Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3

Percentage Accurate: 84.6% → 97.2%

Time: 9.6s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

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)) / (t - z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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)) / (t - z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 / ((t - z) / (y - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 82.8%

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

   1. associate-/l* 97.2%

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

3. Simplified 97.2%

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

4. Final simplification 97.2%

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

Alternative 2: 73.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{+86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -110000:\\ \;\;\;\;\frac{y - z}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 34:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{\frac{t}{z} + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y z)))))
   (if (<= z -3.8e+86)
     t_1
     (if (<= z -110000.0)
       (/ (- y z) (/ t x))
       (if (<= z -2.15e-82)
         t_1
         (if (<= z 34.0) (/ x (/ (- t z) y)) (/ (- x) (+ (/ t z) -1.0))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -3.8e+86) {
		tmp = t_1;
	} else if (z <= -110000.0) {
		tmp = (y - z) / (t / x);
	} else if (z <= -2.15e-82) {
		tmp = t_1;
	} else if (z <= 34.0) {
		tmp = x / ((t - z) / y);
	} else {
		tmp = -x / ((t / z) + -1.0);
	}
	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 = x * (1.0d0 - (y / z))
    if (z <= (-3.8d+86)) then
        tmp = t_1
    else if (z <= (-110000.0d0)) then
        tmp = (y - z) / (t / x)
    else if (z <= (-2.15d-82)) then
        tmp = t_1
    else if (z <= 34.0d0) then
        tmp = x / ((t - z) / y)
    else
        tmp = -x / ((t / z) + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -3.8e+86) {
		tmp = t_1;
	} else if (z <= -110000.0) {
		tmp = (y - z) / (t / x);
	} else if (z <= -2.15e-82) {
		tmp = t_1;
	} else if (z <= 34.0) {
		tmp = x / ((t - z) / y);
	} else {
		tmp = -x / ((t / z) + -1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - (y / z))
	tmp = 0
	if z <= -3.8e+86:
		tmp = t_1
	elif z <= -110000.0:
		tmp = (y - z) / (t / x)
	elif z <= -2.15e-82:
		tmp = t_1
	elif z <= 34.0:
		tmp = x / ((t - z) / y)
	else:
		tmp = -x / ((t / z) + -1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -3.8e+86)
		tmp = t_1;
	elseif (z <= -110000.0)
		tmp = Float64(Float64(y - z) / Float64(t / x));
	elseif (z <= -2.15e-82)
		tmp = t_1;
	elseif (z <= 34.0)
		tmp = Float64(x / Float64(Float64(t - z) / y));
	else
		tmp = Float64(Float64(-x) / Float64(Float64(t / z) + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -3.8e+86)
		tmp = t_1;
	elseif (z <= -110000.0)
		tmp = (y - z) / (t / x);
	elseif (z <= -2.15e-82)
		tmp = t_1;
	elseif (z <= 34.0)
		tmp = x / ((t - z) / y);
	else
		tmp = -x / ((t / z) + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.8e+86], t$95$1, If[LessEqual[z, -110000.0], N[(N[(y - z), $MachinePrecision] / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.15e-82], t$95$1, If[LessEqual[z, 34.0], N[(x / N[(N[(t - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[((-x) / N[(N[(t / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.79999999999999978e86 or -1.1e5 < z < -2.15000000000000009e-82

   1. Initial program 86.8%

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

      1. associate-*r/ 98.1%

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

   3. Simplified 98.1%

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

      1. div-sub 98.1%

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

   5. Applied egg-rr 98.1%

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

   6. Taylor expanded in t around 0 77.5%

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

      1. mul-1-neg 77.5%

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

      2. sub-neg 77.5%

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

   8. Simplified 77.5%

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

   if -3.79999999999999978e86 < z < -1.1e5

   1. Initial program 74.2%

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

      1. associate-*r/ 99.4%

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

   3. Simplified 99.4%

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

      1. associate-*r/ 74.2%

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

      2. *-commutative 74.2%

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

      3. associate-/l* 94.8%

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

   5. Applied egg-rr 94.8%

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

   6. Taylor expanded in t around inf 73.5%

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

   if -2.15000000000000009e-82 < z < 34

   1. Initial program 89.8%

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

      1. associate-/l* 94.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in y around inf 79.4%

