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

Percentage Accurate: 68.4% → 90.6%

Time: 19.9s

Alternatives: 26

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: 68.4% 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: 90.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;t_1 \leq -1 \cdot 10^{-236}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;y - \frac{y - x}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* (- y x) (- t z)) (- a t)))))
   (if (<= t_1 (- INFINITY))
     (+ x (/ (- y x) (/ (- a t) (- z t))))
     (if (<= t_1 -1e-236)
       t_1
       (if (<= t_1 0.0)
         (- y (/ (- y x) (/ t (- z a))))
         (fma (/ (- z t) (- a t)) (- y x) x))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - x) * (t - z)) / (a - t));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else if (t_1 <= -1e-236) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = y - ((y - x) / (t / (z - a)));
	} else {
		tmp = fma(((z - t) / (a - t)), (y - x), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(y - x) * Float64(t - z)) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x + Float64(Float64(y - x) / Float64(Float64(a - t) / Float64(z - t))));
	elseif (t_1 <= -1e-236)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(y - Float64(Float64(y - x) / Float64(t / Float64(z - a))));
	else
		tmp = fma(Float64(Float64(z - t) / Float64(a - t)), Float64(y - x), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(y - x), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -1e-236], t$95$1, If[LessEqual[t$95$1, 0.0], N[(y - N[(N[(y - x), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(y - x), $MachinePrecision] + x), $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 35.9%

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

      1. associate-/l* 86.5%

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

   3. Simplified 86.5%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -1e-236

   1. Initial program 97.5%

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

   if -1e-236 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 10.2%

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

      1. +-commutative 10.2%

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

      2. associate-*r/ 10.2%

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

      3. *-commutative 10.2%

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

      4. fma-def 10.2%

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

   3. Simplified 10.2%

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

   4. Taylor expanded in t around inf 99.8%

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

      1. *-commutative 99.8%

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

      2. cancel-sign-sub-inv 99.8%

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

      3. metadata-eval 99.8%

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

      4. *-lft-identity 99.8%

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

      5. distribute-lft-in 99.8%

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

      6. mul-1-neg 99.8%

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

      7. distribute-rgt-neg-in 99.8%

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

      8. mul-1-neg 99.8%

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

      9. *-commutative 99.8%

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

      10. cancel-sign-sub 99.8%

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

      11. mul-1-neg 99.8%

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

      12. associate-*r* 99.8%

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

      13. distribute-lft-out-- 99.8%

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

      14. associate-*r/ 99.8%

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

      15. mul-1-neg 99.8%

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

   6. Simplified 99.9%

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

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

   1. Initial program 80.7%

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

      1. +-commutative 80.7%

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

      2. associate-*r/ 93.1%

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

      3. *-commutative 93.1%

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

      4. fma-def 93.1%

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

   3. Simplified 93.1%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq -\infty:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq -1 \cdot 10^{-236}:\\ \;\;\;\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{elif}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq 0:\\ \;\;\;\;y - \frac{y - x}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)\\ \end{array} \]

Alternative 2: 86.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq -1 \cdot 10^{-236} \lor \neg \left(t_1 \leq 0\right) \land t_1 \leq 10^{+296}\right):\\ \;\;\;\;y - \frac{y - x}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* (- y x) (- t z)) (- a t)))))
   (if (or (<= t_1 (- INFINITY))
           (not
            (or (<= t_1 -1e-236) (and (not (<= t_1 0.0)) (<= t_1 1e+296)))))
     (- y (/ (- y x) (/ t (- z a))))
     t_1)))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - x) * (t - z)) / (a - t));
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !((t_1 <= -1e-236) || (!(t_1 <= 0.0) && (t_1 <= 1e+296)))) {
		tmp = y - ((y - x) / (t / (z - a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((y - x) * (t - z)) / (a - t));
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !((t_1 <= -1e-236) || (!(t_1 <= 0.0) && (t_1 <= 1e+296)))) {
		tmp = y - ((y - x) / (t / (z - a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (((y - x) * (t - z)) / (a - t))
	tmp = 0
	if (t_1 <= -math.inf) or not ((t_1 <= -1e-236) or (not (t_1 <= 0.0) and (t_1 <= 1e+296))):
		tmp = y - ((y - x) / (t / (z - a)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(y - x) * Float64(t - z)) / Float64(a - t)))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !((t_1 <= -1e-236) || (!(t_1 <= 0.0) && (t_1 <= 1e+296))))
		tmp = Float64(y - Float64(Float64(y - x) / Float64(t / Float64(z - a))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (((y - x) * (t - z)) / (a - t));
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~(((t_1 <= -1e-236) || (~((t_1 <= 0.0)) && (t_1 <= 1e+296)))))
		tmp = y - ((y - x) / (t / (z - a)));
	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] * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[Or[LessEqual[t$95$1, -1e-236], And[N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision], LessEqual[t$95$1, 1e+296]]]], $MachinePrecision]], N[(y - N[(N[(y - x), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -inf.0 or -1e-236 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0 or 9.99999999999999981e295 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 34.5%

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

      1. +-commutative 34.5%

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

      2. associate-*r/ 72.1%

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

      3. *-commutative 72.1%

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

      4. fma-def 72.1%

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

   3. Simplified 72.1%

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

   4. Taylor expanded in t around inf 62.2%

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

      1. *-commutative 62.2%

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

      2. cancel-sign-sub-inv 62.2%

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

      3. metadata-eval 62.2%

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

      4. *-lft-identity 62.2%

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

      5. distribute-lft-in 61.0%

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

      6. mul-1-neg 61.0%

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

      7. distribute-rgt-neg-in 61.0%

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

      8. mul-1-neg 61.0%

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

      9. *-commutative 61.0%

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

      10. cancel-sign-sub 61.0%

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

      11. mul-1-neg 61.0%

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

      12. associate-*r* 61.0%

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

      13. distribute-lft-out-- 61.0%

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

      14. associate-*r/ 61.0%

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

      15. mul-1-neg 61.0%

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

   6. Simplified 73.6%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -1e-236 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 9.99999999999999981e295

   1. Initial program 97.7%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq -\infty \lor \neg \left(x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq -1 \cdot 10^{-236} \lor \neg \left(x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq 0\right) \land x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq 10^{+296}\right):\\ \;\;\;\;y - \frac{y - x}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \end{array} \]

Alternative 3: 90.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - x}{\frac{a - t}{z - t}}\\ t_2 := x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -1 \cdot 10^{-236}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;y - \frac{y - x}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- y x) (/ (- a t) (- z t)))))
        (t_2 (- x (/ (* (- y x) (- t z)) (- a t)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -1e-236)
       t_2
       (if (<= t_2 0.0) (- y (/ (- y x) (/ t (- z a)))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - x) / ((a - t) / (z - t)));
	double t_2 = x - (((y - x) * (t - z)) / (a - t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -1e-236) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y - ((y - x) / (t / (z - a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - x) / ((a - t) / (z - t)));
	double t_2 = x - (((y - x) * (t - z)) / (a - t));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -1e-236) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = y - ((y - x) / (t / (z - a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - x) / ((a - t) / (z - t)))
	t_2 = x - (((y - x) * (t - z)) / (a - t))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -1e-236:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = y - ((y - x) / (t / (z - a)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - x) / Float64(Float64(a - t) / Float64(z - t))))
	t_2 = Float64(x - Float64(Float64(Float64(y - x) * Float64(t - z)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -1e-236)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(y - Float64(Float64(y - x) / Float64(t / Float64(z - a))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - x) / ((a - t) / (z - t)));
	t_2 = x - (((y - x) * (t - z)) / (a - t));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -1e-236)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = y - ((y - x) / (t / (z - a)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(N[(N[(y - x), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -1e-236], t$95$2, If[LessEqual[t$95$2, 0.0], N[(y - N[(N[(y - x), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 68.6%

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

      1. associate-/l* 91.3%

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

   3. Simplified 91.3%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -1e-236

   1. Initial program 97.5%

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

   if -1e-236 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 10.2%

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

      1. +-commutative 10.2%

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

      2. associate-*r/ 10.2%

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

      3. *-commutative 10.2%

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

      4. fma-def 10.2%

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

   3. Simplified 10.2%

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

   4. Taylor expanded in t around inf 99.8%

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

      1. *-commutative 99.8%

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

      2. cancel-sign-sub-inv 99.8%

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

      3. metadata-eval 99.8%

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

      4. *-lft-identity 99.8%

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

      5. distribute-lft-in 99.8%

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

      6. mul-1-neg 99.8%

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

      7. distribute-rgt-neg-in 99.8%

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

      8. mul-1-neg 99.8%

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

      9. *-commutative 99.8%

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

      10. cancel-sign-sub 99.8%

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

      11. mul-1-neg 99.8%

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

      12. associate-*r* 99.8%

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

      13. distribute-lft-out-- 99.8%

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

      14. associate-*r/ 99.8%

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

      15. mul-1-neg 99.8%

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

   6. Simplified 99.9%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq -\infty:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq -1 \cdot 10^{-236}:\\ \;\;\;\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t}\\ \mathbf{elif}\;x - \frac{\left(y - x\right) \cdot \left(t - z\right)}{a - t} \leq 0:\\ \;\;\;\;y - \frac{y - x}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \end{array} \]

Alternative 4: 42.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - z \cdot \frac{y}{t}\\ \mathbf{if}\;t \leq -1.2 \cdot 10^{+121}:\\ \;\;\;\;y \cdot \frac{-t}{a - t}\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{+59}:\\ \;\;\;\;\frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq -5.3 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-70}:\\ \;\;\;\;\frac{-z}{\frac{a - t}{x}}\\ \mathbf{elif}\;t \leq -9.6 \cdot 10^{-91}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-274}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{-235}:\\ \;\;\;\;\frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-14}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 390000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- y (* z (/ y t)))))
   (if (<= t -1.2e+121)
     (* y (/ (- t) (- a t)))
     (if (<= t -1.2e+59)
       (/ (- y x) (/ a z))
       (if (<= t -5.3e-5)
         t_1
         (if (<= t -1.05e-70)
           (/ (- z) (/ (- a t) x))
           (if (<= t -9.6e-91)
             t_1
             (if (<= t -3.8e-274)
               x
               (if (<= t 2.55e-235)
                 (/ z (/ a (- y x)))
                 (if (<= t 1.65e-14)
                   (* y (/ z (- a t)))
                   (if (<= t 390000000.0) x 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 <= -1.2e+121) {
		tmp = y * (-t / (a - t));
	} else if (t <= -1.2e+59) {
		tmp = (y - x) / (a / z);
	} else if (t <= -5.3e-5) {
		tmp = t_1;
	} else if (t <= -1.05e-70) {
		tmp = -z / ((a - t) / x);
	} else if (t <= -9.6e-91) {
		tmp = t_1;
	} else if (t <= -3.8e-274) {
		tmp = x;
	} else if (t <= 2.55e-235) {
		tmp = z / (a / (y - x));
	} else if (t <= 1.65e-14) {
		tmp = y * (z / (a - t));
	} else if (t <= 390000000.0) {
		tmp = 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 = y - (z * (y / t))
    if (t <= (-1.2d+121)) then
        tmp = y * (-t / (a - t))
    else if (t <= (-1.2d+59)) then
        tmp = (y - x) / (a / z)
    else if (t <= (-5.3d-5)) then
        tmp = t_1
    else if (t <= (-1.05d-70)) then
        tmp = -z / ((a - t) / x)
    else if (t <= (-9.6d-91)) then
        tmp = t_1
    else if (t <= (-3.8d-274)) then
        tmp = x
    else if (t <= 2.55d-235) then
        tmp = z / (a / (y - x))
    else if (t <= 1.65d-14) then
        tmp = y * (z / (a - t))
    else if (t <= 390000000.0d0) then
        tmp = 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 = y - (z * (y / t));
	double tmp;
	if (t <= -1.2e+121) {
		tmp = y * (-t / (a - t));
	} else if (t <= -1.2e+59) {
		tmp = (y - x) / (a / z);
	} else if (t <= -5.3e-5) {
		tmp = t_1;
	} else if (t <= -1.05e-70) {
		tmp = -z / ((a - t) / x);
	} else if (t <= -9.6e-91) {
		tmp = t_1;
	} else if (t <= -3.8e-274) {
		tmp = x;
	} else if (t <= 2.55e-235) {
		tmp = z / (a / (y - x));
	} else if (t <= 1.65e-14) {
		tmp = y * (z / (a - t));
	} else if (t <= 390000000.0) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - (z * (y / t))
	tmp = 0
	if t <= -1.2e+121:
		tmp = y * (-t / (a - t))
	elif t <= -1.2e+59:
		tmp = (y - x) / (a / z)
	elif t <= -5.3e-5:
		tmp = t_1
	elif t <= -1.05e-70:
		tmp = -z / ((a - t) / x)
	elif t <= -9.6e-91:
		tmp = t_1
	elif t <= -3.8e-274:
		tmp = x
	elif t <= 2.55e-235:
		tmp = z / (a / (y - x))
	elif t <= 1.65e-14:
		tmp = y * (z / (a - t))
	elif t <= 390000000.0:
		tmp = x
	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 <= -1.2e+121)
		tmp = Float64(y * Float64(Float64(-t) / Float64(a - t)));
	elseif (t <= -1.2e+59)
		tmp = Float64(Float64(y - x) / Float64(a / z));
	elseif (t <= -5.3e-5)
		tmp = t_1;
	elseif (t <= -1.05e-70)
		tmp = Float64(Float64(-z) / Float64(Float64(a - t) / x));
	elseif (t <= -9.6e-91)
		tmp = t_1;
	elseif (t <= -3.8e-274)
		tmp = x;
	elseif (t <= 2.55e-235)
		tmp = Float64(z / Float64(a / Float64(y - x)));
	elseif (t <= 1.65e-14)
		tmp = Float64(y * Float64(z / Float64(a - t)));
	elseif (t <= 390000000.0)
		tmp = x;
	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 <= -1.2e+121)
		tmp = y * (-t / (a - t));
	elseif (t <= -1.2e+59)
		tmp = (y - x) / (a / z);
	elseif (t <= -5.3e-5)
		tmp = t_1;
	elseif (t <= -1.05e-70)
		tmp = -z / ((a - t) / x);
	elseif (t <= -9.6e-91)
		tmp = t_1;
	elseif (t <= -3.8e-274)
		tmp = x;
	elseif (t <= 2.55e-235)
		tmp = z / (a / (y - x));
	elseif (t <= 1.65e-14)
		tmp = y * (z / (a - t));
	elseif (t <= 390000000.0)
		tmp = x;
	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, -1.2e+121], N[(y * N[((-t) / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.2e+59], N[(N[(y - x), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.3e-5], t$95$1, If[LessEqual[t, -1.05e-70], N[((-z) / N[(N[(a - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -9.6e-91], t$95$1, If[LessEqual[t, -3.8e-274], x, If[LessEqual[t, 2.55e-235], N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.65e-14], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 390000000.0], x, t$95$1]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -1.2e121

   1. Initial program 46.9%

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

      1. +-commutative 46.9%

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

      2. associate-*r/ 75.0%

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

      3. *-commutative 75.0%

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

      4. fma-def 75.0%

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

   3. Simplified 75.0%

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

   4. Taylor expanded in y around inf 71.1%

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

      1. div-sub 71.1%

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

      2. *-commutative 71.1%

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

   6. Simplified 71.1%

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

   7. Taylor expanded in z around 0 61.9%

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

      1. neg-mul-1 61.9%

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

      2. distribute-neg-frac 61.9%

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

   9. Simplified 61.9%

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

   if -1.2e121 < t < -1.2000000000000001e59

   1. Initial program 85.4%

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

      1. +-commutative 85.4%

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

      2. associate-*r/ 99.6%

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

      3. *-commutative 99.6%

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

      4. fma-def 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in z around inf 60.9%

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

      1. div-sub 60.9%

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

      2. *-commutative 60.9%

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

      3. associate-*l/ 46.8%

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

      4. associate-/l* 61.2%

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

   6. Simplified 61.2%

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

   7. Taylor expanded in a around inf 49.5%

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

   if -1.2000000000000001e59 < t < -5.3000000000000001e-5 or -1.0500000000000001e-70 < t < -9.60000000000000043e-91 or 3.9e8 < t

   1. Initial program 61.9%

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

      1. +-commutative 61.9%

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

      2. associate-*r/ 81.0%

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

      3. *-commutative 81.0%

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

      4. fma-def 81.0%

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

   3. Simplified 81.0%

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

   4. Taylor expanded in t around inf 72.3%

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

      1. *-commutative 72.3%

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

      2. cancel-sign-sub-inv 72.3%

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

      3. metadata-eval 72.3%

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

      4. *-lft-identity 72.3%

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

      5. distribute-lft-in 72.3%

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

      6. mul-1-neg 72.3%

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

      7. distribute-rgt-neg-in 72.3%

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

      8. mul-1-neg 72.3%

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

      9. *-commutative 72.3%

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

      10. cancel-sign-sub 72.3%

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

      11. mul-1-neg 72.3%

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

      12. associate-*r* 72.3%

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

      13. distribute-lft-out-- 72.3%

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

      14. associate-*r/ 72.3%

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

      15. mul-1-neg 72.3%

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

   6. Simplified 83.1%

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

   7. Taylor expanded in z around inf 74.1%

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

      1. *-commutative 74.1%

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

      2. associate-/l* 80.6%

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

   9. Simplified 80.6%

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

   10. Taylor expanded in y around inf 59.9%

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

       1. associate-*l/ 62.1%

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

   12. Simplified 62.1%

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

   if -5.3000000000000001e-5 < t < -1.0500000000000001e-70

   1. Initial program 65.3%

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

      1. +-commutative 65.3%

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

      2. associate-*r/ 72.9%

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

      3. *-commutative 72.9%

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

      4. fma-def 73.1%

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

   3. Simplified 73.1%

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

   4. Taylor expanded in z around inf 78.4%

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

      1. div-sub 78.4%

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

      2. *-commutative 78.4%

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

      3. associate-*l/ 70.7%

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

      4. associate-/l* 78.8%

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

   6. Simplified 78.8%

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

   7. Taylor expanded in y around 0 55.0%

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

      1. mul-1-neg 55.0%

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

      2. associate-/l* 55.1%

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

   9. Simplified 55.1%

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

   if -9.60000000000000043e-91 < t < -3.79999999999999985e-274 or 1.6499999999999999e-14 < t < 3.9e8

   1. Initial program 91.3%

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

      1. +-commutative 91.3%

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

      2. associate-*r/ 95.4%

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

      3. *-commutative 95.4%

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

      4. fma-def 95.4%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in a around inf 52.5%

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

   if -3.79999999999999985e-274 < t < 2.54999999999999996e-235

   1. Initial program 96.4%

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

      1. +-commutative 96.4%

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

      2. associate-*r/ 86.2%

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

      3. *-commutative 86.2%

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

      4. fma-def 86.2%

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

   3. Simplified 86.2%

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

   4. Taylor expanded in z around inf 60.5%

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

      1. div-sub 60.5%

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

      2. *-commutative 60.5%

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

      3. associate-*l/ 60.8%

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

      4. associate-/l* 50.8%

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

   6. Simplified 50.8%

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

   7. Taylor expanded in a around inf 51.9%

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

      1. associate-/l* 55.2%

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

   9. Simplified 55.2%

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

   if 2.54999999999999996e-235 < t < 1.6499999999999999e-14

   1. Initial program 89.8%

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

      1. +-commutative 89.8%

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

      2. associate-*r/ 96.5%

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

      3. *-commutative 96.5%

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

      4. fma-def 96.5%

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

   3. Simplified 96.5%

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

   4. Taylor expanded in y around inf 63.6%

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

      1. div-sub 63.6%

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

      2. *-commutative 63.6%

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

   6. Simplified 63.6%

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

   7. Taylor expanded in z around inf 56.8%

      \[\leadsto y \cdot \color{blue}{\frac{z}{a - t}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+121}:\\ \;\;\;\;y \cdot \frac{-t}{a - t}\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{+59}:\\ \;\;\;\;\frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq -5.3 \cdot 10^{-5}:\\ \;\;\;\;y - z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-70}:\\ \;\;\;\;\frac{-z}{\frac{a - t}{x}}\\ \mathbf{elif}\;t \leq -9.6 \cdot 10^{-91}:\\ \;\;\;\;y - z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-274}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{-235}:\\ \;\;\;\;\frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-14}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 390000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y - z \cdot \frac{y}{t}\\ \end{array} \]

