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

Percentage Accurate: 68.5% → 88.9%

Time: 19.6s

Alternatives: 23

Speedup: 0.7×

Specification

Math

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

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(Float64(y - z) * 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[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 68.5% accurate, 1.0× speedup

Math

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

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(Float64(y - z) * 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[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 88.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+154} \lor \neg \left(z \leq 1.15 \cdot 10^{+186}\right):\\ \;\;\;\;t + \left(y - a\right) \cdot \left(\left(t - x\right) \cdot \frac{-1}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8.2e+154) (not (<= z 1.15e+186)))
   (+ t (* (- y a) (* (- t x) (/ -1.0 z))))
   (fma (- t x) (/ (- y z) (- a z)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.2e+154) || !(z <= 1.15e+186)) {
		tmp = t + ((y - a) * ((t - x) * (-1.0 / z)));
	} else {
		tmp = fma((t - x), ((y - z) / (a - z)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8.2e+154) || !(z <= 1.15e+186))
		tmp = Float64(t + Float64(Float64(y - a) * Float64(Float64(t - x) * Float64(-1.0 / z))));
	else
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8.2e+154], N[Not[LessEqual[z, 1.15e+186]], $MachinePrecision]], N[(t + N[(N[(y - a), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.2e154 or 1.15000000000000007e186 < z

   1. Initial program 23.6%

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

      1. associate-/l* 49.8%

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

   3. Simplified 49.8%

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

   5. Taylor expanded in z around inf 60.4%

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

      1. associate--l+ 60.4%

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

      2. associate-*r/ 60.4%

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

      3. associate-*r/ 60.4%

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

      4. mul-1-neg 60.4%

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

      5. div-sub 60.4%

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

      6. mul-1-neg 60.4%

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

      7. distribute-lft-out-- 60.4%

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

      8. associate-*r/ 60.4%

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

      9. mul-1-neg 60.4%

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

      10. unsub-neg 60.4%

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

      11. distribute-rgt-out-- 60.7%

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

   7. Simplified 60.7%

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

      1. div-inv 60.7%

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

      2. *-commutative 60.7%

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

      3. associate-*l* 89.0%

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

   9. Applied egg-rr 89.0%

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

   if -8.2e154 < z < 1.15000000000000007e186

   1. Initial program 83.1%

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

      1. +-commutative 83.1%

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

      2. *-commutative 83.1%

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

      3. associate-/l* 93.8%

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

      4. fma-define 93.7%

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

   3. Simplified 93.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+154} \lor \neg \left(z \leq 1.15 \cdot 10^{+186}\right):\\ \;\;\;\;t + \left(y - a\right) \cdot \left(\left(t - x\right) \cdot \frac{-1}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 88.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{t - x}{z - a} \cdot \left(z - y\right)\\ t_2 := x - \frac{\left(t - x\right) \cdot \left(y - z\right)}{z - a}\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{-265}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t - \frac{x \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;t\_2 \leq 10^{+167}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ (- t x) (- z a)) (- z y))))
        (t_2 (- x (/ (* (- t x) (- y z)) (- z a)))))
   (if (<= t_2 -4e-265)
     t_1
     (if (<= t_2 0.0)
       (- t (/ (* x (- a y)) z))
       (if (<= t_2 1e+167) t_2 t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((t - x) / (z - a)) * (z - y));
	double t_2 = x - (((t - x) * (y - z)) / (z - a));
	double tmp;
	if (t_2 <= -4e-265) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t - ((x * (a - y)) / z);
	} else if (t_2 <= 1e+167) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (((t - x) / (z - a)) * (z - y))
    t_2 = x - (((t - x) * (y - z)) / (z - a))
    if (t_2 <= (-4d-265)) then
        tmp = t_1
    else if (t_2 <= 0.0d0) then
        tmp = t - ((x * (a - y)) / z)
    else if (t_2 <= 1d+167) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((t - x) / (z - a)) * (z - y));
	double t_2 = x - (((t - x) * (y - z)) / (z - a));
	double tmp;
	if (t_2 <= -4e-265) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t - ((x * (a - y)) / z);
	} else if (t_2 <= 1e+167) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((t - x) / (z - a)) * (z - y))
	t_2 = x - (((t - x) * (y - z)) / (z - a))
	tmp = 0
	if t_2 <= -4e-265:
		tmp = t_1
	elif t_2 <= 0.0:
		tmp = t - ((x * (a - y)) / z)
	elif t_2 <= 1e+167:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(t - x) / Float64(z - a)) * Float64(z - y)))
	t_2 = Float64(x - Float64(Float64(Float64(t - x) * Float64(y - z)) / Float64(z - a)))
	tmp = 0.0
	if (t_2 <= -4e-265)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(t - Float64(Float64(x * Float64(a - y)) / z));
	elseif (t_2 <= 1e+167)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((t - x) / (z - a)) * (z - y));
	t_2 = x - (((t - x) * (y - z)) / (z - a));
	tmp = 0.0;
	if (t_2 <= -4e-265)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = t - ((x * (a - y)) / z);
	elseif (t_2 <= 1e+167)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(t - x), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(N[(N[(t - x), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -4e-265], t$95$1, If[LessEqual[t$95$2, 0.0], N[(t - N[(N[(x * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+167], t$95$2, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -3.99999999999999994e-265 or 1e167 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 65.3%

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

      1. associate-/l* 86.8%

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

   3. Simplified 86.8%

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

   if -3.99999999999999994e-265 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 6.5%

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

      1. associate-/l* 5.5%

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

   3. Simplified 5.5%

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

   5. Taylor expanded in z around inf 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. associate-*r/ 99.9%

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

      4. mul-1-neg 99.9%

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

      5. div-sub 99.9%

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

      6. mul-1-neg 99.9%

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

      7. distribute-lft-out-- 99.9%

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

      8. associate-*r/ 99.9%

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

      9. mul-1-neg 99.9%

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

      10. unsub-neg 99.9%

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

      11. distribute-rgt-out-- 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in t around 0 99.9%

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

      1. associate-*r/ 99.9%

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

      2. mul-1-neg 99.9%

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

      3. distribute-lft-neg-out 99.9%

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

      4. *-commutative 99.9%

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

   10. Simplified 99.9%

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

   if 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 1e167

   1. Initial program 96.4%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(t - x\right) \cdot \left(y - z\right)}{z - a} \leq -4 \cdot 10^{-265}:\\ \;\;\;\;x + \frac{t - x}{z - a} \cdot \left(z - y\right)\\ \mathbf{elif}\;x - \frac{\left(t - x\right) \cdot \left(y - z\right)}{z - a} \leq 0:\\ \;\;\;\;t - \frac{x \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;x - \frac{\left(t - x\right) \cdot \left(y - z\right)}{z - a} \leq 10^{+167}:\\ \;\;\;\;x - \frac{\left(t - x\right) \cdot \left(y - z\right)}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{z - a} \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{\left(t - x\right) \cdot \left(y - z\right)}{z - a}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{-265} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;x - \frac{t - x}{\frac{a - z}{z - y}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{x \cdot \left(a - y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* (- t x) (- y z)) (- z a)))))
   (if (or (<= t_1 -4e-265) (not (<= t_1 0.0)))
     (- x (/ (- t x) (/ (- a z) (- z y))))
     (- t (/ (* x (- a y)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((t - x) * (y - z)) / (z - a));
	double tmp;
	if ((t_1 <= -4e-265) || !(t_1 <= 0.0)) {
		tmp = x - ((t - x) / ((a - z) / (z - y)));
	} else {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = x - (((t - x) * (y - z)) / (z - a))
    if ((t_1 <= (-4d-265)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x - ((t - x) / ((a - z) / (z - y)))
    else
        tmp = 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 t_1 = x - (((t - x) * (y - z)) / (z - a));
	double tmp;
	if ((t_1 <= -4e-265) || !(t_1 <= 0.0)) {
		tmp = x - ((t - x) / ((a - z) / (z - y)));
	} else {
		tmp = t - ((x * (a - y)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (((t - x) * (y - z)) / (z - a))
	tmp = 0
	if (t_1 <= -4e-265) or not (t_1 <= 0.0):
		tmp = x - ((t - x) / ((a - z) / (z - y)))
	else:
		tmp = t - ((x * (a - y)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(t - x) * Float64(y - z)) / Float64(z - a)))
	tmp = 0.0
	if ((t_1 <= -4e-265) || !(t_1 <= 0.0))
		tmp = Float64(x - Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(z - y))));
	else
		tmp = Float64(t - Float64(Float64(x * Float64(a - y)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (((t - x) * (y - z)) / (z - a));
	tmp = 0.0;
	if ((t_1 <= -4e-265) || ~((t_1 <= 0.0)))
		tmp = x - ((t - x) / ((a - z) / (z - y)));
	else
		tmp = t - ((x * (a - y)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(t - x), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -4e-265], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x - N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(N[(x * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -3.99999999999999994e-265 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 72.3%

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

      1. associate-/l* 87.0%

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

   3. Simplified 87.0%

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

      1. *-commutative 87.0%

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

      2. associate-*l/ 72.3%

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

      3. associate-*r/ 89.7%

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

      4. clear-num 89.6%

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

      5. un-div-inv 89.6%

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

   6. Applied egg-rr 89.6%

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

   if -3.99999999999999994e-265 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 6.5%

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

      1. associate-/l* 5.5%

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

   3. Simplified 5.5%

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

   5. Taylor expanded in z around inf 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. associate-*r/ 99.9%

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

      4. mul-1-neg 99.9%

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

      5. div-sub 99.9%

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

      6. mul-1-neg 99.9%

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

      7. distribute-lft-out-- 99.9%

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

      8. associate-*r/ 99.9%

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

      9. mul-1-neg 99.9%

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

      10. unsub-neg 99.9%

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

      11. distribute-rgt-out-- 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in t around 0 99.9%

