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

Percentage Accurate: 84.3% → 97.1%

Time: 7.3s

Alternatives: 11

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: 84.3% 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: 97.1% 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 81.5%

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

   1. associate-*r/ 96.9%

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

3. Simplified 96.9%

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

4. Final simplification 96.9%

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

Alternative 2: 68.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{t - z}\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{+81}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-157}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-235}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ y (- t z)))))
   (if (<= z -9.5e+81)
     x
     (if (<= z -7.2e-157)
       t_1
       (if (<= z 2.8e-235) (* (- y z) (/ x t)) (if (<= z 6.8e+71) t_1 x))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y / (t - z));
	double tmp;
	if (z <= -9.5e+81) {
		tmp = x;
	} else if (z <= -7.2e-157) {
		tmp = t_1;
	} else if (z <= 2.8e-235) {
		tmp = (y - z) * (x / t);
	} else if (z <= 6.8e+71) {
		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 * (y / (t - z))
    if (z <= (-9.5d+81)) then
        tmp = x
    else if (z <= (-7.2d-157)) then
        tmp = t_1
    else if (z <= 2.8d-235) then
        tmp = (y - z) * (x / t)
    else if (z <= 6.8d+71) 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 * (y / (t - z));
	double tmp;
	if (z <= -9.5e+81) {
		tmp = x;
	} else if (z <= -7.2e-157) {
		tmp = t_1;
	} else if (z <= 2.8e-235) {
		tmp = (y - z) * (x / t);
	} else if (z <= 6.8e+71) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y / (t - z))
	tmp = 0
	if z <= -9.5e+81:
		tmp = x
	elif z <= -7.2e-157:
		tmp = t_1
	elif z <= 2.8e-235:
		tmp = (y - z) * (x / t)
	elif z <= 6.8e+71:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y / Float64(t - z)))
	tmp = 0.0
	if (z <= -9.5e+81)
		tmp = x;
	elseif (z <= -7.2e-157)
		tmp = t_1;
	elseif (z <= 2.8e-235)
		tmp = Float64(Float64(y - z) * Float64(x / t));
	elseif (z <= 6.8e+71)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y / (t - z));
	tmp = 0.0;
	if (z <= -9.5e+81)
		tmp = x;
	elseif (z <= -7.2e-157)
		tmp = t_1;
	elseif (z <= 2.8e-235)
		tmp = (y - z) * (x / t);
	elseif (z <= 6.8e+71)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.5e+81], x, If[LessEqual[z, -7.2e-157], t$95$1, If[LessEqual[z, 2.8e-235], N[(N[(y - z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e+71], t$95$1, x]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.50000000000000083e81 or 6.7999999999999997e71 < z

   1. Initial program 61.8%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 72.7%

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

   if -9.50000000000000083e81 < z < -7.2e-157 or 2.79999999999999995e-235 < z < 6.7999999999999997e71

