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

Percentage Accurate: 67.9% → 88.5%

Time: 15.3s

Alternatives: 30

Speedup: 0.6×

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: 67.9% 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: 88.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;y - \frac{y - x}{t} \cdot \left(z - a\right)\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-32}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right) + x \cdot \left(t - z\right)}{a - t}\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-288} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot a - \mathsf{fma}\left(z, y - x, a \cdot \frac{\left(x - y\right) \cdot \left(a - z\right)}{t}\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_1 (- INFINITY))
     (- y (* (/ (- y x) t) (- z a)))
     (if (<= t_1 -1e-32)
       (+ x (/ (+ (* y (- z t)) (* x (- t z))) (- a t)))
       (if (or (<= t_1 -2e-288) (not (<= t_1 0.0)))
         (fma (- y x) (/ (- z t) (- a t)) x)
         (+
          y
          (/
           (- (* (- y x) a) (fma z (- y x) (* a (/ (* (- x y) (- a z)) t))))
           t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = y - (((y - x) / t) * (z - a));
	} else if (t_1 <= -1e-32) {
		tmp = x + (((y * (z - t)) + (x * (t - z))) / (a - t));
	} else if ((t_1 <= -2e-288) || !(t_1 <= 0.0)) {
		tmp = fma((y - x), ((z - t) / (a - t)), x);
	} else {
		tmp = y + ((((y - x) * a) - fma(z, (y - x), (a * (((x - y) * (a - z)) / t)))) / t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(y - Float64(Float64(Float64(y - x) / t) * Float64(z - a)));
	elseif (t_1 <= -1e-32)
		tmp = Float64(x + Float64(Float64(Float64(y * Float64(z - t)) + Float64(x * Float64(t - z))) / Float64(a - t)));
	elseif ((t_1 <= -2e-288) || !(t_1 <= 0.0))
		tmp = fma(Float64(y - x), Float64(Float64(z - t) / Float64(a - t)), x);
	else
		tmp = Float64(y + Float64(Float64(Float64(Float64(y - x) * a) - fma(z, Float64(y - x), Float64(a * Float64(Float64(Float64(x - y) * Float64(a - z)) / t)))) / t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(y - N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -1e-32], N[(x + N[(N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(x * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$1, -2e-288], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(y + N[(N[(N[(N[(y - x), $MachinePrecision] * a), $MachinePrecision] - N[(z * N[(y - x), $MachinePrecision] + N[(a * N[(N[(N[(x - y), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 33.6%

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

   3. Taylor expanded in t around inf 42.5%

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

      1. associate--l+ 42.5%

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

      2. distribute-lft-out-- 42.5%

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

      3. div-sub 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 42.5%

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

      7. associate-/l* 59.1%

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

      8. associate-/l* 78.0%

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

      9. distribute-rgt-out-- 83.0%

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

   5. Simplified 83.0%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -1.00000000000000006e-32

   1. Initial program 96.7%

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

      1. *-commutative 96.7%

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

      2. sub-neg 96.7%

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

      3. distribute-lft-in 96.7%

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

   4. Applied egg-rr 96.7%

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

   if -1.00000000000000006e-32 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -2.00000000000000012e-288 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 80.0%

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

      1. +-commutative 80.0%

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

      2. associate-/l* 95.6%

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

      3. fma-define 95.6%

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

   3. Simplified 95.6%

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

   if -2.00000000000000012e-288 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   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 99.7%

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

      1. mul-1-neg 99.7%

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

      2. fma-define 99.7%

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

      3. associate-/l* 99.7%

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

      4. distribute-rgt-out-- 99.7%

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

   5. Simplified 99.7%

      \[\leadsto \color{blue}{y + \left(-\frac{\mathsf{fma}\left(z, y - x, a \cdot \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\right) - a \cdot \left(y - x\right)}{t}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -\infty:\\ \;\;\;\;y - \frac{y - x}{t} \cdot \left(z - a\right)\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -1 \cdot 10^{-32}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right) + x \cdot \left(t - z\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -2 \cdot 10^{-288} \lor \neg \left(x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{\left(y - x\right) \cdot a - \mathsf{fma}\left(z, y - x, a \cdot \frac{\left(x - y\right) \cdot \left(a - z\right)}{t}\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 88.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;y - \frac{y - x}{t} \cdot \left(z - a\right)\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-32}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right) + x \cdot \left(t - z\right)}{a - t}\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-288} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y - \frac{\left(y - x\right) \cdot z + a \cdot \left(x - y\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_1 (- INFINITY))
     (- y (* (/ (- y x) t) (- z a)))
     (if (<= t_1 -1e-32)
       (+ x (/ (+ (* y (- z t)) (* x (- t z))) (- a t)))
       (if (or (<= t_1 -2e-288) (not (<= t_1 0.0)))
         (fma (- y x) (/ (- z t) (- a t)) x)
         (- y (/ (+ (* (- y x) z) (* a (- x y))) t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = y - (((y - x) / t) * (z - a));
	} else if (t_1 <= -1e-32) {
		tmp = x + (((y * (z - t)) + (x * (t - z))) / (a - t));
	} else if ((t_1 <= -2e-288) || !(t_1 <= 0.0)) {
		tmp = fma((y - x), ((z - t) / (a - t)), x);
	} else {
		tmp = y - ((((y - x) * z) + (a * (x - y))) / t);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(y - Float64(Float64(Float64(y - x) / t) * Float64(z - a)));
	elseif (t_1 <= -1e-32)
		tmp = Float64(x + Float64(Float64(Float64(y * Float64(z - t)) + Float64(x * Float64(t - z))) / Float64(a - t)));
	elseif ((t_1 <= -2e-288) || !(t_1 <= 0.0))
		tmp = fma(Float64(y - x), Float64(Float64(z - t) / Float64(a - t)), x);
	else
		tmp = Float64(y - Float64(Float64(Float64(Float64(y - x) * z) + Float64(a * Float64(x - y))) / t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(y - N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -1e-32], N[(x + N[(N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(x * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$1, -2e-288], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(y - N[(N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] + N[(a * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 33.6%

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

   3. Taylor expanded in t around inf 42.5%

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

      1. associate--l+ 42.5%

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

      2. distribute-lft-out-- 42.5%

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

      3. div-sub 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 42.5%

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

      7. associate-/l* 59.1%

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

      8. associate-/l* 78.0%

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

      9. distribute-rgt-out-- 83.0%

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

   5. Simplified 83.0%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -1.00000000000000006e-32

   1. Initial program 96.7%

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

      1. *-commutative 96.7%

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

      2. sub-neg 96.7%

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

      3. distribute-lft-in 96.7%

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

   4. Applied egg-rr 96.7%

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

   if -1.00000000000000006e-32 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -2.00000000000000012e-288 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 80.0%

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

      1. +-commutative 80.0%

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

      2. associate-/l* 95.6%

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

      3. fma-define 95.6%

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

   3. Simplified 95.6%

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

   if -2.00000000000000012e-288 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   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 99.7%

      \[\leadsto \color{blue}{y + -1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -\infty:\\ \;\;\;\;y - \frac{y - x}{t} \cdot \left(z - a\right)\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -1 \cdot 10^{-32}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right) + x \cdot \left(t - z\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -2 \cdot 10^{-288} \lor \neg \left(x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;y - \frac{\left(y - x\right) \cdot z + a \cdot \left(x - y\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - \frac{y - x}{t} \cdot \left(z - a\right)\\ t_2 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-288}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;y - \frac{\left(x - y\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+291}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- y (* (/ (- y x) t) (- z a))))
        (t_2 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -2e-288)
       t_2
       (if (<= t_2 0.0)
         (- y (/ (* (- x y) (- a z)) t))
         (if (<= t_2 4e+291) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (((y - x) / t) * (z - a));
	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-288) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y - (((x - y) * (a - z)) / t);
	} else if (t_2 <= 4e+291) {
		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) * (z - a));
	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-288) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y - (((x - y) * (a - z)) / t);
	} else if (t_2 <= 4e+291) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - (((y - x) / t) * (z - a))
	t_2 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -2e-288:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = y - (((x - y) * (a - z)) / t)
	elif t_2 <= 4e+291:
		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(z - a)))
	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-288)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(y - Float64(Float64(Float64(x - y) * Float64(a - z)) / t));
	elseif (t_2 <= 4e+291)
		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) * (z - a));
	t_2 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -2e-288)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = y - (((x - y) * (a - z)) / t);
	elseif (t_2 <= 4e+291)
		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[(z - a), $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-288], t$95$2, If[LessEqual[t$95$2, 0.0], N[(y - N[(N[(N[(x - y), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 4e+291], 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 3.9999999999999998e291 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 35.5%

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

   3. Taylor expanded in t around inf 44.9%

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

      1. associate--l+ 44.9%

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

      2. distribute-lft-out-- 44.9%

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

      3. div-sub 47.5%

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

      4. mul-1-neg 47.5%

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

      5. unsub-neg 47.5%

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

      6. div-sub 44.9%

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

      7. associate-/l* 60.4%

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

      8. associate-/l* 71.3%

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

      9. distribute-rgt-out-- 76.4%

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

   5. Simplified 76.4%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -2.00000000000000012e-288 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 3.9999999999999998e291

   1. Initial program 96.8%

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

   if -2.00000000000000012e-288 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 3.8%

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

      1. +-commutative 3.8%

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

      2. associate-/l* 3.8%

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

      3. fma-define 3.8%

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

   3. Simplified 3.8%

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

      1. clear-num 3.8%

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

      2. associate-/r/ 3.7%

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

   6. Applied egg-rr 3.7%

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

   7. Taylor expanded in t around inf 99.7%

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

      1. associate--l+ 99.7%

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

      2. associate-*r/ 99.7%

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

      3. associate-*r/ 99.7%

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

      4. mul-1-neg 99.7%

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

      5. div-sub 99.7%

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

      6. mul-1-neg 99.7%

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

      7. distribute-lft-out-- 99.7%

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

      8. associate-*r/ 99.7%

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

      9. mul-1-neg 99.7%

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

      10. unsub-neg 99.7%

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

      11. distribute-rgt-out-- 99.6%

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

   9. Simplified 99.6%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -\infty:\\ \;\;\;\;y - \frac{y - x}{t} \cdot \left(z - a\right)\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -2 \cdot 10^{-288}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y - \frac{\left(x - y\right) \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 4 \cdot 10^{+291}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{y - x}{t} \cdot \left(z - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;y - \frac{y - x}{t} \cdot \left(z - a\right)\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-288}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;y - \frac{\left(y - x\right) \cdot z + a \cdot \left(x - y\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \left(\left(x - y\right) \cdot \frac{-1}{a - t}\right) \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_1 (- INFINITY))
     (- y (* (/ (- y x) t) (- z a)))
     (if (<= t_1 -2e-288)
       t_1
       (if (<= t_1 0.0)
         (- y (/ (+ (* (- y x) z) (* a (- x y))) t))
         (- x (* (* (- x y) (/ -1.0 (- a t))) (- t z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = y - (((y - x) / t) * (z - a));
	} else if (t_1 <= -2e-288) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = y - ((((y - x) * z) + (a * (x - y))) / t);
	} else {
		tmp = x - (((x - y) * (-1.0 / (a - t))) * (t - z));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = y - (((y - x) / t) * (z - a));
	} else if (t_1 <= -2e-288) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = y - ((((y - x) * z) + (a * (x - y))) / t);
	} else {
		tmp = x - (((x - y) * (-1.0 / (a - t))) * (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = y - (((y - x) / t) * (z - a))
	elif t_1 <= -2e-288:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = y - ((((y - x) * z) + (a * (x - y))) / t)
	else:
		tmp = x - (((x - y) * (-1.0 / (a - t))) * (t - z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(y - Float64(Float64(Float64(y - x) / t) * Float64(z - a)));
	elseif (t_1 <= -2e-288)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(y - Float64(Float64(Float64(Float64(y - x) * z) + Float64(a * Float64(x - y))) / t));
	else
		tmp = Float64(x - Float64(Float64(Float64(x - y) * Float64(-1.0 / Float64(a - t))) * Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = y - (((y - x) / t) * (z - a));
	elseif (t_1 <= -2e-288)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = y - ((((y - x) * z) + (a * (x - y))) / t);
	else
		tmp = x - (((x - y) * (-1.0 / (a - t))) * (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(y - N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e-288], t$95$1, If[LessEqual[t$95$1, 0.0], N[(y - N[(N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] + N[(a * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(N[(x - y), $MachinePrecision] * N[(-1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 33.6%

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

   3. Taylor expanded in t around inf 42.5%

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

      1. associate--l+ 42.5%

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

      2. distribute-lft-out-- 42.5%

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

      3. div-sub 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 42.5%

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

      7. associate-/l* 59.1%

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

      8. associate-/l* 78.0%

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

      9. distribute-rgt-out-- 83.0%

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

   5. Simplified 83.0%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -2.00000000000000012e-288

   1. Initial program 94.9%

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

   if -2.00000000000000012e-288 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   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 99.7%

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

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

   1. Initial program 76.9%

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

      1. div-inv 76.8%

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

      2. *-commutative 76.8%

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

      3. associate-*l* 94.3%

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

   4. Applied egg-rr 94.3%

      \[\leadsto x + \color{blue}{\left(z - t\right) \cdot \left(\left(y - x\right) \cdot \frac{1}{a - t}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -\infty:\\ \;\;\;\;y - \frac{y - x}{t} \cdot \left(z - a\right)\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -2 \cdot 10^{-288}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y - \frac{\left(y - x\right) \cdot z + a \cdot \left(x - y\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \left(\left(x - y\right) \cdot \frac{-1}{a - t}\right) \cdot \left(t - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;y - \frac{y - x}{t} \cdot \left(z - a\right)\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-288}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;y + \left(z - a\right) \cdot \left(\left(y - x\right) \cdot \frac{-1}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(\left(x - y\right) \cdot \frac{-1}{a - t}\right) \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_1 (- INFINITY))
     (- y (* (/ (- y x) t) (- z a)))
     (if (<= t_1 -2e-288)
       t_1
       (if (<= t_1 0.0)
         (+ y (* (- z a) (* (- y x) (/ -1.0 t))))
         (- x (* (* (- x y) (/ -1.0 (- a t))) (- t z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = y - (((y - x) / t) * (z - a));
	} else if (t_1 <= -2e-288) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = y + ((z - a) * ((y - x) * (-1.0 / t)));
	} else {
		tmp = x - (((x - y) * (-1.0 / (a - t))) * (t - z));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = y - (((y - x) / t) * (z - a));
	} else if (t_1 <= -2e-288) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = y + ((z - a) * ((y - x) * (-1.0 / t)));
	} else {
		tmp = x - (((x - y) * (-1.0 / (a - t))) * (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = y - (((y - x) / t) * (z - a))
	elif t_1 <= -2e-288:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = y + ((z - a) * ((y - x) * (-1.0 / t)))
	else:
		tmp = x - (((x - y) * (-1.0 / (a - t))) * (t - z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(y - Float64(Float64(Float64(y - x) / t) * Float64(z - a)));
	elseif (t_1 <= -2e-288)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(y + Float64(Float64(z - a) * Float64(Float64(y - x) * Float64(-1.0 / t))));
	else
		tmp = Float64(x - Float64(Float64(Float64(x - y) * Float64(-1.0 / Float64(a - t))) * Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = y - (((y - x) / t) * (z - a));
	elseif (t_1 <= -2e-288)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = y + ((z - a) * ((y - x) * (-1.0 / t)));
	else
		tmp = x - (((x - y) * (-1.0 / (a - t))) * (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(y - N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e-288], t$95$1, If[LessEqual[t$95$1, 0.0], N[(y + N[(N[(z - a), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] * N[(-1.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(N[(x - y), $MachinePrecision] * N[(-1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 33.6%

