Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1

Percentage Accurate: 97.2% → 97.1%

Time: 13.4s

Alternatives: 16

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x - y}{z - y} \cdot t \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y}{z - y} \cdot t \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{t}{\frac{y - z}{y - x}} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.9%

   \[\frac{x - y}{z - y} \cdot t \]
2. Step-by-step derivation

   1. *-commutative 96.9%

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

   2. associate-*r/ 84.1%

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

   3. associate-/l* 96.9%

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

   4. sub-neg 96.9%

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

   5. +-commutative 96.9%

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

   6. neg-sub0 96.9%

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

   7. associate-+l- 96.9%

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

   8. sub0-neg 96.9%

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

   9. neg-mul-1 96.9%

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

   10. associate-/r* 96.9%

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

3. Simplified 96.9%

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

4. Final simplification 96.9%

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

Alternative 2: 66.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - x\right) \cdot \frac{t}{y}\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{+151}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-89}:\\ \;\;\;\;\frac{-y}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-91}:\\ \;\;\;\;\frac{t}{y} \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-57}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+136}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y x) (/ t y))))
   (if (<= y -1.7e+151)
     t
     (if (<= y -2.6e-57)
       t_1
       (if (<= y -6e-89)
         (/ (- y) (/ z t))
         (if (<= y -9.5e-91)
           (* (/ t y) (- x))
           (if (<= y 3.8e-57) (/ t (/ z x)) (if (<= y 1.15e+136) t_1 t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - x) * (t / y);
	double tmp;
	if (y <= -1.7e+151) {
		tmp = t;
	} else if (y <= -2.6e-57) {
		tmp = t_1;
	} else if (y <= -6e-89) {
		tmp = -y / (z / t);
	} else if (y <= -9.5e-91) {
		tmp = (t / y) * -x;
	} else if (y <= 3.8e-57) {
		tmp = t / (z / x);
	} else if (y <= 1.15e+136) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - x) * (t / y)
    if (y <= (-1.7d+151)) then
        tmp = t
    else if (y <= (-2.6d-57)) then
        tmp = t_1
    else if (y <= (-6d-89)) then
        tmp = -y / (z / t)
    else if (y <= (-9.5d-91)) then
        tmp = (t / y) * -x
    else if (y <= 3.8d-57) then
        tmp = t / (z / x)
    else if (y <= 1.15d+136) 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 t_1 = (y - x) * (t / y);
	double tmp;
	if (y <= -1.7e+151) {
		tmp = t;
	} else if (y <= -2.6e-57) {
		tmp = t_1;
	} else if (y <= -6e-89) {
		tmp = -y / (z / t);
	} else if (y <= -9.5e-91) {
		tmp = (t / y) * -x;
	} else if (y <= 3.8e-57) {
		tmp = t / (z / x);
	} else if (y <= 1.15e+136) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - x) * (t / y)
	tmp = 0
	if y <= -1.7e+151:
		tmp = t
	elif y <= -2.6e-57:
		tmp = t_1
	elif y <= -6e-89:
		tmp = -y / (z / t)
	elif y <= -9.5e-91:
		tmp = (t / y) * -x
	elif y <= 3.8e-57:
		tmp = t / (z / x)
	elif y <= 1.15e+136:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - x) * Float64(t / y))
	tmp = 0.0
	if (y <= -1.7e+151)
		tmp = t;
	elseif (y <= -2.6e-57)
		tmp = t_1;
	elseif (y <= -6e-89)
		tmp = Float64(Float64(-y) / Float64(z / t));
	elseif (y <= -9.5e-91)
		tmp = Float64(Float64(t / y) * Float64(-x));
	elseif (y <= 3.8e-57)
		tmp = Float64(t / Float64(z / x));
	elseif (y <= 1.15e+136)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - x) * (t / y);
	tmp = 0.0;
	if (y <= -1.7e+151)
		tmp = t;
	elseif (y <= -2.6e-57)
		tmp = t_1;
	elseif (y <= -6e-89)
		tmp = -y / (z / t);
	elseif (y <= -9.5e-91)
		tmp = (t / y) * -x;
	elseif (y <= 3.8e-57)
		tmp = t / (z / x);
	elseif (y <= 1.15e+136)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] * N[(t / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.7e+151], t, If[LessEqual[y, -2.6e-57], t$95$1, If[LessEqual[y, -6e-89], N[((-y) / N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -9.5e-91], N[(N[(t / y), $MachinePrecision] * (-x)), $MachinePrecision], If[LessEqual[y, 3.8e-57], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.15e+136], t$95$1, t]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.7e151 or 1.15e136 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 81.0%

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

   if -1.7e151 < y < -2.59999999999999985e-57 or 3.7999999999999997e-57 < y < 1.15e136

