Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 79.9% → 89.5%

Time: 24.8s

Alternatives: 23

Speedup: 0.2×

Specification

Math

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

FPCore

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

C

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

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 - z) * ((t - x) / (a - z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 79.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 - z) * ((t - x) / (a - z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 89.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - x}{a - z}\\ t_2 := x + \left(y - z\right) \cdot t\_1\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{-68}:\\ \;\;\;\;\mathsf{fma}\left(y - z, t\_1, x\right)\\ \mathbf{elif}\;t\_2 \leq -4 \cdot 10^{-122}:\\ \;\;\;\;t - \frac{x \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-284}:\\ \;\;\;\;x + \frac{z}{a - z} \cdot \left(x - t\right)\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t x) (- a z))) (t_2 (+ x (* (- y z) t_1))))
   (if (<= t_2 -2e-68)
     (fma (- y z) t_1 x)
     (if (<= t_2 -4e-122)
       (- t (/ (* x (- a y)) z))
       (if (<= t_2 -1e-284)
         (+ x (* (/ z (- a z)) (- x t)))
         (if (<= t_2 0.0) (+ t (/ (- x t) (/ z (- y a)))) t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) / (a - z);
	double t_2 = x + ((y - z) * t_1);
	double tmp;
	if (t_2 <= -2e-68) {
		tmp = fma((y - z), t_1, x);
	} else if (t_2 <= -4e-122) {
		tmp = t - ((x * (a - y)) / z);
	} else if (t_2 <= -1e-284) {
		tmp = x + ((z / (a - z)) * (x - t));
	} else if (t_2 <= 0.0) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) / Float64(a - z))
	t_2 = Float64(x + Float64(Float64(y - z) * t_1))
	tmp = 0.0
	if (t_2 <= -2e-68)
		tmp = fma(Float64(y - z), t_1, x);
	elseif (t_2 <= -4e-122)
		tmp = Float64(t - Float64(Float64(x * Float64(a - y)) / z));
	elseif (t_2 <= -1e-284)
		tmp = Float64(x + Float64(Float64(z / Float64(a - z)) * Float64(x - t)));
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e-68], N[(N[(y - z), $MachinePrecision] * t$95$1 + x), $MachinePrecision], If[LessEqual[t$95$2, -4e-122], N[(t - N[(N[(x * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -1e-284], N[(x + N[(N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 0.0], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 5 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2.00000000000000013e-68

   1. Initial program 91.1%

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

      1. +-commutative 91.1%

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

      2. fma-def 91.2%

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

   3. Simplified 91.2%

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

   if -2.00000000000000013e-68 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -4.00000000000000024e-122

   1. Initial program 15.5%

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

   3. Taylor expanded in z around inf 100.0%

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

      1. associate--l+ 100.0%

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

      2. distribute-lft-out-- 100.0%

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

      3. div-sub 100.0%

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

      4. mul-1-neg 100.0%

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

      5. unsub-neg 100.0%

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

      6. distribute-rgt-out-- 100.0%

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

      7. associate-/l* 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in t around 0 100.0%

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

      1. associate-*r/ 100.0%

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

      2. *-commutative 100.0%

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

      3. associate-*r* 100.0%

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

      4. neg-mul-1 100.0%

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

      5. neg-sub0 100.0%

         \[\leadsto t - \frac{\color{blue}{\left(0 - \left(y - a\right)\right)} \cdot x}{z} \]

      6. associate--r- 100.0%

         \[\leadsto t - \frac{\color{blue}{\left(\left(0 - y\right) + a\right)} \cdot x}{z} \]

      7. neg-sub0 100.0%

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

   8. Simplified 100.0%

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

   if -4.00000000000000024e-122 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1.00000000000000004e-284

   1. Initial program 64.3%

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

   3. Taylor expanded in y around 0 81.1%

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

      1. mul-1-neg 81.1%

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

      2. unsub-neg 81.1%

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

      3. associate-/l* 57.8%

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

      4. associate-/r/ 80.8%

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

   5. Simplified 80.8%

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

   if -1.00000000000000004e-284 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.8%

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

   3. Taylor expanded in z around inf 83.8%

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

      1. associate--l+ 83.8%

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

      2. distribute-lft-out-- 83.8%

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

      3. div-sub 83.8%

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

      4. mul-1-neg 83.8%

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

      5. unsub-neg 83.8%

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

      6. distribute-rgt-out-- 83.8%

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

      7. associate-/l* 95.6%

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

   5. Simplified 95.6%

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

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

   1. Initial program 94.3%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing
3. Recombined 5 regimes into one program.

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-68}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -4 \cdot 10^{-122}:\\ \;\;\;\;t - \frac{x \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-284}:\\ \;\;\;\;x + \frac{z}{a - z} \cdot \left(x - t\right)\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 89.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-68}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq -4 \cdot 10^{-122}:\\ \;\;\;\;t - \frac{x \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-284}:\\ \;\;\;\;x + \frac{z}{a - z} \cdot \left(x - t\right)\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_1 -2e-68)
     t_1
     (if (<= t_1 -4e-122)
       (- t (/ (* x (- a y)) z))
       (if (<= t_1 -1e-284)
         (+ x (* (/ z (- a z)) (- x t)))
         (if (<= t_1 0.0) (+ t (/ (- x t) (/ z (- y a)))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -2e-68) {
		tmp = t_1;
	} else if (t_1 <= -4e-122) {
		tmp = t - ((x * (a - y)) / z);
	} else if (t_1 <= -1e-284) {
		tmp = x + ((z / (a - z)) * (x - t));
	} else if (t_1 <= 0.0) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if (t_1 <= (-2d-68)) then
        tmp = t_1
    else if (t_1 <= (-4d-122)) then
        tmp = t - ((x * (a - y)) / z)
    else if (t_1 <= (-1d-284)) then
        tmp = x + ((z / (a - z)) * (x - t))
    else if (t_1 <= 0.0d0) then
        tmp = t + ((x - t) / (z / (y - a)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -2e-68) {
		tmp = t_1;
	} else if (t_1 <= -4e-122) {
		tmp = t - ((x * (a - y)) / z);
	} else if (t_1 <= -1e-284) {
		tmp = x + ((z / (a - z)) * (x - t));
	} else if (t_1 <= 0.0) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_1 <= -2e-68:
		tmp = t_1
	elif t_1 <= -4e-122:
		tmp = t - ((x * (a - y)) / z)
	elif t_1 <= -1e-284:
		tmp = x + ((z / (a - z)) * (x - t))
	elif t_1 <= 0.0:
		tmp = t + ((x - t) / (z / (y - a)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= -2e-68)
		tmp = t_1;
	elseif (t_1 <= -4e-122)
		tmp = Float64(t - Float64(Float64(x * Float64(a - y)) / z));
	elseif (t_1 <= -1e-284)
		tmp = Float64(x + Float64(Float64(z / Float64(a - z)) * Float64(x - t)));
	elseif (t_1 <= 0.0)
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if (t_1 <= -2e-68)
		tmp = t_1;
	elseif (t_1 <= -4e-122)
		tmp = t - ((x * (a - y)) / z);
	elseif (t_1 <= -1e-284)
		tmp = x + ((z / (a - z)) * (x - t));
	elseif (t_1 <= 0.0)
		tmp = t + ((x - t) / (z / (y - 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 - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-68], t$95$1, If[LessEqual[t$95$1, -4e-122], N[(t - N[(N[(x * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -1e-284], N[(x + N[(N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2.00000000000000013e-68 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 92.8%

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

   if -2.00000000000000013e-68 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -4.00000000000000024e-122

   1. Initial program 15.5%

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

   3. Taylor expanded in z around inf 100.0%

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

      1. associate--l+ 100.0%

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

      2. distribute-lft-out-- 100.0%

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

      3. div-sub 100.0%

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

      4. mul-1-neg 100.0%

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

      5. unsub-neg 100.0%

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

      6. distribute-rgt-out-- 100.0%

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

      7. associate-/l* 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in t around 0 100.0%

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

      1. associate-*r/ 100.0%

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

      2. *-commutative 100.0%

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

      3. associate-*r* 100.0%

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

      4. neg-mul-1 100.0%

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

      5. neg-sub0 100.0%

         \[\leadsto t - \frac{\color{blue}{\left(0 - \left(y - a\right)\right)} \cdot x}{z} \]

      6. associate--r- 100.0%

         \[\leadsto t - \frac{\color{blue}{\left(\left(0 - y\right) + a\right)} \cdot x}{z} \]

      7. neg-sub0 100.0%

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

   8. Simplified 100.0%

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

   if -4.00000000000000024e-122 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1.00000000000000004e-284

   1. Initial program 64.3%

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

   3. Taylor expanded in y around 0 81.1%

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

      1. mul-1-neg 81.1%

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

      2. unsub-neg 81.1%

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

      3. associate-/l* 57.8%

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

      4. associate-/r/ 80.8%

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

   5. Simplified 80.8%

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

   if -1.00000000000000004e-284 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.8%

