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

Percentage Accurate: 83.8% → 96.7%

Time: 8.8s

Alternatives: 14

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: 83.8% 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: 96.7% 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 82.0%

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

   1. associate-*r/ 97.3%

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

3. Simplified 97.3%

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

4. Final simplification 97.3%

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

Alternative 2: 60.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{x}{-t}\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{+63}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -7500:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -0.00021:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-63}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+58}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (/ x (- t)))))
   (if (<= z -6.2e+63)
     x
     (if (<= z -7500.0)
       t_1
       (if (<= z -0.00021)
         x
         (if (<= z 6.2e-63) (/ x (/ t y)) (if (<= z 2.6e+58) t_1 x)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x / -t);
	double tmp;
	if (z <= -6.2e+63) {
		tmp = x;
	} else if (z <= -7500.0) {
		tmp = t_1;
	} else if (z <= -0.00021) {
		tmp = x;
	} else if (z <= 6.2e-63) {
		tmp = x / (t / y);
	} else if (z <= 2.6e+58) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = z * (x / -t)
    if (z <= (-6.2d+63)) then
        tmp = x
    else if (z <= (-7500.0d0)) then
        tmp = t_1
    else if (z <= (-0.00021d0)) then
        tmp = x
    else if (z <= 6.2d-63) then
        tmp = x / (t / y)
    else if (z <= 2.6d+58) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (x / -t);
	double tmp;
	if (z <= -6.2e+63) {
		tmp = x;
	} else if (z <= -7500.0) {
		tmp = t_1;
	} else if (z <= -0.00021) {
		tmp = x;
	} else if (z <= 6.2e-63) {
		tmp = x / (t / y);
	} else if (z <= 2.6e+58) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x / -t)
	tmp = 0
	if z <= -6.2e+63:
		tmp = x
	elif z <= -7500.0:
		tmp = t_1
	elif z <= -0.00021:
		tmp = x
	elif z <= 6.2e-63:
		tmp = x / (t / y)
	elif z <= 2.6e+58:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x / Float64(-t)))
	tmp = 0.0
	if (z <= -6.2e+63)
		tmp = x;
	elseif (z <= -7500.0)
		tmp = t_1;
	elseif (z <= -0.00021)
		tmp = x;
	elseif (z <= 6.2e-63)
		tmp = Float64(x / Float64(t / y));
	elseif (z <= 2.6e+58)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x / -t);
	tmp = 0.0;
	if (z <= -6.2e+63)
		tmp = x;
	elseif (z <= -7500.0)
		tmp = t_1;
	elseif (z <= -0.00021)
		tmp = x;
	elseif (z <= 6.2e-63)
		tmp = x / (t / y);
	elseif (z <= 2.6e+58)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x / (-t)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.2e+63], x, If[LessEqual[z, -7500.0], t$95$1, If[LessEqual[z, -0.00021], x, If[LessEqual[z, 6.2e-63], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e+58], t$95$1, x]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.2000000000000001e63 or -7500 < z < -2.1000000000000001e-4 or 2.59999999999999988e58 < z

   1. Initial program 66.2%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 z around inf 62.3%

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

   if -6.2000000000000001e63 < z < -7500 or 6.19999999999999968e-63 < z < 2.59999999999999988e58

   1. Initial program 96.9%

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

      1. associate-/l* 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in t around inf 70.3%