   1. Initial program 97.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. *-commutative 97.8%

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

      2. associate-*r/ 91.5%

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

      3. associate-/l* 97.8%

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

      4. sub-neg 97.8%

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

      5. +-commutative 97.8%

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

      6. neg-sub0 97.8%

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

      7. associate-+l- 97.8%

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

      8. sub0-neg 97.8%

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

      9. neg-mul-1 97.8%

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

      10. associate-/r* 97.8%

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

   3. Simplified 97.8%

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

      1. associate-/r/ 91.2%

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

   5. Applied egg-rr 91.2%

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

   6. Taylor expanded in y around inf 65.2%

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

   if -2.59999999999999985e-57 < y < -5.9999999999999999e-89

   1. Initial program 83.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. *-commutative 83.8%

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

      2. associate-*r/ 100.0%

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

      3. associate-/l* 83.8%

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

      4. sub-neg 83.8%

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

      5. +-commutative 83.8%

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

      6. neg-sub0 83.8%

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

      7. associate-+l- 83.8%

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

      8. sub0-neg 83.8%

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

      9. neg-mul-1 83.8%

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

      10. associate-/r* 83.8%

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

   3. Simplified 83.8%

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

   4. Taylor expanded in x around 0 83.8%

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

      1. div-sub 83.8%

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

      2. *-inverses 83.8%

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

   6. Simplified 83.8%

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

   7. Taylor expanded in z around inf 96.7%

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

      1. mul-1-neg 96.7%

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

      2. associate-/l* 96.7%

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

      3. distribute-neg-frac 96.7%

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

   9. Simplified 96.7%

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

   if -5.9999999999999999e-89 < y < -9.5e-91

   1. Initial program 99.2%

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

   2. Taylor expanded in z around 0 99.2%

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

      1. associate-*r/ 99.2%

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

      2. neg-mul-1 99.2%

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

      3. neg-sub0 99.2%

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

      4. associate--r- 99.2%

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

      5. neg-sub0 99.2%

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

      6. +-commutative 99.2%

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

      7. sub-neg 99.2%

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

   4. Simplified 99.2%

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

   5. Taylor expanded in y around 0 99.2%

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

      1. mul-1-neg 99.2%

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

      2. associate-*l/ 100.0%

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

      3. distribute-rgt-neg-in 100.0%

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

   7. Simplified 100.0%

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

   if -9.5e-91 < y < 3.7999999999999997e-57

   1. Initial program 94.6%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. *-commutative 94.6%

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

      2. associate-*r/ 92.7%

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

      3. associate-/l* 94.7%

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

      4. sub-neg 94.7%

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

      5. +-commutative 94.7%

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

      6. neg-sub0 94.7%

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

      7. associate-+l- 94.7%

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

      8. sub0-neg 94.7%

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

      9. neg-mul-1 94.7%

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

      10. associate-/r* 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in y around 0 77.9%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+151}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-57}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-89}:\\ \;\;\;\;\frac{-y}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-91}:\\ \;\;\;\;\frac{t}{y} \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-57}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+136}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 3: 70.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - x\right) \cdot \frac{t}{y}\\ \mathbf{if}\;y \leq -9 \cdot 10^{+150}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-40}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+132}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y x) (/ t y))))
   (if (<= y -9e+150)
     t
     (if (<= y -4.7e-36)
       t_1
       (if (<= y 8.5e-40) (* t (/ (- x y) z)) (if (<= y 4.7e+132) t_1 t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - x) * (t / y);
	double tmp;
	if (y <= -9e+150) {
		tmp = t;
	} else if (y <= -4.7e-36) {
		tmp = t_1;
	} else if (y <= 8.5e-40) {
		tmp = t * ((x - y) / z);
	} else if (y <= 4.7e+132) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - x) * (t / y)
    if (y <= (-9d+150)) then
        tmp = t
    else if (y <= (-4.7d-36)) then
        tmp = t_1
    else if (y <= 8.5d-40) then
        tmp = t * ((x - y) / z)
    else if (y <= 4.7d+132) 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 t_1 = (y - x) * (t / y);
	double tmp;
	if (y <= -9e+150) {
		tmp = t;
	} else if (y <= -4.7e-36) {
		tmp = t_1;
	} else if (y <= 8.5e-40) {
		tmp = t * ((x - y) / z);
	} else if (y <= 4.7e+132) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - x) * (t / y)
	tmp = 0
	if y <= -9e+150:
		tmp = t
	elif y <= -4.7e-36:
		tmp = t_1
	elif y <= 8.5e-40:
		tmp = t * ((x - y) / z)
	elif y <= 4.7e+132:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - x) * Float64(t / y))
	tmp = 0.0
	if (y <= -9e+150)
		tmp = t;
	elseif (y <= -4.7e-36)
		tmp = t_1;
	elseif (y <= 8.5e-40)
		tmp = Float64(t * Float64(Float64(x - y) / z));
	elseif (y <= 4.7e+132)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - x) * (t / y);
	tmp = 0.0;
	if (y <= -9e+150)
		tmp = t;
	elseif (y <= -4.7e-36)
		tmp = t_1;
	elseif (y <= 8.5e-40)
		tmp = t * ((x - y) / z);
	elseif (y <= 4.7e+132)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] * N[(t / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9e+150], t, If[LessEqual[y, -4.7e-36], t$95$1, If[LessEqual[y, 8.5e-40], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.7e+132], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.00000000000000001e150 or 4.7e132 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 81.0%

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

   if -9.00000000000000001e150 < y < -4.7000000000000003e-36 or 8.4999999999999998e-40 < y < 4.7e132

