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

Percentage Accurate: 96.9% → 96.9%

Time: 10.4s

Alternatives: 15

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: 96.9% 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: 96.9% 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]

Derivation

1. Initial program 97.9%

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

2. Final simplification 97.9%

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

Alternative 2: 75.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2300000000000:\\ \;\;\;\;\frac{y \cdot \left(-t\right)}{z}\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{-34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.92 \cdot 10^{-107}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-20}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ x y)))))
   (if (<= y -4.8e+17)
     t_1
     (if (<= y -2300000000000.0)
       (/ (* y (- t)) z)
       (if (<= y -6.8e-34)
         t_1
         (if (<= y -1.92e-107)
           (* t (/ (- x y) z))
           (if (<= y 1.35e-20) (* t (/ x (- z y))) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -4.8e+17) {
		tmp = t_1;
	} else if (y <= -2300000000000.0) {
		tmp = (y * -t) / z;
	} else if (y <= -6.8e-34) {
		tmp = t_1;
	} else if (y <= -1.92e-107) {
		tmp = t * ((x - y) / z);
	} else if (y <= 1.35e-20) {
		tmp = t * (x / (z - 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 * (1.0d0 - (x / y))
    if (y <= (-4.8d+17)) then
        tmp = t_1
    else if (y <= (-2300000000000.0d0)) then
        tmp = (y * -t) / z
    else if (y <= (-6.8d-34)) then
        tmp = t_1
    else if (y <= (-1.92d-107)) then
        tmp = t * ((x - y) / z)
    else if (y <= 1.35d-20) then
        tmp = t * (x / (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 t_1 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -4.8e+17) {
		tmp = t_1;
	} else if (y <= -2300000000000.0) {
		tmp = (y * -t) / z;
	} else if (y <= -6.8e-34) {
		tmp = t_1;
	} else if (y <= -1.92e-107) {
		tmp = t * ((x - y) / z);
	} else if (y <= 1.35e-20) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (1.0 - (x / y))
	tmp = 0
	if y <= -4.8e+17:
		tmp = t_1
	elif y <= -2300000000000.0:
		tmp = (y * -t) / z
	elif y <= -6.8e-34:
		tmp = t_1
	elif y <= -1.92e-107:
		tmp = t * ((x - y) / z)
	elif y <= 1.35e-20:
		tmp = t * (x / (z - y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -4.8e+17)
		tmp = t_1;
	elseif (y <= -2300000000000.0)
		tmp = Float64(Float64(y * Float64(-t)) / z);
	elseif (y <= -6.8e-34)
		tmp = t_1;
	elseif (y <= -1.92e-107)
		tmp = Float64(t * Float64(Float64(x - y) / z));
	elseif (y <= 1.35e-20)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (1.0 - (x / y));
	tmp = 0.0;
	if (y <= -4.8e+17)
		tmp = t_1;
	elseif (y <= -2300000000000.0)
		tmp = (y * -t) / z;
	elseif (y <= -6.8e-34)
		tmp = t_1;
	elseif (y <= -1.92e-107)
		tmp = t * ((x - y) / z);
	elseif (y <= 1.35e-20)
		tmp = t * (x / (z - y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.8e+17], t$95$1, If[LessEqual[y, -2300000000000.0], N[(N[(y * (-t)), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, -6.8e-34], t$95$1, If[LessEqual[y, -1.92e-107], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.35e-20], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.8e17 or -2.3e12 < y < -6.8000000000000001e-34 or 1.35e-20 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 76.9%

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

      1. associate--l+ 76.9%

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

      2. distribute-lft-out-- 76.9%

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

      3. div-sub 76.9%

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

      4. mul-1-neg 76.9%

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

      5. unsub-neg 76.9%

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

   4. Simplified 76.9%

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

   5. Taylor expanded in x around inf 77.5%

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

   if -4.8e17 < y < -2.3e12

   1. Initial program 99.4%

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

      1. associate-*l/ 100.0%

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

      2. associate-*r/ 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around inf 100.0%

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

   5. Taylor expanded in x around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-lft-neg-out 100.0%

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

      3. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   if -6.8000000000000001e-34 < y < -1.92000000000000014e-107

   1. Initial program 99.6%

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

   2. Taylor expanded in z around inf 87.6%

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

   if -1.92000000000000014e-107 < y < 1.35e-20

   1. Initial program 94.7%

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

   2. Taylor expanded in x around inf 87.6%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+17}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -2300000000000:\\ \;\;\;\;\frac{y \cdot \left(-t\right)}{z}\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{-34}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -1.92 \cdot 10^{-107}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-20}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]