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

   3. Taylor expanded in t around inf 42.5%

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

      1. associate--l+ 42.5%

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

      2. distribute-lft-out-- 42.5%

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

      3. div-sub 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 42.5%

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

      7. associate-/l* 59.1%

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

      8. associate-/l* 78.0%

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

      9. distribute-rgt-out-- 83.0%

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

   5. Simplified 83.0%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -2.00000000000000012e-288

   1. Initial program 94.9%

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

   if -2.00000000000000012e-288 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   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 99.7%

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

      1. associate--l+ 99.7%

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

      2. distribute-lft-out-- 99.7%

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

      3. div-sub 99.7%

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

      4. mul-1-neg 99.7%

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

      5. unsub-neg 99.7%

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

      6. div-sub 99.7%

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

      7. associate-/l* 99.6%

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

      8. associate-/l* 99.6%

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

      9. distribute-rgt-out-- 99.6%

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

   5. Simplified 99.6%

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

      1. frac-2neg 99.6%

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

      2. div-inv 99.6%

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

      3. sub-neg 99.6%

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

      4. distribute-neg-in 99.6%

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

      5. add-sqr-sqrt 37.8%

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

      6. sqrt-unprod 48.7%

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

      7. sqr-neg 48.7%

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

      8. sqrt-unprod 19.9%

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

      9. add-sqr-sqrt 39.2%

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

      10. add-sqr-sqrt 19.3%

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

      11. sqrt-unprod 62.8%

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

      12. sqr-neg 62.8%

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

      13. sqrt-unprod 61.5%

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

      14. add-sqr-sqrt 99.6%

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

   7. Applied egg-rr 99.6%

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

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

   1. Initial program 76.9%

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

      1. div-inv 76.8%

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

      2. *-commutative 76.8%

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

      3. associate-*l* 94.3%

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

   4. Applied egg-rr 94.3%

      \[\leadsto x + \color{blue}{\left(z - t\right) \cdot \left(\left(y - x\right) \cdot \frac{1}{a - t}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -\infty:\\ \;\;\;\;y - \frac{y - x}{t} \cdot \left(z - a\right)\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -2 \cdot 10^{-288}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y + \left(z - a\right) \cdot \left(\left(y - x\right) \cdot \frac{-1}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(\left(x - y\right) \cdot \frac{-1}{a - t}\right) \cdot \left(t - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;y - \frac{y - x}{t} \cdot \left(z - a\right)\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-288}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;y - \frac{\left(x - y\right) \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \left(\left(x - y\right) \cdot \frac{-1}{a - t}\right) \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_1 (- INFINITY))
     (- y (* (/ (- y x) t) (- z a)))
     (if (<= t_1 -2e-288)
       t_1
       (if (<= t_1 0.0)
         (- y (/ (* (- x y) (- a z)) t))
         (- x (* (* (- x y) (/ -1.0 (- a t))) (- t z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = y - (((y - x) / t) * (z - a));
	} else if (t_1 <= -2e-288) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = y - (((x - y) * (a - z)) / t);
	} else {
		tmp = x - (((x - y) * (-1.0 / (a - t))) * (t - z));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = y - (((y - x) / t) * (z - a));
	} else if (t_1 <= -2e-288) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = y - (((x - y) * (a - z)) / t);
	} else {
		tmp = x - (((x - y) * (-1.0 / (a - t))) * (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) * (z - t)) / (a - t))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = y - (((y - x) / t) * (z - a))
	elif t_1 <= -2e-288:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = y - (((x - y) * (a - z)) / t)
	else:
		tmp = x - (((x - y) * (-1.0 / (a - t))) * (t - z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(y - Float64(Float64(Float64(y - x) / t) * Float64(z - a)));
	elseif (t_1 <= -2e-288)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(y - Float64(Float64(Float64(x - y) * Float64(a - z)) / t));
	else
		tmp = Float64(x - Float64(Float64(Float64(x - y) * Float64(-1.0 / Float64(a - t))) * Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = y - (((y - x) / t) * (z - a));
	elseif (t_1 <= -2e-288)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = y - (((x - y) * (a - z)) / t);
	else
		tmp = x - (((x - y) * (-1.0 / (a - t))) * (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(y - N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e-288], t$95$1, If[LessEqual[t$95$1, 0.0], N[(y - N[(N[(N[(x - y), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(N[(x - y), $MachinePrecision] * N[(-1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 33.6%

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

   3. Taylor expanded in t around inf 42.5%

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

      1. associate--l+ 42.5%

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

      2. distribute-lft-out-- 42.5%

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

      3. div-sub 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 42.5%

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

      7. associate-/l* 59.1%

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

      8. associate-/l* 78.0%

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

      9. distribute-rgt-out-- 83.0%

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

   5. Simplified 83.0%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -2.00000000000000012e-288

   1. Initial program 94.9%

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

   if -2.00000000000000012e-288 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 3.8%

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

      1. +-commutative 3.8%

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

      2. associate-/l* 3.8%

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

      3. fma-define 3.8%

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

   3. Simplified 3.8%

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

      1. clear-num 3.8%

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

      2. associate-/r/ 3.7%

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

   6. Applied egg-rr 3.7%

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

   7. Taylor expanded in t around inf 99.7%

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

      1. associate--l+ 99.7%

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

      2. associate-*r/ 99.7%

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

      3. associate-*r/ 99.7%

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

      4. mul-1-neg 99.7%

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

      5. div-sub 99.7%

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

      6. mul-1-neg 99.7%

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

      7. distribute-lft-out-- 99.7%

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

      8. associate-*r/ 99.7%

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

      9. mul-1-neg 99.7%

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

      10. unsub-neg 99.7%

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

      11. distribute-rgt-out-- 99.6%

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

   9. Simplified 99.6%

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

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

   1. Initial program 76.9%

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

      1. div-inv 76.8%

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

      2. *-commutative 76.8%

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

      3. associate-*l* 94.3%

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

   4. Applied egg-rr 94.3%

      \[\leadsto x + \color{blue}{\left(z - t\right) \cdot \left(\left(y - x\right) \cdot \frac{1}{a - t}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -\infty:\\ \;\;\;\;y - \frac{y - x}{t} \cdot \left(z - a\right)\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -2 \cdot 10^{-288}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y - \frac{\left(x - y\right) \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \left(\left(x - y\right) \cdot \frac{-1}{a - t}\right) \cdot \left(t - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 53.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - z \cdot \frac{y}{t}\\ t_2 := x + y \cdot \frac{z}{a}\\ \mathbf{if}\;t \leq -5.5 \cdot 10^{+70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-89}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-289}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-67}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-23}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{-8}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{+40}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- y (* z (/ y t)))) (t_2 (+ x (* y (/ z a)))))
   (if (<= t -5.5e+70)
     t_1
     (if (<= t -2.8e-89)
       (- x (* t (/ y a)))
       (if (<= t -3e-289)
         t_2
         (if (<= t 8.2e-67)
           (- x (* x (/ z a)))
           (if (<= t 7e-23)
             (+ x (/ (* y z) a))
             (if (<= t 9.8e-8)
               (* z (/ (- x y) t))
               (if (<= t 1.22e+40) t_2 t_1)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (z * (y / t));
	double t_2 = x + (y * (z / a));
	double tmp;
	if (t <= -5.5e+70) {
		tmp = t_1;
	} else if (t <= -2.8e-89) {
		tmp = x - (t * (y / a));
	} else if (t <= -3e-289) {
		tmp = t_2;
	} else if (t <= 8.2e-67) {
		tmp = x - (x * (z / a));
	} else if (t <= 7e-23) {
		tmp = x + ((y * z) / a);
	} else if (t <= 9.8e-8) {
		tmp = z * ((x - y) / t);
	} else if (t <= 1.22e+40) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = y - (z * (y / t))
    t_2 = x + (y * (z / a))
    if (t <= (-5.5d+70)) then
        tmp = t_1
    else if (t <= (-2.8d-89)) then
        tmp = x - (t * (y / a))
    else if (t <= (-3d-289)) then
        tmp = t_2
    else if (t <= 8.2d-67) then
        tmp = x - (x * (z / a))
    else if (t <= 7d-23) then
        tmp = x + ((y * z) / a)
    else if (t <= 9.8d-8) then
        tmp = z * ((x - y) / t)
    else if (t <= 1.22d+40) then
        tmp = t_2
    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 = y - (z * (y / t));
	double t_2 = x + (y * (z / a));
	double tmp;
	if (t <= -5.5e+70) {
		tmp = t_1;
	} else if (t <= -2.8e-89) {
		tmp = x - (t * (y / a));
	} else if (t <= -3e-289) {
		tmp = t_2;
	} else if (t <= 8.2e-67) {
		tmp = x - (x * (z / a));
	} else if (t <= 7e-23) {
		tmp = x + ((y * z) / a);
	} else if (t <= 9.8e-8) {
		tmp = z * ((x - y) / t);
	} else if (t <= 1.22e+40) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - (z * (y / t))
	t_2 = x + (y * (z / a))
	tmp = 0
	if t <= -5.5e+70:
		tmp = t_1
	elif t <= -2.8e-89:
		tmp = x - (t * (y / a))
	elif t <= -3e-289:
		tmp = t_2
	elif t <= 8.2e-67:
		tmp = x - (x * (z / a))
	elif t <= 7e-23:
		tmp = x + ((y * z) / a)
	elif t <= 9.8e-8:
		tmp = z * ((x - y) / t)
	elif t <= 1.22e+40:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y - Float64(z * Float64(y / t)))
	t_2 = Float64(x + Float64(y * Float64(z / a)))
	tmp = 0.0
	if (t <= -5.5e+70)
		tmp = t_1;
	elseif (t <= -2.8e-89)
		tmp = Float64(x - Float64(t * Float64(y / a)));
	elseif (t <= -3e-289)
		tmp = t_2;
	elseif (t <= 8.2e-67)
		tmp = Float64(x - Float64(x * Float64(z / a)));
	elseif (t <= 7e-23)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	elseif (t <= 9.8e-8)
		tmp = Float64(z * Float64(Float64(x - y) / t));
	elseif (t <= 1.22e+40)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y - (z * (y / t));
	t_2 = x + (y * (z / a));
	tmp = 0.0;
	if (t <= -5.5e+70)
		tmp = t_1;
	elseif (t <= -2.8e-89)
		tmp = x - (t * (y / a));
	elseif (t <= -3e-289)
		tmp = t_2;
	elseif (t <= 8.2e-67)
		tmp = x - (x * (z / a));
	elseif (t <= 7e-23)
		tmp = x + ((y * z) / a);
	elseif (t <= 9.8e-8)
		tmp = z * ((x - y) / t);
	elseif (t <= 1.22e+40)
		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[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.5e+70], t$95$1, If[LessEqual[t, -2.8e-89], N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3e-289], t$95$2, If[LessEqual[t, 8.2e-67], N[(x - N[(x * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e-23], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.8e-8], N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.22e+40], t$95$2, t$95$1]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -5.49999999999999986e70 or 1.22000000000000004e40 < t

   1. Initial program 44.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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* 74.6%

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

      8. associate-/l* 84.3%

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

      9. distribute-rgt-out-- 84.3%

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

   5. Simplified 84.3%

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

   6. Taylor expanded in z around inf 63.2%

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

      1. associate-/l* 74.7%

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

   8. Simplified 74.7%

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

   9. Taylor expanded in y around inf 59.8%

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

   if -5.49999999999999986e70 < t < -2.7999999999999999e-89

   1. Initial program 77.9%

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

   3. Taylor expanded in y around inf 69.9%

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

      1. *-commutative 69.9%

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

   5. Simplified 69.9%

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

   6. Taylor expanded in a around inf 57.7%

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

   7. Taylor expanded in z around 0 56.0%

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

      1. mul-1-neg 56.0%

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

      2. associate-/l* 56.0%

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

      3. distribute-rgt-neg-in 56.0%

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

      4. mul-1-neg 56.0%

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

      5. associate-*r/ 56.0%

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

      6. neg-mul-1 56.0%

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

   9. Simplified 56.0%

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

   if -2.7999999999999999e-89 < t < -2.9999999999999998e-289 or 9.8000000000000004e-8 < t < 1.22000000000000004e40

   1. Initial program 95.2%

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

   3. Taylor expanded in t around 0 82.8%

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

   4. Taylor expanded in y around inf 73.8%

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

      1. associate-/l* 74.5%

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

   6. Simplified 74.5%

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

   if -2.9999999999999998e-289 < t < 8.1999999999999994e-67

   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 79.6%

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

   4. Taylor expanded in y around 0 70.0%

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

      1. mul-1-neg 70.0%

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

      2. associate-/l* 76.5%

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

      3. distribute-rgt-neg-in 76.5%

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

      4. mul-1-neg 76.5%

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

      5. associate-*r/ 76.5%

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

      6. neg-mul-1 76.5%

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

   6. Simplified 76.5%

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

   if 8.1999999999999994e-67 < t < 6.99999999999999987e-23

   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 60.4%

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

   4. Taylor expanded in y around inf 60.4%

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

      1. *-commutative 60.4%

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

   6. Simplified 60.4%

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

   if 6.99999999999999987e-23 < t < 9.8000000000000004e-8

   1. Initial program 77.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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* 77.1%

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

      9. distribute-rgt-out-- 77.1%

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

   5. Simplified 77.1%

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

   6. Taylor expanded in z around -inf 77.1%

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

      1. mul-1-neg 77.1%

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

      2. associate-/l* 77.1%

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

      3. *-commutative 77.1%

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

      4. distribute-rgt-neg-in 77.1%

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

   8. Simplified 77.1%

      \[\leadsto \color{blue}{\frac{y - x}{t} \cdot \left(-z\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+70}:\\ \;\;\;\;y - z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-89}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-289}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-67}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-23}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{-8}:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{+40}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y - z \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 53.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - z \cdot \frac{y}{t}\\ \mathbf{if}\;t \leq -8.5 \cdot 10^{+103}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.22 \cdot 10^{-287}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-64}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-27}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 3.05 \cdot 10^{+81} \lor \neg \left(t \leq 1.8 \cdot 10^{+111}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- y (* z (/ y t)))))
   (if (<= t -8.5e+103)
     t_1
     (if (<= t -1.22e-287)
       (+ x (* y (/ z a)))
       (if (<= t 2.5e-64)
         (- x (* x (/ z a)))
         (if (<= t 8.2e-27)
           (+ x (/ (* y z) a))
           (if (or (<= t 3.05e+81) (not (<= t 1.8e+111)))
             t_1
             (* x (/ z t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (z * (y / t));
	double tmp;
	if (t <= -8.5e+103) {
		tmp = t_1;
	} else if (t <= -1.22e-287) {
		tmp = x + (y * (z / a));
	} else if (t <= 2.5e-64) {
		tmp = x - (x * (z / a));
	} else if (t <= 8.2e-27) {
		tmp = x + ((y * z) / a);
	} else if ((t <= 3.05e+81) || !(t <= 1.8e+111)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = y - (z * (y / t))
    if (t <= (-8.5d+103)) then
        tmp = t_1
    else if (t <= (-1.22d-287)) then
        tmp = x + (y * (z / a))
    else if (t <= 2.5d-64) then
        tmp = x - (x * (z / a))
    else if (t <= 8.2d-27) then
        tmp = x + ((y * z) / a)
    else if ((t <= 3.05d+81) .or. (.not. (t <= 1.8d+111))) then
        tmp = t_1
    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 t_1 = y - (z * (y / t));
	double tmp;
	if (t <= -8.5e+103) {
		tmp = t_1;
	} else if (t <= -1.22e-287) {
		tmp = x + (y * (z / a));
	} else if (t <= 2.5e-64) {
		tmp = x - (x * (z / a));
	} else if (t <= 8.2e-27) {
		tmp = x + ((y * z) / a);
	} else if ((t <= 3.05e+81) || !(t <= 1.8e+111)) {
		tmp = t_1;
	} else {
		tmp = x * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - (z * (y / t))
	tmp = 0
	if t <= -8.5e+103:
		tmp = t_1
	elif t <= -1.22e-287:
		tmp = x + (y * (z / a))
	elif t <= 2.5e-64:
		tmp = x - (x * (z / a))
	elif t <= 8.2e-27:
		tmp = x + ((y * z) / a)
	elif (t <= 3.05e+81) or not (t <= 1.8e+111):
		tmp = t_1
	else:
		tmp = x * (z / t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y - Float64(z * Float64(y / t)))
	tmp = 0.0
	if (t <= -8.5e+103)
		tmp = t_1;
	elseif (t <= -1.22e-287)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (t <= 2.5e-64)
		tmp = Float64(x - Float64(x * Float64(z / a)));
	elseif (t <= 8.2e-27)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	elseif ((t <= 3.05e+81) || !(t <= 1.8e+111))
		tmp = t_1;
	else
		tmp = Float64(x * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y - (z * (y / t));
	tmp = 0.0;
	if (t <= -8.5e+103)
		tmp = t_1;
	elseif (t <= -1.22e-287)
		tmp = x + (y * (z / a));
	elseif (t <= 2.5e-64)
		tmp = x - (x * (z / a));
	elseif (t <= 8.2e-27)
		tmp = x + ((y * z) / a);
	elseif ((t <= 3.05e+81) || ~((t <= 1.8e+111)))
		tmp = t_1;
	else
		tmp = x * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y - N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.5e+103], t$95$1, If[LessEqual[t, -1.22e-287], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.5e-64], N[(x - N[(x * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.2e-27], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 3.05e+81], N[Not[LessEqual[t, 1.8e+111]], $MachinePrecision]], t$95$1, N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -8.4999999999999992e103 or 8.1999999999999997e-27 < t < 3.05000000000000019e81 or 1.8000000000000001e111 < t