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. *-commutative 99.8%

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

      2. associate-*r/ 91.9%

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

      3. associate-/l* 99.8%

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

      4. sub-neg 99.8%

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

      5. +-commutative 99.8%

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

      6. neg-sub0 99.8%

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

      7. associate-+l- 99.8%

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

      8. sub0-neg 99.8%

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

      9. neg-mul-1 99.8%

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

      10. associate-/r* 99.8%

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

   3. Simplified 99.8%

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

      1. associate-/r/ 90.5%

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

   5. Applied egg-rr 90.5%

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

   6. Taylor expanded in y around inf 67.0%

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

   if -4.7000000000000003e-36 < y < 8.4999999999999998e-40

   1. Initial program 92.6%

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

   2. Taylor expanded in z around inf 79.5%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+150}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{-36}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-40}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+132}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 4: 60.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-52}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-86}:\\ \;\;\;\;\frac{-y}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-63}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+45}:\\ \;\;\;\;t \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -7.5e-52)
   t
   (if (<= y -2.8e-86)
     (/ (- y) (/ z t))
     (if (<= y 1.15e-63)
       (/ t (/ z x))
       (if (<= y 3.2e+45) (* t (/ (- x) y)) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.5e-52) {
		tmp = t;
	} else if (y <= -2.8e-86) {
		tmp = -y / (z / t);
	} else if (y <= 1.15e-63) {
		tmp = t / (z / x);
	} else if (y <= 3.2e+45) {
		tmp = t * (-x / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-7.5d-52)) then
        tmp = t
    else if (y <= (-2.8d-86)) then
        tmp = -y / (z / t)
    else if (y <= 1.15d-63) then
        tmp = t / (z / x)
    else if (y <= 3.2d+45) then
        tmp = t * (-x / y)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.5e-52) {
		tmp = t;
	} else if (y <= -2.8e-86) {
		tmp = -y / (z / t);
	} else if (y <= 1.15e-63) {
		tmp = t / (z / x);
	} else if (y <= 3.2e+45) {
		tmp = t * (-x / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -7.5e-52:
		tmp = t
	elif y <= -2.8e-86:
		tmp = -y / (z / t)
	elif y <= 1.15e-63:
		tmp = t / (z / x)
	elif y <= 3.2e+45:
		tmp = t * (-x / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -7.5e-52)
		tmp = t;
	elseif (y <= -2.8e-86)
		tmp = Float64(Float64(-y) / Float64(z / t));
	elseif (y <= 1.15e-63)
		tmp = Float64(t / Float64(z / x));
	elseif (y <= 3.2e+45)
		tmp = Float64(t * Float64(Float64(-x) / y));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -7.5e-52)
		tmp = t;
	elseif (y <= -2.8e-86)
		tmp = -y / (z / t);
	elseif (y <= 1.15e-63)
		tmp = t / (z / x);
	elseif (y <= 3.2e+45)
		tmp = t * (-x / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -7.5e-52], t, If[LessEqual[y, -2.8e-86], N[((-y) / N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.15e-63], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e+45], N[(t * N[((-x) / y), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.50000000000000006e-52 or 3.2000000000000003e45 < y

   1. Initial program 99.2%

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

   2. Taylor expanded in y around inf 62.4%

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

   if -7.50000000000000006e-52 < y < -2.80000000000000009e-86

   1. Initial program 83.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. *-commutative 83.8%

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

      2. associate-*r/ 100.0%

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

      3. associate-/l* 83.8%

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

      4. sub-neg 83.8%

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

      5. +-commutative 83.8%

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

      6. neg-sub0 83.8%

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

      7. associate-+l- 83.8%

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

      8. sub0-neg 83.8%

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

      9. neg-mul-1 83.8%

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

      10. associate-/r* 83.8%

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

   3. Simplified 83.8%

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

   4. Taylor expanded in x around 0 83.8%

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

      1. div-sub 83.8%

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

      2. *-inverses 83.8%

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

   6. Simplified 83.8%

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

   7. Taylor expanded in z around inf 96.7%

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

      1. mul-1-neg 96.7%

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

      2. associate-/l* 96.7%

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

      3. distribute-neg-frac 96.7%

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

   9. Simplified 96.7%

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

   if -2.80000000000000009e-86 < y < 1.15e-63

   1. Initial program 94.7%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. *-commutative 94.7%

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

      2. associate-*r/ 92.8%

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

      3. associate-/l* 94.8%

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

      4. sub-neg 94.8%

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

      5. +-commutative 94.8%

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

      6. neg-sub0 94.8%

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

      7. associate-+l- 94.8%

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

      8. sub0-neg 94.8%

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

      9. neg-mul-1 94.8%

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

      10. associate-/r* 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in y around 0 76.2%