Alternative 5: 72.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{-13} \lor \neg \left(a \leq 4.1 \cdot 10^{-143} \lor \neg \left(a \leq 2.4 \cdot 10^{-120}\right) \land \left(a \leq 4.8 \cdot 10^{+55} \lor \neg \left(a \leq 2.15 \cdot 10^{+126}\right) \land a \leq 8 \cdot 10^{+154}\right)\right):\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.5e-13)
         (not
          (or (<= a 4.1e-143)
              (and (not (<= a 2.4e-120))
                   (or (<= a 4.8e+55)
                       (and (not (<= a 2.15e+126)) (<= a 8e+154)))))))
   (+ x (/ (- z t) (/ a (- y x))))
   (+ y (/ (- x y) (/ t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.5e-13) || !((a <= 4.1e-143) || (!(a <= 2.4e-120) && ((a <= 4.8e+55) || (!(a <= 2.15e+126) && (a <= 8e+154)))))) {
		tmp = x + ((z - t) / (a / (y - x)));
	} else {
		tmp = y + ((x - y) / (t / z));
	}
	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 ((a <= (-1.5d-13)) .or. (.not. (a <= 4.1d-143) .or. (.not. (a <= 2.4d-120)) .and. (a <= 4.8d+55) .or. (.not. (a <= 2.15d+126)) .and. (a <= 8d+154))) then
        tmp = x + ((z - t) / (a / (y - x)))
    else
        tmp = y + ((x - y) / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.5e-13) || !((a <= 4.1e-143) || (!(a <= 2.4e-120) && ((a <= 4.8e+55) || (!(a <= 2.15e+126) && (a <= 8e+154)))))) {
		tmp = x + ((z - t) / (a / (y - x)));
	} else {
		tmp = y + ((x - y) / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.5e-13) or not ((a <= 4.1e-143) or (not (a <= 2.4e-120) and ((a <= 4.8e+55) or (not (a <= 2.15e+126) and (a <= 8e+154))))):
		tmp = x + ((z - t) / (a / (y - x)))
	else:
		tmp = y + ((x - y) / (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.5e-13) || !((a <= 4.1e-143) || (!(a <= 2.4e-120) && ((a <= 4.8e+55) || (!(a <= 2.15e+126) && (a <= 8e+154))))))
		tmp = Float64(x + Float64(Float64(z - t) / Float64(a / Float64(y - x))));
	else
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.5e-13) || ~(((a <= 4.1e-143) || (~((a <= 2.4e-120)) && ((a <= 4.8e+55) || (~((a <= 2.15e+126)) && (a <= 8e+154)))))))
		tmp = x + ((z - t) / (a / (y - x)));
	else
		tmp = y + ((x - y) / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.5e-13], N[Not[Or[LessEqual[a, 4.1e-143], And[N[Not[LessEqual[a, 2.4e-120]], $MachinePrecision], Or[LessEqual[a, 4.8e+55], And[N[Not[LessEqual[a, 2.15e+126]], $MachinePrecision], LessEqual[a, 8e+154]]]]]], $MachinePrecision]], N[(x + N[(N[(z - t), $MachinePrecision] / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.49999999999999992e-13 or 4.1e-143 < a < 2.3999999999999999e-120 or 4.7999999999999998e55 < a < 2.1500000000000001e126 or 8.0000000000000003e154 < a

   1. Initial program 75.1%

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

      1. +-commutative 75.1%

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

      2. associate-*r/ 92.1%

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

      3. *-commutative 92.1%

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

      4. fma-def 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in a around inf 66.0%

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

      1. +-commutative 66.0%

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

      2. associate-/l* 79.7%

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

   6. Simplified 79.7%

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

   if -1.49999999999999992e-13 < a < 4.1e-143 or 2.3999999999999999e-120 < a < 4.7999999999999998e55 or 2.1500000000000001e126 < a < 8.0000000000000003e154

   1. Initial program 71.1%

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

      1. +-commutative 71.1%

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

      2. associate-*r/ 79.6%

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

      3. *-commutative 79.6%

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

      4. fma-def 79.6%

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

   3. Simplified 79.6%

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

   4. Taylor expanded in t around inf 76.0%

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

      1. *-commutative 76.0%

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

      2. cancel-sign-sub-inv 76.0%

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

      3. metadata-eval 76.0%

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

      4. *-lft-identity 76.0%

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

      5. distribute-lft-in 75.3%

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

      6. mul-1-neg 75.3%

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

      7. distribute-rgt-neg-in 75.3%

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

      8. mul-1-neg 75.3%

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

      9. *-commutative 75.3%

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

      10. cancel-sign-sub 75.3%

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

      11. mul-1-neg 75.3%

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

      12. associate-*r* 75.3%

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

      13. distribute-lft-out-- 75.3%

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

      14. associate-*r/ 75.3%

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

      15. mul-1-neg 75.3%

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

   6. Simplified 81.5%

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

   7. Taylor expanded in z around inf 74.9%

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

      1. *-commutative 74.9%

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

      2. associate-/l* 79.8%

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

   9. Simplified 79.8%

      \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{-13} \lor \neg \left(a \leq 4.1 \cdot 10^{-143} \lor \neg \left(a \leq 2.4 \cdot 10^{-120}\right) \land \left(a \leq 4.8 \cdot 10^{+55} \lor \neg \left(a \leq 2.15 \cdot 10^{+126}\right) \land a \leq 8 \cdot 10^{+154}\right)\right):\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \end{array} \]

Alternative 6: 37.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{\frac{t}{x}}\\ t_2 := z \cdot \frac{y}{a - t}\\ t_3 := y + \frac{y}{\frac{t}{a}}\\ \mathbf{if}\;t \leq -3.5 \cdot 10^{-6}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.6 \cdot 10^{-96}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-248}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+56}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+131} \lor \neg \left(t \leq 1.15 \cdot 10^{+194}\right):\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ z (/ t x)))
        (t_2 (* z (/ y (- a t))))
        (t_3 (+ y (/ y (/ t a)))))
   (if (<= t -3.5e-6)
     t_3
     (if (<= t -1.8e-60)
       t_1
       (if (<= t -3.6e-96)
         t_2
         (if (<= t 4.2e-248)
           x
           (if (<= t 1.75e+56)
             t_2
             (if (or (<= t 4.4e+131) (not (<= t 1.15e+194))) t_3 t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z / (t / x);
	double t_2 = z * (y / (a - t));
	double t_3 = y + (y / (t / a));
	double tmp;
	if (t <= -3.5e-6) {
		tmp = t_3;
	} else if (t <= -1.8e-60) {
		tmp = t_1;
	} else if (t <= -3.6e-96) {
		tmp = t_2;
	} else if (t <= 4.2e-248) {
		tmp = x;
	} else if (t <= 1.75e+56) {
		tmp = t_2;
	} else if ((t <= 4.4e+131) || !(t <= 1.15e+194)) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = z / (t / x)
    t_2 = z * (y / (a - t))
    t_3 = y + (y / (t / a))
    if (t <= (-3.5d-6)) then
        tmp = t_3
    else if (t <= (-1.8d-60)) then
        tmp = t_1
    else if (t <= (-3.6d-96)) then
        tmp = t_2
    else if (t <= 4.2d-248) then
        tmp = x
    else if (t <= 1.75d+56) then
        tmp = t_2
    else if ((t <= 4.4d+131) .or. (.not. (t <= 1.15d+194))) then
        tmp = t_3
    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 = z / (t / x);
	double t_2 = z * (y / (a - t));
	double t_3 = y + (y / (t / a));
	double tmp;
	if (t <= -3.5e-6) {
		tmp = t_3;
	} else if (t <= -1.8e-60) {
		tmp = t_1;
	} else if (t <= -3.6e-96) {
		tmp = t_2;
	} else if (t <= 4.2e-248) {
		tmp = x;
	} else if (t <= 1.75e+56) {
		tmp = t_2;
	} else if ((t <= 4.4e+131) || !(t <= 1.15e+194)) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z / (t / x)
	t_2 = z * (y / (a - t))
	t_3 = y + (y / (t / a))
	tmp = 0
	if t <= -3.5e-6:
		tmp = t_3
	elif t <= -1.8e-60:
		tmp = t_1
	elif t <= -3.6e-96:
		tmp = t_2
	elif t <= 4.2e-248:
		tmp = x
	elif t <= 1.75e+56:
		tmp = t_2
	elif (t <= 4.4e+131) or not (t <= 1.15e+194):
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z / Float64(t / x))
	t_2 = Float64(z * Float64(y / Float64(a - t)))
	t_3 = Float64(y + Float64(y / Float64(t / a)))
	tmp = 0.0
	if (t <= -3.5e-6)
		tmp = t_3;
	elseif (t <= -1.8e-60)
		tmp = t_1;
	elseif (t <= -3.6e-96)
		tmp = t_2;
	elseif (t <= 4.2e-248)
		tmp = x;
	elseif (t <= 1.75e+56)
		tmp = t_2;
	elseif ((t <= 4.4e+131) || !(t <= 1.15e+194))
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z / (t / x);
	t_2 = z * (y / (a - t));
	t_3 = y + (y / (t / a));
	tmp = 0.0;
	if (t <= -3.5e-6)
		tmp = t_3;
	elseif (t <= -1.8e-60)
		tmp = t_1;
	elseif (t <= -3.6e-96)
		tmp = t_2;
	elseif (t <= 4.2e-248)
		tmp = x;
	elseif (t <= 1.75e+56)
		tmp = t_2;
	elseif ((t <= 4.4e+131) || ~((t <= 1.15e+194)))
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z / N[(t / x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y + N[(y / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.5e-6], t$95$3, If[LessEqual[t, -1.8e-60], t$95$1, If[LessEqual[t, -3.6e-96], t$95$2, If[LessEqual[t, 4.2e-248], x, If[LessEqual[t, 1.75e+56], t$95$2, If[Or[LessEqual[t, 4.4e+131], N[Not[LessEqual[t, 1.15e+194]], $MachinePrecision]], t$95$3, t$95$1]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.49999999999999995e-6 or 1.75e56 < t < 4.3999999999999998e131 or 1.15000000000000003e194 < t

   1. Initial program 55.4%

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

      1. +-commutative 55.4%

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

      2. associate-*r/ 79.7%

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

      3. *-commutative 79.7%

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

      4. fma-def 79.7%

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

   3. Simplified 79.7%

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

   4. Taylor expanded in y around inf 72.4%

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

      1. div-sub 72.5%

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

      2. *-commutative 72.5%

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

   6. Simplified 72.5%

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

   7. Taylor expanded in z around 0 59.1%

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

      1. neg-mul-1 59.1%

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

      2. distribute-neg-frac 59.1%

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

   9. Simplified 59.1%

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

   10. Taylor expanded in t around inf 54.6%

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

       1. +-commutative 54.6%

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

       2. *-commutative 54.6%

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

       3. associate-/l* 56.4%

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

   12. Simplified 56.4%

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

   if -3.49999999999999995e-6 < t < -1.8e-60 or 4.3999999999999998e131 < t < 1.15000000000000003e194

   1. Initial program 62.2%

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

      1. +-commutative 62.2%

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

      2. associate-*r/ 80.1%

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

      3. *-commutative 80.1%

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

      4. fma-def 80.2%

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

   3. Simplified 80.2%

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

   4. Taylor expanded in t around inf 65.6%

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

      1. *-commutative 65.6%

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

      2. cancel-sign-sub-inv 65.6%

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

      3. metadata-eval 65.6%

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

      4. *-lft-identity 65.6%

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

      5. distribute-lft-in 65.5%

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

      6. mul-1-neg 65.5%

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

      7. distribute-rgt-neg-in 65.5%

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

      8. mul-1-neg 65.5%

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

      9. *-commutative 65.5%

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

      10. cancel-sign-sub 65.5%

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

      11. mul-1-neg 65.5%

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

      12. associate-*r* 65.5%

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

      13. distribute-lft-out-- 65.5%

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

      14. associate-*r/ 65.5%

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

      15. mul-1-neg 65.5%

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

   6. Simplified 69.1%

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

   7. Taylor expanded in z around inf 64.9%

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

      1. *-commutative 64.9%

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

      2. associate-/l* 68.5%

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

   9. Simplified 68.5%

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

   10. Taylor expanded in y around 0 46.4%

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

       1. associate-/l* 50.0%

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

   12. Simplified 50.0%

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

   if -1.8e-60 < t < -3.60000000000000008e-96 or 4.2e-248 < t < 1.75e56

   1. Initial program 89.6%

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

      1. +-commutative 89.6%

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

      2. associate-*r/ 88.6%

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

      3. *-commutative 88.6%

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

      4. fma-def 88.6%

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

   3. Simplified 88.6%

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

   4. Taylor expanded in y around inf 53.8%

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

      1. div-sub 53.8%

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

      2. *-commutative 53.8%

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

   6. Simplified 53.8%

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

   7. Taylor expanded in z around inf 37.7%

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

      1. associate-/l* 39.1%

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

      2. associate-/r/ 40.9%

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

   9. Simplified 40.9%

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

   if -3.60000000000000008e-96 < t < 4.2e-248

   1. Initial program 92.3%

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

      1. +-commutative 92.3%

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

      2. associate-*r/ 95.2%

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

      3. *-commutative 95.2%

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

      4. fma-def 95.2%

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

   3. Simplified 95.2%

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

   4. Taylor expanded in a around inf 48.8%

      \[\leadsto \color{blue}{x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 50.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-6}:\\ \;\;\;\;y + \frac{y}{\frac{t}{a}}\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-60}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;t \leq -3.6 \cdot 10^{-96}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-248}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+56}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+131} \lor \neg \left(t \leq 1.15 \cdot 10^{+194}\right):\\ \;\;\;\;y + \frac{y}{\frac{t}{a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \end{array} \]

Alternative 7: 44.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - z \cdot \frac{y}{t}\\ \mathbf{if}\;t \leq -5.5 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-81}:\\ \;\;\;\;\frac{z}{\frac{t}{x - y}}\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-97}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-274}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-234}:\\ \;\;\;\;\frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{-15}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- y (* z (/ y t)))))
   (if (<= t -5.5e-7)
     t_1
     (if (<= t -1.5e-81)
       (/ z (/ t (- x y)))
       (if (<= t -1.7e-97)
         (* y (/ z a))
         (if (<= t -3.8e-274)
           x
           (if (<= t 2.4e-234)
             (/ z (/ a (- y x)))
             (if (<= t 6.4e-15)
               (* y (/ z (- a t)))
               (if (<= t 3.2e+15) x 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 <= -5.5e-7) {
		tmp = t_1;
	} else if (t <= -1.5e-81) {
		tmp = z / (t / (x - y));
	} else if (t <= -1.7e-97) {
		tmp = y * (z / a);
	} else if (t <= -3.8e-274) {
		tmp = x;
	} else if (t <= 2.4e-234) {
		tmp = z / (a / (y - x));
	} else if (t <= 6.4e-15) {
		tmp = y * (z / (a - t));
	} else if (t <= 3.2e+15) {
		tmp = 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 = y - (z * (y / t))
    if (t <= (-5.5d-7)) then
        tmp = t_1
    else if (t <= (-1.5d-81)) then
        tmp = z / (t / (x - y))
    else if (t <= (-1.7d-97)) then
        tmp = y * (z / a)
    else if (t <= (-3.8d-274)) then
        tmp = x
    else if (t <= 2.4d-234) then
        tmp = z / (a / (y - x))
    else if (t <= 6.4d-15) then
        tmp = y * (z / (a - t))
    else if (t <= 3.2d+15) then
        tmp = 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 = y - (z * (y / t));
	double tmp;
	if (t <= -5.5e-7) {
		tmp = t_1;
	} else if (t <= -1.5e-81) {
		tmp = z / (t / (x - y));
	} else if (t <= -1.7e-97) {
		tmp = y * (z / a);
	} else if (t <= -3.8e-274) {
		tmp = x;
	} else if (t <= 2.4e-234) {
		tmp = z / (a / (y - x));
	} else if (t <= 6.4e-15) {
		tmp = y * (z / (a - t));
	} else if (t <= 3.2e+15) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - (z * (y / t))
	tmp = 0
	if t <= -5.5e-7:
		tmp = t_1
	elif t <= -1.5e-81:
		tmp = z / (t / (x - y))
	elif t <= -1.7e-97:
		tmp = y * (z / a)
	elif t <= -3.8e-274:
		tmp = x
	elif t <= 2.4e-234:
		tmp = z / (a / (y - x))
	elif t <= 6.4e-15:
		tmp = y * (z / (a - t))
	elif t <= 3.2e+15:
		tmp = x
	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 <= -5.5e-7)
		tmp = t_1;
	elseif (t <= -1.5e-81)
		tmp = Float64(z / Float64(t / Float64(x - y)));
	elseif (t <= -1.7e-97)
		tmp = Float64(y * Float64(z / a));
	elseif (t <= -3.8e-274)
		tmp = x;
	elseif (t <= 2.4e-234)
		tmp = Float64(z / Float64(a / Float64(y - x)));
	elseif (t <= 6.4e-15)
		tmp = Float64(y * Float64(z / Float64(a - t)));
	elseif (t <= 3.2e+15)
		tmp = x;
	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 <= -5.5e-7)
		tmp = t_1;
	elseif (t <= -1.5e-81)
		tmp = z / (t / (x - y));
	elseif (t <= -1.7e-97)
		tmp = y * (z / a);
	elseif (t <= -3.8e-274)
		tmp = x;
	elseif (t <= 2.4e-234)
		tmp = z / (a / (y - x));
	elseif (t <= 6.4e-15)
		tmp = y * (z / (a - t));
	elseif (t <= 3.2e+15)
		tmp = x;
	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, -5.5e-7], t$95$1, If[LessEqual[t, -1.5e-81], N[(z / N[(t / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.7e-97], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.8e-274], x, If[LessEqual[t, 2.4e-234], N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.4e-15], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.2e+15], x, t$95$1]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -5.5000000000000003e-7 or 3.2e15 < t

   1. Initial program 58.6%

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

      1. +-commutative 58.6%

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

      2. associate-*r/ 80.9%

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

      3. *-commutative 80.9%

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

      4. fma-def 80.9%

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

   3. Simplified 80.9%

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

   4. Taylor expanded in t around inf 67.1%

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

      1. *-commutative 67.1%

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

      2. cancel-sign-sub-inv 67.1%

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

      3. metadata-eval 67.1%

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

      4. *-lft-identity 67.1%

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

      5. distribute-lft-in 67.0%

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

      6. mul-1-neg 67.0%

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

      7. distribute-rgt-neg-in 67.0%

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

      8. mul-1-neg 67.0%

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

      9. *-commutative 67.0%

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

      10. cancel-sign-sub 67.0%

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

      11. mul-1-neg 67.0%

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

      12. associate-*r* 67.0%

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

      13. distribute-lft-out-- 67.0%

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

      14. associate-*r/ 67.0%

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

      15. mul-1-neg 67.0%

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

   6. Simplified 75.5%

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

   7. Taylor expanded in z around inf 66.7%

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

      1. *-commutative 66.7%

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

      2. associate-/l* 72.4%

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

   9. Simplified 72.4%

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

   10. Taylor expanded in y around inf 55.4%

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

       1. associate-*l/ 57.5%

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

   12. Simplified 57.5%

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

   if -5.5000000000000003e-7 < t < -1.4999999999999999e-81

   1. Initial program 67.9%

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

      1. +-commutative 67.9%

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

      2. associate-*r/ 73.5%

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

      3. *-commutative 73.5%

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

      4. fma-def 73.7%

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

   3. Simplified 73.7%

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

   4. Taylor expanded in t around inf 56.0%

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

      1. *-commutative 56.0%

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

      2. cancel-sign-sub-inv 56.0%

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

      3. metadata-eval 56.0%

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

      4. *-lft-identity 56.0%

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

      5. distribute-lft-in 56.0%

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

      6. mul-1-neg 56.0%

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

      7. distribute-rgt-neg-in 56.0%

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

      8. mul-1-neg 56.0%

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

      9. *-commutative 56.0%

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

      10. cancel-sign-sub 56.0%

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

      11. mul-1-neg 56.0%

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

      12. associate-*r* 56.0%

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

      13. distribute-lft-out-- 56.0%

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

      14. associate-*r/ 56.0%

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

      15. mul-1-neg 56.0%

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

   6. Simplified 56.1%

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

   7. Taylor expanded in z around inf 48.2%

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

      1. *-commutative 48.2%

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

      2. associate-/l* 48.2%

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

   9. Simplified 48.2%

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

   10. Taylor expanded in x around 0 42.0%

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

       1. associate--l+ 42.0%

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

       2. associate-*l/ 42.0%

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

       3. cancel-sign-sub-inv 42.0%

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

       4. *-commutative 42.0%

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

       5. associate-*l/ 41.8%

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

       6. distribute-rgt-in 48.0%

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

       7. sub-neg 48.0%

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

       8. *-commutative 48.0%

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

       9. +-commutative 48.0%

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

       10. *-commutative 48.0%

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

       11. fma-def 48.1%

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

   12. Simplified 48.1%

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

   13. Taylor expanded in z around inf 48.5%

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

       1. div-sub 48.5%

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

       2. *-commutative 48.5%

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

       3. associate-*r/ 48.7%

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

       4. associate-/l* 48.7%

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

   15. Simplified 48.7%

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

   if -1.4999999999999999e-81 < t < -1.6999999999999999e-97

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-*r/ 100.0%

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

      3. *-commutative 100.0%

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

      4. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 75.0%

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

      1. div-sub 75.0%

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

      2. *-commutative 75.0%

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

   6. Simplified 75.0%

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

   7. Taylor expanded in t around 0 53.7%

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

   if -1.6999999999999999e-97 < t < -3.79999999999999985e-274 or 6.3999999999999999e-15 < t < 3.2e15