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

   3. Taylor expanded in z around inf 83.8%

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

      1. associate--l+ 83.8%

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

      2. distribute-lft-out-- 83.8%

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

      3. div-sub 83.8%

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

      4. mul-1-neg 83.8%

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

      5. unsub-neg 83.8%

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

      6. distribute-rgt-out-- 83.8%

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

      7. associate-/l* 95.6%

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

   5. Simplified 95.6%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-68}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -4 \cdot 10^{-122}:\\ \;\;\;\;t - \frac{x \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-284}:\\ \;\;\;\;x + \frac{z}{a - z} \cdot \left(x - t\right)\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 40.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+106}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{+32}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-67}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-217}:\\ \;\;\;\;\frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{-296}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-173}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+44}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.2e+106)
   t
   (if (<= z -2.4e+32)
     x
     (if (<= z -1.1e-67)
       (/ (* x (- y a)) z)
       (if (<= z -4.1e-217)
         (/ y (/ a (- t x)))
         (if (<= z 1.16e-296)
           x
           (if (<= z 1.6e-173)
             (* (- t x) (/ y a))
             (if (<= z 5.8e+44) x t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.2e+106) {
		tmp = t;
	} else if (z <= -2.4e+32) {
		tmp = x;
	} else if (z <= -1.1e-67) {
		tmp = (x * (y - a)) / z;
	} else if (z <= -4.1e-217) {
		tmp = y / (a / (t - x));
	} else if (z <= 1.16e-296) {
		tmp = x;
	} else if (z <= 1.6e-173) {
		tmp = (t - x) * (y / a);
	} else if (z <= 5.8e+44) {
		tmp = x;
	} else {
		tmp = 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 (z <= (-4.2d+106)) then
        tmp = t
    else if (z <= (-2.4d+32)) then
        tmp = x
    else if (z <= (-1.1d-67)) then
        tmp = (x * (y - a)) / z
    else if (z <= (-4.1d-217)) then
        tmp = y / (a / (t - x))
    else if (z <= 1.16d-296) then
        tmp = x
    else if (z <= 1.6d-173) then
        tmp = (t - x) * (y / a)
    else if (z <= 5.8d+44) then
        tmp = x
    else
        tmp = 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 (z <= -4.2e+106) {
		tmp = t;
	} else if (z <= -2.4e+32) {
		tmp = x;
	} else if (z <= -1.1e-67) {
		tmp = (x * (y - a)) / z;
	} else if (z <= -4.1e-217) {
		tmp = y / (a / (t - x));
	} else if (z <= 1.16e-296) {
		tmp = x;
	} else if (z <= 1.6e-173) {
		tmp = (t - x) * (y / a);
	} else if (z <= 5.8e+44) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.2e+106:
		tmp = t
	elif z <= -2.4e+32:
		tmp = x
	elif z <= -1.1e-67:
		tmp = (x * (y - a)) / z
	elif z <= -4.1e-217:
		tmp = y / (a / (t - x))
	elif z <= 1.16e-296:
		tmp = x
	elif z <= 1.6e-173:
		tmp = (t - x) * (y / a)
	elif z <= 5.8e+44:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.2e+106)
		tmp = t;
	elseif (z <= -2.4e+32)
		tmp = x;
	elseif (z <= -1.1e-67)
		tmp = Float64(Float64(x * Float64(y - a)) / z);
	elseif (z <= -4.1e-217)
		tmp = Float64(y / Float64(a / Float64(t - x)));
	elseif (z <= 1.16e-296)
		tmp = x;
	elseif (z <= 1.6e-173)
		tmp = Float64(Float64(t - x) * Float64(y / a));
	elseif (z <= 5.8e+44)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.2e+106)
		tmp = t;
	elseif (z <= -2.4e+32)
		tmp = x;
	elseif (z <= -1.1e-67)
		tmp = (x * (y - a)) / z;
	elseif (z <= -4.1e-217)
		tmp = y / (a / (t - x));
	elseif (z <= 1.16e-296)
		tmp = x;
	elseif (z <= 1.6e-173)
		tmp = (t - x) * (y / a);
	elseif (z <= 5.8e+44)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.2e+106], t, If[LessEqual[z, -2.4e+32], x, If[LessEqual[z, -1.1e-67], N[(N[(x * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, -4.1e-217], N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.16e-296], x, If[LessEqual[z, 1.6e-173], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e+44], x, t]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.2000000000000001e106 or 5.8000000000000004e44 < z

   1. Initial program 55.8%

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

   3. Taylor expanded in z around inf 53.7%

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

   if -4.2000000000000001e106 < z < -2.39999999999999991e32 or -4.09999999999999975e-217 < z < 1.15999999999999996e-296 or 1.6e-173 < z < 5.8000000000000004e44

   1. Initial program 94.0%

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

   3. Taylor expanded in a around inf 49.2%

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

   if -2.39999999999999991e32 < z < -1.1000000000000001e-67

   1. Initial program 77.5%

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

   3. Taylor expanded in z around inf 52.6%

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

      1. associate--l+ 52.6%

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

      2. distribute-lft-out-- 52.6%

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

      3. div-sub 52.6%

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

      4. mul-1-neg 52.6%

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

      5. unsub-neg 52.6%

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

      6. distribute-rgt-out-- 60.3%

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

      7. associate-/l* 53.3%

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

   5. Simplified 53.3%

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

   6. Taylor expanded in t around 0 45.2%

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

   if -1.1000000000000001e-67 < z < -4.09999999999999975e-217

   1. Initial program 90.1%

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

   3. Taylor expanded in y around inf 59.0%

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

      1. div-sub 59.0%

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

      2. associate-*r/ 54.6%

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

      3. associate-/l* 59.2%

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

      4. associate-/r/ 57.6%

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

   5. Simplified 57.6%

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

      1. *-commutative 57.6%

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

      2. clear-num 57.6%

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

      3. un-div-inv 57.6%

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

   7. Applied egg-rr 57.6%

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

   8. Taylor expanded in a around inf 48.6%

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

      1. associate-/l* 54.8%

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

   10. Simplified 54.8%

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

   if 1.15999999999999996e-296 < z < 1.6e-173

   1. Initial program 82.4%

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

   3. Taylor expanded in y around inf 65.1%

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

      1. div-sub 65.1%

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

      2. associate-*r/ 69.2%

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

      3. associate-/l* 65.2%

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

      4. associate-/r/ 73.3%

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

   5. Simplified 73.3%

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

   6. Taylor expanded in a around inf 68.8%

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

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+106}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{+32}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-67}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-217}:\\ \;\;\;\;\frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{-296}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-173}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+44}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 40.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+106}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{+32}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-67}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-218}:\\ \;\;\;\;\frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-296}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-173}:\\ \;\;\;\;\frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+46}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.2e+106)
   t
   (if (<= z -1.9e+32)
     x
     (if (<= z -2.6e-67)
       (/ (* x (- y a)) z)
       (if (<= z -1.12e-218)
         (/ y (/ a (- t x)))
         (if (<= z 9.2e-296)
           x
           (if (<= z 1.02e-173)
             (/ (- t x) (/ a y))
             (if (<= z 1.2e+46) x t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.2e+106) {
		tmp = t;
	} else if (z <= -1.9e+32) {
		tmp = x;
	} else if (z <= -2.6e-67) {
		tmp = (x * (y - a)) / z;
	} else if (z <= -1.12e-218) {
		tmp = y / (a / (t - x));
	} else if (z <= 9.2e-296) {
		tmp = x;
	} else if (z <= 1.02e-173) {
		tmp = (t - x) / (a / y);
	} else if (z <= 1.2e+46) {
		tmp = x;
	} else {
		tmp = 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 (z <= (-9.2d+106)) then
        tmp = t
    else if (z <= (-1.9d+32)) then
        tmp = x
    else if (z <= (-2.6d-67)) then
        tmp = (x * (y - a)) / z
    else if (z <= (-1.12d-218)) then
        tmp = y / (a / (t - x))
    else if (z <= 9.2d-296) then
        tmp = x
    else if (z <= 1.02d-173) then
        tmp = (t - x) / (a / y)
    else if (z <= 1.2d+46) then
        tmp = x
    else
        tmp = 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 (z <= -9.2e+106) {
		tmp = t;
	} else if (z <= -1.9e+32) {
		tmp = x;
	} else if (z <= -2.6e-67) {
		tmp = (x * (y - a)) / z;
	} else if (z <= -1.12e-218) {
		tmp = y / (a / (t - x));
	} else if (z <= 9.2e-296) {
		tmp = x;
	} else if (z <= 1.02e-173) {
		tmp = (t - x) / (a / y);
	} else if (z <= 1.2e+46) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9.2e+106:
		tmp = t
	elif z <= -1.9e+32:
		tmp = x
	elif z <= -2.6e-67:
		tmp = (x * (y - a)) / z
	elif z <= -1.12e-218:
		tmp = y / (a / (t - x))
	elif z <= 9.2e-296:
		tmp = x
	elif z <= 1.02e-173:
		tmp = (t - x) / (a / y)
	elif z <= 1.2e+46:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.2e+106)
		tmp = t;
	elseif (z <= -1.9e+32)
		tmp = x;
	elseif (z <= -2.6e-67)
		tmp = Float64(Float64(x * Float64(y - a)) / z);
	elseif (z <= -1.12e-218)
		tmp = Float64(y / Float64(a / Float64(t - x)));
	elseif (z <= 9.2e-296)
		tmp = x;
	elseif (z <= 1.02e-173)
		tmp = Float64(Float64(t - x) / Float64(a / y));
	elseif (z <= 1.2e+46)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -9.2e+106)
		tmp = t;
	elseif (z <= -1.9e+32)
		tmp = x;
	elseif (z <= -2.6e-67)
		tmp = (x * (y - a)) / z;
	elseif (z <= -1.12e-218)
		tmp = y / (a / (t - x));
	elseif (z <= 9.2e-296)
		tmp = x;
	elseif (z <= 1.02e-173)
		tmp = (t - x) / (a / y);
	elseif (z <= 1.2e+46)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.2e+106], t, If[LessEqual[z, -1.9e+32], x, If[LessEqual[z, -2.6e-67], N[(N[(x * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, -1.12e-218], N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.2e-296], x, If[LessEqual[z, 1.02e-173], N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e+46], x, t]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -9.2000000000000008e106 or 1.20000000000000004e46 < z

   1. Initial program 55.8%

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

   3. Taylor expanded in z around inf 53.7%

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

   if -9.2000000000000008e106 < z < -1.9000000000000002e32 or -1.11999999999999996e-218 < z < 9.20000000000000016e-296 or 1.02000000000000006e-173 < z < 1.20000000000000004e46