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

   if 1.15e-63 < y < 3.2000000000000003e45

   1. Initial program 95.1%

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

   2. Taylor expanded in z around 0 61.6%

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

      1. associate-*r/ 61.6%

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

      2. neg-mul-1 61.6%

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

      3. neg-sub0 61.6%

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

      4. associate--r- 61.6%

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

      5. neg-sub0 61.6%

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

      6. +-commutative 61.6%

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

      7. sub-neg 61.6%

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

   4. Simplified 61.6%

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

   5. Taylor expanded in y around 0 61.7%

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

      1. neg-mul-1 61.7%

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

      2. distribute-neg-frac 61.7%

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

   7. Simplified 61.7%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-52}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-86}:\\ \;\;\;\;\frac{-y}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-63}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+45}:\\ \;\;\;\;t \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 5: 60.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-52}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{-91}:\\ \;\;\;\;\frac{t \cdot \left(-y\right)}{z}\\ \mathbf{elif}\;y \leq 10^{-54}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+45}:\\ \;\;\;\;t \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.9e-52)
   t
   (if (<= y -9.2e-91)
     (/ (* t (- y)) z)
     (if (<= y 1e-54) (/ t (/ z x)) (if (<= y 1.2e+45) (* t (/ (- x) y)) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.9e-52) {
		tmp = t;
	} else if (y <= -9.2e-91) {
		tmp = (t * -y) / z;
	} else if (y <= 1e-54) {
		tmp = t / (z / x);
	} else if (y <= 1.2e+45) {
		tmp = t * (-x / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.9d-52)) then
        tmp = t
    else if (y <= (-9.2d-91)) then
        tmp = (t * -y) / z
    else if (y <= 1d-54) then
        tmp = t / (z / x)
    else if (y <= 1.2d+45) then
        tmp = t * (-x / y)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.9e-52) {
		tmp = t;
	} else if (y <= -9.2e-91) {
		tmp = (t * -y) / z;
	} else if (y <= 1e-54) {
		tmp = t / (z / x);
	} else if (y <= 1.2e+45) {
		tmp = t * (-x / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.9e-52:
		tmp = t
	elif y <= -9.2e-91:
		tmp = (t * -y) / z
	elif y <= 1e-54:
		tmp = t / (z / x)
	elif y <= 1.2e+45:
		tmp = t * (-x / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.9e-52)
		tmp = t;
	elseif (y <= -9.2e-91)
		tmp = Float64(Float64(t * Float64(-y)) / z);
	elseif (y <= 1e-54)
		tmp = Float64(t / Float64(z / x));
	elseif (y <= 1.2e+45)
		tmp = Float64(t * Float64(Float64(-x) / y));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.9e-52)
		tmp = t;
	elseif (y <= -9.2e-91)
		tmp = (t * -y) / z;
	elseif (y <= 1e-54)
		tmp = t / (z / x);
	elseif (y <= 1.2e+45)
		tmp = t * (-x / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.9e-52], t, If[LessEqual[y, -9.2e-91], N[(N[(t * (-y)), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 1e-54], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e+45], N[(t * N[((-x) / y), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.9000000000000002e-52 or 1.19999999999999995e45 < y

   1. Initial program 99.2%

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

   2. Taylor expanded in y around inf 62.4%

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

   if -1.9000000000000002e-52 < y < -9.19999999999999982e-91

   1. Initial program 87.6%

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

   2. Taylor expanded in z around inf 60.6%

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

   3. Taylor expanded in x around 0 72.6%

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

      1. associate-*r/ 72.6%

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

      2. *-commutative 72.6%

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

      3. associate-*r* 72.6%

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

      4. neg-mul-1 72.6%

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

   5. Simplified 72.6%

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

   if -9.19999999999999982e-91 < y < 1e-54

   1. Initial program 94.6%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. *-commutative 94.6%

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

      2. associate-*r/ 92.7%

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

      3. associate-/l* 94.7%

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

      4. sub-neg 94.7%

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

      5. +-commutative 94.7%

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

      6. neg-sub0 94.7%

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

      7. associate-+l- 94.7%

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

      8. sub0-neg 94.7%

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

      9. neg-mul-1 94.7%

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

      10. associate-/r* 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in y around 0 77.9%