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

   5. Taylor expanded in y around 0 60.6%

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

      1. mul-1-neg 60.6%

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

      2. associate-*r/ 61.5%

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

      3. distribute-rgt-neg-in 61.5%

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

      4. mul-1-neg 61.5%

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

      5. metadata-eval 61.5%

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

      6. times-frac 61.5%

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

      7. *-lft-identity 61.5%

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

      8. neg-mul-1 61.5%

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

   7. Simplified 61.5%

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

   if -2.1000000000000001e-4 < z < 6.19999999999999968e-63

   1. Initial program 93.4%

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

      1. associate-/l* 93.8%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in z around 0 80.0%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+63}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -7500:\\ \;\;\;\;z \cdot \frac{x}{-t}\\ \mathbf{elif}\;z \leq -0.00021:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-63}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+58}:\\ \;\;\;\;z \cdot \frac{x}{-t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 58.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{-t}{z}}\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{+65}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -7000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -0.017:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-63}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+153}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (/ (- t) z))))
   (if (<= z -2.9e+65)
     x
     (if (<= z -7000.0)
       t_1
       (if (<= z -0.017)
         x
         (if (<= z 4.2e-63) (/ x (/ t y)) (if (<= z 4.6e+153) t_1 x)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (-t / z);
	double tmp;
	if (z <= -2.9e+65) {
		tmp = x;
	} else if (z <= -7000.0) {
		tmp = t_1;
	} else if (z <= -0.017) {
		tmp = x;
	} else if (z <= 4.2e-63) {
		tmp = x / (t / y);
	} else if (z <= 4.6e+153) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x / (-t / z)
    if (z <= (-2.9d+65)) then
        tmp = x
    else if (z <= (-7000.0d0)) then
        tmp = t_1
    else if (z <= (-0.017d0)) then
        tmp = x
    else if (z <= 4.2d-63) then
        tmp = x / (t / y)
    else if (z <= 4.6d+153) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (-t / z);
	double tmp;
	if (z <= -2.9e+65) {
		tmp = x;
	} else if (z <= -7000.0) {
		tmp = t_1;
	} else if (z <= -0.017) {
		tmp = x;
	} else if (z <= 4.2e-63) {
		tmp = x / (t / y);
	} else if (z <= 4.6e+153) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (-t / z)
	tmp = 0
	if z <= -2.9e+65:
		tmp = x
	elif z <= -7000.0:
		tmp = t_1
	elif z <= -0.017:
		tmp = x
	elif z <= 4.2e-63:
		tmp = x / (t / y)
	elif z <= 4.6e+153:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(-t) / z))
	tmp = 0.0
	if (z <= -2.9e+65)
		tmp = x;
	elseif (z <= -7000.0)
		tmp = t_1;
	elseif (z <= -0.017)
		tmp = x;
	elseif (z <= 4.2e-63)
		tmp = Float64(x / Float64(t / y));
	elseif (z <= 4.6e+153)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (-t / z);
	tmp = 0.0;
	if (z <= -2.9e+65)
		tmp = x;
	elseif (z <= -7000.0)
		tmp = t_1;
	elseif (z <= -0.017)
		tmp = x;
	elseif (z <= 4.2e-63)
		tmp = x / (t / y);
	elseif (z <= 4.6e+153)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[((-t) / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.9e+65], x, If[LessEqual[z, -7000.0], t$95$1, If[LessEqual[z, -0.017], x, If[LessEqual[z, 4.2e-63], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.6e+153], t$95$1, x]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.9e65 or -7e3 < z < -0.017000000000000001 or 4.6000000000000003e153 < z

   1. Initial program 64.6%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 z around inf 67.9%

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

   if -2.9e65 < z < -7e3 or 4.2e-63 < z < 4.6000000000000003e153

   1. Initial program 90.2%

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

      1. associate-/l* 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in t around inf 64.0%