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

      1. associate-*r/ 99.9%

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

      2. mul-1-neg 99.9%

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

      3. distribute-lft-neg-out 99.9%

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

      4. *-commutative 99.9%

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

   10. Simplified 99.9%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{\left(t - x\right) \cdot \left(y - z\right)}{z - a} \leq -4 \cdot 10^{-265} \lor \neg \left(x - \frac{\left(t - x\right) \cdot \left(y - z\right)}{z - a} \leq 0\right):\\ \;\;\;\;x - \frac{t - x}{\frac{a - z}{z - y}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{x \cdot \left(a - y\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 36.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -3.3 \cdot 10^{+46}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.32 \cdot 10^{-50}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -1.08 \cdot 10^{-156}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-272}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-298}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.75 \cdot 10^{-278}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 85:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y a))))
   (if (<= a -3.3e+46)
     x
     (if (<= a -2.9e+24)
       t_1
       (if (<= a -1.32e-50)
         t
         (if (<= a -1.08e-156)
           t_1
           (if (<= a -2.9e-272)
             (* x (/ y z))
             (if (<= a -2.8e-298)
               t
               (if (<= a 2.75e-278) (/ t (/ a y)) (if (<= a 85.0) t x))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (a <= -3.3e+46) {
		tmp = x;
	} else if (a <= -2.9e+24) {
		tmp = t_1;
	} else if (a <= -1.32e-50) {
		tmp = t;
	} else if (a <= -1.08e-156) {
		tmp = t_1;
	} else if (a <= -2.9e-272) {
		tmp = x * (y / z);
	} else if (a <= -2.8e-298) {
		tmp = t;
	} else if (a <= 2.75e-278) {
		tmp = t / (a / y);
	} else if (a <= 85.0) {
		tmp = t;
	} else {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = t * (y / a)
    if (a <= (-3.3d+46)) then
        tmp = x
    else if (a <= (-2.9d+24)) then
        tmp = t_1
    else if (a <= (-1.32d-50)) then
        tmp = t
    else if (a <= (-1.08d-156)) then
        tmp = t_1
    else if (a <= (-2.9d-272)) then
        tmp = x * (y / z)
    else if (a <= (-2.8d-298)) then
        tmp = t
    else if (a <= 2.75d-278) then
        tmp = t / (a / y)
    else if (a <= 85.0d0) then
        tmp = t
    else
        tmp = x
    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 * (y / a);
	double tmp;
	if (a <= -3.3e+46) {
		tmp = x;
	} else if (a <= -2.9e+24) {
		tmp = t_1;
	} else if (a <= -1.32e-50) {
		tmp = t;
	} else if (a <= -1.08e-156) {
		tmp = t_1;
	} else if (a <= -2.9e-272) {
		tmp = x * (y / z);
	} else if (a <= -2.8e-298) {
		tmp = t;
	} else if (a <= 2.75e-278) {
		tmp = t / (a / y);
	} else if (a <= 85.0) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / a)
	tmp = 0
	if a <= -3.3e+46:
		tmp = x
	elif a <= -2.9e+24:
		tmp = t_1
	elif a <= -1.32e-50:
		tmp = t
	elif a <= -1.08e-156:
		tmp = t_1
	elif a <= -2.9e-272:
		tmp = x * (y / z)
	elif a <= -2.8e-298:
		tmp = t
	elif a <= 2.75e-278:
		tmp = t / (a / y)
	elif a <= 85.0:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / a))
	tmp = 0.0
	if (a <= -3.3e+46)
		tmp = x;
	elseif (a <= -2.9e+24)
		tmp = t_1;
	elseif (a <= -1.32e-50)
		tmp = t;
	elseif (a <= -1.08e-156)
		tmp = t_1;
	elseif (a <= -2.9e-272)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= -2.8e-298)
		tmp = t;
	elseif (a <= 2.75e-278)
		tmp = Float64(t / Float64(a / y));
	elseif (a <= 85.0)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / a);
	tmp = 0.0;
	if (a <= -3.3e+46)
		tmp = x;
	elseif (a <= -2.9e+24)
		tmp = t_1;
	elseif (a <= -1.32e-50)
		tmp = t;
	elseif (a <= -1.08e-156)
		tmp = t_1;
	elseif (a <= -2.9e-272)
		tmp = x * (y / z);
	elseif (a <= -2.8e-298)
		tmp = t;
	elseif (a <= 2.75e-278)
		tmp = t / (a / y);
	elseif (a <= 85.0)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.3e+46], x, If[LessEqual[a, -2.9e+24], t$95$1, If[LessEqual[a, -1.32e-50], t, If[LessEqual[a, -1.08e-156], t$95$1, If[LessEqual[a, -2.9e-272], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.8e-298], t, If[LessEqual[a, 2.75e-278], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 85.0], t, x]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -3.2999999999999998e46 or 85 < a

   1. Initial program 70.5%

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

      1. associate-/l* 85.2%

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

   3. Simplified 85.2%

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

   5. Taylor expanded in a around inf 46.2%

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

   if -3.2999999999999998e46 < a < -2.89999999999999979e24 or -1.31999999999999989e-50 < a < -1.08e-156

   1. Initial program 93.2%

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

      1. associate-/l* 90.1%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in y around -inf 80.6%

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

   6. Taylor expanded in a around inf 63.4%

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

   7. Taylor expanded in t around inf 48.1%

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

      1. associate-/l* 54.4%

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

   9. Simplified 54.4%

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

   if -2.89999999999999979e24 < a < -1.31999999999999989e-50 or -2.89999999999999995e-272 < a < -2.79999999999999992e-298 or 2.74999999999999995e-278 < a < 85

   1. Initial program 56.9%

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

      1. associate-/l* 75.7%

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

   3. Simplified 75.7%

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

   5. Taylor expanded in z around inf 49.7%

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

   if -1.08e-156 < a < -2.89999999999999995e-272

   1. Initial program 56.3%

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

      1. associate-/l* 71.4%

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

   3. Simplified 71.4%

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

   5. Taylor expanded in x around -inf 57.1%

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

      1. associate-*r* 57.1%

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

      2. neg-mul-1 57.1%

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

   7. Simplified 57.1%

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

   8. Taylor expanded in a around 0 52.2%

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

      1. associate-/l* 52.3%

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

   10. Simplified 52.3%

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

   if -2.79999999999999992e-298 < a < 2.74999999999999995e-278

   1. Initial program 86.5%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around -inf 86.5%

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

   6. Taylor expanded in a around inf 58.4%

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

   7. Taylor expanded in t around inf 59.6%

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

      1. associate-/l* 73.0%

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

   9. Simplified 73.0%

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

       1. clear-num 73.0%

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

       2. un-div-inv 73.0%

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

   11. Applied egg-rr 73.0%

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

Alternative 5: 59.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a - z}\\ t_2 := x - x \cdot \frac{y}{a}\\ \mathbf{if}\;x \leq -9.5 \cdot 10^{+181}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -9.2 \cdot 10^{+97}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{+37}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{-33}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+148}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) (- a z)))) (t_2 (- x (* x (/ y a)))))
   (if (<= x -9.5e+181)
     t_2
     (if (<= x -9.2e+97)
       t_1
       (if (<= x -2.8e+37)
         t_2
         (if (<= x 1.02e-33)
           (* t (/ (- y z) (- a z)))
           (if (<= x 5e+148) t_1 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 = x - (x * (y / a));
	double tmp;
	if (x <= -9.5e+181) {
		tmp = t_2;
	} else if (x <= -9.2e+97) {
		tmp = t_1;
	} else if (x <= -2.8e+37) {
		tmp = t_2;
	} else if (x <= 1.02e-33) {
		tmp = t * ((y - z) / (a - z));
	} else if (x <= 5e+148) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((t - x) / (a - z))
    t_2 = x - (x * (y / a))
    if (x <= (-9.5d+181)) then
        tmp = t_2
    else if (x <= (-9.2d+97)) then
        tmp = t_1
    else if (x <= (-2.8d+37)) then
        tmp = t_2
    else if (x <= 1.02d-33) then
        tmp = t * ((y - z) / (a - z))
    else if (x <= 5d+148) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double t_2 = x - (x * (y / a));
	double tmp;
	if (x <= -9.5e+181) {
		tmp = t_2;
	} else if (x <= -9.2e+97) {
		tmp = t_1;
	} else if (x <= -2.8e+37) {
		tmp = t_2;
	} else if (x <= 1.02e-33) {
		tmp = t * ((y - z) / (a - z));
	} else if (x <= 5e+148) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / (a - z))
	t_2 = x - (x * (y / a))
	tmp = 0
	if x <= -9.5e+181:
		tmp = t_2
	elif x <= -9.2e+97:
		tmp = t_1
	elif x <= -2.8e+37:
		tmp = t_2
	elif x <= 1.02e-33:
		tmp = t * ((y - z) / (a - z))
	elif x <= 5e+148:
		tmp = t_1
	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(x - Float64(x * Float64(y / a)))
	tmp = 0.0
	if (x <= -9.5e+181)
		tmp = t_2;
	elseif (x <= -9.2e+97)
		tmp = t_1;
	elseif (x <= -2.8e+37)
		tmp = t_2;
	elseif (x <= 1.02e-33)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (x <= 5e+148)
		tmp = t_1;
	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 = x - (x * (y / a));
	tmp = 0.0;
	if (x <= -9.5e+181)
		tmp = t_2;
	elseif (x <= -9.2e+97)
		tmp = t_1;
	elseif (x <= -2.8e+37)
		tmp = t_2;
	elseif (x <= 1.02e-33)
		tmp = t * ((y - z) / (a - z));
	elseif (x <= 5e+148)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9.5e+181], t$95$2, If[LessEqual[x, -9.2e+97], t$95$1, If[LessEqual[x, -2.8e+37], t$95$2, If[LessEqual[x, 1.02e-33], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5e+148], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.50000000000000032e181 or -9.20000000000000022e97 < x < -2.7999999999999998e37 or 5.00000000000000024e148 < x