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

   if 1e-54 < y < 1.19999999999999995e45

   1. Initial program 95.1%

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

   2. Taylor expanded in z around 0 61.6%

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

      1. associate-*r/ 61.6%

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

      2. neg-mul-1 61.6%

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

      3. neg-sub0 61.6%

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

      4. associate--r- 61.6%

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

      5. neg-sub0 61.6%

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

      6. +-commutative 61.6%

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

      7. sub-neg 61.6%

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

   4. Simplified 61.6%

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

   5. Taylor expanded in y around 0 61.7%

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

      1. neg-mul-1 61.7%

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

      2. distribute-neg-frac 61.7%

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

   7. Simplified 61.7%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-52}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{-91}:\\ \;\;\;\;\frac{t \cdot \left(-y\right)}{z}\\ \mathbf{elif}\;y \leq 10^{-54}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+45}:\\ \;\;\;\;t \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 6: 75.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{\frac{z - y}{x}}\\ \mathbf{if}\;x \leq -6.4 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-31}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+71}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ t (/ (- z y) x))))
   (if (<= x -6.4e+69)
     t_1
     (if (<= x 7e-31)
       (/ t (- 1.0 (/ z y)))
       (if (<= x 6.8e+71) (* t (/ (- y x) y)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t / ((z - y) / x);
	double tmp;
	if (x <= -6.4e+69) {
		tmp = t_1;
	} else if (x <= 7e-31) {
		tmp = t / (1.0 - (z / y));
	} else if (x <= 6.8e+71) {
		tmp = t * ((y - x) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t / ((z - y) / x)
    if (x <= (-6.4d+69)) then
        tmp = t_1
    else if (x <= 7d-31) then
        tmp = t / (1.0d0 - (z / y))
    else if (x <= 6.8d+71) then
        tmp = t * ((y - x) / 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 t_1 = t / ((z - y) / x);
	double tmp;
	if (x <= -6.4e+69) {
		tmp = t_1;
	} else if (x <= 7e-31) {
		tmp = t / (1.0 - (z / y));
	} else if (x <= 6.8e+71) {
		tmp = t * ((y - x) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t / ((z - y) / x)
	tmp = 0
	if x <= -6.4e+69:
		tmp = t_1
	elif x <= 7e-31:
		tmp = t / (1.0 - (z / y))
	elif x <= 6.8e+71:
		tmp = t * ((y - x) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t / Float64(Float64(z - y) / x))
	tmp = 0.0
	if (x <= -6.4e+69)
		tmp = t_1;
	elseif (x <= 7e-31)
		tmp = Float64(t / Float64(1.0 - Float64(z / y)));
	elseif (x <= 6.8e+71)
		tmp = Float64(t * Float64(Float64(y - x) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t / ((z - y) / x);
	tmp = 0.0;
	if (x <= -6.4e+69)
		tmp = t_1;
	elseif (x <= 7e-31)
		tmp = t / (1.0 - (z / y));
	elseif (x <= 6.8e+71)
		tmp = t * ((y - x) / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.4e+69], t$95$1, If[LessEqual[x, 7e-31], N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.8e+71], N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.3999999999999997e69 or 6.7999999999999997e71 < x

   1. Initial program 95.9%

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

   2. Taylor expanded in x around inf 81.1%

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

      1. associate-/l* 83.9%

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

   4. Simplified 83.9%

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

   if -6.3999999999999997e69 < x < 6.99999999999999971e-31

   1. Initial program 97.1%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. *-commutative 97.1%

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

      2. associate-*r/ 81.1%

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

      3. associate-/l* 97.2%

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

      4. sub-neg 97.2%

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

      5. +-commutative 97.2%

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

      6. neg-sub0 97.2%

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

      7. associate-+l- 97.2%

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

      8. sub0-neg 97.2%

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

      9. neg-mul-1 97.2%

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

      10. associate-/r* 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in x around 0 84.0%

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

      1. div-sub 84.0%

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

      2. *-inverses 84.0%

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

   6. Simplified 84.0%

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

   if 6.99999999999999971e-31 < x < 6.7999999999999997e71

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 83.0%

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

      1. associate-*r/ 83.0%

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

      2. neg-mul-1 83.0%

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

      3. neg-sub0 83.0%

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

      4. associate--r- 83.0%

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

      5. neg-sub0 83.0%

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

      6. +-commutative 83.0%

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

      7. sub-neg 83.0%

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

   4. Simplified 83.0%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{+69}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-31}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+71}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \end{array} \]

Alternative 7: 90.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+149}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+138}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{t}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -6.5e+149)
   (/ t (- 1.0 (/ z y)))
   (if (<= y 2.8e+138) (* (- y x) (/ t (- y z))) (* t (/ (- y x) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.5e+149) {
		tmp = t / (1.0 - (z / y));
	} else if (y <= 2.8e+138) {
		tmp = (y - x) * (t / (y - z));
	} else {
		tmp = t * ((y - x) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-6.5d+149)) then
        tmp = t / (1.0d0 - (z / y))
    else if (y <= 2.8d+138) then
        tmp = (y - x) * (t / (y - z))
    else
        tmp = t * ((y - x) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.5e+149) {
		tmp = t / (1.0 - (z / y));
	} else if (y <= 2.8e+138) {
		tmp = (y - x) * (t / (y - z));
	} else {
		tmp = t * ((y - x) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -6.5e+149:
		tmp = t / (1.0 - (z / y))
	elif y <= 2.8e+138:
		tmp = (y - x) * (t / (y - z))
	else:
		tmp = t * ((y - x) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -6.5e+149)
		tmp = Float64(t / Float64(1.0 - Float64(z / y)));
	elseif (y <= 2.8e+138)
		tmp = Float64(Float64(y - x) * Float64(t / Float64(y - z)));
	else
		tmp = Float64(t * Float64(Float64(y - x) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -6.5e+149)
		tmp = t / (1.0 - (z / y));
	elseif (y <= 2.8e+138)
		tmp = (y - x) * (t / (y - z));
	else
		tmp = t * ((y - x) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -6.5e+149], N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e+138], N[(N[(y - x), $MachinePrecision] * N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.50000000000000015e149

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. *-commutative 99.9%

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

      2. associate-*r/ 68.3%

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

      3. associate-/l* 99.9%

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

      4. sub-neg 99.9%

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

      5. +-commutative 99.9%

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

      6. neg-sub0 99.9%

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

      7. associate-+l- 99.9%

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

      8. sub0-neg 99.9%

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

      9. neg-mul-1 99.9%

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

      10. associate-/r* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 86.7%

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

      1. div-sub 86.7%

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

      2. *-inverses 86.7%

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

   6. Simplified 86.7%

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

   if -6.50000000000000015e149 < y < 2.8000000000000001e138

   1. Initial program 95.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. *-commutative 95.8%

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

      2. associate-*r/ 92.0%

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

      3. associate-/l* 95.9%

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

      4. sub-neg 95.9%

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

      5. +-commutative 95.9%

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

      6. neg-sub0 95.9%

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

      7. associate-+l- 95.9%

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

      8. sub0-neg 95.9%

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

      9. neg-mul-1 95.9%

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

      10. associate-/r* 95.9%

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

   3. Simplified 95.9%

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

      1. associate-/r/ 90.7%

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

   5. Applied egg-rr 90.7%

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

   if 2.8000000000000001e138 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 100.0%

