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

Percentage Accurate: 84.0% → 96.9%

Time: 12.4s

Alternatives: 17

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: 84.0% 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: 96.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.8%

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

   1. associate-/l* 98.3%

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

3. Simplified 98.3%

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

4. Final simplification 98.3%

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

Alternative 2: 67.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y - z}{t}\\ \mathbf{if}\;z \leq -4.1 \cdot 10^{+114}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -140000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-21}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-239}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.28 \cdot 10^{-95}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 8100000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (- y z) t))))
   (if (<= z -4.1e+114)
     x
     (if (<= z -140000000.0)
       t_1
       (if (<= z -1.9e-21)
         x
         (if (<= z 2e-239)
           t_1
           (if (<= z 1.28e-95)
             (* x (/ y (- t z)))
             (if (<= z 8100000000.0) t_1 x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y - z) / t);
	double tmp;
	if (z <= -4.1e+114) {
		tmp = x;
	} else if (z <= -140000000.0) {
		tmp = t_1;
	} else if (z <= -1.9e-21) {
		tmp = x;
	} else if (z <= 2e-239) {
		tmp = t_1;
	} else if (z <= 1.28e-95) {
		tmp = x * (y / (t - z));
	} else if (z <= 8100000000.0) {
		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 - z) / t)
    if (z <= (-4.1d+114)) then
        tmp = x
    else if (z <= (-140000000.0d0)) then
        tmp = t_1
    else if (z <= (-1.9d-21)) then
        tmp = x
    else if (z <= 2d-239) then
        tmp = t_1
    else if (z <= 1.28d-95) then
        tmp = x * (y / (t - z))
    else if (z <= 8100000000.0d0) 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 - z) / t);
	double tmp;
	if (z <= -4.1e+114) {
		tmp = x;
	} else if (z <= -140000000.0) {
		tmp = t_1;
	} else if (z <= -1.9e-21) {
		tmp = x;
	} else if (z <= 2e-239) {
		tmp = t_1;
	} else if (z <= 1.28e-95) {
		tmp = x * (y / (t - z));
	} else if (z <= 8100000000.0) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y - z) / t)
	tmp = 0
	if z <= -4.1e+114:
		tmp = x
	elif z <= -140000000.0:
		tmp = t_1
	elif z <= -1.9e-21:
		tmp = x
	elif z <= 2e-239:
		tmp = t_1
	elif z <= 1.28e-95:
		tmp = x * (y / (t - z))
	elif z <= 8100000000.0:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y - z) / t))
	tmp = 0.0
	if (z <= -4.1e+114)
		tmp = x;
	elseif (z <= -140000000.0)
		tmp = t_1;
	elseif (z <= -1.9e-21)
		tmp = x;
	elseif (z <= 2e-239)
		tmp = t_1;
	elseif (z <= 1.28e-95)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	elseif (z <= 8100000000.0)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y - z) / t);
	tmp = 0.0;
	if (z <= -4.1e+114)
		tmp = x;
	elseif (z <= -140000000.0)
		tmp = t_1;
	elseif (z <= -1.9e-21)
		tmp = x;
	elseif (z <= 2e-239)
		tmp = t_1;
	elseif (z <= 1.28e-95)
		tmp = x * (y / (t - z));
	elseif (z <= 8100000000.0)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.1e+114], x, If[LessEqual[z, -140000000.0], t$95$1, If[LessEqual[z, -1.9e-21], x, If[LessEqual[z, 2e-239], t$95$1, If[LessEqual[z, 1.28e-95], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8100000000.0], t$95$1, x]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.1000000000000001e114 or -1.4e8 < z < -1.8999999999999999e-21 or 8.1e9 < z

   1. Initial program 75.8%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 68.5%

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

   if -4.1000000000000001e114 < z < -1.4e8 or -1.8999999999999999e-21 < z < 2.0000000000000002e-239 or 1.28000000000000005e-95 < z < 8.1e9

   1. Initial program 93.9%

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

      1. associate-*r/ 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in t around inf 78.4%

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

   if 2.0000000000000002e-239 < z < 1.28000000000000005e-95

   1. Initial program 90.4%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 y around inf 80.4%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+114}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -140000000:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-21}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-239}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{elif}\;z \leq 1.28 \cdot 10^{-95}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 8100000000:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 67.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y - z}{t}\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{+111}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -165000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-21}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-239}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-94}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 5700000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (- y z) t))))
   (if (<= z -1.55e+111)
     x
     (if (<= z -165000000.0)
       t_1
       (if (<= z -3.1e-21)
         x
         (if (<= z 1.9e-239)
           (* (- y z) (/ x t))
           (if (<= z 8.5e-94)
             (* x (/ y (- t z)))
             (if (<= z 5700000000.0) t_1 x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y - z) / t);
	double tmp;
	if (z <= -1.55e+111) {
		tmp = x;
	} else if (z <= -165000000.0) {
		tmp = t_1;
	} else if (z <= -3.1e-21) {
		tmp = x;
	} else if (z <= 1.9e-239) {
		tmp = (y - z) * (x / t);
	} else if (z <= 8.5e-94) {
		tmp = x * (y / (t - z));
	} else if (z <= 5700000000.0) {
		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 - z) / t)
    if (z <= (-1.55d+111)) then
        tmp = x
    else if (z <= (-165000000.0d0)) then
        tmp = t_1
    else if (z <= (-3.1d-21)) then
        tmp = x
    else if (z <= 1.9d-239) then
        tmp = (y - z) * (x / t)
    else if (z <= 8.5d-94) then
        tmp = x * (y / (t - z))
    else if (z <= 5700000000.0d0) 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 - z) / t);
	double tmp;
	if (z <= -1.55e+111) {
		tmp = x;
	} else if (z <= -165000000.0) {
		tmp = t_1;
	} else if (z <= -3.1e-21) {
		tmp = x;
	} else if (z <= 1.9e-239) {
		tmp = (y - z) * (x / t);
	} else if (z <= 8.5e-94) {
		tmp = x * (y / (t - z));
	} else if (z <= 5700000000.0) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y - z) / t)
	tmp = 0
	if z <= -1.55e+111:
		tmp = x
	elif z <= -165000000.0:
		tmp = t_1
	elif z <= -3.1e-21:
		tmp = x
	elif z <= 1.9e-239:
		tmp = (y - z) * (x / t)
	elif z <= 8.5e-94:
		tmp = x * (y / (t - z))
	elif z <= 5700000000.0:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y - z) / t))
	tmp = 0.0
	if (z <= -1.55e+111)
		tmp = x;
	elseif (z <= -165000000.0)
		tmp = t_1;
	elseif (z <= -3.1e-21)
		tmp = x;
	elseif (z <= 1.9e-239)
		tmp = Float64(Float64(y - z) * Float64(x / t));
	elseif (z <= 8.5e-94)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	elseif (z <= 5700000000.0)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y - z) / t);
	tmp = 0.0;
	if (z <= -1.55e+111)
		tmp = x;
	elseif (z <= -165000000.0)
		tmp = t_1;
	elseif (z <= -3.1e-21)
		tmp = x;
	elseif (z <= 1.9e-239)
		tmp = (y - z) * (x / t);
	elseif (z <= 8.5e-94)
		tmp = x * (y / (t - z));
	elseif (z <= 5700000000.0)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.55e+111], x, If[LessEqual[z, -165000000.0], t$95$1, If[LessEqual[z, -3.1e-21], x, If[LessEqual[z, 1.9e-239], N[(N[(y - z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e-94], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5700000000.0], t$95$1, x]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.55e111 or -1.65e8 < z < -3.0999999999999998e-21 or 5.7e9 < z