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

   if 34 < z

   1. Initial program 72.0%

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

      1. associate-*r/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around 0 55.9%

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

      1. mul-1-neg 55.9%

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

      2. associate-/l* 78.0%

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

      3. distribute-neg-frac 78.0%

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

      4. div-sub 78.1%

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

      5. sub-neg 78.1%

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

      6. *-inverses 78.1%

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

      7. metadata-eval 78.1%

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

   6. Simplified 78.1%

      \[\leadsto \color{blue}{\frac{-x}{\frac{t}{z} + -1}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+86}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -110000:\\ \;\;\;\;\frac{y - z}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-82}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 34:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{\frac{t}{z} + -1}\\ \end{array} \]

Alternative 3: 73.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-x}{\frac{z}{y - z}}\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{+86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -26000:\\ \;\;\;\;\frac{y - z}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-78}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 0.28:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{\frac{t}{z} + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x) (/ z (- y z)))))
   (if (<= z -3.3e+86)
     t_1
     (if (<= z -26000.0)
       (/ (- y z) (/ t x))
       (if (<= z -4.2e-78)
         t_1
         (if (<= z 0.28) (/ x (/ (- t z) y)) (/ (- x) (+ (/ t z) -1.0))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -x / (z / (y - z));
	double tmp;
	if (z <= -3.3e+86) {
		tmp = t_1;
	} else if (z <= -26000.0) {
		tmp = (y - z) / (t / x);
	} else if (z <= -4.2e-78) {
		tmp = t_1;
	} else if (z <= 0.28) {
		tmp = x / ((t - z) / y);
	} else {
		tmp = -x / ((t / z) + -1.0);
	}
	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 = -x / (z / (y - z))
    if (z <= (-3.3d+86)) then
        tmp = t_1
    else if (z <= (-26000.0d0)) then
        tmp = (y - z) / (t / x)
    else if (z <= (-4.2d-78)) then
        tmp = t_1
    else if (z <= 0.28d0) then
        tmp = x / ((t - z) / y)
    else
        tmp = -x / ((t / z) + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = -x / (z / (y - z));
	double tmp;
	if (z <= -3.3e+86) {
		tmp = t_1;
	} else if (z <= -26000.0) {
		tmp = (y - z) / (t / x);
	} else if (z <= -4.2e-78) {
		tmp = t_1;
	} else if (z <= 0.28) {
		tmp = x / ((t - z) / y);
	} else {
		tmp = -x / ((t / z) + -1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -x / (z / (y - z))
	tmp = 0
	if z <= -3.3e+86:
		tmp = t_1
	elif z <= -26000.0:
		tmp = (y - z) / (t / x)
	elif z <= -4.2e-78:
		tmp = t_1
	elif z <= 0.28:
		tmp = x / ((t - z) / y)
	else:
		tmp = -x / ((t / z) + -1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(-x) / Float64(z / Float64(y - z)))
	tmp = 0.0
	if (z <= -3.3e+86)
		tmp = t_1;
	elseif (z <= -26000.0)
		tmp = Float64(Float64(y - z) / Float64(t / x));
	elseif (z <= -4.2e-78)
		tmp = t_1;
	elseif (z <= 0.28)
		tmp = Float64(x / Float64(Float64(t - z) / y));
	else
		tmp = Float64(Float64(-x) / Float64(Float64(t / z) + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -x / (z / (y - z));
	tmp = 0.0;
	if (z <= -3.3e+86)
		tmp = t_1;
	elseif (z <= -26000.0)
		tmp = (y - z) / (t / x);
	elseif (z <= -4.2e-78)
		tmp = t_1;
	elseif (z <= 0.28)
		tmp = x / ((t - z) / y);
	else
		tmp = -x / ((t / z) + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[((-x) / N[(z / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.3e+86], t$95$1, If[LessEqual[z, -26000.0], N[(N[(y - z), $MachinePrecision] / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.2e-78], t$95$1, If[LessEqual[z, 0.28], N[(x / N[(N[(t - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[((-x) / N[(N[(t / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.2999999999999999e86 or -26000 < z < -4.2000000000000001e-78

   1. Initial program 86.5%

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

      1. associate-*r/ 98.1%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in t around 0 67.1%