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

   5. Taylor expanded in y around 0 53.6%

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

      1. associate-*r/ 53.6%

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

      2. neg-mul-1 53.6%

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

   7. Simplified 53.6%

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

   if -0.017000000000000001 < z < 4.2e-63

   1. Initial program 93.4%

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

      1. associate-/l* 93.8%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in z around 0 80.0%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+65}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -7000:\\ \;\;\;\;\frac{x}{\frac{-t}{z}}\\ \mathbf{elif}\;z \leq -0.017:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-63}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+153}:\\ \;\;\;\;\frac{x}{\frac{-t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 68.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -5.5 \cdot 10^{-40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-71}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{elif}\;z \leq 19000000000000:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y z)))))
   (if (<= z -5.5e-40)
     t_1
     (if (<= z 1.2e-71)
       (/ (* x y) t)
       (if (<= z 19000000000000.0) (/ (* x (- z)) t) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -5.5e-40) {
		tmp = t_1;
	} else if (z <= 1.2e-71) {
		tmp = (x * y) / t;
	} else if (z <= 19000000000000.0) {
		tmp = (x * -z) / t;
	} 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 = x * (1.0d0 - (y / z))
    if (z <= (-5.5d-40)) then
        tmp = t_1
    else if (z <= 1.2d-71) then
        tmp = (x * y) / t
    else if (z <= 19000000000000.0d0) then
        tmp = (x * -z) / t
    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 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -5.5e-40) {
		tmp = t_1;
	} else if (z <= 1.2e-71) {
		tmp = (x * y) / t;
	} else if (z <= 19000000000000.0) {
		tmp = (x * -z) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - (y / z))
	tmp = 0
	if z <= -5.5e-40:
		tmp = t_1
	elif z <= 1.2e-71:
		tmp = (x * y) / t
	elif z <= 19000000000000.0:
		tmp = (x * -z) / t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -5.5e-40)
		tmp = t_1;
	elseif (z <= 1.2e-71)
		tmp = Float64(Float64(x * y) / t);
	elseif (z <= 19000000000000.0)
		tmp = Float64(Float64(x * Float64(-z)) / t);
	else
		tmp = t_1;
	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 <= -5.5e-40)
		tmp = t_1;
	elseif (z <= 1.2e-71)
		tmp = (x * y) / t;
	elseif (z <= 19000000000000.0)
		tmp = (x * -z) / t;
	else
		tmp = t_1;
	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, -5.5e-40], t$95$1, If[LessEqual[z, 1.2e-71], N[(N[(x * y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 19000000000000.0], N[(N[(x * (-z)), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.50000000000000002e-40 or 1.9e13 < z

   1. Initial program 69.6%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around 0 74.6%

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

      1. associate-*r/ 74.6%

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

      2. neg-mul-1 74.6%

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

      3. neg-sub0 74.6%

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

      4. associate--r- 74.6%

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

      5. neg-sub0 74.6%

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

   6. Simplified 74.6%

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

   7. Taylor expanded in y around 0 74.6%

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

      1. +-commutative 74.6%

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

      2. mul-1-neg 74.6%

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

      3. unsub-neg 74.6%

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

   9. Simplified 74.6%

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

   if -5.50000000000000002e-40 < z < 1.2e-71

   1. Initial program 95.7%

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

      1. associate-*r/ 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in z around 0 82.1%

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

   if 1.2e-71 < z < 1.9e13

   1. Initial program 94.2%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 t around inf 83.0%

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

   5. Taylor expanded in y around 0 68.2%

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

      1. mul-1-neg 68.2%

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

      2. associate-*r/ 66.3%

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

      3. distribute-rgt-neg-in 66.3%

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

      4. mul-1-neg 66.3%

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

      5. metadata-eval 66.3%

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

      6. times-frac 66.3%

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

      7. *-lft-identity 66.3%

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

      8. neg-mul-1 66.3%

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

   7. Simplified 66.3%

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

      1. *-commutative 66.3%

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

      2. frac-2neg 66.3%

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

      3. remove-double-neg 66.3%

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

      4. associate-*l/ 68.2%

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

   9. Applied egg-rr 68.2%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-40}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-71}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{elif}\;z \leq 19000000000000:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]

Alternative 5: 75.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{-86}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 15000000000000:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y z)))))
   (if (<= z -2.8e-8)
     t_1
     (if (<= z 2.75e-86)
       (* x (/ y (- t z)))
       (if (<= z 15000000000000.0) (* (- y z) (/ x t)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -2.8e-8) {
		tmp = t_1;
	} else if (z <= 2.75e-86) {
		tmp = x * (y / (t - z));
	} else if (z <= 15000000000000.0) {
		tmp = (y - z) * (x / t);
	} 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 = x * (1.0d0 - (y / z))
    if (z <= (-2.8d-8)) then
        tmp = t_1
    else if (z <= 2.75d-86) then
        tmp = x * (y / (t - z))
    else if (z <= 15000000000000.0d0) then
        tmp = (y - z) * (x / t)
    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 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -2.8e-8) {
		tmp = t_1;
	} else if (z <= 2.75e-86) {
		tmp = x * (y / (t - z));
	} else if (z <= 15000000000000.0) {
		tmp = (y - z) * (x / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - (y / z))
	tmp = 0
	if z <= -2.8e-8:
		tmp = t_1
	elif z <= 2.75e-86:
		tmp = x * (y / (t - z))
	elif z <= 15000000000000.0:
		tmp = (y - z) * (x / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -2.8e-8)
		tmp = t_1;
	elseif (z <= 2.75e-86)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	elseif (z <= 15000000000000.0)
		tmp = Float64(Float64(y - z) * Float64(x / t));
	else
		tmp = t_1;
	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 <= -2.8e-8)
		tmp = t_1;
	elseif (z <= 2.75e-86)
		tmp = x * (y / (t - z));
	elseif (z <= 15000000000000.0)
		tmp = (y - z) * (x / t);
	else
		tmp = t_1;
	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, -2.8e-8], t$95$1, If[LessEqual[z, 2.75e-86], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 15000000000000.0], N[(N[(y - z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.7999999999999999e-8 or 1.5e13 < z