   1. Initial program 75.8%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 68.5%

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

   if -1.55e111 < z < -1.65e8 or 8.50000000000000003e-94 < z < 5.7e9

   1. Initial program 95.5%

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

      1. associate-*r/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in t around inf 73.6%

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

   if -3.0999999999999998e-21 < z < 1.9000000000000001e-239

   1. Initial program 92.7%

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

      1. associate-*l/ 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in t around inf 82.4%

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

   if 1.9000000000000001e-239 < z < 8.50000000000000003e-94

   1. Initial program 90.4%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 y around inf 80.4%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+111}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -165000000:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-21}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-239}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-94}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 5700000000:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 59.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+68}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -165000000:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{t}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-18}:\\ \;\;\;\;\frac{z}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-156}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-120}:\\ \;\;\;\;x \cdot \frac{-y}{z}\\ \mathbf{elif}\;z \leq 4100:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.15e+68)
   x
   (if (<= z -165000000.0)
     (/ (* x (- z)) t)
     (if (<= z -6.2e-18)
       (/ z (/ z x))
       (if (<= z 4.5e-156)
         (/ (* x y) t)
         (if (<= z 3.8e-120)
           (* x (/ (- y) z))
           (if (<= z 4100.0) (* x (/ y t)) x)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.15e+68) {
		tmp = x;
	} else if (z <= -165000000.0) {
		tmp = (x * -z) / t;
	} else if (z <= -6.2e-18) {
		tmp = z / (z / x);
	} else if (z <= 4.5e-156) {
		tmp = (x * y) / t;
	} else if (z <= 3.8e-120) {
		tmp = x * (-y / z);
	} else if (z <= 4100.0) {
		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 <= (-1.15d+68)) then
        tmp = x
    else if (z <= (-165000000.0d0)) then
        tmp = (x * -z) / t
    else if (z <= (-6.2d-18)) then
        tmp = z / (z / x)
    else if (z <= 4.5d-156) then
        tmp = (x * y) / t
    else if (z <= 3.8d-120) then
        tmp = x * (-y / z)
    else if (z <= 4100.0d0) 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 <= -1.15e+68) {
		tmp = x;
	} else if (z <= -165000000.0) {
		tmp = (x * -z) / t;
	} else if (z <= -6.2e-18) {
		tmp = z / (z / x);
	} else if (z <= 4.5e-156) {
		tmp = (x * y) / t;
	} else if (z <= 3.8e-120) {
		tmp = x * (-y / z);
	} else if (z <= 4100.0) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.15e+68:
		tmp = x
	elif z <= -165000000.0:
		tmp = (x * -z) / t
	elif z <= -6.2e-18:
		tmp = z / (z / x)
	elif z <= 4.5e-156:
		tmp = (x * y) / t
	elif z <= 3.8e-120:
		tmp = x * (-y / z)
	elif z <= 4100.0:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.15e+68)
		tmp = x;
	elseif (z <= -165000000.0)
		tmp = Float64(Float64(x * Float64(-z)) / t);
	elseif (z <= -6.2e-18)
		tmp = Float64(z / Float64(z / x));
	elseif (z <= 4.5e-156)
		tmp = Float64(Float64(x * y) / t);
	elseif (z <= 3.8e-120)
		tmp = Float64(x * Float64(Float64(-y) / z));
	elseif (z <= 4100.0)
		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 <= -1.15e+68)
		tmp = x;
	elseif (z <= -165000000.0)
		tmp = (x * -z) / t;
	elseif (z <= -6.2e-18)
		tmp = z / (z / x);
	elseif (z <= 4.5e-156)
		tmp = (x * y) / t;
	elseif (z <= 3.8e-120)
		tmp = x * (-y / z);
	elseif (z <= 4100.0)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.15e+68], x, If[LessEqual[z, -165000000.0], N[(N[(x * (-z)), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, -6.2e-18], N[(z / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e-156], N[(N[(x * y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 3.8e-120], N[(x * N[((-y) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4100.0], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.15e68 or 4100 < z

   1. Initial program 75.6%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 z around inf 66.4%

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

   if -1.15e68 < z < -1.65e8

   1. Initial program 93.6%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in t around inf 71.9%

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

   5. Taylor expanded in y around 0 44.7%

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

      1. mul-1-neg 44.7%

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

   7. Simplified 44.7%

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

   if -1.65e8 < z < -6.20000000000000014e-18

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around 0 84.1%

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

      1. associate-*r/ 84.1%

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

      2. neg-mul-1 84.1%

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

      3. neg-sub0 84.1%

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

      4. associate--r- 84.1%

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

      5. neg-sub0 84.1%

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

   6. Simplified 84.1%

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

   7. Taylor expanded in x around 0 83.9%

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

      1. associate-/l* 83.9%

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

   9. Simplified 83.9%

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

   10. Taylor expanded in z around inf 73.0%

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

   if -6.20000000000000014e-18 < z < 4.49999999999999986e-156

   1. Initial program 92.4%

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

      1. associate-*r/ 94.9%

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

   3. Simplified 94.9%

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

   4. Taylor expanded in z around 0 77.1%

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

   if 4.49999999999999986e-156 < z < 3.7999999999999997e-120

   1. Initial program 84.6%

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

      1. associate-*r/ 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around inf 68.6%