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

      1. mul-1-neg 67.1%

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

      2. associate-/l* 77.2%

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

      3. distribute-neg-frac 77.2%

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

   6. Simplified 77.2%

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

   if -3.2999999999999999e86 < z < -26000

   1. Initial program 74.2%

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

      1. associate-*r/ 99.4%

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

   3. Simplified 99.4%

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

      1. associate-*r/ 74.2%

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

      2. *-commutative 74.2%

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

      3. associate-/l* 94.8%

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

   5. Applied egg-rr 94.8%

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

   6. Taylor expanded in t around inf 73.5%

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

   if -4.2000000000000001e-78 < z < 0.28000000000000003

   1. Initial program 89.8%

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

      1. associate-/l* 94.4%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in y around inf 79.5%

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

   if 0.28000000000000003 < z

   1. Initial program 72.0%

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

      1. associate-*r/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around 0 55.9%

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

      1. mul-1-neg 55.9%

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

      2. associate-/l* 78.0%

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

      3. distribute-neg-frac 78.0%

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

      4. div-sub 78.1%

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

      5. sub-neg 78.1%

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

      6. *-inverses 78.1%

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

      7. metadata-eval 78.1%

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

   6. Simplified 78.1%

      \[\leadsto \color{blue}{\frac{-x}{\frac{t}{z} + -1}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+86}:\\ \;\;\;\;\frac{-x}{\frac{z}{y - z}}\\ \mathbf{elif}\;z \leq -26000:\\ \;\;\;\;\frac{y - z}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-78}:\\ \;\;\;\;\frac{-x}{\frac{z}{y - z}}\\ \mathbf{elif}\;z \leq 0.28:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{\frac{t}{z} + -1}\\ \end{array} \]

Alternative 4: 74.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{+86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -220000:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-78} \lor \neg \left(z \leq 1.48 \cdot 10^{-24}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y z)))))
   (if (<= z -3.4e+86)
     t_1
     (if (<= z -220000.0)
       (* (- y z) (/ x t))
       (if (or (<= z -3.9e-78) (not (<= z 1.48e-24)))
         t_1
         (* x (/ y (- t z))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -3.4e+86) {
		tmp = t_1;
	} else if (z <= -220000.0) {
		tmp = (y - z) * (x / t);
	} else if ((z <= -3.9e-78) || !(z <= 1.48e-24)) {
		tmp = t_1;
	} else {
		tmp = x * (y / (t - 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) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / z))
    if (z <= (-3.4d+86)) then
        tmp = t_1
    else if (z <= (-220000.0d0)) then
        tmp = (y - z) * (x / t)
    else if ((z <= (-3.9d-78)) .or. (.not. (z <= 1.48d-24))) then
        tmp = t_1
    else
        tmp = x * (y / (t - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -3.4e+86) {
		tmp = t_1;
	} else if (z <= -220000.0) {
		tmp = (y - z) * (x / t);
	} else if ((z <= -3.9e-78) || !(z <= 1.48e-24)) {
		tmp = t_1;
	} else {
		tmp = x * (y / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - (y / z))
	tmp = 0
	if z <= -3.4e+86:
		tmp = t_1
	elif z <= -220000.0:
		tmp = (y - z) * (x / t)
	elif (z <= -3.9e-78) or not (z <= 1.48e-24):
		tmp = t_1
	else:
		tmp = x * (y / (t - z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -3.4e+86)
		tmp = t_1;
	elseif (z <= -220000.0)
		tmp = Float64(Float64(y - z) * Float64(x / t));
	elseif ((z <= -3.9e-78) || !(z <= 1.48e-24))
		tmp = t_1;
	else
		tmp = Float64(x * Float64(y / Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -3.4e+86)
		tmp = t_1;
	elseif (z <= -220000.0)
		tmp = (y - z) * (x / t);
	elseif ((z <= -3.9e-78) || ~((z <= 1.48e-24)))
		tmp = t_1;
	else
		tmp = x * (y / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.4e+86], t$95$1, If[LessEqual[z, -220000.0], N[(N[(y - z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -3.9e-78], N[Not[LessEqual[z, 1.48e-24]], $MachinePrecision]], t$95$1, N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.3999999999999998e86 or -2.2e5 < z < -3.9000000000000002e-78 or 1.48000000000000003e-24 < z

