \[\leadsto y - \color{blue}{\left(z - a\right) \cdot \frac{y - x}{t}} \]

      2. clear-num 74.5%

         \[\leadsto y - \left(z - a\right) \cdot \color{blue}{\frac{1}{\frac{t}{y - x}}} \]

      3. un-div-inv 74.5%

         \[\leadsto y - \color{blue}{\frac{z - a}{\frac{t}{y - x}}} \]

   7. Applied egg-rr 74.5%

      \[\leadsto y - \color{blue}{\frac{z - a}{\frac{t}{y - x}}} \]

   8. Taylor expanded in y around 0 66.3%

      \[\leadsto y - \color{blue}{-1 \cdot \frac{x \cdot \left(z - a\right)}{t}} \]
   9. Step-by-step derivation

      1. mul-1-neg 66.3%

         \[\leadsto y - \color{blue}{\left(-\frac{x \cdot \left(z - a\right)}{t}\right)} \]

      2. associate-/l* 66.4%

         \[\leadsto y - \left(-\color{blue}{x \cdot \frac{z - a}{t}}\right) \]

   10. Simplified 66.4%

       \[\leadsto y - \color{blue}{\left(-x \cdot \frac{z - a}{t}\right)} \]

   11. Taylor expanded in z around 0 60.2%

       \[\leadsto \color{blue}{y + -1 \cdot \frac{a \cdot x}{t}} \]
   12. Step-by-step derivation

       1. mul-1-neg 60.2%

          \[\leadsto y + \color{blue}{\left(-\frac{a \cdot x}{t}\right)} \]

       2. *-commutative 60.2%

          \[\leadsto y + \left(-\frac{\color{blue}{x \cdot a}}{t}\right) \]

       3. associate-*r/ 59.1%

          \[\leadsto y + \left(-\color{blue}{x \cdot \frac{a}{t}}\right) \]

       4. unsub-neg 59.1%

          \[\leadsto \color{blue}{y - x \cdot \frac{a}{t}} \]

   13. Simplified 59.1%

       \[\leadsto \color{blue}{y - x \cdot \frac{a}{t}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{-21}:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-155}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-281}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-246}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-87}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y - x \cdot \frac{a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 35: 57.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{z}}\\ t_2 := y + x \cdot \frac{z}{t}\\ \mathbf{if}\;t \leq -9.5 \cdot 10^{-23}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-151}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-281}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-245}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-87}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a z)))) (t_2 (+ y (* x (/ z t)))))
   (if (<= t -9.5e-23)
     t_2
     (if (<= t -2.4e-151)
       t_1
       (if (<= t -8e-281)
         (* x (- 1.0 (/ z a)))
         (if (<= t 3e-245)
           (+ x (/ (* y z) a))
           (if (<= t 5.2e-87) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / z));
	double t_2 = y + (x * (z / t));
	double tmp;
	if (t <= -9.5e-23) {
		tmp = t_2;
	} else if (t <= -2.4e-151) {
		tmp = t_1;
	} else if (t <= -8e-281) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 3e-245) {
		tmp = x + ((y * z) / a);
	} else if (t <= 5.2e-87) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (y / (a / z))
    t_2 = y + (x * (z / t))
    if (t <= (-9.5d-23)) then
        tmp = t_2
    else if (t <= (-2.4d-151)) then
        tmp = t_1
    else if (t <= (-8d-281)) then
        tmp = x * (1.0d0 - (z / a))
    else if (t <= 3d-245) then
        tmp = x + ((y * z) / a)
    else if (t <= 5.2d-87) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / z));
	double t_2 = y + (x * (z / t));
	double tmp;
	if (t <= -9.5e-23) {
		tmp = t_2;
	} else if (t <= -2.4e-151) {
		tmp = t_1;
	} else if (t <= -8e-281) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 3e-245) {
		tmp = x + ((y * z) / a);
	} else if (t <= 5.2e-87) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / z))
	t_2 = y + (x * (z / t))
	tmp = 0
	if t <= -9.5e-23:
		tmp = t_2
	elif t <= -2.4e-151:
		tmp = t_1
	elif t <= -8e-281:
		tmp = x * (1.0 - (z / a))
	elif t <= 3e-245:
		tmp = x + ((y * z) / a)
	elif t <= 5.2e-87:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / z)))
	t_2 = Float64(y + Float64(x * Float64(z / t)))
	tmp = 0.0
	if (t <= -9.5e-23)
		tmp = t_2;
	elseif (t <= -2.4e-151)
		tmp = t_1;
	elseif (t <= -8e-281)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (t <= 3e-245)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	elseif (t <= 5.2e-87)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / z));
	t_2 = y + (x * (z / t));
	tmp = 0.0;
	if (t <= -9.5e-23)
		tmp = t_2;
	elseif (t <= -2.4e-151)
		tmp = t_1;
	elseif (t <= -8e-281)
		tmp = x * (1.0 - (z / a));
	elseif (t <= 3e-245)
		tmp = x + ((y * z) / a);
	elseif (t <= 5.2e-87)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.5e-23], t$95$2, If[LessEqual[t, -2.4e-151], t$95$1, If[LessEqual[t, -8e-281], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3e-245], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.2e-87], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -9.50000000000000058e-23 or 5.20000000000000005e-87 < t