   1. Initial program 58.1%

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

      1. associate-/l* 75.8%

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

   3. Simplified 75.8%

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

   5. Taylor expanded in x around -inf 70.9%

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

      1. associate-*r* 70.9%

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

      2. neg-mul-1 70.9%

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

   7. Simplified 70.9%

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

   8. Taylor expanded in z around 0 61.3%

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

   9. Taylor expanded in y around 0 56.0%

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

       1. neg-mul-1 56.0%

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

       2. unsub-neg 56.0%

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

       3. associate-/l* 61.4%

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

   11. Simplified 61.4%

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

   if -9.50000000000000032e181 < x < -9.20000000000000022e97 or 1.02e-33 < x < 5.00000000000000024e148

   1. Initial program 57.8%

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

      1. associate-/l* 80.8%

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

   3. Simplified 80.8%

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

   5. Taylor expanded in y around inf 66.6%

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

      1. div-sub 66.6%

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

   7. Simplified 66.6%

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

   if -2.7999999999999998e37 < x < 1.02e-33

   1. Initial program 78.6%

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

      1. associate-/l* 86.4%

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

   3. Simplified 86.4%

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

   5. Taylor expanded in x around 0 62.8%

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

      1. associate-/l* 75.7%

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

   7. Simplified 75.7%

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

Alternative 6: 48.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - x \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+42}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-90}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-233}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-200}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+79}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* x (/ y a)))))
   (if (<= z -1.8e+42)
     t
     (if (<= z -8.2e-90)
       (/ (* y (- x t)) z)
       (if (<= z 2.8e-233)
         t_1
         (if (<= z 2.3e-200) (/ t (/ a y)) (if (<= z 5e+79) t_1 t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x * (y / a));
	double tmp;
	if (z <= -1.8e+42) {
		tmp = t;
	} else if (z <= -8.2e-90) {
		tmp = (y * (x - t)) / z;
	} else if (z <= 2.8e-233) {
		tmp = t_1;
	} else if (z <= 2.3e-200) {
		tmp = t / (a / y);
	} else if (z <= 5e+79) {
		tmp = t_1;
	} 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 = x - (x * (y / a))
    if (z <= (-1.8d+42)) then
        tmp = t
    else if (z <= (-8.2d-90)) then
        tmp = (y * (x - t)) / z
    else if (z <= 2.8d-233) then
        tmp = t_1
    else if (z <= 2.3d-200) then
        tmp = t / (a / y)
    else if (z <= 5d+79) then
        tmp = t_1
    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 = x - (x * (y / a));
	double tmp;
	if (z <= -1.8e+42) {
		tmp = t;
	} else if (z <= -8.2e-90) {
		tmp = (y * (x - t)) / z;
	} else if (z <= 2.8e-233) {
		tmp = t_1;
	} else if (z <= 2.3e-200) {
		tmp = t / (a / y);
	} else if (z <= 5e+79) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (x * (y / a))
	tmp = 0
	if z <= -1.8e+42:
		tmp = t
	elif z <= -8.2e-90:
		tmp = (y * (x - t)) / z
	elif z <= 2.8e-233:
		tmp = t_1
	elif z <= 2.3e-200:
		tmp = t / (a / y)
	elif z <= 5e+79:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(x * Float64(y / a)))
	tmp = 0.0
	if (z <= -1.8e+42)
		tmp = t;
	elseif (z <= -8.2e-90)
		tmp = Float64(Float64(y * Float64(x - t)) / z);
	elseif (z <= 2.8e-233)
		tmp = t_1;
	elseif (z <= 2.3e-200)
		tmp = Float64(t / Float64(a / y));
	elseif (z <= 5e+79)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (x * (y / a));
	tmp = 0.0;
	if (z <= -1.8e+42)
		tmp = t;
	elseif (z <= -8.2e-90)
		tmp = (y * (x - t)) / z;
	elseif (z <= 2.8e-233)
		tmp = t_1;
	elseif (z <= 2.3e-200)
		tmp = t / (a / y);
	elseif (z <= 5e+79)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.8e+42], t, If[LessEqual[z, -8.2e-90], N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 2.8e-233], t$95$1, If[LessEqual[z, 2.3e-200], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e+79], t$95$1, t]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.8e42 or 5e79 < z

   1. Initial program 36.8%

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

      1. associate-/l* 64.7%

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

   3. Simplified 64.7%

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

   5. Taylor expanded in z around inf 48.0%

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

   if -1.8e42 < z < -8.2000000000000007e-90

   1. Initial program 84.1%

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

      1. associate-/l* 84.1%

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

   3. Simplified 84.1%

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

   5. Taylor expanded in y around -inf 71.9%

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

   6. Taylor expanded in a around 0 51.3%

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

      1. associate-*r/ 51.3%

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

      2. associate-*r* 51.3%

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

      3. neg-mul-1 51.3%

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

   8. Simplified 51.3%

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

   if -8.2000000000000007e-90 < z < 2.8000000000000001e-233 or 2.30000000000000007e-200 < z < 5e79

   1. Initial program 91.6%

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

      1. associate-/l* 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in x around -inf 60.8%

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

      1. associate-*r* 60.8%

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

      2. neg-mul-1 60.8%

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

   7. Simplified 60.8%

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

   8. Taylor expanded in z around 0 55.6%

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

   9. Taylor expanded in y around 0 52.1%

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

       1. neg-mul-1 52.1%

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

       2. unsub-neg 52.1%

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

       3. associate-/l* 55.6%

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

   11. Simplified 55.6%

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

   if 2.8000000000000001e-233 < z < 2.30000000000000007e-200

   1. Initial program 99.8%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around -inf 86.7%

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

   6. Taylor expanded in a around inf 74.2%

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

   7. Taylor expanded in t around inf 63.2%

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

      1. associate-/l* 86.4%

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

   9. Simplified 86.4%

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

       1. clear-num 86.6%

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

       2. un-div-inv 86.8%

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

   11. Applied egg-rr 86.8%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+42}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-90}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-233}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-200}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+79}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 37.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -1 \cdot 10^{+44}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-51}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-156}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-272}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 520:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y a))))
   (if (<= a -1e+44)
     x
     (if (<= a -1.3e+25)
       t_1
       (if (<= a -3.4e-51)
         t
         (if (<= a -5.5e-156)
           t_1
           (if (<= a -3.1e-272) (* x (/ y z)) (if (<= a 520.0) t x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (a <= -1e+44) {
		tmp = x;
	} else if (a <= -1.3e+25) {
		tmp = t_1;
	} else if (a <= -3.4e-51) {
		tmp = t;
	} else if (a <= -5.5e-156) {
		tmp = t_1;
	} else if (a <= -3.1e-272) {
		tmp = x * (y / z);
	} else if (a <= 520.0) {
		tmp = t;
	} else {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = t * (y / a)
    if (a <= (-1d+44)) then
        tmp = x
    else if (a <= (-1.3d+25)) then
        tmp = t_1
    else if (a <= (-3.4d-51)) then
        tmp = t
    else if (a <= (-5.5d-156)) then
        tmp = t_1
    else if (a <= (-3.1d-272)) then
        tmp = x * (y / z)
    else if (a <= 520.0d0) then
        tmp = t
    else
        tmp = x
    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 * (y / a);
	double tmp;
	if (a <= -1e+44) {
		tmp = x;
	} else if (a <= -1.3e+25) {
		tmp = t_1;
	} else if (a <= -3.4e-51) {
		tmp = t;
	} else if (a <= -5.5e-156) {
		tmp = t_1;
	} else if (a <= -3.1e-272) {
		tmp = x * (y / z);
	} else if (a <= 520.0) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / a)
	tmp = 0
	if a <= -1e+44:
		tmp = x
	elif a <= -1.3e+25:
		tmp = t_1
	elif a <= -3.4e-51:
		tmp = t
	elif a <= -5.5e-156:
		tmp = t_1
	elif a <= -3.1e-272:
		tmp = x * (y / z)
	elif a <= 520.0:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / a))
	tmp = 0.0
	if (a <= -1e+44)
		tmp = x;
	elseif (a <= -1.3e+25)
		tmp = t_1;
	elseif (a <= -3.4e-51)
		tmp = t;
	elseif (a <= -5.5e-156)
		tmp = t_1;
	elseif (a <= -3.1e-272)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 520.0)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / a);
	tmp = 0.0;
	if (a <= -1e+44)
		tmp = x;
	elseif (a <= -1.3e+25)
		tmp = t_1;
	elseif (a <= -3.4e-51)
		tmp = t;
	elseif (a <= -5.5e-156)
		tmp = t_1;
	elseif (a <= -3.1e-272)
		tmp = x * (y / z);
	elseif (a <= 520.0)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1e+44], x, If[LessEqual[a, -1.3e+25], t$95$1, If[LessEqual[a, -3.4e-51], t, If[LessEqual[a, -5.5e-156], t$95$1, If[LessEqual[a, -3.1e-272], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 520.0], t, x]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.0000000000000001e44 or 520 < a

   1. Initial program 70.5%

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

      1. associate-/l* 85.2%

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

   3. Simplified 85.2%

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

   5. Taylor expanded in a around inf 46.2%

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

   if -1.0000000000000001e44 < a < -1.2999999999999999e25 or -3.40000000000000003e-51 < a < -5.4999999999999998e-156

   1. Initial program 93.2%

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

      1. associate-/l* 90.1%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in y around -inf 80.6%

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

   6. Taylor expanded in a around inf 63.4%

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

   7. Taylor expanded in t around inf 48.1%

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

      1. associate-/l* 54.4%

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

   9. Simplified 54.4%

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

   if -1.2999999999999999e25 < a < -3.40000000000000003e-51 or -3.10000000000000029e-272 < a < 520