   1. Initial program 78.8%

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

      1. associate-*r/ 99.0%

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

   3. Simplified 99.0%

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

      1. div-sub 99.0%

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

   5. Applied egg-rr 99.0%

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

   6. Taylor expanded in t around 0 74.6%

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

      1. mul-1-neg 74.6%

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

      2. sub-neg 74.6%

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

   8. Simplified 74.6%

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

   if -3.3999999999999998e86 < z < -2.2e5

   1. Initial program 74.2%

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

      1. associate-*r/ 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in t around inf 57.8%

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

      1. div-inv 57.8%

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

      2. *-commutative 57.8%

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

      3. associate-*l* 73.2%

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

      4. div-inv 73.4%

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

   6. Applied egg-rr 73.4%

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

   if -3.9000000000000002e-78 < z < 1.48000000000000003e-24

   1. Initial program 89.6%

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

      1. associate-*r/ 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in y around inf 79.3%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+86}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -220000:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-78} \lor \neg \left(z \leq 1.48 \cdot 10^{-24}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \]

Alternative 5: 72.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{z}\right)\\ t_2 := \frac{x}{\frac{t}{y - z}}\\ \mathbf{if}\;t \leq -1.6 \cdot 10^{+71}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-125}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-62}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y z)))) (t_2 (/ x (/ t (- y z)))))
   (if (<= t -1.6e+71)
     t_2
     (if (<= t 8.5e-125)
       t_1
       (if (<= t 2.2e-62) (* x (/ y (- t z))) (if (<= t 5e+74) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double t_2 = x / (t / (y - z));
	double tmp;
	if (t <= -1.6e+71) {
		tmp = t_2;
	} else if (t <= 8.5e-125) {
		tmp = t_1;
	} else if (t <= 2.2e-62) {
		tmp = x * (y / (t - z));
	} else if (t <= 5e+74) {
		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 * (1.0d0 - (y / z))
    t_2 = x / (t / (y - z))
    if (t <= (-1.6d+71)) then
        tmp = t_2
    else if (t <= 8.5d-125) then
        tmp = t_1
    else if (t <= 2.2d-62) then
        tmp = x * (y / (t - z))
    else if (t <= 5d+74) 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 * (1.0 - (y / z));
	double t_2 = x / (t / (y - z));
	double tmp;
	if (t <= -1.6e+71) {
		tmp = t_2;
	} else if (t <= 8.5e-125) {
		tmp = t_1;
	} else if (t <= 2.2e-62) {
		tmp = x * (y / (t - z));
	} else if (t <= 5e+74) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - (y / z))
	t_2 = x / (t / (y - z))
	tmp = 0
	if t <= -1.6e+71:
		tmp = t_2
	elif t <= 8.5e-125:
		tmp = t_1
	elif t <= 2.2e-62:
		tmp = x * (y / (t - z))
	elif t <= 5e+74:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - Float64(y / z)))
	t_2 = Float64(x / Float64(t / Float64(y - z)))
	tmp = 0.0
	if (t <= -1.6e+71)
		tmp = t_2;
	elseif (t <= 8.5e-125)
		tmp = t_1;
	elseif (t <= 2.2e-62)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	elseif (t <= 5e+74)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - (y / z));
	t_2 = x / (t / (y - z));
	tmp = 0.0;
	if (t <= -1.6e+71)
		tmp = t_2;
	elseif (t <= 8.5e-125)
		tmp = t_1;
	elseif (t <= 2.2e-62)
		tmp = x * (y / (t - z));
	elseif (t <= 5e+74)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.6e+71], t$95$2, If[LessEqual[t, 8.5e-125], t$95$1, If[LessEqual[t, 2.2e-62], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5e+74], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.60000000000000012e71 or 4.99999999999999963e74 < t

   1. Initial program 76.8%

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

      1. associate-*r/ 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in t around inf 63.7%

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

      1. associate-/l* 75.4%

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

   6. Simplified 75.4%

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

   if -1.60000000000000012e71 < t < 8.5000000000000002e-125 or 2.20000000000000017e-62 < t < 4.99999999999999963e74