Alternative 3: 88.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - y\right) \cdot \frac{t}{z - y}\\ t_2 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{+164}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{-287}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-110}:\\ \;\;\;\;\frac{x \cdot t}{z - y}\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+147}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- x y) (/ t (- z y)))) (t_2 (* t (- 1.0 (/ x y)))))
   (if (<= y -5.5e+164)
     t_2
     (if (<= y 9.6e-287)
       t_1
       (if (<= y 1.9e-110)
         (/ (* x t) (- z y))
         (if (<= y 1.12e+147) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) * (t / (z - y));
	double t_2 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -5.5e+164) {
		tmp = t_2;
	} else if (y <= 9.6e-287) {
		tmp = t_1;
	} else if (y <= 1.9e-110) {
		tmp = (x * t) / (z - y);
	} else if (y <= 1.12e+147) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = (x - y) * (t / (z - y))
    t_2 = t * (1.0d0 - (x / y))
    if (y <= (-5.5d+164)) then
        tmp = t_2
    else if (y <= 9.6d-287) then
        tmp = t_1
    else if (y <= 1.9d-110) then
        tmp = (x * t) / (z - y)
    else if (y <= 1.12d+147) 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 t_1 = (x - y) * (t / (z - y));
	double t_2 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -5.5e+164) {
		tmp = t_2;
	} else if (y <= 9.6e-287) {
		tmp = t_1;
	} else if (y <= 1.9e-110) {
		tmp = (x * t) / (z - y);
	} else if (y <= 1.12e+147) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) * (t / (z - y))
	t_2 = t * (1.0 - (x / y))
	tmp = 0
	if y <= -5.5e+164:
		tmp = t_2
	elif y <= 9.6e-287:
		tmp = t_1
	elif y <= 1.9e-110:
		tmp = (x * t) / (z - y)
	elif y <= 1.12e+147:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) * Float64(t / Float64(z - y)))
	t_2 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -5.5e+164)
		tmp = t_2;
	elseif (y <= 9.6e-287)
		tmp = t_1;
	elseif (y <= 1.9e-110)
		tmp = Float64(Float64(x * t) / Float64(z - y));
	elseif (y <= 1.12e+147)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) * (t / (z - y));
	t_2 = t * (1.0 - (x / y));
	tmp = 0.0;
	if (y <= -5.5e+164)
		tmp = t_2;
	elseif (y <= 9.6e-287)
		tmp = t_1;
	elseif (y <= 1.9e-110)
		tmp = (x * t) / (z - y);
	elseif (y <= 1.12e+147)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.5e+164], t$95$2, If[LessEqual[y, 9.6e-287], t$95$1, If[LessEqual[y, 1.9e-110], N[(N[(x * t), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.12e+147], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.4999999999999998e164 or 1.12e147 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in y around inf 92.6%

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

      1. associate--l+ 92.6%

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

      2. distribute-lft-out-- 92.6%

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

      3. div-sub 92.6%

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

      4. mul-1-neg 92.6%

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

      5. unsub-neg 92.6%

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

   4. Simplified 92.6%

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

   5. Taylor expanded in x around inf 92.8%

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

   if -5.4999999999999998e164 < y < 9.59999999999999997e-287 or 1.8999999999999999e-110 < y < 1.12e147

   1. Initial program 97.8%

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

      1. associate-*l/ 87.0%

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

      2. associate-*r/ 95.5%

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

   3. Simplified 95.5%

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

   if 9.59999999999999997e-287 < y < 1.8999999999999999e-110

   1. Initial program 94.3%

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

      1. associate-*l/ 99.7%

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

      2. associate-*r/ 83.6%

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

   3. Simplified 83.6%

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

   4. Taylor expanded in x around inf 97.0%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+164}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{-287}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-110}:\\ \;\;\;\;\frac{x \cdot t}{z - y}\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+147}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]

Alternative 4: 75.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -49000000:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-34}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-108}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-21}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-y}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -49000000.0)
   (/ t (- 1.0 (/ z y)))
   (if (<= y -4e-34)
     (* t (- 1.0 (/ x y)))
     (if (<= y -4.2e-108)
       (* t (/ (- x y) z))
       (if (<= y 5.6e-21) (* t (/ x (- z y))) (* t (/ (- y) (- z y))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -49000000.0) {
		tmp = t / (1.0 - (z / y));
	} else if (y <= -4e-34) {
		tmp = t * (1.0 - (x / y));
	} else if (y <= -4.2e-108) {
		tmp = t * ((x - y) / z);
	} else if (y <= 5.6e-21) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t * (-y / (z - 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 <= (-49000000.0d0)) then
        tmp = t / (1.0d0 - (z / y))
    else if (y <= (-4d-34)) then
        tmp = t * (1.0d0 - (x / y))
    else if (y <= (-4.2d-108)) then
        tmp = t * ((x - y) / z)
    else if (y <= 5.6d-21) then
        tmp = t * (x / (z - y))
    else
        tmp = t * (-y / (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -49000000.0) {
		tmp = t / (1.0 - (z / y));
	} else if (y <= -4e-34) {
		tmp = t * (1.0 - (x / y));
	} else if (y <= -4.2e-108) {
		tmp = t * ((x - y) / z);
	} else if (y <= 5.6e-21) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t * (-y / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -49000000.0:
		tmp = t / (1.0 - (z / y))
	elif y <= -4e-34:
		tmp = t * (1.0 - (x / y))
	elif y <= -4.2e-108:
		tmp = t * ((x - y) / z)
	elif y <= 5.6e-21:
		tmp = t * (x / (z - y))
	else:
		tmp = t * (-y / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -49000000.0)
		tmp = Float64(t / Float64(1.0 - Float64(z / y)));
	elseif (y <= -4e-34)
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	elseif (y <= -4.2e-108)
		tmp = Float64(t * Float64(Float64(x - y) / z));
	elseif (y <= 5.6e-21)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	else
		tmp = Float64(t * Float64(Float64(-y) / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -49000000.0)
		tmp = t / (1.0 - (z / y));
	elseif (y <= -4e-34)
		tmp = t * (1.0 - (x / y));
	elseif (y <= -4.2e-108)
		tmp = t * ((x - y) / z);
	elseif (y <= 5.6e-21)
		tmp = t * (x / (z - y));
	else
		tmp = t * (-y / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -49000000.0], N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4e-34], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.2e-108], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.6e-21], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[((-y) / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -4.9e7