   1. Initial program 48.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 65.6%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 65.6%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 65.6%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 65.6%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 65.6%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 65.6%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 65.6%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 72.5%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 77.9%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 77.9%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 77.9%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]
   6. Step-by-step derivation

      1. *-commutative 77.9%

         \[\leadsto y - \color{blue}{\left(z - a\right) \cdot \frac{y - x}{t}} \]

      2. clear-num 77.9%

         \[\leadsto y - \left(z - a\right) \cdot \color{blue}{\frac{1}{\frac{t}{y - x}}} \]

      3. un-div-inv 77.9%

         \[\leadsto y - \color{blue}{\frac{z - a}{\frac{t}{y - x}}} \]

   7. Applied egg-rr 77.9%

      \[\leadsto y - \color{blue}{\frac{z - a}{\frac{t}{y - x}}} \]

   8. Taylor expanded in y around 0 65.7%

      \[\leadsto y - \color{blue}{-1 \cdot \frac{x \cdot \left(z - a\right)}{t}} \]
   9. Step-by-step derivation

      1. mul-1-neg 65.7%

         \[\leadsto y - \color{blue}{\left(-\frac{x \cdot \left(z - a\right)}{t}\right)} \]

      2. associate-/l* 68.3%

         \[\leadsto y - \left(-\color{blue}{x \cdot \frac{z - a}{t}}\right) \]

   10. Simplified 68.3%

       \[\leadsto y - \color{blue}{\left(-x \cdot \frac{z - a}{t}\right)} \]

   11. Taylor expanded in a around 0 56.0%

       \[\leadsto \color{blue}{y + \frac{x \cdot z}{t}} \]
   12. Step-by-step derivation

       1. +-commutative 56.0%

          \[\leadsto \color{blue}{\frac{x \cdot z}{t} + y} \]

       2. associate-/l* 57.9%

          \[\leadsto \color{blue}{x \cdot \frac{z}{t}} + y \]

   13. Simplified 57.9%

       \[\leadsto \color{blue}{x \cdot \frac{z}{t} + y} \]

   if -9.50000000000000058e-23 < t < -2.4e-151 or 3.0000000000000002e-245 < t < 5.20000000000000005e-87

   1. Initial program 85.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 72.5%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. associate-/l* 77.3%

         \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   5. Simplified 77.3%

      \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]
   6. Step-by-step derivation

      1. clear-num 77.3%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

      2. un-div-inv 77.3%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

   7. Applied egg-rr 77.3%

      \[\leadsto x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

   8. Taylor expanded in t around 0 66.8%

      \[\leadsto x + \frac{y}{\color{blue}{\frac{a}{z}}} \]

   if -2.4e-151 < t < -8.0000000000000001e-281

   1. Initial program 96.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 64.6%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]

   4. Taylor expanded in x around inf 58.1%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z}{a}\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 58.1%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{z}{a}\right)}\right) \]

      2. unsub-neg 58.1%

         \[\leadsto x \cdot \color{blue}{\left(1 - \frac{z}{a}\right)} \]

   6. Simplified 58.1%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{a}\right)} \]

   if -8.0000000000000001e-281 < t < 3.0000000000000002e-245

   1. Initial program 99.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 79.9%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. associate-/l* 75.3%

         \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   5. Simplified 75.3%

      \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   6. Taylor expanded in t around 0 79.9%

