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

Percentage Accurate: 84.8% → 96.9%

Time: 10.7s

Alternatives: 13

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: 84.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.9% 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 85.4%

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

   1. associate-*r/ 98.7%

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

3. Simplified 98.7%

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

4. Final simplification 98.7%

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

Alternative 2: 74.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z}{z - t}\\ \mathbf{if}\;z \leq -3.6 \cdot 10^{+132}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.25 \cdot 10^{+28}:\\ \;\;\;\;\frac{x}{z} \cdot \left(z - y\right)\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-45}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-12}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+65}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{t - y}{z} + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ z (- z t)))))
   (if (<= z -3.6e+132)
     t_1
     (if (<= z -3.25e+28)
       (* (/ x z) (- z y))
       (if (<= z -1.5e-45)
         (/ x (- 1.0 (/ t z)))
         (if (<= z 6.2e-12)
           (* x (/ y (- t z)))
           (if (<= z 1.02e+65) t_1 (* x (+ (/ (- t y) z) 1.0)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (z / (z - t));
	double tmp;
	if (z <= -3.6e+132) {
		tmp = t_1;
	} else if (z <= -3.25e+28) {
		tmp = (x / z) * (z - y);
	} else if (z <= -1.5e-45) {
		tmp = x / (1.0 - (t / z));
	} else if (z <= 6.2e-12) {
		tmp = x * (y / (t - z));
	} else if (z <= 1.02e+65) {
		tmp = t_1;
	} else {
		tmp = x * (((t - y) / z) + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (z / (z - t))
    if (z <= (-3.6d+132)) then
        tmp = t_1
    else if (z <= (-3.25d+28)) then
        tmp = (x / z) * (z - y)
    else if (z <= (-1.5d-45)) then
        tmp = x / (1.0d0 - (t / z))
    else if (z <= 6.2d-12) then
        tmp = x * (y / (t - z))
    else if (z <= 1.02d+65) then
        tmp = t_1
    else
        tmp = x * (((t - y) / z) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (z / (z - t));
	double tmp;
	if (z <= -3.6e+132) {
		tmp = t_1;
	} else if (z <= -3.25e+28) {
		tmp = (x / z) * (z - y);
	} else if (z <= -1.5e-45) {
		tmp = x / (1.0 - (t / z));
	} else if (z <= 6.2e-12) {
		tmp = x * (y / (t - z));
	} else if (z <= 1.02e+65) {
		tmp = t_1;
	} else {
		tmp = x * (((t - y) / z) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (z / (z - t))
	tmp = 0
	if z <= -3.6e+132:
		tmp = t_1
	elif z <= -3.25e+28:
		tmp = (x / z) * (z - y)
	elif z <= -1.5e-45:
		tmp = x / (1.0 - (t / z))
	elif z <= 6.2e-12:
		tmp = x * (y / (t - z))
	elif z <= 1.02e+65:
		tmp = t_1
	else:
		tmp = x * (((t - y) / z) + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(z / Float64(z - t)))
	tmp = 0.0
	if (z <= -3.6e+132)
		tmp = t_1;
	elseif (z <= -3.25e+28)
		tmp = Float64(Float64(x / z) * Float64(z - y));
	elseif (z <= -1.5e-45)
		tmp = Float64(x / Float64(1.0 - Float64(t / z)));
	elseif (z <= 6.2e-12)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	elseif (z <= 1.02e+65)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(Float64(t - y) / z) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (z / (z - t));
	tmp = 0.0;
	if (z <= -3.6e+132)
		tmp = t_1;
	elseif (z <= -3.25e+28)
		tmp = (x / z) * (z - y);
	elseif (z <= -1.5e-45)
		tmp = x / (1.0 - (t / z));
	elseif (z <= 6.2e-12)
		tmp = x * (y / (t - z));
	elseif (z <= 1.02e+65)
		tmp = t_1;
	else
		tmp = x * (((t - y) / z) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.6e+132], t$95$1, If[LessEqual[z, -3.25e+28], N[(N[(x / z), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.5e-45], N[(x / N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.2e-12], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.02e+65], t$95$1, N[(x * N[(N[(N[(t - y), $MachinePrecision] / z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.60000000000000016e132 or 6.2000000000000002e-12 < z < 1.02000000000000005e65