   1. Initial program 94.0%

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

   3. Taylor expanded in a around inf 49.2%

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

   if -1.9000000000000002e32 < z < -2.5999999999999999e-67

   1. Initial program 77.5%

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

   3. Taylor expanded in z around inf 52.6%

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

      1. associate--l+ 52.6%

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

      2. distribute-lft-out-- 52.6%

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

      3. div-sub 52.6%

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

      4. mul-1-neg 52.6%

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

      5. unsub-neg 52.6%

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

      6. distribute-rgt-out-- 60.3%

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

      7. associate-/l* 53.3%

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

   5. Simplified 53.3%

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

   6. Taylor expanded in t around 0 45.2%

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

   if -2.5999999999999999e-67 < z < -1.11999999999999996e-218

   1. Initial program 90.1%

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

   3. Taylor expanded in y around inf 59.0%

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

      1. div-sub 59.0%

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

      2. associate-*r/ 54.6%

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

      3. associate-/l* 59.2%

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

      4. associate-/r/ 57.6%

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

   5. Simplified 57.6%

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

      1. *-commutative 57.6%

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

      2. clear-num 57.6%

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

      3. un-div-inv 57.6%

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

   7. Applied egg-rr 57.6%

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

   8. Taylor expanded in a around inf 48.6%

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

      1. associate-/l* 54.8%

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

   10. Simplified 54.8%

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

   if 9.20000000000000016e-296 < z < 1.02000000000000006e-173

   1. Initial program 82.4%

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

   3. Taylor expanded in y around inf 65.1%

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

      1. div-sub 65.1%

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

      2. associate-*r/ 69.2%

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

      3. associate-/l* 65.2%

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

      4. associate-/r/ 73.3%

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

   5. Simplified 73.3%

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

      1. *-commutative 73.3%

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

      2. clear-num 73.4%

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

      3. un-div-inv 73.5%

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

   7. Applied egg-rr 73.5%

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

   8. Taylor expanded in a around inf 69.0%

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

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+106}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{+32}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-67}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-218}:\\ \;\;\;\;\frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-296}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-173}:\\ \;\;\;\;\frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+46}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;z \leq -7.8 \cdot 10^{+138}:\\ \;\;\;\;\frac{-t}{\frac{a}{z} + -1}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-232}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-278}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-130}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+30}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) (- a z)))))
   (if (<= z -7.8e+138)
     (/ (- t) (+ (/ a z) -1.0))
     (if (<= z -2.8e-232)
       t_1
       (if (<= z -1.65e-278)
         x
         (if (<= z 1.7e-130)
           t_1
           (if (<= z 2.05e+30) x (* (- y z) (/ t (- a z))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double tmp;
	if (z <= -7.8e+138) {
		tmp = -t / ((a / z) + -1.0);
	} else if (z <= -2.8e-232) {
		tmp = t_1;
	} else if (z <= -1.65e-278) {
		tmp = x;
	} else if (z <= 1.7e-130) {
		tmp = t_1;
	} else if (z <= 2.05e+30) {
		tmp = x;
	} else {
		tmp = (y - z) * (t / (a - 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) :: t_1
    real(8) :: tmp
    t_1 = y * ((t - x) / (a - z))
    if (z <= (-7.8d+138)) then
        tmp = -t / ((a / z) + (-1.0d0))
    else if (z <= (-2.8d-232)) then
        tmp = t_1
    else if (z <= (-1.65d-278)) then
        tmp = x
    else if (z <= 1.7d-130) then
        tmp = t_1
    else if (z <= 2.05d+30) then
        tmp = x
    else
        tmp = (y - z) * (t / (a - z))
    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 * ((t - x) / (a - z));
	double tmp;
	if (z <= -7.8e+138) {
		tmp = -t / ((a / z) + -1.0);
	} else if (z <= -2.8e-232) {
		tmp = t_1;
	} else if (z <= -1.65e-278) {
		tmp = x;
	} else if (z <= 1.7e-130) {
		tmp = t_1;
	} else if (z <= 2.05e+30) {
		tmp = x;
	} else {
		tmp = (y - z) * (t / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / (a - z))
	tmp = 0
	if z <= -7.8e+138:
		tmp = -t / ((a / z) + -1.0)
	elif z <= -2.8e-232:
		tmp = t_1
	elif z <= -1.65e-278:
		tmp = x
	elif z <= 1.7e-130:
		tmp = t_1
	elif z <= 2.05e+30:
		tmp = x
	else:
		tmp = (y - z) * (t / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / Float64(a - z)))
	tmp = 0.0
	if (z <= -7.8e+138)
		tmp = Float64(Float64(-t) / Float64(Float64(a / z) + -1.0));
	elseif (z <= -2.8e-232)
		tmp = t_1;
	elseif (z <= -1.65e-278)
		tmp = x;
	elseif (z <= 1.7e-130)
		tmp = t_1;
	elseif (z <= 2.05e+30)
		tmp = x;
	else
		tmp = Float64(Float64(y - z) * Float64(t / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / (a - z));
	tmp = 0.0;
	if (z <= -7.8e+138)
		tmp = -t / ((a / z) + -1.0);
	elseif (z <= -2.8e-232)
		tmp = t_1;
	elseif (z <= -1.65e-278)
		tmp = x;
	elseif (z <= 1.7e-130)
		tmp = t_1;
	elseif (z <= 2.05e+30)
		tmp = x;
	else
		tmp = (y - z) * (t / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.8e+138], N[((-t) / N[(N[(a / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.8e-232], t$95$1, If[LessEqual[z, -1.65e-278], x, If[LessEqual[z, 1.7e-130], t$95$1, If[LessEqual[z, 2.05e+30], x, N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.7999999999999996e138

   1. Initial program 42.3%

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

   3. Taylor expanded in y around 0 24.7%

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

      1. mul-1-neg 24.7%

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

      2. unsub-neg 24.7%

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

      3. associate-/l* 42.3%

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

      4. associate-/r/ 49.6%

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

   5. Simplified 49.6%

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

   6. Taylor expanded in x around 0 41.9%

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

      1. mul-1-neg 41.9%

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

      2. associate-/l* 64.1%

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

      3. div-sub 64.1%

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

      4. sub-neg 64.1%

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

      5. *-inverses 64.1%

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

      6. metadata-eval 64.1%

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

   8. Simplified 64.1%

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

   if -7.7999999999999996e138 < z < -2.79999999999999993e-232 or -1.6499999999999999e-278 < z < 1.70000000000000003e-130

   1. Initial program 90.4%

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

   3. Taylor expanded in y around -inf 52.4%

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

      1. associate-/l* 55.4%

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

      2. div-inv 55.3%

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

      3. clear-num 55.3%

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

   5. Applied egg-rr 55.3%

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

   if -2.79999999999999993e-232 < z < -1.6499999999999999e-278 or 1.70000000000000003e-130 < z < 2.05000000000000003e30

   1. Initial program 89.2%

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

   3. Taylor expanded in a around inf 59.7%

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

   if 2.05000000000000003e30 < z

   1. Initial program 61.8%

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

   3. Taylor expanded in x around 0 48.9%

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

      1. associate-/l* 74.1%

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

      2. associate-/r/ 64.3%

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

   5. Simplified 64.3%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+138}:\\ \;\;\;\;\frac{-t}{\frac{a}{z} + -1}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-232}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-278}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-130}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+30}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 43.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-t}{\frac{a}{z} + -1}\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.95 \cdot 10^{-214}:\\ \;\;\;\;\frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-297}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-174}:\\ \;\;\;\;\frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+41}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t) (+ (/ a z) -1.0))))
   (if (<= z -4.2e+49)
     t_1
     (if (<= z -2.95e-214)
       (/ y (/ a (- t x)))
       (if (<= z 1.3e-297)
         x
         (if (<= z 3.3e-174) (/ (- t x) (/ a y)) (if (<= z 8e+41) x t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -t / ((a / z) + -1.0);
	double tmp;
	if (z <= -4.2e+49) {
		tmp = t_1;
	} else if (z <= -2.95e-214) {
		tmp = y / (a / (t - x));
	} else if (z <= 1.3e-297) {
		tmp = x;
	} else if (z <= 3.3e-174) {
		tmp = (t - x) / (a / y);
	} else if (z <= 8e+41) {
		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 = -t / ((a / z) + (-1.0d0))
    if (z <= (-4.2d+49)) then
        tmp = t_1
    else if (z <= (-2.95d-214)) then
        tmp = y / (a / (t - x))
    else if (z <= 1.3d-297) then
        tmp = x
    else if (z <= 3.3d-174) then
        tmp = (t - x) / (a / y)
    else if (z <= 8d+41) 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 = -t / ((a / z) + -1.0);
	double tmp;
	if (z <= -4.2e+49) {
		tmp = t_1;
	} else if (z <= -2.95e-214) {
		tmp = y / (a / (t - x));
	} else if (z <= 1.3e-297) {
		tmp = x;
	} else if (z <= 3.3e-174) {
		tmp = (t - x) / (a / y);
	} else if (z <= 8e+41) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -t / ((a / z) + -1.0)
	tmp = 0
	if z <= -4.2e+49:
		tmp = t_1
	elif z <= -2.95e-214:
		tmp = y / (a / (t - x))
	elif z <= 1.3e-297:
		tmp = x
	elif z <= 3.3e-174:
		tmp = (t - x) / (a / y)
	elif z <= 8e+41:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-t) / Float64(Float64(a / z) + -1.0))
	tmp = 0.0
	if (z <= -4.2e+49)
		tmp = t_1;
	elseif (z <= -2.95e-214)
		tmp = Float64(y / Float64(a / Float64(t - x)));
	elseif (z <= 1.3e-297)
		tmp = x;
	elseif (z <= 3.3e-174)
		tmp = Float64(Float64(t - x) / Float64(a / y));
	elseif (z <= 8e+41)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -t / ((a / z) + -1.0);
	tmp = 0.0;
	if (z <= -4.2e+49)
		tmp = t_1;
	elseif (z <= -2.95e-214)
		tmp = y / (a / (t - x));
	elseif (z <= 1.3e-297)
		tmp = x;
	elseif (z <= 3.3e-174)
		tmp = (t - x) / (a / y);
	elseif (z <= 8e+41)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-t) / N[(N[(a / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.2e+49], t$95$1, If[LessEqual[z, -2.95e-214], N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e-297], x, If[LessEqual[z, 3.3e-174], N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e+41], x, t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.20000000000000022e49 or 8.00000000000000005e41 < z

   1. Initial program 61.1%

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

   3. Taylor expanded in y around 0 29.1%

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

      1. mul-1-neg 29.1%

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

      2. unsub-neg 29.1%

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

      3. associate-/l* 43.3%

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

      4. associate-/r/ 48.3%

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

   5. Simplified 48.3%

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

   6. Taylor expanded in x around 0 37.9%

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

      1. mul-1-neg 37.9%

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

      2. associate-/l* 58.0%

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

      3. div-sub 58.0%

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

      4. sub-neg 58.0%

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

      5. *-inverses 58.0%

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

      6. metadata-eval 58.0%

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

   8. Simplified 58.0%

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

   if -4.20000000000000022e49 < z < -2.9499999999999999e-214

   1. Initial program 88.2%

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

   3. Taylor expanded in y around inf 56.0%

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

      1. div-sub 56.0%

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

      2. associate-*r/ 51.2%

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

      3. associate-/l* 56.0%

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

      4. associate-/r/ 53.3%

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

   5. Simplified 53.3%

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

      1. *-commutative 53.3%

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

      2. clear-num 53.3%

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

      3. un-div-inv 53.3%

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

   7. Applied egg-rr 53.3%

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

   8. Taylor expanded in a around inf 39.2%

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

      1. associate-/l* 44.9%

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

   10. Simplified 44.9%

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

   if -2.9499999999999999e-214 < z < 1.3e-297 or 3.3000000000000001e-174 < z < 8.00000000000000005e41