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{a}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-23}:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-151}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-281}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-245}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-87}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 36: 44.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+220}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{+65}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{+23}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-82}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-61}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.5e+220)
   y
   (if (<= t -3.3e+65)
     (* x (/ (- z a) t))
     (if (<= t -5.8e+23)
       (+ y x)
       (if (<= t -7.5e-82)
         (* y (/ (- z t) a))
         (if (<= t 1.4e-61) (* x (- 1.0 (/ z a))) y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.5e+220) {
		tmp = y;
	} else if (t <= -3.3e+65) {
		tmp = x * ((z - a) / t);
	} else if (t <= -5.8e+23) {
		tmp = y + x;
	} else if (t <= -7.5e-82) {
		tmp = y * ((z - t) / a);
	} else if (t <= 1.4e-61) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.5d+220)) then
        tmp = y
    else if (t <= (-3.3d+65)) then
        tmp = x * ((z - a) / t)
    else if (t <= (-5.8d+23)) then
        tmp = y + x
    else if (t <= (-7.5d-82)) then
        tmp = y * ((z - t) / a)
    else if (t <= 1.4d-61) then
        tmp = x * (1.0d0 - (z / a))
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.5e+220) {
		tmp = y;
	} else if (t <= -3.3e+65) {
		tmp = x * ((z - a) / t);
	} else if (t <= -5.8e+23) {
		tmp = y + x;
	} else if (t <= -7.5e-82) {
		tmp = y * ((z - t) / a);
	} else if (t <= 1.4e-61) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.5e+220:
		tmp = y
	elif t <= -3.3e+65:
		tmp = x * ((z - a) / t)
	elif t <= -5.8e+23:
		tmp = y + x
	elif t <= -7.5e-82:
		tmp = y * ((z - t) / a)
	elif t <= 1.4e-61:
		tmp = x * (1.0 - (z / a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.5e+220)
		tmp = y;
	elseif (t <= -3.3e+65)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (t <= -5.8e+23)
		tmp = Float64(y + x);
	elseif (t <= -7.5e-82)
		tmp = Float64(y * Float64(Float64(z - t) / a));
	elseif (t <= 1.4e-61)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.5e+220)
		tmp = y;
	elseif (t <= -3.3e+65)
		tmp = x * ((z - a) / t);
	elseif (t <= -5.8e+23)
		tmp = y + x;
	elseif (t <= -7.5e-82)
		tmp = y * ((z - t) / a);
	elseif (t <= 1.4e-61)
		tmp = x * (1.0 - (z / a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.5e+220], y, If[LessEqual[t, -3.3e+65], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.8e+23], N[(y + x), $MachinePrecision], If[LessEqual[t, -7.5e-82], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.4e-61], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.5000000000000001e220 or 1.4000000000000001e-61 < t

   1. Initial program 40.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 58.7%

      \[\leadsto \color{blue}{y} \]

   if -2.5000000000000001e220 < t < -3.30000000000000023e65

   1. Initial program 49.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 63.3%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 63.3%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 63.3%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 63.3%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 63.3%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 63.3%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 63.3%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 75.1%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 81.2%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 81.2%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 81.2%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]

   6. Taylor expanded in y around 0 33.9%

      \[\leadsto \color{blue}{\frac{x \cdot \left(z - a\right)}{t}} \]
   7. Step-by-step derivation

      1. associate-/l* 39.7%

         \[\leadsto \color{blue}{x \cdot \frac{z - a}{t}} \]

   8. Simplified 39.7%

      \[\leadsto \color{blue}{x \cdot \frac{z - a}{t}} \]

   if -3.30000000000000023e65 < t < -5.80000000000000025e23

   1. Initial program 75.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 60.6%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. associate-/l* 60.7%

         \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   5. Simplified 60.7%

      \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   6. Taylor expanded in t around inf 48.9%

      \[\leadsto \color{blue}{x + y} \]

   if -5.80000000000000025e23 < t < -7.4999999999999997e-82

   1. Initial program 82.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 82.5%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. +-commutative 82.5%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. +-commutative 82.5%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{a - t} + 1\right)} \]

      3. distribute-lft-in 82.6%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \color{blue}{\left(x \cdot \left(-1 \cdot \frac{z - t}{a - t}\right) + x \cdot 1\right)} \]

      4. mul-1-neg 82.6%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(x \cdot \color{blue}{\left(-\frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      5. distribute-rgt-neg-in 82.6%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{\left(-x \cdot \frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      6. associate-/l* 82.0%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\left(-\color{blue}{\frac{x \cdot \left(z - t\right)}{a - t}}\right) + x \cdot 1\right) \]

      7. mul-1-neg 82.0%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} + x \cdot 1\right) \]

      8. *-rgt-identity 82.0%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \color{blue}{x}\right) \]

      9. associate-+l+ 82.1%

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(z - t\right)}{a - t} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) + x} \]

   5. Simplified 91.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)} \]

   6. Taylor expanded in y around inf 54.9%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 54.9%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

   8. Simplified 54.9%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   9. Taylor expanded in a around inf 37.8%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a}} \]
   10. Step-by-step derivation

       1. associate-/l* 42.2%

          \[\leadsto \color{blue}{y \cdot \frac{z - t}{a}} \]

   11. Simplified 42.2%

       \[\leadsto \color{blue}{y \cdot \frac{z - t}{a}} \]

   if -7.4999999999999997e-82 < t < 1.4000000000000001e-61

   1. Initial program 92.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 73.2%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]

   4. Taylor expanded in x around inf 56.9%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z}{a}\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 56.9%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{z}{a}\right)}\right) \]

      2. unsub-neg 56.9%

         \[\leadsto x \cdot \color{blue}{\left(1 - \frac{z}{a}\right)} \]