   1. Initial program 45.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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* 73.0%

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

      8. associate-/l* 83.8%

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

      9. distribute-rgt-out-- 83.8%

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

   5. Simplified 83.8%

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

   6. Taylor expanded in z around inf 62.4%

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

      1. associate-/l* 73.3%

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

   8. Simplified 73.3%

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

   9. Taylor expanded in y around inf 61.9%

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

   if -8.4999999999999992e103 < t < -1.21999999999999996e-287

   1. Initial program 84.1%

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

   3. Taylor expanded in t around 0 62.5%

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

   4. Taylor expanded in y around inf 57.4%

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

      1. associate-/l* 58.6%

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

   6. Simplified 58.6%

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

   if -1.21999999999999996e-287 < t < 2.50000000000000017e-64

   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 79.6%

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

   4. Taylor expanded in x around inf 76.5%

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

      1. mul-1-neg 76.5%

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

      2. unsub-neg 76.5%

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

   6. Simplified 76.5%

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

   7. Taylor expanded in z around 0 70.0%

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

      1. associate-*r/ 76.5%

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

      2. associate-*r* 76.5%

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

      3. neg-mul-1 76.5%

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

      4. cancel-sign-sub-inv 76.5%

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

   9. Simplified 76.5%

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

   if 2.50000000000000017e-64 < t < 8.1999999999999997e-27

   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 65.4%

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

   4. Taylor expanded in y around inf 65.4%

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

      1. *-commutative 65.4%

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

   6. Simplified 65.4%

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

   if 3.05000000000000019e81 < t < 1.8000000000000001e111

   1. Initial program 63.6%

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

   3. Taylor expanded in t around inf 76.8%

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

      1. associate--l+ 76.8%

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

      2. distribute-lft-out-- 76.8%

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

      3. div-sub 76.8%

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

      4. mul-1-neg 76.8%

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

      5. unsub-neg 76.8%

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

      6. div-sub 76.8%

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

      7. associate-/l* 88.3%

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

      8. associate-/l* 88.3%

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

      9. distribute-rgt-out-- 88.3%

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

   5. Simplified 88.3%

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

   6. Taylor expanded in z around inf 74.8%

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

      1. associate-/l* 86.4%

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

   8. Simplified 86.4%

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

   9. Taylor expanded in y around 0 51.4%

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

       1. associate-/l* 62.9%

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

   11. Simplified 62.9%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+103}:\\ \;\;\;\;y - z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq -1.22 \cdot 10^{-287}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-64}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-27}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 3.05 \cdot 10^{+81} \lor \neg \left(t \leq 1.8 \cdot 10^{+111}\right):\\ \;\;\;\;y - z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 53.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{a}\\ t_2 := y - z \cdot \frac{y}{t}\\ \mathbf{if}\;t \leq -1.02 \cdot 10^{+105}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-290}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-64}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-22}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 0.013:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq 5.3 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z a)))) (t_2 (- y (* z (/ y t)))))
   (if (<= t -1.02e+105)
     t_2
     (if (<= t -4.6e-290)
       t_1
       (if (<= t 2.6e-64)
         (- x (* x (/ z a)))
         (if (<= t 4.2e-22)
           (+ x (/ (* y z) a))
           (if (<= t 0.013)
             (* z (/ (- x y) t))
             (if (<= t 5.3e+40) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / a));
	double t_2 = y - (z * (y / t));
	double tmp;
	if (t <= -1.02e+105) {
		tmp = t_2;
	} else if (t <= -4.6e-290) {
		tmp = t_1;
	} else if (t <= 2.6e-64) {
		tmp = x - (x * (z / a));
	} else if (t <= 4.2e-22) {
		tmp = x + ((y * z) / a);
	} else if (t <= 0.013) {
		tmp = z * ((x - y) / t);
	} else if (t <= 5.3e+40) {
		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 * (z / a))
    t_2 = y - (z * (y / t))
    if (t <= (-1.02d+105)) then
        tmp = t_2
    else if (t <= (-4.6d-290)) then
        tmp = t_1
    else if (t <= 2.6d-64) then
        tmp = x - (x * (z / a))
    else if (t <= 4.2d-22) then
        tmp = x + ((y * z) / a)
    else if (t <= 0.013d0) then
        tmp = z * ((x - y) / t)
    else if (t <= 5.3d+40) 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 * (z / a));
	double t_2 = y - (z * (y / t));
	double tmp;
	if (t <= -1.02e+105) {
		tmp = t_2;
	} else if (t <= -4.6e-290) {
		tmp = t_1;
	} else if (t <= 2.6e-64) {
		tmp = x - (x * (z / a));
	} else if (t <= 4.2e-22) {
		tmp = x + ((y * z) / a);
	} else if (t <= 0.013) {
		tmp = z * ((x - y) / t);
	} else if (t <= 5.3e+40) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (z / a))
	t_2 = y - (z * (y / t))
	tmp = 0
	if t <= -1.02e+105:
		tmp = t_2
	elif t <= -4.6e-290:
		tmp = t_1
	elif t <= 2.6e-64:
		tmp = x - (x * (z / a))
	elif t <= 4.2e-22:
		tmp = x + ((y * z) / a)
	elif t <= 0.013:
		tmp = z * ((x - y) / t)
	elif t <= 5.3e+40:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(z / a)))
	t_2 = Float64(y - Float64(z * Float64(y / t)))
	tmp = 0.0
	if (t <= -1.02e+105)
		tmp = t_2;
	elseif (t <= -4.6e-290)
		tmp = t_1;
	elseif (t <= 2.6e-64)
		tmp = Float64(x - Float64(x * Float64(z / a)));
	elseif (t <= 4.2e-22)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	elseif (t <= 0.013)
		tmp = Float64(z * Float64(Float64(x - y) / t));
	elseif (t <= 5.3e+40)
		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 * (z / a));
	t_2 = y - (z * (y / t));
	tmp = 0.0;
	if (t <= -1.02e+105)
		tmp = t_2;
	elseif (t <= -4.6e-290)
		tmp = t_1;
	elseif (t <= 2.6e-64)
		tmp = x - (x * (z / a));
	elseif (t <= 4.2e-22)
		tmp = x + ((y * z) / a);
	elseif (t <= 0.013)
		tmp = z * ((x - y) / t);
	elseif (t <= 5.3e+40)
		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[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y - N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.02e+105], t$95$2, If[LessEqual[t, -4.6e-290], t$95$1, If[LessEqual[t, 2.6e-64], N[(x - N[(x * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.2e-22], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.013], N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.3e+40], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.02e105 or 5.3e40 < t

   1. Initial program 42.8%

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

   3. Taylor expanded in t around inf 64.6%

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

      1. associate--l+ 64.6%

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

      2. distribute-lft-out-- 64.6%

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

      3. div-sub 64.6%

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

      4. mul-1-neg 64.6%

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

      5. unsub-neg 64.6%

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

      6. div-sub 64.6%

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

      7. associate-/l* 76.6%

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

      8. associate-/l* 87.6%

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

      9. distribute-rgt-out-- 87.6%

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

   5. Simplified 87.6%

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

   6. Taylor expanded in z around inf 64.6%

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

      1. associate-/l* 76.6%

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

   8. Simplified 76.6%

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

   9. Taylor expanded in y around inf 62.0%

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

   if -1.02e105 < t < -4.6000000000000001e-290 or 0.0129999999999999994 < t < 5.3e40

   1. Initial program 83.9%

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

   3. Taylor expanded in t around 0 62.8%

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

   4. Taylor expanded in y around inf 58.0%

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

      1. associate-/l* 59.1%

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

   6. Simplified 59.1%

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

   if -4.6000000000000001e-290 < t < 2.6e-64

   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 79.6%

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

   4. Taylor expanded in x around inf 76.5%

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

      1. mul-1-neg 76.5%

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

      2. unsub-neg 76.5%

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

   6. Simplified 76.5%

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

   7. Taylor expanded in z around 0 70.0%

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

      1. associate-*r/ 76.5%

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

      2. associate-*r* 76.5%

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

      3. neg-mul-1 76.5%

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

      4. cancel-sign-sub-inv 76.5%

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

   9. Simplified 76.5%

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

   if 2.6e-64 < t < 4.20000000000000016e-22

   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 60.4%

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

   4. Taylor expanded in y around inf 60.4%

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

      1. *-commutative 60.4%

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

   6. Simplified 60.4%

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

   if 4.20000000000000016e-22 < t < 0.0129999999999999994

   1. Initial program 77.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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* 77.1%

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

      9. distribute-rgt-out-- 77.1%

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

   5. Simplified 77.1%

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

   6. Taylor expanded in z around -inf 77.1%

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

      1. mul-1-neg 77.1%

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

      2. associate-/l* 77.1%

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

      3. *-commutative 77.1%

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

      4. distribute-rgt-neg-in 77.1%

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

   8. Simplified 77.1%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{+105}:\\ \;\;\;\;y - z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-290}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-64}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-22}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 0.013:\\ \;\;\;\;z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq 5.3 \cdot 10^{+40}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y - z \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 50.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - x \cdot \frac{z}{a}\\ t_2 := x + y \cdot \frac{z}{a}\\ \mathbf{if}\;t \leq -1.3 \cdot 10^{+116}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{+75}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{+70}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-145}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-290}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 2.85 \cdot 10^{+54}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* x (/ z a)))) (t_2 (+ x (* y (/ z a)))))
   (if (<= t -1.3e+116)
     y
     (if (<= t -1.7e+75)
       t_2
       (if (<= t -3.3e+70)
         y
         (if (<= t -7e-145)
           t_1
           (if (<= t -4.2e-290) t_2 (if (<= t 2.85e+54) t_1 y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x * (z / a));
	double t_2 = x + (y * (z / a));
	double tmp;
	if (t <= -1.3e+116) {
		tmp = y;
	} else if (t <= -1.7e+75) {
		tmp = t_2;
	} else if (t <= -3.3e+70) {
		tmp = y;
	} else if (t <= -7e-145) {
		tmp = t_1;
	} else if (t <= -4.2e-290) {
		tmp = t_2;
	} else if (t <= 2.85e+54) {
		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 - (x * (z / a))
    t_2 = x + (y * (z / a))
    if (t <= (-1.3d+116)) then
        tmp = y
    else if (t <= (-1.7d+75)) then
        tmp = t_2
    else if (t <= (-3.3d+70)) then
        tmp = y
    else if (t <= (-7d-145)) then
        tmp = t_1
    else if (t <= (-4.2d-290)) then
        tmp = t_2
    else if (t <= 2.85d+54) 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 - (x * (z / a));
	double t_2 = x + (y * (z / a));
	double tmp;
	if (t <= -1.3e+116) {
		tmp = y;
	} else if (t <= -1.7e+75) {
		tmp = t_2;
	} else if (t <= -3.3e+70) {
		tmp = y;
	} else if (t <= -7e-145) {
		tmp = t_1;
	} else if (t <= -4.2e-290) {
		tmp = t_2;
	} else if (t <= 2.85e+54) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (x * (z / a))
	t_2 = x + (y * (z / a))
	tmp = 0
	if t <= -1.3e+116:
		tmp = y
	elif t <= -1.7e+75:
		tmp = t_2
	elif t <= -3.3e+70:
		tmp = y
	elif t <= -7e-145:
		tmp = t_1
	elif t <= -4.2e-290:
		tmp = t_2
	elif t <= 2.85e+54:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(x * Float64(z / a)))
	t_2 = Float64(x + Float64(y * Float64(z / a)))
	tmp = 0.0
	if (t <= -1.3e+116)
		tmp = y;
	elseif (t <= -1.7e+75)
		tmp = t_2;
	elseif (t <= -3.3e+70)
		tmp = y;
	elseif (t <= -7e-145)
		tmp = t_1;
	elseif (t <= -4.2e-290)
		tmp = t_2;
	elseif (t <= 2.85e+54)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (x * (z / a));
	t_2 = x + (y * (z / a));
	tmp = 0.0;
	if (t <= -1.3e+116)
		tmp = y;
	elseif (t <= -1.7e+75)
		tmp = t_2;
	elseif (t <= -3.3e+70)
		tmp = y;
	elseif (t <= -7e-145)
		tmp = t_1;
	elseif (t <= -4.2e-290)
		tmp = t_2;
	elseif (t <= 2.85e+54)
		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[(x * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.3e+116], y, If[LessEqual[t, -1.7e+75], t$95$2, If[LessEqual[t, -3.3e+70], y, If[LessEqual[t, -7e-145], t$95$1, If[LessEqual[t, -4.2e-290], t$95$2, If[LessEqual[t, 2.85e+54], t$95$1, y]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.29999999999999993e116 or -1.70000000000000006e75 < t < -3.30000000000000016e70 or 2.8499999999999998e54 < 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 56.6%

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

   if -1.29999999999999993e116 < t < -1.70000000000000006e75 or -6.99999999999999994e-145 < t < -4.2000000000000002e-290

   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 t around 0 83.1%

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

   4. Taylor expanded in y around inf 78.9%

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

      1. associate-/l* 79.7%

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

   6. Simplified 79.7%

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

   if -3.30000000000000016e70 < t < -6.99999999999999994e-145 or -4.2000000000000002e-290 < t < 2.8499999999999998e54