   1. Initial program 99.8%

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

      1. associate-*l/ 75.4%

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

      2. associate-*r/ 70.6%

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

   3. Simplified 70.6%

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

      1. associate-*r/ 75.4%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

      4. clear-num 99.7%

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

      5. un-div-inv 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around 0 77.3%

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

      1. mul-1-neg 77.3%

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

      2. neg-sub0 77.3%

         \[\leadsto \frac{t}{\color{blue}{0 - \frac{z - y}{y}}} \]

      3. div-sub 77.3%

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

      4. *-inverses 77.3%

         \[\leadsto \frac{t}{0 - \left(\frac{z}{y} - \color{blue}{1}\right)} \]

      5. associate-+l- 77.3%

         \[\leadsto \frac{t}{\color{blue}{\left(0 - \frac{z}{y}\right) + 1}} \]

      6. neg-sub0 77.3%

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

      7. neg-mul-1 77.3%

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

      8. +-commutative 77.3%

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

      9. neg-mul-1 77.3%

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

      10. unsub-neg 77.3%

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

   8. Simplified 77.3%

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

   if -4.9e7 < y < -3.99999999999999971e-34

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 91.0%

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

      1. associate--l+ 91.0%

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

      2. distribute-lft-out-- 91.0%

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

      3. div-sub 91.0%

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

      4. mul-1-neg 91.0%

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

      5. unsub-neg 91.0%

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

   4. Simplified 91.0%

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

   5. Taylor expanded in x around inf 91.0%

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

   if -3.99999999999999971e-34 < y < -4.1999999999999998e-108

   1. Initial program 99.6%

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

   2. Taylor expanded in z around inf 87.6%

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

   if -4.1999999999999998e-108 < y < 5.60000000000000008e-21

   1. Initial program 94.7%

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

   2. Taylor expanded in x around inf 87.6%

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

   if 5.60000000000000008e-21 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 78.1%

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

      1. neg-mul-1 78.1%

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

      2. distribute-neg-frac 78.1%

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

   4. Simplified 78.1%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -49000000:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-34}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-108}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-21}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-y}{z - y}\\ \end{array} \]

Alternative 5: 75.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2300000000000:\\ \;\;\;\;\frac{y \cdot \left(-t\right)}{z}\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-34} \lor \neg \left(y \leq 6.5 \cdot 10^{-20}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ x y)))))
   (if (<= y -4.8e+17)
     t_1
     (if (<= y -2300000000000.0)
       (/ (* y (- t)) z)
       (if (or (<= y -4.4e-34) (not (<= y 6.5e-20)))
         t_1
         (* x (/ t (- z y))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -4.8e+17) {
		tmp = t_1;
	} else if (y <= -2300000000000.0) {
		tmp = (y * -t) / z;
	} else if ((y <= -4.4e-34) || !(y <= 6.5e-20)) {
		tmp = t_1;
	} else {
		tmp = x * (t / (z - 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) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (x / y))
    if (y <= (-4.8d+17)) then
        tmp = t_1
    else if (y <= (-2300000000000.0d0)) then
        tmp = (y * -t) / z
    else if ((y <= (-4.4d-34)) .or. (.not. (y <= 6.5d-20))) then
        tmp = t_1
    else
        tmp = x * (t / (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -4.8e+17) {
		tmp = t_1;
	} else if (y <= -2300000000000.0) {
		tmp = (y * -t) / z;
	} else if ((y <= -4.4e-34) || !(y <= 6.5e-20)) {
		tmp = t_1;
	} else {
		tmp = x * (t / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (1.0 - (x / y))
	tmp = 0
	if y <= -4.8e+17:
		tmp = t_1
	elif y <= -2300000000000.0:
		tmp = (y * -t) / z
	elif (y <= -4.4e-34) or not (y <= 6.5e-20):
		tmp = t_1
	else:
		tmp = x * (t / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -4.8e+17)
		tmp = t_1;
	elseif (y <= -2300000000000.0)
		tmp = Float64(Float64(y * Float64(-t)) / z);
	elseif ((y <= -4.4e-34) || !(y <= 6.5e-20))
		tmp = t_1;
	else
		tmp = Float64(x * Float64(t / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (1.0 - (x / y));
	tmp = 0.0;
	if (y <= -4.8e+17)
		tmp = t_1;
	elseif (y <= -2300000000000.0)
		tmp = (y * -t) / z;
	elseif ((y <= -4.4e-34) || ~((y <= 6.5e-20)))
		tmp = t_1;
	else
		tmp = x * (t / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.8e+17], t$95$1, If[LessEqual[y, -2300000000000.0], N[(N[(y * (-t)), $MachinePrecision] / z), $MachinePrecision], If[Or[LessEqual[y, -4.4e-34], N[Not[LessEqual[y, 6.5e-20]], $MachinePrecision]], t$95$1, N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.8e17 or -2.3e12 < y < -4.3999999999999998e-34 or 6.50000000000000032e-20 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 76.9%