   1. Initial program 90.9%

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

      1. +-commutative 90.9%

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

      2. associate-*r/ 95.2%

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

      3. *-commutative 95.2%

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

      4. fma-def 95.2%

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

   3. Simplified 95.2%

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

   4. Taylor expanded in a around inf 54.9%

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

   if -3.79999999999999985e-274 < t < 2.3999999999999999e-234

   1. Initial program 96.4%

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

      1. +-commutative 96.4%

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

      2. associate-*r/ 86.2%

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

      3. *-commutative 86.2%

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

      4. fma-def 86.2%

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

   3. Simplified 86.2%

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

   4. Taylor expanded in z around inf 60.5%

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

      1. div-sub 60.5%

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

      2. *-commutative 60.5%

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

      3. associate-*l/ 60.8%

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

      4. associate-/l* 50.8%

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

   6. Simplified 50.8%

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

   7. Taylor expanded in a around inf 51.9%

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

      1. associate-/l* 55.2%

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

   9. Simplified 55.2%

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

   if 2.3999999999999999e-234 < t < 6.3999999999999999e-15

   1. Initial program 89.8%

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

      1. +-commutative 89.8%

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

      2. associate-*r/ 96.5%

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

      3. *-commutative 96.5%

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

      4. fma-def 96.5%

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

   3. Simplified 96.5%

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

   4. Taylor expanded in y around inf 63.6%

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

      1. div-sub 63.6%

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

      2. *-commutative 63.6%

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

   6. Simplified 63.6%

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

   7. Taylor expanded in z around inf 56.8%

      \[\leadsto y \cdot \color{blue}{\frac{z}{a - t}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{-7}:\\ \;\;\;\;y - z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-81}:\\ \;\;\;\;\frac{z}{\frac{t}{x - y}}\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-97}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-274}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-234}:\\ \;\;\;\;\frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{-15}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y - z \cdot \frac{y}{t}\\ \end{array} \]

Alternative 8: 44.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - z \cdot \frac{y}{t}\\ \mathbf{if}\;t \leq -4.4 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-71}:\\ \;\;\;\;\frac{-z}{\frac{a - t}{x}}\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-274}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-234}:\\ \;\;\;\;\frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-15}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 38000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- y (* z (/ y t)))))
   (if (<= t -4.4e-7)
     t_1
     (if (<= t -1e-71)
       (/ (- z) (/ (- a t) x))
       (if (<= t -6.2e-89)
         t_1
         (if (<= t -3.8e-274)
           x
           (if (<= t 1.9e-234)
             (/ z (/ a (- y x)))
             (if (<= t 8.5e-15)
               (* y (/ z (- a t)))
               (if (<= t 38000000000.0) x 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 <= -4.4e-7) {
		tmp = t_1;
	} else if (t <= -1e-71) {
		tmp = -z / ((a - t) / x);
	} else if (t <= -6.2e-89) {
		tmp = t_1;
	} else if (t <= -3.8e-274) {
		tmp = x;
	} else if (t <= 1.9e-234) {
		tmp = z / (a / (y - x));
	} else if (t <= 8.5e-15) {
		tmp = y * (z / (a - t));
	} else if (t <= 38000000000.0) {
		tmp = 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 = y - (z * (y / t))
    if (t <= (-4.4d-7)) then
        tmp = t_1
    else if (t <= (-1d-71)) then
        tmp = -z / ((a - t) / x)
    else if (t <= (-6.2d-89)) then
        tmp = t_1
    else if (t <= (-3.8d-274)) then
        tmp = x
    else if (t <= 1.9d-234) then
        tmp = z / (a / (y - x))
    else if (t <= 8.5d-15) then
        tmp = y * (z / (a - t))
    else if (t <= 38000000000.0d0) then
        tmp = 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 = y - (z * (y / t));
	double tmp;
	if (t <= -4.4e-7) {
		tmp = t_1;
	} else if (t <= -1e-71) {
		tmp = -z / ((a - t) / x);
	} else if (t <= -6.2e-89) {
		tmp = t_1;
	} else if (t <= -3.8e-274) {
		tmp = x;
	} else if (t <= 1.9e-234) {
		tmp = z / (a / (y - x));
	} else if (t <= 8.5e-15) {
		tmp = y * (z / (a - t));
	} else if (t <= 38000000000.0) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - (z * (y / t))
	tmp = 0
	if t <= -4.4e-7:
		tmp = t_1
	elif t <= -1e-71:
		tmp = -z / ((a - t) / x)
	elif t <= -6.2e-89:
		tmp = t_1
	elif t <= -3.8e-274:
		tmp = x
	elif t <= 1.9e-234:
		tmp = z / (a / (y - x))
	elif t <= 8.5e-15:
		tmp = y * (z / (a - t))
	elif t <= 38000000000.0:
		tmp = x
	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 <= -4.4e-7)
		tmp = t_1;
	elseif (t <= -1e-71)
		tmp = Float64(Float64(-z) / Float64(Float64(a - t) / x));
	elseif (t <= -6.2e-89)
		tmp = t_1;
	elseif (t <= -3.8e-274)
		tmp = x;
	elseif (t <= 1.9e-234)
		tmp = Float64(z / Float64(a / Float64(y - x)));
	elseif (t <= 8.5e-15)
		tmp = Float64(y * Float64(z / Float64(a - t)));
	elseif (t <= 38000000000.0)
		tmp = x;
	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 <= -4.4e-7)
		tmp = t_1;
	elseif (t <= -1e-71)
		tmp = -z / ((a - t) / x);
	elseif (t <= -6.2e-89)
		tmp = t_1;
	elseif (t <= -3.8e-274)
		tmp = x;
	elseif (t <= 1.9e-234)
		tmp = z / (a / (y - x));
	elseif (t <= 8.5e-15)
		tmp = y * (z / (a - t));
	elseif (t <= 38000000000.0)
		tmp = x;
	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, -4.4e-7], t$95$1, If[LessEqual[t, -1e-71], N[((-z) / N[(N[(a - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6.2e-89], t$95$1, If[LessEqual[t, -3.8e-274], x, If[LessEqual[t, 1.9e-234], N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.5e-15], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 38000000000.0], x, t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -4.4000000000000002e-7 or -9.9999999999999992e-72 < t < -6.19999999999999993e-89 or 3.8e10 < t

   1. Initial program 59.7%

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

      1. +-commutative 59.7%

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

      2. associate-*r/ 81.0%

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

      3. *-commutative 81.0%

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

      4. fma-def 81.0%

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

   3. Simplified 81.0%

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

   4. Taylor expanded in t around inf 67.8%

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

      1. *-commutative 67.8%

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

      2. cancel-sign-sub-inv 67.8%

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

      3. metadata-eval 67.8%

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

      4. *-lft-identity 67.8%

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

      5. distribute-lft-in 67.7%

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

      6. mul-1-neg 67.7%

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

      7. distribute-rgt-neg-in 67.7%

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

      8. mul-1-neg 67.7%

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

      9. *-commutative 67.7%

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

      10. cancel-sign-sub 67.7%

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

      11. mul-1-neg 67.7%

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

      12. associate-*r* 67.7%

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

      13. distribute-lft-out-- 67.7%

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

      14. associate-*r/ 67.7%

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

      15. mul-1-neg 67.7%

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

   6. Simplified 75.8%

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

   7. Taylor expanded in z around inf 66.8%

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

      1. *-commutative 66.8%

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

      2. associate-/l* 72.2%

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

   9. Simplified 72.2%

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

   10. Taylor expanded in y around inf 55.9%

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

       1. associate-*l/ 58.0%

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

   12. Simplified 58.0%

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

   if -4.4000000000000002e-7 < t < -9.9999999999999992e-72

   1. Initial program 65.3%

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

      1. +-commutative 65.3%

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

      2. associate-*r/ 72.9%

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

      3. *-commutative 72.9%

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

      4. fma-def 73.1%

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

   3. Simplified 73.1%

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

   4. Taylor expanded in z around inf 78.4%

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

      1. div-sub 78.4%

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

      2. *-commutative 78.4%

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

      3. associate-*l/ 70.7%

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

      4. associate-/l* 78.8%

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

   6. Simplified 78.8%

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

   7. Taylor expanded in y around 0 55.0%

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

      1. mul-1-neg 55.0%

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

      2. associate-/l* 55.1%

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

   9. Simplified 55.1%

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

   if -6.19999999999999993e-89 < t < -3.79999999999999985e-274 or 8.50000000000000007e-15 < t < 3.8e10

   1. Initial program 91.3%

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

      1. +-commutative 91.3%

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

      2. associate-*r/ 95.4%

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

      3. *-commutative 95.4%

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

      4. fma-def 95.4%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in a around inf 52.5%

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

   if -3.79999999999999985e-274 < t < 1.89999999999999992e-234

   1. Initial program 96.4%

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

      1. +-commutative 96.4%

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

      2. associate-*r/ 86.2%

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

      3. *-commutative 86.2%

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

      4. fma-def 86.2%

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

   3. Simplified 86.2%

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

   4. Taylor expanded in z around inf 60.5%

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

      1. div-sub 60.5%

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

      2. *-commutative 60.5%

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

      3. associate-*l/ 60.8%

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

      4. associate-/l* 50.8%

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

   6. Simplified 50.8%

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

   7. Taylor expanded in a around inf 51.9%

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

      1. associate-/l* 55.2%

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

   9. Simplified 55.2%

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

   if 1.89999999999999992e-234 < t < 8.50000000000000007e-15

   1. Initial program 89.8%

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

      1. +-commutative 89.8%

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

      2. associate-*r/ 96.5%

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

      3. *-commutative 96.5%

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

      4. fma-def 96.5%

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

   3. Simplified 96.5%

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

   4. Taylor expanded in y around inf 63.6%

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

      1. div-sub 63.6%

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

      2. *-commutative 63.6%

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

   6. Simplified 63.6%

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

   7. Taylor expanded in z around inf 56.8%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{-7}:\\ \;\;\;\;y - z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-71}:\\ \;\;\;\;\frac{-z}{\frac{a - t}{x}}\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-89}:\\ \;\;\;\;y - z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-274}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-234}:\\ \;\;\;\;\frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-15}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 38000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y - z \cdot \frac{y}{t}\\ \end{array} \]

Alternative 9: 45.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \frac{x}{t}\\ \mathbf{if}\;t \leq -2.8 \cdot 10^{-5}:\\ \;\;\;\;y - z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-81}:\\ \;\;\;\;\frac{z}{\frac{t}{x - y}}\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-274}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-234}:\\ \;\;\;\;\frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{-15}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 14000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* z (/ x t)))))
   (if (<= t -2.8e-5)
     (- y (* z (/ y t)))
     (if (<= t -5.2e-81)
       (/ z (/ t (- x y)))
       (if (<= t -1.8e-98)
         t_1
         (if (<= t -3.8e-274)
           x
           (if (<= t 2.4e-234)
             (/ z (/ a (- y x)))
             (if (<= t 5.1e-15)
               (* y (/ z (- a t)))
               (if (<= t 14000000000.0) x 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 <= -2.8e-5) {
		tmp = y - (z * (y / t));
	} else if (t <= -5.2e-81) {
		tmp = z / (t / (x - y));
	} else if (t <= -1.8e-98) {
		tmp = t_1;
	} else if (t <= -3.8e-274) {
		tmp = x;
	} else if (t <= 2.4e-234) {
		tmp = z / (a / (y - x));
	} else if (t <= 5.1e-15) {
		tmp = y * (z / (a - t));
	} else if (t <= 14000000000.0) {
		tmp = 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 = y + (z * (x / t))
    if (t <= (-2.8d-5)) then
        tmp = y - (z * (y / t))
    else if (t <= (-5.2d-81)) then
        tmp = z / (t / (x - y))
    else if (t <= (-1.8d-98)) then
        tmp = t_1
    else if (t <= (-3.8d-274)) then
        tmp = x
    else if (t <= 2.4d-234) then
        tmp = z / (a / (y - x))
    else if (t <= 5.1d-15) then
        tmp = y * (z / (a - t))
    else if (t <= 14000000000.0d0) then
        tmp = 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 = y + (z * (x / t));
	double tmp;
	if (t <= -2.8e-5) {
		tmp = y - (z * (y / t));
	} else if (t <= -5.2e-81) {
		tmp = z / (t / (x - y));
	} else if (t <= -1.8e-98) {
		tmp = t_1;
	} else if (t <= -3.8e-274) {
		tmp = x;
	} else if (t <= 2.4e-234) {
		tmp = z / (a / (y - x));
	} else if (t <= 5.1e-15) {
		tmp = y * (z / (a - t));
	} else if (t <= 14000000000.0) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + (z * (x / t))
	tmp = 0
	if t <= -2.8e-5:
		tmp = y - (z * (y / t))
	elif t <= -5.2e-81:
		tmp = z / (t / (x - y))
	elif t <= -1.8e-98:
		tmp = t_1
	elif t <= -3.8e-274:
		tmp = x
	elif t <= 2.4e-234:
		tmp = z / (a / (y - x))
	elif t <= 5.1e-15:
		tmp = y * (z / (a - t))
	elif t <= 14000000000.0:
		tmp = x
	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 <= -2.8e-5)
		tmp = Float64(y - Float64(z * Float64(y / t)));
	elseif (t <= -5.2e-81)
		tmp = Float64(z / Float64(t / Float64(x - y)));
	elseif (t <= -1.8e-98)
		tmp = t_1;
	elseif (t <= -3.8e-274)
		tmp = x;
	elseif (t <= 2.4e-234)
		tmp = Float64(z / Float64(a / Float64(y - x)));
	elseif (t <= 5.1e-15)
		tmp = Float64(y * Float64(z / Float64(a - t)));
	elseif (t <= 14000000000.0)
		tmp = x;
	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 <= -2.8e-5)
		tmp = y - (z * (y / t));
	elseif (t <= -5.2e-81)
		tmp = z / (t / (x - y));
	elseif (t <= -1.8e-98)
		tmp = t_1;
	elseif (t <= -3.8e-274)
		tmp = x;
	elseif (t <= 2.4e-234)
		tmp = z / (a / (y - x));
	elseif (t <= 5.1e-15)
		tmp = y * (z / (a - t));
	elseif (t <= 14000000000.0)
		tmp = x;
	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, -2.8e-5], N[(y - N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.2e-81], N[(z / N[(t / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.8e-98], t$95$1, If[LessEqual[t, -3.8e-274], x, If[LessEqual[t, 2.4e-234], N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.1e-15], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 14000000000.0], x, t$95$1]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -2.79999999999999996e-5

   1. Initial program 60.6%

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

      1. +-commutative 60.6%

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

      2. associate-*r/ 80.5%

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

      3. *-commutative 80.5%

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

      4. fma-def 80.5%

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

   3. Simplified 80.5%

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

   4. Taylor expanded in t around inf 66.8%

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

      1. *-commutative 66.8%

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

      2. cancel-sign-sub-inv 66.8%

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

      3. metadata-eval 66.8%

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

      4. *-lft-identity 66.8%

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

      5. distribute-lft-in 66.7%

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

      6. mul-1-neg 66.7%

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

      7. distribute-rgt-neg-in 66.7%

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

      8. mul-1-neg 66.7%

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

      9. *-commutative 66.7%

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

      10. cancel-sign-sub 66.7%

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

      11. mul-1-neg 66.7%

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

      12. associate-*r* 66.7%

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

      13. distribute-lft-out-- 66.7%

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

      14. associate-*r/ 66.7%

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

      15. mul-1-neg 66.7%

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

   6. Simplified 69.7%

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

   7. Taylor expanded in z around inf 62.4%

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

      1. *-commutative 62.4%

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

      2. associate-/l* 65.3%

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

   9. Simplified 65.3%

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

   10. Taylor expanded in y around inf 57.8%

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

       1. associate-*l/ 59.3%

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

   12. Simplified 59.3%

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

   if -2.79999999999999996e-5 < t < -5.1999999999999998e-81

   1. Initial program 67.9%

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

      1. +-commutative 67.9%

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

      2. associate-*r/ 73.5%

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

      3. *-commutative 73.5%

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

      4. fma-def 73.7%

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

   3. Simplified 73.7%

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

   4. Taylor expanded in t around inf 56.0%

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

      1. *-commutative 56.0%

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

      2. cancel-sign-sub-inv 56.0%

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

      3. metadata-eval 56.0%

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

      4. *-lft-identity 56.0%

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

      5. distribute-lft-in 56.0%

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

      6. mul-1-neg 56.0%

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

      7. distribute-rgt-neg-in 56.0%

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

      8. mul-1-neg 56.0%

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

      9. *-commutative 56.0%

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

      10. cancel-sign-sub 56.0%

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

      11. mul-1-neg 56.0%

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

      12. associate-*r* 56.0%

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

      13. distribute-lft-out-- 56.0%

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

      14. associate-*r/ 56.0%

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

      15. mul-1-neg 56.0%

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

   6. Simplified 56.1%

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

   7. Taylor expanded in z around inf 48.2%

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

      1. *-commutative 48.2%

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

      2. associate-/l* 48.2%

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

   9. Simplified 48.2%

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

   10. Taylor expanded in x around 0 42.0%

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

       1. associate--l+ 42.0%

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

       2. associate-*l/ 42.0%

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

       3. cancel-sign-sub-inv 42.0%

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

       4. *-commutative 42.0%

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

       5. associate-*l/ 41.8%

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

       6. distribute-rgt-in 48.0%

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

       7. sub-neg 48.0%

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

       8. *-commutative 48.0%

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

       9. +-commutative 48.0%

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

       10. *-commutative 48.0%

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

       11. fma-def 48.1%

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

   12. Simplified 48.1%

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

   13. Taylor expanded in z around inf 48.5%

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

       1. div-sub 48.5%

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

       2. *-commutative 48.5%

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

       3. associate-*r/ 48.7%

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

       4. associate-/l* 48.7%

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

   15. Simplified 48.7%

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

   if -5.1999999999999998e-81 < t < -1.8000000000000001e-98 or 1.4e10 < t

   1. Initial program 59.1%

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

      1. +-commutative 59.1%

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

      2. associate-*r/ 82.3%

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

      3. *-commutative 82.3%

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

      4. fma-def 82.3%

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

   3. Simplified 82.3%

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

   4. Taylor expanded in t around inf 67.8%

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

      1. *-commutative 67.8%

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

      2. cancel-sign-sub-inv 67.8%

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

      3. metadata-eval 67.8%

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

      4. *-lft-identity 67.8%

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

      5. distribute-lft-in 67.8%

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

      6. mul-1-neg 67.8%

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

      7. distribute-rgt-neg-in 67.8%

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

      8. mul-1-neg 67.8%

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

      9. *-commutative 67.8%

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

      10. cancel-sign-sub 67.8%

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

      11. mul-1-neg 67.8%

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

      12. associate-*r* 67.8%

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

      13. distribute-lft-out-- 67.8%

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

      14. associate-*r/ 67.8%

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

      15. mul-1-neg 67.8%

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

   6. Simplified 80.8%

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

   7. Taylor expanded in z around inf 71.3%

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

      1. *-commutative 71.3%

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

      2. associate-/l* 79.1%

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

   9. Simplified 79.1%

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

   10. Taylor expanded in y around 0 67.1%

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

       1. mul-1-neg 67.1%

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

       2. *-commutative 67.1%

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

       3. associate-*l/ 72.3%

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

       4. distribute-rgt-neg-in 72.3%

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

   12. Simplified 72.3%

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

   if -1.8000000000000001e-98 < t < -3.79999999999999985e-274 or 5.1e-15 < t < 1.4e10