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

      1. associate-*r/ 100.0%

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

      2. neg-mul-1 100.0%

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

      3. neg-sub0 100.0%

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

      4. associate--r- 100.0%

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

      5. neg-sub0 100.0%

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

      6. +-commutative 100.0%

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

      7. sub-neg 100.0%

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

   4. Simplified 100.0%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+149}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+138}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{t}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \end{array} \]

Alternative 8: 61.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-32}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-54}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+44}:\\ \;\;\;\;\frac{t}{y} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.3e-32)
   t
   (if (<= y 2.3e-54) (/ t (/ z x)) (if (<= y 1.75e+44) (* (/ t y) (- x)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.3e-32) {
		tmp = t;
	} else if (y <= 2.3e-54) {
		tmp = t / (z / x);
	} else if (y <= 1.75e+44) {
		tmp = (t / y) * -x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.3d-32)) then
        tmp = t
    else if (y <= 2.3d-54) then
        tmp = t / (z / x)
    else if (y <= 1.75d+44) then
        tmp = (t / y) * -x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.3e-32) {
		tmp = t;
	} else if (y <= 2.3e-54) {
		tmp = t / (z / x);
	} else if (y <= 1.75e+44) {
		tmp = (t / y) * -x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.3e-32:
		tmp = t
	elif y <= 2.3e-54:
		tmp = t / (z / x)
	elif y <= 1.75e+44:
		tmp = (t / y) * -x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.3e-32)
		tmp = t;
	elseif (y <= 2.3e-54)
		tmp = Float64(t / Float64(z / x));
	elseif (y <= 1.75e+44)
		tmp = Float64(Float64(t / y) * Float64(-x));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.3e-32)
		tmp = t;
	elseif (y <= 2.3e-54)
		tmp = t / (z / x);
	elseif (y <= 1.75e+44)
		tmp = (t / y) * -x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.3e-32], t, If[LessEqual[y, 2.3e-54], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.75e+44], N[(N[(t / y), $MachinePrecision] * (-x)), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.2999999999999999e-32 or 1.75e44 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 63.9%

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

   if -1.2999999999999999e-32 < y < 2.2999999999999999e-54

   1. Initial program 93.4%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. *-commutative 93.4%

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

      2. associate-*r/ 92.6%

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

      3. associate-/l* 93.4%

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

      4. sub-neg 93.4%

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

      5. +-commutative 93.4%

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

      6. neg-sub0 93.4%

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

      7. associate-+l- 93.4%

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

      8. sub0-neg 93.4%

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

      9. neg-mul-1 93.4%

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

      10. associate-/r* 93.4%

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

   3. Simplified 93.4%

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

   4. Taylor expanded in y around 0 70.8%

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

   if 2.2999999999999999e-54 < y < 1.75e44

   1. Initial program 95.1%

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

   2. Taylor expanded in z around 0 61.6%

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

      1. associate-*r/ 61.6%

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

      2. neg-mul-1 61.6%

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

      3. neg-sub0 61.6%

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

      4. associate--r- 61.6%

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

      5. neg-sub0 61.6%

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

      6. +-commutative 61.6%

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

      7. sub-neg 61.6%

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

   4. Simplified 61.6%

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

   5. Taylor expanded in y around 0 61.6%

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

      1. mul-1-neg 61.6%

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

      2. associate-*l/ 60.3%

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

      3. distribute-rgt-neg-in 60.3%

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

   7. Simplified 60.3%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-32}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-54}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+44}:\\ \;\;\;\;\frac{t}{y} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 9: 61.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-34}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-54}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+44}:\\ \;\;\;\;t \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.5e-34)
   t
   (if (<= y 2.35e-54) (/ t (/ z x)) (if (<= y 2.5e+44) (* t (/ (- x) y)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.5e-34) {
		tmp = t;
	} else if (y <= 2.35e-54) {
		tmp = t / (z / x);
	} else if (y <= 2.5e+44) {
		tmp = t * (-x / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-5.5d-34)) then
        tmp = t
    else if (y <= 2.35d-54) then
        tmp = t / (z / x)
    else if (y <= 2.5d+44) then
        tmp = t * (-x / y)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.5e-34) {
		tmp = t;
	} else if (y <= 2.35e-54) {
		tmp = t / (z / x);
	} else if (y <= 2.5e+44) {
		tmp = t * (-x / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.5e-34:
		tmp = t
	elif y <= 2.35e-54:
		tmp = t / (z / x)
	elif y <= 2.5e+44:
		tmp = t * (-x / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.5e-34)
		tmp = t;
	elseif (y <= 2.35e-54)
		tmp = Float64(t / Float64(z / x));
	elseif (y <= 2.5e+44)
		tmp = Float64(t * Float64(Float64(-x) / y));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.5e-34)
		tmp = t;
	elseif (y <= 2.35e-54)
		tmp = t / (z / x);
	elseif (y <= 2.5e+44)
		tmp = t * (-x / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.5e-34], t, If[LessEqual[y, 2.35e-54], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e+44], N[(t * N[((-x) / y), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.50000000000000014e-34 or 2.4999999999999998e44 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 63.9%