   1. Initial program 70.2%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 t around 0 75.3%

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

      1. associate-*r/ 75.3%

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

      2. neg-mul-1 75.3%

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

      3. neg-sub0 75.3%

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

      4. associate--r- 75.3%

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

      5. neg-sub0 75.3%

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

   6. Simplified 75.3%

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

   7. Taylor expanded in y around 0 75.3%

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

      1. +-commutative 75.3%

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

      2. mul-1-neg 75.3%

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

      3. unsub-neg 75.3%

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

   9. Simplified 75.3%

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

   if -2.7999999999999999e-8 < z < 2.75e-86

   1. Initial program 94.0%

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

      1. associate-*r/ 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in y around inf 86.6%

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

   if 2.75e-86 < z < 1.5e13

   1. Initial program 95.1%

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

      1. associate-*l/ 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in t around inf 88.6%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{-86}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 15000000000000:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]

Alternative 6: 75.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-5} \lor \neg \left(z \leq 1.4 \cdot 10^{+54}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.15e-5) (not (<= z 1.4e+54)))
   (* x (- 1.0 (/ y z)))
   (* x (/ y (- t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.15e-5) || !(z <= 1.4e+54)) {
		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 <= (-1.15d-5)) .or. (.not. (z <= 1.4d+54))) 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 <= -1.15e-5) || !(z <= 1.4e+54)) {
		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 <= -1.15e-5) or not (z <= 1.4e+54):
		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 <= -1.15e-5) || !(z <= 1.4e+54))
		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 <= -1.15e-5) || ~((z <= 1.4e+54)))
		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, -1.15e-5], N[Not[LessEqual[z, 1.4e+54]], $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 < -1.15e-5 or 1.40000000000000008e54 < z

   1. Initial program 68.5%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around 0 77.0%

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

      1. associate-*r/ 77.0%

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

      2. neg-mul-1 77.0%

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

      3. neg-sub0 77.0%

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

      4. associate--r- 77.0%

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

      5. neg-sub0 77.0%

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

   6. Simplified 77.0%

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

   7. Taylor expanded in y around 0 77.0%

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

      1. +-commutative 77.0%

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

      2. mul-1-neg 77.0%

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

      3. unsub-neg 77.0%

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

   9. Simplified 77.0%

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

   if -1.15e-5 < z < 1.40000000000000008e54

   1. Initial program 94.4%

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

      1. associate-*r/ 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in y around inf 80.9%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-5} \lor \neg \left(z \leq 1.4 \cdot 10^{+54}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \]

Alternative 7: 73.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-6} \lor \neg \left(z \leq 3.7 \cdot 10^{+32}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.1e-6) (not (<= z 3.7e+32)))
   (* x (- 1.0 (/ y z)))
   (/ x (/ t (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.1e-6) || !(z <= 3.7e+32)) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = x / (t / (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-3.1d-6)) .or. (.not. (z <= 3.7d+32))) then
        tmp = x * (1.0d0 - (y / z))
    else
        tmp = x / (t / (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.1e-6) || !(z <= 3.7e+32)) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = x / (t / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.1e-6) or not (z <= 3.7e+32):
		tmp = x * (1.0 - (y / z))
	else:
		tmp = x / (t / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.1e-6) || !(z <= 3.7e+32))
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(x / Float64(t / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.1e-6) || ~((z <= 3.7e+32)))
		tmp = x * (1.0 - (y / z));
	else
		tmp = x / (t / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.1e-6], N[Not[LessEqual[z, 3.7e+32]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.1e-6 or 3.7e32 < z