   1. Initial program 86.0%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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. Taylor expanded in y around 0 87.3%

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

      1. associate-*r/ 87.3%

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

      2. neg-mul-1 87.3%

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

      3. neg-sub0 87.3%

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

      4. associate--r- 87.3%

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

      5. neg-sub0 87.3%

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

   6. Simplified 87.3%

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

   7. Taylor expanded in x around 0 76.8%

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

      1. associate-/l* 54.1%

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

      2. associate-/r/ 87.3%

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

   9. Applied egg-rr 87.3%

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

   if -3.60000000000000016e132 < z < -3.25e28

   1. Initial program 83.2%

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

      1. associate-*l/ 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in t around 0 76.7%

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

      1. associate-*r/ 76.7%

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

      2. neg-mul-1 76.7%

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

   6. Simplified 76.7%

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

   if -3.25e28 < z < -1.50000000000000005e-45

   1. Initial program 94.3%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 77.8%

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

      1. associate-*r/ 77.8%

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

      2. neg-mul-1 77.8%

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

      3. neg-sub0 77.8%

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

      4. associate--r- 77.8%

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

      5. neg-sub0 77.8%

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

   6. Simplified 77.8%

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

   7. Taylor expanded in t around 0 77.8%

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

      1. mul-1-neg 77.8%

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

      2. unsub-neg 77.8%

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

   9. Simplified 77.8%

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

   if -1.50000000000000005e-45 < z < 6.2000000000000002e-12

   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 86.6%

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

   if 1.02000000000000005e65 < z

   1. Initial program 65.8%

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

      1. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 83.0%

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

      1. +-commutative 83.0%

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

      2. associate--l+ 83.0%

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

      3. associate-*r/ 83.0%

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

      4. associate-*r/ 83.0%

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

      5. div-sub 83.0%

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

      6. distribute-lft-out-- 83.0%

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

      7. associate-*r/ 83.0%

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

      8. mul-1-neg 83.0%

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

      9. unsub-neg 83.0%

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

   6. Simplified 83.0%

      \[\leadsto x \cdot \color{blue}{\left(1 - \frac{y - t}{z}\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+132}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq -3.25 \cdot 10^{+28}:\\ \;\;\;\;\frac{x}{z} \cdot \left(z - y\right)\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-45}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-12}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+65}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{t - y}{z} + 1\right)\\ \end{array} \]