   1. Initial program 84.1%

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

   3. Taylor expanded in t around 0 60.1%

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

   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%

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

   7. Taylor expanded in z around 0 52.3%

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

      1. associate-*r/ 56.9%

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

      2. associate-*r* 56.9%

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

      3. neg-mul-1 56.9%

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

      4. cancel-sign-sub-inv 56.9%

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

   9. Simplified 56.9%

      \[\leadsto \color{blue}{x - x \cdot \frac{z}{a}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 11: 50.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ t_2 := x + y \cdot \frac{z}{a}\\ \mathbf{if}\;t \leq -5 \cdot 10^{+103}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{+75}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{+70}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -3.05 \cdot 10^{-143}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-287}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+55}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))) (t_2 (+ x (* y (/ z a)))))
   (if (<= t -5e+103)
     y
     (if (<= t -2.9e+75)
       t_2
       (if (<= t -1.9e+70)
         y
         (if (<= t -3.05e-143)
           t_1
           (if (<= t -1.3e-287) t_2 (if (<= t 2.2e+55) 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 t_2 = x + (y * (z / a));
	double tmp;
	if (t <= -5e+103) {
		tmp = y;
	} else if (t <= -2.9e+75) {
		tmp = t_2;
	} else if (t <= -1.9e+70) {
		tmp = y;
	} else if (t <= -3.05e-143) {
		tmp = t_1;
	} else if (t <= -1.3e-287) {
		tmp = t_2;
	} else if (t <= 2.2e+55) {
		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 * (1.0d0 - (z / a))
    t_2 = x + (y * (z / a))
    if (t <= (-5d+103)) then
        tmp = y
    else if (t <= (-2.9d+75)) then
        tmp = t_2
    else if (t <= (-1.9d+70)) then
        tmp = y
    else if (t <= (-3.05d-143)) then
        tmp = t_1
    else if (t <= (-1.3d-287)) then
        tmp = t_2
    else if (t <= 2.2d+55) 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 t_2 = x + (y * (z / a));
	double tmp;
	if (t <= -5e+103) {
		tmp = y;
	} else if (t <= -2.9e+75) {
		tmp = t_2;
	} else if (t <= -1.9e+70) {
		tmp = y;
	} else if (t <= -3.05e-143) {
		tmp = t_1;
	} else if (t <= -1.3e-287) {
		tmp = t_2;
	} else if (t <= 2.2e+55) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	t_2 = x + (y * (z / a))
	tmp = 0
	if t <= -5e+103:
		tmp = y
	elif t <= -2.9e+75:
		tmp = t_2
	elif t <= -1.9e+70:
		tmp = y
	elif t <= -3.05e-143:
		tmp = t_1
	elif t <= -1.3e-287:
		tmp = t_2
	elif t <= 2.2e+55:
		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)))
	t_2 = Float64(x + Float64(y * Float64(z / a)))
	tmp = 0.0
	if (t <= -5e+103)
		tmp = y;
	elseif (t <= -2.9e+75)
		tmp = t_2;
	elseif (t <= -1.9e+70)
		tmp = y;
	elseif (t <= -3.05e-143)
		tmp = t_1;
	elseif (t <= -1.3e-287)
		tmp = t_2;
	elseif (t <= 2.2e+55)
		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));
	t_2 = x + (y * (z / a));
	tmp = 0.0;
	if (t <= -5e+103)
		tmp = y;
	elseif (t <= -2.9e+75)
		tmp = t_2;
	elseif (t <= -1.9e+70)
		tmp = y;
	elseif (t <= -3.05e-143)
		tmp = t_1;
	elseif (t <= -1.3e-287)
		tmp = t_2;
	elseif (t <= 2.2e+55)
		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]}, Block[{t$95$2 = N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5e+103], y, If[LessEqual[t, -2.9e+75], t$95$2, If[LessEqual[t, -1.9e+70], y, If[LessEqual[t, -3.05e-143], t$95$1, If[LessEqual[t, -1.3e-287], t$95$2, If[LessEqual[t, 2.2e+55], t$95$1, y]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5e103 or -2.8999999999999998e75 < t < -1.8999999999999999e70 or 2.2000000000000001e55 < 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 56.6%

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

   if -5e103 < t < -2.8999999999999998e75 or -3.04999999999999996e-143 < t < -1.3e-287

   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 t around 0 83.1%

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

   4. Taylor expanded in y around inf 78.9%

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

      1. associate-/l* 79.7%

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

   6. Simplified 79.7%

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

   if -1.8999999999999999e70 < t < -3.04999999999999996e-143 or -1.3e-287 < t < 2.2000000000000001e55

   1. Initial program 84.1%

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

   3. Taylor expanded in t around 0 60.1%

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

   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 3 regimes into one program.
4. Add Preprocessing

Alternative 12: 78.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot \left(t - z\right)}{t - a}\\ t_2 := y - \frac{y - x}{t} \cdot \left(z - a\right)\\ t_3 := x + z \cdot \frac{y - x}{a - t}\\ \mathbf{if}\;t \leq -1.9 \cdot 10^{+58}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-142}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{-19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+40}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y (- t z)) (- t a))))
        (t_2 (- y (* (/ (- y x) t) (- z a))))
        (t_3 (+ x (* z (/ (- y x) (- a t))))))
   (if (<= t -1.9e+58)
     t_2
     (if (<= t -2.7e-89)
       t_1
       (if (<= t 1.75e-142)
         t_3
         (if (<= t 5.1e-19) t_1 (if (<= t 1.55e+40) t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * (t - z)) / (t - a));
	double t_2 = y - (((y - x) / t) * (z - a));
	double t_3 = x + (z * ((y - x) / (a - t)));
	double tmp;
	if (t <= -1.9e+58) {
		tmp = t_2;
	} else if (t <= -2.7e-89) {
		tmp = t_1;
	} else if (t <= 1.75e-142) {
		tmp = t_3;
	} else if (t <= 5.1e-19) {
		tmp = t_1;
	} else if (t <= 1.55e+40) {
		tmp = t_3;
	} 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) :: tmp
    t_1 = x + ((y * (t - z)) / (t - a))
    t_2 = y - (((y - x) / t) * (z - a))
    t_3 = x + (z * ((y - x) / (a - t)))
    if (t <= (-1.9d+58)) then
        tmp = t_2
    else if (t <= (-2.7d-89)) then
        tmp = t_1
    else if (t <= 1.75d-142) then
        tmp = t_3
    else if (t <= 5.1d-19) then
        tmp = t_1
    else if (t <= 1.55d+40) then
        tmp = t_3
    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 * (t - z)) / (t - a));
	double t_2 = y - (((y - x) / t) * (z - a));
	double t_3 = x + (z * ((y - x) / (a - t)));
	double tmp;
	if (t <= -1.9e+58) {
		tmp = t_2;
	} else if (t <= -2.7e-89) {
		tmp = t_1;
	} else if (t <= 1.75e-142) {
		tmp = t_3;
	} else if (t <= 5.1e-19) {
		tmp = t_1;
	} else if (t <= 1.55e+40) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * (t - z)) / (t - a))
	t_2 = y - (((y - x) / t) * (z - a))
	t_3 = x + (z * ((y - x) / (a - t)))
	tmp = 0
	if t <= -1.9e+58:
		tmp = t_2
	elif t <= -2.7e-89:
		tmp = t_1
	elif t <= 1.75e-142:
		tmp = t_3
	elif t <= 5.1e-19:
		tmp = t_1
	elif t <= 1.55e+40:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * Float64(t - z)) / Float64(t - a)))
	t_2 = Float64(y - Float64(Float64(Float64(y - x) / t) * Float64(z - a)))
	t_3 = Float64(x + Float64(z * Float64(Float64(y - x) / Float64(a - t))))
	tmp = 0.0
	if (t <= -1.9e+58)
		tmp = t_2;
	elseif (t <= -2.7e-89)
		tmp = t_1;
	elseif (t <= 1.75e-142)
		tmp = t_3;
	elseif (t <= 5.1e-19)
		tmp = t_1;
	elseif (t <= 1.55e+40)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * (t - z)) / (t - a));
	t_2 = y - (((y - x) / t) * (z - a));
	t_3 = x + (z * ((y - x) / (a - t)));
	tmp = 0.0;
	if (t <= -1.9e+58)
		tmp = t_2;
	elseif (t <= -2.7e-89)
		tmp = t_1;
	elseif (t <= 1.75e-142)
		tmp = t_3;
	elseif (t <= 5.1e-19)
		tmp = t_1;
	elseif (t <= 1.55e+40)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y - N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.9e+58], t$95$2, If[LessEqual[t, -2.7e-89], t$95$1, If[LessEqual[t, 1.75e-142], t$95$3, If[LessEqual[t, 5.1e-19], t$95$1, If[LessEqual[t, 1.55e+40], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.8999999999999999e58 or 1.5499999999999999e40 < t

   1. Initial program 45.9%

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

   3. Taylor expanded in t around inf 63.5%

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

      1. associate--l+ 63.5%

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

      2. distribute-lft-out-- 63.5%

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

      3. div-sub 63.5%

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

      4. mul-1-neg 63.5%

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

      5. unsub-neg 63.5%

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

      6. div-sub 63.5%

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

      7. associate-/l* 74.6%

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

      8. associate-/l* 84.0%

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

      9. distribute-rgt-out-- 84.0%

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

   5. Simplified 84.0%

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

   if -1.8999999999999999e58 < t < -2.69999999999999988e-89 or 1.75000000000000007e-142 < t < 5.0999999999999998e-19

   1. Initial program 81.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. *-commutative 79.9%

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

   5. Simplified 79.9%

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

   if -2.69999999999999988e-89 < t < 1.75000000000000007e-142 or 5.0999999999999998e-19 < t < 1.5499999999999999e40

   1. Initial program 94.0%

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

   3. Taylor expanded in z around inf 88.8%

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

      1. associate-/l* 92.5%

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

   5. Simplified 92.5%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+58}:\\ \;\;\;\;y - \frac{y - x}{t} \cdot \left(z - a\right)\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-89}:\\ \;\;\;\;x + \frac{y \cdot \left(t - z\right)}{t - a}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-142}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{-19}:\\ \;\;\;\;x + \frac{y \cdot \left(t - z\right)}{t - a}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+40}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{y - x}{t} \cdot \left(z - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 75.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot \left(t - z\right)}{t - a}\\ t_2 := x + z \cdot \frac{y - x}{a - t}\\ \mathbf{if}\;t \leq -1.65 \cdot 10^{+58}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq -2.95 \cdot 10^{-89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-142}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+40}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;y + \frac{z}{\frac{t}{x - y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y (- t z)) (- t a))))
        (t_2 (+ x (* z (/ (- y x) (- a t))))))
   (if (<= t -1.65e+58)
     (+ y (* z (/ (- x y) t)))
     (if (<= t -2.95e-89)
       t_1
       (if (<= t 1.55e-142)
         t_2
         (if (<= t 2.4e-19)
           t_1
           (if (<= t 5.5e+40) t_2 (+ y (/ z (/ t (- x y)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * (t - z)) / (t - a));
	double t_2 = x + (z * ((y - x) / (a - t)));
	double tmp;
	if (t <= -1.65e+58) {
		tmp = y + (z * ((x - y) / t));
	} else if (t <= -2.95e-89) {
		tmp = t_1;
	} else if (t <= 1.55e-142) {
		tmp = t_2;
	} else if (t <= 2.4e-19) {
		tmp = t_1;
	} else if (t <= 5.5e+40) {
		tmp = t_2;
	} else {
		tmp = y + (z / (t / (x - 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 * (t - z)) / (t - a))
    t_2 = x + (z * ((y - x) / (a - t)))
    if (t <= (-1.65d+58)) then
        tmp = y + (z * ((x - y) / t))
    else if (t <= (-2.95d-89)) then
        tmp = t_1
    else if (t <= 1.55d-142) then
        tmp = t_2
    else if (t <= 2.4d-19) then
        tmp = t_1
    else if (t <= 5.5d+40) then
        tmp = t_2
    else
        tmp = y + (z / (t / (x - 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 * (t - z)) / (t - a));
	double t_2 = x + (z * ((y - x) / (a - t)));
	double tmp;
	if (t <= -1.65e+58) {
		tmp = y + (z * ((x - y) / t));
	} else if (t <= -2.95e-89) {
		tmp = t_1;
	} else if (t <= 1.55e-142) {
		tmp = t_2;
	} else if (t <= 2.4e-19) {
		tmp = t_1;
	} else if (t <= 5.5e+40) {
		tmp = t_2;
	} else {
		tmp = y + (z / (t / (x - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * (t - z)) / (t - a))
	t_2 = x + (z * ((y - x) / (a - t)))
	tmp = 0
	if t <= -1.65e+58:
		tmp = y + (z * ((x - y) / t))
	elif t <= -2.95e-89:
		tmp = t_1
	elif t <= 1.55e-142:
		tmp = t_2
	elif t <= 2.4e-19:
		tmp = t_1
	elif t <= 5.5e+40:
		tmp = t_2
	else:
		tmp = y + (z / (t / (x - y)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * Float64(t - z)) / Float64(t - a)))
	t_2 = Float64(x + Float64(z * Float64(Float64(y - x) / Float64(a - t))))
	tmp = 0.0
	if (t <= -1.65e+58)
		tmp = Float64(y + Float64(z * Float64(Float64(x - y) / t)));
	elseif (t <= -2.95e-89)
		tmp = t_1;
	elseif (t <= 1.55e-142)
		tmp = t_2;
	elseif (t <= 2.4e-19)
		tmp = t_1;
	elseif (t <= 5.5e+40)
		tmp = t_2;
	else
		tmp = Float64(y + Float64(z / Float64(t / Float64(x - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * (t - z)) / (t - a));
	t_2 = x + (z * ((y - x) / (a - t)));
	tmp = 0.0;
	if (t <= -1.65e+58)
		tmp = y + (z * ((x - y) / t));
	elseif (t <= -2.95e-89)
		tmp = t_1;
	elseif (t <= 1.55e-142)
		tmp = t_2;
	elseif (t <= 2.4e-19)
		tmp = t_1;
	elseif (t <= 5.5e+40)
		tmp = t_2;
	else
		tmp = y + (z / (t / (x - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.65e+58], N[(y + N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.95e-89], t$95$1, If[LessEqual[t, 1.55e-142], t$95$2, If[LessEqual[t, 2.4e-19], t$95$1, If[LessEqual[t, 5.5e+40], t$95$2, N[(y + N[(z / N[(t / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.64999999999999991e58

   1. Initial program 44.9%

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

   3. Taylor expanded in t around inf 61.6%

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

      1. associate--l+ 61.6%

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

      2. distribute-lft-out-- 61.6%

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

      3. div-sub 61.6%

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

      4. mul-1-neg 61.6%

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

      5. unsub-neg 61.6%

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

      6. div-sub 61.6%

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

      7. associate-/l* 68.7%

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

      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. Taylor expanded in z around inf 67.4%

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

      1. associate-/l* 74.6%

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

   8. Simplified 74.6%

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

   if -1.64999999999999991e58 < t < -2.9500000000000001e-89 or 1.55e-142 < t < 2.40000000000000023e-19

   1. Initial program 81.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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. *-commutative 79.9%

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

   5. Simplified 79.9%

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

   if -2.9500000000000001e-89 < t < 1.55e-142 or 2.40000000000000023e-19 < t < 5.49999999999999974e40