   1. Initial program 59.5%

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

      1. associate-/l* 77.9%

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

   3. Simplified 77.9%

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

   5. Taylor expanded in z around inf 45.5%

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

   if -5.4999999999999998e-156 < a < -3.10000000000000029e-272

   1. Initial program 56.3%

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

      1. associate-/l* 71.4%

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

   3. Simplified 71.4%

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

   5. Taylor expanded in x around -inf 57.1%

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

      1. associate-*r* 57.1%

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

      2. neg-mul-1 57.1%

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

   7. Simplified 57.1%

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

   8. Taylor expanded in a around 0 52.2%

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

      1. associate-/l* 52.3%

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

   10. Simplified 52.3%

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

Alternative 8: 72.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{\left(y - a\right) \cdot \left(x - t\right)}{z}\\ t_2 := x - \left(t - x\right) \cdot \frac{z - y}{a}\\ \mathbf{if}\;a \leq -1.8 \cdot 10^{+25}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-153}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 14.5:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (/ (* (- y a) (- x t)) z)))
        (t_2 (- x (* (- t x) (/ (- z y) a)))))
   (if (<= a -1.8e+25)
     t_2
     (if (<= a -7.5e-49)
       t_1
       (if (<= a -1.9e-153)
         (* y (/ (- t x) (- a z)))
         (if (<= a 14.5) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (((y - a) * (x - t)) / z);
	double t_2 = x - ((t - x) * ((z - y) / a));
	double tmp;
	if (a <= -1.8e+25) {
		tmp = t_2;
	} else if (a <= -7.5e-49) {
		tmp = t_1;
	} else if (a <= -1.9e-153) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 14.5) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t + (((y - a) * (x - t)) / z)
    t_2 = x - ((t - x) * ((z - y) / a))
    if (a <= (-1.8d+25)) then
        tmp = t_2
    else if (a <= (-7.5d-49)) then
        tmp = t_1
    else if (a <= (-1.9d-153)) then
        tmp = y * ((t - x) / (a - z))
    else if (a <= 14.5d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (((y - a) * (x - t)) / z);
	double t_2 = x - ((t - x) * ((z - y) / a));
	double tmp;
	if (a <= -1.8e+25) {
		tmp = t_2;
	} else if (a <= -7.5e-49) {
		tmp = t_1;
	} else if (a <= -1.9e-153) {
		tmp = y * ((t - x) / (a - z));
	} else if (a <= 14.5) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (((y - a) * (x - t)) / z)
	t_2 = x - ((t - x) * ((z - y) / a))
	tmp = 0
	if a <= -1.8e+25:
		tmp = t_2
	elif a <= -7.5e-49:
		tmp = t_1
	elif a <= -1.9e-153:
		tmp = y * ((t - x) / (a - z))
	elif a <= 14.5:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(Float64(y - a) * Float64(x - t)) / z))
	t_2 = Float64(x - Float64(Float64(t - x) * Float64(Float64(z - y) / a)))
	tmp = 0.0
	if (a <= -1.8e+25)
		tmp = t_2;
	elseif (a <= -7.5e-49)
		tmp = t_1;
	elseif (a <= -1.9e-153)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (a <= 14.5)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (((y - a) * (x - t)) / z);
	t_2 = x - ((t - x) * ((z - y) / a));
	tmp = 0.0;
	if (a <= -1.8e+25)
		tmp = t_2;
	elseif (a <= -7.5e-49)
		tmp = t_1;
	elseif (a <= -1.9e-153)
		tmp = y * ((t - x) / (a - z));
	elseif (a <= 14.5)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(N[(y - a), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(N[(t - x), $MachinePrecision] * N[(N[(z - y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.8e+25], t$95$2, If[LessEqual[a, -7.5e-49], t$95$1, If[LessEqual[a, -1.9e-153], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 14.5], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.80000000000000008e25 or 14.5 < a

   1. Initial program 71.7%

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

      1. associate-/l* 85.8%

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

   3. Simplified 85.8%

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

   5. Taylor expanded in a around inf 63.9%

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

      1. associate-/l* 77.2%

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

   7. Simplified 77.2%

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

   if -1.80000000000000008e25 < a < -7.4999999999999998e-49 or -1.90000000000000011e-153 < a < 14.5

   1. Initial program 60.3%

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

      1. associate-/l* 77.2%

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

   3. Simplified 77.2%

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

   5. Taylor expanded in z around inf 81.5%

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

      1. associate--l+ 81.5%

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

      2. associate-*r/ 81.5%

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

      3. associate-*r/ 81.5%

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

      4. mul-1-neg 81.5%

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

      5. div-sub 81.6%

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

      6. mul-1-neg 81.6%

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

      7. distribute-lft-out-- 81.6%

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

      8. associate-*r/ 81.6%

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

      9. mul-1-neg 81.6%

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

      10. unsub-neg 81.6%

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

      11. distribute-rgt-out-- 81.6%

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

   7. Simplified 81.6%

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

   if -7.4999999999999998e-49 < a < -1.90000000000000011e-153

   1. Initial program 90.4%

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

      1. associate-/l* 86.1%

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

   3. Simplified 86.1%

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

   5. Taylor expanded in y around inf 80.9%

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

      1. div-sub 81.3%

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

   7. Simplified 81.3%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{+25}:\\ \;\;\;\;x - \left(t - x\right) \cdot \frac{z - y}{a}\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-49}:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-153}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 14.5:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot \left(x - t\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \left(t - x\right) \cdot \frac{z - y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -7.9 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-90}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-106}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+78}:\\ \;\;\;\;x - \frac{t}{a} \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= z -7.9e+23)
     t_1
     (if (<= z -9e-90)
       (/ (* y (- t x)) (- a z))
       (if (<= z 1.9e-106)
         (+ x (/ (- t x) (/ a y)))
         (if (<= z 2.1e+78) (- x (* (/ t a) (- z y))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -7.9e+23) {
		tmp = t_1;
	} else if (z <= -9e-90) {
		tmp = (y * (t - x)) / (a - z);
	} else if (z <= 1.9e-106) {
		tmp = x + ((t - x) / (a / y));
	} else if (z <= 2.1e+78) {
		tmp = x - ((t / a) * (z - y));
	} 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 * ((y - z) / (a - z))
    if (z <= (-7.9d+23)) then
        tmp = t_1
    else if (z <= (-9d-90)) then
        tmp = (y * (t - x)) / (a - z)
    else if (z <= 1.9d-106) then
        tmp = x + ((t - x) / (a / y))
    else if (z <= 2.1d+78) then
        tmp = x - ((t / a) * (z - y))
    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 * ((y - z) / (a - z));
	double tmp;
	if (z <= -7.9e+23) {
		tmp = t_1;
	} else if (z <= -9e-90) {
		tmp = (y * (t - x)) / (a - z);
	} else if (z <= 1.9e-106) {
		tmp = x + ((t - x) / (a / y));
	} else if (z <= 2.1e+78) {
		tmp = x - ((t / a) * (z - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -7.9e+23:
		tmp = t_1
	elif z <= -9e-90:
		tmp = (y * (t - x)) / (a - z)
	elif z <= 1.9e-106:
		tmp = x + ((t - x) / (a / y))
	elif z <= 2.1e+78:
		tmp = x - ((t / a) * (z - y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -7.9e+23)
		tmp = t_1;
	elseif (z <= -9e-90)
		tmp = Float64(Float64(y * Float64(t - x)) / Float64(a - z));
	elseif (z <= 1.9e-106)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	elseif (z <= 2.1e+78)
		tmp = Float64(x - Float64(Float64(t / a) * Float64(z - y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -7.9e+23)
		tmp = t_1;
	elseif (z <= -9e-90)
		tmp = (y * (t - x)) / (a - z);
	elseif (z <= 1.9e-106)
		tmp = x + ((t - x) / (a / y));
	elseif (z <= 2.1e+78)
		tmp = x - ((t / a) * (z - y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.9e+23], t$95$1, If[LessEqual[z, -9e-90], N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e-106], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e+78], N[(x - N[(N[(t / a), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.9e23 or 2.1000000000000001e78 < z