Alternative 3: 74.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z}{z - t}\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+132}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.22 \cdot 10^{+29}:\\ \;\;\;\;\frac{x}{z} \cdot \left(z - y\right)\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-45}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-11}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{-z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ z (- z t)))))
   (if (<= z -3.5e+132)
     t_1
     (if (<= z -1.22e+29)
       (* (/ x z) (- z y))
       (if (<= z -7e-45)
         (/ x (- 1.0 (/ t z)))
         (if (<= z 5.6e-11)
           (* x (/ y (- t z)))
           (if (<= z 4.4e+64) t_1 (/ x (/ (- z) (- y z))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (z / (z - t));
	double tmp;
	if (z <= -3.5e+132) {
		tmp = t_1;
	} else if (z <= -1.22e+29) {
		tmp = (x / z) * (z - y);
	} else if (z <= -7e-45) {
		tmp = x / (1.0 - (t / z));
	} else if (z <= 5.6e-11) {
		tmp = x * (y / (t - z));
	} else if (z <= 4.4e+64) {
		tmp = t_1;
	} else {
		tmp = x / (-z / (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (z / (z - t))
    if (z <= (-3.5d+132)) then
        tmp = t_1
    else if (z <= (-1.22d+29)) then
        tmp = (x / z) * (z - y)
    else if (z <= (-7d-45)) then
        tmp = x / (1.0d0 - (t / z))
    else if (z <= 5.6d-11) then
        tmp = x * (y / (t - z))
    else if (z <= 4.4d+64) then
        tmp = t_1
    else
        tmp = x / (-z / (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (z / (z - t));
	double tmp;
	if (z <= -3.5e+132) {
		tmp = t_1;
	} else if (z <= -1.22e+29) {
		tmp = (x / z) * (z - y);
	} else if (z <= -7e-45) {
		tmp = x / (1.0 - (t / z));
	} else if (z <= 5.6e-11) {
		tmp = x * (y / (t - z));
	} else if (z <= 4.4e+64) {
		tmp = t_1;
	} else {
		tmp = x / (-z / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (z / (z - t))
	tmp = 0
	if z <= -3.5e+132:
		tmp = t_1
	elif z <= -1.22e+29:
		tmp = (x / z) * (z - y)
	elif z <= -7e-45:
		tmp = x / (1.0 - (t / z))
	elif z <= 5.6e-11:
		tmp = x * (y / (t - z))
	elif z <= 4.4e+64:
		tmp = t_1
	else:
		tmp = x / (-z / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(z / Float64(z - t)))
	tmp = 0.0
	if (z <= -3.5e+132)
		tmp = t_1;
	elseif (z <= -1.22e+29)
		tmp = Float64(Float64(x / z) * Float64(z - y));
	elseif (z <= -7e-45)
		tmp = Float64(x / Float64(1.0 - Float64(t / z)));
	elseif (z <= 5.6e-11)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	elseif (z <= 4.4e+64)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(Float64(-z) / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (z / (z - t));
	tmp = 0.0;
	if (z <= -3.5e+132)
		tmp = t_1;
	elseif (z <= -1.22e+29)
		tmp = (x / z) * (z - y);
	elseif (z <= -7e-45)
		tmp = x / (1.0 - (t / z));
	elseif (z <= 5.6e-11)
		tmp = x * (y / (t - z));
	elseif (z <= 4.4e+64)
		tmp = t_1;
	else
		tmp = x / (-z / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.5e+132], t$95$1, If[LessEqual[z, -1.22e+29], N[(N[(x / z), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7e-45], N[(x / N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.6e-11], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.4e+64], t$95$1, N[(x / N[((-z) / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.5000000000000002e132 or 5.6e-11 < z < 4.40000000000000004e64

   1. Initial program 86.0%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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. Taylor expanded in y around 0 87.3%

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

      1. associate-*r/ 87.3%

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

      2. neg-mul-1 87.3%

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

      3. neg-sub0 87.3%

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

      4. associate--r- 87.3%

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

      5. neg-sub0 87.3%

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

   6. Simplified 87.3%

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

   7. Taylor expanded in x around 0 76.8%

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

      1. associate-/l* 54.1%

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

      2. associate-/r/ 87.3%

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

   9. Applied egg-rr 87.3%

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

   if -3.5000000000000002e132 < z < -1.22e29

   1. Initial program 83.2%

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

      1. associate-*l/ 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in t around 0 76.7%

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

      1. associate-*r/ 76.7%

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

      2. neg-mul-1 76.7%

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

   6. Simplified 76.7%

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

   if -1.22e29 < z < -7e-45

   1. Initial program 94.3%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 77.8%

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

      1. associate-*r/ 77.8%

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

      2. neg-mul-1 77.8%

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

      3. neg-sub0 77.8%

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

      4. associate--r- 77.8%

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

      5. neg-sub0 77.8%

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

   6. Simplified 77.8%

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

   7. Taylor expanded in t around 0 77.8%

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

      1. mul-1-neg 77.8%

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

      2. unsub-neg 77.8%

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

   9. Simplified 77.8%

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

   if -7e-45 < z < 5.6e-11

   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 86.6%

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

   if 4.40000000000000004e64 < z

   1. Initial program 65.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around 0 82.8%

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

      1. neg-mul-1 82.8%

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

      2. distribute-neg-frac 82.8%

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

   6. Simplified 82.8%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+132}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq -1.22 \cdot 10^{+29}:\\ \;\;\;\;\frac{x}{z} \cdot \left(z - y\right)\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-45}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-11}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+64}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{-z}{y - z}}\\ \end{array} \]