   1. Initial program 69.5%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 t around 0 76.2%

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

      1. associate-*r/ 76.2%

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

      2. neg-mul-1 76.2%

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

      3. neg-sub0 76.2%

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

      4. associate--r- 76.2%

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

      5. neg-sub0 76.2%

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

   6. Simplified 76.2%

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

   7. Taylor expanded in y around 0 76.3%

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

      1. +-commutative 76.3%

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

      2. mul-1-neg 76.3%

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

      3. unsub-neg 76.3%

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

   9. Simplified 76.3%

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

   if -3.1e-6 < z < 3.7e32

   1. Initial program 94.3%

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

      1. associate-/l* 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in t around inf 84.0%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-6} \lor \neg \left(z \leq 3.7 \cdot 10^{+32}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \end{array} \]

Alternative 8: 73.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-40} \lor \neg \left(z \leq 6.8 \cdot 10^{+32}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -9e-40) (not (<= z 6.8e+32)))
   (* x (- 1.0 (/ y z)))
   (/ (* x (- y z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9e-40) || !(z <= 6.8e+32)) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = (x * (y - z)) / 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 ((z <= (-9d-40)) .or. (.not. (z <= 6.8d+32))) then
        tmp = x * (1.0d0 - (y / z))
    else
        tmp = (x * (y - z)) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9e-40) || !(z <= 6.8e+32)) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = (x * (y - z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -9e-40) or not (z <= 6.8e+32):
		tmp = x * (1.0 - (y / z))
	else:
		tmp = (x * (y - z)) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -9e-40) || !(z <= 6.8e+32))
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(Float64(x * Float64(y - z)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -9e-40) || ~((z <= 6.8e+32)))
		tmp = x * (1.0 - (y / z));
	else
		tmp = (x * (y - z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -9e-40], N[Not[LessEqual[z, 6.8e+32]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.0000000000000002e-40 or 6.79999999999999957e32 < z

   1. Initial program 68.9%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around 0 75.5%

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

      1. associate-*r/ 75.5%

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

      2. neg-mul-1 75.5%

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

      3. neg-sub0 75.5%

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

      4. associate--r- 75.5%

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

      5. neg-sub0 75.5%

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

   6. Simplified 75.5%

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

   7. Taylor expanded in y around 0 75.5%

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

      1. +-commutative 75.5%

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

      2. mul-1-neg 75.5%

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

      3. unsub-neg 75.5%

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

   9. Simplified 75.5%

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

   if -9.0000000000000002e-40 < z < 6.79999999999999957e32

   1. Initial program 95.6%

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

      1. associate-*r/ 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in t around inf 86.3%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-40} \lor \neg \left(z \leq 6.8 \cdot 10^{+32}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t}\\ \end{array} \]

Alternative 9: 73.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-36}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 28:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z - t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.1e-36)
   (* x (- 1.0 (/ y z)))
   (if (<= z 28.0) (/ (* x (- y z)) t) (/ x (/ (- z t) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.1e-36) {
		tmp = x * (1.0 - (y / z));
	} else if (z <= 28.0) {
		tmp = (x * (y - z)) / t;
	} else {
		tmp = x / ((z - 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 <= (-2.1d-36)) then
        tmp = x * (1.0d0 - (y / z))
    else if (z <= 28.0d0) then
        tmp = (x * (y - z)) / t
    else
        tmp = x / ((z - 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 <= -2.1e-36) {
		tmp = x * (1.0 - (y / z));
	} else if (z <= 28.0) {
		tmp = (x * (y - z)) / t;
	} else {
		tmp = x / ((z - t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.1e-36:
		tmp = x * (1.0 - (y / z))
	elif z <= 28.0:
		tmp = (x * (y - z)) / t
	else:
		tmp = x / ((z - t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.1e-36)
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	elseif (z <= 28.0)
		tmp = Float64(Float64(x * Float64(y - z)) / t);
	else
		tmp = Float64(x / Float64(Float64(z - t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.1e-36)
		tmp = x * (1.0 - (y / z));
	elseif (z <= 28.0)
		tmp = (x * (y - z)) / t;
	else
		tmp = x / ((z - t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.1e-36], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 28.0], N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], N[(x / N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.09999999999999991e-36