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

      1. associate--l+ 76.9%

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

      2. distribute-lft-out-- 76.9%

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

      3. div-sub 76.9%

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

      4. mul-1-neg 76.9%

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

      5. unsub-neg 76.9%

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

   4. Simplified 76.9%

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

   5. Taylor expanded in x around inf 77.5%

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

   if -4.8e17 < y < -2.3e12

   1. Initial program 99.4%

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

      1. associate-*l/ 100.0%

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

      2. associate-*r/ 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around inf 100.0%

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

   5. Taylor expanded in x around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-lft-neg-out 100.0%

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

      3. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   if -4.3999999999999998e-34 < y < 6.50000000000000032e-20

   1. Initial program 95.5%

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

      1. associate-*l/ 89.9%

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

      2. associate-*r/ 91.6%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in x around inf 78.3%

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

      1. associate-*l/ 79.0%

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

      2. *-commutative 79.0%

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

   6. Simplified 79.0%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+17}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -2300000000000:\\ \;\;\;\;\frac{y \cdot \left(-t\right)}{z}\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-34} \lor \neg \left(y \leq 6.5 \cdot 10^{-20}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \]

Alternative 6: 71.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ t_2 := \left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{if}\;z \leq -36000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-35}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq 70000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ x y)))) (t_2 (* (- x y) (/ t z))))
   (if (<= z -36000000000.0)
     t_2
     (if (<= z -3.8e-22)
       t_1
       (if (<= z -4.7e-35) (/ t (/ z x)) (if (<= z 70000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double t_2 = (x - y) * (t / z);
	double tmp;
	if (z <= -36000000000.0) {
		tmp = t_2;
	} else if (z <= -3.8e-22) {
		tmp = t_1;
	} else if (z <= -4.7e-35) {
		tmp = t / (z / x);
	} else if (z <= 70000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = t * (1.0d0 - (x / y))
    t_2 = (x - y) * (t / z)
    if (z <= (-36000000000.0d0)) then
        tmp = t_2
    else if (z <= (-3.8d-22)) then
        tmp = t_1
    else if (z <= (-4.7d-35)) then
        tmp = t / (z / x)
    else if (z <= 70000.0d0) 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 t_1 = t * (1.0 - (x / y));
	double t_2 = (x - y) * (t / z);
	double tmp;
	if (z <= -36000000000.0) {
		tmp = t_2;
	} else if (z <= -3.8e-22) {
		tmp = t_1;
	} else if (z <= -4.7e-35) {
		tmp = t / (z / x);
	} else if (z <= 70000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (1.0 - (x / y))
	t_2 = (x - y) * (t / z)
	tmp = 0
	if z <= -36000000000.0:
		tmp = t_2
	elif z <= -3.8e-22:
		tmp = t_1
	elif z <= -4.7e-35:
		tmp = t / (z / x)
	elif z <= 70000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(1.0 - Float64(x / y)))
	t_2 = Float64(Float64(x - y) * Float64(t / z))
	tmp = 0.0
	if (z <= -36000000000.0)
		tmp = t_2;
	elseif (z <= -3.8e-22)
		tmp = t_1;
	elseif (z <= -4.7e-35)
		tmp = Float64(t / Float64(z / x));
	elseif (z <= 70000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (1.0 - (x / y));
	t_2 = (x - y) * (t / z);
	tmp = 0.0;
	if (z <= -36000000000.0)
		tmp = t_2;
	elseif (z <= -3.8e-22)
		tmp = t_1;
	elseif (z <= -4.7e-35)
		tmp = t / (z / x);
	elseif (z <= 70000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -36000000000.0], t$95$2, If[LessEqual[z, -3.8e-22], t$95$1, If[LessEqual[z, -4.7e-35], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 70000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.6e10 or 7e4 < z