   1. Initial program 86.7%

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

      1. associate-*r/ 96.4%

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

   3. Simplified 96.4%

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

      1. div-sub 96.5%

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

   5. Applied egg-rr 96.5%

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

   6. Taylor expanded in t around 0 76.7%

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

      1. mul-1-neg 76.7%

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

      2. sub-neg 76.7%

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

   8. Simplified 76.7%

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

   if 8.5000000000000002e-125 < t < 2.20000000000000017e-62

   1. Initial program 92.0%

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

      1. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 91.0%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+71}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-125}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-62}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+74}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \end{array} \]

Alternative 6: 72.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{z}\right)\\ t_2 := \frac{x}{\frac{t}{y - z}}\\ \mathbf{if}\;t \leq -2 \cdot 10^{+69}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-125}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-67}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+73}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y z)))) (t_2 (/ x (/ t (- y z)))))
   (if (<= t -2e+69)
     t_2
     (if (<= t 8.5e-125)
       t_1
       (if (<= t 9.5e-67) (/ x (/ (- t z) y)) (if (<= t 2e+73) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double t_2 = x / (t / (y - z));
	double tmp;
	if (t <= -2e+69) {
		tmp = t_2;
	} else if (t <= 8.5e-125) {
		tmp = t_1;
	} else if (t <= 9.5e-67) {
		tmp = x / ((t - z) / y);
	} else if (t <= 2e+73) {
		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 * (1.0d0 - (y / z))
    t_2 = x / (t / (y - z))
    if (t <= (-2d+69)) then
        tmp = t_2
    else if (t <= 8.5d-125) then
        tmp = t_1
    else if (t <= 9.5d-67) then
        tmp = x / ((t - z) / y)
    else if (t <= 2d+73) 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 * (1.0 - (y / z));
	double t_2 = x / (t / (y - z));
	double tmp;
	if (t <= -2e+69) {
		tmp = t_2;
	} else if (t <= 8.5e-125) {
		tmp = t_1;
	} else if (t <= 9.5e-67) {
		tmp = x / ((t - z) / y);
	} else if (t <= 2e+73) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - (y / z))
	t_2 = x / (t / (y - z))
	tmp = 0
	if t <= -2e+69:
		tmp = t_2
	elif t <= 8.5e-125:
		tmp = t_1
	elif t <= 9.5e-67:
		tmp = x / ((t - z) / y)
	elif t <= 2e+73:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - Float64(y / z)))
	t_2 = Float64(x / Float64(t / Float64(y - z)))
	tmp = 0.0
	if (t <= -2e+69)
		tmp = t_2;
	elseif (t <= 8.5e-125)
		tmp = t_1;
	elseif (t <= 9.5e-67)
		tmp = Float64(x / Float64(Float64(t - z) / y));
	elseif (t <= 2e+73)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - (y / z));
	t_2 = x / (t / (y - z));
	tmp = 0.0;
	if (t <= -2e+69)
		tmp = t_2;
	elseif (t <= 8.5e-125)
		tmp = t_1;
	elseif (t <= 9.5e-67)
		tmp = x / ((t - z) / y);
	elseif (t <= 2e+73)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2e+69], t$95$2, If[LessEqual[t, 8.5e-125], t$95$1, If[LessEqual[t, 9.5e-67], N[(x / N[(N[(t - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2e+73], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.0000000000000001e69 or 1.99999999999999997e73 < t

   1. Initial program 76.8%

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

      1. associate-*r/ 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in t around inf 63.7%

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

      1. associate-/l* 75.4%

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

   6. Simplified 75.4%

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

   if -2.0000000000000001e69 < t < 8.5000000000000002e-125 or 9.4999999999999994e-67 < t < 1.99999999999999997e73

   1. Initial program 86.7%

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

      1. associate-*r/ 96.4%

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

   3. Simplified 96.4%

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

      1. div-sub 96.5%

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

   5. Applied egg-rr 96.5%

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

   6. Taylor expanded in t around 0 76.7%

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

      1. mul-1-neg 76.7%

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

      2. sub-neg 76.7%

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

   8. Simplified 76.7%

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

   if 8.5000000000000002e-125 < t < 9.4999999999999994e-67

   1. Initial program 92.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 91.1%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+69}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-125}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-67}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+73}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \end{array} \]