   1. Initial program 91.7%

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

   3. Taylor expanded in a around inf 52.4%

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

   if 1.3e-297 < z < 3.3000000000000001e-174

   1. Initial program 82.4%

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

   3. Taylor expanded in y around inf 65.1%

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

      1. div-sub 65.1%

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

      2. associate-*r/ 69.2%

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

      3. associate-/l* 65.2%

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

      4. associate-/r/ 73.3%

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

   5. Simplified 73.3%

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

      1. *-commutative 73.3%

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

      2. clear-num 73.4%

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

      3. un-div-inv 73.5%

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

   7. Applied egg-rr 73.5%

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

   8. Taylor expanded in a around inf 69.0%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+49}:\\ \;\;\;\;\frac{-t}{\frac{a}{z} + -1}\\ \mathbf{elif}\;z \leq -2.95 \cdot 10^{-214}:\\ \;\;\;\;\frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-297}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-174}:\\ \;\;\;\;\frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+41}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{\frac{a}{z} + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 48.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a - z}\\ t_2 := \frac{-t}{\frac{a}{z} + -1}\\ \mathbf{if}\;z \leq -5.7 \cdot 10^{+132}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-231}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-279}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-127}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+41}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) (- a z)))) (t_2 (/ (- t) (+ (/ a z) -1.0))))
   (if (<= z -5.7e+132)
     t_2
     (if (<= z -1.55e-231)
       t_1
       (if (<= z -1.2e-279)
         x
         (if (<= z 2.1e-127) t_1 (if (<= z 3.5e+41) x t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double t_2 = -t / ((a / z) + -1.0);
	double tmp;
	if (z <= -5.7e+132) {
		tmp = t_2;
	} else if (z <= -1.55e-231) {
		tmp = t_1;
	} else if (z <= -1.2e-279) {
		tmp = x;
	} else if (z <= 2.1e-127) {
		tmp = t_1;
	} else if (z <= 3.5e+41) {
		tmp = 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 * ((t - x) / (a - z))
    t_2 = -t / ((a / z) + (-1.0d0))
    if (z <= (-5.7d+132)) then
        tmp = t_2
    else if (z <= (-1.55d-231)) then
        tmp = t_1
    else if (z <= (-1.2d-279)) then
        tmp = x
    else if (z <= 2.1d-127) then
        tmp = t_1
    else if (z <= 3.5d+41) then
        tmp = 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 * ((t - x) / (a - z));
	double t_2 = -t / ((a / z) + -1.0);
	double tmp;
	if (z <= -5.7e+132) {
		tmp = t_2;
	} else if (z <= -1.55e-231) {
		tmp = t_1;
	} else if (z <= -1.2e-279) {
		tmp = x;
	} else if (z <= 2.1e-127) {
		tmp = t_1;
	} else if (z <= 3.5e+41) {
		tmp = x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / (a - z))
	t_2 = -t / ((a / z) + -1.0)
	tmp = 0
	if z <= -5.7e+132:
		tmp = t_2
	elif z <= -1.55e-231:
		tmp = t_1
	elif z <= -1.2e-279:
		tmp = x
	elif z <= 2.1e-127:
		tmp = t_1
	elif z <= 3.5e+41:
		tmp = x
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / Float64(a - z)))
	t_2 = Float64(Float64(-t) / Float64(Float64(a / z) + -1.0))
	tmp = 0.0
	if (z <= -5.7e+132)
		tmp = t_2;
	elseif (z <= -1.55e-231)
		tmp = t_1;
	elseif (z <= -1.2e-279)
		tmp = x;
	elseif (z <= 2.1e-127)
		tmp = t_1;
	elseif (z <= 3.5e+41)
		tmp = x;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / (a - z));
	t_2 = -t / ((a / z) + -1.0);
	tmp = 0.0;
	if (z <= -5.7e+132)
		tmp = t_2;
	elseif (z <= -1.55e-231)
		tmp = t_1;
	elseif (z <= -1.2e-279)
		tmp = x;
	elseif (z <= 2.1e-127)
		tmp = t_1;
	elseif (z <= 3.5e+41)
		tmp = 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[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[((-t) / N[(N[(a / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.7e+132], t$95$2, If[LessEqual[z, -1.55e-231], t$95$1, If[LessEqual[z, -1.2e-279], x, If[LessEqual[z, 2.1e-127], t$95$1, If[LessEqual[z, 3.5e+41], x, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.6999999999999998e132 or 3.4999999999999999e41 < z

   1. Initial program 54.2%

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

   3. Taylor expanded in y around 0 25.0%

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

      1. mul-1-neg 25.0%

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

      2. unsub-neg 25.0%

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

      3. associate-/l* 40.3%

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

      4. associate-/r/ 46.3%

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

   5. Simplified 46.3%

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

   6. Taylor expanded in x around 0 40.2%

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

      1. mul-1-neg 40.2%

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

      2. associate-/l* 62.6%

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

      3. div-sub 62.6%

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

      4. sub-neg 62.6%

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

      5. *-inverses 62.6%

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

      6. metadata-eval 62.6%

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

   8. Simplified 62.6%

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

   if -5.6999999999999998e132 < z < -1.54999999999999994e-231 or -1.19999999999999995e-279 < z < 2.1000000000000001e-127

   1. Initial program 90.4%

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

   3. Taylor expanded in y around -inf 52.4%

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

      1. associate-/l* 55.4%

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

      2. div-inv 55.3%

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

      3. clear-num 55.3%

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

   5. Applied egg-rr 55.3%

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

   if -1.54999999999999994e-231 < z < -1.19999999999999995e-279 or 2.1000000000000001e-127 < z < 3.4999999999999999e41

   1. Initial program 87.8%

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

   3. Taylor expanded in a around inf 56.5%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.7 \cdot 10^{+132}:\\ \;\;\;\;\frac{-t}{\frac{a}{z} + -1}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-231}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-279}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-127}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+41}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{\frac{a}{z} + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 37.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+107}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{+32}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-158}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-297}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-140}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+46}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1e+107)
   t
   (if (<= z -2.8e+32)
     x
     (if (<= z -5.5e-158)
       (* x (/ (- y a) z))
       (if (<= z 3.7e-297)
         x
         (if (<= z 5.8e-140) (* t (/ y (- a z))) (if (<= z 1.8e+46) x t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1e+107) {
		tmp = t;
	} else if (z <= -2.8e+32) {
		tmp = x;
	} else if (z <= -5.5e-158) {
		tmp = x * ((y - a) / z);
	} else if (z <= 3.7e-297) {
		tmp = x;
	} else if (z <= 5.8e-140) {
		tmp = t * (y / (a - z));
	} else if (z <= 1.8e+46) {
		tmp = x;
	} else {
		tmp = 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 (z <= (-1d+107)) then
        tmp = t
    else if (z <= (-2.8d+32)) then
        tmp = x
    else if (z <= (-5.5d-158)) then
        tmp = x * ((y - a) / z)
    else if (z <= 3.7d-297) then
        tmp = x
    else if (z <= 5.8d-140) then
        tmp = t * (y / (a - z))
    else if (z <= 1.8d+46) then
        tmp = x
    else
        tmp = 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 (z <= -1e+107) {
		tmp = t;
	} else if (z <= -2.8e+32) {
		tmp = x;
	} else if (z <= -5.5e-158) {
		tmp = x * ((y - a) / z);
	} else if (z <= 3.7e-297) {
		tmp = x;
	} else if (z <= 5.8e-140) {
		tmp = t * (y / (a - z));
	} else if (z <= 1.8e+46) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1e+107:
		tmp = t
	elif z <= -2.8e+32:
		tmp = x
	elif z <= -5.5e-158:
		tmp = x * ((y - a) / z)
	elif z <= 3.7e-297:
		tmp = x
	elif z <= 5.8e-140:
		tmp = t * (y / (a - z))
	elif z <= 1.8e+46:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1e+107)
		tmp = t;
	elseif (z <= -2.8e+32)
		tmp = x;
	elseif (z <= -5.5e-158)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (z <= 3.7e-297)
		tmp = x;
	elseif (z <= 5.8e-140)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (z <= 1.8e+46)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1e+107)
		tmp = t;
	elseif (z <= -2.8e+32)
		tmp = x;
	elseif (z <= -5.5e-158)
		tmp = x * ((y - a) / z);
	elseif (z <= 3.7e-297)
		tmp = x;
	elseif (z <= 5.8e-140)
		tmp = t * (y / (a - z));
	elseif (z <= 1.8e+46)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1e+107], t, If[LessEqual[z, -2.8e+32], x, If[LessEqual[z, -5.5e-158], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.7e-297], x, If[LessEqual[z, 5.8e-140], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e+46], x, t]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.9999999999999997e106 or 1.7999999999999999e46 < z

   1. Initial program 55.8%

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

   3. Taylor expanded in z around inf 53.7%

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

   if -9.9999999999999997e106 < z < -2.8e32 or -5.50000000000000025e-158 < z < 3.7e-297 or 5.79999999999999995e-140 < z < 1.7999999999999999e46