Alternative 4: 74.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z}{z - t}\\ \mathbf{if}\;z \leq -1.02 \cdot 10^{+133}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{+24}:\\ \;\;\;\;\frac{x}{z} \cdot \left(z - y\right)\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-48}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-12}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 1.86 \cdot 10^{+65}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ z (- z t)))))
   (if (<= z -1.02e+133)
     t_1
     (if (<= z -4.6e+24)
       (* (/ x z) (- z y))
       (if (<= z -6.4e-48)
         (/ x (- 1.0 (/ t z)))
         (if (<= z 9e-12)
           (* x (/ y (- t z)))
           (if (<= z 1.86e+65) t_1 (- x (* y (/ x z))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (z / (z - t));
	double tmp;
	if (z <= -1.02e+133) {
		tmp = t_1;
	} else if (z <= -4.6e+24) {
		tmp = (x / z) * (z - y);
	} else if (z <= -6.4e-48) {
		tmp = x / (1.0 - (t / z));
	} else if (z <= 9e-12) {
		tmp = x * (y / (t - z));
	} else if (z <= 1.86e+65) {
		tmp = t_1;
	} else {
		tmp = x - (y * (x / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (z / (z - t))
    if (z <= (-1.02d+133)) then
        tmp = t_1
    else if (z <= (-4.6d+24)) then
        tmp = (x / z) * (z - y)
    else if (z <= (-6.4d-48)) then
        tmp = x / (1.0d0 - (t / z))
    else if (z <= 9d-12) then
        tmp = x * (y / (t - z))
    else if (z <= 1.86d+65) then
        tmp = t_1
    else
        tmp = x - (y * (x / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (z / (z - t));
	double tmp;
	if (z <= -1.02e+133) {
		tmp = t_1;
	} else if (z <= -4.6e+24) {
		tmp = (x / z) * (z - y);
	} else if (z <= -6.4e-48) {
		tmp = x / (1.0 - (t / z));
	} else if (z <= 9e-12) {
		tmp = x * (y / (t - z));
	} else if (z <= 1.86e+65) {
		tmp = t_1;
	} else {
		tmp = x - (y * (x / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (z / (z - t))
	tmp = 0
	if z <= -1.02e+133:
		tmp = t_1
	elif z <= -4.6e+24:
		tmp = (x / z) * (z - y)
	elif z <= -6.4e-48:
		tmp = x / (1.0 - (t / z))
	elif z <= 9e-12:
		tmp = x * (y / (t - z))
	elif z <= 1.86e+65:
		tmp = t_1
	else:
		tmp = x - (y * (x / z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(z / Float64(z - t)))
	tmp = 0.0
	if (z <= -1.02e+133)
		tmp = t_1;
	elseif (z <= -4.6e+24)
		tmp = Float64(Float64(x / z) * Float64(z - y));
	elseif (z <= -6.4e-48)
		tmp = Float64(x / Float64(1.0 - Float64(t / z)));
	elseif (z <= 9e-12)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	elseif (z <= 1.86e+65)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(y * Float64(x / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (z / (z - t));
	tmp = 0.0;
	if (z <= -1.02e+133)
		tmp = t_1;
	elseif (z <= -4.6e+24)
		tmp = (x / z) * (z - y);
	elseif (z <= -6.4e-48)
		tmp = x / (1.0 - (t / z));
	elseif (z <= 9e-12)
		tmp = x * (y / (t - z));
	elseif (z <= 1.86e+65)
		tmp = t_1;
	else
		tmp = x - (y * (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.02e+133], t$95$1, If[LessEqual[z, -4.6e+24], N[(N[(x / z), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.4e-48], N[(x / N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e-12], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.86e+65], t$95$1, N[(x - N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.02e133 or 8.99999999999999962e-12 < z < 1.8599999999999999e65