   1. Initial program 94.0%

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

   3. Taylor expanded in z around inf 88.8%

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

      1. associate-/l* 92.5%

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

   5. Simplified 92.5%

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

   if 5.49999999999999974e40 < t

   1. Initial program 46.9%

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

   3. Taylor expanded in t around inf 65.3%

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

      1. associate--l+ 65.3%

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

      2. distribute-lft-out-- 65.3%

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

      3. div-sub 65.3%

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

      4. mul-1-neg 65.3%

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

      5. unsub-neg 65.3%

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

      6. div-sub 65.3%

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

      7. associate-/l* 79.9%

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

      8. associate-/l* 83.3%

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

      9. distribute-rgt-out-- 83.3%

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

   5. Simplified 83.3%

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

   6. Taylor expanded in z around inf 60.2%

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

      1. associate-/l* 74.8%

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

   8. Simplified 74.8%

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

      1. clear-num 74.8%

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

      2. un-div-inv 74.8%

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

   10. Applied egg-rr 74.8%

       \[\leadsto y - \color{blue}{\frac{z}{\frac{t}{y - x}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+58}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq -2.95 \cdot 10^{-89}:\\ \;\;\;\;x + \frac{y \cdot \left(t - z\right)}{t - a}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-142}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-19}:\\ \;\;\;\;x + \frac{y \cdot \left(t - z\right)}{t - a}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+40}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{z}{\frac{t}{x - y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 56.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \frac{x}{t}\\ \mathbf{if}\;t \leq -6.8 \cdot 10^{+57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.95 \cdot 10^{-89}:\\ \;\;\;\;x - \frac{y \cdot t}{a}\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-290}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{-67}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-29}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* z (/ x t)))))
   (if (<= t -6.8e+57)
     t_1
     (if (<= t -2.95e-89)
       (- x (/ (* y t) a))
       (if (<= t -2.8e-290)
         (+ x (* y (/ z a)))
         (if (<= t 2.65e-67)
           (- x (* x (/ z a)))
           (if (<= t 3.7e-29) (+ x (/ (* y z) a)) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (z * (x / t));
	double tmp;
	if (t <= -6.8e+57) {
		tmp = t_1;
	} else if (t <= -2.95e-89) {
		tmp = x - ((y * t) / a);
	} else if (t <= -2.8e-290) {
		tmp = x + (y * (z / a));
	} else if (t <= 2.65e-67) {
		tmp = x - (x * (z / a));
	} else if (t <= 3.7e-29) {
		tmp = x + ((y * z) / a);
	} 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 = y + (z * (x / t))
    if (t <= (-6.8d+57)) then
        tmp = t_1
    else if (t <= (-2.95d-89)) then
        tmp = x - ((y * t) / a)
    else if (t <= (-2.8d-290)) then
        tmp = x + (y * (z / a))
    else if (t <= 2.65d-67) then
        tmp = x - (x * (z / a))
    else if (t <= 3.7d-29) then
        tmp = x + ((y * z) / a)
    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 = y + (z * (x / t));
	double tmp;
	if (t <= -6.8e+57) {
		tmp = t_1;
	} else if (t <= -2.95e-89) {
		tmp = x - ((y * t) / a);
	} else if (t <= -2.8e-290) {
		tmp = x + (y * (z / a));
	} else if (t <= 2.65e-67) {
		tmp = x - (x * (z / a));
	} else if (t <= 3.7e-29) {
		tmp = x + ((y * z) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + (z * (x / t))
	tmp = 0
	if t <= -6.8e+57:
		tmp = t_1
	elif t <= -2.95e-89:
		tmp = x - ((y * t) / a)
	elif t <= -2.8e-290:
		tmp = x + (y * (z / a))
	elif t <= 2.65e-67:
		tmp = x - (x * (z / a))
	elif t <= 3.7e-29:
		tmp = x + ((y * z) / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(z * Float64(x / t)))
	tmp = 0.0
	if (t <= -6.8e+57)
		tmp = t_1;
	elseif (t <= -2.95e-89)
		tmp = Float64(x - Float64(Float64(y * t) / a));
	elseif (t <= -2.8e-290)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (t <= 2.65e-67)
		tmp = Float64(x - Float64(x * Float64(z / a)));
	elseif (t <= 3.7e-29)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + (z * (x / t));
	tmp = 0.0;
	if (t <= -6.8e+57)
		tmp = t_1;
	elseif (t <= -2.95e-89)
		tmp = x - ((y * t) / a);
	elseif (t <= -2.8e-290)
		tmp = x + (y * (z / a));
	elseif (t <= 2.65e-67)
		tmp = x - (x * (z / a));
	elseif (t <= 3.7e-29)
		tmp = x + ((y * z) / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.8e+57], t$95$1, If[LessEqual[t, -2.95e-89], N[(x - N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.8e-290], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.65e-67], N[(x - N[(x * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.7e-29], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -6.79999999999999984e57 or 3.6999999999999997e-29 < t

   1. Initial program 48.9%

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

   3. Taylor expanded in t around inf 62.5%

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

      1. associate--l+ 62.5%

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

      2. distribute-lft-out-- 62.5%

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

      3. div-sub 62.5%

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

      4. mul-1-neg 62.5%

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

      5. unsub-neg 62.5%

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

      6. div-sub 62.5%

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

      7. associate-/l* 72.7%

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

      8. associate-/l* 81.3%

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

      9. distribute-rgt-out-- 81.3%

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

   5. Simplified 81.3%

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

   6. Taylor expanded in z around inf 62.7%

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

      1. associate-/l* 72.9%

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

   8. Simplified 72.9%

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

   9. Taylor expanded in y around 0 65.6%

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

       1. neg-mul-1 65.6%

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

       2. distribute-neg-frac 65.6%

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

   11. Simplified 65.6%

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

   if -6.79999999999999984e57 < t < -2.9500000000000001e-89

   1. Initial program 78.2%

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

   3. Taylor expanded in y around inf 74.1%

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

      1. *-commutative 74.1%

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

   5. Simplified 74.1%

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

   6. Taylor expanded in a around inf 60.6%

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

   7. Taylor expanded in z around 0 58.8%

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

      1. mul-1-neg 58.8%

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

      2. distribute-lft-neg-out 58.8%

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

      3. *-commutative 58.8%

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

   9. Simplified 58.8%

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

   if -2.9500000000000001e-89 < t < -2.79999999999999997e-290

   1. Initial program 96.9%

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

   3. Taylor expanded in t around 0 84.4%

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

   4. Taylor expanded in y around inf 74.3%

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

      1. associate-/l* 75.0%

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

   6. Simplified 75.0%

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

   if -2.79999999999999997e-290 < t < 2.64999999999999986e-67

   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 79.6%

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

   4. Taylor expanded in y around 0 70.0%

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

      1. mul-1-neg 70.0%

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

      2. associate-/l* 76.5%

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

      3. distribute-rgt-neg-in 76.5%

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

      4. mul-1-neg 76.5%

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

      5. associate-*r/ 76.5%

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

      6. neg-mul-1 76.5%

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

   6. Simplified 76.5%

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

   if 2.64999999999999986e-67 < t < 3.6999999999999997e-29

   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 65.4%

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

   4. Taylor expanded in y around inf 65.4%

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

      1. *-commutative 65.4%

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

   6. Simplified 65.4%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+57}:\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq -2.95 \cdot 10^{-89}:\\ \;\;\;\;x - \frac{y \cdot t}{a}\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-290}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{-67}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-29}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 61.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \frac{x}{t}\\ t_2 := x - y \cdot \frac{t - z}{a}\\ \mathbf{if}\;a \leq -1 \cdot 10^{-18}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{-240}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+51}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;a \leq 10^{+111}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* z (/ x t)))) (t_2 (- x (* y (/ (- t z) a)))))
   (if (<= a -1e-18)
     t_2
     (if (<= a 1.02e-240)
       t_1
       (if (<= a 1.6e+51)
         (* (- z t) (/ y (- a t)))
         (if (<= a 1e+111) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (z * (x / t));
	double t_2 = x - (y * ((t - z) / a));
	double tmp;
	if (a <= -1e-18) {
		tmp = t_2;
	} else if (a <= 1.02e-240) {
		tmp = t_1;
	} else if (a <= 1.6e+51) {
		tmp = (z - t) * (y / (a - t));
	} else if (a <= 1e+111) {
		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 = y + (z * (x / t))
    t_2 = x - (y * ((t - z) / a))
    if (a <= (-1d-18)) then
        tmp = t_2
    else if (a <= 1.02d-240) then
        tmp = t_1
    else if (a <= 1.6d+51) then
        tmp = (z - t) * (y / (a - t))
    else if (a <= 1d+111) 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 = y + (z * (x / t));
	double t_2 = x - (y * ((t - z) / a));
	double tmp;
	if (a <= -1e-18) {
		tmp = t_2;
	} else if (a <= 1.02e-240) {
		tmp = t_1;
	} else if (a <= 1.6e+51) {
		tmp = (z - t) * (y / (a - t));
	} else if (a <= 1e+111) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + (z * (x / t))
	t_2 = x - (y * ((t - z) / a))
	tmp = 0
	if a <= -1e-18:
		tmp = t_2
	elif a <= 1.02e-240:
		tmp = t_1
	elif a <= 1.6e+51:
		tmp = (z - t) * (y / (a - t))
	elif a <= 1e+111:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(z * Float64(x / t)))
	t_2 = Float64(x - Float64(y * Float64(Float64(t - z) / a)))
	tmp = 0.0
	if (a <= -1e-18)
		tmp = t_2;
	elseif (a <= 1.02e-240)
		tmp = t_1;
	elseif (a <= 1.6e+51)
		tmp = Float64(Float64(z - t) * Float64(y / Float64(a - t)));
	elseif (a <= 1e+111)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + (z * (x / t));
	t_2 = x - (y * ((t - z) / a));
	tmp = 0.0;
	if (a <= -1e-18)
		tmp = t_2;
	elseif (a <= 1.02e-240)
		tmp = t_1;
	elseif (a <= 1.6e+51)
		tmp = (z - t) * (y / (a - t));
	elseif (a <= 1e+111)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1e-18], t$95$2, If[LessEqual[a, 1.02e-240], t$95$1, If[LessEqual[a, 1.6e+51], N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1e+111], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.0000000000000001e-18 or 9.99999999999999957e110 < a

   1. Initial program 70.6%

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

   3. Taylor expanded in y around inf 68.3%

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

      1. *-commutative 68.3%

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

   5. Simplified 68.3%

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

   6. Taylor expanded in a around inf 65.5%

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

      1. associate-/l* 69.5%

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

   8. Simplified 69.5%

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

   if -1.0000000000000001e-18 < a < 1.02e-240 or 1.6000000000000001e51 < a < 9.99999999999999957e110

   1. Initial program 71.2%

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

   3. Taylor expanded in t around inf 72.3%

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

      1. associate--l+ 72.3%

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

      2. distribute-lft-out-- 72.3%

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

      3. div-sub 72.3%

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

      4. mul-1-neg 72.3%

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

      5. unsub-neg 72.3%

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

      6. div-sub 72.3%

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

      7. associate-/l* 75.8%

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

      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-- 75.8%

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

   5. Simplified 75.8%

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

   6. Taylor expanded in z around inf 67.0%

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

      1. associate-/l* 70.5%

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

   8. Simplified 70.5%

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

   9. Taylor expanded in y around 0 71.8%

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

       1. neg-mul-1 71.8%

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

       2. distribute-neg-frac 71.8%

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

   11. Simplified 71.8%

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

   if 1.02e-240 < a < 1.6000000000000001e51

   1. Initial program 68.4%

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

      1. +-commutative 68.4%

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

      2. associate-/l* 83.1%

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

      3. fma-define 83.1%

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

   3. Simplified 83.1%

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

      1. clear-num 83.1%

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

      2. associate-/r/ 83.1%

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

   6. Applied egg-rr 83.1%

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

   7. Taylor expanded in y around inf 70.7%

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

      1. div-sub 70.7%

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

      2. associate-*r/ 54.5%

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

      3. *-commutative 54.5%

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

      4. associate-*r/ 69.3%

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

   9. Simplified 69.3%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{-18}:\\ \;\;\;\;x - y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{-240}:\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+51}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;a \leq 10^{+111}:\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t - z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 58.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - x \cdot \frac{z}{a}\\ t_2 := \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{if}\;y \leq -9.6 \cdot 10^{-40}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-270}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-188}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-77}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* x (/ z a)))) (t_2 (* (- z t) (/ y (- a t)))))
   (if (<= y -9.6e-40)
     t_2
     (if (<= y 3.5e-270)
       t_1
       (if (<= y 2.2e-188)
         (* x (/ (- z a) t))
         (if (<= y 1.65e-77) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x * (z / a));
	double t_2 = (z - t) * (y / (a - t));
	double tmp;
	if (y <= -9.6e-40) {
		tmp = t_2;
	} else if (y <= 3.5e-270) {
		tmp = t_1;
	} else if (y <= 2.2e-188) {
		tmp = x * ((z - a) / t);
	} else if (y <= 1.65e-77) {
		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 - (x * (z / a))
    t_2 = (z - t) * (y / (a - t))
    if (y <= (-9.6d-40)) then
        tmp = t_2
    else if (y <= 3.5d-270) then
        tmp = t_1
    else if (y <= 2.2d-188) then
        tmp = x * ((z - a) / t)
    else if (y <= 1.65d-77) 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 - (x * (z / a));
	double t_2 = (z - t) * (y / (a - t));
	double tmp;
	if (y <= -9.6e-40) {
		tmp = t_2;
	} else if (y <= 3.5e-270) {
		tmp = t_1;
	} else if (y <= 2.2e-188) {
		tmp = x * ((z - a) / t);
	} else if (y <= 1.65e-77) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (x * (z / a))
	t_2 = (z - t) * (y / (a - t))
	tmp = 0
	if y <= -9.6e-40:
		tmp = t_2
	elif y <= 3.5e-270:
		tmp = t_1
	elif y <= 2.2e-188:
		tmp = x * ((z - a) / t)
	elif y <= 1.65e-77:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(x * Float64(z / a)))
	t_2 = Float64(Float64(z - t) * Float64(y / Float64(a - t)))
	tmp = 0.0
	if (y <= -9.6e-40)
		tmp = t_2;
	elseif (y <= 3.5e-270)
		tmp = t_1;
	elseif (y <= 2.2e-188)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (y <= 1.65e-77)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (x * (z / a));
	t_2 = (z - t) * (y / (a - t));
	tmp = 0.0;
	if (y <= -9.6e-40)
		tmp = t_2;
	elseif (y <= 3.5e-270)
		tmp = t_1;
	elseif (y <= 2.2e-188)
		tmp = x * ((z - a) / t);
	elseif (y <= 1.65e-77)
		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[(x * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.6e-40], t$95$2, If[LessEqual[y, 3.5e-270], t$95$1, If[LessEqual[y, 2.2e-188], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.65e-77], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.59999999999999965e-40 or 1.64999999999999996e-77 < y

   1. Initial program 69.2%

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

      1. +-commutative 69.2%

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

      2. associate-/l* 90.1%

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

      3. fma-define 90.1%

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

   3. Simplified 90.1%

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

      1. clear-num 89.5%

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

      2. associate-/r/ 89.9%

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

   6. Applied egg-rr 89.9%

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

   7. Taylor expanded in y around inf 71.6%

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

      1. div-sub 71.6%

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

      2. associate-*r/ 53.2%

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

      3. *-commutative 53.2%

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

      4. associate-*r/ 69.0%

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

   9. Simplified 69.0%

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

   if -9.59999999999999965e-40 < y < 3.49999999999999994e-270 or 2.2e-188 < y < 1.64999999999999996e-77