   1. Initial program 96.7%

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

      1. associate-*l/ 85.2%

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

      2. associate-*r/ 86.7%

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

   3. Simplified 86.7%

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

   4. Taylor expanded in z around inf 76.5%

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

   if -3.6e10 < z < -3.80000000000000023e-22 or -4.7e-35 < z < 7e4

   1. Initial program 99.1%

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

   2. Taylor expanded in y around inf 84.6%

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

      1. associate--l+ 84.6%

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

      2. distribute-lft-out-- 84.6%

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

      3. div-sub 84.6%

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

      4. mul-1-neg 84.6%

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

      5. unsub-neg 84.6%

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

   4. Simplified 84.6%

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

   5. Taylor expanded in x around inf 84.7%

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

   if -3.80000000000000023e-22 < z < -4.7e-35

   1. Initial program 99.1%

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

      1. associate-*l/ 99.7%

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

      2. associate-*r/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around 0 99.7%

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

      1. associate-/l* 100.0%

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

   6. Simplified 100.0%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -36000000000:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-22}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-35}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq 70000:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \end{array} \]

Alternative 7: 75.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{1 - \frac{z}{y}}\\ \mathbf{if}\;y \leq -50000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-34}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-106}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-20}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ t (- 1.0 (/ z y)))))
   (if (<= y -50000000.0)
     t_1
     (if (<= y -6.5e-34)
       (* t (- 1.0 (/ x y)))
       (if (<= y -4.8e-106)
         (* t (/ (- x y) z))
         (if (<= y 5.6e-20) (* t (/ x (- z y))) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t / (1.0 - (z / y));
	double tmp;
	if (y <= -50000000.0) {
		tmp = t_1;
	} else if (y <= -6.5e-34) {
		tmp = t * (1.0 - (x / y));
	} else if (y <= -4.8e-106) {
		tmp = t * ((x - y) / z);
	} else if (y <= 5.6e-20) {
		tmp = t * (x / (z - 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 / (1.0d0 - (z / y))
    if (y <= (-50000000.0d0)) then
        tmp = t_1
    else if (y <= (-6.5d-34)) then
        tmp = t * (1.0d0 - (x / y))
    else if (y <= (-4.8d-106)) then
        tmp = t * ((x - y) / z)
    else if (y <= 5.6d-20) then
        tmp = t * (x / (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 t_1 = t / (1.0 - (z / y));
	double tmp;
	if (y <= -50000000.0) {
		tmp = t_1;
	} else if (y <= -6.5e-34) {
		tmp = t * (1.0 - (x / y));
	} else if (y <= -4.8e-106) {
		tmp = t * ((x - y) / z);
	} else if (y <= 5.6e-20) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t / (1.0 - (z / y))
	tmp = 0
	if y <= -50000000.0:
		tmp = t_1
	elif y <= -6.5e-34:
		tmp = t * (1.0 - (x / y))
	elif y <= -4.8e-106:
		tmp = t * ((x - y) / z)
	elif y <= 5.6e-20:
		tmp = t * (x / (z - y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t / Float64(1.0 - Float64(z / y)))
	tmp = 0.0
	if (y <= -50000000.0)
		tmp = t_1;
	elseif (y <= -6.5e-34)
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	elseif (y <= -4.8e-106)
		tmp = Float64(t * Float64(Float64(x - y) / z));
	elseif (y <= 5.6e-20)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t / (1.0 - (z / y));
	tmp = 0.0;
	if (y <= -50000000.0)
		tmp = t_1;
	elseif (y <= -6.5e-34)
		tmp = t * (1.0 - (x / y));
	elseif (y <= -4.8e-106)
		tmp = t * ((x - y) / z);
	elseif (y <= 5.6e-20)
		tmp = t * (x / (z - y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -50000000.0], t$95$1, If[LessEqual[y, -6.5e-34], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.8e-106], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.6e-20], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5e7 or 5.6000000000000005e-20 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 76.7%

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

      2. associate-*r/ 75.7%

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

   3. Simplified 75.7%

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

      1. associate-*r/ 76.7%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

      4. clear-num 99.7%

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

      5. un-div-inv 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around 0 77.7%

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

      1. mul-1-neg 77.7%

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

      2. neg-sub0 77.7%

         \[\leadsto \frac{t}{\color{blue}{0 - \frac{z - y}{y}}} \]

      3. div-sub 77.7%

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

      4. *-inverses 77.7%

         \[\leadsto \frac{t}{0 - \left(\frac{z}{y} - \color{blue}{1}\right)} \]

      5. associate-+l- 77.7%

         \[\leadsto \frac{t}{\color{blue}{\left(0 - \frac{z}{y}\right) + 1}} \]

      6. neg-sub0 77.7%

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

      7. neg-mul-1 77.7%

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

      8. +-commutative 77.7%

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

      9. neg-mul-1 77.7%

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

      10. unsub-neg 77.7%

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

   8. Simplified 77.7%

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

   if -5e7 < y < -6.49999999999999985e-34

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 91.0%

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

      1. associate--l+ 91.0%

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

      2. distribute-lft-out-- 91.0%

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

      3. div-sub 91.0%

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

      4. mul-1-neg 91.0%

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

      5. unsub-neg 91.0%

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

   4. Simplified 91.0%

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

   5. Taylor expanded in x around inf 91.0%

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

   if -6.49999999999999985e-34 < y < -4.7999999999999995e-106

   1. Initial program 99.6%

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

   2. Taylor expanded in z around inf 87.6%

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

   if -4.7999999999999995e-106 < y < 5.6000000000000005e-20

   1. Initial program 94.7%

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

   2. Taylor expanded in x around inf 87.6%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -50000000:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-34}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-106}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-20}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \end{array} \]