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

   5. Taylor expanded in t around 0 53.1%

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

      1. associate-*r/ 53.1%

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

      2. neg-mul-1 53.1%

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

   7. Simplified 53.1%

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

   if 3.7999999999999997e-120 < z < 4100

   1. Initial program 96.4%

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

      1. associate-*r/ 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in z around 0 58.7%

      \[\leadsto x \cdot \color{blue}{\frac{y}{t}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+68}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -165000000:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{t}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-18}:\\ \;\;\;\;\frac{z}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-156}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-120}:\\ \;\;\;\;x \cdot \frac{-y}{z}\\ \mathbf{elif}\;z \leq 4100:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 59.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+69}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -180000000:\\ \;\;\;\;z \cdot \frac{-x}{t}\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-17}:\\ \;\;\;\;\frac{z}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-156}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-120}:\\ \;\;\;\;x \cdot \frac{-y}{z}\\ \mathbf{elif}\;z \leq 26500:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.3e+69)
   x
   (if (<= z -180000000.0)
     (* z (/ (- x) t))
     (if (<= z -1.15e-17)
       (/ z (/ z x))
       (if (<= z 4.5e-156)
         (/ (* x y) t)
         (if (<= z 3.8e-120)
           (* x (/ (- y) z))
           (if (<= z 26500.0) (* x (/ y t)) x)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.3e+69) {
		tmp = x;
	} else if (z <= -180000000.0) {
		tmp = z * (-x / t);
	} else if (z <= -1.15e-17) {
		tmp = z / (z / x);
	} else if (z <= 4.5e-156) {
		tmp = (x * y) / t;
	} else if (z <= 3.8e-120) {
		tmp = x * (-y / z);
	} else if (z <= 26500.0) {
		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 <= (-2.3d+69)) then
        tmp = x
    else if (z <= (-180000000.0d0)) then
        tmp = z * (-x / t)
    else if (z <= (-1.15d-17)) then
        tmp = z / (z / x)
    else if (z <= 4.5d-156) then
        tmp = (x * y) / t
    else if (z <= 3.8d-120) then
        tmp = x * (-y / z)
    else if (z <= 26500.0d0) 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 <= -2.3e+69) {
		tmp = x;
	} else if (z <= -180000000.0) {
		tmp = z * (-x / t);
	} else if (z <= -1.15e-17) {
		tmp = z / (z / x);
	} else if (z <= 4.5e-156) {
		tmp = (x * y) / t;
	} else if (z <= 3.8e-120) {
		tmp = x * (-y / z);
	} else if (z <= 26500.0) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.3e+69:
		tmp = x
	elif z <= -180000000.0:
		tmp = z * (-x / t)
	elif z <= -1.15e-17:
		tmp = z / (z / x)
	elif z <= 4.5e-156:
		tmp = (x * y) / t
	elif z <= 3.8e-120:
		tmp = x * (-y / z)
	elif z <= 26500.0:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.3e+69)
		tmp = x;
	elseif (z <= -180000000.0)
		tmp = Float64(z * Float64(Float64(-x) / t));
	elseif (z <= -1.15e-17)
		tmp = Float64(z / Float64(z / x));
	elseif (z <= 4.5e-156)
		tmp = Float64(Float64(x * y) / t);
	elseif (z <= 3.8e-120)
		tmp = Float64(x * Float64(Float64(-y) / z));
	elseif (z <= 26500.0)
		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 <= -2.3e+69)
		tmp = x;
	elseif (z <= -180000000.0)
		tmp = z * (-x / t);
	elseif (z <= -1.15e-17)
		tmp = z / (z / x);
	elseif (z <= 4.5e-156)
		tmp = (x * y) / t;
	elseif (z <= 3.8e-120)
		tmp = x * (-y / z);
	elseif (z <= 26500.0)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.3e+69], x, If[LessEqual[z, -180000000.0], N[(z * N[((-x) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.15e-17], N[(z / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e-156], N[(N[(x * y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 3.8e-120], N[(x * N[((-y) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 26500.0], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -2.30000000000000017e69 or 26500 < z

   1. Initial program 75.6%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 z around inf 66.4%

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

   if -2.30000000000000017e69 < z < -1.8e8

   1. Initial program 93.6%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in t around inf 71.9%

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

   5. Taylor expanded in y around 0 44.7%

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

      1. mul-1-neg 44.7%

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

      2. distribute-neg-frac 44.7%

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

      3. distribute-lft-neg-out 44.7%

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

      4. associate-*r/ 44.9%

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

      5. distribute-lft-neg-out 44.9%

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

      6. distribute-rgt-neg-in 44.9%

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

   7. Simplified 44.9%

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

   if -1.8e8 < z < -1.15000000000000004e-17

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around 0 84.1%

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

      1. associate-*r/ 84.1%

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

      2. neg-mul-1 84.1%

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

      3. neg-sub0 84.1%

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

      4. associate--r- 84.1%

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

      5. neg-sub0 84.1%

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

   6. Simplified 84.1%

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

   7. Taylor expanded in x around 0 83.9%

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

      1. associate-/l* 83.9%

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

   9. Simplified 83.9%

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

   10. Taylor expanded in z around inf 73.0%

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

   if -1.15000000000000004e-17 < z < 4.49999999999999986e-156

   1. Initial program 92.4%

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

      1. associate-*r/ 94.9%

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

   3. Simplified 94.9%

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

   4. Taylor expanded in z around 0 77.1%

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

   if 4.49999999999999986e-156 < z < 3.7999999999999997e-120

   1. Initial program 84.6%

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

      1. associate-*r/ 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around inf 68.6%

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

   5. Taylor expanded in t around 0 53.1%

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

      1. associate-*r/ 53.1%

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

      2. neg-mul-1 53.1%

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

   7. Simplified 53.1%

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

   if 3.7999999999999997e-120 < z < 26500

   1. Initial program 96.4%

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

      1. associate-*r/ 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in z around 0 58.7%

      \[\leadsto x \cdot \color{blue}{\frac{y}{t}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+69}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -180000000:\\ \;\;\;\;z \cdot \frac{-x}{t}\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-17}:\\ \;\;\;\;\frac{z}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-156}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-120}:\\ \;\;\;\;x \cdot \frac{-y}{z}\\ \mathbf{elif}\;z \leq 26500:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 59.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+68}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -165000000:\\ \;\;\;\;\frac{x}{\frac{-t}{z}}\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-17}:\\ \;\;\;\;\frac{z}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-156}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-120}:\\ \;\;\;\;x \cdot \frac{-y}{z}\\ \mathbf{elif}\;z \leq 56000:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.5e+68)
   x
   (if (<= z -165000000.0)
     (/ x (/ (- t) z))
     (if (<= z -5.2e-17)
       (/ z (/ z x))
       (if (<= z 4.5e-156)
         (/ (* x y) t)
         (if (<= z 3.8e-120)
           (* x (/ (- y) z))
           (if (<= z 56000.0) (* x (/ y t)) x)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.5e+68) {
		tmp = x;
	} else if (z <= -165000000.0) {
		tmp = x / (-t / z);
	} else if (z <= -5.2e-17) {
		tmp = z / (z / x);
	} else if (z <= 4.5e-156) {
		tmp = (x * y) / t;
	} else if (z <= 3.8e-120) {
		tmp = x * (-y / z);
	} else if (z <= 56000.0) {
		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 <= (-2.5d+68)) then
        tmp = x
    else if (z <= (-165000000.0d0)) then
        tmp = x / (-t / z)
    else if (z <= (-5.2d-17)) then
        tmp = z / (z / x)
    else if (z <= 4.5d-156) then
        tmp = (x * y) / t
    else if (z <= 3.8d-120) then
        tmp = x * (-y / z)
    else if (z <= 56000.0d0) 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 <= -2.5e+68) {
		tmp = x;
	} else if (z <= -165000000.0) {
		tmp = x / (-t / z);
	} else if (z <= -5.2e-17) {
		tmp = z / (z / x);
	} else if (z <= 4.5e-156) {
		tmp = (x * y) / t;
	} else if (z <= 3.8e-120) {
		tmp = x * (-y / z);
	} else if (z <= 56000.0) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.5e+68:
		tmp = x
	elif z <= -165000000.0:
		tmp = x / (-t / z)
	elif z <= -5.2e-17:
		tmp = z / (z / x)
	elif z <= 4.5e-156:
		tmp = (x * y) / t
	elif z <= 3.8e-120:
		tmp = x * (-y / z)
	elif z <= 56000.0:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.5e+68)
		tmp = x;
	elseif (z <= -165000000.0)
		tmp = Float64(x / Float64(Float64(-t) / z));
	elseif (z <= -5.2e-17)
		tmp = Float64(z / Float64(z / x));
	elseif (z <= 4.5e-156)
		tmp = Float64(Float64(x * y) / t);
	elseif (z <= 3.8e-120)
		tmp = Float64(x * Float64(Float64(-y) / z));
	elseif (z <= 56000.0)
		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 <= -2.5e+68)
		tmp = x;
	elseif (z <= -165000000.0)
		tmp = x / (-t / z);
	elseif (z <= -5.2e-17)
		tmp = z / (z / x);
	elseif (z <= 4.5e-156)
		tmp = (x * y) / t;
	elseif (z <= 3.8e-120)
		tmp = x * (-y / z);
	elseif (z <= 56000.0)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.5e+68], x, If[LessEqual[z, -165000000.0], N[(x / N[((-t) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.2e-17], N[(z / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e-156], N[(N[(x * y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 3.8e-120], N[(x * N[((-y) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 56000.0], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -2.5000000000000002e68 or 56000 < z