   6. Simplified 56.9%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{a}\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 53.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+220}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{+65}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{+23}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-82}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-61}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 37: 44.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+219}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{+65}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -1.62 \cdot 10^{+22}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-87}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-61}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.2e+219)
   y
   (if (<= t -3.4e+65)
     (* x (/ (- z a) t))
     (if (<= t -1.62e+22)
       (+ y x)
       (if (<= t -6.2e-87)
         (* y (/ z (- a t)))
         (if (<= t 1.4e-61) (* x (- 1.0 (/ z a))) y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.2e+219) {
		tmp = y;
	} else if (t <= -3.4e+65) {
		tmp = x * ((z - a) / t);
	} else if (t <= -1.62e+22) {
		tmp = y + x;
	} else if (t <= -6.2e-87) {
		tmp = y * (z / (a - t));
	} else if (t <= 1.4e-61) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-4.2d+219)) then
        tmp = y
    else if (t <= (-3.4d+65)) then
        tmp = x * ((z - a) / t)
    else if (t <= (-1.62d+22)) then
        tmp = y + x
    else if (t <= (-6.2d-87)) then
        tmp = y * (z / (a - t))
    else if (t <= 1.4d-61) then
        tmp = x * (1.0d0 - (z / a))
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.2e+219) {
		tmp = y;
	} else if (t <= -3.4e+65) {
		tmp = x * ((z - a) / t);
	} else if (t <= -1.62e+22) {
		tmp = y + x;
	} else if (t <= -6.2e-87) {
		tmp = y * (z / (a - t));
	} else if (t <= 1.4e-61) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.2e+219:
		tmp = y
	elif t <= -3.4e+65:
		tmp = x * ((z - a) / t)
	elif t <= -1.62e+22:
		tmp = y + x
	elif t <= -6.2e-87:
		tmp = y * (z / (a - t))
	elif t <= 1.4e-61:
		tmp = x * (1.0 - (z / a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.2e+219)
		tmp = y;
	elseif (t <= -3.4e+65)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (t <= -1.62e+22)
		tmp = Float64(y + x);
	elseif (t <= -6.2e-87)
		tmp = Float64(y * Float64(z / Float64(a - t)));
	elseif (t <= 1.4e-61)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.2e+219)
		tmp = y;
	elseif (t <= -3.4e+65)
		tmp = x * ((z - a) / t);
	elseif (t <= -1.62e+22)
		tmp = y + x;
	elseif (t <= -6.2e-87)
		tmp = y * (z / (a - t));
	elseif (t <= 1.4e-61)
		tmp = x * (1.0 - (z / a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.2e+219], y, If[LessEqual[t, -3.4e+65], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.62e+22], N[(y + x), $MachinePrecision], If[LessEqual[t, -6.2e-87], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.4e-61], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -4.19999999999999976e219 or 1.4000000000000001e-61 < t

   1. Initial program 40.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 58.7%

      \[\leadsto \color{blue}{y} \]

   if -4.19999999999999976e219 < t < -3.3999999999999999e65

   1. Initial program 49.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 63.3%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 63.3%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 63.3%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 63.3%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 63.3%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 63.3%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 63.3%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 75.1%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 81.2%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 81.2%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 81.2%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]

   6. Taylor expanded in y around 0 33.9%

      \[\leadsto \color{blue}{\frac{x \cdot \left(z - a\right)}{t}} \]
   7. Step-by-step derivation

      1. associate-/l* 39.7%

         \[\leadsto \color{blue}{x \cdot \frac{z - a}{t}} \]

   8. Simplified 39.7%

      \[\leadsto \color{blue}{x \cdot \frac{z - a}{t}} \]

   if -3.3999999999999999e65 < t < -1.62e22

   1. Initial program 75.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 60.6%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. associate-/l* 60.7%

         \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   5. Simplified 60.7%

      \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   6. Taylor expanded in t around inf 48.9%

      \[\leadsto \color{blue}{x + y} \]

   if -1.62e22 < t < -6.19999999999999995e-87

   1. Initial program 83.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 83.3%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. +-commutative 83.3%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. +-commutative 83.3%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{a - t} + 1\right)} \]

      3. distribute-lft-in 83.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \color{blue}{\left(x \cdot \left(-1 \cdot \frac{z - t}{a - t}\right) + x \cdot 1\right)} \]

      4. mul-1-neg 83.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(x \cdot \color{blue}{\left(-\frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      5. distribute-rgt-neg-in 83.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{\left(-x \cdot \frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      6. associate-/l* 82.7%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\left(-\color{blue}{\frac{x \cdot \left(z - t\right)}{a - t}}\right) + x \cdot 1\right) \]

      7. mul-1-neg 82.7%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} + x \cdot 1\right) \]

      8. *-rgt-identity 82.7%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \color{blue}{x}\right) \]

      9. associate-+l+ 82.8%

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(z - t\right)}{a - t} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) + x} \]

   5. Simplified 92.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)} \]

   6. Taylor expanded in y around inf 56.8%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 56.8%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

   8. Simplified 56.8%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   9. Taylor expanded in z around inf 35.6%

      \[\leadsto \color{blue}{\frac{y \cdot z}{a - t}} \]
   10. Step-by-step derivation

       1. associate-/l* 39.9%

          \[\leadsto \color{blue}{y \cdot \frac{z}{a - t}} \]

   11. Simplified 39.9%

       \[\leadsto \color{blue}{y \cdot \frac{z}{a - t}} \]

   if -6.19999999999999995e-87 < t < 1.4000000000000001e-61

   1. Initial program 92.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 73.0%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]