   1. Initial program 37.7%

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

      1. associate-/l* 65.7%

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

   3. Simplified 65.7%

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

   5. Taylor expanded in x around 0 44.7%

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

      1. associate-/l* 65.4%

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

   7. Simplified 65.4%

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

   if -7.9e23 < z < -9.00000000000000017e-90

   1. Initial program 82.7%

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

      1. associate-/l* 82.6%

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

   3. Simplified 82.6%

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

   5. Taylor expanded in y around -inf 77.9%

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

   if -9.00000000000000017e-90 < z < 1.9e-106

   1. Initial program 94.0%

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

      1. associate-/l* 96.4%

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

   3. Simplified 96.4%

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

      1. *-commutative 96.4%

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

      2. associate-*l/ 94.0%

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

      3. associate-*r/ 97.5%

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

      4. clear-num 97.5%

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

      5. un-div-inv 97.5%

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

   6. Applied egg-rr 97.5%

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

   7. Taylor expanded in z around 0 87.5%

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

   if 1.9e-106 < z < 2.1000000000000001e78

   1. Initial program 90.6%

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

      1. associate-/l* 96.8%

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

   3. Simplified 96.8%

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

      1. *-commutative 96.8%

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

      2. associate-*l/ 90.6%

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

      3. associate-*r/ 96.8%

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

      4. clear-num 96.8%

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

      5. un-div-inv 96.8%

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

   6. Applied egg-rr 96.8%

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

   7. Taylor expanded in a around inf 74.3%

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

   8. Taylor expanded in t around inf 68.0%

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

      1. associate-*l/ 69.7%

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

      2. *-commutative 69.7%

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

   10. Simplified 69.7%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.9 \cdot 10^{+23}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-90}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-106}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+78}:\\ \;\;\;\;x - \frac{t}{a} \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -3.9 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-90}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-107}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+77}:\\ \;\;\;\;x - \frac{t}{a} \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= z -3.9e+23)
     t_1
     (if (<= z -1.55e-90)
       (* y (/ (- t x) (- a z)))
       (if (<= z 9.5e-107)
         (+ x (/ (- t x) (/ a y)))
         (if (<= z 3.6e+77) (- x (* (/ t a) (- z y))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -3.9e+23) {
		tmp = t_1;
	} else if (z <= -1.55e-90) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 9.5e-107) {
		tmp = x + ((t - x) / (a / y));
	} else if (z <= 3.6e+77) {
		tmp = x - ((t / a) * (z - y));
	} 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 * ((y - z) / (a - z))
    if (z <= (-3.9d+23)) then
        tmp = t_1
    else if (z <= (-1.55d-90)) then
        tmp = y * ((t - x) / (a - z))
    else if (z <= 9.5d-107) then
        tmp = x + ((t - x) / (a / y))
    else if (z <= 3.6d+77) then
        tmp = x - ((t / a) * (z - y))
    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 * ((y - z) / (a - z));
	double tmp;
	if (z <= -3.9e+23) {
		tmp = t_1;
	} else if (z <= -1.55e-90) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 9.5e-107) {
		tmp = x + ((t - x) / (a / y));
	} else if (z <= 3.6e+77) {
		tmp = x - ((t / a) * (z - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -3.9e+23:
		tmp = t_1
	elif z <= -1.55e-90:
		tmp = y * ((t - x) / (a - z))
	elif z <= 9.5e-107:
		tmp = x + ((t - x) / (a / y))
	elif z <= 3.6e+77:
		tmp = x - ((t / a) * (z - y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -3.9e+23)
		tmp = t_1;
	elseif (z <= -1.55e-90)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (z <= 9.5e-107)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	elseif (z <= 3.6e+77)
		tmp = Float64(x - Float64(Float64(t / a) * Float64(z - y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -3.9e+23)
		tmp = t_1;
	elseif (z <= -1.55e-90)
		tmp = y * ((t - x) / (a - z));
	elseif (z <= 9.5e-107)
		tmp = x + ((t - x) / (a / y));
	elseif (z <= 3.6e+77)
		tmp = x - ((t / a) * (z - y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.9e+23], t$95$1, If[LessEqual[z, -1.55e-90], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e-107], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e+77], N[(x - N[(N[(t / a), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.9e23 or 3.5999999999999998e77 < z

   1. Initial program 37.7%

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

      1. associate-/l* 65.7%

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

   3. Simplified 65.7%

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

   5. Taylor expanded in x around 0 44.7%

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

      1. associate-/l* 65.4%

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

   7. Simplified 65.4%

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

   if -3.9e23 < z < -1.5500000000000001e-90

   1. Initial program 82.7%

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

      1. associate-/l* 82.6%

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

   3. Simplified 82.6%

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

   5. Taylor expanded in y around inf 73.6%

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

      1. div-sub 73.7%

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

   7. Simplified 73.7%

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

   if -1.5500000000000001e-90 < z < 9.4999999999999999e-107

   1. Initial program 94.0%

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

      1. associate-/l* 96.4%

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

   3. Simplified 96.4%

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

      1. *-commutative 96.4%

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

      2. associate-*l/ 94.0%

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

      3. associate-*r/ 97.5%

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

      4. clear-num 97.5%

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

      5. un-div-inv 97.5%

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

   6. Applied egg-rr 97.5%

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

   7. Taylor expanded in z around 0 87.5%

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

   if 9.4999999999999999e-107 < z < 3.5999999999999998e77

   1. Initial program 90.6%

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

      1. associate-/l* 96.8%

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

   3. Simplified 96.8%

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

      1. *-commutative 96.8%

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

      2. associate-*l/ 90.6%

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

      3. associate-*r/ 96.8%

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

      4. clear-num 96.8%

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

      5. un-div-inv 96.8%

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

   6. Applied egg-rr 96.8%

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

   7. Taylor expanded in a around inf 74.3%

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

   8. Taylor expanded in t around inf 68.0%

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

      1. associate-*l/ 69.7%

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

      2. *-commutative 69.7%

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

   10. Simplified 69.7%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+23}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-90}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-107}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+77}:\\ \;\;\;\;x - \frac{t}{a} \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 65.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -9 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-90}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-106}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+77}:\\ \;\;\;\;x - \frac{t}{a} \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= z -9e+23)
     t_1
     (if (<= z -6e-90)
       (* y (/ (- t x) (- a z)))
       (if (<= z 1.9e-106)
         (+ x (* y (/ (- t x) a)))
         (if (<= z 3.6e+77) (- x (* (/ t a) (- z y))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -9e+23) {
		tmp = t_1;
	} else if (z <= -6e-90) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 1.9e-106) {
		tmp = x + (y * ((t - x) / a));
	} else if (z <= 3.6e+77) {
		tmp = x - ((t / a) * (z - y));
	} 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 * ((y - z) / (a - z))
    if (z <= (-9d+23)) then
        tmp = t_1
    else if (z <= (-6d-90)) then
        tmp = y * ((t - x) / (a - z))
    else if (z <= 1.9d-106) then
        tmp = x + (y * ((t - x) / a))
    else if (z <= 3.6d+77) then
        tmp = x - ((t / a) * (z - y))
    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 * ((y - z) / (a - z));
	double tmp;
	if (z <= -9e+23) {
		tmp = t_1;
	} else if (z <= -6e-90) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 1.9e-106) {
		tmp = x + (y * ((t - x) / a));
	} else if (z <= 3.6e+77) {
		tmp = x - ((t / a) * (z - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -9e+23:
		tmp = t_1
	elif z <= -6e-90:
		tmp = y * ((t - x) / (a - z))
	elif z <= 1.9e-106:
		tmp = x + (y * ((t - x) / a))
	elif z <= 3.6e+77:
		tmp = x - ((t / a) * (z - y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -9e+23)
		tmp = t_1;
	elseif (z <= -6e-90)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (z <= 1.9e-106)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	elseif (z <= 3.6e+77)
		tmp = Float64(x - Float64(Float64(t / a) * Float64(z - y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -9e+23)
		tmp = t_1;
	elseif (z <= -6e-90)
		tmp = y * ((t - x) / (a - z));
	elseif (z <= 1.9e-106)
		tmp = x + (y * ((t - x) / a));
	elseif (z <= 3.6e+77)
		tmp = x - ((t / a) * (z - y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9e+23], t$95$1, If[LessEqual[z, -6e-90], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e-106], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e+77], N[(x - N[(N[(t / a), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.99999999999999958e23 or 3.5999999999999998e77 < z

   1. Initial program 37.7%

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

      1. associate-/l* 65.7%

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

   3. Simplified 65.7%

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

   5. Taylor expanded in x around 0 44.7%

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

      1. associate-/l* 65.4%

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

   7. Simplified 65.4%

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

   if -8.99999999999999958e23 < z < -6.00000000000000041e-90

   1. Initial program 82.7%

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

      1. associate-/l* 82.6%

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

   3. Simplified 82.6%

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

   5. Taylor expanded in y around inf 73.6%

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

      1. div-sub 73.7%

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

   7. Simplified 73.7%

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

   if -6.00000000000000041e-90 < z < 1.9e-106

   1. Initial program 94.0%

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

      1. associate-/l* 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in z around 0 82.9%

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

      1. associate-/l* 85.6%

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

   7. Simplified 85.6%

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

   if 1.9e-106 < z < 3.5999999999999998e77

   1. Initial program 90.6%

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

      1. associate-/l* 96.8%

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

   3. Simplified 96.8%

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

      1. *-commutative 96.8%

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

      2. associate-*l/ 90.6%

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

      3. associate-*r/ 96.8%

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

      4. clear-num 96.8%

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

      5. un-div-inv 96.8%

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

   6. Applied egg-rr 96.8%

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

   7. Taylor expanded in a around inf 74.3%

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

   8. Taylor expanded in t around inf 68.0%

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

      1. associate-*l/ 69.7%

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

      2. *-commutative 69.7%

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

   10. Simplified 69.7%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+23}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-90}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-106}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+77}:\\ \;\;\;\;x - \frac{t}{a} \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 49.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - x \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -1.02 \cdot 10^{+91}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-232}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-200}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+79}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* x (/ y a)))))
   (if (<= z -1.02e+91)
     t
     (if (<= z 1.75e-232)
       t_1
       (if (<= z 2.3e-200) (/ t (/ a y)) (if (<= z 3.5e+79) t_1 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x * (y / a));
	double tmp;
	if (z <= -1.02e+91) {
		tmp = t;
	} else if (z <= 1.75e-232) {
		tmp = t_1;
	} else if (z <= 2.3e-200) {
		tmp = t / (a / y);
	} else if (z <= 3.5e+79) {
		tmp = t_1;
	} 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 = x - (x * (y / a))
    if (z <= (-1.02d+91)) then
        tmp = t
    else if (z <= 1.75d-232) then
        tmp = t_1
    else if (z <= 2.3d-200) then
        tmp = t / (a / y)
    else if (z <= 3.5d+79) then
        tmp = t_1
    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 = x - (x * (y / a));
	double tmp;
	if (z <= -1.02e+91) {
		tmp = t;
	} else if (z <= 1.75e-232) {
		tmp = t_1;
	} else if (z <= 2.3e-200) {
		tmp = t / (a / y);
	} else if (z <= 3.5e+79) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (x * (y / a))
	tmp = 0
	if z <= -1.02e+91:
		tmp = t
	elif z <= 1.75e-232:
		tmp = t_1
	elif z <= 2.3e-200:
		tmp = t / (a / y)
	elif z <= 3.5e+79:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(x * Float64(y / a)))
	tmp = 0.0
	if (z <= -1.02e+91)
		tmp = t;
	elseif (z <= 1.75e-232)
		tmp = t_1;
	elseif (z <= 2.3e-200)
		tmp = Float64(t / Float64(a / y));
	elseif (z <= 3.5e+79)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (x * (y / a));
	tmp = 0.0;
	if (z <= -1.02e+91)
		tmp = t;
	elseif (z <= 1.75e-232)
		tmp = t_1;
	elseif (z <= 2.3e-200)
		tmp = t / (a / y);
	elseif (z <= 3.5e+79)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.02e+91], t, If[LessEqual[z, 1.75e-232], t$95$1, If[LessEqual[z, 2.3e-200], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e+79], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.01999999999999992e91 or 3.4999999999999998e79 < z