   1. Initial program 86.0%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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. Taylor expanded in y around 0 87.3%

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

      1. associate-*r/ 87.3%

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

      2. neg-mul-1 87.3%

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

      3. neg-sub0 87.3%

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

      4. associate--r- 87.3%

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

      5. neg-sub0 87.3%

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

   6. Simplified 87.3%

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

   7. Taylor expanded in x around 0 76.8%

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

      1. associate-/l* 54.1%

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

      2. associate-/r/ 87.3%

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

   9. Applied egg-rr 87.3%

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

   if -1.02e133 < z < -4.5999999999999998e24

   1. Initial program 83.2%

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

      1. associate-*l/ 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in t around 0 76.7%

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

      1. associate-*r/ 76.7%

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

      2. neg-mul-1 76.7%

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

   6. Simplified 76.7%

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

   if -4.5999999999999998e24 < z < -6.39999999999999959e-48

   1. Initial program 94.3%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 77.8%

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

      1. associate-*r/ 77.8%

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

      2. neg-mul-1 77.8%

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

      3. neg-sub0 77.8%

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

      4. associate--r- 77.8%

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

      5. neg-sub0 77.8%

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

   6. Simplified 77.8%

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

   7. Taylor expanded in t around 0 77.8%

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

      1. mul-1-neg 77.8%

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

      2. unsub-neg 77.8%

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

   9. Simplified 77.8%

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

   if -6.39999999999999959e-48 < z < 8.99999999999999962e-12

   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 86.6%

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

   if 1.8599999999999999e65 < z

   1. Initial program 65.8%

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

      1. associate-*l/ 69.8%

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

   3. Simplified 69.8%

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

   4. Taylor expanded in t around 0 56.8%

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

      1. associate-*r/ 56.8%

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

      2. neg-mul-1 56.8%

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

   6. Simplified 56.8%

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

   7. Taylor expanded in z around 0 76.4%

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

      1. +-commutative 76.4%

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

      2. mul-1-neg 76.4%

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

      3. unsub-neg 76.4%

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

      4. associate-*r/ 76.8%

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

   9. Simplified 76.8%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+133}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{+24}:\\ \;\;\;\;\frac{x}{z} \cdot \left(z - y\right)\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-48}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-12}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 1.86 \cdot 10^{+65}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{x}{z}\\ \end{array} \]

Alternative 5: 60.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-41}:\\ \;\;\;\;\left(-z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+112}:\\ \;\;\;\;x \cdot \frac{-y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.2e+19)
   x
   (if (<= z -1.05e-41)
     (* (- z) (/ x t))
     (if (<= z 5.5e-13)
       (* x (/ y t))
       (if (<= z 2.8e+38) x (if (<= z 1.8e+112) (* x (/ (- y) z)) x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.2e+19) {
		tmp = x;
	} else if (z <= -1.05e-41) {
		tmp = -z * (x / t);
	} else if (z <= 5.5e-13) {
		tmp = x * (y / t);
	} else if (z <= 2.8e+38) {
		tmp = x;
	} else if (z <= 1.8e+112) {
		tmp = x * (-y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.2d+19)) then
        tmp = x
    else if (z <= (-1.05d-41)) then
        tmp = -z * (x / t)
    else if (z <= 5.5d-13) then
        tmp = x * (y / t)
    else if (z <= 2.8d+38) then
        tmp = x
    else if (z <= 1.8d+112) then
        tmp = x * (-y / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.2e+19) {
		tmp = x;
	} else if (z <= -1.05e-41) {
		tmp = -z * (x / t);
	} else if (z <= 5.5e-13) {
		tmp = x * (y / t);
	} else if (z <= 2.8e+38) {
		tmp = x;
	} else if (z <= 1.8e+112) {
		tmp = x * (-y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.2e+19:
		tmp = x
	elif z <= -1.05e-41:
		tmp = -z * (x / t)
	elif z <= 5.5e-13:
		tmp = x * (y / t)
	elif z <= 2.8e+38:
		tmp = x
	elif z <= 1.8e+112:
		tmp = x * (-y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.2e+19)
		tmp = x;
	elseif (z <= -1.05e-41)
		tmp = Float64(Float64(-z) * Float64(x / t));
	elseif (z <= 5.5e-13)
		tmp = Float64(x * Float64(y / t));
	elseif (z <= 2.8e+38)
		tmp = x;
	elseif (z <= 1.8e+112)
		tmp = Float64(x * Float64(Float64(-y) / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.2e+19)
		tmp = x;
	elseif (z <= -1.05e-41)
		tmp = -z * (x / t);
	elseif (z <= 5.5e-13)
		tmp = x * (y / t);
	elseif (z <= 2.8e+38)
		tmp = x;
	elseif (z <= 1.8e+112)
		tmp = x * (-y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.2e+19], x, If[LessEqual[z, -1.05e-41], N[((-z) * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.5e-13], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e+38], x, If[LessEqual[z, 1.8e+112], N[(x * N[((-y) / z), $MachinePrecision]), $MachinePrecision], x]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.2e19 or 5.49999999999999979e-13 < z < 2.8e38 or 1.8e112 < z