   1. Initial program 75.6%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 z around inf 66.4%

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

   if -2.5000000000000002e68 < z < -1.65e8

   1. Initial program 93.6%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in t around inf 71.9%

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

   5. Taylor expanded in y around 0 50.6%

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

      1. associate-*r/ 50.6%

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

      2. mul-1-neg 50.6%

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

   7. Simplified 50.6%

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

   if -1.65e8 < z < -5.20000000000000006e-17

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around 0 84.1%

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

      1. associate-*r/ 84.1%

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

      2. neg-mul-1 84.1%

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

      3. neg-sub0 84.1%

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

      4. associate--r- 84.1%

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

      5. neg-sub0 84.1%

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

   6. Simplified 84.1%

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

   7. Taylor expanded in x around 0 83.9%

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

      1. associate-/l* 83.9%

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

   9. Simplified 83.9%

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

   10. Taylor expanded in z around inf 73.0%

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

   if -5.20000000000000006e-17 < z < 4.49999999999999986e-156

   1. Initial program 92.4%

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

      1. associate-*r/ 94.9%

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

   3. Simplified 94.9%

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

   4. Taylor expanded in z around 0 77.1%

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

   if 4.49999999999999986e-156 < z < 3.7999999999999997e-120

   1. Initial program 84.6%

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

      1. associate-*r/ 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around inf 68.6%

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

   5. Taylor expanded in t around 0 53.1%

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

      1. associate-*r/ 53.1%

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

      2. neg-mul-1 53.1%

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

   7. Simplified 53.1%

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

   if 3.7999999999999997e-120 < z < 56000

   1. Initial program 96.4%

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

      1. associate-*r/ 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in z around 0 58.7%

      \[\leadsto x \cdot \color{blue}{\frac{y}{t}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+68}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -165000000:\\ \;\;\;\;\frac{x}{\frac{-t}{z}}\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-17}:\\ \;\;\;\;\frac{z}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-156}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-120}:\\ \;\;\;\;x \cdot \frac{-y}{z}\\ \mathbf{elif}\;z \leq 56000:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 59.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+68}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -180000000:\\ \;\;\;\;\frac{x}{\frac{-t}{z}}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-16}:\\ \;\;\;\;\frac{z}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-156}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-120}:\\ \;\;\;\;\frac{y}{\frac{-z}{x}}\\ \mathbf{elif}\;z \leq 820000000:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.8e+68)
   x
   (if (<= z -180000000.0)
     (/ x (/ (- t) z))
     (if (<= z -3.5e-16)
       (/ z (/ z x))
       (if (<= z 4.5e-156)
         (/ (* x y) t)
         (if (<= z 3.8e-120)
           (/ y (/ (- z) x))
           (if (<= z 820000000.0) (* x (/ y t)) x)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.8e+68) {
		tmp = x;
	} else if (z <= -180000000.0) {
		tmp = x / (-t / z);
	} else if (z <= -3.5e-16) {
		tmp = z / (z / x);
	} else if (z <= 4.5e-156) {
		tmp = (x * y) / t;
	} else if (z <= 3.8e-120) {
		tmp = y / (-z / x);
	} else if (z <= 820000000.0) {
		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 <= (-5.8d+68)) then
        tmp = x
    else if (z <= (-180000000.0d0)) then
        tmp = x / (-t / z)
    else if (z <= (-3.5d-16)) then
        tmp = z / (z / x)
    else if (z <= 4.5d-156) then
        tmp = (x * y) / t
    else if (z <= 3.8d-120) then
        tmp = y / (-z / x)
    else if (z <= 820000000.0d0) 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 <= -5.8e+68) {
		tmp = x;
	} else if (z <= -180000000.0) {
		tmp = x / (-t / z);
	} else if (z <= -3.5e-16) {
		tmp = z / (z / x);
	} else if (z <= 4.5e-156) {
		tmp = (x * y) / t;
	} else if (z <= 3.8e-120) {
		tmp = y / (-z / x);
	} else if (z <= 820000000.0) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.8e+68:
		tmp = x
	elif z <= -180000000.0:
		tmp = x / (-t / z)
	elif z <= -3.5e-16:
		tmp = z / (z / x)
	elif z <= 4.5e-156:
		tmp = (x * y) / t
	elif z <= 3.8e-120:
		tmp = y / (-z / x)
	elif z <= 820000000.0:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.8e+68)
		tmp = x;
	elseif (z <= -180000000.0)
		tmp = Float64(x / Float64(Float64(-t) / z));
	elseif (z <= -3.5e-16)
		tmp = Float64(z / Float64(z / x));
	elseif (z <= 4.5e-156)
		tmp = Float64(Float64(x * y) / t);
	elseif (z <= 3.8e-120)
		tmp = Float64(y / Float64(Float64(-z) / x));
	elseif (z <= 820000000.0)
		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 <= -5.8e+68)
		tmp = x;
	elseif (z <= -180000000.0)
		tmp = x / (-t / z);
	elseif (z <= -3.5e-16)
		tmp = z / (z / x);
	elseif (z <= 4.5e-156)
		tmp = (x * y) / t;
	elseif (z <= 3.8e-120)
		tmp = y / (-z / x);
	elseif (z <= 820000000.0)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.8e+68], x, If[LessEqual[z, -180000000.0], N[(x / N[((-t) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.5e-16], N[(z / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e-156], N[(N[(x * y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 3.8e-120], N[(y / N[((-z) / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 820000000.0], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -5.80000000000000023e68 or 8.2e8 < z