   1. Initial program 74.6%

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

   3. Taylor expanded in t around 0 62.0%

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

   4. Taylor expanded in y around 0 59.9%

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

      1. mul-1-neg 59.9%

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

      2. associate-/l* 64.1%

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

      3. distribute-rgt-neg-in 64.1%

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

      4. mul-1-neg 64.1%

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

      5. associate-*r/ 64.1%

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

      6. neg-mul-1 64.1%

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

   6. Simplified 64.1%

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

   if 3.49999999999999994e-270 < y < 2.2e-188

   1. Initial program 55.3%

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

   3. Taylor expanded in t around inf 55.7%

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

      1. associate--l+ 55.7%

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

      2. distribute-lft-out-- 55.7%

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

      3. div-sub 55.7%

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

      4. mul-1-neg 55.7%

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

      5. unsub-neg 55.7%

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

      6. div-sub 55.7%

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

      7. associate-/l* 68.0%

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

      8. associate-/l* 80.4%

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

      9. distribute-rgt-out-- 80.4%

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

   5. Simplified 80.4%

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

   6. Taylor expanded in y around 0 49.2%

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

      1. associate-/l* 73.9%

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

   8. Simplified 73.9%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.6 \cdot 10^{-40}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-270}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-188}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-77}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 53.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - z \cdot \frac{y}{t}\\ \mathbf{if}\;t \leq -2.5 \cdot 10^{+70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.95 \cdot 10^{-89}:\\ \;\;\;\;x - \frac{y \cdot t}{a}\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{-289}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+40}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- y (* z (/ y t)))))
   (if (<= t -2.5e+70)
     t_1
     (if (<= t -2.95e-89)
       (- x (/ (* y t) a))
       (if (<= t -8.2e-289)
         (+ x (* y (/ z a)))
         (if (<= t 1.05e+40) (- x (* x (/ z a))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (z * (y / t));
	double tmp;
	if (t <= -2.5e+70) {
		tmp = t_1;
	} else if (t <= -2.95e-89) {
		tmp = x - ((y * t) / a);
	} else if (t <= -8.2e-289) {
		tmp = x + (y * (z / a));
	} else if (t <= 1.05e+40) {
		tmp = x - (x * (z / a));
	} 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 = y - (z * (y / t))
    if (t <= (-2.5d+70)) then
        tmp = t_1
    else if (t <= (-2.95d-89)) then
        tmp = x - ((y * t) / a)
    else if (t <= (-8.2d-289)) then
        tmp = x + (y * (z / a))
    else if (t <= 1.05d+40) then
        tmp = x - (x * (z / a))
    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 = y - (z * (y / t));
	double tmp;
	if (t <= -2.5e+70) {
		tmp = t_1;
	} else if (t <= -2.95e-89) {
		tmp = x - ((y * t) / a);
	} else if (t <= -8.2e-289) {
		tmp = x + (y * (z / a));
	} else if (t <= 1.05e+40) {
		tmp = x - (x * (z / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - (z * (y / t))
	tmp = 0
	if t <= -2.5e+70:
		tmp = t_1
	elif t <= -2.95e-89:
		tmp = x - ((y * t) / a)
	elif t <= -8.2e-289:
		tmp = x + (y * (z / a))
	elif t <= 1.05e+40:
		tmp = x - (x * (z / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y - Float64(z * Float64(y / t)))
	tmp = 0.0
	if (t <= -2.5e+70)
		tmp = t_1;
	elseif (t <= -2.95e-89)
		tmp = Float64(x - Float64(Float64(y * t) / a));
	elseif (t <= -8.2e-289)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (t <= 1.05e+40)
		tmp = Float64(x - Float64(x * Float64(z / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y - (z * (y / t));
	tmp = 0.0;
	if (t <= -2.5e+70)
		tmp = t_1;
	elseif (t <= -2.95e-89)
		tmp = x - ((y * t) / a);
	elseif (t <= -8.2e-289)
		tmp = x + (y * (z / a));
	elseif (t <= 1.05e+40)
		tmp = x - (x * (z / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y - N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.5e+70], t$95$1, If[LessEqual[t, -2.95e-89], N[(x - N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -8.2e-289], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.05e+40], N[(x - N[(x * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.5000000000000001e70 or 1.05000000000000005e40 < t

   1. Initial program 44.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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* 74.6%

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

      8. associate-/l* 84.3%

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

      9. distribute-rgt-out-- 84.3%

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

   5. Simplified 84.3%

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

   6. Taylor expanded in z around inf 63.2%

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

      1. associate-/l* 74.7%

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

   8. Simplified 74.7%

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

   9. Taylor expanded in y around inf 59.8%

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

   if -2.5000000000000001e70 < t < -2.9500000000000001e-89

   1. Initial program 77.9%

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

   3. Taylor expanded in y around inf 69.9%

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

      1. *-commutative 69.9%

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

   5. Simplified 69.9%

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

   6. Taylor expanded in a around inf 57.7%

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

   7. Taylor expanded in z around 0 56.0%

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

      1. mul-1-neg 56.0%

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

      2. distribute-lft-neg-out 56.0%

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

      3. *-commutative 56.0%

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

   9. Simplified 56.0%

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

   if -2.9500000000000001e-89 < t < -8.1999999999999996e-289

   1. Initial program 96.9%

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

   3. Taylor expanded in t around 0 84.4%

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

   4. Taylor expanded in y around inf 74.3%

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

      1. associate-/l* 75.0%

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

   6. Simplified 75.0%

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

   if -8.1999999999999996e-289 < t < 1.05000000000000005e40

   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 71.9%

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

   4. Taylor expanded in y around 0 58.6%

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

      1. mul-1-neg 58.6%

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

      2. associate-/l* 64.4%

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

      3. distribute-rgt-neg-in 64.4%

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

      4. mul-1-neg 64.4%

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

      5. associate-*r/ 64.4%

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

      6. neg-mul-1 64.4%

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

   6. Simplified 64.4%

      \[\leadsto x + \color{blue}{x \cdot \frac{-z}{a}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+70}:\\ \;\;\;\;y - z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq -2.95 \cdot 10^{-89}:\\ \;\;\;\;x - \frac{y \cdot t}{a}\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{-289}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+40}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y - z \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 53.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - z \cdot \frac{y}{t}\\ \mathbf{if}\;t \leq -4.5 \cdot 10^{+70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.95 \cdot 10^{-89}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq -1.02 \cdot 10^{-288}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.42 \cdot 10^{+40}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- y (* z (/ y t)))))
   (if (<= t -4.5e+70)
     t_1
     (if (<= t -2.95e-89)
       (- x (* t (/ y a)))
       (if (<= t -1.02e-288)
         (+ x (* y (/ z a)))
         (if (<= t 1.42e+40) (- x (* x (/ z a))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (z * (y / t));
	double tmp;
	if (t <= -4.5e+70) {
		tmp = t_1;
	} else if (t <= -2.95e-89) {
		tmp = x - (t * (y / a));
	} else if (t <= -1.02e-288) {
		tmp = x + (y * (z / a));
	} else if (t <= 1.42e+40) {
		tmp = x - (x * (z / a));
	} 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 = y - (z * (y / t))
    if (t <= (-4.5d+70)) then
        tmp = t_1
    else if (t <= (-2.95d-89)) then
        tmp = x - (t * (y / a))
    else if (t <= (-1.02d-288)) then
        tmp = x + (y * (z / a))
    else if (t <= 1.42d+40) then
        tmp = x - (x * (z / a))
    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 = y - (z * (y / t));
	double tmp;
	if (t <= -4.5e+70) {
		tmp = t_1;
	} else if (t <= -2.95e-89) {
		tmp = x - (t * (y / a));
	} else if (t <= -1.02e-288) {
		tmp = x + (y * (z / a));
	} else if (t <= 1.42e+40) {
		tmp = x - (x * (z / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - (z * (y / t))
	tmp = 0
	if t <= -4.5e+70:
		tmp = t_1
	elif t <= -2.95e-89:
		tmp = x - (t * (y / a))
	elif t <= -1.02e-288:
		tmp = x + (y * (z / a))
	elif t <= 1.42e+40:
		tmp = x - (x * (z / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y - Float64(z * Float64(y / t)))
	tmp = 0.0
	if (t <= -4.5e+70)
		tmp = t_1;
	elseif (t <= -2.95e-89)
		tmp = Float64(x - Float64(t * Float64(y / a)));
	elseif (t <= -1.02e-288)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (t <= 1.42e+40)
		tmp = Float64(x - Float64(x * Float64(z / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y - (z * (y / t));
	tmp = 0.0;
	if (t <= -4.5e+70)
		tmp = t_1;
	elseif (t <= -2.95e-89)
		tmp = x - (t * (y / a));
	elseif (t <= -1.02e-288)
		tmp = x + (y * (z / a));
	elseif (t <= 1.42e+40)
		tmp = x - (x * (z / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y - N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.5e+70], t$95$1, If[LessEqual[t, -2.95e-89], N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.02e-288], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.42e+40], N[(x - N[(x * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.4999999999999999e70 or 1.42e40 < t

   1. Initial program 44.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   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* 74.6%

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

      8. associate-/l* 84.3%

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

      9. distribute-rgt-out-- 84.3%

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

   5. Simplified 84.3%

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

   6. Taylor expanded in z around inf 63.2%

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

      1. associate-/l* 74.7%

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

   8. Simplified 74.7%

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

   9. Taylor expanded in y around inf 59.8%

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

   if -4.4999999999999999e70 < t < -2.9500000000000001e-89

   1. Initial program 77.9%

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

   3. Taylor expanded in y around inf 69.9%

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

      1. *-commutative 69.9%

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

   5. Simplified 69.9%

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

   6. Taylor expanded in a around inf 57.7%

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

   7. Taylor expanded in z around 0 56.0%

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

      1. mul-1-neg 56.0%

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

      2. associate-/l* 56.0%

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

      3. distribute-rgt-neg-in 56.0%

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

      4. mul-1-neg 56.0%

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

      5. associate-*r/ 56.0%

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

      6. neg-mul-1 56.0%

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

   9. Simplified 56.0%

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

   if -2.9500000000000001e-89 < t < -1.0199999999999999e-288

   1. Initial program 96.9%

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

   3. Taylor expanded in t around 0 84.4%

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

   4. Taylor expanded in y around inf 74.3%

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

      1. associate-/l* 75.0%

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

   6. Simplified 75.0%

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

   if -1.0199999999999999e-288 < t < 1.42e40

   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 71.9%

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

   4. Taylor expanded in x around inf 64.4%

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

      1. mul-1-neg 64.4%

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

      2. unsub-neg 64.4%

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

   6. Simplified 64.4%

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

   7. Taylor expanded in z around 0 58.6%

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

      1. associate-*r/ 64.4%

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

      2. associate-*r* 64.4%

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

      3. neg-mul-1 64.4%

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

      4. cancel-sign-sub-inv 64.4%

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

   9. Simplified 64.4%

      \[\leadsto \color{blue}{x - x \cdot \frac{z}{a}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+70}:\\ \;\;\;\;y - z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq -2.95 \cdot 10^{-89}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq -1.02 \cdot 10^{-288}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.42 \cdot 10^{+40}:\\ \;\;\;\;x - x \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y - z \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 48.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;t \leq -1.1 \cdot 10^{+108}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-144}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-270}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+54}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= t -1.1e+108)
     y
     (if (<= t -9.2e-144)
       t_1
       (if (<= t -1.5e-270) (* z (/ (- y x) a)) (if (<= t 4.6e+54) 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 <= -1.1e+108) {
		tmp = y;
	} else if (t <= -9.2e-144) {
		tmp = t_1;
	} else if (t <= -1.5e-270) {
		tmp = z * ((y - x) / a);
	} else if (t <= 4.6e+54) {
		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 <= (-1.1d+108)) then
        tmp = y
    else if (t <= (-9.2d-144)) then
        tmp = t_1
    else if (t <= (-1.5d-270)) then
        tmp = z * ((y - x) / a)
    else if (t <= 4.6d+54) 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 <= -1.1e+108) {
		tmp = y;
	} else if (t <= -9.2e-144) {
		tmp = t_1;
	} else if (t <= -1.5e-270) {
		tmp = z * ((y - x) / a);
	} else if (t <= 4.6e+54) {
		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 <= -1.1e+108:
		tmp = y
	elif t <= -9.2e-144:
		tmp = t_1
	elif t <= -1.5e-270:
		tmp = z * ((y - x) / a)
	elif t <= 4.6e+54:
		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 <= -1.1e+108)
		tmp = y;
	elseif (t <= -9.2e-144)
		tmp = t_1;
	elseif (t <= -1.5e-270)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	elseif (t <= 4.6e+54)
		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 <= -1.1e+108)
		tmp = y;
	elseif (t <= -9.2e-144)
		tmp = t_1;
	elseif (t <= -1.5e-270)
		tmp = z * ((y - x) / a);
	elseif (t <= 4.6e+54)
		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, -1.1e+108], y, If[LessEqual[t, -9.2e-144], t$95$1, If[LessEqual[t, -1.5e-270], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.6e+54], t$95$1, y]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.1000000000000001e108 or 4.59999999999999988e54 < t

   1. Initial program 41.7%

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

   3. Taylor expanded in t around inf 55.6%

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

   if -1.1000000000000001e108 < t < -9.2e-144 or -1.50000000000000006e-270 < t < 4.59999999999999988e54

   1. Initial program 82.9%

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

   3. Taylor expanded in t around 0 61.1%

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

   4. Taylor expanded in x around inf 55.9%

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

      1. mul-1-neg 55.9%

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

      2. unsub-neg 55.9%

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

   6. Simplified 55.9%

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

   if -9.2e-144 < t < -1.50000000000000006e-270

   1. Initial program 98.7%

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

   3. Taylor expanded in t around 0 87.8%

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

   4. Taylor expanded in z around -inf 63.0%

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

      1. associate-/l* 89.0%

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

      2. *-commutative 89.0%

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

   6. Applied egg-rr 64.1%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+108}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-144}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-270}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+54}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 48.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;t \leq -8.5 \cdot 10^{+103}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-147}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-269}:\\ \;\;\;\;z \cdot \frac{y - x}{a}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+55}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= t -8.5e+103)
     y
     (if (<= t -5.2e-147)
       t_1
       (if (<= t -3e-269) (* z (/ (- y x) a)) (if (<= t 5.5e+55) 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 <= -8.5e+103) {
		tmp = y;
	} else if (t <= -5.2e-147) {
		tmp = t_1;
	} else if (t <= -3e-269) {
		tmp = z * ((y - x) / a);
	} else if (t <= 5.5e+55) {
		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 <= (-8.5d+103)) then
        tmp = y
    else if (t <= (-5.2d-147)) then
        tmp = t_1
    else if (t <= (-3d-269)) then
        tmp = z * ((y - x) / a)
    else if (t <= 5.5d+55) 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 <= -8.5e+103) {
		tmp = y;
	} else if (t <= -5.2e-147) {
		tmp = t_1;
	} else if (t <= -3e-269) {
		tmp = z * ((y - x) / a);
	} else if (t <= 5.5e+55) {
		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 <= -8.5e+103:
		tmp = y
	elif t <= -5.2e-147:
		tmp = t_1
	elif t <= -3e-269:
		tmp = z * ((y - x) / a)
	elif t <= 5.5e+55:
		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 <= -8.5e+103)
		tmp = y;
	elseif (t <= -5.2e-147)
		tmp = t_1;
	elseif (t <= -3e-269)
		tmp = Float64(z * Float64(Float64(y - x) / a));
	elseif (t <= 5.5e+55)
		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 <= -8.5e+103)
		tmp = y;
	elseif (t <= -5.2e-147)
		tmp = t_1;
	elseif (t <= -3e-269)
		tmp = z * ((y - x) / a);
	elseif (t <= 5.5e+55)
		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, -8.5e+103], y, If[LessEqual[t, -5.2e-147], t$95$1, If[LessEqual[t, -3e-269], N[(z * N[(N[(y - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e+55], t$95$1, y]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.4999999999999992e103 or 5.5000000000000004e55 < t

   1. Initial program 41.7%

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

   3. Taylor expanded in t around inf 55.6%

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

   if -8.4999999999999992e103 < t < -5.1999999999999997e-147 or -2.9999999999999999e-269 < t < 5.5000000000000004e55