   1. Initial program 77.8%

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

      1. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 62.7%

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

   if -1.2e19 < z < -1.05000000000000006e-41

   1. Initial program 92.6%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 78.2%

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

      1. associate-*r/ 78.2%

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

      2. neg-mul-1 78.2%

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

      3. neg-sub0 78.2%

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

      4. associate--r- 78.2%

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

      5. neg-sub0 78.2%

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

   6. Simplified 78.2%

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

   7. Taylor expanded in t around inf 70.5%

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

      1. mul-1-neg 70.5%

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

      2. associate-*r/ 70.4%

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

      3. distribute-rgt-neg-in 70.4%

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

   9. Simplified 70.4%

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

   if -1.05000000000000006e-41 < z < 5.49999999999999979e-13

   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 z around 0 74.1%

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

   if 2.8e38 < z < 1.8e112

   1. Initial program 83.2%

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

      1. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 60.9%

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

   5. Taylor expanded in t around 0 49.6%

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

      1. associate-*r/ 49.6%

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

      2. neg-mul-1 49.6%

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

   7. Simplified 49.6%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-41}:\\ \;\;\;\;\left(-z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+112}:\\ \;\;\;\;x \cdot \frac{-y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 60.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{+21}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-41}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{t}\\ \mathbf{elif}\;z \leq 4.45 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+112}:\\ \;\;\;\;x \cdot \frac{-y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.08e+21)
   x
   (if (<= z -1.05e-41)
     (/ (* x (- z)) t)
     (if (<= z 4.45e-13)
       (* x (/ y t))
       (if (<= z 2.95e+38) x (if (<= z 1.7e+112) (* x (/ (- y) z)) x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.08e+21) {
		tmp = x;
	} else if (z <= -1.05e-41) {
		tmp = (x * -z) / t;
	} else if (z <= 4.45e-13) {
		tmp = x * (y / t);
	} else if (z <= 2.95e+38) {
		tmp = x;
	} else if (z <= 1.7e+112) {
		tmp = x * (-y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.08d+21)) then
        tmp = x
    else if (z <= (-1.05d-41)) then
        tmp = (x * -z) / t
    else if (z <= 4.45d-13) then
        tmp = x * (y / t)
    else if (z <= 2.95d+38) then
        tmp = x
    else if (z <= 1.7d+112) then
        tmp = x * (-y / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.08e+21) {
		tmp = x;
	} else if (z <= -1.05e-41) {
		tmp = (x * -z) / t;
	} else if (z <= 4.45e-13) {
		tmp = x * (y / t);
	} else if (z <= 2.95e+38) {
		tmp = x;
	} else if (z <= 1.7e+112) {
		tmp = x * (-y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.08e+21:
		tmp = x
	elif z <= -1.05e-41:
		tmp = (x * -z) / t
	elif z <= 4.45e-13:
		tmp = x * (y / t)
	elif z <= 2.95e+38:
		tmp = x
	elif z <= 1.7e+112:
		tmp = x * (-y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.08e+21)
		tmp = x;
	elseif (z <= -1.05e-41)
		tmp = Float64(Float64(x * Float64(-z)) / t);
	elseif (z <= 4.45e-13)
		tmp = Float64(x * Float64(y / t));
	elseif (z <= 2.95e+38)
		tmp = x;
	elseif (z <= 1.7e+112)
		tmp = Float64(x * Float64(Float64(-y) / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.08e+21)
		tmp = x;
	elseif (z <= -1.05e-41)
		tmp = (x * -z) / t;
	elseif (z <= 4.45e-13)
		tmp = x * (y / t);
	elseif (z <= 2.95e+38)
		tmp = x;
	elseif (z <= 1.7e+112)
		tmp = x * (-y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.08e+21], x, If[LessEqual[z, -1.05e-41], N[(N[(x * (-z)), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 4.45e-13], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.95e+38], x, If[LessEqual[z, 1.7e+112], N[(x * N[((-y) / z), $MachinePrecision]), $MachinePrecision], x]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.08e21 or 4.4500000000000002e-13 < z < 2.94999999999999991e38 or 1.69999999999999997e112 < z