   1. Initial program 30.7%

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

      1. associate-/l* 60.3%

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

   3. Simplified 60.3%

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

   5. Taylor expanded in z around inf 50.6%

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

   if -1.01999999999999992e91 < z < 1.7499999999999999e-232 or 2.30000000000000007e-200 < z < 3.4999999999999998e79

   1. Initial program 89.8%

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

      1. associate-/l* 94.7%

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

   3. Simplified 94.7%

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

   5. Taylor expanded in x around -inf 59.0%

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

      1. associate-*r* 59.0%

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

      2. neg-mul-1 59.0%

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

   7. Simplified 59.0%

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

   8. Taylor expanded in z around 0 49.7%

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

   9. Taylor expanded in y around 0 46.4%

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

       1. neg-mul-1 46.4%

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

       2. unsub-neg 46.4%

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

       3. associate-/l* 49.7%

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

   11. Simplified 49.7%

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

   if 1.7499999999999999e-232 < z < 2.30000000000000007e-200

   1. Initial program 99.8%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around -inf 86.7%

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

   6. Taylor expanded in a around inf 74.2%

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

   7. Taylor expanded in t around inf 63.2%

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

      1. associate-/l* 86.4%

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

   9. Simplified 86.4%

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

       1. clear-num 86.6%

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

       2. un-div-inv 86.8%

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

   11. Applied egg-rr 86.8%

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

Alternative 13: 37.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -2.7 \cdot 10^{+44}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-51}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-195}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 260:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y a))))
   (if (<= a -2.7e+44)
     x
     (if (<= a -3.5e+24)
       t_1
       (if (<= a -4.4e-51)
         t
         (if (<= a -3.6e-195) t_1 (if (<= a 260.0) t x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (a <= -2.7e+44) {
		tmp = x;
	} else if (a <= -3.5e+24) {
		tmp = t_1;
	} else if (a <= -4.4e-51) {
		tmp = t;
	} else if (a <= -3.6e-195) {
		tmp = t_1;
	} else if (a <= 260.0) {
		tmp = t;
	} else {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = t * (y / a)
    if (a <= (-2.7d+44)) then
        tmp = x
    else if (a <= (-3.5d+24)) then
        tmp = t_1
    else if (a <= (-4.4d-51)) then
        tmp = t
    else if (a <= (-3.6d-195)) then
        tmp = t_1
    else if (a <= 260.0d0) then
        tmp = t
    else
        tmp = x
    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 * (y / a);
	double tmp;
	if (a <= -2.7e+44) {
		tmp = x;
	} else if (a <= -3.5e+24) {
		tmp = t_1;
	} else if (a <= -4.4e-51) {
		tmp = t;
	} else if (a <= -3.6e-195) {
		tmp = t_1;
	} else if (a <= 260.0) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / a)
	tmp = 0
	if a <= -2.7e+44:
		tmp = x
	elif a <= -3.5e+24:
		tmp = t_1
	elif a <= -4.4e-51:
		tmp = t
	elif a <= -3.6e-195:
		tmp = t_1
	elif a <= 260.0:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / a))
	tmp = 0.0
	if (a <= -2.7e+44)
		tmp = x;
	elseif (a <= -3.5e+24)
		tmp = t_1;
	elseif (a <= -4.4e-51)
		tmp = t;
	elseif (a <= -3.6e-195)
		tmp = t_1;
	elseif (a <= 260.0)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / a);
	tmp = 0.0;
	if (a <= -2.7e+44)
		tmp = x;
	elseif (a <= -3.5e+24)
		tmp = t_1;
	elseif (a <= -4.4e-51)
		tmp = t;
	elseif (a <= -3.6e-195)
		tmp = t_1;
	elseif (a <= 260.0)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.7e+44], x, If[LessEqual[a, -3.5e+24], t$95$1, If[LessEqual[a, -4.4e-51], t, If[LessEqual[a, -3.6e-195], t$95$1, If[LessEqual[a, 260.0], t, x]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.7e44 or 260 < a

   1. Initial program 70.5%

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

      1. associate-/l* 85.2%

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

   3. Simplified 85.2%

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

   5. Taylor expanded in a around inf 46.2%

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

   if -2.7e44 < a < -3.5000000000000002e24 or -4.4e-51 < a < -3.6e-195

   1. Initial program 84.7%

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

      1. associate-/l* 82.4%

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

   3. Simplified 82.4%

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

   5. Taylor expanded in y around -inf 82.5%

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

   6. Taylor expanded in a around inf 57.1%

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

   7. Taylor expanded in t around inf 42.7%

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

      1. associate-/l* 50.0%

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

   9. Simplified 50.0%

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

   if -3.5000000000000002e24 < a < -4.4e-51 or -3.6e-195 < a < 260

   1. Initial program 59.0%

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

      1. associate-/l* 78.2%

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

   3. Simplified 78.2%

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

   5. Taylor expanded in z around inf 43.4%

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

Alternative 14: 73.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-119}:\\ \;\;\;\;x - \frac{t - x}{\frac{z - a}{y}}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+78}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= z -4.5e+25)
     t_1
     (if (<= z 4.5e-119)
       (- x (/ (- t x) (/ (- z a) y)))
       (if (<= z 2.5e+78) (+ x (/ (- t x) (/ a (- y z)))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -4.5e+25) {
		tmp = t_1;
	} else if (z <= 4.5e-119) {
		tmp = x - ((t - x) / ((z - a) / y));
	} else if (z <= 2.5e+78) {
		tmp = x + ((t - x) / (a / (y - 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 = t * ((y - z) / (a - z))
    if (z <= (-4.5d+25)) then
        tmp = t_1
    else if (z <= 4.5d-119) then
        tmp = x - ((t - x) / ((z - a) / y))
    else if (z <= 2.5d+78) then
        tmp = x + ((t - x) / (a / (y - 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 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -4.5e+25) {
		tmp = t_1;
	} else if (z <= 4.5e-119) {
		tmp = x - ((t - x) / ((z - a) / y));
	} else if (z <= 2.5e+78) {
		tmp = x + ((t - x) / (a / (y - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -4.5e+25:
		tmp = t_1
	elif z <= 4.5e-119:
		tmp = x - ((t - x) / ((z - a) / y))
	elif z <= 2.5e+78:
		tmp = x + ((t - x) / (a / (y - z)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -4.5e+25)
		tmp = t_1;
	elseif (z <= 4.5e-119)
		tmp = Float64(x - Float64(Float64(t - x) / Float64(Float64(z - a) / y)));
	elseif (z <= 2.5e+78)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / Float64(y - z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -4.5e+25)
		tmp = t_1;
	elseif (z <= 4.5e-119)
		tmp = x - ((t - x) / ((z - a) / y));
	elseif (z <= 2.5e+78)
		tmp = x + ((t - x) / (a / (y - z)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.5e+25], t$95$1, If[LessEqual[z, 4.5e-119], N[(x - N[(N[(t - x), $MachinePrecision] / N[(N[(z - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e+78], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.5000000000000003e25 or 2.49999999999999992e78 < z

   1. Initial program 37.7%

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

      1. associate-/l* 65.7%

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

   3. Simplified 65.7%

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

   5. Taylor expanded in x around 0 44.7%

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

      1. associate-/l* 65.4%

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

   7. Simplified 65.4%

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

   if -4.5000000000000003e25 < z < 4.5000000000000003e-119

   1. Initial program 91.3%

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

      1. associate-/l* 93.2%

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

   3. Simplified 93.2%

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

      1. *-commutative 93.2%

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

      2. associate-*l/ 91.3%

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

      3. associate-*r/ 95.1%

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

      4. clear-num 95.0%

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

      5. un-div-inv 95.0%

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

   6. Applied egg-rr 95.0%

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

   7. Taylor expanded in y around inf 92.0%

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

   if 4.5000000000000003e-119 < z < 2.49999999999999992e78

   1. Initial program 91.1%

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

      1. associate-/l* 96.9%

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

   3. Simplified 96.9%

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

      1. *-commutative 96.9%

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

      2. associate-*l/ 91.1%

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

      3. associate-*r/ 97.0%

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

      4. clear-num 96.9%

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

      5. un-div-inv 97.0%

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

   6. Applied egg-rr 97.0%

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

   7. Taylor expanded in a around inf 76.0%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+25}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-119}:\\ \;\;\;\;x - \frac{t - x}{\frac{z - a}{y}}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+78}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 68.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -4.1 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.65 \cdot 10^{-90}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+77}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= z -4.1e+23)
     t_1
     (if (<= z -3.65e-90)
       (/ (* y (- t x)) (- a z))
       (if (<= z 2.3e+77) (+ x (/ (- t x) (/ a (- y z)))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -4.1e+23) {
		tmp = t_1;
	} else if (z <= -3.65e-90) {
		tmp = (y * (t - x)) / (a - z);
	} else if (z <= 2.3e+77) {
		tmp = x + ((t - x) / (a / (y - 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 = t * ((y - z) / (a - z))
    if (z <= (-4.1d+23)) then
        tmp = t_1
    else if (z <= (-3.65d-90)) then
        tmp = (y * (t - x)) / (a - z)
    else if (z <= 2.3d+77) then
        tmp = x + ((t - x) / (a / (y - 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 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -4.1e+23) {
		tmp = t_1;
	} else if (z <= -3.65e-90) {
		tmp = (y * (t - x)) / (a - z);
	} else if (z <= 2.3e+77) {
		tmp = x + ((t - x) / (a / (y - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -4.1e+23:
		tmp = t_1
	elif z <= -3.65e-90:
		tmp = (y * (t - x)) / (a - z)
	elif z <= 2.3e+77:
		tmp = x + ((t - x) / (a / (y - z)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -4.1e+23)
		tmp = t_1;
	elseif (z <= -3.65e-90)
		tmp = Float64(Float64(y * Float64(t - x)) / Float64(a - z));
	elseif (z <= 2.3e+77)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / Float64(y - z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -4.1e+23)
		tmp = t_1;
	elseif (z <= -3.65e-90)
		tmp = (y * (t - x)) / (a - z);
	elseif (z <= 2.3e+77)
		tmp = x + ((t - x) / (a / (y - z)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.1e+23], t$95$1, If[LessEqual[z, -3.65e-90], N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.3e+77], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.09999999999999996e23 or 2.29999999999999995e77 < z