   1. Initial program 82.9%

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

   3. Taylor expanded in t around 0 61.1%

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

   4. Taylor expanded in x around inf 55.9%

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

      1. mul-1-neg 55.9%

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

      2. unsub-neg 55.9%

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

   6. Simplified 55.9%

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

   if -5.1999999999999997e-147 < t < -2.9999999999999999e-269

   1. Initial program 98.7%

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

   3. Taylor expanded in t around 0 87.8%

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

   4. Taylor expanded in z around inf 64.1%

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

      1. div-sub 64.1%

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

   6. Simplified 64.1%

      \[\leadsto \color{blue}{z \cdot \frac{y - x}{a}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 21: 75.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+57}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq -3.9 \cdot 10^{-54}:\\ \;\;\;\;x - y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+40}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{z}{\frac{t}{x - y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.5e+57)
   (+ y (* z (/ (- x y) t)))
   (if (<= t -3.9e-54)
     (- x (* y (/ (- t z) a)))
     (if (<= t 6e+40)
       (+ x (* z (/ (- y x) (- a t))))
       (+ y (/ z (/ t (- x y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.5e+57) {
		tmp = y + (z * ((x - y) / t));
	} else if (t <= -3.9e-54) {
		tmp = x - (y * ((t - z) / a));
	} else if (t <= 6e+40) {
		tmp = x + (z * ((y - x) / (a - t)));
	} else {
		tmp = y + (z / (t / (x - 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 <= (-4.5d+57)) then
        tmp = y + (z * ((x - y) / t))
    else if (t <= (-3.9d-54)) then
        tmp = x - (y * ((t - z) / a))
    else if (t <= 6d+40) then
        tmp = x + (z * ((y - x) / (a - t)))
    else
        tmp = y + (z / (t / (x - 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 <= -4.5e+57) {
		tmp = y + (z * ((x - y) / t));
	} else if (t <= -3.9e-54) {
		tmp = x - (y * ((t - z) / a));
	} else if (t <= 6e+40) {
		tmp = x + (z * ((y - x) / (a - t)));
	} else {
		tmp = y + (z / (t / (x - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.5e+57:
		tmp = y + (z * ((x - y) / t))
	elif t <= -3.9e-54:
		tmp = x - (y * ((t - z) / a))
	elif t <= 6e+40:
		tmp = x + (z * ((y - x) / (a - t)))
	else:
		tmp = y + (z / (t / (x - y)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.5e+57)
		tmp = Float64(y + Float64(z * Float64(Float64(x - y) / t)));
	elseif (t <= -3.9e-54)
		tmp = Float64(x - Float64(y * Float64(Float64(t - z) / a)));
	elseif (t <= 6e+40)
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / Float64(a - t))));
	else
		tmp = Float64(y + Float64(z / Float64(t / Float64(x - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.5e+57)
		tmp = y + (z * ((x - y) / t));
	elseif (t <= -3.9e-54)
		tmp = x - (y * ((t - z) / a));
	elseif (t <= 6e+40)
		tmp = x + (z * ((y - x) / (a - t)));
	else
		tmp = y + (z / (t / (x - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.5e+57], N[(y + N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.9e-54], N[(x - N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e+40], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(z / N[(t / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.49999999999999996e57

   1. Initial program 44.9%

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

   3. Taylor expanded in t around inf 61.6%

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

      1. associate--l+ 61.6%

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

      2. distribute-lft-out-- 61.6%

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

      3. div-sub 61.6%

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

      4. mul-1-neg 61.6%

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

      5. unsub-neg 61.6%

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

      6. div-sub 61.6%

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

      7. associate-/l* 68.7%

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

      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. Taylor expanded in z around inf 67.4%

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

      1. associate-/l* 74.6%

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

   8. Simplified 74.6%

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

   if -4.49999999999999996e57 < t < -3.9e-54

   1. Initial program 79.4%

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

   3. Taylor expanded in y around inf 77.3%

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

      1. *-commutative 77.3%

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

   5. Simplified 77.3%

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

   6. Taylor expanded in a around inf 63.7%

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

      1. associate-/l* 66.5%

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

   8. Simplified 66.5%

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

   if -3.9e-54 < t < 6.0000000000000004e40

   1. Initial program 91.2%

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

   3. Taylor expanded in z around inf 80.5%

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

      1. associate-/l* 85.0%

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

   5. Simplified 85.0%

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

   if 6.0000000000000004e40 < t

   1. Initial program 46.9%

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

   3. Taylor expanded in t around inf 65.3%

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

      1. associate--l+ 65.3%

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

      2. distribute-lft-out-- 65.3%

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

      3. div-sub 65.3%

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

      4. mul-1-neg 65.3%

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

      5. unsub-neg 65.3%

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

      6. div-sub 65.3%

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

      7. associate-/l* 79.9%

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

      8. associate-/l* 83.3%

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

      9. distribute-rgt-out-- 83.3%

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

   5. Simplified 83.3%

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

   6. Taylor expanded in z around inf 60.2%

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

      1. associate-/l* 74.8%

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

   8. Simplified 74.8%

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

      1. clear-num 74.8%

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

      2. un-div-inv 74.8%

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

   10. Applied egg-rr 74.8%

       \[\leadsto y - \color{blue}{\frac{z}{\frac{t}{y - x}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+57}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq -3.9 \cdot 10^{-54}:\\ \;\;\;\;x - y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+40}:\\ \;\;\;\;x + z \cdot \frac{y - x}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{z}{\frac{t}{x - y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 69.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+57}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq -2.55 \cdot 10^{-89}:\\ \;\;\;\;x - y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+40}:\\ \;\;\;\;x - z \cdot \frac{x - y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{z}{\frac{t}{x - y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.8e+57)
   (+ y (* z (/ (- x y) t)))
   (if (<= t -2.55e-89)
     (- x (* y (/ (- t z) a)))
     (if (<= t 1.35e+40)
       (- x (* z (/ (- x y) a)))
       (+ y (/ z (/ t (- x y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.8e+57) {
		tmp = y + (z * ((x - y) / t));
	} else if (t <= -2.55e-89) {
		tmp = x - (y * ((t - z) / a));
	} else if (t <= 1.35e+40) {
		tmp = x - (z * ((x - y) / a));
	} else {
		tmp = y + (z / (t / (x - 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 <= (-3.8d+57)) then
        tmp = y + (z * ((x - y) / t))
    else if (t <= (-2.55d-89)) then
        tmp = x - (y * ((t - z) / a))
    else if (t <= 1.35d+40) then
        tmp = x - (z * ((x - y) / a))
    else
        tmp = y + (z / (t / (x - 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 <= -3.8e+57) {
		tmp = y + (z * ((x - y) / t));
	} else if (t <= -2.55e-89) {
		tmp = x - (y * ((t - z) / a));
	} else if (t <= 1.35e+40) {
		tmp = x - (z * ((x - y) / a));
	} else {
		tmp = y + (z / (t / (x - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.8e+57:
		tmp = y + (z * ((x - y) / t))
	elif t <= -2.55e-89:
		tmp = x - (y * ((t - z) / a))
	elif t <= 1.35e+40:
		tmp = x - (z * ((x - y) / a))
	else:
		tmp = y + (z / (t / (x - y)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.8e+57)
		tmp = Float64(y + Float64(z * Float64(Float64(x - y) / t)));
	elseif (t <= -2.55e-89)
		tmp = Float64(x - Float64(y * Float64(Float64(t - z) / a)));
	elseif (t <= 1.35e+40)
		tmp = Float64(x - Float64(z * Float64(Float64(x - y) / a)));
	else
		tmp = Float64(y + Float64(z / Float64(t / Float64(x - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.8e+57)
		tmp = y + (z * ((x - y) / t));
	elseif (t <= -2.55e-89)
		tmp = x - (y * ((t - z) / a));
	elseif (t <= 1.35e+40)
		tmp = x - (z * ((x - y) / a));
	else
		tmp = y + (z / (t / (x - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.8e+57], N[(y + N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.55e-89], N[(x - N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e+40], N[(x - N[(z * N[(N[(x - y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(z / N[(t / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.7999999999999999e57

   1. Initial program 44.9%

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

   3. Taylor expanded in t around inf 61.6%

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

      1. associate--l+ 61.6%

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

      2. distribute-lft-out-- 61.6%

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

      3. div-sub 61.6%

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

      4. mul-1-neg 61.6%

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

      5. unsub-neg 61.6%

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

      6. div-sub 61.6%

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

      7. associate-/l* 68.7%

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

      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. Taylor expanded in z around inf 67.4%

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

      1. associate-/l* 74.6%

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

   8. Simplified 74.6%

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

   if -3.7999999999999999e57 < t < -2.55000000000000002e-89

   1. Initial program 78.2%

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

   3. Taylor expanded in y around inf 74.1%

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

      1. *-commutative 74.1%

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

   5. Simplified 74.1%

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

   6. Taylor expanded in a around inf 60.6%

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

      1. associate-/l* 62.8%

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

   8. Simplified 62.8%

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

   if -2.55000000000000002e-89 < t < 1.35000000000000005e40

   1. Initial program 92.5%

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

   3. Taylor expanded in t around 0 77.0%

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

      1. associate-/l* 81.7%

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

      2. *-commutative 81.7%

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

   5. Applied egg-rr 81.7%

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

   if 1.35000000000000005e40 < t

   1. Initial program 46.9%

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

   3. Taylor expanded in t around inf 65.3%

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

      1. associate--l+ 65.3%

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

      2. distribute-lft-out-- 65.3%

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

      3. div-sub 65.3%

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

      4. mul-1-neg 65.3%

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

      5. unsub-neg 65.3%

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

      6. div-sub 65.3%

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

      7. associate-/l* 79.9%

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

      8. associate-/l* 83.3%

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

      9. distribute-rgt-out-- 83.3%

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

   5. Simplified 83.3%

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

   6. Taylor expanded in z around inf 60.2%

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

      1. associate-/l* 74.8%

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

   8. Simplified 74.8%

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

      1. clear-num 74.8%

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

      2. un-div-inv 74.8%

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

   10. Applied egg-rr 74.8%

       \[\leadsto y - \color{blue}{\frac{z}{\frac{t}{y - x}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+57}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq -2.55 \cdot 10^{-89}:\\ \;\;\;\;x - y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+40}:\\ \;\;\;\;x - z \cdot \frac{x - y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{z}{\frac{t}{x - y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 69.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \frac{x - y}{t}\\ \mathbf{if}\;t \leq -6.5 \cdot 10^{+57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.75 \cdot 10^{-89}:\\ \;\;\;\;x - y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+39}:\\ \;\;\;\;x - z \cdot \frac{x - y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* z (/ (- x y) t)))))
   (if (<= t -6.5e+57)
     t_1
     (if (<= t -2.75e-89)
       (- x (* y (/ (- t z) a)))
       (if (<= t 9e+39) (- x (* z (/ (- x y) a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (z * ((x - y) / t));
	double tmp;
	if (t <= -6.5e+57) {
		tmp = t_1;
	} else if (t <= -2.75e-89) {
		tmp = x - (y * ((t - z) / a));
	} else if (t <= 9e+39) {
		tmp = x - (z * ((x - y) / a));
	} 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 = y + (z * ((x - y) / t))
    if (t <= (-6.5d+57)) then
        tmp = t_1
    else if (t <= (-2.75d-89)) then
        tmp = x - (y * ((t - z) / a))
    else if (t <= 9d+39) then
        tmp = x - (z * ((x - y) / a))
    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 = y + (z * ((x - y) / t));
	double tmp;
	if (t <= -6.5e+57) {
		tmp = t_1;
	} else if (t <= -2.75e-89) {
		tmp = x - (y * ((t - z) / a));
	} else if (t <= 9e+39) {
		tmp = x - (z * ((x - y) / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + (z * ((x - y) / t))
	tmp = 0
	if t <= -6.5e+57:
		tmp = t_1
	elif t <= -2.75e-89:
		tmp = x - (y * ((t - z) / a))
	elif t <= 9e+39:
		tmp = x - (z * ((x - y) / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(z * Float64(Float64(x - y) / t)))
	tmp = 0.0
	if (t <= -6.5e+57)
		tmp = t_1;
	elseif (t <= -2.75e-89)
		tmp = Float64(x - Float64(y * Float64(Float64(t - z) / a)));
	elseif (t <= 9e+39)
		tmp = Float64(x - Float64(z * Float64(Float64(x - y) / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + (z * ((x - y) / t));
	tmp = 0.0;
	if (t <= -6.5e+57)
		tmp = t_1;
	elseif (t <= -2.75e-89)
		tmp = x - (y * ((t - z) / a));
	elseif (t <= 9e+39)
		tmp = x - (z * ((x - y) / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.5e+57], t$95$1, If[LessEqual[t, -2.75e-89], N[(x - N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9e+39], N[(x - N[(z * N[(N[(x - y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.4999999999999997e57 or 8.99999999999999991e39 < t

   1. Initial program 45.9%

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

   3. Taylor expanded in t around inf 63.5%

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

      1. associate--l+ 63.5%

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

      2. distribute-lft-out-- 63.5%

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

      3. div-sub 63.5%

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

      4. mul-1-neg 63.5%

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

      5. unsub-neg 63.5%

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

      6. div-sub 63.5%

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

      7. associate-/l* 74.6%

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

      8. associate-/l* 84.0%

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

      9. distribute-rgt-out-- 84.0%

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

   5. Simplified 84.0%

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

   6. Taylor expanded in z around inf 63.6%

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

      1. associate-/l* 74.7%

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

   8. Simplified 74.7%

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

   if -6.4999999999999997e57 < t < -2.75000000000000006e-89

   1. Initial program 78.2%

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

   3. Taylor expanded in y around inf 74.1%

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

      1. *-commutative 74.1%

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

   5. Simplified 74.1%

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

   6. Taylor expanded in a around inf 60.6%

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

      1. associate-/l* 62.8%

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

   8. Simplified 62.8%

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

   if -2.75000000000000006e-89 < t < 8.99999999999999991e39

   1. Initial program 92.5%

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

   3. Taylor expanded in t around 0 77.0%

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

      1. associate-/l* 81.7%

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

      2. *-commutative 81.7%

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

   5. Applied egg-rr 81.7%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+57}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq -2.75 \cdot 10^{-89}:\\ \;\;\;\;x - y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+39}:\\ \;\;\;\;x - z \cdot \frac{x - y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 66.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \frac{x}{t}\\ \mathbf{if}\;t \leq -9.2 \cdot 10^{+57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-89}:\\ \;\;\;\;x - y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+40}:\\ \;\;\;\;x - z \cdot \frac{x - y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* z (/ x t)))))
   (if (<= t -9.2e+57)
     t_1
     (if (<= t -2.6e-89)
       (- x (* y (/ (- t z) a)))
       (if (<= t 1.4e+40) (- x (* z (/ (- x y) a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (z * (x / t));
	double tmp;
	if (t <= -9.2e+57) {
		tmp = t_1;
	} else if (t <= -2.6e-89) {
		tmp = x - (y * ((t - z) / a));
	} else if (t <= 1.4e+40) {
		tmp = x - (z * ((x - y) / a));
	} 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 = y + (z * (x / t))
    if (t <= (-9.2d+57)) then
        tmp = t_1
    else if (t <= (-2.6d-89)) then
        tmp = x - (y * ((t - z) / a))
    else if (t <= 1.4d+40) then
        tmp = x - (z * ((x - y) / a))
    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 = y + (z * (x / t));
	double tmp;
	if (t <= -9.2e+57) {
		tmp = t_1;
	} else if (t <= -2.6e-89) {
		tmp = x - (y * ((t - z) / a));
	} else if (t <= 1.4e+40) {
		tmp = x - (z * ((x - y) / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + (z * (x / t))
	tmp = 0
	if t <= -9.2e+57:
		tmp = t_1
	elif t <= -2.6e-89:
		tmp = x - (y * ((t - z) / a))
	elif t <= 1.4e+40:
		tmp = x - (z * ((x - y) / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(z * Float64(x / t)))
	tmp = 0.0
	if (t <= -9.2e+57)
		tmp = t_1;
	elseif (t <= -2.6e-89)
		tmp = Float64(x - Float64(y * Float64(Float64(t - z) / a)));
	elseif (t <= 1.4e+40)
		tmp = Float64(x - Float64(z * Float64(Float64(x - y) / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + (z * (x / t));
	tmp = 0.0;
	if (t <= -9.2e+57)
		tmp = t_1;
	elseif (t <= -2.6e-89)
		tmp = x - (y * ((t - z) / a));
	elseif (t <= 1.4e+40)
		tmp = x - (z * ((x - y) / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.2e+57], t$95$1, If[LessEqual[t, -2.6e-89], N[(x - N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.4e+40], N[(x - N[(z * N[(N[(x - y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.1999999999999995e57 or 1.4000000000000001e40 < t