   1. Initial program 90.9%

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

      1. +-commutative 90.9%

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

      2. associate-*r/ 95.2%

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

      3. *-commutative 95.2%

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

      4. fma-def 95.2%

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

   3. Simplified 95.2%

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

   4. Taylor expanded in a around inf 54.9%

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

   if -3.79999999999999985e-274 < t < 2.3999999999999999e-234

   1. Initial program 96.4%

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

      1. +-commutative 96.4%

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

      2. associate-*r/ 86.2%

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

      3. *-commutative 86.2%

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

      4. fma-def 86.2%

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

   3. Simplified 86.2%

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

   4. Taylor expanded in z around inf 60.5%

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

      1. div-sub 60.5%

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

      2. *-commutative 60.5%

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

      3. associate-*l/ 60.8%

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

      4. associate-/l* 50.8%

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

   6. Simplified 50.8%

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

   7. Taylor expanded in a around inf 51.9%

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

      1. associate-/l* 55.2%

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

   9. Simplified 55.2%

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

   if 2.3999999999999999e-234 < t < 5.1e-15

   1. Initial program 89.8%

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

      1. +-commutative 89.8%

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

      2. associate-*r/ 96.5%

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

      3. *-commutative 96.5%

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

      4. fma-def 96.5%

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

   3. Simplified 96.5%

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

   4. Taylor expanded in y around inf 63.6%

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

      1. div-sub 63.6%

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

      2. *-commutative 63.6%

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

   6. Simplified 63.6%

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

   7. Taylor expanded in z around inf 56.8%

      \[\leadsto y \cdot \color{blue}{\frac{z}{a - t}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{-5}:\\ \;\;\;\;y - z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-81}:\\ \;\;\;\;\frac{z}{\frac{t}{x - y}}\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-98}:\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-274}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-234}:\\ \;\;\;\;\frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{-15}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 14000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \end{array} \]

Alternative 10: 72.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \frac{x - y}{\frac{t}{z}}\\ t_2 := x + \frac{z - t}{\frac{a}{y - x}}\\ \mathbf{if}\;a \leq -1.05 \cdot 10^{-12}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{-143}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-120}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+153}:\\ \;\;\;\;x - \frac{t}{\frac{a - t}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (/ (- x y) (/ t z)))) (t_2 (+ x (/ (- z t) (/ a (- y x))))))
   (if (<= a -1.05e-12)
     t_2
     (if (<= a 4.1e-143)
       t_1
       (if (<= a 2.4e-120)
         t_2
         (if (<= a 4.8e+17)
           t_1
           (if (<= a 3.4e+153) (- x (/ t (/ (- a t) (- y x)))) t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((x - y) / (t / z));
	double t_2 = x + ((z - t) / (a / (y - x)));
	double tmp;
	if (a <= -1.05e-12) {
		tmp = t_2;
	} else if (a <= 4.1e-143) {
		tmp = t_1;
	} else if (a <= 2.4e-120) {
		tmp = t_2;
	} else if (a <= 4.8e+17) {
		tmp = t_1;
	} else if (a <= 3.4e+153) {
		tmp = x - (t / ((a - t) / (y - x)));
	} 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 + ((x - y) / (t / z))
    t_2 = x + ((z - t) / (a / (y - x)))
    if (a <= (-1.05d-12)) then
        tmp = t_2
    else if (a <= 4.1d-143) then
        tmp = t_1
    else if (a <= 2.4d-120) then
        tmp = t_2
    else if (a <= 4.8d+17) then
        tmp = t_1
    else if (a <= 3.4d+153) then
        tmp = x - (t / ((a - t) / (y - x)))
    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 + ((x - y) / (t / z));
	double t_2 = x + ((z - t) / (a / (y - x)));
	double tmp;
	if (a <= -1.05e-12) {
		tmp = t_2;
	} else if (a <= 4.1e-143) {
		tmp = t_1;
	} else if (a <= 2.4e-120) {
		tmp = t_2;
	} else if (a <= 4.8e+17) {
		tmp = t_1;
	} else if (a <= 3.4e+153) {
		tmp = x - (t / ((a - t) / (y - x)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + ((x - y) / (t / z))
	t_2 = x + ((z - t) / (a / (y - x)))
	tmp = 0
	if a <= -1.05e-12:
		tmp = t_2
	elif a <= 4.1e-143:
		tmp = t_1
	elif a <= 2.4e-120:
		tmp = t_2
	elif a <= 4.8e+17:
		tmp = t_1
	elif a <= 3.4e+153:
		tmp = x - (t / ((a - t) / (y - x)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(Float64(x - y) / Float64(t / z)))
	t_2 = Float64(x + Float64(Float64(z - t) / Float64(a / Float64(y - x))))
	tmp = 0.0
	if (a <= -1.05e-12)
		tmp = t_2;
	elseif (a <= 4.1e-143)
		tmp = t_1;
	elseif (a <= 2.4e-120)
		tmp = t_2;
	elseif (a <= 4.8e+17)
		tmp = t_1;
	elseif (a <= 3.4e+153)
		tmp = Float64(x - Float64(t / Float64(Float64(a - t) / Float64(y - x))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + ((x - y) / (t / z));
	t_2 = x + ((z - t) / (a / (y - x)));
	tmp = 0.0;
	if (a <= -1.05e-12)
		tmp = t_2;
	elseif (a <= 4.1e-143)
		tmp = t_1;
	elseif (a <= 2.4e-120)
		tmp = t_2;
	elseif (a <= 4.8e+17)
		tmp = t_1;
	elseif (a <= 3.4e+153)
		tmp = x - (t / ((a - t) / (y - x)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(z - t), $MachinePrecision] / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.05e-12], t$95$2, If[LessEqual[a, 4.1e-143], t$95$1, If[LessEqual[a, 2.4e-120], t$95$2, If[LessEqual[a, 4.8e+17], t$95$1, If[LessEqual[a, 3.4e+153], N[(x - N[(t / N[(N[(a - t), $MachinePrecision] / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.04999999999999997e-12 or 4.1e-143 < a < 2.3999999999999999e-120 or 3.3999999999999997e153 < a

   1. Initial program 73.2%

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

      1. +-commutative 73.2%

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

      2. associate-*r/ 90.9%

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

      3. *-commutative 90.9%

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

      4. fma-def 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in a around inf 63.5%

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

      1. +-commutative 63.5%

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

      2. associate-/l* 78.4%

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

   6. Simplified 78.4%

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

   if -1.04999999999999997e-12 < a < 4.1e-143 or 2.3999999999999999e-120 < a < 4.8e17

   1. Initial program 70.4%

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

      1. +-commutative 70.4%

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

      2. associate-*r/ 76.2%

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

      3. *-commutative 76.2%

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

      4. fma-def 76.3%

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

   3. Simplified 76.3%

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

   4. Taylor expanded in t around inf 78.7%

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

      1. *-commutative 78.7%

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

      2. cancel-sign-sub-inv 78.7%

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

      3. metadata-eval 78.7%

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

      4. *-lft-identity 78.7%

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

      5. distribute-lft-in 78.7%

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

      6. mul-1-neg 78.7%

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

      7. distribute-rgt-neg-in 78.7%

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

      8. mul-1-neg 78.7%

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

      9. *-commutative 78.7%

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

      10. cancel-sign-sub 78.7%

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

      11. mul-1-neg 78.7%

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

      12. associate-*r* 78.7%

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

      13. distribute-lft-out-- 78.7%

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

      14. associate-*r/ 78.7%

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

      15. mul-1-neg 78.7%

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

   6. Simplified 82.8%

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

   7. Taylor expanded in z around inf 76.1%

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

      1. *-commutative 76.1%

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

      2. associate-/l* 81.0%

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

   9. Simplified 81.0%

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

   if 4.8e17 < a < 3.3999999999999997e153

   1. Initial program 81.3%

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

      1. +-commutative 81.3%

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

      2. associate-*r/ 100.0%

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

      3. *-commutative 100.0%

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

      4. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 70.1%

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

      1. fma-def 70.1%

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

      2. associate-*r/ 78.1%

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

      3. fma-def 78.1%

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

      4. neg-mul-1 78.1%

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

      5. +-commutative 78.1%

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

      6. unsub-neg 78.1%

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

      7. associate-*r/ 70.1%

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

      8. associate-/l* 78.1%

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

   6. Simplified 78.1%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{-12}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y - x}}\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{-143}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-120}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y - x}}\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+17}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+153}:\\ \;\;\;\;x - \frac{t}{\frac{a - t}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y - x}}\\ \end{array} \]

Alternative 11: 74.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \frac{x - y}{\frac{t}{z - a}}\\ t_2 := x + \frac{z - t}{\frac{a}{y - x}}\\ \mathbf{if}\;a \leq -7 \cdot 10^{-14}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{-143}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-120}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+154}:\\ \;\;\;\;x - \frac{t}{\frac{a - t}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (/ (- x y) (/ t (- z a)))))
        (t_2 (+ x (/ (- z t) (/ a (- y x))))))
   (if (<= a -7e-14)
     t_2
     (if (<= a 4.1e-143)
       t_1
       (if (<= a 2.4e-120)
         t_2
         (if (<= a 1.9e+17)
           t_1
           (if (<= a 1.45e+154) (- x (/ t (/ (- a t) (- y x)))) t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((x - y) / (t / (z - a)));
	double t_2 = x + ((z - t) / (a / (y - x)));
	double tmp;
	if (a <= -7e-14) {
		tmp = t_2;
	} else if (a <= 4.1e-143) {
		tmp = t_1;
	} else if (a <= 2.4e-120) {
		tmp = t_2;
	} else if (a <= 1.9e+17) {
		tmp = t_1;
	} else if (a <= 1.45e+154) {
		tmp = x - (t / ((a - t) / (y - x)));
	} 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 + ((x - y) / (t / (z - a)))
    t_2 = x + ((z - t) / (a / (y - x)))
    if (a <= (-7d-14)) then
        tmp = t_2
    else if (a <= 4.1d-143) then
        tmp = t_1
    else if (a <= 2.4d-120) then
        tmp = t_2
    else if (a <= 1.9d+17) then
        tmp = t_1
    else if (a <= 1.45d+154) then
        tmp = x - (t / ((a - t) / (y - x)))
    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 + ((x - y) / (t / (z - a)));
	double t_2 = x + ((z - t) / (a / (y - x)));
	double tmp;
	if (a <= -7e-14) {
		tmp = t_2;
	} else if (a <= 4.1e-143) {
		tmp = t_1;
	} else if (a <= 2.4e-120) {
		tmp = t_2;
	} else if (a <= 1.9e+17) {
		tmp = t_1;
	} else if (a <= 1.45e+154) {
		tmp = x - (t / ((a - t) / (y - x)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + ((x - y) / (t / (z - a)))
	t_2 = x + ((z - t) / (a / (y - x)))
	tmp = 0
	if a <= -7e-14:
		tmp = t_2
	elif a <= 4.1e-143:
		tmp = t_1
	elif a <= 2.4e-120:
		tmp = t_2
	elif a <= 1.9e+17:
		tmp = t_1
	elif a <= 1.45e+154:
		tmp = x - (t / ((a - t) / (y - x)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))))
	t_2 = Float64(x + Float64(Float64(z - t) / Float64(a / Float64(y - x))))
	tmp = 0.0
	if (a <= -7e-14)
		tmp = t_2;
	elseif (a <= 4.1e-143)
		tmp = t_1;
	elseif (a <= 2.4e-120)
		tmp = t_2;
	elseif (a <= 1.9e+17)
		tmp = t_1;
	elseif (a <= 1.45e+154)
		tmp = Float64(x - Float64(t / Float64(Float64(a - t) / Float64(y - x))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + ((x - y) / (t / (z - a)));
	t_2 = x + ((z - t) / (a / (y - x)));
	tmp = 0.0;
	if (a <= -7e-14)
		tmp = t_2;
	elseif (a <= 4.1e-143)
		tmp = t_1;
	elseif (a <= 2.4e-120)
		tmp = t_2;
	elseif (a <= 1.9e+17)
		tmp = t_1;
	elseif (a <= 1.45e+154)
		tmp = x - (t / ((a - t) / (y - x)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(z - t), $MachinePrecision] / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7e-14], t$95$2, If[LessEqual[a, 4.1e-143], t$95$1, If[LessEqual[a, 2.4e-120], t$95$2, If[LessEqual[a, 1.9e+17], t$95$1, If[LessEqual[a, 1.45e+154], N[(x - N[(t / N[(N[(a - t), $MachinePrecision] / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.0000000000000005e-14 or 4.1e-143 < a < 2.3999999999999999e-120 or 1.4499999999999999e154 < a

   1. Initial program 73.2%

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

      1. +-commutative 73.2%

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

      2. associate-*r/ 90.9%

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

      3. *-commutative 90.9%

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

      4. fma-def 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in a around inf 63.5%

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

      1. +-commutative 63.5%

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

      2. associate-/l* 78.4%

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

   6. Simplified 78.4%

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

   if -7.0000000000000005e-14 < a < 4.1e-143 or 2.3999999999999999e-120 < a < 1.9e17

   1. Initial program 70.4%

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

      1. +-commutative 70.4%

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

      2. associate-*r/ 76.2%

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

      3. *-commutative 76.2%

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

      4. fma-def 76.3%

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

   3. Simplified 76.3%

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

   4. Taylor expanded in t around inf 78.7%

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

      1. *-commutative 78.7%

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

      2. cancel-sign-sub-inv 78.7%

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

      3. metadata-eval 78.7%

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

      4. *-lft-identity 78.7%

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

      5. distribute-lft-in 78.7%

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

      6. mul-1-neg 78.7%

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

      7. distribute-rgt-neg-in 78.7%

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

      8. mul-1-neg 78.7%

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

      9. *-commutative 78.7%

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

      10. cancel-sign-sub 78.7%

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

      11. mul-1-neg 78.7%

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

      12. associate-*r* 78.7%

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

      13. distribute-lft-out-- 78.7%

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

      14. associate-*r/ 78.7%

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

      15. mul-1-neg 78.7%

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

   6. Simplified 82.8%

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

   if 1.9e17 < a < 1.4499999999999999e154

   1. Initial program 81.3%

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

      1. +-commutative 81.3%

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

      2. associate-*r/ 100.0%

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

      3. *-commutative 100.0%

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

      4. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 70.1%

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

      1. fma-def 70.1%

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

      2. associate-*r/ 78.1%

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

      3. fma-def 78.1%

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

      4. neg-mul-1 78.1%

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

      5. +-commutative 78.1%

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

      6. unsub-neg 78.1%

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

      7. associate-*r/ 70.1%

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

      8. associate-/l* 78.1%

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

   6. Simplified 78.1%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{-14}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y - x}}\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{-143}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-120}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y - x}}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+17}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+154}:\\ \;\;\;\;x - \frac{t}{\frac{a - t}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y - x}}\\ \end{array} \]

Alternative 12: 38.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{a - t}\\ \mathbf{if}\;t \leq -2.8 \cdot 10^{-5}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -3.6 \cdot 10^{-60}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-206}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+55}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z (- a t)))))
   (if (<= t -2.8e-5)
     y
     (if (<= t -3.6e-60)
       (/ z (/ t x))
       (if (<= t -2.8e-95)
         t_1
         (if (<= t 2.1e-206) x (if (<= t 1.65e+55) t_1 y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / (a - t));
	double tmp;
	if (t <= -2.8e-5) {
		tmp = y;
	} else if (t <= -3.6e-60) {
		tmp = z / (t / x);
	} else if (t <= -2.8e-95) {
		tmp = t_1;
	} else if (t <= 2.1e-206) {
		tmp = x;
	} else if (t <= 1.65e+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 = y * (z / (a - t))
    if (t <= (-2.8d-5)) then
        tmp = y
    else if (t <= (-3.6d-60)) then
        tmp = z / (t / x)
    else if (t <= (-2.8d-95)) then
        tmp = t_1
    else if (t <= 2.1d-206) then
        tmp = x
    else if (t <= 1.65d+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 = y * (z / (a - t));
	double tmp;
	if (t <= -2.8e-5) {
		tmp = y;
	} else if (t <= -3.6e-60) {
		tmp = z / (t / x);
	} else if (t <= -2.8e-95) {
		tmp = t_1;
	} else if (t <= 2.1e-206) {
		tmp = x;
	} else if (t <= 1.65e+55) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / (a - t))
	tmp = 0
	if t <= -2.8e-5:
		tmp = y
	elif t <= -3.6e-60:
		tmp = z / (t / x)
	elif t <= -2.8e-95:
		tmp = t_1
	elif t <= 2.1e-206:
		tmp = x
	elif t <= 1.65e+55:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / Float64(a - t)))
	tmp = 0.0
	if (t <= -2.8e-5)
		tmp = y;
	elseif (t <= -3.6e-60)
		tmp = Float64(z / Float64(t / x));
	elseif (t <= -2.8e-95)
		tmp = t_1;
	elseif (t <= 2.1e-206)
		tmp = x;
	elseif (t <= 1.65e+55)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / (a - t));
	tmp = 0.0;
	if (t <= -2.8e-5)
		tmp = y;
	elseif (t <= -3.6e-60)
		tmp = z / (t / x);
	elseif (t <= -2.8e-95)
		tmp = t_1;
	elseif (t <= 2.1e-206)
		tmp = x;
	elseif (t <= 1.65e+55)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.8e-5], y, If[LessEqual[t, -3.6e-60], N[(z / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.8e-95], t$95$1, If[LessEqual[t, 2.1e-206], x, If[LessEqual[t, 1.65e+55], t$95$1, y]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.79999999999999996e-5 or 1.65e55 < t

   1. Initial program 56.6%

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

      1. +-commutative 56.6%

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

      2. associate-*r/ 80.8%

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

      3. *-commutative 80.8%

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

      4. fma-def 80.8%

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

   3. Simplified 80.8%

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

   4. Taylor expanded in t around inf 51.4%

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

   if -2.79999999999999996e-5 < t < -3.6e-60

   1. Initial program 58.5%

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

      1. +-commutative 58.5%

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

      2. associate-*r/ 67.7%

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

      3. *-commutative 67.7%

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

      4. fma-def 67.9%

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

   3. Simplified 67.9%

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

   4. Taylor expanded in t around inf 59.2%

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

      1. *-commutative 59.2%

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

      2. cancel-sign-sub-inv 59.2%

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

      3. metadata-eval 59.2%

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

      4. *-lft-identity 59.2%

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

      5. distribute-lft-in 59.2%

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

      6. mul-1-neg 59.2%

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

      7. distribute-rgt-neg-in 59.2%

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

      8. mul-1-neg 59.2%

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

      9. *-commutative 59.2%

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

      10. cancel-sign-sub 59.2%

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

      11. mul-1-neg 59.2%

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

      12. associate-*r* 59.2%

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

      13. distribute-lft-out-- 59.2%

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

      14. associate-*r/ 59.2%

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

      15. mul-1-neg 59.2%

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

   6. Simplified 59.2%

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

   7. Taylor expanded in z around inf 56.0%

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

      1. *-commutative 56.0%

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

      2. associate-/l* 56.0%

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

   9. Simplified 56.0%

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

   10. Taylor expanded in y around 0 47.2%

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

       1. associate-/l* 47.2%

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

   12. Simplified 47.2%

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

   if -3.6e-60 < t < -2.7999999999999999e-95 or 2.1000000000000001e-206 < t < 1.65e55

   1. Initial program 88.1%

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

      1. +-commutative 88.1%

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

      2. associate-*r/ 92.5%

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

      3. *-commutative 92.5%

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

      4. fma-def 92.5%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in y around inf 58.0%