   1. Initial program 92.7%

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

      1. associate-*r/ 97.8%

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

   3. Simplified 97.8%

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

   4. Taylor expanded in y around inf 77.2%

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

   if -7.2e-157 < z < 2.79999999999999995e-235

   1. Initial program 94.7%

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

      1. associate-*l/ 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in t around inf 92.3%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+81}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-157}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-235}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+71}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 75.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{t - z}\\ t_2 := x \cdot \frac{z}{z - t}\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{+30}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-157}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.3 \cdot 10^{-235}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+65}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ y (- t z)))) (t_2 (* x (/ z (- z t)))))
   (if (<= z -2.5e+30)
     t_2
     (if (<= z -7e-157)
       t_1
       (if (<= z 6.3e-235) (* (- y z) (/ x t)) (if (<= z 2.3e+65) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y / (t - z));
	double t_2 = x * (z / (z - t));
	double tmp;
	if (z <= -2.5e+30) {
		tmp = t_2;
	} else if (z <= -7e-157) {
		tmp = t_1;
	} else if (z <= 6.3e-235) {
		tmp = (y - z) * (x / t);
	} else if (z <= 2.3e+65) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (y / (t - z))
    t_2 = x * (z / (z - t))
    if (z <= (-2.5d+30)) then
        tmp = t_2
    else if (z <= (-7d-157)) then
        tmp = t_1
    else if (z <= 6.3d-235) then
        tmp = (y - z) * (x / t)
    else if (z <= 2.3d+65) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (y / (t - z));
	double t_2 = x * (z / (z - t));
	double tmp;
	if (z <= -2.5e+30) {
		tmp = t_2;
	} else if (z <= -7e-157) {
		tmp = t_1;
	} else if (z <= 6.3e-235) {
		tmp = (y - z) * (x / t);
	} else if (z <= 2.3e+65) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y / (t - z))
	t_2 = x * (z / (z - t))
	tmp = 0
	if z <= -2.5e+30:
		tmp = t_2
	elif z <= -7e-157:
		tmp = t_1
	elif z <= 6.3e-235:
		tmp = (y - z) * (x / t)
	elif z <= 2.3e+65:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y / Float64(t - z)))
	t_2 = Float64(x * Float64(z / Float64(z - t)))
	tmp = 0.0
	if (z <= -2.5e+30)
		tmp = t_2;
	elseif (z <= -7e-157)
		tmp = t_1;
	elseif (z <= 6.3e-235)
		tmp = Float64(Float64(y - z) * Float64(x / t));
	elseif (z <= 2.3e+65)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y / (t - z));
	t_2 = x * (z / (z - t));
	tmp = 0.0;
	if (z <= -2.5e+30)
		tmp = t_2;
	elseif (z <= -7e-157)
		tmp = t_1;
	elseif (z <= 6.3e-235)
		tmp = (y - z) * (x / t);
	elseif (z <= 2.3e+65)
		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[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.5e+30], t$95$2, If[LessEqual[z, -7e-157], t$95$1, If[LessEqual[z, 6.3e-235], N[(N[(y - z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.3e+65], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.4999999999999999e30 or 2.3e65 < z

   1. Initial program 62.7%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 83.5%

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

      1. associate-*r/ 83.5%

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

      2. neg-mul-1 83.5%

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

      3. neg-sub0 83.5%

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

      4. associate--r- 83.5%

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

      5. neg-sub0 83.5%

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

   6. Simplified 83.5%

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

   7. Taylor expanded in x around 0 52.9%

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

      1. associate-/l* 64.0%

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

      2. associate-/r/ 83.5%

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

   9. Simplified 83.5%

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

   if -2.4999999999999999e30 < z < -7.0000000000000004e-157 or 6.2999999999999995e-235 < z < 2.3e65

   1. Initial program 94.9%

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

      1. associate-*r/ 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in y around inf 81.7%

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

   if -7.0000000000000004e-157 < z < 6.2999999999999995e-235

   1. Initial program 94.7%

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

      1. associate-*l/ 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in t around inf 92.3%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+30}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-157}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 6.3 \cdot 10^{-235}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+65}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \]

Alternative 4: 75.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{t - z}{y}}\\ t_2 := x \cdot \frac{z}{z - t}\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{+30}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-150}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-235}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{+63}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (/ (- t z) y))) (t_2 (* x (/ z (- z t)))))
   (if (<= z -2.8e+30)
     t_2
     (if (<= z -1.02e-150)
       t_1
       (if (<= z 4.4e-235) (* (- y z) (/ x t)) (if (<= z 5.9e+63) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((t - z) / y);
	double t_2 = x * (z / (z - t));
	double tmp;
	if (z <= -2.8e+30) {
		tmp = t_2;
	} else if (z <= -1.02e-150) {
		tmp = t_1;
	} else if (z <= 4.4e-235) {
		tmp = (y - z) * (x / t);
	} else if (z <= 5.9e+63) {
		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 / ((t - z) / y)
    t_2 = x * (z / (z - t))
    if (z <= (-2.8d+30)) then
        tmp = t_2
    else if (z <= (-1.02d-150)) then
        tmp = t_1
    else if (z <= 4.4d-235) then
        tmp = (y - z) * (x / t)
    else if (z <= 5.9d+63) 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 / ((t - z) / y);
	double t_2 = x * (z / (z - t));
	double tmp;
	if (z <= -2.8e+30) {
		tmp = t_2;
	} else if (z <= -1.02e-150) {
		tmp = t_1;
	} else if (z <= 4.4e-235) {
		tmp = (y - z) * (x / t);
	} else if (z <= 5.9e+63) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((t - z) / y)
	t_2 = x * (z / (z - t))
	tmp = 0
	if z <= -2.8e+30:
		tmp = t_2
	elif z <= -1.02e-150:
		tmp = t_1
	elif z <= 4.4e-235:
		tmp = (y - z) * (x / t)
	elif z <= 5.9e+63:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(t - z) / y))
	t_2 = Float64(x * Float64(z / Float64(z - t)))
	tmp = 0.0
	if (z <= -2.8e+30)
		tmp = t_2;
	elseif (z <= -1.02e-150)
		tmp = t_1;
	elseif (z <= 4.4e-235)
		tmp = Float64(Float64(y - z) * Float64(x / t));
	elseif (z <= 5.9e+63)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / ((t - z) / y);
	t_2 = x * (z / (z - t));
	tmp = 0.0;
	if (z <= -2.8e+30)
		tmp = t_2;
	elseif (z <= -1.02e-150)
		tmp = t_1;
	elseif (z <= 4.4e-235)
		tmp = (y - z) * (x / t);
	elseif (z <= 5.9e+63)
		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[(N[(t - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.8e+30], t$95$2, If[LessEqual[z, -1.02e-150], t$95$1, If[LessEqual[z, 4.4e-235], N[(N[(y - z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.9e+63], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.79999999999999983e30 or 5.90000000000000029e63 < z