   1. Initial program 45.9%

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

   3. Taylor expanded in t around inf 63.5%

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

      1. associate--l+ 63.5%

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

      2. distribute-lft-out-- 63.5%

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

      3. div-sub 63.5%

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

      4. mul-1-neg 63.5%

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

      5. unsub-neg 63.5%

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

      6. div-sub 63.5%

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

      7. associate-/l* 74.6%

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

      8. associate-/l* 84.0%

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

      9. distribute-rgt-out-- 84.0%

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

   5. Simplified 84.0%

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

   6. Taylor expanded in z around inf 63.6%

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

      1. associate-/l* 74.7%

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

   8. Simplified 74.7%

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

   9. Taylor expanded in y around 0 67.6%

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

       1. neg-mul-1 67.6%

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

       2. distribute-neg-frac 67.6%

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

   11. Simplified 67.6%

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

   if -9.1999999999999995e57 < t < -2.5999999999999999e-89

   1. Initial program 78.2%

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

   3. Taylor expanded in y around inf 74.1%

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

      1. *-commutative 74.1%

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

   5. Simplified 74.1%

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

   6. Taylor expanded in a around inf 60.6%

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

      1. associate-/l* 62.8%

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

   8. Simplified 62.8%

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

   if -2.5999999999999999e-89 < t < 1.4000000000000001e40

   1. Initial program 92.5%

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

   3. Taylor expanded in t around 0 77.0%

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

      1. associate-/l* 81.7%

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

      2. *-commutative 81.7%

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

   5. Applied egg-rr 81.7%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{+57}:\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-89}:\\ \;\;\;\;x - y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+40}:\\ \;\;\;\;x - z \cdot \frac{x - y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 66.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \frac{x}{t}\\ \mathbf{if}\;t \leq -5.2 \cdot 10^{+57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-89}:\\ \;\;\;\;x - y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{+40}:\\ \;\;\;\;x - z \cdot \frac{x - y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* z (/ x t)))))
   (if (<= t -5.2e+57)
     t_1
     (if (<= t -2.7e-89)
       (- x (* y (/ (- t z) a)))
       (if (<= t 1.32e+40) (- x (* z (/ (- x y) a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + (z * (x / t));
	double tmp;
	if (t <= -5.2e+57) {
		tmp = t_1;
	} else if (t <= -2.7e-89) {
		tmp = x - (y * ((t - z) / a));
	} else if (t <= 1.32e+40) {
		tmp = x - (z * ((x - y) / a));
	} 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 = y + (z * (x / t))
    if (t <= (-5.2d+57)) then
        tmp = t_1
    else if (t <= (-2.7d-89)) then
        tmp = x - (y * ((t - z) / a))
    else if (t <= 1.32d+40) then
        tmp = x - (z * ((x - y) / a))
    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 = y + (z * (x / t));
	double tmp;
	if (t <= -5.2e+57) {
		tmp = t_1;
	} else if (t <= -2.7e-89) {
		tmp = x - (y * ((t - z) / a));
	} else if (t <= 1.32e+40) {
		tmp = x - (z * ((x - y) / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + (z * (x / t))
	tmp = 0
	if t <= -5.2e+57:
		tmp = t_1
	elif t <= -2.7e-89:
		tmp = x - (y * ((t - z) / a))
	elif t <= 1.32e+40:
		tmp = x - (z * ((x - y) / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(z * Float64(x / t)))
	tmp = 0.0
	if (t <= -5.2e+57)
		tmp = t_1;
	elseif (t <= -2.7e-89)
		tmp = Float64(x - Float64(y * Float64(Float64(t - z) / a)));
	elseif (t <= 1.32e+40)
		tmp = Float64(x - Float64(z * Float64(Float64(x - y) / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + (z * (x / t));
	tmp = 0.0;
	if (t <= -5.2e+57)
		tmp = t_1;
	elseif (t <= -2.7e-89)
		tmp = x - (y * ((t - z) / a));
	elseif (t <= 1.32e+40)
		tmp = x - (z * ((x - y) / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.2e+57], t$95$1, If[LessEqual[t, -2.7e-89], N[(x - N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.32e+40], N[(x - N[(z * N[(N[(x - y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.2e57 or 1.32000000000000008e40 < t

   1. Initial program 45.9%

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

   3. Taylor expanded in t around inf 63.5%

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

      1. associate--l+ 63.5%

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

      2. distribute-lft-out-- 63.5%

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

      3. div-sub 63.5%

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

      4. mul-1-neg 63.5%

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

      5. unsub-neg 63.5%

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

      6. div-sub 63.5%

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

      7. associate-/l* 74.6%

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

      8. associate-/l* 84.0%

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

      9. distribute-rgt-out-- 84.0%

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

   5. Simplified 84.0%

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

   6. Taylor expanded in z around inf 63.6%

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

      1. associate-/l* 74.7%

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

   8. Simplified 74.7%

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

   9. Taylor expanded in y around 0 67.6%

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

       1. neg-mul-1 67.6%

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

       2. distribute-neg-frac 67.6%

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

   11. Simplified 67.6%

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

   if -5.2e57 < t < -2.69999999999999988e-89

   1. Initial program 78.2%

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

   3. Taylor expanded in y around inf 74.1%

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

      1. *-commutative 74.1%

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

   5. Simplified 74.1%

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

   6. Taylor expanded in a around inf 60.6%

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

      1. associate-/l* 62.8%

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

   8. Simplified 62.8%

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

   if -2.69999999999999988e-89 < t < 1.32000000000000008e40

   1. Initial program 92.5%

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

   3. Taylor expanded in t around 0 77.0%

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

      1. associate-/l* 81.7%

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

   5. Simplified 81.7%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+57}:\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-89}:\\ \;\;\;\;x - y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{+40}:\\ \;\;\;\;x - z \cdot \frac{x - y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 38.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+55}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-139}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-271}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-40}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7e+55)
   y
   (if (<= t -2e-139)
     x
     (if (<= t -3.4e-271) (* y (/ z a)) (if (<= t 1.4e-40) x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7e+55) {
		tmp = y;
	} else if (t <= -2e-139) {
		tmp = x;
	} else if (t <= -3.4e-271) {
		tmp = y * (z / a);
	} else if (t <= 1.4e-40) {
		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 <= (-7d+55)) then
        tmp = y
    else if (t <= (-2d-139)) then
        tmp = x
    else if (t <= (-3.4d-271)) then
        tmp = y * (z / a)
    else if (t <= 1.4d-40) 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 <= -7e+55) {
		tmp = y;
	} else if (t <= -2e-139) {
		tmp = x;
	} else if (t <= -3.4e-271) {
		tmp = y * (z / a);
	} else if (t <= 1.4e-40) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -7e+55:
		tmp = y
	elif t <= -2e-139:
		tmp = x
	elif t <= -3.4e-271:
		tmp = y * (z / a)
	elif t <= 1.4e-40:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7e+55)
		tmp = y;
	elseif (t <= -2e-139)
		tmp = x;
	elseif (t <= -3.4e-271)
		tmp = Float64(y * Float64(z / a));
	elseif (t <= 1.4e-40)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -7e+55)
		tmp = y;
	elseif (t <= -2e-139)
		tmp = x;
	elseif (t <= -3.4e-271)
		tmp = y * (z / a);
	elseif (t <= 1.4e-40)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7e+55], y, If[LessEqual[t, -2e-139], x, If[LessEqual[t, -3.4e-271], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.4e-40], x, y]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.00000000000000021e55 or 1.4e-40 < t

   1. Initial program 50.5%

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

   3. Taylor expanded in t around inf 47.9%

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

   if -7.00000000000000021e55 < t < -2.00000000000000006e-139 or -3.4000000000000001e-271 < t < 1.4e-40

   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 a around inf 46.7%

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

   if -2.00000000000000006e-139 < t < -3.4000000000000001e-271

   1. Initial program 95.3%

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

   3. Taylor expanded in t around 0 84.8%

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

   4. Taylor expanded in z around -inf 60.9%

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

   5. Taylor expanded in y around inf 54.1%

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

      1. associate-/l* 79.0%

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

   7. Simplified 55.2%

      \[\leadsto \color{blue}{y \cdot \frac{z}{a}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 27: 73.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+57}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+40}:\\ \;\;\;\;x - \left(y - x\right) \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{z}{\frac{t}{x - y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.8e+57)
   (+ y (* z (/ (- x y) t)))
   (if (<= t 1.1e+40)
     (- x (* (- y x) (/ (- t z) a)))
     (+ y (/ z (/ t (- x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.8e+57) {
		tmp = y + (z * ((x - y) / t));
	} else if (t <= 1.1e+40) {
		tmp = x - ((y - x) * ((t - z) / a));
	} else {
		tmp = y + (z / (t / (x - 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 <= (-3.8d+57)) then
        tmp = y + (z * ((x - y) / t))
    else if (t <= 1.1d+40) then
        tmp = x - ((y - x) * ((t - z) / a))
    else
        tmp = y + (z / (t / (x - 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 <= -3.8e+57) {
		tmp = y + (z * ((x - y) / t));
	} else if (t <= 1.1e+40) {
		tmp = x - ((y - x) * ((t - z) / a));
	} else {
		tmp = y + (z / (t / (x - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.8e+57:
		tmp = y + (z * ((x - y) / t))
	elif t <= 1.1e+40:
		tmp = x - ((y - x) * ((t - z) / a))
	else:
		tmp = y + (z / (t / (x - y)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.8e+57)
		tmp = Float64(y + Float64(z * Float64(Float64(x - y) / t)));
	elseif (t <= 1.1e+40)
		tmp = Float64(x - Float64(Float64(y - x) * Float64(Float64(t - z) / a)));
	else
		tmp = Float64(y + Float64(z / Float64(t / Float64(x - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.8e+57)
		tmp = y + (z * ((x - y) / t));
	elseif (t <= 1.1e+40)
		tmp = x - ((y - x) * ((t - z) / a));
	else
		tmp = y + (z / (t / (x - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.8e+57], N[(y + N[(z * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.1e+40], N[(x - N[(N[(y - x), $MachinePrecision] * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(z / N[(t / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.7999999999999999e57

   1. Initial program 44.9%

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

   3. Taylor expanded in t around inf 61.6%

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

      1. associate--l+ 61.6%

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

      2. distribute-lft-out-- 61.6%

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

      3. div-sub 61.6%

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

      4. mul-1-neg 61.6%

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

      5. unsub-neg 61.6%

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

      6. div-sub 61.6%

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

      7. associate-/l* 68.7%

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

      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. Taylor expanded in z around inf 67.4%

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

      1. associate-/l* 74.6%

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

   8. Simplified 74.6%

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

   if -3.7999999999999999e57 < t < 1.0999999999999999e40

   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 a around inf 74.9%

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

      1. associate-/l* 78.7%

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

   5. Simplified 78.7%

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

   if 1.0999999999999999e40 < t

   1. Initial program 46.9%

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

   3. Taylor expanded in t around inf 65.3%

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

      1. associate--l+ 65.3%

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

      2. distribute-lft-out-- 65.3%

         \[\leadsto y + \color{blue}{-1 \cdot \left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      3. div-sub 65.3%

         \[\leadsto y + -1 \cdot \color{blue}{\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      4. mul-1-neg 65.3%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      5. unsub-neg 65.3%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      6. div-sub 65.3%

         \[\leadsto y - \color{blue}{\left(\frac{z \cdot \left(y - x\right)}{t} - \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      7. associate-/l* 79.9%

         \[\leadsto y - \left(\color{blue}{z \cdot \frac{y - x}{t}} - \frac{a \cdot \left(y - x\right)}{t}\right) \]

      8. associate-/l* 83.3%

         \[\leadsto y - \left(z \cdot \frac{y - x}{t} - \color{blue}{a \cdot \frac{y - x}{t}}\right) \]

      9. distribute-rgt-out-- 83.3%

         \[\leadsto y - \color{blue}{\frac{y - x}{t} \cdot \left(z - a\right)} \]

   5. Simplified 83.3%

      \[\leadsto \color{blue}{y - \frac{y - x}{t} \cdot \left(z - a\right)} \]

   6. Taylor expanded in z around inf 60.2%

      \[\leadsto y - \color{blue}{\frac{z \cdot \left(y - x\right)}{t}} \]
   7. Step-by-step derivation

      1. associate-/l* 74.8%

         \[\leadsto y - \color{blue}{z \cdot \frac{y - x}{t}} \]

   8. Simplified 74.8%

      \[\leadsto y - \color{blue}{z \cdot \frac{y - x}{t}} \]
   9. Step-by-step derivation

      1. clear-num 74.8%

         \[\leadsto y - z \cdot \color{blue}{\frac{1}{\frac{t}{y - x}}} \]

      2. un-div-inv 74.8%

         \[\leadsto y - \color{blue}{\frac{z}{\frac{t}{y - x}}} \]

   10. Applied egg-rr 74.8%

       \[\leadsto y - \color{blue}{\frac{z}{\frac{t}{y - x}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+57}:\\ \;\;\;\;y + z \cdot \frac{x - y}{t}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+40}:\\ \;\;\;\;x - \left(y - x\right) \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{z}{\frac{t}{x - y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 49.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+104}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{+51}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.1e+104) y (if (<= t 9.2e+51) (* x (- 1.0 (/ z a))) y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.1e+104) {
		tmp = y;
	} else if (t <= 9.2e+51) {
		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 <= (-3.1d+104)) then
        tmp = y
    else if (t <= 9.2d+51) 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 <= -3.1e+104) {
		tmp = y;
	} else if (t <= 9.2e+51) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.1e+104:
		tmp = y
	elif t <= 9.2e+51:
		tmp = x * (1.0 - (z / a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.1e+104)
		tmp = y;
	elseif (t <= 9.2e+51)
		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 <= -3.1e+104)
		tmp = y;
	elseif (t <= 9.2e+51)
		tmp = x * (1.0 - (z / a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.1e+104], y, If[LessEqual[t, 9.2e+51], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if t < -3.10000000000000017e104 or 9.2000000000000002e51 < t

   1. Initial program 41.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 55.6%

      \[\leadsto \color{blue}{y} \]

   if -3.10000000000000017e104 < t < 9.2000000000000002e51

   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 t around 0 65.4%

      \[\leadsto x + \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]

   4. Taylor expanded in x around inf 53.7%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z}{a}\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 53.7%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{z}{a}\right)}\right) \]

      2. unsub-neg 53.7%

         \[\leadsto x \cdot \color{blue}{\left(1 - \frac{z}{a}\right)} \]

   6. Simplified 53.7%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{a}\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 29: 38.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.75 \cdot 10^{+56}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-40}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.75e+56) y (if (<= t 1.9e-40) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.75e+56) {
		tmp = y;
	} else if (t <= 1.9e-40) {
		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 <= (-2.75d+56)) then
        tmp = y
    else if (t <= 1.9d-40) 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 <= -2.75e+56) {
		tmp = y;
	} else if (t <= 1.9e-40) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.75e+56:
		tmp = y
	elif t <= 1.9e-40:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.75e+56)
		tmp = y;
	elseif (t <= 1.9e-40)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.75e+56)
		tmp = y;
	elseif (t <= 1.9e-40)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.75e+56], y, If[LessEqual[t, 1.9e-40], x, y]]

Derivation

1. Split input into 2 regimes

2. if t < -2.7500000000000001e56 or 1.8999999999999999e-40 < t

   1. Initial program 50.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 47.9%

      \[\leadsto \color{blue}{y} \]

   if -2.7500000000000001e56 < t < 1.8999999999999999e-40

   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 a around inf 42.5%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 30: 25.1% 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 70.2%

   \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
2. Add Preprocessing

3. Taylor expanded in a around inf 27.8%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Developer target: 86.3% 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 2024103 
(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))))