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

      1. div-sub 58.0%

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

      2. *-commutative 58.0%

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

   6. Simplified 58.0%

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

   7. Taylor expanded in z around inf 42.6%

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

   if -2.7999999999999999e-95 < t < 2.1000000000000001e-206

   1. Initial program 93.2%

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

      1. +-commutative 93.2%

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

      2. associate-*r/ 91.5%

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

      3. *-commutative 91.5%

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

      4. fma-def 91.5%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in a around inf 46.2%

      \[\leadsto \color{blue}{x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 48.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{-5}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -3.6 \cdot 10^{-60}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-95}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-206}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+55}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 13: 37.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y}{a - t}\\ \mathbf{if}\;t \leq -2.8 \cdot 10^{-5}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{-60}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-248}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ y (- a t)))))
   (if (<= t -2.8e-5)
     y
     (if (<= t -2.05e-60)
       (/ z (/ t x))
       (if (<= t -2.9e-96)
         t_1
         (if (<= t 2e-248) x (if (<= t 3.2e+57) t_1 y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (y / (a - t));
	double tmp;
	if (t <= -2.8e-5) {
		tmp = y;
	} else if (t <= -2.05e-60) {
		tmp = z / (t / x);
	} else if (t <= -2.9e-96) {
		tmp = t_1;
	} else if (t <= 2e-248) {
		tmp = x;
	} else if (t <= 3.2e+57) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (y / (a - t))
    if (t <= (-2.8d-5)) then
        tmp = y
    else if (t <= (-2.05d-60)) then
        tmp = z / (t / x)
    else if (t <= (-2.9d-96)) then
        tmp = t_1
    else if (t <= 2d-248) then
        tmp = x
    else if (t <= 3.2d+57) then
        tmp = t_1
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (y / (a - t));
	double tmp;
	if (t <= -2.8e-5) {
		tmp = y;
	} else if (t <= -2.05e-60) {
		tmp = z / (t / x);
	} else if (t <= -2.9e-96) {
		tmp = t_1;
	} else if (t <= 2e-248) {
		tmp = x;
	} else if (t <= 3.2e+57) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * (y / (a - t))
	tmp = 0
	if t <= -2.8e-5:
		tmp = y
	elif t <= -2.05e-60:
		tmp = z / (t / x)
	elif t <= -2.9e-96:
		tmp = t_1
	elif t <= 2e-248:
		tmp = x
	elif t <= 3.2e+57:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(y / Float64(a - t)))
	tmp = 0.0
	if (t <= -2.8e-5)
		tmp = y;
	elseif (t <= -2.05e-60)
		tmp = Float64(z / Float64(t / x));
	elseif (t <= -2.9e-96)
		tmp = t_1;
	elseif (t <= 2e-248)
		tmp = x;
	elseif (t <= 3.2e+57)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * (y / (a - t));
	tmp = 0.0;
	if (t <= -2.8e-5)
		tmp = y;
	elseif (t <= -2.05e-60)
		tmp = z / (t / x);
	elseif (t <= -2.9e-96)
		tmp = t_1;
	elseif (t <= 2e-248)
		tmp = x;
	elseif (t <= 3.2e+57)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.8e-5], y, If[LessEqual[t, -2.05e-60], N[(z / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.9e-96], t$95$1, If[LessEqual[t, 2e-248], x, If[LessEqual[t, 3.2e+57], t$95$1, y]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.79999999999999996e-5 or 3.20000000000000029e57 < t

   1. Initial program 56.6%

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

      1. +-commutative 56.6%

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

      2. associate-*r/ 80.8%

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

      3. *-commutative 80.8%

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

      4. fma-def 80.8%

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

   3. Simplified 80.8%

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

   4. Taylor expanded in t around inf 51.4%

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

   if -2.79999999999999996e-5 < t < -2.05000000000000006e-60

   1. Initial program 58.5%

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

      1. +-commutative 58.5%

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

      2. associate-*r/ 67.7%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 67.7%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 67.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 67.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in t around inf 59.2%

      \[\leadsto \color{blue}{y + \frac{\left(-1 \cdot z - -1 \cdot a\right) \cdot \left(y - x\right)}{t}} \]
   5. Step-by-step derivation

      1. *-commutative 59.2%

         \[\leadsto y + \frac{\color{blue}{\left(y - x\right) \cdot \left(-1 \cdot z - -1 \cdot a\right)}}{t} \]

      2. cancel-sign-sub-inv 59.2%

         \[\leadsto y + \frac{\left(y - x\right) \cdot \color{blue}{\left(-1 \cdot z + \left(--1\right) \cdot a\right)}}{t} \]

      3. metadata-eval 59.2%

         \[\leadsto y + \frac{\left(y - x\right) \cdot \left(-1 \cdot z + \color{blue}{1} \cdot a\right)}{t} \]

      4. *-lft-identity 59.2%

         \[\leadsto y + \frac{\left(y - x\right) \cdot \left(-1 \cdot z + \color{blue}{a}\right)}{t} \]

      5. distribute-lft-in 59.2%

         \[\leadsto y + \frac{\color{blue}{\left(y - x\right) \cdot \left(-1 \cdot z\right) + \left(y - x\right) \cdot a}}{t} \]

      6. mul-1-neg 59.2%

         \[\leadsto y + \frac{\left(y - x\right) \cdot \color{blue}{\left(-z\right)} + \left(y - x\right) \cdot a}{t} \]

      7. distribute-rgt-neg-in 59.2%

         \[\leadsto y + \frac{\color{blue}{\left(-\left(y - x\right) \cdot z\right)} + \left(y - x\right) \cdot a}{t} \]

      8. mul-1-neg 59.2%

         \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(\left(y - x\right) \cdot z\right)} + \left(y - x\right) \cdot a}{t} \]

      9. *-commutative 59.2%

         \[\leadsto y + \frac{-1 \cdot \left(\left(y - x\right) \cdot z\right) + \color{blue}{a \cdot \left(y - x\right)}}{t} \]

      10. cancel-sign-sub 59.2%

          \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(\left(y - x\right) \cdot z\right) - \left(-a\right) \cdot \left(y - x\right)}}{t} \]

      11. mul-1-neg 59.2%

          \[\leadsto y + \frac{-1 \cdot \left(\left(y - x\right) \cdot z\right) - \color{blue}{\left(-1 \cdot a\right)} \cdot \left(y - x\right)}{t} \]

      12. associate-*r* 59.2%

          \[\leadsto y + \frac{-1 \cdot \left(\left(y - x\right) \cdot z\right) - \color{blue}{-1 \cdot \left(a \cdot \left(y - x\right)\right)}}{t} \]

      13. distribute-lft-out-- 59.2%

          \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(\left(y - x\right) \cdot z - a \cdot \left(y - x\right)\right)}}{t} \]

      14. associate-*r/ 59.2%

          \[\leadsto y + \color{blue}{-1 \cdot \frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}} \]

      15. mul-1-neg 59.2%

          \[\leadsto y + \color{blue}{\left(-\frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}\right)} \]

   6. Simplified 59.2%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]

   7. Taylor expanded in z around inf 56.0%

      \[\leadsto y - \color{blue}{\frac{z \cdot \left(y - x\right)}{t}} \]
   8. Step-by-step derivation

      1. *-commutative 56.0%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot z}}{t} \]

      2. associate-/l* 56.0%

         \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z}}} \]

   9. Simplified 56.0%

      \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z}}} \]

   10. Taylor expanded in y around 0 47.2%

       \[\leadsto \color{blue}{\frac{z \cdot x}{t}} \]
   11. Step-by-step derivation

       1. associate-/l* 47.2%

          \[\leadsto \color{blue}{\frac{z}{\frac{t}{x}}} \]

   12. Simplified 47.2%

       \[\leadsto \color{blue}{\frac{z}{\frac{t}{x}}} \]

   if -2.05000000000000006e-60 < t < -2.89999999999999994e-96 or 1.99999999999999996e-248 < t < 3.20000000000000029e57

   1. Initial program 89.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 89.6%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 88.6%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 88.6%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 88.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 88.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in y around inf 53.8%

      \[\leadsto \color{blue}{\left(\frac{z}{a - t} - \frac{t}{a - t}\right) \cdot y} \]
   5. Step-by-step derivation

      1. div-sub 53.8%

         \[\leadsto \color{blue}{\frac{z - t}{a - t}} \cdot y \]

      2. *-commutative 53.8%

         \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   6. Simplified 53.8%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   7. Taylor expanded in z around inf 37.7%

      \[\leadsto \color{blue}{\frac{y \cdot z}{a - t}} \]
   8. Step-by-step derivation

      1. associate-/l* 39.1%

         \[\leadsto \color{blue}{\frac{y}{\frac{a - t}{z}}} \]

      2. associate-/r/ 40.9%

         \[\leadsto \color{blue}{\frac{y}{a - t} \cdot z} \]

   9. Simplified 40.9%

      \[\leadsto \color{blue}{\frac{y}{a - t} \cdot z} \]

   if -2.89999999999999994e-96 < t < 1.99999999999999996e-248

   1. Initial program 92.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 92.3%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 95.2%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 95.2%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 95.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 95.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in a around inf 48.8%

      \[\leadsto \color{blue}{x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 48.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{-5}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{-60}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-96}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-248}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+57}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 14: 44.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - z \cdot \frac{y}{t}\\ \mathbf{if}\;t \leq -7 \cdot 10^{-92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.6 \cdot 10^{-274}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-236}:\\ \;\;\;\;\frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 6.3 \cdot 10^{-15}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 1100000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- y (* z (/ y t)))))
   (if (<= t -7e-92)
     t_1
     (if (<= t -3.6e-274)
       x
       (if (<= t 7.8e-236)
         (/ z (/ a (- y x)))
         (if (<= t 6.3e-15)
           (* y (/ z (- a t)))
           (if (<= t 1100000000.0) x 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 <= -7e-92) {
		tmp = t_1;
	} else if (t <= -3.6e-274) {
		tmp = x;
	} else if (t <= 7.8e-236) {
		tmp = z / (a / (y - x));
	} else if (t <= 6.3e-15) {
		tmp = y * (z / (a - t));
	} else if (t <= 1100000000.0) {
		tmp = 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 = y - (z * (y / t))
    if (t <= (-7d-92)) then
        tmp = t_1
    else if (t <= (-3.6d-274)) then
        tmp = x
    else if (t <= 7.8d-236) then
        tmp = z / (a / (y - x))
    else if (t <= 6.3d-15) then
        tmp = y * (z / (a - t))
    else if (t <= 1100000000.0d0) then
        tmp = 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 = y - (z * (y / t));
	double tmp;
	if (t <= -7e-92) {
		tmp = t_1;
	} else if (t <= -3.6e-274) {
		tmp = x;
	} else if (t <= 7.8e-236) {
		tmp = z / (a / (y - x));
	} else if (t <= 6.3e-15) {
		tmp = y * (z / (a - t));
	} else if (t <= 1100000000.0) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - (z * (y / t))
	tmp = 0
	if t <= -7e-92:
		tmp = t_1
	elif t <= -3.6e-274:
		tmp = x
	elif t <= 7.8e-236:
		tmp = z / (a / (y - x))
	elif t <= 6.3e-15:
		tmp = y * (z / (a - t))
	elif t <= 1100000000.0:
		tmp = x
	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 <= -7e-92)
		tmp = t_1;
	elseif (t <= -3.6e-274)
		tmp = x;
	elseif (t <= 7.8e-236)
		tmp = Float64(z / Float64(a / Float64(y - x)));
	elseif (t <= 6.3e-15)
		tmp = Float64(y * Float64(z / Float64(a - t)));
	elseif (t <= 1100000000.0)
		tmp = x;
	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 <= -7e-92)
		tmp = t_1;
	elseif (t <= -3.6e-274)
		tmp = x;
	elseif (t <= 7.8e-236)
		tmp = z / (a / (y - x));
	elseif (t <= 6.3e-15)
		tmp = y * (z / (a - t));
	elseif (t <= 1100000000.0)
		tmp = x;
	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, -7e-92], t$95$1, If[LessEqual[t, -3.6e-274], x, If[LessEqual[t, 7.8e-236], N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.3e-15], N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1100000000.0], x, t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7e-92 or 1.1e9 < t

   1. Initial program 60.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 60.2%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 80.4%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 80.4%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 80.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 80.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in t around inf 66.3%

      \[\leadsto \color{blue}{y + \frac{\left(-1 \cdot z - -1 \cdot a\right) \cdot \left(y - x\right)}{t}} \]
   5. Step-by-step derivation

      1. *-commutative 66.3%

         \[\leadsto y + \frac{\color{blue}{\left(y - x\right) \cdot \left(-1 \cdot z - -1 \cdot a\right)}}{t} \]

      2. cancel-sign-sub-inv 66.3%

         \[\leadsto y + \frac{\left(y - x\right) \cdot \color{blue}{\left(-1 \cdot z + \left(--1\right) \cdot a\right)}}{t} \]

      3. metadata-eval 66.3%

         \[\leadsto y + \frac{\left(y - x\right) \cdot \left(-1 \cdot z + \color{blue}{1} \cdot a\right)}{t} \]

      4. *-lft-identity 66.3%

         \[\leadsto y + \frac{\left(y - x\right) \cdot \left(-1 \cdot z + \color{blue}{a}\right)}{t} \]

      5. distribute-lft-in 66.3%

         \[\leadsto y + \frac{\color{blue}{\left(y - x\right) \cdot \left(-1 \cdot z\right) + \left(y - x\right) \cdot a}}{t} \]

      6. mul-1-neg 66.3%

         \[\leadsto y + \frac{\left(y - x\right) \cdot \color{blue}{\left(-z\right)} + \left(y - x\right) \cdot a}{t} \]

      7. distribute-rgt-neg-in 66.3%

         \[\leadsto y + \frac{\color{blue}{\left(-\left(y - x\right) \cdot z\right)} + \left(y - x\right) \cdot a}{t} \]

      8. mul-1-neg 66.3%

         \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(\left(y - x\right) \cdot z\right)} + \left(y - x\right) \cdot a}{t} \]

      9. *-commutative 66.3%

         \[\leadsto y + \frac{-1 \cdot \left(\left(y - x\right) \cdot z\right) + \color{blue}{a \cdot \left(y - x\right)}}{t} \]

      10. cancel-sign-sub 66.3%

          \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(\left(y - x\right) \cdot z\right) - \left(-a\right) \cdot \left(y - x\right)}}{t} \]

      11. mul-1-neg 66.3%

          \[\leadsto y + \frac{-1 \cdot \left(\left(y - x\right) \cdot z\right) - \color{blue}{\left(-1 \cdot a\right)} \cdot \left(y - x\right)}{t} \]

      12. associate-*r* 66.3%

          \[\leadsto y + \frac{-1 \cdot \left(\left(y - x\right) \cdot z\right) - \color{blue}{-1 \cdot \left(a \cdot \left(y - x\right)\right)}}{t} \]

      13. distribute-lft-out-- 66.3%

          \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(\left(y - x\right) \cdot z - a \cdot \left(y - x\right)\right)}}{t} \]

      14. associate-*r/ 66.3%

          \[\leadsto y + \color{blue}{-1 \cdot \frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}} \]

      15. mul-1-neg 66.3%

          \[\leadsto y + \color{blue}{\left(-\frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}\right)} \]

   6. Simplified 73.8%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]

   7. Taylor expanded in z around inf 65.2%

      \[\leadsto y - \color{blue}{\frac{z \cdot \left(y - x\right)}{t}} \]
   8. Step-by-step derivation

      1. *-commutative 65.2%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot z}}{t} \]

      2. associate-/l* 70.2%

         \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z}}} \]

   9. Simplified 70.2%

      \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z}}} \]

   10. Taylor expanded in y around inf 52.4%

       \[\leadsto y - \color{blue}{\frac{y \cdot z}{t}} \]
   11. Step-by-step derivation

       1. associate-*l/ 54.3%

          \[\leadsto y - \color{blue}{\frac{y}{t} \cdot z} \]

   12. Simplified 54.3%

       \[\leadsto y - \color{blue}{\frac{y}{t} \cdot z} \]

   if -7e-92 < t < -3.59999999999999983e-274 or 6.29999999999999982e-15 < t < 1.1e9

   1. Initial program 91.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 91.3%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 95.4%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 95.4%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 95.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 95.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in a around inf 52.5%

      \[\leadsto \color{blue}{x} \]

   if -3.59999999999999983e-274 < t < 7.8000000000000001e-236

   1. Initial program 96.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 96.4%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 86.2%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 86.2%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 86.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 86.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in z around inf 60.5%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   5. Step-by-step derivation

      1. div-sub 60.5%

         \[\leadsto z \cdot \color{blue}{\frac{y - x}{a - t}} \]

      2. *-commutative 60.5%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot z} \]

      3. associate-*l/ 60.8%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot z}{a - t}} \]

      4. associate-/l* 50.8%

         \[\leadsto \color{blue}{\frac{y - x}{\frac{a - t}{z}}} \]

   6. Simplified 50.8%

      \[\leadsto \color{blue}{\frac{y - x}{\frac{a - t}{z}}} \]

   7. Taylor expanded in a around inf 51.9%

      \[\leadsto \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]
   8. Step-by-step derivation

      1. associate-/l* 55.2%

         \[\leadsto \color{blue}{\frac{z}{\frac{a}{y - x}}} \]

   9. Simplified 55.2%

      \[\leadsto \color{blue}{\frac{z}{\frac{a}{y - x}}} \]

   if 7.8000000000000001e-236 < t < 6.29999999999999982e-15

   1. Initial program 89.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 89.8%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 96.5%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 96.5%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 96.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 96.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in y around inf 63.6%

      \[\leadsto \color{blue}{\left(\frac{z}{a - t} - \frac{t}{a - t}\right) \cdot y} \]
   5. Step-by-step derivation

      1. div-sub 63.6%

         \[\leadsto \color{blue}{\frac{z - t}{a - t}} \cdot y \]

      2. *-commutative 63.6%

         \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   6. Simplified 63.6%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   7. Taylor expanded in z around inf 56.8%

      \[\leadsto y \cdot \color{blue}{\frac{z}{a - t}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{-92}:\\ \;\;\;\;y - z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq -3.6 \cdot 10^{-274}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-236}:\\ \;\;\;\;\frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 6.3 \cdot 10^{-15}:\\ \;\;\;\;y \cdot \frac{z}{a - t}\\ \mathbf{elif}\;t \leq 1100000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y - z \cdot \frac{y}{t}\\ \end{array} \]

Alternative 15: 52.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t \leq -1.05 \cdot 10^{-95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-274}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-234}:\\ \;\;\;\;\frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+28}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t -1.05e-95)
     t_1
     (if (<= t -3.5e-274)
       x
       (if (<= t 2.4e-234)
         (/ z (/ a (- y x)))
         (if (<= t 4e+28) t_1 (+ y (* z (/ x t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -1.05e-95) {
		tmp = t_1;
	} else if (t <= -3.5e-274) {
		tmp = x;
	} else if (t <= 2.4e-234) {
		tmp = z / (a / (y - x));
	} else if (t <= 4e+28) {
		tmp = t_1;
	} else {
		tmp = y + (z * (x / 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 - t) / (a - t))
    if (t <= (-1.05d-95)) then
        tmp = t_1
    else if (t <= (-3.5d-274)) then
        tmp = x
    else if (t <= 2.4d-234) then
        tmp = z / (a / (y - x))
    else if (t <= 4d+28) then
        tmp = t_1
    else
        tmp = y + (z * (x / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t <= -1.05e-95) {
		tmp = t_1;
	} else if (t <= -3.5e-274) {
		tmp = x;
	} else if (t <= 2.4e-234) {
		tmp = z / (a / (y - x));
	} else if (t <= 4e+28) {
		tmp = t_1;
	} else {
		tmp = y + (z * (x / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if t <= -1.05e-95:
		tmp = t_1
	elif t <= -3.5e-274:
		tmp = x
	elif t <= 2.4e-234:
		tmp = z / (a / (y - x))
	elif t <= 4e+28:
		tmp = t_1
	else:
		tmp = y + (z * (x / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t <= -1.05e-95)
		tmp = t_1;
	elseif (t <= -3.5e-274)
		tmp = x;
	elseif (t <= 2.4e-234)
		tmp = Float64(z / Float64(a / Float64(y - x)));
	elseif (t <= 4e+28)
		tmp = t_1;
	else
		tmp = Float64(y + Float64(z * Float64(x / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t <= -1.05e-95)
		tmp = t_1;
	elseif (t <= -3.5e-274)
		tmp = x;
	elseif (t <= 2.4e-234)
		tmp = z / (a / (y - x));
	elseif (t <= 4e+28)
		tmp = t_1;
	else
		tmp = y + (z * (x / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.05e-95], t$95$1, If[LessEqual[t, -3.5e-274], x, If[LessEqual[t, 2.4e-234], N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e+28], t$95$1, N[(y + N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.05e-95 or 2.3999999999999999e-234 < t < 3.99999999999999983e28

   1. Initial program 72.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 72.6%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 85.4%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 85.4%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 85.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 85.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in y around inf 64.6%

      \[\leadsto \color{blue}{\left(\frac{z}{a - t} - \frac{t}{a - t}\right) \cdot y} \]
   5. Step-by-step derivation

      1. div-sub 64.6%

         \[\leadsto \color{blue}{\frac{z - t}{a - t}} \cdot y \]

      2. *-commutative 64.6%

         \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   6. Simplified 64.6%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   if -1.05e-95 < t < -3.49999999999999982e-274

   1. Initial program 90.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 90.2%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 94.8%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 94.8%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 94.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 94.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in a around inf 51.4%

      \[\leadsto \color{blue}{x} \]

   if -3.49999999999999982e-274 < t < 2.3999999999999999e-234

   1. Initial program 96.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 96.4%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 86.2%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 86.2%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 86.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 86.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in z around inf 60.5%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   5. Step-by-step derivation

      1. div-sub 60.5%

         \[\leadsto z \cdot \color{blue}{\frac{y - x}{a - t}} \]

      2. *-commutative 60.5%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot z} \]

      3. associate-*l/ 60.8%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot z}{a - t}} \]