Alternative 8: 60.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+94}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-26}:\\ \;\;\;\;\frac{t}{y} \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-21}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.15e+94)
   t
   (if (<= y -3.3e-26) (* (/ t y) (- x)) (if (<= y 2.9e-21) (* t (/ x z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.15e+94) {
		tmp = t;
	} else if (y <= -3.3e-26) {
		tmp = (t / y) * -x;
	} else if (y <= 2.9e-21) {
		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 <= (-2.15d+94)) then
        tmp = t
    else if (y <= (-3.3d-26)) then
        tmp = (t / y) * -x
    else if (y <= 2.9d-21) 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 <= -2.15e+94) {
		tmp = t;
	} else if (y <= -3.3e-26) {
		tmp = (t / y) * -x;
	} else if (y <= 2.9e-21) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.15e+94:
		tmp = t
	elif y <= -3.3e-26:
		tmp = (t / y) * -x
	elif y <= 2.9e-21:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.15e+94)
		tmp = t;
	elseif (y <= -3.3e-26)
		tmp = Float64(Float64(t / y) * Float64(-x));
	elseif (y <= 2.9e-21)
		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 <= -2.15e+94)
		tmp = t;
	elseif (y <= -3.3e-26)
		tmp = (t / y) * -x;
	elseif (y <= 2.9e-21)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.15e+94], t, If[LessEqual[y, -3.3e-26], N[(N[(t / y), $MachinePrecision] * (-x)), $MachinePrecision], If[LessEqual[y, 2.9e-21], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.15e94 or 2.9e-21 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 74.4%

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

      2. associate-*r/ 71.6%

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

   3. Simplified 71.6%

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

   4. Taylor expanded in y around inf 66.4%

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

   if -2.15e94 < y < -3.2999999999999998e-26

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 44.4%

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

   3. Taylor expanded in z around 0 41.7%

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

      1. associate-*r/ 41.7%

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

      2. neg-mul-1 41.7%

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

   5. Simplified 41.7%

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

      1. distribute-frac-neg 41.7%

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

      2. distribute-lft-neg-out 41.7%

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

      3. associate-/r/ 41.7%

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

      4. div-inv 41.6%

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

      5. clear-num 41.7%

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

   7. Applied egg-rr 41.7%

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

   if -3.2999999999999998e-26 < y < 2.9e-21

   1. Initial program 95.5%

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

   2. Taylor expanded in y around 0 70.9%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+94}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-26}:\\ \;\;\;\;\frac{t}{y} \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-21}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 9: 59.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.52 \cdot 10^{+94}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -8.4 \cdot 10^{-50}:\\ \;\;\;\;\frac{-y}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-19}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.52e+94)
   t
   (if (<= y -8.4e-50)
     (/ (- y) (/ z t))
     (if (<= y 1.65e-19) (* t (/ x z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.52e+94) {
		tmp = t;
	} else if (y <= -8.4e-50) {
		tmp = -y / (z / t);
	} else if (y <= 1.65e-19) {
		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 <= (-1.52d+94)) then
        tmp = t
    else if (y <= (-8.4d-50)) then
        tmp = -y / (z / t)
    else if (y <= 1.65d-19) 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 <= -1.52e+94) {
		tmp = t;
	} else if (y <= -8.4e-50) {
		tmp = -y / (z / t);
	} else if (y <= 1.65e-19) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.52e+94:
		tmp = t
	elif y <= -8.4e-50:
		tmp = -y / (z / t)
	elif y <= 1.65e-19:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.52e+94)
		tmp = t;
	elseif (y <= -8.4e-50)
		tmp = Float64(Float64(-y) / Float64(z / t));
	elseif (y <= 1.65e-19)
		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 <= -1.52e+94)
		tmp = t;
	elseif (y <= -8.4e-50)
		tmp = -y / (z / t);
	elseif (y <= 1.65e-19)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.52e+94], t, If[LessEqual[y, -8.4e-50], N[((-y) / N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.65e-19], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.5199999999999999e94 or 1.6499999999999999e-19 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 74.4%

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

      2. associate-*r/ 71.6%

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

   3. Simplified 71.6%

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

   4. Taylor expanded in y around inf 66.4%

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

   if -1.5199999999999999e94 < y < -8.4000000000000003e-50

   1. Initial program 99.8%

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

      1. associate-*l/ 94.3%

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

      2. associate-*r/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around inf 50.0%