Alternative 7: 60.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.85 \cdot 10^{+86}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -0.085:\\ \;\;\;\;\frac{-x}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-78}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-22}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.85e+86)
   x
   (if (<= z -0.085)
     (/ (- x) (/ t z))
     (if (<= z -4.2e-78) x (if (<= z 6.4e-22) (* x (/ y t)) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.85e+86) {
		tmp = x;
	} else if (z <= -0.085) {
		tmp = -x / (t / z);
	} else if (z <= -4.2e-78) {
		tmp = x;
	} else if (z <= 6.4e-22) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	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 (z <= (-3.85d+86)) then
        tmp = x
    else if (z <= (-0.085d0)) then
        tmp = -x / (t / z)
    else if (z <= (-4.2d-78)) then
        tmp = x
    else if (z <= 6.4d-22) then
        tmp = x * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.85e+86) {
		tmp = x;
	} else if (z <= -0.085) {
		tmp = -x / (t / z);
	} else if (z <= -4.2e-78) {
		tmp = x;
	} else if (z <= 6.4e-22) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.85e+86:
		tmp = x
	elif z <= -0.085:
		tmp = -x / (t / z)
	elif z <= -4.2e-78:
		tmp = x
	elif z <= 6.4e-22:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.85e+86)
		tmp = x;
	elseif (z <= -0.085)
		tmp = Float64(Float64(-x) / Float64(t / z));
	elseif (z <= -4.2e-78)
		tmp = x;
	elseif (z <= 6.4e-22)
		tmp = Float64(x * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.85e+86)
		tmp = x;
	elseif (z <= -0.085)
		tmp = -x / (t / z);
	elseif (z <= -4.2e-78)
		tmp = x;
	elseif (z <= 6.4e-22)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.85e+86], x, If[LessEqual[z, -0.085], N[((-x) / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.2e-78], x, If[LessEqual[z, 6.4e-22], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.85000000000000026e86 or -0.0850000000000000061 < z < -4.2000000000000001e-78 or 6.39999999999999975e-22 < z

   1. Initial program 78.5%

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

      1. associate-*r/ 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in z around inf 58.3%

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

   if -3.85000000000000026e86 < z < -0.0850000000000000061

   1. Initial program 76.7%

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

      1. associate-*r/ 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in t around inf 57.0%

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

   5. Taylor expanded in y around 0 37.9%

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

      1. mul-1-neg 37.9%

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

      2. associate-/l* 50.7%

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

      3. distribute-neg-frac 50.7%

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

   7. Simplified 50.7%

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

   if -4.2000000000000001e-78 < z < 6.39999999999999975e-22

   1. Initial program 89.6%

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

      1. associate-*r/ 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in z around 0 68.4%

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

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.85 \cdot 10^{+86}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -0.085:\\ \;\;\;\;\frac{-x}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-78}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-22}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 69.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-100} \lor \neg \left(z \leq 1.06 \cdot 10^{-77}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.2e-100) (not (<= z 1.06e-77)))
   (* x (- 1.0 (/ y z)))
   (/ y (/ t x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.2e-100) || !(z <= 1.06e-77)) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = y / (t / x);
	}
	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 ((z <= (-4.2d-100)) .or. (.not. (z <= 1.06d-77))) then
        tmp = x * (1.0d0 - (y / z))
    else
        tmp = y / (t / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.2e-100) || !(z <= 1.06e-77)) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = y / (t / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4.2e-100) or not (z <= 1.06e-77):
		tmp = x * (1.0 - (y / z))
	else:
		tmp = y / (t / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.2e-100) || !(z <= 1.06e-77))
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(y / Float64(t / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4.2e-100) || ~((z <= 1.06e-77)))
		tmp = x * (1.0 - (y / z));
	else
		tmp = y / (t / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4.2e-100], N[Not[LessEqual[z, 1.06e-77]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(t / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.20000000000000019e-100 or 1.05999999999999991e-77 < z