   1. Initial program 75.6%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 z around inf 66.4%

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

   if -5.80000000000000023e68 < z < -1.8e8

   1. Initial program 93.6%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in t around inf 71.9%

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

   5. Taylor expanded in y around 0 50.6%

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

      1. associate-*r/ 50.6%

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

      2. mul-1-neg 50.6%

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

   7. Simplified 50.6%

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

   if -1.8e8 < z < -3.50000000000000017e-16

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around 0 84.1%

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

      1. associate-*r/ 84.1%

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

      2. neg-mul-1 84.1%

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

      3. neg-sub0 84.1%

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

      4. associate--r- 84.1%

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

      5. neg-sub0 84.1%

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

   6. Simplified 84.1%

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

   7. Taylor expanded in x around 0 83.9%

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

      1. associate-/l* 83.9%

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

   9. Simplified 83.9%

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

   10. Taylor expanded in z around inf 73.0%

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

   if -3.50000000000000017e-16 < z < 4.49999999999999986e-156

   1. Initial program 92.4%

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

      1. associate-*r/ 94.9%

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

   3. Simplified 94.9%

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

   4. Taylor expanded in z around 0 77.1%

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

   if 4.49999999999999986e-156 < z < 3.7999999999999997e-120

   1. Initial program 84.6%

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

      1. associate-*r/ 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around inf 68.6%

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

   5. Taylor expanded in t around 0 45.1%

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

      1. mul-1-neg 45.1%

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

      2. associate-*r/ 53.0%

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

      3. distribute-rgt-neg-in 53.0%

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

      4. distribute-neg-frac 53.0%

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

   7. Simplified 53.0%

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

      1. associate-*r/ 45.1%

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

      2. frac-2neg 45.1%

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

      3. add-sqr-sqrt 3.3%

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

      4. sqrt-unprod 4.4%

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

      5. sqr-neg 4.4%

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

      6. sqrt-unprod 1.0%

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

      7. add-sqr-sqrt 3.8%

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

      8. distribute-rgt-neg-out 3.8%

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

      9. add-sqr-sqrt 2.8%

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

      10. sqrt-unprod 36.6%

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

      11. sqr-neg 36.6%

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

      12. sqrt-unprod 41.8%

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

      13. add-sqr-sqrt 45.1%

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

   9. Applied egg-rr 45.1%

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

       1. associate-/l* 53.2%

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

   11. Simplified 53.2%

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

   if 3.7999999999999997e-120 < z < 8.2e8

   1. Initial program 96.4%

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

      1. associate-*r/ 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in z around 0 58.7%

      \[\leadsto x \cdot \color{blue}{\frac{y}{t}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+68}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -180000000:\\ \;\;\;\;\frac{x}{\frac{-t}{z}}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-16}:\\ \;\;\;\;\frac{z}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-156}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-120}:\\ \;\;\;\;\frac{y}{\frac{-z}{x}}\\ \mathbf{elif}\;z \leq 820000000:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 68.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{t - z}\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{+145}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -39000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-16}:\\ \;\;\;\;\frac{z}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ y (- t z)))))
   (if (<= z -1.9e+145)
     x
     (if (<= z -39000000.0)
       t_1
       (if (<= z -4.5e-16) (/ z (/ z x)) (if (<= z 3.3e+24) 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 <= -1.9e+145) {
		tmp = x;
	} else if (z <= -39000000.0) {
		tmp = t_1;
	} else if (z <= -4.5e-16) {
		tmp = z / (z / x);
	} else if (z <= 3.3e+24) {
		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 <= (-1.9d+145)) then
        tmp = x
    else if (z <= (-39000000.0d0)) then
        tmp = t_1
    else if (z <= (-4.5d-16)) then
        tmp = z / (z / x)
    else if (z <= 3.3d+24) 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 <= -1.9e+145) {
		tmp = x;
	} else if (z <= -39000000.0) {
		tmp = t_1;
	} else if (z <= -4.5e-16) {
		tmp = z / (z / x);
	} else if (z <= 3.3e+24) {
		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 <= -1.9e+145:
		tmp = x
	elif z <= -39000000.0:
		tmp = t_1
	elif z <= -4.5e-16:
		tmp = z / (z / x)
	elif z <= 3.3e+24:
		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 <= -1.9e+145)
		tmp = x;
	elseif (z <= -39000000.0)
		tmp = t_1;
	elseif (z <= -4.5e-16)
		tmp = Float64(z / Float64(z / x));
	elseif (z <= 3.3e+24)
		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 <= -1.9e+145)
		tmp = x;
	elseif (z <= -39000000.0)
		tmp = t_1;
	elseif (z <= -4.5e-16)
		tmp = z / (z / x);
	elseif (z <= 3.3e+24)
		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, -1.9e+145], x, If[LessEqual[z, -39000000.0], t$95$1, If[LessEqual[z, -4.5e-16], N[(z / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.3e+24], t$95$1, x]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.90000000000000006e145 or 3.2999999999999999e24 < z

   1. Initial program 72.9%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 71.1%

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

   if -1.90000000000000006e145 < z < -3.9e7 or -4.5000000000000002e-16 < z < 3.2999999999999999e24

   1. Initial program 92.8%

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

      1. associate-*r/ 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in y around inf 70.8%

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

   if -3.9e7 < z < -4.5000000000000002e-16

   1. Initial program 99.7%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 0 100.0%

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

      1. associate-*r/ 100.0%

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

      2. neg-mul-1 100.0%

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

      3. neg-sub0 100.0%

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

      4. associate--r- 100.0%

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

      5. neg-sub0 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in x around 0 99.7%