      4. associate-/l* 50.8%

         \[\leadsto \color{blue}{\frac{y - x}{\frac{a - t}{z}}} \]

   6. Simplified 50.8%

      \[\leadsto \color{blue}{\frac{y - x}{\frac{a - t}{z}}} \]

   7. Taylor expanded in a around inf 51.9%

      \[\leadsto \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]
   8. Step-by-step derivation

      1. associate-/l* 55.2%

         \[\leadsto \color{blue}{\frac{z}{\frac{a}{y - x}}} \]

   9. Simplified 55.2%

      \[\leadsto \color{blue}{\frac{z}{\frac{a}{y - x}}} \]

   if 3.99999999999999983e28 < t

   1. Initial program 54.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 54.0%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 80.1%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 80.1%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 80.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 80.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in t around inf 66.8%

      \[\leadsto \color{blue}{y + \frac{\left(-1 \cdot z - -1 \cdot a\right) \cdot \left(y - x\right)}{t}} \]
   5. Step-by-step derivation

      1. *-commutative 66.8%

         \[\leadsto y + \frac{\color{blue}{\left(y - x\right) \cdot \left(-1 \cdot z - -1 \cdot a\right)}}{t} \]

      2. cancel-sign-sub-inv 66.8%

         \[\leadsto y + \frac{\left(y - x\right) \cdot \color{blue}{\left(-1 \cdot z + \left(--1\right) \cdot a\right)}}{t} \]

      3. metadata-eval 66.8%

         \[\leadsto y + \frac{\left(y - x\right) \cdot \left(-1 \cdot z + \color{blue}{1} \cdot a\right)}{t} \]

      4. *-lft-identity 66.8%

         \[\leadsto y + \frac{\left(y - x\right) \cdot \left(-1 \cdot z + \color{blue}{a}\right)}{t} \]

      5. distribute-lft-in 66.8%

         \[\leadsto y + \frac{\color{blue}{\left(y - x\right) \cdot \left(-1 \cdot z\right) + \left(y - x\right) \cdot a}}{t} \]

      6. mul-1-neg 66.8%

         \[\leadsto y + \frac{\left(y - x\right) \cdot \color{blue}{\left(-z\right)} + \left(y - x\right) \cdot a}{t} \]

      7. distribute-rgt-neg-in 66.8%

         \[\leadsto y + \frac{\color{blue}{\left(-\left(y - x\right) \cdot z\right)} + \left(y - x\right) \cdot a}{t} \]

      8. mul-1-neg 66.8%

         \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(\left(y - x\right) \cdot z\right)} + \left(y - x\right) \cdot a}{t} \]

      9. *-commutative 66.8%

         \[\leadsto y + \frac{-1 \cdot \left(\left(y - x\right) \cdot z\right) + \color{blue}{a \cdot \left(y - x\right)}}{t} \]

      10. cancel-sign-sub 66.8%

          \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(\left(y - x\right) \cdot z\right) - \left(-a\right) \cdot \left(y - x\right)}}{t} \]

      11. mul-1-neg 66.8%

          \[\leadsto y + \frac{-1 \cdot \left(\left(y - x\right) \cdot z\right) - \color{blue}{\left(-1 \cdot a\right)} \cdot \left(y - x\right)}{t} \]

      12. associate-*r* 66.8%

          \[\leadsto y + \frac{-1 \cdot \left(\left(y - x\right) \cdot z\right) - \color{blue}{-1 \cdot \left(a \cdot \left(y - x\right)\right)}}{t} \]

      13. distribute-lft-out-- 66.8%

          \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(\left(y - x\right) \cdot z - a \cdot \left(y - x\right)\right)}}{t} \]

      14. associate-*r/ 66.8%

          \[\leadsto y + \color{blue}{-1 \cdot \frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}} \]

      15. mul-1-neg 66.8%

          \[\leadsto y + \color{blue}{\left(-\frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}\right)} \]

   6. Simplified 81.5%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]

   7. Taylor expanded in z around inf 70.8%

      \[\leadsto y - \color{blue}{\frac{z \cdot \left(y - x\right)}{t}} \]
   8. Step-by-step derivation

      1. *-commutative 70.8%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot z}}{t} \]

      2. associate-/l* 79.6%

         \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z}}} \]

   9. Simplified 79.6%

      \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z}}} \]

   10. Taylor expanded in y around 0 67.4%

       \[\leadsto y - \color{blue}{-1 \cdot \frac{z \cdot x}{t}} \]
   11. Step-by-step derivation

       1. mul-1-neg 67.4%

          \[\leadsto y - \color{blue}{\left(-\frac{z \cdot x}{t}\right)} \]

       2. *-commutative 67.4%

          \[\leadsto y - \left(-\frac{\color{blue}{x \cdot z}}{t}\right) \]

       3. associate-*l/ 73.3%

          \[\leadsto y - \left(-\color{blue}{\frac{x}{t} \cdot z}\right) \]

       4. distribute-rgt-neg-in 73.3%

          \[\leadsto y - \color{blue}{\frac{x}{t} \cdot \left(-z\right)} \]

   12. Simplified 73.3%

       \[\leadsto y - \color{blue}{\frac{x}{t} \cdot \left(-z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-95}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-274}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-234}:\\ \;\;\;\;\frac{z}{\frac{a}{y - x}}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+28}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \end{array} \]

Alternative 16: 67.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{-8}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-65}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{a - t}\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-95}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;t \leq 18000000000000:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.7e-8)
   (* y (/ (- z t) (- a t)))
   (if (<= t -1.1e-65)
     (/ (* (- y x) z) (- a t))
     (if (<= t -2.6e-95)
       (/ (* y (- z t)) (- a t))
       (if (<= t 18000000000000.0)
         (- x (/ (- x y) (/ a z)))
         (+ y (/ (- x y) (/ t z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.7e-8) {
		tmp = y * ((z - t) / (a - t));
	} else if (t <= -1.1e-65) {
		tmp = ((y - x) * z) / (a - t);
	} else if (t <= -2.6e-95) {
		tmp = (y * (z - t)) / (a - t);
	} else if (t <= 18000000000000.0) {
		tmp = x - ((x - y) / (a / z));
	} else {
		tmp = y + ((x - y) / (t / z));
	}
	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 <= (-4.7d-8)) then
        tmp = y * ((z - t) / (a - t))
    else if (t <= (-1.1d-65)) then
        tmp = ((y - x) * z) / (a - t)
    else if (t <= (-2.6d-95)) then
        tmp = (y * (z - t)) / (a - t)
    else if (t <= 18000000000000.0d0) then
        tmp = x - ((x - y) / (a / z))
    else
        tmp = y + ((x - y) / (t / z))
    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 <= -4.7e-8) {
		tmp = y * ((z - t) / (a - t));
	} else if (t <= -1.1e-65) {
		tmp = ((y - x) * z) / (a - t);
	} else if (t <= -2.6e-95) {
		tmp = (y * (z - t)) / (a - t);
	} else if (t <= 18000000000000.0) {
		tmp = x - ((x - y) / (a / z));
	} else {
		tmp = y + ((x - y) / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.7e-8:
		tmp = y * ((z - t) / (a - t))
	elif t <= -1.1e-65:
		tmp = ((y - x) * z) / (a - t)
	elif t <= -2.6e-95:
		tmp = (y * (z - t)) / (a - t)
	elif t <= 18000000000000.0:
		tmp = x - ((x - y) / (a / z))
	else:
		tmp = y + ((x - y) / (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.7e-8)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (t <= -1.1e-65)
		tmp = Float64(Float64(Float64(y - x) * z) / Float64(a - t));
	elseif (t <= -2.6e-95)
		tmp = Float64(Float64(y * Float64(z - t)) / Float64(a - t));
	elseif (t <= 18000000000000.0)
		tmp = Float64(x - Float64(Float64(x - y) / Float64(a / z)));
	else
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.7e-8)
		tmp = y * ((z - t) / (a - t));
	elseif (t <= -1.1e-65)
		tmp = ((y - x) * z) / (a - t);
	elseif (t <= -2.6e-95)
		tmp = (y * (z - t)) / (a - t);
	elseif (t <= 18000000000000.0)
		tmp = x - ((x - y) / (a / z));
	else
		tmp = y + ((x - y) / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.7e-8], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.1e-65], N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.6e-95], N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 18000000000000.0], N[(x - N[(N[(x - y), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -4.6999999999999997e-8

   1. Initial program 60.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 60.6%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 80.5%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 80.5%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 80.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 80.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in y around inf 72.3%

      \[\leadsto \color{blue}{\left(\frac{z}{a - t} - \frac{t}{a - t}\right) \cdot y} \]
   5. Step-by-step derivation

      1. div-sub 72.3%

         \[\leadsto \color{blue}{\frac{z - t}{a - t}} \cdot y \]

      2. *-commutative 72.3%

         \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   6. Simplified 72.3%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   if -4.6999999999999997e-8 < t < -1.10000000000000011e-65

   1. Initial program 62.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 62.2%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 70.5%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 70.5%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 70.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 70.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in z around inf 85.4%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   5. Step-by-step derivation

      1. div-sub 85.4%

         \[\leadsto z \cdot \color{blue}{\frac{y - x}{a - t}} \]

      2. *-commutative 85.4%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot z} \]

      3. associate-*l/ 76.9%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot z}{a - t}} \]

   6. Simplified 76.9%

      \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot z}{a - t}} \]

   if -1.10000000000000011e-65 < t < -2.60000000000000001e-95

   1. Initial program 87.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 87.9%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 87.7%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 87.7%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 87.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 87.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in y around -inf 75.6%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]

   if -2.60000000000000001e-95 < t < 1.8e13

   1. Initial program 92.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 92.1%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 93.3%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 93.3%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 93.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 93.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in t around 0 74.4%

      \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot z}{a} + x} \]
   5. Step-by-step derivation

      1. +-commutative 74.4%

         \[\leadsto \color{blue}{x + \frac{\left(y - x\right) \cdot z}{a}} \]

      2. associate-/l* 75.8%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a}{z}}} \]

   6. Simplified 75.8%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a}{z}}} \]

   if 1.8e13 < t

   1. Initial program 56.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 56.7%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 81.3%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 81.3%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 81.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 81.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in t around inf 67.3%

      \[\leadsto \color{blue}{y + \frac{\left(-1 \cdot z - -1 \cdot a\right) \cdot \left(y - x\right)}{t}} \]
   5. Step-by-step derivation

      1. *-commutative 67.3%

         \[\leadsto y + \frac{\color{blue}{\left(y - x\right) \cdot \left(-1 \cdot z - -1 \cdot a\right)}}{t} \]

      2. cancel-sign-sub-inv 67.3%

         \[\leadsto y + \frac{\left(y - x\right) \cdot \color{blue}{\left(-1 \cdot z + \left(--1\right) \cdot a\right)}}{t} \]

      3. metadata-eval 67.3%

         \[\leadsto y + \frac{\left(y - x\right) \cdot \left(-1 \cdot z + \color{blue}{1} \cdot a\right)}{t} \]

      4. *-lft-identity 67.3%

         \[\leadsto y + \frac{\left(y - x\right) \cdot \left(-1 \cdot z + \color{blue}{a}\right)}{t} \]

      5. distribute-lft-in 67.3%

         \[\leadsto y + \frac{\color{blue}{\left(y - x\right) \cdot \left(-1 \cdot z\right) + \left(y - x\right) \cdot a}}{t} \]

      6. mul-1-neg 67.3%

         \[\leadsto y + \frac{\left(y - x\right) \cdot \color{blue}{\left(-z\right)} + \left(y - x\right) \cdot a}{t} \]

      7. distribute-rgt-neg-in 67.3%

         \[\leadsto y + \frac{\color{blue}{\left(-\left(y - x\right) \cdot z\right)} + \left(y - x\right) \cdot a}{t} \]

      8. mul-1-neg 67.3%

         \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(\left(y - x\right) \cdot z\right)} + \left(y - x\right) \cdot a}{t} \]

      9. *-commutative 67.3%

         \[\leadsto y + \frac{-1 \cdot \left(\left(y - x\right) \cdot z\right) + \color{blue}{a \cdot \left(y - x\right)}}{t} \]

      10. cancel-sign-sub 67.3%

          \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(\left(y - x\right) \cdot z\right) - \left(-a\right) \cdot \left(y - x\right)}}{t} \]

      11. mul-1-neg 67.3%

          \[\leadsto y + \frac{-1 \cdot \left(\left(y - x\right) \cdot z\right) - \color{blue}{\left(-1 \cdot a\right)} \cdot \left(y - x\right)}{t} \]

      12. associate-*r* 67.3%

          \[\leadsto y + \frac{-1 \cdot \left(\left(y - x\right) \cdot z\right) - \color{blue}{-1 \cdot \left(a \cdot \left(y - x\right)\right)}}{t} \]

      13. distribute-lft-out-- 67.3%

          \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(\left(y - x\right) \cdot z - a \cdot \left(y - x\right)\right)}}{t} \]

      14. associate-*r/ 67.3%

          \[\leadsto y + \color{blue}{-1 \cdot \frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}} \]

      15. mul-1-neg 67.3%

          \[\leadsto y + \color{blue}{\left(-\frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}\right)} \]

   6. Simplified 81.1%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]

   7. Taylor expanded in z around inf 71.1%

      \[\leadsto y - \color{blue}{\frac{z \cdot \left(y - x\right)}{t}} \]
   8. Step-by-step derivation

      1. *-commutative 71.1%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot z}}{t} \]

      2. associate-/l* 79.4%

         \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z}}} \]

   9. Simplified 79.4%

      \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{-8}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-65}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{a - t}\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-95}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;t \leq 18000000000000:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \end{array} \]

Alternative 17: 36.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{-6}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-75}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-95}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-247}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-101}:\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+105}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.65e-6)
   y
   (if (<= t -4.2e-75)
     (/ z (/ t x))
     (if (<= t -2.9e-95)
       y
       (if (<= t 2.5e-247)
         x
         (if (<= t 6e-101) (/ z (/ a y)) (if (<= t 2.8e+105) x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.65e-6) {
		tmp = y;
	} else if (t <= -4.2e-75) {
		tmp = z / (t / x);
	} else if (t <= -2.9e-95) {
		tmp = y;
	} else if (t <= 2.5e-247) {
		tmp = x;
	} else if (t <= 6e-101) {
		tmp = z / (a / y);
	} else if (t <= 2.8e+105) {
		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 <= (-1.65d-6)) then
        tmp = y
    else if (t <= (-4.2d-75)) then
        tmp = z / (t / x)
    else if (t <= (-2.9d-95)) then
        tmp = y
    else if (t <= 2.5d-247) then
        tmp = x
    else if (t <= 6d-101) then
        tmp = z / (a / y)
    else if (t <= 2.8d+105) 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 <= -1.65e-6) {
		tmp = y;
	} else if (t <= -4.2e-75) {
		tmp = z / (t / x);
	} else if (t <= -2.9e-95) {
		tmp = y;
	} else if (t <= 2.5e-247) {
		tmp = x;
	} else if (t <= 6e-101) {
		tmp = z / (a / y);
	} else if (t <= 2.8e+105) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.65e-6:
		tmp = y
	elif t <= -4.2e-75:
		tmp = z / (t / x)
	elif t <= -2.9e-95:
		tmp = y
	elif t <= 2.5e-247:
		tmp = x
	elif t <= 6e-101:
		tmp = z / (a / y)
	elif t <= 2.8e+105:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.65e-6)
		tmp = y;
	elseif (t <= -4.2e-75)
		tmp = Float64(z / Float64(t / x));
	elseif (t <= -2.9e-95)
		tmp = y;
	elseif (t <= 2.5e-247)
		tmp = x;
	elseif (t <= 6e-101)
		tmp = Float64(z / Float64(a / y));
	elseif (t <= 2.8e+105)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.65e-6)
		tmp = y;
	elseif (t <= -4.2e-75)
		tmp = z / (t / x);
	elseif (t <= -2.9e-95)
		tmp = y;
	elseif (t <= 2.5e-247)
		tmp = x;
	elseif (t <= 6e-101)
		tmp = z / (a / y);
	elseif (t <= 2.8e+105)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.65e-6], y, If[LessEqual[t, -4.2e-75], N[(z / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.9e-95], y, If[LessEqual[t, 2.5e-247], x, If[LessEqual[t, 6e-101], N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.8e+105], x, y]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.65000000000000008e-6 or -4.2000000000000002e-75 < t < -2.90000000000000002e-95 or 2.8000000000000001e105 < t

   1. Initial program 58.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 58.2%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 80.1%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 80.1%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 80.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 80.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in t around inf 51.8%

      \[\leadsto \color{blue}{y} \]

   if -1.65000000000000008e-6 < t < -4.2000000000000002e-75

   1. Initial program 65.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 65.3%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 72.9%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 72.9%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 73.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 73.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in t around inf 49.4%

      \[\leadsto \color{blue}{y + \frac{\left(-1 \cdot z - -1 \cdot a\right) \cdot \left(y - x\right)}{t}} \]
   5. Step-by-step derivation

      1. *-commutative 49.4%

         \[\leadsto y + \frac{\color{blue}{\left(y - x\right) \cdot \left(-1 \cdot z - -1 \cdot a\right)}}{t} \]

      2. cancel-sign-sub-inv 49.4%

         \[\leadsto y + \frac{\left(y - x\right) \cdot \color{blue}{\left(-1 \cdot z + \left(--1\right) \cdot a\right)}}{t} \]

      3. metadata-eval 49.4%

         \[\leadsto y + \frac{\left(y - x\right) \cdot \left(-1 \cdot z + \color{blue}{1} \cdot a\right)}{t} \]

      4. *-lft-identity 49.4%

         \[\leadsto y + \frac{\left(y - x\right) \cdot \left(-1 \cdot z + \color{blue}{a}\right)}{t} \]

      5. distribute-lft-in 49.4%

         \[\leadsto y + \frac{\color{blue}{\left(y - x\right) \cdot \left(-1 \cdot z\right) + \left(y - x\right) \cdot a}}{t} \]

      6. mul-1-neg 49.4%

         \[\leadsto y + \frac{\left(y - x\right) \cdot \color{blue}{\left(-z\right)} + \left(y - x\right) \cdot a}{t} \]

      7. distribute-rgt-neg-in 49.4%

         \[\leadsto y + \frac{\color{blue}{\left(-\left(y - x\right) \cdot z\right)} + \left(y - x\right) \cdot a}{t} \]

      8. mul-1-neg 49.4%

         \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(\left(y - x\right) \cdot z\right)} + \left(y - x\right) \cdot a}{t} \]

      9. *-commutative 49.4%

         \[\leadsto y + \frac{-1 \cdot \left(\left(y - x\right) \cdot z\right) + \color{blue}{a \cdot \left(y - x\right)}}{t} \]

      10. cancel-sign-sub 49.4%

          \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(\left(y - x\right) \cdot z\right) - \left(-a\right) \cdot \left(y - x\right)}}{t} \]

      11. mul-1-neg 49.4%

          \[\leadsto y + \frac{-1 \cdot \left(\left(y - x\right) \cdot z\right) - \color{blue}{\left(-1 \cdot a\right)} \cdot \left(y - x\right)}{t} \]

      12. associate-*r* 49.4%

          \[\leadsto y + \frac{-1 \cdot \left(\left(y - x\right) \cdot z\right) - \color{blue}{-1 \cdot \left(a \cdot \left(y - x\right)\right)}}{t} \]

      13. distribute-lft-out-- 49.4%

          \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(\left(y - x\right) \cdot z - a \cdot \left(y - x\right)\right)}}{t} \]

      14. associate-*r/ 49.4%

          \[\leadsto y + \color{blue}{-1 \cdot \frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}} \]

      15. mul-1-neg 49.4%

          \[\leadsto y + \color{blue}{\left(-\frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}\right)} \]

   6. Simplified 49.4%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]

   7. Taylor expanded in z around inf 46.8%

      \[\leadsto y - \color{blue}{\frac{z \cdot \left(y - x\right)}{t}} \]
   8. Step-by-step derivation

      1. *-commutative 46.8%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot z}}{t} \]

      2. associate-/l* 46.8%

         \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z}}} \]

   9. Simplified 46.8%

      \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z}}} \]

   10. Taylor expanded in y around 0 39.6%

       \[\leadsto \color{blue}{\frac{z \cdot x}{t}} \]
   11. Step-by-step derivation

       1. associate-/l* 39.6%

          \[\leadsto \color{blue}{\frac{z}{\frac{t}{x}}} \]

   12. Simplified 39.6%

       \[\leadsto \color{blue}{\frac{z}{\frac{t}{x}}} \]

   if -2.90000000000000002e-95 < t < 2.49999999999999989e-247 or 6.0000000000000006e-101 < t < 2.8000000000000001e105