   4. Taylor expanded in x around inf 57.4%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z}{a}\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 57.4%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{z}{a}\right)}\right) \]

      2. unsub-neg 57.4%

         \[\leadsto x \cdot \color{blue}{\left(1 - \frac{z}{a}\right)} \]

   6. Simplified 57.4%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{a}\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+219}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{+65}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -1.62 \cdot 10^{+22}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-87}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-61}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 38: 47.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;t \leq -1.26 \cdot 10^{+101}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -7.3 \cdot 10^{-87}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-62}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= t -1.26e+101)
     y
     (if (<= t -3e-51)
       t_1
       (if (<= t -7.3e-87) (/ y (/ a z)) (if (<= t 3.6e-62) t_1 y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -1.26e+101) {
		tmp = y;
	} else if (t <= -3e-51) {
		tmp = t_1;
	} else if (t <= -7.3e-87) {
		tmp = y / (a / z);
	} else if (t <= 3.6e-62) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    if (t <= (-1.26d+101)) then
        tmp = y
    else if (t <= (-3d-51)) then
        tmp = t_1
    else if (t <= (-7.3d-87)) then
        tmp = y / (a / z)
    else if (t <= 3.6d-62) then
        tmp = t_1
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (t <= -1.26e+101) {
		tmp = y;
	} else if (t <= -3e-51) {
		tmp = t_1;
	} else if (t <= -7.3e-87) {
		tmp = y / (a / z);
	} else if (t <= 3.6e-62) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	tmp = 0
	if t <= -1.26e+101:
		tmp = y
	elif t <= -3e-51:
		tmp = t_1
	elif t <= -7.3e-87:
		tmp = y / (a / z)
	elif t <= 3.6e-62:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (t <= -1.26e+101)
		tmp = y;
	elseif (t <= -3e-51)
		tmp = t_1;
	elseif (t <= -7.3e-87)
		tmp = Float64(y / Float64(a / z));
	elseif (t <= 3.6e-62)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (t <= -1.26e+101)
		tmp = y;
	elseif (t <= -3e-51)
		tmp = t_1;
	elseif (t <= -7.3e-87)
		tmp = y / (a / z);
	elseif (t <= 3.6e-62)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.26e+101], y, If[LessEqual[t, -3e-51], t$95$1, If[LessEqual[t, -7.3e-87], N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.6e-62], t$95$1, y]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.2600000000000001e101 or 3.6e-62 < t

   1. Initial program 41.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 53.2%

      \[\leadsto \color{blue}{y} \]

   if -1.2600000000000001e101 < t < -3.00000000000000002e-51 or -7.29999999999999967e-87 < t < 3.6e-62

   1. Initial program 88.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 63.0%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]

   4. Taylor expanded in x around inf 51.3%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z}{a}\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 51.3%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{z}{a}\right)}\right) \]

      2. unsub-neg 51.3%

         \[\leadsto x \cdot \color{blue}{\left(1 - \frac{z}{a}\right)} \]

   6. Simplified 51.3%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{a}\right)} \]

   if -3.00000000000000002e-51 < t < -7.29999999999999967e-87

   1. Initial program 80.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 80.3%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. +-commutative 80.3%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]

      2. +-commutative 80.3%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + x \cdot \color{blue}{\left(-1 \cdot \frac{z - t}{a - t} + 1\right)} \]

      3. distribute-lft-in 80.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \color{blue}{\left(x \cdot \left(-1 \cdot \frac{z - t}{a - t}\right) + x \cdot 1\right)} \]

      4. mul-1-neg 80.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(x \cdot \color{blue}{\left(-\frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      5. distribute-rgt-neg-in 80.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{\left(-x \cdot \frac{z - t}{a - t}\right)} + x \cdot 1\right) \]

      6. associate-/l* 80.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\left(-\color{blue}{\frac{x \cdot \left(z - t\right)}{a - t}}\right) + x \cdot 1\right) \]

      7. mul-1-neg 80.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(\color{blue}{-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}} + x \cdot 1\right) \]

      8. *-rgt-identity 80.4%

         \[\leadsto \frac{y \cdot \left(z - t\right)}{a - t} + \left(-1 \cdot \frac{x \cdot \left(z - t\right)}{a - t} + \color{blue}{x}\right) \]

      9. associate-+l+ 80.5%

         \[\leadsto \color{blue}{\left(\frac{y \cdot \left(z - t\right)}{a - t} + -1 \cdot \frac{x \cdot \left(z - t\right)}{a - t}\right) + x} \]

   5. Simplified 90.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y - x}{a - t}, x\right)} \]

   6. Taylor expanded in y around inf 61.1%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 61.1%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

   8. Simplified 61.1%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   9. Taylor expanded in t around 0 37.1%

      \[\leadsto \color{blue}{\frac{y \cdot z}{a}} \]
   10. Step-by-step derivation

       1. associate-/l* 64.1%

          \[\leadsto x + \color{blue}{y \cdot \frac{z}{a}} \]