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

      1. associate-/l* 99.7%

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

   9. Simplified 99.7%

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

   10. Taylor expanded in z around inf 86.7%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+145}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -39000000:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-16}:\\ \;\;\;\;\frac{z}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+24}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 72.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.18 \cdot 10^{+36}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \mathbf{elif}\;t \leq 1.56 \cdot 10^{-44}:\\ \;\;\;\;\frac{x}{\frac{z}{z - y}}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+56}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+152}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.18e+36)
   (/ x (/ t (- y z)))
   (if (<= t 1.56e-44)
     (/ x (/ z (- z y)))
     (if (<= t 4.2e+56)
       (* x (/ y (- t z)))
       (if (<= t 1.75e+152) (/ x (- 1.0 (/ t z))) (* (- y z) (/ x t)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.18e+36) {
		tmp = x / (t / (y - z));
	} else if (t <= 1.56e-44) {
		tmp = x / (z / (z - y));
	} else if (t <= 4.2e+56) {
		tmp = x * (y / (t - z));
	} else if (t <= 1.75e+152) {
		tmp = x / (1.0 - (t / z));
	} else {
		tmp = (y - z) * (x / 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 (t <= (-1.18d+36)) then
        tmp = x / (t / (y - z))
    else if (t <= 1.56d-44) then
        tmp = x / (z / (z - y))
    else if (t <= 4.2d+56) then
        tmp = x * (y / (t - z))
    else if (t <= 1.75d+152) then
        tmp = x / (1.0d0 - (t / z))
    else
        tmp = (y - z) * (x / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.18e+36) {
		tmp = x / (t / (y - z));
	} else if (t <= 1.56e-44) {
		tmp = x / (z / (z - y));
	} else if (t <= 4.2e+56) {
		tmp = x * (y / (t - z));
	} else if (t <= 1.75e+152) {
		tmp = x / (1.0 - (t / z));
	} else {
		tmp = (y - z) * (x / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.18e+36:
		tmp = x / (t / (y - z))
	elif t <= 1.56e-44:
		tmp = x / (z / (z - y))
	elif t <= 4.2e+56:
		tmp = x * (y / (t - z))
	elif t <= 1.75e+152:
		tmp = x / (1.0 - (t / z))
	else:
		tmp = (y - z) * (x / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.18e+36)
		tmp = Float64(x / Float64(t / Float64(y - z)));
	elseif (t <= 1.56e-44)
		tmp = Float64(x / Float64(z / Float64(z - y)));
	elseif (t <= 4.2e+56)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	elseif (t <= 1.75e+152)
		tmp = Float64(x / Float64(1.0 - Float64(t / z)));
	else
		tmp = Float64(Float64(y - z) * Float64(x / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.18e+36)
		tmp = x / (t / (y - z));
	elseif (t <= 1.56e-44)
		tmp = x / (z / (z - y));
	elseif (t <= 4.2e+56)
		tmp = x * (y / (t - z));
	elseif (t <= 1.75e+152)
		tmp = x / (1.0 - (t / z));
	else
		tmp = (y - z) * (x / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.18e+36], N[(x / N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.56e-44], N[(x / N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.2e+56], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.75e+152], N[(x / N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.17999999999999997e36

   1. Initial program 82.6%

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

      1. associate-/l* 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in t around inf 77.5%

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

   if -1.17999999999999997e36 < t < 1.56e-44

   1. Initial program 83.8%

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

      1. associate-/l* 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in t around 0 83.5%

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

      1. neg-mul-1 83.5%

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

      2. distribute-neg-frac 83.5%

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

   6. Simplified 83.5%

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

      1. frac-2neg 83.5%

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

      2. div-inv 83.3%

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

      3. remove-double-neg 83.3%

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

      4. sub-neg 83.3%

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

      5. distribute-neg-in 83.3%

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

      6. remove-double-neg 83.3%

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

   8. Applied egg-rr 83.3%

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

      1. associate-*r/ 83.5%

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

      2. *-rgt-identity 83.5%

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

      3. +-commutative 83.5%

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

      4. unsub-neg 83.5%

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

   10. Simplified 83.5%

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

   if 1.56e-44 < t < 4.20000000000000034e56

   1. Initial program 94.2%

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

      1. associate-*r/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 75.6%

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

   if 4.20000000000000034e56 < t < 1.74999999999999991e152

   1. Initial program 83.4%

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

      1. div-sub 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in y around 0 72.2%

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

      1. mul-1-neg 72.2%

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

      2. unsub-neg 72.2%

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

   8. Simplified 72.2%

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

   if 1.74999999999999991e152 < t

   1. Initial program 91.8%

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

      1. associate-*l/ 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in t around inf 86.7%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.18 \cdot 10^{+36}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \mathbf{elif}\;t \leq 1.56 \cdot 10^{-44}:\\ \;\;\;\;\frac{x}{\frac{z}{z - y}}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+56}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+152}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \end{array} \]

Alternative 10: 71.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+50}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-43}:\\ \;\;\;\;\frac{x}{\frac{z}{z - y}}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+54}:\\ \;\;\;\;\frac{x \cdot y}{t - z}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+152}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -4.6e+50)
   (/ x (/ t (- y z)))
   (if (<= t 2.7e-43)
     (/ x (/ z (- z y)))
     (if (<= t 3.2e+54)
       (/ (* x y) (- t z))
       (if (<= t 3.2e+152) (/ x (- 1.0 (/ t z))) (* (- y z) (/ x t)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.6e+50) {
		tmp = x / (t / (y - z));
	} else if (t <= 2.7e-43) {
		tmp = x / (z / (z - y));
	} else if (t <= 3.2e+54) {
		tmp = (x * y) / (t - z);
	} else if (t <= 3.2e+152) {
		tmp = x / (1.0 - (t / z));
	} else {
		tmp = (y - z) * (x / 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 (t <= (-4.6d+50)) then
        tmp = x / (t / (y - z))
    else if (t <= 2.7d-43) then
        tmp = x / (z / (z - y))
    else if (t <= 3.2d+54) then
        tmp = (x * y) / (t - z)
    else if (t <= 3.2d+152) then
        tmp = x / (1.0d0 - (t / z))
    else
        tmp = (y - z) * (x / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.6e+50) {
		tmp = x / (t / (y - z));
	} else if (t <= 2.7e-43) {
		tmp = x / (z / (z - y));
	} else if (t <= 3.2e+54) {
		tmp = (x * y) / (t - z);
	} else if (t <= 3.2e+152) {
		tmp = x / (1.0 - (t / z));
	} else {
		tmp = (y - z) * (x / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -4.6e+50:
		tmp = x / (t / (y - z))
	elif t <= 2.7e-43:
		tmp = x / (z / (z - y))
	elif t <= 3.2e+54:
		tmp = (x * y) / (t - z)
	elif t <= 3.2e+152:
		tmp = x / (1.0 - (t / z))
	else:
		tmp = (y - z) * (x / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -4.6e+50)
		tmp = Float64(x / Float64(t / Float64(y - z)));
	elseif (t <= 2.7e-43)
		tmp = Float64(x / Float64(z / Float64(z - y)));
	elseif (t <= 3.2e+54)
		tmp = Float64(Float64(x * y) / Float64(t - z));
	elseif (t <= 3.2e+152)
		tmp = Float64(x / Float64(1.0 - Float64(t / z)));
	else
		tmp = Float64(Float64(y - z) * Float64(x / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -4.6e+50)
		tmp = x / (t / (y - z));
	elseif (t <= 2.7e-43)
		tmp = x / (z / (z - y));
	elseif (t <= 3.2e+54)
		tmp = (x * y) / (t - z);
	elseif (t <= 3.2e+152)
		tmp = x / (1.0 - (t / z));
	else
		tmp = (y - z) * (x / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -4.6e+50], N[(x / N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.7e-43], N[(x / N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.2e+54], N[(N[(x * y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.2e+152], N[(x / N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -4.59999999999999994e50