   1. Initial program 92.9%

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

   3. Taylor expanded in a around inf 46.5%

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

   if -2.8e32 < z < -5.50000000000000025e-158

   1. Initial program 82.3%

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

   3. Taylor expanded in z around inf 45.3%

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

      1. associate--l+ 45.3%

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

      2. distribute-lft-out-- 45.3%

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

      3. div-sub 45.3%

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

      4. mul-1-neg 45.3%

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

      5. unsub-neg 45.3%

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

      6. distribute-rgt-out-- 49.9%

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

      7. associate-/l* 45.8%

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

   5. Simplified 45.8%

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

   6. Taylor expanded in t around 0 41.7%

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

      1. associate-*r/ 41.5%

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

   8. Simplified 41.5%

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

   if 3.7e-297 < z < 5.79999999999999995e-140

   1. Initial program 85.7%

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

   3. Taylor expanded in y around inf 64.4%

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

      1. div-sub 64.4%

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

      2. associate-*r/ 67.6%

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

      3. associate-/l* 64.4%

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

      4. associate-/r/ 67.6%

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

   5. Simplified 67.6%

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

   6. Taylor expanded in t around inf 53.0%

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

      1. associate-*r/ 53.1%

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

   8. Simplified 53.1%

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

4. Final simplification 49.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+107}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{+32}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-158}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-297}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-140}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+46}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 41.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{+44}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-218}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-295}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{-176}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+42}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- t x) (/ y a))))
   (if (<= z -4.5e+44)
     t
     (if (<= z -9.5e-218)
       t_1
       (if (<= z 6.5e-295)
         x
         (if (<= z 8.4e-176) t_1 (if (<= z 1.35e+42) x t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) * (y / a);
	double tmp;
	if (z <= -4.5e+44) {
		tmp = t;
	} else if (z <= -9.5e-218) {
		tmp = t_1;
	} else if (z <= 6.5e-295) {
		tmp = x;
	} else if (z <= 8.4e-176) {
		tmp = t_1;
	} else if (z <= 1.35e+42) {
		tmp = x;
	} else {
		tmp = 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 = (t - x) * (y / a)
    if (z <= (-4.5d+44)) then
        tmp = t
    else if (z <= (-9.5d-218)) then
        tmp = t_1
    else if (z <= 6.5d-295) then
        tmp = x
    else if (z <= 8.4d-176) then
        tmp = t_1
    else if (z <= 1.35d+42) then
        tmp = x
    else
        tmp = 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 = (t - x) * (y / a);
	double tmp;
	if (z <= -4.5e+44) {
		tmp = t;
	} else if (z <= -9.5e-218) {
		tmp = t_1;
	} else if (z <= 6.5e-295) {
		tmp = x;
	} else if (z <= 8.4e-176) {
		tmp = t_1;
	} else if (z <= 1.35e+42) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t - x) * (y / a)
	tmp = 0
	if z <= -4.5e+44:
		tmp = t
	elif z <= -9.5e-218:
		tmp = t_1
	elif z <= 6.5e-295:
		tmp = x
	elif z <= 8.4e-176:
		tmp = t_1
	elif z <= 1.35e+42:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) * Float64(y / a))
	tmp = 0.0
	if (z <= -4.5e+44)
		tmp = t;
	elseif (z <= -9.5e-218)
		tmp = t_1;
	elseif (z <= 6.5e-295)
		tmp = x;
	elseif (z <= 8.4e-176)
		tmp = t_1;
	elseif (z <= 1.35e+42)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t - x) * (y / a);
	tmp = 0.0;
	if (z <= -4.5e+44)
		tmp = t;
	elseif (z <= -9.5e-218)
		tmp = t_1;
	elseif (z <= 6.5e-295)
		tmp = x;
	elseif (z <= 8.4e-176)
		tmp = t_1;
	elseif (z <= 1.35e+42)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.5e+44], t, If[LessEqual[z, -9.5e-218], t$95$1, If[LessEqual[z, 6.5e-295], x, If[LessEqual[z, 8.4e-176], t$95$1, If[LessEqual[z, 1.35e+42], x, t]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.5e44 or 1.35e42 < z

   1. Initial program 61.1%

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

   3. Taylor expanded in z around inf 50.7%

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

   if -4.5e44 < z < -9.49999999999999967e-218 or 6.4999999999999998e-295 < z < 8.39999999999999969e-176

   1. Initial program 86.4%

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

   3. Taylor expanded in y around inf 58.8%

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

      1. div-sub 58.8%

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

      2. associate-*r/ 56.7%

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

      3. associate-/l* 58.8%

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

      4. associate-/r/ 59.4%

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

   5. Simplified 59.4%

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

   6. Taylor expanded in a around inf 51.0%

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

   if -9.49999999999999967e-218 < z < 6.4999999999999998e-295 or 8.39999999999999969e-176 < z < 1.35e42

   1. Initial program 91.7%

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

   3. Taylor expanded in a around inf 52.4%

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

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+44}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-218}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-295}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{-176}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+42}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 41.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+48}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-216}:\\ \;\;\;\;\frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-294}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{-173}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+42}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.85e+48)
   t
   (if (<= z -4.8e-216)
     (/ y (/ a (- t x)))
     (if (<= z 1.05e-294)
       x
       (if (<= z 1.16e-173) (* (- t x) (/ y a)) (if (<= z 8.2e+42) x t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.85e+48) {
		tmp = t;
	} else if (z <= -4.8e-216) {
		tmp = y / (a / (t - x));
	} else if (z <= 1.05e-294) {
		tmp = x;
	} else if (z <= 1.16e-173) {
		tmp = (t - x) * (y / a);
	} else if (z <= 8.2e+42) {
		tmp = x;
	} else {
		tmp = 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 (z <= (-1.85d+48)) then
        tmp = t
    else if (z <= (-4.8d-216)) then
        tmp = y / (a / (t - x))
    else if (z <= 1.05d-294) then
        tmp = x
    else if (z <= 1.16d-173) then
        tmp = (t - x) * (y / a)
    else if (z <= 8.2d+42) then
        tmp = x
    else
        tmp = 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 (z <= -1.85e+48) {
		tmp = t;
	} else if (z <= -4.8e-216) {
		tmp = y / (a / (t - x));
	} else if (z <= 1.05e-294) {
		tmp = x;
	} else if (z <= 1.16e-173) {
		tmp = (t - x) * (y / a);
	} else if (z <= 8.2e+42) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.85e+48:
		tmp = t
	elif z <= -4.8e-216:
		tmp = y / (a / (t - x))
	elif z <= 1.05e-294:
		tmp = x
	elif z <= 1.16e-173:
		tmp = (t - x) * (y / a)
	elif z <= 8.2e+42:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.85e+48)
		tmp = t;
	elseif (z <= -4.8e-216)
		tmp = Float64(y / Float64(a / Float64(t - x)));
	elseif (z <= 1.05e-294)
		tmp = x;
	elseif (z <= 1.16e-173)
		tmp = Float64(Float64(t - x) * Float64(y / a));
	elseif (z <= 8.2e+42)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.85e+48)
		tmp = t;
	elseif (z <= -4.8e-216)
		tmp = y / (a / (t - x));
	elseif (z <= 1.05e-294)
		tmp = x;
	elseif (z <= 1.16e-173)
		tmp = (t - x) * (y / a);
	elseif (z <= 8.2e+42)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.85e+48], t, If[LessEqual[z, -4.8e-216], N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.05e-294], x, If[LessEqual[z, 1.16e-173], N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.2e+42], x, t]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.85e48 or 8.2000000000000001e42 < z

   1. Initial program 61.1%

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

   3. Taylor expanded in z around inf 50.7%

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

   if -1.85e48 < z < -4.80000000000000007e-216

   1. Initial program 88.2%

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

   3. Taylor expanded in y around inf 56.0%

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

      1. div-sub 56.0%

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

      2. associate-*r/ 51.2%

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

      3. associate-/l* 56.0%

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

      4. associate-/r/ 53.3%

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

   5. Simplified 53.3%

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

      1. *-commutative 53.3%

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

      2. clear-num 53.3%

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

      3. un-div-inv 53.3%

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

   7. Applied egg-rr 53.3%

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

   8. Taylor expanded in a around inf 39.2%

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

      1. associate-/l* 44.9%

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

   10. Simplified 44.9%

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

   if -4.80000000000000007e-216 < z < 1.04999999999999992e-294 or 1.16000000000000004e-173 < z < 8.2000000000000001e42

   1. Initial program 91.7%

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

   3. Taylor expanded in a around inf 52.4%

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

   if 1.04999999999999992e-294 < z < 1.16000000000000004e-173

   1. Initial program 82.4%

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

   3. Taylor expanded in y around inf 65.1%

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

      1. div-sub 65.1%

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

      2. associate-*r/ 69.2%

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

      3. associate-/l* 65.2%

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

      4. associate-/r/ 73.3%

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

   5. Simplified 73.3%

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

   6. Taylor expanded in a around inf 68.8%

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

4. Final simplification 51.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+48}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-216}:\\ \;\;\;\;\frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-294}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{-173}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+42}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 56.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{if}\;t \leq -6.8 \cdot 10^{-100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{-212}:\\ \;\;\;\;x \cdot \left(\frac{z}{a - z} + 1\right)\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-38}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- y z) (/ t (- a z)))))
   (if (<= t -6.8e-100)
     t_1
     (if (<= t -1.85e-212)
       (* x (+ (/ z (- a z)) 1.0))
       (if (<= t 1.3e-38) (* (- t x) (/ y (- a z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - z) * (t / (a - z));
	double tmp;
	if (t <= -6.8e-100) {
		tmp = t_1;
	} else if (t <= -1.85e-212) {
		tmp = x * ((z / (a - z)) + 1.0);
	} else if (t <= 1.3e-38) {
		tmp = (t - x) * (y / (a - z));
	} 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) * (t / (a - z))
    if (t <= (-6.8d-100)) then
        tmp = t_1
    else if (t <= (-1.85d-212)) then
        tmp = x * ((z / (a - z)) + 1.0d0)
    else if (t <= 1.3d-38) then
        tmp = (t - x) * (y / (a - z))
    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) * (t / (a - z));
	double tmp;
	if (t <= -6.8e-100) {
		tmp = t_1;
	} else if (t <= -1.85e-212) {
		tmp = x * ((z / (a - z)) + 1.0);
	} else if (t <= 1.3e-38) {
		tmp = (t - x) * (y / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - z) * (t / (a - z))
	tmp = 0
	if t <= -6.8e-100:
		tmp = t_1
	elif t <= -1.85e-212:
		tmp = x * ((z / (a - z)) + 1.0)
	elif t <= 1.3e-38:
		tmp = (t - x) * (y / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - z) * Float64(t / Float64(a - z)))
	tmp = 0.0
	if (t <= -6.8e-100)
		tmp = t_1;
	elseif (t <= -1.85e-212)
		tmp = Float64(x * Float64(Float64(z / Float64(a - z)) + 1.0));
	elseif (t <= 1.3e-38)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - z) * (t / (a - z));
	tmp = 0.0;
	if (t <= -6.8e-100)
		tmp = t_1;
	elseif (t <= -1.85e-212)
		tmp = x * ((z / (a - z)) + 1.0);
	elseif (t <= 1.3e-38)
		tmp = (t - x) * (y / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.8e-100], t$95$1, If[LessEqual[t, -1.85e-212], N[(x * N[(N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.3e-38], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.79999999999999953e-100 or 1.30000000000000005e-38 < t