   1. Initial program 62.7%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 83.5%

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

      1. associate-*r/ 83.5%

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

      2. neg-mul-1 83.5%

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

      3. neg-sub0 83.5%

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

      4. associate--r- 83.5%

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

      5. neg-sub0 83.5%

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

   6. Simplified 83.5%

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

   7. Taylor expanded in x around 0 52.9%

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

      1. associate-/l* 64.0%

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

      2. associate-/r/ 83.5%

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

   9. Simplified 83.5%

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

   if -2.79999999999999983e30 < z < -1.0199999999999999e-150 or 4.39999999999999968e-235 < z < 5.90000000000000029e63

   1. Initial program 94.7%

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

      1. associate-/l* 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in y around inf 81.1%

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

   if -1.0199999999999999e-150 < z < 4.39999999999999968e-235

   1. Initial program 94.9%

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

      1. associate-*l/ 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in t around inf 92.6%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+30}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-150}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-235}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{+63}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \]

Alternative 5: 59.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+42}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-172}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-117}:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{z}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+25}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.1e+42)
   x
   (if (<= z 5.4e-172)
     (/ (* x y) t)
     (if (<= z 2.7e-117)
       (/ (* x (- y)) z)
       (if (<= z 7e+25) (/ x (/ t y)) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.1e+42) {
		tmp = x;
	} else if (z <= 5.4e-172) {
		tmp = (x * y) / t;
	} else if (z <= 2.7e-117) {
		tmp = (x * -y) / z;
	} else if (z <= 7e+25) {
		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 <= (-4.1d+42)) then
        tmp = x
    else if (z <= 5.4d-172) then
        tmp = (x * y) / t
    else if (z <= 2.7d-117) then
        tmp = (x * -y) / z
    else if (z <= 7d+25) 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 <= -4.1e+42) {
		tmp = x;
	} else if (z <= 5.4e-172) {
		tmp = (x * y) / t;
	} else if (z <= 2.7e-117) {
		tmp = (x * -y) / z;
	} else if (z <= 7e+25) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.1e+42:
		tmp = x
	elif z <= 5.4e-172:
		tmp = (x * y) / t
	elif z <= 2.7e-117:
		tmp = (x * -y) / z
	elif z <= 7e+25:
		tmp = x / (t / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.1e+42)
		tmp = x;
	elseif (z <= 5.4e-172)
		tmp = Float64(Float64(x * y) / t);
	elseif (z <= 2.7e-117)
		tmp = Float64(Float64(x * Float64(-y)) / z);
	elseif (z <= 7e+25)
		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 <= -4.1e+42)
		tmp = x;
	elseif (z <= 5.4e-172)
		tmp = (x * y) / t;
	elseif (z <= 2.7e-117)
		tmp = (x * -y) / z;
	elseif (z <= 7e+25)
		tmp = x / (t / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.1e+42], x, If[LessEqual[z, 5.4e-172], N[(N[(x * y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 2.7e-117], N[(N[(x * (-y)), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 7e+25], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.1e42 or 6.99999999999999999e25 < z

   1. Initial program 63.2%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 68.4%

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

   if -4.1e42 < z < 5.40000000000000051e-172

   1. Initial program 96.4%

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

      1. associate-*r/ 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in z around 0 73.4%