   11. Simplified 46.3%

       \[\leadsto \color{blue}{y \cdot \frac{z}{a}} \]
   12. Step-by-step derivation

       1. clear-num 46.3%

          \[\leadsto y \cdot \color{blue}{\frac{1}{\frac{a}{z}}} \]

       2. div-inv 46.3%

          \[\leadsto \color{blue}{\frac{y}{\frac{a}{z}}} \]

   13. Applied egg-rr 46.3%

       \[\leadsto \color{blue}{\frac{y}{\frac{a}{z}}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 39: 45.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{+219}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -3.9 \cdot 10^{+64}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-71}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.7e+219)
   y
   (if (<= t -3.9e+64)
     (* x (/ (- z a) t))
     (if (<= t 9.2e-71) (* x (- 1.0 (/ z a))) y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.7e+219) {
		tmp = y;
	} else if (t <= -3.9e+64) {
		tmp = x * ((z - a) / t);
	} else if (t <= 9.2e-71) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-3.7d+219)) then
        tmp = y
    else if (t <= (-3.9d+64)) then
        tmp = x * ((z - a) / t)
    else if (t <= 9.2d-71) then
        tmp = x * (1.0d0 - (z / a))
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.7e+219) {
		tmp = y;
	} else if (t <= -3.9e+64) {
		tmp = x * ((z - a) / t);
	} else if (t <= 9.2e-71) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.7e+219:
		tmp = y
	elif t <= -3.9e+64:
		tmp = x * ((z - a) / t)
	elif t <= 9.2e-71:
		tmp = x * (1.0 - (z / a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.7e+219)
		tmp = y;
	elseif (t <= -3.9e+64)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (t <= 9.2e-71)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.7e+219)
		tmp = y;
	elseif (t <= -3.9e+64)
		tmp = x * ((z - a) / t);
	elseif (t <= 9.2e-71)
		tmp = x * (1.0 - (z / a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.7e+219], y, If[LessEqual[t, -3.9e+64], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.2e-71], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.7e219 or 9.1999999999999994e-71 < t

   1. Initial program 41.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 58.1%

      \[\leadsto \color{blue}{y} \]

   if -3.7e219 < t < -3.8999999999999998e64

   1. Initial program 49.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 63.3%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 63.3%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 63.3%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 63.3%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 63.3%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 63.3%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 63.3%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 75.1%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 81.2%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 81.2%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 81.2%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]

   6. Taylor expanded in y around 0 33.9%

      \[\leadsto \color{blue}{\frac{x \cdot \left(z - a\right)}{t}} \]
   7. Step-by-step derivation

      1. associate-/l* 39.7%

         \[\leadsto \color{blue}{x \cdot \frac{z - a}{t}} \]

   8. Simplified 39.7%

      \[\leadsto \color{blue}{x \cdot \frac{z - a}{t}} \]

   if -3.8999999999999998e64 < t < 9.1999999999999994e-71

   1. Initial program 89.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 65.0%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]

   4. Taylor expanded in x around inf 50.0%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z}{a}\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 50.0%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{z}{a}\right)}\right) \]

      2. unsub-neg 50.0%

         \[\leadsto x \cdot \color{blue}{\left(1 - \frac{z}{a}\right)} \]

   6. Simplified 50.0%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{a}\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 40: 31.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+219}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq 7.1 \cdot 10^{+40}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;x \leq 4.15 \cdot 10^{+151}:\\ \;\;\;\;a \cdot \frac{x}{-t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.55e+219)
   (* z (/ x t))
   (if (<= x 7.1e+40)
     (+ y x)
     (if (<= x 4.15e+151) (* a (/ x (- t))) (* x (/ z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.55e+219) {
		tmp = z * (x / t);
	} else if (x <= 7.1e+40) {
		tmp = y + x;
	} else if (x <= 4.15e+151) {
		tmp = a * (x / -t);
	} else {
		tmp = x * (z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-1.55d+219)) then
        tmp = z * (x / t)
    else if (x <= 7.1d+40) then
        tmp = y + x
    else if (x <= 4.15d+151) then
        tmp = a * (x / -t)
    else
        tmp = x * (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.55e+219) {
		tmp = z * (x / t);
	} else if (x <= 7.1e+40) {
		tmp = y + x;
	} else if (x <= 4.15e+151) {
		tmp = a * (x / -t);
	} else {
		tmp = x * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.55e+219:
		tmp = z * (x / t)
	elif x <= 7.1e+40:
		tmp = y + x
	elif x <= 4.15e+151:
		tmp = a * (x / -t)
	else:
		tmp = x * (z / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.55e+219)
		tmp = Float64(z * Float64(x / t));
	elseif (x <= 7.1e+40)
		tmp = Float64(y + x);
	elseif (x <= 4.15e+151)
		tmp = Float64(a * Float64(x / Float64(-t)));
	else
		tmp = Float64(x * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.55e+219)
		tmp = z * (x / t);
	elseif (x <= 7.1e+40)
		tmp = y + x;
	elseif (x <= 4.15e+151)
		tmp = a * (x / -t);
	else
		tmp = x * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.55e+219], N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.1e+40], N[(y + x), $MachinePrecision], If[LessEqual[x, 4.15e+151], N[(a * N[(x / (-t)), $MachinePrecision]), $MachinePrecision], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.54999999999999984e219