   1. Initial program 85.7%

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

   3. Taylor expanded in x around 0 50.4%

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

      1. associate-/l* 70.5%

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

      2. associate-/r/ 67.3%

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

   5. Simplified 67.3%

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

   if -6.79999999999999953e-100 < t < -1.84999999999999995e-212

   1. Initial program 57.5%

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

   3. Taylor expanded in y around 0 37.1%

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

      1. mul-1-neg 37.1%

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

      2. unsub-neg 37.1%

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

      3. associate-/l* 43.1%

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

      4. associate-/r/ 44.1%

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

   5. Simplified 44.1%

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

   6. Taylor expanded in x around inf 40.6%

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

      1. cancel-sign-sub-inv 40.6%

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

      2. metadata-eval 40.6%

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

      3. *-lft-identity 40.6%

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

   8. Simplified 40.6%

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

   if -1.84999999999999995e-212 < t < 1.30000000000000005e-38

   1. Initial program 60.9%

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

   3. Taylor expanded in y around inf 42.3%

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

      1. div-sub 42.3%

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

      2. associate-*r/ 44.8%

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

      3. associate-/l* 41.8%

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

      4. associate-/r/ 44.9%

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

   5. Simplified 44.9%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{-100}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{-212}:\\ \;\;\;\;x \cdot \left(\frac{z}{a - z} + 1\right)\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-38}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 54.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{if}\;t \leq -20000000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-280}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-41}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- y z) (/ t (- a z)))))
   (if (<= t -20000000000000.0)
     t_1
     (if (<= t -9e-280)
       (+ t (/ a (/ z (- t x))))
       (if (<= t 4.3e-41) (* (- t x) (/ y (- a z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - z) * (t / (a - z));
	double tmp;
	if (t <= -20000000000000.0) {
		tmp = t_1;
	} else if (t <= -9e-280) {
		tmp = t + (a / (z / (t - x)));
	} else if (t <= 4.3e-41) {
		tmp = (t - x) * (y / (a - z));
	} 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) * (t / (a - z))
    if (t <= (-20000000000000.0d0)) then
        tmp = t_1
    else if (t <= (-9d-280)) then
        tmp = t + (a / (z / (t - x)))
    else if (t <= 4.3d-41) then
        tmp = (t - x) * (y / (a - z))
    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) * (t / (a - z));
	double tmp;
	if (t <= -20000000000000.0) {
		tmp = t_1;
	} else if (t <= -9e-280) {
		tmp = t + (a / (z / (t - x)));
	} else if (t <= 4.3e-41) {
		tmp = (t - x) * (y / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - z) * (t / (a - z))
	tmp = 0
	if t <= -20000000000000.0:
		tmp = t_1
	elif t <= -9e-280:
		tmp = t + (a / (z / (t - x)))
	elif t <= 4.3e-41:
		tmp = (t - x) * (y / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - z) * Float64(t / Float64(a - z)))
	tmp = 0.0
	if (t <= -20000000000000.0)
		tmp = t_1;
	elseif (t <= -9e-280)
		tmp = Float64(t + Float64(a / Float64(z / Float64(t - x))));
	elseif (t <= 4.3e-41)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - z) * (t / (a - z));
	tmp = 0.0;
	if (t <= -20000000000000.0)
		tmp = t_1;
	elseif (t <= -9e-280)
		tmp = t + (a / (z / (t - x)));
	elseif (t <= 4.3e-41)
		tmp = (t - x) * (y / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -20000000000000.0], t$95$1, If[LessEqual[t, -9e-280], N[(t + N[(a / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.3e-41], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2e13 or 4.2999999999999999e-41 < t

   1. Initial program 87.5%

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

   3. Taylor expanded in x around 0 49.1%

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

      1. associate-/l* 72.7%

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

      2. associate-/r/ 70.0%

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

   5. Simplified 70.0%

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

   if -2e13 < t < -8.9999999999999991e-280

   1. Initial program 57.7%

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

   3. Taylor expanded in z around inf 53.5%

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

      1. associate--l+ 53.5%

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

      2. distribute-lft-out-- 53.5%

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

      3. div-sub 55.3%

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

      4. mul-1-neg 55.3%

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

      5. unsub-neg 55.3%

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

      6. distribute-rgt-out-- 55.3%

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

      7. associate-/l* 59.0%

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

   5. Simplified 59.0%

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

   6. Taylor expanded in y around 0 42.2%

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

      1. sub-neg 42.2%

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

      2. mul-1-neg 42.2%

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

      3. remove-double-neg 42.2%

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

      4. associate-/l* 45.9%

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

   8. Simplified 45.9%

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

   if -8.9999999999999991e-280 < t < 4.2999999999999999e-41

   1. Initial program 65.8%

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

   3. Taylor expanded in y around inf 45.5%

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

      1. div-sub 45.6%

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

      2. associate-*r/ 46.3%

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

      3. associate-/l* 45.0%

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

      4. associate-/r/ 47.9%

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

   5. Simplified 47.9%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -20000000000000:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-280}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-41}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 39.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+106}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-295}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-140}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+47}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.3e+106)
   t
   (if (<= z 3.2e-295)
     x
     (if (<= z 5.5e-140) (* t (/ y (- a z))) (if (<= z 9.5e+47) x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.3e+106) {
		tmp = t;
	} else if (z <= 3.2e-295) {
		tmp = x;
	} else if (z <= 5.5e-140) {
		tmp = t * (y / (a - z));
	} else if (z <= 9.5e+47) {
		tmp = x;
	} else {
		tmp = 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 (z <= (-3.3d+106)) then
        tmp = t
    else if (z <= 3.2d-295) then
        tmp = x
    else if (z <= 5.5d-140) then
        tmp = t * (y / (a - z))
    else if (z <= 9.5d+47) then
        tmp = x
    else
        tmp = 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 (z <= -3.3e+106) {
		tmp = t;
	} else if (z <= 3.2e-295) {
		tmp = x;
	} else if (z <= 5.5e-140) {
		tmp = t * (y / (a - z));
	} else if (z <= 9.5e+47) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.3e+106:
		tmp = t
	elif z <= 3.2e-295:
		tmp = x
	elif z <= 5.5e-140:
		tmp = t * (y / (a - z))
	elif z <= 9.5e+47:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.3e+106)
		tmp = t;
	elseif (z <= 3.2e-295)
		tmp = x;
	elseif (z <= 5.5e-140)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (z <= 9.5e+47)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.3e+106)
		tmp = t;
	elseif (z <= 3.2e-295)
		tmp = x;
	elseif (z <= 5.5e-140)
		tmp = t * (y / (a - z));
	elseif (z <= 9.5e+47)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.3e+106], t, If[LessEqual[z, 3.2e-295], x, If[LessEqual[z, 5.5e-140], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e+47], x, t]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.30000000000000008e106 or 9.50000000000000001e47 < z

   1. Initial program 55.8%

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

   3. Taylor expanded in z around inf 53.7%

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

   if -3.30000000000000008e106 < z < 3.2e-295 or 5.50000000000000026e-140 < z < 9.50000000000000001e47

   1. Initial program 90.9%

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

   3. Taylor expanded in a around inf 41.9%

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

   if 3.2e-295 < z < 5.50000000000000026e-140

   1. Initial program 85.7%

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

   3. Taylor expanded in y around inf 64.4%

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

      1. div-sub 64.4%

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

      2. associate-*r/ 67.6%

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

      3. associate-/l* 64.4%

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

      4. associate-/r/ 67.6%

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

   5. Simplified 67.6%

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

   6. Taylor expanded in t around inf 53.0%

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

      1. associate-*r/ 53.1%

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

   8. Simplified 53.1%

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

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+106}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-295}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-140}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+47}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 38.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+106}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-297}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-174}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+44}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.2e+106)
   t
   (if (<= z 8.2e-297)
     x
     (if (<= z 8.5e-174) (/ t (/ a y)) (if (<= z 7e+44) x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.2e+106) {
		tmp = t;
	} else if (z <= 8.2e-297) {
		tmp = x;
	} else if (z <= 8.5e-174) {
		tmp = t / (a / y);
	} else if (z <= 7e+44) {
		tmp = x;
	} else {
		tmp = 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 (z <= (-6.2d+106)) then
        tmp = t
    else if (z <= 8.2d-297) then
        tmp = x
    else if (z <= 8.5d-174) then
        tmp = t / (a / y)
    else if (z <= 7d+44) then
        tmp = x
    else
        tmp = 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 (z <= -6.2e+106) {
		tmp = t;
	} else if (z <= 8.2e-297) {
		tmp = x;
	} else if (z <= 8.5e-174) {
		tmp = t / (a / y);
	} else if (z <= 7e+44) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.2e+106:
		tmp = t
	elif z <= 8.2e-297:
		tmp = x
	elif z <= 8.5e-174:
		tmp = t / (a / y)
	elif z <= 7e+44:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.2e+106)
		tmp = t;
	elseif (z <= 8.2e-297)
		tmp = x;
	elseif (z <= 8.5e-174)
		tmp = Float64(t / Float64(a / y));
	elseif (z <= 7e+44)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.2e+106)
		tmp = t;
	elseif (z <= 8.2e-297)
		tmp = x;
	elseif (z <= 8.5e-174)
		tmp = t / (a / y);
	elseif (z <= 7e+44)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.2e+106], t, If[LessEqual[z, 8.2e-297], x, If[LessEqual[z, 8.5e-174], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7e+44], x, t]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.1999999999999999e106 or 6.9999999999999998e44 < z

   1. Initial program 55.8%

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

   3. Taylor expanded in z around inf 53.7%

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

   if -6.1999999999999999e106 < z < 8.2000000000000004e-297 or 8.4999999999999996e-174 < z < 6.9999999999999998e44

   1. Initial program 91.3%

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

   3. Taylor expanded in a around inf 41.9%

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

   if 8.2000000000000004e-297 < z < 8.4999999999999996e-174

   1. Initial program 82.4%

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

   3. Taylor expanded in x around 0 55.5%

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

      1. associate-/l* 59.8%

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

      2. associate-/r/ 55.6%

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

   5. Simplified 55.6%

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

   6. Taylor expanded in z around 0 51.2%

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

      1. associate-/l* 55.5%

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

   8. Simplified 55.5%

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

4. Final simplification 48.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+106}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-297}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-174}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+44}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 76.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{+61} \lor \neg \left(z \leq 2.05 \cdot 10^{+21}\right):\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.45e+61) (not (<= z 2.05e+21)))
   (+ t (/ (- x t) (/ z (- y a))))
   (+ x (/ (- t x) (/ a (- y z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.45e+61) || !(z <= 2.05e+21)) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else {
		tmp = x + ((t - x) / (a / (y - 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 ((z <= (-2.45d+61)) .or. (.not. (z <= 2.05d+21))) then
        tmp = t + ((x - t) / (z / (y - a)))
    else
        tmp = x + ((t - x) / (a / (y - 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 ((z <= -2.45e+61) || !(z <= 2.05e+21)) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else {
		tmp = x + ((t - x) / (a / (y - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.45e+61) or not (z <= 2.05e+21):
		tmp = t + ((x - t) / (z / (y - a)))
	else:
		tmp = x + ((t - x) / (a / (y - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.45e+61) || !(z <= 2.05e+21))
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / Float64(y - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.45e+61) || ~((z <= 2.05e+21)))
		tmp = t + ((x - t) / (z / (y - a)));
	else
		tmp = x + ((t - x) / (a / (y - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.45e+61], N[Not[LessEqual[z, 2.05e+21]], $MachinePrecision]], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.45000000000000013e61 or 2.05e21 < z