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

   5. Taylor expanded in x around 0 46.9%

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

      1. mul-1-neg 46.9%

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

      2. associate-/l* 44.4%

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

   7. Simplified 44.4%

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

   if -8.4000000000000003e-50 < y < 1.6499999999999999e-19

   1. Initial program 95.3%

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

   2. Taylor expanded in y around 0 72.5%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.52 \cdot 10^{+94}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -8.4 \cdot 10^{-50}:\\ \;\;\;\;\frac{-y}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-19}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 10: 59.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.4 \cdot 10^{+94}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-49}:\\ \;\;\;\;\left(-t\right) \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-19}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -8.4e+94)
   t
   (if (<= y -1.9e-49) (* (- t) (/ y z)) (if (<= y 2.5e-19) (* t (/ x z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8.4e+94) {
		tmp = t;
	} else if (y <= -1.9e-49) {
		tmp = -t * (y / z);
	} else if (y <= 2.5e-19) {
		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 <= (-8.4d+94)) then
        tmp = t
    else if (y <= (-1.9d-49)) then
        tmp = -t * (y / z)
    else if (y <= 2.5d-19) 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 <= -8.4e+94) {
		tmp = t;
	} else if (y <= -1.9e-49) {
		tmp = -t * (y / z);
	} else if (y <= 2.5e-19) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -8.4e+94:
		tmp = t
	elif y <= -1.9e-49:
		tmp = -t * (y / z)
	elif y <= 2.5e-19:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -8.4e+94)
		tmp = t;
	elseif (y <= -1.9e-49)
		tmp = Float64(Float64(-t) * Float64(y / z));
	elseif (y <= 2.5e-19)
		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 <= -8.4e+94)
		tmp = t;
	elseif (y <= -1.9e-49)
		tmp = -t * (y / z);
	elseif (y <= 2.5e-19)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -8.4e+94], t, If[LessEqual[y, -1.9e-49], N[((-t) * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e-19], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.39999999999999958e94 or 2.5000000000000002e-19 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 74.4%

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

      2. associate-*r/ 71.6%

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

   3. Simplified 71.6%

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

   4. Taylor expanded in y around inf 66.4%

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

   if -8.39999999999999958e94 < y < -1.8999999999999999e-49

   1. Initial program 99.8%

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

      1. associate-*l/ 94.3%

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

      2. associate-*r/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around inf 47.1%

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

   5. Taylor expanded in x around 0 46.9%

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

      1. mul-1-neg 46.9%

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

      2. distribute-lft-neg-out 46.9%

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

      3. *-commutative 46.9%

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

   7. Simplified 46.9%

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

   8. Taylor expanded in t around 0 46.9%

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

      1. associate-*r/ 46.9%

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

      2. *-commutative 46.9%

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

      3. associate-*r* 46.9%

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

      4. neg-mul-1 46.9%

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

      5. associate-*r/ 47.0%

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

   10. Simplified 47.0%

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

   if -1.8999999999999999e-49 < y < 2.5000000000000002e-19

   1. Initial program 95.3%

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

   2. Taylor expanded in y around 0 72.5%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.4 \cdot 10^{+94}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-49}:\\ \;\;\;\;\left(-t\right) \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-19}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 11: 67.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.62 \cdot 10^{+94}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.62e+94) t (if (<= y 2.8e-19) (* x (/ t (- z y))) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.62e+94) {
		tmp = t;
	} else if (y <= 2.8e-19) {
		tmp = x * (t / (z - 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 <= (-1.62d+94)) then
        tmp = t
    else if (y <= 2.8d-19) then
        tmp = x * (t / (z - 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 <= -1.62e+94) {
		tmp = t;
	} else if (y <= 2.8e-19) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.62e+94:
		tmp = t
	elif y <= 2.8e-19:
		tmp = x * (t / (z - y))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.62e+94)
		tmp = t;
	elseif (y <= 2.8e-19)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.62e+94)
		tmp = t;
	elseif (y <= 2.8e-19)
		tmp = x * (t / (z - y));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.62e+94], t, If[LessEqual[y, 2.8e-19], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.61999999999999997e94 or 2.80000000000000003e-19 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 74.4%

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

      2. associate-*r/ 71.6%

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

   3. Simplified 71.6%

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

   4. Taylor expanded in y around inf 66.4%

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

   if -1.61999999999999997e94 < y < 2.80000000000000003e-19

   1. Initial program 96.3%

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

      1. associate-*l/ 90.7%

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

      2. associate-*r/ 93.3%

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

   3. Simplified 93.3%

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

   4. Taylor expanded in x around inf 69.8%

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

      1. associate-*l/ 71.6%

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

      2. *-commutative 71.6%

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

   6. Simplified 71.6%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.62 \cdot 10^{+94}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 12: 38.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-53}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-21}:\\ \;\;\;\;t \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.45e-53) t (if (<= y 1.15e-21) (* t (/ y z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.45e-53) {
		tmp = t;
	} else if (y <= 1.15e-21) {
		tmp = t * (y / 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-53)) then
        tmp = t
    else if (y <= 1.15d-21) then
        tmp = t * (y / 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-53) {
		tmp = t;
	} else if (y <= 1.15e-21) {
		tmp = t * (y / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.45e-53:
		tmp = t
	elif y <= 1.15e-21:
		tmp = t * (y / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.45e-53)
		tmp = t;
	elseif (y <= 1.15e-21)
		tmp = Float64(t * Float64(y / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.45e-53)
		tmp = t;
	elseif (y <= 1.15e-21)
		tmp = t * (y / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.45e-53], t, If[LessEqual[y, 1.15e-21], N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4499999999999999e-53 or 1.15e-21 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 79.1%