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

   if 5.40000000000000051e-172 < z < 2.70000000000000003e-117

   1. Initial program 86.0%

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

      1. associate-*r/ 86.2%

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

   3. Simplified 86.2%

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

   4. Taylor expanded in y around inf 86.0%

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

   5. Taylor expanded in t around 0 86.0%

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

      1. associate-*r/ 86.0%

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

      2. mul-1-neg 86.0%

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

      3. distribute-rgt-neg-in 86.0%

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

   7. Simplified 86.0%

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

   if 2.70000000000000003e-117 < z < 6.99999999999999999e25

   1. Initial program 92.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 59.8%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+42}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-172}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-117}:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{z}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+25}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 75.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+30} \lor \neg \left(z \leq 2.6 \cdot 10^{+34}\right):\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.4e+30) (not (<= z 2.6e+34)))
   (* x (/ z (- z t)))
   (/ (* x y) (- t z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.4e+30) || !(z <= 2.6e+34)) {
		tmp = x * (z / (z - t));
	} 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 <= (-3.4d+30)) .or. (.not. (z <= 2.6d+34))) then
        tmp = x * (z / (z - t))
    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 <= -3.4e+30) || !(z <= 2.6e+34)) {
		tmp = x * (z / (z - t));
	} else {
		tmp = (x * y) / (t - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.4e+30) or not (z <= 2.6e+34):
		tmp = x * (z / (z - t))
	else:
		tmp = (x * y) / (t - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.4e+30) || !(z <= 2.6e+34))
		tmp = Float64(x * Float64(z / Float64(z - t)));
	else
		tmp = Float64(Float64(x * y) / Float64(t - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.4e+30) || ~((z <= 2.6e+34)))
		tmp = x * (z / (z - t));
	else
		tmp = (x * y) / (t - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.4e+30], N[Not[LessEqual[z, 2.6e+34]], $MachinePrecision]], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.4000000000000002e30 or 2.59999999999999997e34 < z

   1. Initial program 63.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 81.9%

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

      1. associate-*r/ 81.9%

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

      2. neg-mul-1 81.9%

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

      3. neg-sub0 81.9%

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

      4. associate--r- 81.9%

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

      5. neg-sub0 81.9%

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

   6. Simplified 81.9%

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

   7. Taylor expanded in x around 0 52.9%

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

      1. associate-/l* 62.6%

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

      2. associate-/r/ 81.9%

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

   9. Simplified 81.9%

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

   if -3.4000000000000002e30 < z < 2.59999999999999997e34

   1. Initial program 95.2%

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

      1. associate-*r/ 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in y around inf 84.8%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+30} \lor \neg \left(z \leq 2.6 \cdot 10^{+34}\right):\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{t - z}\\ \end{array} \]

Alternative 7: 69.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+79}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{+69}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -6.5e+79) x (if (<= z 1.16e+69) (* x (/ y (- t z))) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.5e+79) {
		tmp = x;
	} else if (z <= 1.16e+69) {
		tmp = x * (y / (t - z));
	} 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 <= (-6.5d+79)) then
        tmp = x
    else if (z <= 1.16d+69) then
        tmp = x * (y / (t - z))
    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 <= -6.5e+79) {
		tmp = x;
	} else if (z <= 1.16e+69) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -6.5e+79:
		tmp = x
	elif z <= 1.16e+69:
		tmp = x * (y / (t - z))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6.5e+79)
		tmp = x;
	elseif (z <= 1.16e+69)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -6.5e+79)
		tmp = x;
	elseif (z <= 1.16e+69)
		tmp = x * (y / (t - z));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -6.5e+79], x, If[LessEqual[z, 1.16e+69], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -6.49999999999999954e79 or 1.16000000000000005e69 < z