   1. Initial program 79.6%

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

      1. associate-*r/ 98.6%

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

   3. Simplified 98.6%

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

      1. div-sub 98.6%

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

   5. Applied egg-rr 98.6%

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

   6. Taylor expanded in t around 0 68.2%

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

      1. mul-1-neg 68.2%

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

      2. sub-neg 68.2%

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

   8. Simplified 68.2%

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

   if -4.20000000000000019e-100 < z < 1.05999999999999991e-77

   1. Initial program 89.5%

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

      1. associate-*r/ 93.4%

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

   3. Simplified 93.4%

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

      1. div-sub 93.4%

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

   5. Applied egg-rr 93.4%

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

   6. Taylor expanded in z around 0 67.3%

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

      1. associate-/l* 73.2%

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

      2. associate-/r/ 73.2%

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

   8. Simplified 73.2%

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

      1. *-commutative 73.2%

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

      2. clear-num 73.0%

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

      3. un-div-inv 73.7%

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

   10. Applied egg-rr 73.7%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-100} \lor \neg \left(z \leq 1.06 \cdot 10^{-77}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{x}}\\ \end{array} \]

Alternative 9: 75.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-78} \lor \neg \left(z \leq 2.32 \cdot 10^{-23}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.2e-78) (not (<= z 2.32e-23)))
   (* x (- 1.0 (/ y z)))
   (* x (/ y (- t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.2e-78) || !(z <= 2.32e-23)) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = x * (y / (t - 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 ((z <= (-4.2d-78)) .or. (.not. (z <= 2.32d-23))) then
        tmp = x * (1.0d0 - (y / z))
    else
        tmp = x * (y / (t - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.2e-78) || !(z <= 2.32e-23)) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = x * (y / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4.2e-78) or not (z <= 2.32e-23):
		tmp = x * (1.0 - (y / z))
	else:
		tmp = x * (y / (t - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.2e-78) || !(z <= 2.32e-23))
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(x * Float64(y / Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4.2e-78) || ~((z <= 2.32e-23)))
		tmp = x * (1.0 - (y / z));
	else
		tmp = x * (y / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4.2e-78], N[Not[LessEqual[z, 2.32e-23]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.2000000000000001e-78 or 2.3199999999999999e-23 < z

   1. Initial program 78.3%

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

      1. associate-*r/ 99.1%

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

   3. Simplified 99.1%

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

      1. div-sub 99.1%

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

   5. Applied egg-rr 99.1%

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

   6. Taylor expanded in t around 0 69.4%

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

      1. mul-1-neg 69.4%

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

      2. sub-neg 69.4%

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

   8. Simplified 69.4%

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

   if -4.2000000000000001e-78 < z < 2.3199999999999999e-23

   1. Initial program 89.6%

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

      1. associate-*r/ 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in y around inf 79.3%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-78} \lor \neg \left(z \leq 2.32 \cdot 10^{-23}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \]

Alternative 10: 60.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-78}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-24}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.2e-78) x (if (<= z 1.55e-24) (* x (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.2e-78) {
		tmp = x;
	} else if (z <= 1.55e-24) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	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 (z <= (-4.2d-78)) then
        tmp = x
    else if (z <= 1.55d-24) then
        tmp = x * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.2e-78) {
		tmp = x;
	} else if (z <= 1.55e-24) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.2e-78:
		tmp = x
	elif z <= 1.55e-24:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.2e-78)
		tmp = x;
	elseif (z <= 1.55e-24)
		tmp = Float64(x * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.2e-78)
		tmp = x;
	elseif (z <= 1.55e-24)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.2e-78], x, If[LessEqual[z, 1.55e-24], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -4.2000000000000001e-78 or 1.55e-24 < z

   1. Initial program 78.3%

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

      1. associate-*r/ 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in z around inf 53.6%

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

   if -4.2000000000000001e-78 < z < 1.55e-24

   1. Initial program 89.6%

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

      1. associate-*r/ 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in z around 0 68.4%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-78}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-24}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 97.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) / (t - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 82.8%

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

   1. associate-*r/ 96.8%

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

3. Simplified 96.8%

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

4. Final simplification 96.8%

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

Alternative 12: 35.2% accurate, 9.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return 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 = x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 82.8%

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

   1. associate-*r/ 96.8%

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

3. Simplified 96.8%

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

4. Taylor expanded in z around inf 36.0%

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

5. Final simplification 36.0%

   \[\leadsto x \]

Developer target: 97.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 / ((t - z) / (y - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023312 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64

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

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