   1. Initial program 87.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 87.3%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 94.0%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 94.0%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 94.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 94.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in a around inf 43.8%

      \[\leadsto \color{blue}{x} \]

   if 2.49999999999999989e-247 < t < 6.0000000000000006e-101

   1. Initial program 91.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 91.2%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 85.4%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 85.4%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 85.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 85.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in z around inf 62.6%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   5. Step-by-step derivation

      1. div-sub 70.0%

         \[\leadsto z \cdot \color{blue}{\frac{y - x}{a - t}} \]

      2. *-commutative 70.0%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot z} \]

      3. associate-*l/ 69.9%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot z}{a - t}} \]

      4. associate-/l* 59.6%

         \[\leadsto \color{blue}{\frac{y - x}{\frac{a - t}{z}}} \]

   6. Simplified 59.6%

      \[\leadsto \color{blue}{\frac{y - x}{\frac{a - t}{z}}} \]

   7. Taylor expanded in a around inf 49.8%

      \[\leadsto \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]
   8. Step-by-step derivation

      1. associate-/l* 53.9%

         \[\leadsto \color{blue}{\frac{z}{\frac{a}{y - x}}} \]

   9. Simplified 53.9%

      \[\leadsto \color{blue}{\frac{z}{\frac{a}{y - x}}} \]

   10. Taylor expanded in y around inf 49.0%

       \[\leadsto \frac{z}{\color{blue}{\frac{a}{y}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{-6}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-75}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-95}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-247}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-101}:\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+105}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 18: 67.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{-5}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-96}:\\ \;\;\;\;\frac{y - x}{\frac{a - t}{z}}\\ \mathbf{elif}\;t \leq 116000000:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.02e-5)
   (* y (/ (- z t) (- a t)))
   (if (<= t -2.8e-96)
     (/ (- y x) (/ (- a t) z))
     (if (<= t 116000000.0)
       (- x (/ (- x y) (/ a z)))
       (+ y (/ (- x y) (/ t z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.02e-5) {
		tmp = y * ((z - t) / (a - t));
	} else if (t <= -2.8e-96) {
		tmp = (y - x) / ((a - t) / z);
	} else if (t <= 116000000.0) {
		tmp = x - ((x - y) / (a / z));
	} else {
		tmp = y + ((x - y) / (t / z));
	}
	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 <= (-1.02d-5)) then
        tmp = y * ((z - t) / (a - t))
    else if (t <= (-2.8d-96)) then
        tmp = (y - x) / ((a - t) / z)
    else if (t <= 116000000.0d0) then
        tmp = x - ((x - y) / (a / z))
    else
        tmp = y + ((x - y) / (t / z))
    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 <= -1.02e-5) {
		tmp = y * ((z - t) / (a - t));
	} else if (t <= -2.8e-96) {
		tmp = (y - x) / ((a - t) / z);
	} else if (t <= 116000000.0) {
		tmp = x - ((x - y) / (a / z));
	} else {
		tmp = y + ((x - y) / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.02e-5:
		tmp = y * ((z - t) / (a - t))
	elif t <= -2.8e-96:
		tmp = (y - x) / ((a - t) / z)
	elif t <= 116000000.0:
		tmp = x - ((x - y) / (a / z))
	else:
		tmp = y + ((x - y) / (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.02e-5)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (t <= -2.8e-96)
		tmp = Float64(Float64(y - x) / Float64(Float64(a - t) / z));
	elseif (t <= 116000000.0)
		tmp = Float64(x - Float64(Float64(x - y) / Float64(a / z)));
	else
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.02e-5)
		tmp = y * ((z - t) / (a - t));
	elseif (t <= -2.8e-96)
		tmp = (y - x) / ((a - t) / z);
	elseif (t <= 116000000.0)
		tmp = x - ((x - y) / (a / z));
	else
		tmp = y + ((x - y) / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.02e-5], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.8e-96], N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 116000000.0], N[(x - N[(N[(x - y), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.0200000000000001e-5

   1. Initial program 60.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 60.6%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 80.5%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 80.5%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 80.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 80.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in y around inf 72.3%

      \[\leadsto \color{blue}{\left(\frac{z}{a - t} - \frac{t}{a - t}\right) \cdot y} \]
   5. Step-by-step derivation

      1. div-sub 72.3%

         \[\leadsto \color{blue}{\frac{z - t}{a - t}} \cdot y \]

      2. *-commutative 72.3%

         \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   6. Simplified 72.3%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   if -1.0200000000000001e-5 < t < -2.80000000000000015e-96

   1. Initial program 74.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 74.3%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 78.8%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 78.8%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 78.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 78.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in z around inf 68.2%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   5. Step-by-step derivation

      1. div-sub 68.2%

         \[\leadsto z \cdot \color{blue}{\frac{y - x}{a - t}} \]

      2. *-commutative 68.2%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot z} \]

      3. associate-*l/ 63.5%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot z}{a - t}} \]

      4. associate-/l* 68.3%

         \[\leadsto \color{blue}{\frac{y - x}{\frac{a - t}{z}}} \]

   6. Simplified 68.3%

      \[\leadsto \color{blue}{\frac{y - x}{\frac{a - t}{z}}} \]

   if -2.80000000000000015e-96 < t < 1.16e8

   1. Initial program 92.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 92.0%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 93.2%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 93.2%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 93.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 93.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in t around 0 75.1%

      \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot z}{a} + x} \]
   5. Step-by-step derivation

      1. +-commutative 75.1%

         \[\leadsto \color{blue}{x + \frac{\left(y - x\right) \cdot z}{a}} \]

      2. associate-/l* 76.6%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a}{z}}} \]

   6. Simplified 76.6%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a}{z}}} \]

   if 1.16e8 < t

   1. Initial program 56.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 56.7%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 81.3%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 81.3%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 81.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 81.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in t around inf 67.3%

      \[\leadsto \color{blue}{y + \frac{\left(-1 \cdot z - -1 \cdot a\right) \cdot \left(y - x\right)}{t}} \]
   5. Step-by-step derivation

      1. *-commutative 67.3%

         \[\leadsto y + \frac{\color{blue}{\left(y - x\right) \cdot \left(-1 \cdot z - -1 \cdot a\right)}}{t} \]

      2. cancel-sign-sub-inv 67.3%

         \[\leadsto y + \frac{\left(y - x\right) \cdot \color{blue}{\left(-1 \cdot z + \left(--1\right) \cdot a\right)}}{t} \]

      3. metadata-eval 67.3%

         \[\leadsto y + \frac{\left(y - x\right) \cdot \left(-1 \cdot z + \color{blue}{1} \cdot a\right)}{t} \]

      4. *-lft-identity 67.3%

         \[\leadsto y + \frac{\left(y - x\right) \cdot \left(-1 \cdot z + \color{blue}{a}\right)}{t} \]

      5. distribute-lft-in 67.3%

         \[\leadsto y + \frac{\color{blue}{\left(y - x\right) \cdot \left(-1 \cdot z\right) + \left(y - x\right) \cdot a}}{t} \]

      6. mul-1-neg 67.3%

         \[\leadsto y + \frac{\left(y - x\right) \cdot \color{blue}{\left(-z\right)} + \left(y - x\right) \cdot a}{t} \]

      7. distribute-rgt-neg-in 67.3%

         \[\leadsto y + \frac{\color{blue}{\left(-\left(y - x\right) \cdot z\right)} + \left(y - x\right) \cdot a}{t} \]

      8. mul-1-neg 67.3%

         \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(\left(y - x\right) \cdot z\right)} + \left(y - x\right) \cdot a}{t} \]

      9. *-commutative 67.3%

         \[\leadsto y + \frac{-1 \cdot \left(\left(y - x\right) \cdot z\right) + \color{blue}{a \cdot \left(y - x\right)}}{t} \]

      10. cancel-sign-sub 67.3%

          \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(\left(y - x\right) \cdot z\right) - \left(-a\right) \cdot \left(y - x\right)}}{t} \]

      11. mul-1-neg 67.3%

          \[\leadsto y + \frac{-1 \cdot \left(\left(y - x\right) \cdot z\right) - \color{blue}{\left(-1 \cdot a\right)} \cdot \left(y - x\right)}{t} \]

      12. associate-*r* 67.3%

          \[\leadsto y + \frac{-1 \cdot \left(\left(y - x\right) \cdot z\right) - \color{blue}{-1 \cdot \left(a \cdot \left(y - x\right)\right)}}{t} \]

      13. distribute-lft-out-- 67.3%

          \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(\left(y - x\right) \cdot z - a \cdot \left(y - x\right)\right)}}{t} \]

      14. associate-*r/ 67.3%

          \[\leadsto y + \color{blue}{-1 \cdot \frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}} \]

      15. mul-1-neg 67.3%

          \[\leadsto y + \color{blue}{\left(-\frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}\right)} \]

   6. Simplified 81.1%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]

   7. Taylor expanded in z around inf 71.1%

      \[\leadsto y - \color{blue}{\frac{z \cdot \left(y - x\right)}{t}} \]
   8. Step-by-step derivation

      1. *-commutative 71.1%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot z}}{t} \]

      2. associate-/l* 79.4%

         \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z}}} \]

   9. Simplified 79.4%

      \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{-5}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-96}:\\ \;\;\;\;\frac{y - x}{\frac{a - t}{z}}\\ \mathbf{elif}\;t \leq 116000000:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \end{array} \]

Alternative 19: 42.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - z \cdot \frac{y}{t}\\ \mathbf{if}\;t \leq -1.16 \cdot 10^{-89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-248}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+14}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- y (* z (/ y t)))))
   (if (<= t -1.16e-89)
     t_1
     (if (<= t 9.5e-248) x (if (<= t 3.2e+14) (* z (/ y (- a t))) 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 <= -1.16e-89) {
		tmp = t_1;
	} else if (t <= 9.5e-248) {
		tmp = x;
	} else if (t <= 3.2e+14) {
		tmp = z * (y / (a - t));
	} 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 <= (-1.16d-89)) then
        tmp = t_1
    else if (t <= 9.5d-248) then
        tmp = x
    else if (t <= 3.2d+14) then
        tmp = z * (y / (a - t))
    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 <= -1.16e-89) {
		tmp = t_1;
	} else if (t <= 9.5e-248) {
		tmp = x;
	} else if (t <= 3.2e+14) {
		tmp = z * (y / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - (z * (y / t))
	tmp = 0
	if t <= -1.16e-89:
		tmp = t_1
	elif t <= 9.5e-248:
		tmp = x
	elif t <= 3.2e+14:
		tmp = z * (y / (a - t))
	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 <= -1.16e-89)
		tmp = t_1;
	elseif (t <= 9.5e-248)
		tmp = x;
	elseif (t <= 3.2e+14)
		tmp = Float64(z * Float64(y / Float64(a - t)));
	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 <= -1.16e-89)
		tmp = t_1;
	elseif (t <= 9.5e-248)
		tmp = x;
	elseif (t <= 3.2e+14)
		tmp = z * (y / (a - t));
	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, -1.16e-89], t$95$1, If[LessEqual[t, 9.5e-248], x, If[LessEqual[t, 3.2e+14], N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.15999999999999993e-89 or 3.2e14 < t

   1. Initial program 60.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 60.2%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 80.4%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 80.4%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 80.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 80.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in t around inf 66.3%

      \[\leadsto \color{blue}{y + \frac{\left(-1 \cdot z - -1 \cdot a\right) \cdot \left(y - x\right)}{t}} \]
   5. Step-by-step derivation

      1. *-commutative 66.3%

         \[\leadsto y + \frac{\color{blue}{\left(y - x\right) \cdot \left(-1 \cdot z - -1 \cdot a\right)}}{t} \]

      2. cancel-sign-sub-inv 66.3%

         \[\leadsto y + \frac{\left(y - x\right) \cdot \color{blue}{\left(-1 \cdot z + \left(--1\right) \cdot a\right)}}{t} \]

      3. metadata-eval 66.3%

         \[\leadsto y + \frac{\left(y - x\right) \cdot \left(-1 \cdot z + \color{blue}{1} \cdot a\right)}{t} \]

      4. *-lft-identity 66.3%

         \[\leadsto y + \frac{\left(y - x\right) \cdot \left(-1 \cdot z + \color{blue}{a}\right)}{t} \]

      5. distribute-lft-in 66.3%

         \[\leadsto y + \frac{\color{blue}{\left(y - x\right) \cdot \left(-1 \cdot z\right) + \left(y - x\right) \cdot a}}{t} \]

      6. mul-1-neg 66.3%

         \[\leadsto y + \frac{\left(y - x\right) \cdot \color{blue}{\left(-z\right)} + \left(y - x\right) \cdot a}{t} \]

      7. distribute-rgt-neg-in 66.3%

         \[\leadsto y + \frac{\color{blue}{\left(-\left(y - x\right) \cdot z\right)} + \left(y - x\right) \cdot a}{t} \]

      8. mul-1-neg 66.3%

         \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(\left(y - x\right) \cdot z\right)} + \left(y - x\right) \cdot a}{t} \]

      9. *-commutative 66.3%

         \[\leadsto y + \frac{-1 \cdot \left(\left(y - x\right) \cdot z\right) + \color{blue}{a \cdot \left(y - x\right)}}{t} \]

      10. cancel-sign-sub 66.3%

          \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(\left(y - x\right) \cdot z\right) - \left(-a\right) \cdot \left(y - x\right)}}{t} \]

      11. mul-1-neg 66.3%

          \[\leadsto y + \frac{-1 \cdot \left(\left(y - x\right) \cdot z\right) - \color{blue}{\left(-1 \cdot a\right)} \cdot \left(y - x\right)}{t} \]

      12. associate-*r* 66.3%

          \[\leadsto y + \frac{-1 \cdot \left(\left(y - x\right) \cdot z\right) - \color{blue}{-1 \cdot \left(a \cdot \left(y - x\right)\right)}}{t} \]

      13. distribute-lft-out-- 66.3%

          \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(\left(y - x\right) \cdot z - a \cdot \left(y - x\right)\right)}}{t} \]

      14. associate-*r/ 66.3%

          \[\leadsto y + \color{blue}{-1 \cdot \frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}} \]

      15. mul-1-neg 66.3%

          \[\leadsto y + \color{blue}{\left(-\frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}\right)} \]

   6. Simplified 73.8%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]

   7. Taylor expanded in z around inf 65.2%

      \[\leadsto y - \color{blue}{\frac{z \cdot \left(y - x\right)}{t}} \]
   8. Step-by-step derivation

      1. *-commutative 65.2%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot z}}{t} \]

      2. associate-/l* 70.2%

         \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z}}} \]

   9. Simplified 70.2%

      \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z}}} \]

   10. Taylor expanded in y around inf 52.4%

       \[\leadsto y - \color{blue}{\frac{y \cdot z}{t}} \]
   11. Step-by-step derivation

       1. associate-*l/ 54.3%

          \[\leadsto y - \color{blue}{\frac{y}{t} \cdot z} \]

   12. Simplified 54.3%

       \[\leadsto y - \color{blue}{\frac{y}{t} \cdot z} \]

   if -1.15999999999999993e-89 < t < 9.49999999999999971e-248

   1. Initial program 92.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 92.4%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 95.3%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 95.3%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 95.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 95.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in a around inf 48.1%

      \[\leadsto \color{blue}{x} \]

   if 9.49999999999999971e-248 < t < 3.2e14

   1. Initial program 91.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 91.8%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 90.3%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 90.3%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 90.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 90.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in y around inf 51.9%

      \[\leadsto \color{blue}{\left(\frac{z}{a - t} - \frac{t}{a - t}\right) \cdot y} \]
   5. Step-by-step derivation

      1. div-sub 51.9%

         \[\leadsto \color{blue}{\frac{z - t}{a - t}} \cdot y \]

      2. *-commutative 51.9%

         \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   6. Simplified 51.9%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   7. Taylor expanded in z around inf 42.3%

      \[\leadsto \color{blue}{\frac{y \cdot z}{a - t}} \]
   8. Step-by-step derivation

      1. associate-/l* 44.5%

         \[\leadsto \color{blue}{\frac{y}{\frac{a - t}{z}}} \]

      2. associate-/r/ 47.0%

         \[\leadsto \color{blue}{\frac{y}{a - t} \cdot z} \]

   9. Simplified 47.0%

      \[\leadsto \color{blue}{\frac{y}{a - t} \cdot z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 51.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.16 \cdot 10^{-89}:\\ \;\;\;\;y - z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-248}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+14}:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y - z \cdot \frac{y}{t}\\ \end{array} \]

Alternative 20: 65.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-95}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+14}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.6e-95)
   (* y (/ (- z t) (- a t)))
   (if (<= t 2.2e+14) (- x (/ (- x y) (/ a z))) (+ y (* z (/ x t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.6e-95) {
		tmp = y * ((z - t) / (a - t));
	} else if (t <= 2.2e+14) {
		tmp = x - ((x - y) / (a / z));
	} else {
		tmp = y + (z * (x / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.6d-95)) then
        tmp = y * ((z - t) / (a - t))
    else if (t <= 2.2d+14) then
        tmp = x - ((x - y) / (a / z))
    else
        tmp = y + (z * (x / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.6e-95) {
		tmp = y * ((z - t) / (a - t));
	} else if (t <= 2.2e+14) {
		tmp = x - ((x - y) / (a / z));
	} else {
		tmp = y + (z * (x / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.6e-95:
		tmp = y * ((z - t) / (a - t))
	elif t <= 2.2e+14:
		tmp = x - ((x - y) / (a / z))
	else:
		tmp = y + (z * (x / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.6e-95)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (t <= 2.2e+14)
		tmp = Float64(x - Float64(Float64(x - y) / Float64(a / z)));
	else
		tmp = Float64(y + Float64(z * Float64(x / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.6e-95)
		tmp = y * ((z - t) / (a - t));
	elseif (t <= 2.2e+14)
		tmp = x - ((x - y) / (a / z));
	else
		tmp = y + (z * (x / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.6e-95], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.2e+14], N[(x - N[(N[(x - y), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.5999999999999999e-95

   1. Initial program 63.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 63.4%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 79.9%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 79.9%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 79.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 79.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in y around inf 67.2%

      \[\leadsto \color{blue}{\left(\frac{z}{a - t} - \frac{t}{a - t}\right) \cdot y} \]
   5. Step-by-step derivation

      1. div-sub 67.2%

         \[\leadsto \color{blue}{\frac{z - t}{a - t}} \cdot y \]

      2. *-commutative 67.2%

         \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   6. Simplified 67.2%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   if -1.5999999999999999e-95 < t < 2.2e14

   1. Initial program 92.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 92.1%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 93.3%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 93.3%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 93.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 93.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in t around 0 74.4%

      \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot z}{a} + x} \]
   5. Step-by-step derivation

      1. +-commutative 74.4%

         \[\leadsto \color{blue}{x + \frac{\left(y - x\right) \cdot z}{a}} \]

      2. associate-/l* 75.8%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a}{z}}} \]

   6. Simplified 75.8%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a}{z}}} \]

   if 2.2e14 < t

   1. Initial program 56.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 56.7%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 81.3%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 81.3%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 81.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 81.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in t around inf 67.3%

      \[\leadsto \color{blue}{y + \frac{\left(-1 \cdot z - -1 \cdot a\right) \cdot \left(y - x\right)}{t}} \]
   5. Step-by-step derivation

      1. *-commutative 67.3%

         \[\leadsto y + \frac{\color{blue}{\left(y - x\right) \cdot \left(-1 \cdot z - -1 \cdot a\right)}}{t} \]

      2. cancel-sign-sub-inv 67.3%

         \[\leadsto y + \frac{\left(y - x\right) \cdot \color{blue}{\left(-1 \cdot z + \left(--1\right) \cdot a\right)}}{t} \]

      3. metadata-eval 67.3%

         \[\leadsto y + \frac{\left(y - x\right) \cdot \left(-1 \cdot z + \color{blue}{1} \cdot a\right)}{t} \]

      4. *-lft-identity 67.3%

         \[\leadsto y + \frac{\left(y - x\right) \cdot \left(-1 \cdot z + \color{blue}{a}\right)}{t} \]

      5. distribute-lft-in 67.3%

         \[\leadsto y + \frac{\color{blue}{\left(y - x\right) \cdot \left(-1 \cdot z\right) + \left(y - x\right) \cdot a}}{t} \]

      6. mul-1-neg 67.3%

         \[\leadsto y + \frac{\left(y - x\right) \cdot \color{blue}{\left(-z\right)} + \left(y - x\right) \cdot a}{t} \]

      7. distribute-rgt-neg-in 67.3%

         \[\leadsto y + \frac{\color{blue}{\left(-\left(y - x\right) \cdot z\right)} + \left(y - x\right) \cdot a}{t} \]