   1. Initial program 69.0%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around 0 75.7%

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

      1. associate-*r/ 75.7%

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

      2. neg-mul-1 75.7%

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

      3. neg-sub0 75.7%

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

      4. associate--r- 75.7%

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

      5. neg-sub0 75.7%

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

   6. Simplified 75.7%

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

   7. Taylor expanded in y around 0 75.8%

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

      1. +-commutative 75.8%

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

      2. mul-1-neg 75.8%

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

      3. unsub-neg 75.8%

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

   9. Simplified 75.8%

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

   if -2.09999999999999991e-36 < z < 28

   1. Initial program 95.3%

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

      1. associate-*r/ 94.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in t around inf 87.1%

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

   if 28 < z

   1. Initial program 72.6%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 0 77.0%

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

      1. associate-*r/ 77.0%

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

      2. neg-mul-1 77.0%

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

      3. neg-sub0 77.0%

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

      4. associate--r- 77.0%

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

      5. neg-sub0 77.0%

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

   6. Simplified 77.0%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-36}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 28:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z - t}{z}}\\ \end{array} \]

Alternative 10: 38.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{-63}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-24}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.9e-63) x (if (<= z 7.5e-24) (* x (/ z t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.9e-63) {
		tmp = x;
	} else if (z <= 7.5e-24) {
		tmp = x * (z / 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 <= (-3.9d-63)) then
        tmp = x
    else if (z <= 7.5d-24) then
        tmp = x * (z / 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 <= -3.9e-63) {
		tmp = x;
	} else if (z <= 7.5e-24) {
		tmp = x * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.9e-63:
		tmp = x
	elif z <= 7.5e-24:
		tmp = x * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.9e-63)
		tmp = x;
	elseif (z <= 7.5e-24)
		tmp = Float64(x * Float64(z / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.9e-63)
		tmp = x;
	elseif (z <= 7.5e-24)
		tmp = x * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.9e-63], x, If[LessEqual[z, 7.5e-24], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -3.90000000000000022e-63 or 7.50000000000000007e-24 < z

   1. Initial program 71.5%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 z around inf 52.4%

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

   if -3.90000000000000022e-63 < z < 7.50000000000000007e-24

   1. Initial program 95.2%

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

      1. associate-/l* 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in t around inf 85.1%

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

   5. Taylor expanded in y around 0 25.5%

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

      1. mul-1-neg 25.5%

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

      2. associate-*r/ 25.6%

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

      3. distribute-rgt-neg-in 25.6%

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

      4. mul-1-neg 25.6%

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

      5. metadata-eval 25.6%

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

      6. times-frac 25.6%

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

      7. *-lft-identity 25.6%

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

      8. neg-mul-1 25.6%

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

   7. Simplified 25.6%

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

      1. expm1-log1p-u 23.6%

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

      2. expm1-udef 16.7%

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

      3. add-sqr-sqrt 7.6%

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

      4. sqrt-unprod 17.9%

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

      5. sqr-neg 17.9%

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

      6. sqrt-unprod 10.5%

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

      7. add-sqr-sqrt 19.7%

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

   9. Applied egg-rr 19.7%

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

       1. expm1-def 19.9%

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

       2. expm1-log1p 21.1%

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

       3. associate-*r/ 17.0%

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

       4. associate-*l/ 16.9%

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

       5. *-commutative 16.9%

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

   11. Simplified 16.9%

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

4. Final simplification 36.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{-63}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-24}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 39.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-63}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-24}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4e-63) x (if (<= z 8e-24) (* z (/ x t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4e-63) {
		tmp = x;
	} else if (z <= 8e-24) {
		tmp = z * (x / 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 <= (-4d-63)) then
        tmp = x
    else if (z <= 8d-24) then
        tmp = z * (x / 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 <= -4e-63) {
		tmp = x;
	} else if (z <= 8e-24) {
		tmp = z * (x / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4e-63:
		tmp = x
	elif z <= 8e-24:
		tmp = z * (x / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4e-63)
		tmp = x;
	elseif (z <= 8e-24)
		tmp = Float64(z * Float64(x / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4e-63)
		tmp = x;
	elseif (z <= 8e-24)
		tmp = z * (x / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4e-63], x, If[LessEqual[z, 8e-24], N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -4.00000000000000027e-63 or 7.99999999999999939e-24 < z