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

      2. associate-*r/ 78.2%

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

   3. Simplified 78.2%

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

   4. Taylor expanded in y around inf 56.0%

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

   if -1.4499999999999999e-53 < y < 1.15e-21

   1. Initial program 95.3%

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

      1. associate-*l/ 89.6%

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

      2. associate-*r/ 91.4%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in z around inf 77.0%

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

   5. Taylor expanded in x around 0 24.8%

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

      1. mul-1-neg 24.8%

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

      2. distribute-lft-neg-out 24.8%

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

      3. *-commutative 24.8%

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

   7. Simplified 24.8%

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

      1. expm1-log1p-u 21.7%

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

      2. expm1-udef 16.0%

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

      3. div-inv 16.0%

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

      4. associate-*l* 16.0%

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

      5. add-sqr-sqrt 7.7%

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

      6. sqrt-unprod 16.3%

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

      7. sqr-neg 16.3%

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

      8. sqrt-unprod 8.6%

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

      9. add-sqr-sqrt 14.8%

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

      10. div-inv 14.8%

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

   9. Applied egg-rr 14.8%

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

       1. expm1-def 14.7%

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

       2. expm1-log1p 15.0%

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

   11. Simplified 15.0%

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

4. Final simplification 38.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-53}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-21}:\\ \;\;\;\;t \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 13: 59.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{-34}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -7.2e-34) t (if (<= y 1.7e-19) (* x (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.2e-34) {
		tmp = t;
	} else if (y <= 1.7e-19) {
		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 <= (-7.2d-34)) then
        tmp = t
    else if (y <= 1.7d-19) 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 <= -7.2e-34) {
		tmp = t;
	} else if (y <= 1.7e-19) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -7.2e-34:
		tmp = t
	elif y <= 1.7e-19:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -7.2e-34)
		tmp = t;
	elseif (y <= 1.7e-19)
		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 <= -7.2e-34)
		tmp = t;
	elseif (y <= 1.7e-19)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -7.2e-34], t, If[LessEqual[y, 1.7e-19], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -7.20000000000000016e-34 or 1.7000000000000001e-19 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 78.5%

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

      2. associate-*r/ 77.6%

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

   3. Simplified 77.6%

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

   4. Taylor expanded in y around inf 57.4%

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

   if -7.20000000000000016e-34 < y < 1.7000000000000001e-19

   1. Initial program 95.5%

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

      1. associate-*l/ 89.9%

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

      2. associate-*r/ 91.6%

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

   3. Simplified 91.6%

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

      1. associate-*r/ 89.9%

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

      2. associate-*l/ 95.5%

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

      3. *-commutative 95.5%

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

      4. clear-num 94.7%

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

      5. un-div-inv 95.1%

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

   5. Applied egg-rr 95.1%

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

   6. Taylor expanded in y around 0 66.3%

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

      1. associate-*l/ 67.7%

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

      2. *-commutative 67.7%

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

   8. Simplified 67.7%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{-34}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 14: 60.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-34}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-20}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -7.5e-34) t (if (<= y 5.5e-20) (* t (/ x z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.5e-34) {
		tmp = t;
	} else if (y <= 5.5e-20) {
		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 <= (-7.5d-34)) then
        tmp = t
    else if (y <= 5.5d-20) 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 <= -7.5e-34) {
		tmp = t;
	} else if (y <= 5.5e-20) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -7.5e-34:
		tmp = t
	elif y <= 5.5e-20:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -7.5e-34)
		tmp = t;
	elseif (y <= 5.5e-20)
		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 <= -7.5e-34)
		tmp = t;
	elseif (y <= 5.5e-20)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -7.5e-34], t, If[LessEqual[y, 5.5e-20], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -7.5000000000000004e-34 or 5.4999999999999996e-20 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 78.5%

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

      2. associate-*r/ 77.6%

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

   3. Simplified 77.6%

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

   4. Taylor expanded in y around inf 57.4%

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

   if -7.5000000000000004e-34 < y < 5.4999999999999996e-20

   1. Initial program 95.5%

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

   2. Taylor expanded in y around 0 71.5%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-34}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-20}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 15: 34.4% 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 97.9%

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

   1. associate-*l/ 83.7%

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

   2. associate-*r/ 84.0%

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

3. Simplified 84.0%

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

4. Taylor expanded in y around inf 33.6%

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

5. Final simplification 33.6%

   \[\leadsto t \]

Developer target: 96.9% 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 2023221 
(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))