      8. mul-1-neg 67.3%

         \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(\left(y - x\right) \cdot z\right)} + \left(y - x\right) \cdot a}{t} \]

      9. *-commutative 67.3%

         \[\leadsto y + \frac{-1 \cdot \left(\left(y - x\right) \cdot z\right) + \color{blue}{a \cdot \left(y - x\right)}}{t} \]

      10. cancel-sign-sub 67.3%

          \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(\left(y - x\right) \cdot z\right) - \left(-a\right) \cdot \left(y - x\right)}}{t} \]

      11. mul-1-neg 67.3%

          \[\leadsto y + \frac{-1 \cdot \left(\left(y - x\right) \cdot z\right) - \color{blue}{\left(-1 \cdot a\right)} \cdot \left(y - x\right)}{t} \]

      12. associate-*r* 67.3%

          \[\leadsto y + \frac{-1 \cdot \left(\left(y - x\right) \cdot z\right) - \color{blue}{-1 \cdot \left(a \cdot \left(y - x\right)\right)}}{t} \]

      13. distribute-lft-out-- 67.3%

          \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(\left(y - x\right) \cdot z - a \cdot \left(y - x\right)\right)}}{t} \]

      14. associate-*r/ 67.3%

          \[\leadsto y + \color{blue}{-1 \cdot \frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}} \]

      15. mul-1-neg 67.3%

          \[\leadsto y + \color{blue}{\left(-\frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}\right)} \]

   6. Simplified 81.1%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]

   7. Taylor expanded in z around inf 71.1%

      \[\leadsto y - \color{blue}{\frac{z \cdot \left(y - x\right)}{t}} \]
   8. Step-by-step derivation

      1. *-commutative 71.1%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot z}}{t} \]

      2. associate-/l* 79.4%

         \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z}}} \]

   9. Simplified 79.4%

      \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z}}} \]

   10. Taylor expanded in y around 0 66.5%

       \[\leadsto y - \color{blue}{-1 \cdot \frac{z \cdot x}{t}} \]
   11. Step-by-step derivation

       1. mul-1-neg 66.5%

          \[\leadsto y - \color{blue}{\left(-\frac{z \cdot x}{t}\right)} \]

       2. *-commutative 66.5%

          \[\leadsto y - \left(-\frac{\color{blue}{x \cdot z}}{t}\right) \]

       3. associate-*l/ 72.0%

          \[\leadsto y - \left(-\color{blue}{\frac{x}{t} \cdot z}\right) \]

       4. distribute-rgt-neg-in 72.0%

          \[\leadsto y - \color{blue}{\frac{x}{t} \cdot \left(-z\right)} \]

   12. Simplified 72.0%

       \[\leadsto y - \color{blue}{\frac{x}{t} \cdot \left(-z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-95}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+14}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y + z \cdot \frac{x}{t}\\ \end{array} \]

Alternative 21: 67.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-95}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 8200000000:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.05e-95)
   (* y (/ (- z t) (- a t)))
   (if (<= t 8200000000.0)
     (- x (/ (- x y) (/ a z)))
     (+ y (/ (- x y) (/ t z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.05e-95) {
		tmp = y * ((z - t) / (a - t));
	} else if (t <= 8200000000.0) {
		tmp = x - ((x - y) / (a / z));
	} else {
		tmp = y + ((x - y) / (t / z));
	}
	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 <= (-1.05d-95)) then
        tmp = y * ((z - t) / (a - t))
    else if (t <= 8200000000.0d0) then
        tmp = x - ((x - y) / (a / z))
    else
        tmp = y + ((x - y) / (t / z))
    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 <= -1.05e-95) {
		tmp = y * ((z - t) / (a - t));
	} else if (t <= 8200000000.0) {
		tmp = x - ((x - y) / (a / z));
	} else {
		tmp = y + ((x - y) / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.05e-95:
		tmp = y * ((z - t) / (a - t))
	elif t <= 8200000000.0:
		tmp = x - ((x - y) / (a / z))
	else:
		tmp = y + ((x - y) / (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.05e-95)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (t <= 8200000000.0)
		tmp = Float64(x - Float64(Float64(x - y) / Float64(a / z)));
	else
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.05e-95)
		tmp = y * ((z - t) / (a - t));
	elseif (t <= 8200000000.0)
		tmp = x - ((x - y) / (a / z));
	else
		tmp = y + ((x - y) / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.05e-95], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8200000000.0], N[(x - N[(N[(x - y), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.05e-95

   1. Initial program 63.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 63.4%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 79.9%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 79.9%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 79.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 79.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in y around inf 67.2%

      \[\leadsto \color{blue}{\left(\frac{z}{a - t} - \frac{t}{a - t}\right) \cdot y} \]
   5. Step-by-step derivation

      1. div-sub 67.2%

         \[\leadsto \color{blue}{\frac{z - t}{a - t}} \cdot y \]

      2. *-commutative 67.2%

         \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   6. Simplified 67.2%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   if -1.05e-95 < t < 8.2e9

   1. Initial program 92.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 92.1%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 93.3%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 93.3%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 93.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 93.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in t around 0 74.4%

      \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot z}{a} + x} \]
   5. Step-by-step derivation

      1. +-commutative 74.4%

         \[\leadsto \color{blue}{x + \frac{\left(y - x\right) \cdot z}{a}} \]

      2. associate-/l* 75.8%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a}{z}}} \]

   6. Simplified 75.8%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a}{z}}} \]

   if 8.2e9 < t

   1. Initial program 56.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 56.7%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 81.3%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 81.3%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 81.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 81.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in t around inf 67.3%

      \[\leadsto \color{blue}{y + \frac{\left(-1 \cdot z - -1 \cdot a\right) \cdot \left(y - x\right)}{t}} \]
   5. Step-by-step derivation

      1. *-commutative 67.3%

         \[\leadsto y + \frac{\color{blue}{\left(y - x\right) \cdot \left(-1 \cdot z - -1 \cdot a\right)}}{t} \]

      2. cancel-sign-sub-inv 67.3%

         \[\leadsto y + \frac{\left(y - x\right) \cdot \color{blue}{\left(-1 \cdot z + \left(--1\right) \cdot a\right)}}{t} \]

      3. metadata-eval 67.3%

         \[\leadsto y + \frac{\left(y - x\right) \cdot \left(-1 \cdot z + \color{blue}{1} \cdot a\right)}{t} \]

      4. *-lft-identity 67.3%

         \[\leadsto y + \frac{\left(y - x\right) \cdot \left(-1 \cdot z + \color{blue}{a}\right)}{t} \]

      5. distribute-lft-in 67.3%

         \[\leadsto y + \frac{\color{blue}{\left(y - x\right) \cdot \left(-1 \cdot z\right) + \left(y - x\right) \cdot a}}{t} \]

      6. mul-1-neg 67.3%

         \[\leadsto y + \frac{\left(y - x\right) \cdot \color{blue}{\left(-z\right)} + \left(y - x\right) \cdot a}{t} \]

      7. distribute-rgt-neg-in 67.3%

         \[\leadsto y + \frac{\color{blue}{\left(-\left(y - x\right) \cdot z\right)} + \left(y - x\right) \cdot a}{t} \]

      8. mul-1-neg 67.3%

         \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(\left(y - x\right) \cdot z\right)} + \left(y - x\right) \cdot a}{t} \]

      9. *-commutative 67.3%

         \[\leadsto y + \frac{-1 \cdot \left(\left(y - x\right) \cdot z\right) + \color{blue}{a \cdot \left(y - x\right)}}{t} \]

      10. cancel-sign-sub 67.3%

          \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(\left(y - x\right) \cdot z\right) - \left(-a\right) \cdot \left(y - x\right)}}{t} \]

      11. mul-1-neg 67.3%

          \[\leadsto y + \frac{-1 \cdot \left(\left(y - x\right) \cdot z\right) - \color{blue}{\left(-1 \cdot a\right)} \cdot \left(y - x\right)}{t} \]

      12. associate-*r* 67.3%

          \[\leadsto y + \frac{-1 \cdot \left(\left(y - x\right) \cdot z\right) - \color{blue}{-1 \cdot \left(a \cdot \left(y - x\right)\right)}}{t} \]

      13. distribute-lft-out-- 67.3%

          \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(\left(y - x\right) \cdot z - a \cdot \left(y - x\right)\right)}}{t} \]

      14. associate-*r/ 67.3%

          \[\leadsto y + \color{blue}{-1 \cdot \frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}} \]

      15. mul-1-neg 67.3%

          \[\leadsto y + \color{blue}{\left(-\frac{\left(y - x\right) \cdot z - a \cdot \left(y - x\right)}{t}\right)} \]

   6. Simplified 81.1%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]

   7. Taylor expanded in z around inf 71.1%

      \[\leadsto y - \color{blue}{\frac{z \cdot \left(y - x\right)}{t}} \]
   8. Step-by-step derivation

      1. *-commutative 71.1%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot z}}{t} \]

      2. associate-/l* 79.4%

         \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z}}} \]

   9. Simplified 79.4%

      \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-95}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;t \leq 8200000000:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \end{array} \]

Alternative 22: 36.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{-95}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-202}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-97}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 3.45 \cdot 10^{+105}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.9e-95)
   y
   (if (<= t 1.15e-202)
     x
     (if (<= t 1.65e-97) (* y (/ z a)) (if (<= t 3.45e+105) x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.9e-95) {
		tmp = y;
	} else if (t <= 1.15e-202) {
		tmp = x;
	} else if (t <= 1.65e-97) {
		tmp = y * (z / a);
	} else if (t <= 3.45e+105) {
		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 <= (-2.9d-95)) then
        tmp = y
    else if (t <= 1.15d-202) then
        tmp = x
    else if (t <= 1.65d-97) then
        tmp = y * (z / a)
    else if (t <= 3.45d+105) 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 <= -2.9e-95) {
		tmp = y;
	} else if (t <= 1.15e-202) {
		tmp = x;
	} else if (t <= 1.65e-97) {
		tmp = y * (z / a);
	} else if (t <= 3.45e+105) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.9e-95:
		tmp = y
	elif t <= 1.15e-202:
		tmp = x
	elif t <= 1.65e-97:
		tmp = y * (z / a)
	elif t <= 3.45e+105:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.9e-95)
		tmp = y;
	elseif (t <= 1.15e-202)
		tmp = x;
	elseif (t <= 1.65e-97)
		tmp = Float64(y * Float64(z / a));
	elseif (t <= 3.45e+105)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.9e-95)
		tmp = y;
	elseif (t <= 1.15e-202)
		tmp = x;
	elseif (t <= 1.65e-97)
		tmp = y * (z / a);
	elseif (t <= 3.45e+105)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.9e-95], y, If[LessEqual[t, 1.15e-202], x, If[LessEqual[t, 1.65e-97], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.45e+105], x, y]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.90000000000000002e-95 or 3.45000000000000018e105 < t

   1. Initial program 58.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 58.9%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 79.4%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 79.4%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 79.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 79.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in t around inf 47.3%

      \[\leadsto \color{blue}{y} \]

   if -2.90000000000000002e-95 < t < 1.1499999999999999e-202 or 1.6500000000000001e-97 < t < 3.45000000000000018e105

   1. Initial program 88.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 88.2%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 91.6%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 91.6%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 91.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 91.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in a around inf 42.5%

      \[\leadsto \color{blue}{x} \]

   if 1.1499999999999999e-202 < t < 1.6500000000000001e-97

   1. Initial program 87.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 87.6%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 94.9%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 94.9%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 94.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 94.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in y around inf 68.7%

      \[\leadsto \color{blue}{\left(\frac{z}{a - t} - \frac{t}{a - t}\right) \cdot y} \]
   5. Step-by-step derivation

      1. div-sub 68.7%

         \[\leadsto \color{blue}{\frac{z - t}{a - t}} \cdot y \]

      2. *-commutative 68.7%

         \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   6. Simplified 68.7%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   7. Taylor expanded in t around 0 56.9%

      \[\leadsto y \cdot \color{blue}{\frac{z}{a}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 46.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{-95}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-202}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-97}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 3.45 \cdot 10^{+105}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 23: 35.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{-95}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-248}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-93}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{+108}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.8e-95)
   y
   (if (<= t 2.7e-248)
     x
     (if (<= t 6.5e-93) (* z (/ y a)) (if (<= t 1.08e+108) x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.8e-95) {
		tmp = y;
	} else if (t <= 2.7e-248) {
		tmp = x;
	} else if (t <= 6.5e-93) {
		tmp = z * (y / a);
	} else if (t <= 1.08e+108) {
		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 <= (-2.8d-95)) then
        tmp = y
    else if (t <= 2.7d-248) then
        tmp = x
    else if (t <= 6.5d-93) then
        tmp = z * (y / a)
    else if (t <= 1.08d+108) 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 <= -2.8e-95) {
		tmp = y;
	} else if (t <= 2.7e-248) {
		tmp = x;
	} else if (t <= 6.5e-93) {
		tmp = z * (y / a);
	} else if (t <= 1.08e+108) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.8e-95:
		tmp = y
	elif t <= 2.7e-248:
		tmp = x
	elif t <= 6.5e-93:
		tmp = z * (y / a)
	elif t <= 1.08e+108:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.8e-95)
		tmp = y;
	elseif (t <= 2.7e-248)
		tmp = x;
	elseif (t <= 6.5e-93)
		tmp = Float64(z * Float64(y / a));
	elseif (t <= 1.08e+108)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.8e-95)
		tmp = y;
	elseif (t <= 2.7e-248)
		tmp = x;
	elseif (t <= 6.5e-93)
		tmp = z * (y / a);
	elseif (t <= 1.08e+108)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.8e-95], y, If[LessEqual[t, 2.7e-248], x, If[LessEqual[t, 6.5e-93], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.08e+108], x, y]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.7999999999999999e-95 or 1.0800000000000001e108 < t

   1. Initial program 58.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 58.9%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 79.4%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 79.4%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 79.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 79.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in t around inf 47.3%

      \[\leadsto \color{blue}{y} \]

   if -2.7999999999999999e-95 < t < 2.7000000000000001e-248 or 6.5e-93 < t < 1.0800000000000001e108

   1. Initial program 87.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 87.3%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 94.0%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 94.0%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 94.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 94.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in a around inf 43.8%

      \[\leadsto \color{blue}{x} \]

   if 2.7000000000000001e-248 < t < 6.5e-93

   1. Initial program 91.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 91.2%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 85.4%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 85.4%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 85.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 85.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in y around inf 56.1%

      \[\leadsto \color{blue}{\left(\frac{z}{a - t} - \frac{t}{a - t}\right) \cdot y} \]
   5. Step-by-step derivation

      1. div-sub 56.1%

         \[\leadsto \color{blue}{\frac{z - t}{a - t}} \cdot y \]

      2. *-commutative 56.1%

         \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   6. Simplified 56.1%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   7. Taylor expanded in t around 0 47.7%

      \[\leadsto y \cdot \color{blue}{\frac{z}{a}} \]

   8. Taylor expanded in y around 0 45.0%

      \[\leadsto \color{blue}{\frac{y \cdot z}{a}} \]
   9. Step-by-step derivation

      1. associate-*l/ 48.5%

         \[\leadsto \color{blue}{\frac{y}{a} \cdot z} \]

   10. Simplified 48.5%

       \[\leadsto \color{blue}{\frac{y}{a} \cdot z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 46.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{-95}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-248}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-93}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{+108}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 24: 35.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{-95}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-247}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-101}:\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+105}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.9e-95)
   y
   (if (<= t 1.55e-247)
     x
     (if (<= t 3.3e-101) (/ z (/ a y)) (if (<= t 8.5e+105) x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.9e-95) {
		tmp = y;
	} else if (t <= 1.55e-247) {
		tmp = x;
	} else if (t <= 3.3e-101) {
		tmp = z / (a / y);
	} else if (t <= 8.5e+105) {
		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 <= (-2.9d-95)) then
        tmp = y
    else if (t <= 1.55d-247) then
        tmp = x
    else if (t <= 3.3d-101) then
        tmp = z / (a / y)
    else if (t <= 8.5d+105) 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 <= -2.9e-95) {
		tmp = y;
	} else if (t <= 1.55e-247) {
		tmp = x;
	} else if (t <= 3.3e-101) {
		tmp = z / (a / y);
	} else if (t <= 8.5e+105) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.9e-95:
		tmp = y
	elif t <= 1.55e-247:
		tmp = x
	elif t <= 3.3e-101:
		tmp = z / (a / y)
	elif t <= 8.5e+105:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.9e-95)
		tmp = y;
	elseif (t <= 1.55e-247)
		tmp = x;
	elseif (t <= 3.3e-101)
		tmp = Float64(z / Float64(a / y));
	elseif (t <= 8.5e+105)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.9e-95)
		tmp = y;
	elseif (t <= 1.55e-247)
		tmp = x;
	elseif (t <= 3.3e-101)
		tmp = z / (a / y);
	elseif (t <= 8.5e+105)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.9e-95], y, If[LessEqual[t, 1.55e-247], x, If[LessEqual[t, 3.3e-101], N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.5e+105], x, y]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.90000000000000002e-95 or 8.49999999999999986e105 < t

   1. Initial program 58.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 58.9%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 79.4%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 79.4%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 79.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 79.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in t around inf 47.3%

      \[\leadsto \color{blue}{y} \]

   if -2.90000000000000002e-95 < t < 1.55000000000000008e-247 or 3.29999999999999984e-101 < t < 8.49999999999999986e105

   1. Initial program 87.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 87.3%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 94.0%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 94.0%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 94.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 94.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in a around inf 43.8%

      \[\leadsto \color{blue}{x} \]

   if 1.55000000000000008e-247 < t < 3.29999999999999984e-101

   1. Initial program 91.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 91.2%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 85.4%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 85.4%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 85.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 85.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in z around inf 62.6%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   5. Step-by-step derivation

      1. div-sub 70.0%

         \[\leadsto z \cdot \color{blue}{\frac{y - x}{a - t}} \]

      2. *-commutative 70.0%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot z} \]

      3. associate-*l/ 69.9%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot z}{a - t}} \]

      4. associate-/l* 59.6%

         \[\leadsto \color{blue}{\frac{y - x}{\frac{a - t}{z}}} \]

   6. Simplified 59.6%

      \[\leadsto \color{blue}{\frac{y - x}{\frac{a - t}{z}}} \]

   7. Taylor expanded in a around inf 49.8%

      \[\leadsto \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]
   8. Step-by-step derivation

      1. associate-/l* 53.9%

         \[\leadsto \color{blue}{\frac{z}{\frac{a}{y - x}}} \]

   9. Simplified 53.9%

      \[\leadsto \color{blue}{\frac{z}{\frac{a}{y - x}}} \]

   10. Taylor expanded in y around inf 49.0%

       \[\leadsto \frac{z}{\color{blue}{\frac{a}{y}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 46.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{-95}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-247}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-101}:\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+105}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 25: 36.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{-95}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+105}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.9e-95) y (if (<= t 2.8e+105) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.9e-95) {
		tmp = y;
	} else if (t <= 2.8e+105) {
		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 <= (-2.9d-95)) then
        tmp = y
    else if (t <= 2.8d+105) 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 <= -2.9e-95) {
		tmp = y;
	} else if (t <= 2.8e+105) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.9e-95:
		tmp = y
	elif t <= 2.8e+105:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.9e-95)
		tmp = y;
	elseif (t <= 2.8e+105)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.9e-95)
		tmp = y;
	elseif (t <= 2.8e+105)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.9e-95], y, If[LessEqual[t, 2.8e+105], x, y]]

Derivation

1. Split input into 2 regimes

2. if t < -2.90000000000000002e-95 or 2.8000000000000001e105 < t

   1. Initial program 58.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 58.9%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 79.4%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 79.4%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 79.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 79.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in t around inf 47.3%

      \[\leadsto \color{blue}{y} \]

   if -2.90000000000000002e-95 < t < 2.8000000000000001e105

   1. Initial program 88.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 88.1%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*r/ 92.1%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

      3. *-commutative 92.1%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      4. fma-def 92.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 92.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   4. Taylor expanded in a around inf 38.2%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{-95}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+105}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 26: 25.0% 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 73.0%

   \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
2. Step-by-step derivation

   1. +-commutative 73.0%

      \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

   2. associate-*r/ 85.6%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t}} + x \]

   3. *-commutative 85.6%

      \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

   4. fma-def 85.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

3. Simplified 85.6%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

4. Taylor expanded in a around inf 25.2%

   \[\leadsto \color{blue}{x} \]

5. Final simplification 25.2%

   \[\leadsto x \]

Developer target: 87.0% accurate, 0.7× 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 2023176 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (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))))