   1. Initial program 61.5%

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

   3. Taylor expanded in z around inf 68.3%

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

      1. associate--l+ 68.3%

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

      2. distribute-lft-out-- 68.3%

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

      3. div-sub 68.3%

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

      4. mul-1-neg 68.3%

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

      5. unsub-neg 68.3%

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

      6. distribute-rgt-out-- 68.4%

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

      7. associate-/l* 80.9%

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

   5. Simplified 80.9%

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

   if -2.45000000000000013e61 < z < 2.05e21

   1. Initial program 89.2%

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

   3. Taylor expanded in a around inf 76.3%

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

      1. associate-/l* 82.2%

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

   5. Simplified 82.2%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{+61} \lor \neg \left(z \leq 2.05 \cdot 10^{+21}\right):\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 69.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+106}:\\ \;\;\;\;t - \frac{x \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+20}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.7e+106)
   (- t (/ (* x (- a y)) z))
   (if (<= z 5.4e+20)
     (+ x (* (- y z) (/ (- t x) a)))
     (- t (/ (- t x) (/ z y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.7e+106) {
		tmp = t - ((x * (a - y)) / z);
	} else if (z <= 5.4e+20) {
		tmp = x + ((y - z) * ((t - x) / a));
	} else {
		tmp = t - ((t - x) / (z / 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 (z <= (-3.7d+106)) then
        tmp = t - ((x * (a - y)) / z)
    else if (z <= 5.4d+20) then
        tmp = x + ((y - z) * ((t - x) / a))
    else
        tmp = t - ((t - x) / (z / 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 (z <= -3.7e+106) {
		tmp = t - ((x * (a - y)) / z);
	} else if (z <= 5.4e+20) {
		tmp = x + ((y - z) * ((t - x) / a));
	} else {
		tmp = t - ((t - x) / (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.7e+106:
		tmp = t - ((x * (a - y)) / z)
	elif z <= 5.4e+20:
		tmp = x + ((y - z) * ((t - x) / a))
	else:
		tmp = t - ((t - x) / (z / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.7e+106)
		tmp = Float64(t - Float64(Float64(x * Float64(a - y)) / z));
	elseif (z <= 5.4e+20)
		tmp = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / a)));
	else
		tmp = Float64(t - Float64(Float64(t - x) / Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.7e+106)
		tmp = t - ((x * (a - y)) / z);
	elseif (z <= 5.4e+20)
		tmp = x + ((y - z) * ((t - x) / a));
	else
		tmp = t - ((t - x) / (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.7e+106], N[(t - N[(N[(x * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.4e+20], N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(N[(t - x), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.69999999999999995e106

   1. Initial program 47.9%

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

   3. Taylor expanded in z around inf 77.8%

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

      1. associate--l+ 77.8%

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

      2. distribute-lft-out-- 77.8%

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

      3. div-sub 77.8%

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

      4. mul-1-neg 77.8%

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

      5. unsub-neg 77.8%

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

      6. distribute-rgt-out-- 77.8%

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

      7. associate-/l* 82.2%

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

   5. Simplified 82.2%

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

   6. Taylor expanded in t around 0 78.5%

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

      1. associate-*r/ 78.5%

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

      2. *-commutative 78.5%

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

      3. associate-*r* 78.5%

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

      4. neg-mul-1 78.5%

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

      5. neg-sub0 78.5%

         \[\leadsto t - \frac{\color{blue}{\left(0 - \left(y - a\right)\right)} \cdot x}{z} \]

      6. associate--r- 78.5%

         \[\leadsto t - \frac{\color{blue}{\left(\left(0 - y\right) + a\right)} \cdot x}{z} \]

      7. neg-sub0 78.5%

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

   8. Simplified 78.5%

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

   if -3.69999999999999995e106 < z < 5.4e20

   1. Initial program 90.2%

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

   3. Taylor expanded in a around inf 76.9%

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

   if 5.4e20 < z

   1. Initial program 63.4%

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

   3. Taylor expanded in z around inf 65.3%

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

      1. associate--l+ 65.3%

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

      2. distribute-lft-out-- 65.3%

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

      3. div-sub 65.3%

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

      4. mul-1-neg 65.3%

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

      5. unsub-neg 65.3%

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

      6. distribute-rgt-out-- 65.5%

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

      7. associate-/l* 83.7%

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

   5. Simplified 83.7%

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

   6. Taylor expanded in y around inf 76.1%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+106}:\\ \;\;\;\;t - \frac{x \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+20}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 71.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+106}:\\ \;\;\;\;t - \frac{x \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+21}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.3e+106)
   (- t (/ (* x (- a y)) z))
   (if (<= z 1.9e+21)
     (+ x (/ (- t x) (/ a (- y z))))
     (- t (/ (- t x) (/ z y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.3e+106) {
		tmp = t - ((x * (a - y)) / z);
	} else if (z <= 1.9e+21) {
		tmp = x + ((t - x) / (a / (y - z)));
	} else {
		tmp = t - ((t - x) / (z / 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 (z <= (-3.3d+106)) then
        tmp = t - ((x * (a - y)) / z)
    else if (z <= 1.9d+21) then
        tmp = x + ((t - x) / (a / (y - z)))
    else
        tmp = t - ((t - x) / (z / 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 (z <= -3.3e+106) {
		tmp = t - ((x * (a - y)) / z);
	} else if (z <= 1.9e+21) {
		tmp = x + ((t - x) / (a / (y - z)));
	} else {
		tmp = t - ((t - x) / (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.3e+106:
		tmp = t - ((x * (a - y)) / z)
	elif z <= 1.9e+21:
		tmp = x + ((t - x) / (a / (y - z)))
	else:
		tmp = t - ((t - x) / (z / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.3e+106)
		tmp = Float64(t - Float64(Float64(x * Float64(a - y)) / z));
	elseif (z <= 1.9e+21)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / Float64(y - z))));
	else
		tmp = Float64(t - Float64(Float64(t - x) / Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.3e+106)
		tmp = t - ((x * (a - y)) / z);
	elseif (z <= 1.9e+21)
		tmp = x + ((t - x) / (a / (y - z)));
	else
		tmp = t - ((t - x) / (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.3e+106], N[(t - N[(N[(x * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e+21], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(N[(t - x), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.30000000000000008e106

   1. Initial program 47.9%

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

   3. Taylor expanded in z around inf 77.8%

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

      1. associate--l+ 77.8%

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

      2. distribute-lft-out-- 77.8%

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

      3. div-sub 77.8%

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

      4. mul-1-neg 77.8%

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

      5. unsub-neg 77.8%

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

      6. distribute-rgt-out-- 77.8%

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

      7. associate-/l* 82.2%

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

   5. Simplified 82.2%

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

   6. Taylor expanded in t around 0 78.5%

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

      1. associate-*r/ 78.5%

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

      2. *-commutative 78.5%

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

      3. associate-*r* 78.5%

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

      4. neg-mul-1 78.5%

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

      5. neg-sub0 78.5%

         \[\leadsto t - \frac{\color{blue}{\left(0 - \left(y - a\right)\right)} \cdot x}{z} \]

      6. associate--r- 78.5%

         \[\leadsto t - \frac{\color{blue}{\left(\left(0 - y\right) + a\right)} \cdot x}{z} \]

      7. neg-sub0 78.5%

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

   8. Simplified 78.5%

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

   if -3.30000000000000008e106 < z < 1.9e21

   1. Initial program 90.2%

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

   3. Taylor expanded in a around inf 72.1%

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

      1. associate-/l* 78.8%

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

   5. Simplified 78.8%

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

   if 1.9e21 < z

   1. Initial program 63.4%

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

   3. Taylor expanded in z around inf 65.3%

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

      1. associate--l+ 65.3%

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

      2. distribute-lft-out-- 65.3%

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

      3. div-sub 65.3%

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

      4. mul-1-neg 65.3%

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

      5. unsub-neg 65.3%

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

      6. distribute-rgt-out-- 65.5%

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

      7. associate-/l* 83.7%

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

   5. Simplified 83.7%

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

   6. Taylor expanded in y around inf 76.1%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+106}:\\ \;\;\;\;t - \frac{x \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+21}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 71.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+61}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+23}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.2e+61)
   (+ t (/ (* (- t x) (- a y)) z))
   (if (<= z 1.5e+23)
     (+ x (/ (- t x) (/ a (- y z))))
     (- t (/ (- t x) (/ z y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.2e+61) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (z <= 1.5e+23) {
		tmp = x + ((t - x) / (a / (y - z)));
	} else {
		tmp = t - ((t - x) / (z / 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 (z <= (-2.2d+61)) then
        tmp = t + (((t - x) * (a - y)) / z)
    else if (z <= 1.5d+23) then
        tmp = x + ((t - x) / (a / (y - z)))
    else
        tmp = t - ((t - x) / (z / 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 (z <= -2.2e+61) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (z <= 1.5e+23) {
		tmp = x + ((t - x) / (a / (y - z)));
	} else {
		tmp = t - ((t - x) / (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.2e+61:
		tmp = t + (((t - x) * (a - y)) / z)
	elif z <= 1.5e+23:
		tmp = x + ((t - x) / (a / (y - z)))
	else:
		tmp = t - ((t - x) / (z / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.2e+61)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	elseif (z <= 1.5e+23)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / Float64(y - z))));
	else
		tmp = Float64(t - Float64(Float64(t - x) / Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.2e+61)
		tmp = t + (((t - x) * (a - y)) / z);
	elseif (z <= 1.5e+23)
		tmp = x + ((t - x) / (a / (y - z)));
	else
		tmp = t - ((t - x) / (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.2e+61], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e+23], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(N[(t - x), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.2e61