   1. Initial program 54.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 39.1%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 39.1%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 39.1%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 45.0%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 45.0%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 45.0%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 39.1%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 44.1%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 43.7%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 61.9%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 61.9%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]

   6. Taylor expanded in z around inf 49.7%

      \[\leadsto \color{blue}{z \cdot \left(\frac{x}{t} - \frac{y}{t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 50.1%

         \[\leadsto z \cdot \color{blue}{\frac{x - y}{t}} \]

   8. Simplified 50.1%

      \[\leadsto \color{blue}{z \cdot \frac{x - y}{t}} \]

   9. Taylor expanded in x around inf 48.5%

      \[\leadsto z \cdot \color{blue}{\frac{x}{t}} \]

   if -1.54999999999999984e219 < x < 7.10000000000000037e40

   1. Initial program 72.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 62.2%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. associate-/l* 77.3%

         \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   5. Simplified 77.3%

      \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   6. Taylor expanded in t around inf 39.6%

      \[\leadsto \color{blue}{x + y} \]

   if 7.10000000000000037e40 < x < 4.14999999999999995e151

   1. Initial program 48.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 55.2%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 55.2%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 55.2%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 58.9%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 58.9%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 58.9%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 55.2%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 58.3%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 61.4%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 65.3%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 65.3%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]

   6. Taylor expanded in y around 0 31.0%

      \[\leadsto \color{blue}{\frac{x \cdot \left(z - a\right)}{t}} \]

   7. Taylor expanded in z around 0 20.7%

      \[\leadsto \color{blue}{-1 \cdot \frac{a \cdot x}{t}} \]
   8. Step-by-step derivation

      1. mul-1-neg 20.7%

         \[\leadsto \color{blue}{-\frac{a \cdot x}{t}} \]

      2. associate-/l* 30.7%

         \[\leadsto -\color{blue}{a \cdot \frac{x}{t}} \]

      3. distribute-rgt-neg-in 30.7%

         \[\leadsto \color{blue}{a \cdot \left(-\frac{x}{t}\right)} \]

      4. mul-1-neg 30.7%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \frac{x}{t}\right)} \]

      5. associate-*r/ 30.7%

         \[\leadsto a \cdot \color{blue}{\frac{-1 \cdot x}{t}} \]

      6. neg-mul-1 30.7%

         \[\leadsto a \cdot \frac{\color{blue}{-x}}{t} \]

   9. Simplified 30.7%

      \[\leadsto \color{blue}{a \cdot \frac{-x}{t}} \]

   if 4.14999999999999995e151 < x

   1. Initial program 51.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 52.1%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   4. Step-by-step derivation

      1. associate--l+ 52.1%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. distribute-lft-out-- 52.1%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 55.9%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 55.9%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 55.9%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 52.1%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 55.7%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 47.5%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 59.5%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 59.5%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]

   6. Taylor expanded in y around 0 41.2%

      \[\leadsto \color{blue}{\frac{x \cdot \left(z - a\right)}{t}} \]

   7. Taylor expanded in z around inf 34.0%

      \[\leadsto \color{blue}{\frac{x \cdot z}{t}} \]
   8. Step-by-step derivation

      1. associate-/l* 40.9%

         \[\leadsto \color{blue}{x \cdot \frac{z}{t}} \]

   9. Simplified 40.9%

      \[\leadsto \color{blue}{x \cdot \frac{z}{t}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 39.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+219}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq 7.1 \cdot 10^{+40}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;x \leq 4.15 \cdot 10^{+151}:\\ \;\;\;\;a \cdot \frac{x}{-t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 41: 39.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+30}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-74}:\\ \;\;\;\;t \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.1e+30) y (if (<= t -2e-74) (* t (/ x t)) (if (<= t 3e-14) x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.1e+30) {
		tmp = y;
	} else if (t <= -2e-74) {
		tmp = t * (x / t);
	} else if (t <= 3e-14) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.1d+30)) then
        tmp = y
    else if (t <= (-2d-74)) then
        tmp = t * (x / t)
    else if (t <= 3d-14) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.1e+30) {
		tmp = y;
	} else if (t <= -2e-74) {
		tmp = t * (x / t);
	} else if (t <= 3e-14) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.1e+30:
		tmp = y
	elif t <= -2e-74:
		tmp = t * (x / t)
	elif t <= 3e-14:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.1e+30)
		tmp = y;
	elseif (t <= -2e-74)
		tmp = Float64(t * Float64(x / t));
	elseif (t <= 3e-14)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.1e+30)
		tmp = y;
	elseif (t <= -2e-74)
		tmp = t * (x / t);
	elseif (t <= 3e-14)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.1e+30], y, If[LessEqual[t, -2e-74], N[(t * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3e-14], x, y]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.1e30 or 2.9999999999999998e-14 < t