   1. Initial program 37.7%

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

      1. associate-/l* 65.7%

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

   3. Simplified 65.7%

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

   5. Taylor expanded in x around 0 44.7%

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

      1. associate-/l* 65.4%

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

   7. Simplified 65.4%

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

   if -4.09999999999999996e23 < z < -3.64999999999999999e-90

   1. Initial program 82.7%

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

      1. associate-/l* 82.6%

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

   3. Simplified 82.6%

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

   5. Taylor expanded in y around -inf 77.9%

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

   if -3.64999999999999999e-90 < z < 2.29999999999999995e77

   1. Initial program 92.8%

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

      1. associate-/l* 96.5%

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

   3. Simplified 96.5%

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

      1. *-commutative 96.5%

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

      2. associate-*l/ 92.8%

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

      3. associate-*r/ 97.2%

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

      4. clear-num 97.2%

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

      5. un-div-inv 97.2%

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

   6. Applied egg-rr 97.2%

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

   7. Taylor expanded in a around inf 83.5%

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

Alternative 16: 68.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -1.45 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-90}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+77}:\\ \;\;\;\;x - \left(t - x\right) \cdot \frac{z - y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= z -1.45e+25)
     t_1
     (if (<= z -9e-90)
       (/ (* y (- t x)) (- a z))
       (if (<= z 8.8e+77) (- x (* (- t x) (/ (- z y) a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -1.45e+25) {
		tmp = t_1;
	} else if (z <= -9e-90) {
		tmp = (y * (t - x)) / (a - z);
	} else if (z <= 8.8e+77) {
		tmp = x - ((t - x) * ((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 = t * ((y - z) / (a - z))
    if (z <= (-1.45d+25)) then
        tmp = t_1
    else if (z <= (-9d-90)) then
        tmp = (y * (t - x)) / (a - z)
    else if (z <= 8.8d+77) then
        tmp = x - ((t - x) * ((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 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -1.45e+25) {
		tmp = t_1;
	} else if (z <= -9e-90) {
		tmp = (y * (t - x)) / (a - z);
	} else if (z <= 8.8e+77) {
		tmp = x - ((t - x) * ((z - y) / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -1.45e+25:
		tmp = t_1
	elif z <= -9e-90:
		tmp = (y * (t - x)) / (a - z)
	elif z <= 8.8e+77:
		tmp = x - ((t - x) * ((z - y) / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -1.45e+25)
		tmp = t_1;
	elseif (z <= -9e-90)
		tmp = Float64(Float64(y * Float64(t - x)) / Float64(a - z));
	elseif (z <= 8.8e+77)
		tmp = Float64(x - Float64(Float64(t - x) * Float64(Float64(z - y) / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -1.45e+25)
		tmp = t_1;
	elseif (z <= -9e-90)
		tmp = (y * (t - x)) / (a - z);
	elseif (z <= 8.8e+77)
		tmp = x - ((t - x) * ((z - y) / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.45e+25], t$95$1, If[LessEqual[z, -9e-90], N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.8e+77], N[(x - N[(N[(t - x), $MachinePrecision] * N[(N[(z - y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.44999999999999995e25 or 8.8000000000000002e77 < z

   1. Initial program 37.7%

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

      1. associate-/l* 65.7%

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

   3. Simplified 65.7%

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

   5. Taylor expanded in x around 0 44.7%

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

      1. associate-/l* 65.4%

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

   7. Simplified 65.4%

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

   if -1.44999999999999995e25 < z < -9.00000000000000017e-90

   1. Initial program 82.7%

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

      1. associate-/l* 82.6%

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

   3. Simplified 82.6%

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

   5. Taylor expanded in y around -inf 77.9%

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

   if -9.00000000000000017e-90 < z < 8.8000000000000002e77

   1. Initial program 92.8%

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

      1. associate-/l* 96.5%

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

   3. Simplified 96.5%

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

   5. Taylor expanded in a around inf 78.9%

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

      1. associate-/l* 83.5%

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

   7. Simplified 83.5%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+25}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-90}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+77}:\\ \;\;\;\;x - \left(t - x\right) \cdot \frac{z - y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 66.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-90}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-29}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= z -2.9e+23)
     t_1
     (if (<= z -8e-90)
       (* y (/ (- t x) (- a z)))
       (if (<= z 9.5e-29) (+ x (* y (/ (- t x) a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -2.9e+23) {
		tmp = t_1;
	} else if (z <= -8e-90) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 9.5e-29) {
		tmp = x + (y * ((t - x) / 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 = t * ((y - z) / (a - z))
    if (z <= (-2.9d+23)) then
        tmp = t_1
    else if (z <= (-8d-90)) then
        tmp = y * ((t - x) / (a - z))
    else if (z <= 9.5d-29) then
        tmp = x + (y * ((t - x) / 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 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -2.9e+23) {
		tmp = t_1;
	} else if (z <= -8e-90) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 9.5e-29) {
		tmp = x + (y * ((t - x) / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -2.9e+23:
		tmp = t_1
	elif z <= -8e-90:
		tmp = y * ((t - x) / (a - z))
	elif z <= 9.5e-29:
		tmp = x + (y * ((t - x) / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -2.9e+23)
		tmp = t_1;
	elseif (z <= -8e-90)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (z <= 9.5e-29)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -2.9e+23)
		tmp = t_1;
	elseif (z <= -8e-90)
		tmp = y * ((t - x) / (a - z));
	elseif (z <= 9.5e-29)
		tmp = x + (y * ((t - x) / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.9e+23], t$95$1, If[LessEqual[z, -8e-90], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e-29], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.90000000000000013e23 or 9.50000000000000023e-29 < z

   1. Initial program 47.7%

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

      1. associate-/l* 71.9%

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

   3. Simplified 71.9%

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

   5. Taylor expanded in x around 0 46.1%

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

      1. associate-/l* 63.0%

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

   7. Simplified 63.0%

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

   if -2.90000000000000013e23 < z < -7.99999999999999996e-90

   1. Initial program 82.7%

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

      1. associate-/l* 82.6%

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

   3. Simplified 82.6%

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

   5. Taylor expanded in y around inf 73.6%

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

      1. div-sub 73.7%

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

   7. Simplified 73.7%

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

   if -7.99999999999999996e-90 < z < 9.50000000000000023e-29

   1. Initial program 95.0%

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

      1. associate-/l* 97.0%

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

   3. Simplified 97.0%

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

   5. Taylor expanded in z around 0 80.7%

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

      1. associate-/l* 83.0%

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

   7. Simplified 83.0%

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

Alternative 18: 89.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+136} \lor \neg \left(z \leq 2.85 \cdot 10^{+187}\right):\\ \;\;\;\;t + \left(y - a\right) \cdot \left(\left(t - x\right) \cdot \frac{-1}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t - x}{\frac{a - z}{z - y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.3e+136) (not (<= z 2.85e+187)))
   (+ t (* (- y a) (* (- t x) (/ -1.0 z))))
   (- x (/ (- t x) (/ (- a z) (- z y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.3e+136) || !(z <= 2.85e+187)) {
		tmp = t + ((y - a) * ((t - x) * (-1.0 / z)));
	} else {
		tmp = x - ((t - x) / ((a - z) / (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 <= (-1.3d+136)) .or. (.not. (z <= 2.85d+187))) then
        tmp = t + ((y - a) * ((t - x) * ((-1.0d0) / z)))
    else
        tmp = x - ((t - x) / ((a - z) / (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 <= -1.3e+136) || !(z <= 2.85e+187)) {
		tmp = t + ((y - a) * ((t - x) * (-1.0 / z)));
	} else {
		tmp = x - ((t - x) / ((a - z) / (z - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.3e+136) or not (z <= 2.85e+187):
		tmp = t + ((y - a) * ((t - x) * (-1.0 / z)))
	else:
		tmp = x - ((t - x) / ((a - z) / (z - y)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.3e+136) || !(z <= 2.85e+187))
		tmp = Float64(t + Float64(Float64(y - a) * Float64(Float64(t - x) * Float64(-1.0 / z))));
	else
		tmp = Float64(x - Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(z - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.3e+136) || ~((z <= 2.85e+187)))
		tmp = t + ((y - a) * ((t - x) * (-1.0 / z)));
	else
		tmp = x - ((t - x) / ((a - z) / (z - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.3e+136], N[Not[LessEqual[z, 2.85e+187]], $MachinePrecision]], N[(t + N[(N[(y - a), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3000000000000001e136 or 2.8500000000000002e187 < z