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

   if -5.50000000000000014e-34 < y < 2.35e-54

   1. Initial program 93.4%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. *-commutative 93.4%

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

      2. associate-*r/ 92.6%

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

      3. associate-/l* 93.4%

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

      4. sub-neg 93.4%

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

      5. +-commutative 93.4%

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

      6. neg-sub0 93.4%

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

      7. associate-+l- 93.4%

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

      8. sub0-neg 93.4%

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

      9. neg-mul-1 93.4%

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

      10. associate-/r* 93.4%

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

   3. Simplified 93.4%

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

   4. Taylor expanded in y around 0 70.8%

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

   if 2.35e-54 < y < 2.4999999999999998e44

   1. Initial program 95.1%

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

   2. Taylor expanded in z around 0 61.6%

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

      1. associate-*r/ 61.6%

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

      2. neg-mul-1 61.6%

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

      3. neg-sub0 61.6%

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

      4. associate--r- 61.6%

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

      5. neg-sub0 61.6%

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

      6. +-commutative 61.6%

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

      7. sub-neg 61.6%

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

   4. Simplified 61.6%

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

   5. Taylor expanded in y around 0 61.7%

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

      1. neg-mul-1 61.7%

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

      2. distribute-neg-frac 61.7%

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

   7. Simplified 61.7%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-34}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-54}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+44}:\\ \;\;\;\;t \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 10: 74.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-42} \lor \neg \left(y \leq 8.5 \cdot 10^{-40}\right):\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.2e-42) (not (<= y 8.5e-40)))
   (* t (/ (- y x) y))
   (* t (/ (- x y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.2e-42) || !(y <= 8.5e-40)) {
		tmp = t * ((y - x) / y);
	} else {
		tmp = t * ((x - y) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-4.2d-42)) .or. (.not. (y <= 8.5d-40))) then
        tmp = t * ((y - x) / y)
    else
        tmp = t * ((x - y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.2e-42) || !(y <= 8.5e-40)) {
		tmp = t * ((y - x) / y);
	} else {
		tmp = t * ((x - y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4.2e-42) or not (y <= 8.5e-40):
		tmp = t * ((y - x) / y)
	else:
		tmp = t * ((x - y) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.2e-42) || !(y <= 8.5e-40))
		tmp = Float64(t * Float64(Float64(y - x) / y));
	else
		tmp = Float64(t * Float64(Float64(x - y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -4.2e-42) || ~((y <= 8.5e-40)))
		tmp = t * ((y - x) / y);
	else
		tmp = t * ((x - y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.2e-42], N[Not[LessEqual[y, 8.5e-40]], $MachinePrecision]], N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.20000000000000013e-42 or 8.4999999999999998e-40 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 78.0%

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

      1. associate-*r/ 78.0%

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

      2. neg-mul-1 78.0%

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

      3. neg-sub0 78.0%

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

      4. associate--r- 78.0%

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

      5. neg-sub0 78.0%

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

      6. +-commutative 78.0%

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

      7. sub-neg 78.0%

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

   4. Simplified 78.0%

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

   if -4.20000000000000013e-42 < y < 8.4999999999999998e-40

   1. Initial program 92.6%

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

   2. Taylor expanded in z around inf 79.5%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-42} \lor \neg \left(y \leq 8.5 \cdot 10^{-40}\right):\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \end{array} \]

Alternative 11: 60.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.16 \cdot 10^{-33}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+43}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.16e-33) t (if (<= y 1.35e+43) (* x (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.16e-33) {
		tmp = t;
	} else if (y <= 1.35e+43) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.16d-33)) then
        tmp = t
    else if (y <= 1.35d+43) then
        tmp = x * (t / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.16e-33) {
		tmp = t;
	} else if (y <= 1.35e+43) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.16e-33:
		tmp = t
	elif y <= 1.35e+43:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.16e-33)
		tmp = t;
	elseif (y <= 1.35e+43)
		tmp = Float64(x * Float64(t / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.16e-33)
		tmp = t;
	elseif (y <= 1.35e+43)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.16e-33], t, If[LessEqual[y, 1.35e+43], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.1600000000000001e-33 or 1.3500000000000001e43 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 63.9%

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

   if -1.1600000000000001e-33 < y < 1.3500000000000001e43

   1. Initial program 93.6%

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

   2. Taylor expanded in y around 0 61.6%

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

      1. associate-/l* 63.8%

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

      2. associate-/r/ 61.1%

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

   4. Simplified 61.1%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.16 \cdot 10^{-33}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+43}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 12: 61.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-32}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+44}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.45e-32) t (if (<= y 2e+44) (* t (/ x z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.45e-32) {
		tmp = t;
	} else if (y <= 2e+44) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.45d-32)) then
        tmp = t
    else if (y <= 2d+44) then
        tmp = t * (x / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.45e-32) {
		tmp = t;
	} else if (y <= 2e+44) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.45e-32:
		tmp = t
	elif y <= 2e+44:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.45e-32)
		tmp = t;
	elseif (y <= 2e+44)
		tmp = Float64(t * Float64(x / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.45e-32)
		tmp = t;
	elseif (y <= 2e+44)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.45e-32], t, If[LessEqual[y, 2e+44], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.44999999999999998e-32 or 2.0000000000000002e44 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 63.9%