   1. Initial program 82.6%

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

      1. associate-/l* 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in t around inf 77.5%

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

   if -4.59999999999999994e50 < t < 2.69999999999999991e-43

   1. Initial program 83.8%

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

      1. associate-/l* 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in t around 0 83.5%

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

      1. neg-mul-1 83.5%

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

      2. distribute-neg-frac 83.5%

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

   6. Simplified 83.5%

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

      1. frac-2neg 83.5%

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

      2. div-inv 83.3%

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

      3. remove-double-neg 83.3%

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

      4. sub-neg 83.3%

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

      5. distribute-neg-in 83.3%

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

      6. remove-double-neg 83.3%

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

   8. Applied egg-rr 83.3%

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

      1. associate-*r/ 83.5%

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

      2. *-rgt-identity 83.5%

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

      3. +-commutative 83.5%

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

      4. unsub-neg 83.5%

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

   10. Simplified 83.5%

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

   if 2.69999999999999991e-43 < t < 3.2e54

   1. Initial program 94.2%

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

      1. associate-*r/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 76.0%

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

   if 3.2e54 < t < 3.20000000000000005e152

   1. Initial program 83.4%

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

      1. div-sub 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in y around 0 72.2%

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

      1. mul-1-neg 72.2%

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

      2. unsub-neg 72.2%

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

   8. Simplified 72.2%

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

   if 3.20000000000000005e152 < t

   1. Initial program 91.8%

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

      1. associate-*l/ 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in t around inf 86.7%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+50}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-43}:\\ \;\;\;\;\frac{x}{\frac{z}{z - y}}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+54}:\\ \;\;\;\;\frac{x \cdot y}{t - z}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+152}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \end{array} \]

Alternative 11: 71.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+49}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{-43}:\\ \;\;\;\;x \cdot \frac{z - y}{z}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+54}:\\ \;\;\;\;\frac{x \cdot y}{t - z}\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{+150}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -3e+49)
   (/ x (/ t (- y z)))
   (if (<= t 2.45e-43)
     (* x (/ (- z y) z))
     (if (<= t 4.5e+54)
       (/ (* x y) (- t z))
       (if (<= t 4.7e+150) (/ x (- 1.0 (/ t z))) (* (- y z) (/ x t)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3e+49) {
		tmp = x / (t / (y - z));
	} else if (t <= 2.45e-43) {
		tmp = x * ((z - y) / z);
	} else if (t <= 4.5e+54) {
		tmp = (x * y) / (t - z);
	} else if (t <= 4.7e+150) {
		tmp = x / (1.0 - (t / z));
	} else {
		tmp = (y - z) * (x / 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 (t <= (-3d+49)) then
        tmp = x / (t / (y - z))
    else if (t <= 2.45d-43) then
        tmp = x * ((z - y) / z)
    else if (t <= 4.5d+54) then
        tmp = (x * y) / (t - z)
    else if (t <= 4.7d+150) then
        tmp = x / (1.0d0 - (t / z))
    else
        tmp = (y - z) * (x / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3e+49) {
		tmp = x / (t / (y - z));
	} else if (t <= 2.45e-43) {
		tmp = x * ((z - y) / z);
	} else if (t <= 4.5e+54) {
		tmp = (x * y) / (t - z);
	} else if (t <= 4.7e+150) {
		tmp = x / (1.0 - (t / z));
	} else {
		tmp = (y - z) * (x / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -3e+49:
		tmp = x / (t / (y - z))
	elif t <= 2.45e-43:
		tmp = x * ((z - y) / z)
	elif t <= 4.5e+54:
		tmp = (x * y) / (t - z)
	elif t <= 4.7e+150:
		tmp = x / (1.0 - (t / z))
	else:
		tmp = (y - z) * (x / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -3e+49)
		tmp = Float64(x / Float64(t / Float64(y - z)));
	elseif (t <= 2.45e-43)
		tmp = Float64(x * Float64(Float64(z - y) / z));
	elseif (t <= 4.5e+54)
		tmp = Float64(Float64(x * y) / Float64(t - z));
	elseif (t <= 4.7e+150)
		tmp = Float64(x / Float64(1.0 - Float64(t / z)));
	else
		tmp = Float64(Float64(y - z) * Float64(x / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -3e+49)
		tmp = x / (t / (y - z));
	elseif (t <= 2.45e-43)
		tmp = x * ((z - y) / z);
	elseif (t <= 4.5e+54)
		tmp = (x * y) / (t - z);
	elseif (t <= 4.7e+150)
		tmp = x / (1.0 - (t / z));
	else
		tmp = (y - z) * (x / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -3e+49], N[(x / N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.45e-43], N[(x * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.5e+54], N[(N[(x * y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.7e+150], N[(x / N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -3.0000000000000002e49

   1. Initial program 82.6%

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

      1. associate-/l* 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in t around inf 77.5%

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

   if -3.0000000000000002e49 < t < 2.44999999999999994e-43

   1. Initial program 83.8%

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

      1. associate-*r/ 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in t around 0 83.6%

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

      1. associate-*r/ 83.6%

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

      2. neg-mul-1 83.6%

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

      3. neg-sub0 83.6%

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

      4. associate--r- 83.6%

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

      5. neg-sub0 83.6%

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

   6. Simplified 83.6%

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

   if 2.44999999999999994e-43 < t < 4.49999999999999984e54

   1. Initial program 94.2%

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

      1. associate-*r/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 76.0%

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

   if 4.49999999999999984e54 < t < 4.70000000000000004e150

   1. Initial program 83.4%

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

      1. div-sub 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in y around 0 72.2%

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

      1. mul-1-neg 72.2%

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

      2. unsub-neg 72.2%

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

   8. Simplified 72.2%

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

   if 4.70000000000000004e150 < t

   1. Initial program 91.8%

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

      1. associate-*l/ 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in t around inf 86.7%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+49}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{-43}:\\ \;\;\;\;x \cdot \frac{z - y}{z}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+54}:\\ \;\;\;\;\frac{x \cdot y}{t - z}\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{+150}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \end{array} \]