   1. Initial program 61.8%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 72.7%

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

   if -6.49999999999999954e79 < z < 1.16000000000000005e69

   1. Initial program 93.4%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 78.7%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+79}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{+69}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 75.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+29}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+31}:\\ \;\;\;\;\frac{x \cdot y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.2e+29)
   (* x (/ z (- z t)))
   (if (<= z 2.4e+31) (/ (* x y) (- t z)) (* x (/ (- z y) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.2e+29) {
		tmp = x * (z / (z - t));
	} else if (z <= 2.4e+31) {
		tmp = (x * y) / (t - z);
	} else {
		tmp = x * ((z - 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 <= (-2.2d+29)) then
        tmp = x * (z / (z - t))
    else if (z <= 2.4d+31) then
        tmp = (x * y) / (t - z)
    else
        tmp = x * ((z - 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 <= -2.2e+29) {
		tmp = x * (z / (z - t));
	} else if (z <= 2.4e+31) {
		tmp = (x * y) / (t - z);
	} else {
		tmp = x * ((z - y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.2e+29:
		tmp = x * (z / (z - t))
	elif z <= 2.4e+31:
		tmp = (x * y) / (t - z)
	else:
		tmp = x * ((z - y) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.2e+29)
		tmp = Float64(x * Float64(z / Float64(z - t)));
	elseif (z <= 2.4e+31)
		tmp = Float64(Float64(x * y) / Float64(t - z));
	else
		tmp = Float64(x * Float64(Float64(z - y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.2e+29)
		tmp = x * (z / (z - t));
	elseif (z <= 2.4e+31)
		tmp = (x * y) / (t - z);
	else
		tmp = x * ((z - y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.2e+29], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.4e+31], N[(N[(x * y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.2000000000000001e29

   1. Initial program 55.7%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 85.5%

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

      1. associate-*r/ 85.5%

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

      2. neg-mul-1 85.5%

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

      3. neg-sub0 85.5%

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

      4. associate--r- 85.5%

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

      5. neg-sub0 85.5%

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

   6. Simplified 85.5%

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

   7. Taylor expanded in x around 0 49.0%

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

      1. associate-/l* 71.9%

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

      2. associate-/r/ 85.5%

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

   9. Simplified 85.5%

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

   if -2.2000000000000001e29 < z < 2.39999999999999982e31

   1. Initial program 95.2%

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

      1. associate-*r/ 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in y around inf 84.8%

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

   if 2.39999999999999982e31 < z

   1. Initial program 72.3%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 84.4%

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

      1. associate-*r/ 84.4%

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

      2. neg-mul-1 84.4%

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

      3. neg-sub0 84.4%

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

      4. associate--r- 84.4%

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

      5. neg-sub0 84.4%

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

   6. Simplified 84.4%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+29}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+31}:\\ \;\;\;\;\frac{x \cdot y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - y}{z}\\ \end{array} \]

Alternative 9: 61.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+77}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+32}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.6e+77) x (if (<= z 2e+32) (* x (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.6e+77) {
		tmp = x;
	} else if (z <= 2e+32) {
		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 <= (-5.6d+77)) then
        tmp = x
    else if (z <= 2d+32) 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 <= -5.6e+77) {
		tmp = x;
	} else if (z <= 2e+32) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.6e+77:
		tmp = x
	elif z <= 2e+32:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.6e+77)
		tmp = x;
	elseif (z <= 2e+32)
		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 <= -5.6e+77)
		tmp = x;
	elseif (z <= 2e+32)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.6e+77], x, If[LessEqual[z, 2e+32], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -5.60000000000000001e77 or 2.00000000000000011e32 < z

   1. Initial program 63.5%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 70.9%

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

   if -5.60000000000000001e77 < z < 2.00000000000000011e32

   1. Initial program 93.7%

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

      1. associate-*r/ 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in z around 0 65.6%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+77}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+32}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 60.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+43}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+25}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.9e+43) x (if (<= z 2.8e+25) (/ (* x y) t) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.9e+43) {
		tmp = x;
	} else if (z <= 2.8e+25) {
		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 <= (-1.9d+43)) then
        tmp = x
    else if (z <= 2.8d+25) 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 <= -1.9e+43) {
		tmp = x;
	} else if (z <= 2.8e+25) {
		tmp = (x * y) / t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.9e+43:
		tmp = x
	elif z <= 2.8e+25:
		tmp = (x * y) / t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.9e+43)
		tmp = x;
	elseif (z <= 2.8e+25)
		tmp = Float64(Float64(x * y) / t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.9e+43)
		tmp = x;
	elseif (z <= 2.8e+25)
		tmp = (x * y) / t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.9e+43], x, If[LessEqual[z, 2.8e+25], N[(N[(x * y), $MachinePrecision] / t), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.90000000000000004e43 or 2.8000000000000002e25 < z

   1. Initial program 63.2%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 68.4%

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

   if -1.90000000000000004e43 < z < 2.8000000000000002e25

   1. Initial program 95.3%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 z around 0 67.6%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+43}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+25}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 35.6% 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 81.5%

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

   1. associate-*r/ 96.9%

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

3. Simplified 96.9%

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

4. Taylor expanded in z around inf 34.3%

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

5. Final simplification 34.3%

   \[\leadsto x \]

Developer target: 97.0% 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 2023238 
(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)))