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

   if -1.44999999999999998e-32 < y < 2.0000000000000002e44

   1. Initial program 93.6%

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

   2. Taylor expanded in y around 0 63.8%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-32}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+44}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 13: 61.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-32}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+45}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.45e-32) t (if (<= y 2e+45) (/ t (/ z x)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.45e-32) {
		tmp = t;
	} else if (y <= 2e+45) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.45d-32)) then
        tmp = t
    else if (y <= 2d+45) then
        tmp = t / (z / x)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.45e-32) {
		tmp = t;
	} else if (y <= 2e+45) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.45e-32:
		tmp = t
	elif y <= 2e+45:
		tmp = t / (z / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.45e-32)
		tmp = t;
	elseif (y <= 2e+45)
		tmp = Float64(t / Float64(z / x));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.45e-32)
		tmp = t;
	elseif (y <= 2e+45)
		tmp = t / (z / x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.45e-32], t, If[LessEqual[y, 2e+45], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.44999999999999998e-32 or 1.9999999999999999e45 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 63.9%

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

   if -1.44999999999999998e-32 < y < 1.9999999999999999e45

   1. Initial program 93.6%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. *-commutative 93.6%

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

      2. associate-*r/ 93.8%

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

      3. associate-/l* 93.7%

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

      4. sub-neg 93.7%

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

      5. +-commutative 93.7%

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

      6. neg-sub0 93.7%

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

      7. associate-+l- 93.7%

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

      8. sub0-neg 93.7%

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

      9. neg-mul-1 93.7%

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

      10. associate-/r* 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in y around 0 63.8%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-32}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+45}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 14: 97.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ t \cdot \frac{x - y}{z - y} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

2. Final simplification 96.9%

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

Alternative 15: 34.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+106}:\\ \;\;\;\;t \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= x -1.5e+106) (* t (/ x y)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.5e+106) {
		tmp = t * (x / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-1.5d+106)) then
        tmp = t * (x / y)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.5e+106) {
		tmp = t * (x / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.5e+106:
		tmp = t * (x / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.5e+106)
		tmp = Float64(t * Float64(x / y));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.5e+106)
		tmp = t * (x / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.5e+106], N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if x < -1.5e106

   1. Initial program 92.2%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. *-commutative 92.2%

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

      2. associate-*r/ 89.4%

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

      3. associate-/l* 92.1%

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

      4. sub-neg 92.1%

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

      5. +-commutative 92.1%

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

      6. neg-sub0 92.1%

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

      7. associate-+l- 92.1%

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

      8. sub0-neg 92.1%

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

      9. neg-mul-1 92.1%

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

      10. associate-/r* 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in z around 0 45.4%

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

   5. Taylor expanded in y around 0 39.6%

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

      1. associate-*r/ 39.6%

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

      2. mul-1-neg 39.6%

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

      3. distribute-rgt-neg-out 39.6%

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

   7. Simplified 39.6%

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

      1. expm1-log1p-u 21.5%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{t \cdot \left(-x\right)}{y}\right)\right)} \]

      2. expm1-udef 17.1%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{t \cdot \left(-x\right)}{y}\right)} - 1} \]

      3. associate-/l* 17.1%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{t}{\frac{y}{-x}}}\right)} - 1 \]

      4. associate-/r/ 17.1%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{t}{y} \cdot \left(-x\right)}\right)} - 1 \]

      5. add-sqr-sqrt 17.1%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{t}{y} \cdot \color{blue}{\left(\sqrt{-x} \cdot \sqrt{-x}\right)}\right)} - 1 \]

      6. sqrt-unprod 11.7%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{t}{y} \cdot \color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}\right)} - 1 \]

      7. sqr-neg 11.7%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{t}{y} \cdot \sqrt{\color{blue}{x \cdot x}}\right)} - 1 \]

      8. sqrt-unprod 0.0%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{t}{y} \cdot \color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)}\right)} - 1 \]

      9. add-sqr-sqrt 12.7%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{t}{y} \cdot \color{blue}{x}\right)} - 1 \]

   9. Applied egg-rr 12.7%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{t}{y} \cdot x\right)} - 1} \]
   10. Step-by-step derivation

       1. expm1-def 10.0%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{t}{y} \cdot x\right)\right)} \]

       2. expm1-log1p 24.0%

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

       3. associate-*l/ 23.9%

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

       4. associate-*r/ 24.0%

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

   11. Simplified 24.0%

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

   if -1.5e106 < x

   1. Initial program 97.7%

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

   2. Taylor expanded in y around inf 42.9%

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

4. Final simplification 40.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+106}:\\ \;\;\;\;t \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 16: 35.7% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ t \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 t)

C

double code(double x, double y, double z, double t) {
	return t;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = t
end function

Java

public static double code(double x, double y, double z, double t) {
	return t;
}

Python

def code(x, y, z, t):
	return t

Julia

function code(x, y, z, t)
	return t
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = t;
end

Wolfram

code[x_, y_, z_, t_] := t

Derivation

1. Initial program 96.9%

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

2. Taylor expanded in y around inf 38.1%

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

3. Final simplification 38.1%

   \[\leadsto t \]

Developer target: 97.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{t}{\frac{z - y}{x - y}} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023274 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (/ t (/ (- z y) (- x y)))

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