Alternative 12: 61.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+68}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -170000000:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{t}\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 95000000:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.7e+68)
   x
   (if (<= z -170000000.0)
     (/ (* x (- z)) t)
     (if (<= z -4.5e-22) x (if (<= z 95000000.0) (* x (/ y t)) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.7e+68) {
		tmp = x;
	} else if (z <= -170000000.0) {
		tmp = (x * -z) / t;
	} else if (z <= -4.5e-22) {
		tmp = x;
	} else if (z <= 95000000.0) {
		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 <= (-1.7d+68)) then
        tmp = x
    else if (z <= (-170000000.0d0)) then
        tmp = (x * -z) / t
    else if (z <= (-4.5d-22)) then
        tmp = x
    else if (z <= 95000000.0d0) 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 <= -1.7e+68) {
		tmp = x;
	} else if (z <= -170000000.0) {
		tmp = (x * -z) / t;
	} else if (z <= -4.5e-22) {
		tmp = x;
	} else if (z <= 95000000.0) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.7e+68:
		tmp = x
	elif z <= -170000000.0:
		tmp = (x * -z) / t
	elif z <= -4.5e-22:
		tmp = x
	elif z <= 95000000.0:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.7e+68)
		tmp = x;
	elseif (z <= -170000000.0)
		tmp = Float64(Float64(x * Float64(-z)) / t);
	elseif (z <= -4.5e-22)
		tmp = x;
	elseif (z <= 95000000.0)
		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 <= -1.7e+68)
		tmp = x;
	elseif (z <= -170000000.0)
		tmp = (x * -z) / t;
	elseif (z <= -4.5e-22)
		tmp = x;
	elseif (z <= 95000000.0)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.7e+68], x, If[LessEqual[z, -170000000.0], N[(N[(x * (-z)), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, -4.5e-22], x, If[LessEqual[z, 95000000.0], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.70000000000000008e68 or -1.7e8 < z < -4.49999999999999987e-22 or 9.5e7 < z

   1. Initial program 77.2%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 66.5%

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

   if -1.70000000000000008e68 < z < -1.7e8

   1. Initial program 93.6%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in t around inf 71.9%

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

   5. Taylor expanded in y around 0 44.7%

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

      1. mul-1-neg 44.7%

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

   7. Simplified 44.7%

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

   if -4.49999999999999987e-22 < z < 9.5e7

   1. Initial program 92.4%

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

      1. associate-*r/ 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in z around 0 67.0%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+68}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -170000000:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{t}\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 95000000:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 72.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+40} \lor \neg \left(t \leq 2.9 \cdot 10^{-43}\right):\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.3e+40) (not (<= t 2.9e-43)))
   (* x (/ (- y z) t))
   (- x (/ (* x y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.3e+40) || !(t <= 2.9e-43)) {
		tmp = x * ((y - z) / t);
	} else {
		tmp = x - ((x * y) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-2.3d+40)) .or. (.not. (t <= 2.9d-43))) then
        tmp = x * ((y - z) / t)
    else
        tmp = x - ((x * y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.3e+40) || !(t <= 2.9e-43)) {
		tmp = x * ((y - z) / t);
	} else {
		tmp = x - ((x * y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.3e+40) or not (t <= 2.9e-43):
		tmp = x * ((y - z) / t)
	else:
		tmp = x - ((x * y) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.3e+40) || !(t <= 2.9e-43))
		tmp = Float64(x * Float64(Float64(y - z) / t));
	else
		tmp = Float64(x - Float64(Float64(x * y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2.3e+40) || ~((t <= 2.9e-43)))
		tmp = x * ((y - z) / t);
	else
		tmp = x - ((x * y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.3e+40], N[Not[LessEqual[t, 2.9e-43]], $MachinePrecision]], N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.29999999999999994e40 or 2.9000000000000001e-43 < t

   1. Initial program 86.0%

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

      1. associate-*r/ 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in t around inf 74.2%

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

   if -2.29999999999999994e40 < t < 2.9000000000000001e-43

   1. Initial program 83.8%

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

      1. associate-/l* 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in t around 0 83.5%

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

      1. neg-mul-1 83.5%

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

      2. distribute-neg-frac 83.5%

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

   6. Simplified 83.5%

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

   7. Taylor expanded in z around 0 77.5%

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

      1. +-commutative 77.5%

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

      2. mul-1-neg 77.5%

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

      3. unsub-neg 77.5%

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

   9. Simplified 77.5%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+40} \lor \neg \left(t \leq 2.9 \cdot 10^{-43}\right):\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x \cdot y}{z}\\ \end{array} \]

Alternative 14: 76.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{-23} \lor \neg \left(z \leq 230\right):\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.9e-23) (not (<= z 230.0)))
   (/ x (- 1.0 (/ t z)))
   (* x (/ y (- t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.9e-23) || !(z <= 230.0)) {
		tmp = x / (1.0 - (t / 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 <= (-3.9d-23)) .or. (.not. (z <= 230.0d0))) then
        tmp = x / (1.0d0 - (t / 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 <= -3.9e-23) || !(z <= 230.0)) {
		tmp = x / (1.0 - (t / z));
	} else {
		tmp = x * (y / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.9e-23) or not (z <= 230.0):
		tmp = x / (1.0 - (t / z))
	else:
		tmp = x * (y / (t - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.9e-23) || !(z <= 230.0))
		tmp = Float64(x / Float64(1.0 - Float64(t / 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 <= -3.9e-23) || ~((z <= 230.0)))
		tmp = x / (1.0 - (t / z));
	else
		tmp = x * (y / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.9e-23], N[Not[LessEqual[z, 230.0]], $MachinePrecision]], N[(x / N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.9e-23 or 230 < z

   1. Initial program 79.0%

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

      1. div-sub 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in y around 0 78.4%

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

      1. mul-1-neg 78.4%

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

      2. unsub-neg 78.4%

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

   8. Simplified 78.4%

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

   if -3.9e-23 < z < 230

   1. Initial program 92.4%

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

      1. associate-*r/ 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in y around inf 76.9%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{-23} \lor \neg \left(z \leq 230\right):\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \]

Alternative 15: 61.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-21}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7800000000:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.1e-21) x (if (<= z 7800000000.0) (* x (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.1e-21) {
		tmp = x;
	} else if (z <= 7800000000.0) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-3.1d-21)) then
        tmp = x
    else if (z <= 7800000000.0d0) then
        tmp = x * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.1e-21) {
		tmp = x;
	} else if (z <= 7800000000.0) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.1e-21:
		tmp = x
	elif z <= 7800000000.0:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.1e-21)
		tmp = x;
	elseif (z <= 7800000000.0)
		tmp = Float64(x * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.1e-21)
		tmp = x;
	elseif (z <= 7800000000.0)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.1e-21], x, If[LessEqual[z, 7800000000.0], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -3.0999999999999998e-21 or 7.8e9 < z

   1. Initial program 79.0%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 z around inf 60.8%

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

   if -3.0999999999999998e-21 < z < 7.8e9

   1. Initial program 92.4%

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

      1. associate-*r/ 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in z around 0 67.0%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-21}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7800000000:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16: 96.9% 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 84.8%

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

   1. associate-*r/ 98.3%

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

3. Simplified 98.3%

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

4. Final simplification 98.3%

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

Alternative 17: 34.8% 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 84.8%

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

   1. associate-*r/ 98.3%

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

3. Simplified 98.3%

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

4. Taylor expanded in z around inf 40.2%

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

5. Final simplification 40.2%

   \[\leadsto x \]

Developer target: 96.9% 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 2023192 
(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)))