   1. Initial program 24.3%

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

      1. associate-/l* 52.1%

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

   3. Simplified 52.1%

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

   5. Taylor expanded in z around inf 60.8%

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

      1. associate--l+ 60.8%

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

      2. associate-*r/ 60.8%

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

      3. associate-*r/ 60.8%

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

      4. mul-1-neg 60.8%

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

      5. div-sub 60.8%

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

      6. mul-1-neg 60.8%

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

      7. distribute-lft-out-- 60.8%

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

      8. associate-*r/ 60.8%

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

      9. mul-1-neg 60.8%

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

      10. unsub-neg 60.8%

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

      11. distribute-rgt-out-- 61.0%

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

   7. Simplified 61.0%

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

      1. div-inv 61.1%

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

      2. *-commutative 61.1%

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

      3. associate-*l* 89.5%

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

   9. Applied egg-rr 89.5%

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

   if -1.3000000000000001e136 < z < 2.8500000000000002e187

   1. Initial program 83.8%

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

      1. associate-/l* 92.7%

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

   3. Simplified 92.7%

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

      1. *-commutative 92.7%

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

      2. associate-*l/ 83.8%

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

      3. associate-*r/ 93.7%

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

      4. clear-num 93.6%

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

      5. un-div-inv 93.6%

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

   6. Applied egg-rr 93.6%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+136} \lor \neg \left(z \leq 2.85 \cdot 10^{+187}\right):\\ \;\;\;\;t + \left(y - a\right) \cdot \left(\left(t - x\right) \cdot \frac{-1}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t - x}{\frac{a - z}{z - y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 59.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+37} \lor \neg \left(x \leq 9 \cdot 10^{+138}\right):\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -2.6e+37) (not (<= x 9e+138)))
   (- x (* x (/ y a)))
   (* t (/ (- y z) (- a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -2.6e+37) || !(x <= 9e+138)) {
		tmp = x - (x * (y / a));
	} else {
		tmp = t * ((y - z) / (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 ((x <= (-2.6d+37)) .or. (.not. (x <= 9d+138))) then
        tmp = x - (x * (y / a))
    else
        tmp = t * ((y - z) / (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 ((x <= -2.6e+37) || !(x <= 9e+138)) {
		tmp = x - (x * (y / a));
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -2.6e+37) or not (x <= 9e+138):
		tmp = x - (x * (y / a))
	else:
		tmp = t * ((y - z) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -2.6e+37) || !(x <= 9e+138))
		tmp = Float64(x - Float64(x * Float64(y / a)));
	else
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -2.6e+37) || ~((x <= 9e+138)))
		tmp = x - (x * (y / a));
	else
		tmp = t * ((y - z) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -2.6e+37], N[Not[LessEqual[x, 9e+138]], $MachinePrecision]], N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.5999999999999999e37 or 8.99999999999999963e138 < x

   1. Initial program 57.2%

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

      1. associate-/l* 78.5%

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

   3. Simplified 78.5%

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

   5. Taylor expanded in x around -inf 72.6%

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

      1. associate-*r* 72.6%

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

      2. neg-mul-1 72.6%

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

   7. Simplified 72.6%

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

   8. Taylor expanded in z around 0 58.7%

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

   9. Taylor expanded in y around 0 52.4%

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

       1. neg-mul-1 52.4%

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

       2. unsub-neg 52.4%

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

       3. associate-/l* 58.8%

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

   11. Simplified 58.8%

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

   if -2.5999999999999999e37 < x < 8.99999999999999963e138

   1. Initial program 75.2%

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

      1. associate-/l* 84.4%

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

   3. Simplified 84.4%

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

   5. Taylor expanded in x around 0 57.2%

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

      1. associate-/l* 70.0%

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

   7. Simplified 70.0%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+37} \lor \neg \left(x \leq 9 \cdot 10^{+138}\right):\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 81.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.45 \cdot 10^{+260}:\\ \;\;\;\;x + \frac{t - x}{z - a} \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z 1.45e+260)
   (+ x (* (/ (- t x) (- z a)) (- z y)))
   (* t (/ (- y z) (- a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= 1.45e+260) {
		tmp = x + (((t - x) / (z - a)) * (z - y));
	} else {
		tmp = t * ((y - z) / (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 <= 1.45d+260) then
        tmp = x + (((t - x) / (z - a)) * (z - y))
    else
        tmp = t * ((y - z) / (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 <= 1.45e+260) {
		tmp = x + (((t - x) / (z - a)) * (z - y));
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= 1.45e+260:
		tmp = x + (((t - x) / (z - a)) * (z - y))
	else:
		tmp = t * ((y - z) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= 1.45e+260)
		tmp = Float64(x + Float64(Float64(Float64(t - x) / Float64(z - a)) * Float64(z - y)));
	else
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= 1.45e+260)
		tmp = x + (((t - x) / (z - a)) * (z - y));
	else
		tmp = t * ((y - z) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, 1.45e+260], N[(x + N[(N[(N[(t - x), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.4499999999999999e260

   1. Initial program 69.8%

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

      1. associate-/l* 85.1%

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

   3. Simplified 85.1%

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

   if 1.4499999999999999e260 < z

   1. Initial program 42.5%

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

      1. associate-/l* 27.2%

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

   3. Simplified 27.2%

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

   5. Taylor expanded in x around 0 76.9%

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

      1. associate-/l* 92.2%

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

   7. Simplified 92.2%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.45 \cdot 10^{+260}:\\ \;\;\;\;x + \frac{t - x}{z - a} \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 37.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -62 \lor \neg \left(y \leq 1.3 \cdot 10^{+118}\right):\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -62.0) (not (<= y 1.3e+118))) (* y (/ (- t x) a)) t))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -62.0) || !(y <= 1.3e+118)) {
		tmp = y * ((t - x) / a);
	} 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 ((y <= (-62.0d0)) .or. (.not. (y <= 1.3d+118))) then
        tmp = y * ((t - x) / a)
    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 ((y <= -62.0) || !(y <= 1.3e+118)) {
		tmp = y * ((t - x) / a);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -62.0) or not (y <= 1.3e+118):
		tmp = y * ((t - x) / a)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -62.0) || !(y <= 1.3e+118))
		tmp = Float64(y * Float64(Float64(t - x) / a));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -62.0) || ~((y <= 1.3e+118)))
		tmp = y * ((t - x) / a);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -62.0], N[Not[LessEqual[y, 1.3e+118]], $MachinePrecision]], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if y < -62 or 1.30000000000000008e118 < y

   1. Initial program 70.0%

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

      1. associate-/l* 90.9%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in y around -inf 63.6%

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

   6. Taylor expanded in a around inf 48.6%

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

      1. associate-/l* 52.1%

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

   8. Applied egg-rr 52.1%

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

   if -62 < y < 1.30000000000000008e118

   1. Initial program 67.4%

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

      1. associate-/l* 76.0%

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

   3. Simplified 76.0%

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

   5. Taylor expanded in z around inf 38.0%

      \[\leadsto \color{blue}{t} \]
3. Recombined 2 regimes into one program.

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -62 \lor \neg \left(y \leq 1.3 \cdot 10^{+118}\right):\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 38.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.06 \cdot 10^{+54}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1550:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.06e+54) x (if (<= a 1550.0) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.06e+54) {
		tmp = x;
	} else if (a <= 1550.0) {
		tmp = t;
	} else {
		tmp = 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 (a <= (-1.06d+54)) then
        tmp = x
    else if (a <= 1550.0d0) then
        tmp = t
    else
        tmp = 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 (a <= -1.06e+54) {
		tmp = x;
	} else if (a <= 1550.0) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.06e+54:
		tmp = x
	elif a <= 1550.0:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.06e+54)
		tmp = x;
	elseif (a <= 1550.0)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.06e+54)
		tmp = x;
	elseif (a <= 1550.0)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.06e+54], x, If[LessEqual[a, 1550.0], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.06e54 or 1550 < a

   1. Initial program 70.3%

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

      1. associate-/l* 85.5%

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

   3. Simplified 85.5%

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

   5. Taylor expanded in a around inf 46.0%

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

   if -1.06e54 < a < 1550

   1. Initial program 66.8%

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

      1. associate-/l* 79.3%

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

   3. Simplified 79.3%

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

   5. Taylor expanded in z around inf 36.0%

      \[\leadsto \color{blue}{t} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 23: 25.7% 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 68.4%

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

   1. associate-/l* 82.2%

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

3. Simplified 82.2%

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

5. Taylor expanded in z around inf 25.5%

   \[\leadsto \color{blue}{t} \]
6. Add Preprocessing

Developer target: 84.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{if}\;z < -1.2536131056095036 \cdot 10^{+188}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* (/ y z) (- t x)))))
   (if (< z -1.2536131056095036e+188)
     t_1
     (if (< z 4.446702369113811e+64)
       (+ x (/ (- y z) (/ (- a z) (- t x))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - 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 - ((y / z) * (t - x))
    if (z < (-1.2536131056095036d+188)) then
        tmp = t_1
    else if (z < 4.446702369113811d+64) then
        tmp = x + ((y - z) / ((a - z) / (t - 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 - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((y / z) * (t - x))
	tmp = 0
	if z < -1.2536131056095036e+188:
		tmp = t_1
	elif z < 4.446702369113811e+64:
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(y / z) * Float64(t - x)))
	tmp = 0.0
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - ((y / z) * (t - x));
	tmp = 0.0;
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = x + ((y - z) / ((a - z) / (t - 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[(y / z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -1.2536131056095036e+188], t$95$1, If[Less[z, 4.446702369113811e+64], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024110 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64

  :alt
  (if (< z -1.2536131056095036e+188) (- t (* (/ y z) (- t x))) (if (< z 4.446702369113811e+64) (+ x (/ (- y z) (/ (- a z) (- t x)))) (- t (* (/ y z) (- t x)))))

  (+ x (/ (* (- y z) (- t x)) (- a z))))