   1. Initial program 41.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 52.2%

      \[\leadsto \color{blue}{y} \]

   if -2.1e30 < t < -1.99999999999999992e-74

   1. Initial program 82.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 67.3%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   4. Step-by-step derivation

      1. associate-/l* 71.6%

         \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   5. Simplified 71.6%

      \[\leadsto x + \color{blue}{y \cdot \frac{z - t}{a - t}} \]
   6. Step-by-step derivation

      1. clear-num 71.6%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

      2. inv-pow 71.6%

         \[\leadsto x + y \cdot \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}} \]

   7. Applied egg-rr 71.6%

      \[\leadsto x + y \cdot \color{blue}{{\left(\frac{a - t}{z - t}\right)}^{-1}} \]
   8. Step-by-step derivation

      1. unpow-1 71.6%

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

   9. Simplified 71.6%

      \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}} \]

   10. Taylor expanded in z around 0 41.9%

       \[\leadsto \color{blue}{x + -1 \cdot \frac{t \cdot y}{a - t}} \]
   11. Step-by-step derivation

       1. mul-1-neg 41.9%

          \[\leadsto x + \color{blue}{\left(-\frac{t \cdot y}{a - t}\right)} \]

       2. unsub-neg 41.9%

          \[\leadsto \color{blue}{x - \frac{t \cdot y}{a - t}} \]

       3. associate-/l* 41.9%

          \[\leadsto x - \color{blue}{t \cdot \frac{y}{a - t}} \]

   12. Simplified 41.9%

       \[\leadsto \color{blue}{x - t \cdot \frac{y}{a - t}} \]

   13. Taylor expanded in t around 0 34.3%

       \[\leadsto x - \color{blue}{\frac{t \cdot y}{a}} \]
   14. Step-by-step derivation

       1. associate-/l* 34.3%

          \[\leadsto x - \color{blue}{t \cdot \frac{y}{a}} \]

   15. Simplified 34.3%

       \[\leadsto x - \color{blue}{t \cdot \frac{y}{a}} \]

   16. Taylor expanded in t around inf 34.2%

       \[\leadsto \color{blue}{t \cdot \left(\frac{x}{t} - \frac{y}{a}\right)} \]

   17. Taylor expanded in x around inf 28.6%

       \[\leadsto t \cdot \color{blue}{\frac{x}{t}} \]

   if -1.99999999999999992e-74 < t < 2.9999999999999998e-14

   1. Initial program 89.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 34.8%

      \[\leadsto \color{blue}{x} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 42: 36.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+30}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 8.3 \cdot 10^{-165}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.4e+30) y (if (<= t 8.3e-165) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.4e+30) {
		tmp = y;
	} else if (t <= 8.3e-165) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-3.4d+30)) then
        tmp = y
    else if (t <= 8.3d-165) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.4e+30) {
		tmp = y;
	} else if (t <= 8.3e-165) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.4e+30:
		tmp = y
	elif t <= 8.3e-165:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.4e+30)
		tmp = y;
	elseif (t <= 8.3e-165)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.4e+30)
		tmp = y;
	elseif (t <= 8.3e-165)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.4e+30], y, If[LessEqual[t, 8.3e-165], x, y]]

Derivation

1. Split input into 2 regimes

2. if t < -3.4000000000000002e30 or 8.2999999999999996e-165 < t

   1. Initial program 49.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 45.0%

      \[\leadsto \color{blue}{y} \]

   if -3.4000000000000002e30 < t < 8.2999999999999996e-165

   1. Initial program 90.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 36.1%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 43: 25.2% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a) {
	return x;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x;
}

Python

def code(x, y, z, t, a):
	return x

Julia

function code(x, y, z, t, a)
	return x
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 66.7%

   \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
2. Add Preprocessing

3. Taylor expanded in a around inf 21.4%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Developer target: 86.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;a < -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a < 3.774403170083174 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))
   (if (< a -1.6153062845442575e-142)
     t_1
     (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - x) / 1.0d0) * ((z - t) / (a - t)))
    if (a < (-1.6153062845442575d-142)) then
        tmp = t_1
    else if (a < 3.774403170083174d-182) then
        tmp = y - ((z / t) * (y - x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)))
	tmp = 0
	if a < -1.6153062845442575e-142:
		tmp = t_1
	elif a < 3.774403170083174e-182:
		tmp = y - ((z / t) * (y - x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) / 1.0) * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = Float64(y - Float64(Float64(z / t) * Float64(y - x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	tmp = 0.0;
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = y - ((z / t) * (y - x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] / 1.0), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[a, -1.6153062845442575e-142], t$95$1, If[Less[a, 3.774403170083174e-182], N[(y - N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024107 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

  :alt
  (if (< a -1.6153062845442575e-142) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t)))) (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))

  (+ x (/ (* (- y x) (- z t)) (- a t))))