   1. Initial program 59.0%

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

      1. add-cube-cbrt 58.3%

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

      2. pow3 58.2%

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

   4. Applied egg-rr 58.2%

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

   5. Taylor expanded in z around inf 72.2%

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

      1. associate--l+ 72.2%

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

      2. associate-*r/ 72.2%

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

      3. mul-1-neg 72.2%

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

      4. distribute-rgt-neg-out 72.2%

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

      5. associate-*r/ 72.2%

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

      6. div-sub 72.2%

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

      7. distribute-rgt-neg-out 72.2%

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

      8. mul-1-neg 72.2%

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

      9. distribute-lft-out-- 72.2%

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

      10. associate-*r/ 72.2%

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

      11. mul-1-neg 72.2%

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

      12. unsub-neg 72.2%

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

   7. Simplified 72.2%

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

   if -2.2e61 < z < 1.5e23

   1. Initial program 89.2%

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

   3. Taylor expanded in a around inf 76.3%

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

      1. associate-/l* 82.2%

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

   5. Simplified 82.2%

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

   if 1.5e23 < z

   1. Initial program 63.4%

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

   3. Taylor expanded in z around inf 65.3%

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

      1. associate--l+ 65.3%

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

      2. distribute-lft-out-- 65.3%

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

      3. div-sub 65.3%

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

      4. mul-1-neg 65.3%

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

      5. unsub-neg 65.3%

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

      6. distribute-rgt-out-- 65.5%

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

      7. associate-/l* 83.7%

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

   5. Simplified 83.7%

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

   6. Taylor expanded in y around inf 76.1%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+61}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+23}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 70.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+61} \lor \neg \left(z \leq 1.8 \cdot 10^{+21}\right):\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -7.2e+61) (not (<= z 1.8e+21)))
   (- t (/ (- t x) (/ z y)))
   (+ x (/ y (/ a (- t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.2e+61) || !(z <= 1.8e+21)) {
		tmp = t - ((t - x) / (z / y));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	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 ((z <= (-7.2d+61)) .or. (.not. (z <= 1.8d+21))) then
        tmp = t - ((t - x) / (z / y))
    else
        tmp = x + (y / (a / (t - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.2e+61) || !(z <= 1.8e+21)) {
		tmp = t - ((t - x) / (z / y));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -7.2e+61) or not (z <= 1.8e+21):
		tmp = t - ((t - x) / (z / y))
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -7.2e+61) || !(z <= 1.8e+21))
		tmp = Float64(t - Float64(Float64(t - x) / Float64(z / y)));
	else
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -7.2e+61) || ~((z <= 1.8e+21)))
		tmp = t - ((t - x) / (z / y));
	else
		tmp = x + (y / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -7.2e+61], N[Not[LessEqual[z, 1.8e+21]], $MachinePrecision]], N[(t - N[(N[(t - x), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.20000000000000021e61 or 1.8e21 < z

   1. Initial program 61.5%

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

   3. Taylor expanded in z around inf 68.3%

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

      1. associate--l+ 68.3%

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

      2. distribute-lft-out-- 68.3%

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

      3. div-sub 68.3%

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

      4. mul-1-neg 68.3%

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

      5. unsub-neg 68.3%

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

      6. distribute-rgt-out-- 68.4%

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

      7. associate-/l* 80.9%

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

   5. Simplified 80.9%

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

   6. Taylor expanded in y around inf 72.0%

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

   if -7.20000000000000021e61 < z < 1.8e21

   1. Initial program 89.2%

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

   3. Taylor expanded in z around 0 74.4%

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

      1. associate-/l* 78.0%

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

   5. Simplified 78.0%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+61} \lor \neg \left(z \leq 1.8 \cdot 10^{+21}\right):\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 62.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+134}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+30}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7.2e+134)
   (+ t (/ a (/ z (- t x))))
   (if (<= z 2.05e+30) (+ x (/ y (/ a (- t x)))) (* (- y z) (/ t (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.2e+134) {
		tmp = t + (a / (z / (t - x)));
	} else if (z <= 2.05e+30) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = (y - z) * (t / (a - 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 (z <= (-7.2d+134)) then
        tmp = t + (a / (z / (t - x)))
    else if (z <= 2.05d+30) then
        tmp = x + (y / (a / (t - x)))
    else
        tmp = (y - z) * (t / (a - 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 (z <= -7.2e+134) {
		tmp = t + (a / (z / (t - x)));
	} else if (z <= 2.05e+30) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = (y - z) * (t / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7.2e+134:
		tmp = t + (a / (z / (t - x)))
	elif z <= 2.05e+30:
		tmp = x + (y / (a / (t - x)))
	else:
		tmp = (y - z) * (t / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7.2e+134)
		tmp = Float64(t + Float64(a / Float64(z / Float64(t - x))));
	elseif (z <= 2.05e+30)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	else
		tmp = Float64(Float64(y - z) * Float64(t / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -7.2e+134)
		tmp = t + (a / (z / (t - x)));
	elseif (z <= 2.05e+30)
		tmp = x + (y / (a / (t - x)));
	else
		tmp = (y - z) * (t / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7.2e+134], N[(t + N[(a / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.05e+30], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.19999999999999976e134

   1. Initial program 42.3%

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

   3. Taylor expanded in z around inf 79.3%

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

      1. associate--l+ 79.3%

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

      2. distribute-lft-out-- 79.3%

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

      3. div-sub 79.3%

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

      4. mul-1-neg 79.3%

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

      5. unsub-neg 79.3%

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

      6. distribute-rgt-out-- 79.3%

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

      7. associate-/l* 82.9%

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

   5. Simplified 82.9%

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

   6. Taylor expanded in y around 0 67.6%

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

      1. sub-neg 67.6%

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

      2. mul-1-neg 67.6%

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

      3. remove-double-neg 67.6%

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

      4. associate-/l* 73.3%

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

   8. Simplified 73.3%

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

   if -7.19999999999999976e134 < z < 2.05000000000000003e30

   1. Initial program 90.1%

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

   3. Taylor expanded in z around 0 69.0%

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

      1. associate-/l* 72.7%

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

   5. Simplified 72.7%

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

   if 2.05000000000000003e30 < z

   1. Initial program 61.8%

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

   3. Taylor expanded in x around 0 48.9%

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

      1. associate-/l* 74.1%

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

      2. associate-/r/ 64.3%

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

   5. Simplified 64.3%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+134}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+30}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 67.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+106}:\\ \;\;\;\;t - \frac{x \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+21}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.3e+106)
   (- t (/ (* x (- a y)) z))
   (if (<= z 6.8e+21) (+ x (/ y (/ a (- t x)))) (- t (/ (- t x) (/ z y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.3e+106) {
		tmp = t - ((x * (a - y)) / z);
	} else if (z <= 6.8e+21) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t - ((t - x) / (z / 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 (z <= (-3.3d+106)) then
        tmp = t - ((x * (a - y)) / z)
    else if (z <= 6.8d+21) then
        tmp = x + (y / (a / (t - x)))
    else
        tmp = t - ((t - x) / (z / 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 (z <= -3.3e+106) {
		tmp = t - ((x * (a - y)) / z);
	} else if (z <= 6.8e+21) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t - ((t - x) / (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.3e+106:
		tmp = t - ((x * (a - y)) / z)
	elif z <= 6.8e+21:
		tmp = x + (y / (a / (t - x)))
	else:
		tmp = t - ((t - x) / (z / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.3e+106)
		tmp = Float64(t - Float64(Float64(x * Float64(a - y)) / z));
	elseif (z <= 6.8e+21)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	else
		tmp = Float64(t - Float64(Float64(t - x) / Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.3e+106)
		tmp = t - ((x * (a - y)) / z);
	elseif (z <= 6.8e+21)
		tmp = x + (y / (a / (t - x)));
	else
		tmp = t - ((t - x) / (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.3e+106], N[(t - N[(N[(x * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e+21], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(N[(t - x), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.30000000000000008e106

   1. Initial program 47.9%

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

   3. Taylor expanded in z around inf 77.8%

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

      1. associate--l+ 77.8%

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

      2. distribute-lft-out-- 77.8%

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

      3. div-sub 77.8%

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

      4. mul-1-neg 77.8%

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

      5. unsub-neg 77.8%

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

      6. distribute-rgt-out-- 77.8%

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

      7. associate-/l* 82.2%

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

   5. Simplified 82.2%

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

   6. Taylor expanded in t around 0 78.5%

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

      1. associate-*r/ 78.5%

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

      2. *-commutative 78.5%

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

      3. associate-*r* 78.5%

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

      4. neg-mul-1 78.5%

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

      5. neg-sub0 78.5%

         \[\leadsto t - \frac{\color{blue}{\left(0 - \left(y - a\right)\right)} \cdot x}{z} \]

      6. associate--r- 78.5%

         \[\leadsto t - \frac{\color{blue}{\left(\left(0 - y\right) + a\right)} \cdot x}{z} \]

      7. neg-sub0 78.5%

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

   8. Simplified 78.5%

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

   if -3.30000000000000008e106 < z < 6.8e21

   1. Initial program 90.2%

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

   3. Taylor expanded in z around 0 71.1%

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

      1. associate-/l* 75.1%

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

   5. Simplified 75.1%

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

   if 6.8e21 < z

   1. Initial program 63.4%

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

   3. Taylor expanded in z around inf 65.3%

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

      1. associate--l+ 65.3%

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

      2. distribute-lft-out-- 65.3%

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

      3. div-sub 65.3%

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

      4. mul-1-neg 65.3%

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

      5. unsub-neg 65.3%

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

      6. distribute-rgt-out-- 65.5%

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

      7. associate-/l* 83.7%

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

   5. Simplified 83.7%

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

   6. Taylor expanded in y around inf 76.1%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+106}:\\ \;\;\;\;t - \frac{x \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+21}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 38.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+106}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+42}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.2e+106) t (if (<= z 3.3e+42) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.2e+106) {
		tmp = t;
	} else if (z <= 3.3e+42) {
		tmp = x;
	} else {
		tmp = 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 (z <= (-9.2d+106)) then
        tmp = t
    else if (z <= 3.3d+42) then
        tmp = x
    else
        tmp = 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 (z <= -9.2e+106) {
		tmp = t;
	} else if (z <= 3.3e+42) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9.2e+106:
		tmp = t
	elif z <= 3.3e+42:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.2e+106)
		tmp = t;
	elseif (z <= 3.3e+42)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -9.2e+106)
		tmp = t;
	elseif (z <= 3.3e+42)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.2e+106], t, If[LessEqual[z, 3.3e+42], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -9.2000000000000008e106 or 3.2999999999999999e42 < z

   1. Initial program 55.8%

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

   3. Taylor expanded in z around inf 53.7%

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

   if -9.2000000000000008e106 < z < 3.2999999999999999e42

   1. Initial program 90.0%

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

   3. Taylor expanded in a around inf 38.3%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 44.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+106}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+42}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 25.6% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ t \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 t)

C

double code(double x, double y, double z, double t, double a) {
	return 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 = t
end function

Java

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

Python

def code(x, y, z, t, a):
	return t

Julia

function code(x, y, z, t, a)
	return t
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = t;
end

Wolfram

code[x_, y_, z_, t_, a_] := t

Derivation

1. Initial program 75.3%

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

3. Taylor expanded in z around inf 27.9%

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

4. Final simplification 27.9%

   \[\leadsto t \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024026 
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  :precision binary64
  (+ x (* (- y z) (/ (- t x) (- a z)))))