   1. Initial program 71.5%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 z around inf 52.4%

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

   if -4.00000000000000027e-63 < z < 7.99999999999999939e-24

   1. Initial program 95.2%

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

      1. associate-/l* 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in t around inf 85.1%

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

   5. Taylor expanded in y around 0 25.5%

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

      1. mul-1-neg 25.5%

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

      2. associate-*r/ 25.6%

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

      3. distribute-rgt-neg-in 25.6%

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

      4. mul-1-neg 25.6%

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

      5. metadata-eval 25.6%

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

      6. times-frac 25.6%

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

      7. *-lft-identity 25.6%

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

      8. neg-mul-1 25.6%

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

   7. Simplified 25.6%

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

      1. expm1-log1p-u 23.6%

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

      2. expm1-udef 16.7%

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

      3. add-sqr-sqrt 7.6%

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

      4. sqrt-unprod 17.9%

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

      5. sqr-neg 17.9%

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

      6. sqrt-unprod 10.5%

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

      7. add-sqr-sqrt 19.7%

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

   9. Applied egg-rr 19.7%

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

       1. expm1-def 19.9%

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

       2. expm1-log1p 21.1%

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

   11. Simplified 21.1%

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

4. Final simplification 38.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-63}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-24}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 61.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.0008:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 35000000000000:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -0.0008) x (if (<= z 35000000000000.0) (* y (/ x t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -0.0008) {
		tmp = x;
	} else if (z <= 35000000000000.0) {
		tmp = y * (x / 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 <= (-0.0008d0)) then
        tmp = x
    else if (z <= 35000000000000.0d0) then
        tmp = y * (x / 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 <= -0.0008) {
		tmp = x;
	} else if (z <= 35000000000000.0) {
		tmp = y * (x / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -0.0008:
		tmp = x
	elif z <= 35000000000000.0:
		tmp = y * (x / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -0.0008)
		tmp = x;
	elseif (z <= 35000000000000.0)
		tmp = Float64(y * Float64(x / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -0.0008)
		tmp = x;
	elseif (z <= 35000000000000.0)
		tmp = y * (x / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -0.0008], x, If[LessEqual[z, 35000000000000.0], N[(y * N[(x / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -8.00000000000000038e-4 or 3.5e13 < z

   1. Initial program 70.2%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 z around inf 56.4%

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

   if -8.00000000000000038e-4 < z < 3.5e13

   1. Initial program 94.1%

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

      1. associate-/l* 93.8%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in z around 0 74.9%

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

      1. associate-/r/ 69.5%

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

   6. Applied egg-rr 69.5%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0008:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 35000000000000:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 61.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+54}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.2e-5) x (if (<= z 4.9e+54) (/ x (/ t y)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.2e-5) {
		tmp = x;
	} else if (z <= 4.9e+54) {
		tmp = x / (t / y);
	} 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 <= (-1.2d-5)) then
        tmp = x
    else if (z <= 4.9d+54) then
        tmp = x / (t / y)
    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 <= -1.2e-5) {
		tmp = x;
	} else if (z <= 4.9e+54) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.2e-5:
		tmp = x
	elif z <= 4.9e+54:
		tmp = x / (t / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.2e-5)
		tmp = x;
	elseif (z <= 4.9e+54)
		tmp = Float64(x / Float64(t / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.2e-5)
		tmp = x;
	elseif (z <= 4.9e+54)
		tmp = x / (t / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.2e-5], x, If[LessEqual[z, 4.9e+54], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.2e-5 or 4.90000000000000001e54 < z

   1. Initial program 68.5%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 57.7%

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

   if -1.2e-5 < z < 4.90000000000000001e54

   1. Initial program 94.4%

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

      1. associate-/l* 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in z around 0 73.3%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+54}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14: 34.7% 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 82.0%

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

   1. associate-*r/ 97.3%

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

3. Simplified 97.3%

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

4. Taylor expanded in z around inf 31.9%

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

5. Final simplification 31.9%

   \[\leadsto x \]

Developer target: 96.6% 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 2023200 
(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)))