   1. Initial program 77.8%

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

      1. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 62.7%

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

   if -1.08e21 < z < -1.05000000000000006e-41

   1. Initial program 92.6%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 78.2%

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

      1. associate-*r/ 78.2%

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

      2. neg-mul-1 78.2%

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

      3. neg-sub0 78.2%

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

      4. associate--r- 78.2%

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

      5. neg-sub0 78.2%

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

   6. Simplified 78.2%

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

   7. Taylor expanded in t around 0 78.2%

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

      1. mul-1-neg 78.2%

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

      2. unsub-neg 78.2%

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

   9. Simplified 78.2%

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

   10. Taylor expanded in t around inf 70.5%

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

       1. associate-*r/ 70.5%

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

       2. *-commutative 70.5%

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

       3. neg-mul-1 70.5%

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

       4. distribute-rgt-neg-in 70.5%

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

   12. Simplified 70.5%

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

   if -1.05000000000000006e-41 < z < 4.4500000000000002e-13

   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 z around 0 74.1%

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

   if 2.94999999999999991e38 < z < 1.69999999999999997e112

   1. Initial program 83.2%

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

      1. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 60.9%

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

   5. Taylor expanded in t around 0 49.6%

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

      1. associate-*r/ 49.6%

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

      2. neg-mul-1 49.6%

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

   7. Simplified 49.6%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{+21}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-41}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{t}\\ \mathbf{elif}\;z \leq 4.45 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+112}:\\ \;\;\;\;x \cdot \frac{-y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 67.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+54}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-9} \lor \neg \left(z \leq 4.2 \cdot 10^{+34}\right) \land z \leq 7.2 \cdot 10^{+129}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.2e+54)
   x
   (if (or (<= z 1.7e-9) (and (not (<= z 4.2e+34)) (<= z 7.2e+129)))
     (* x (/ y (- t z)))
     x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.2e+54) {
		tmp = x;
	} else if ((z <= 1.7e-9) || (!(z <= 4.2e+34) && (z <= 7.2e+129))) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-5.2d+54)) then
        tmp = x
    else if ((z <= 1.7d-9) .or. (.not. (z <= 4.2d+34)) .and. (z <= 7.2d+129)) then
        tmp = x * (y / (t - z))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.2e+54) {
		tmp = x;
	} else if ((z <= 1.7e-9) || (!(z <= 4.2e+34) && (z <= 7.2e+129))) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.2e+54:
		tmp = x
	elif (z <= 1.7e-9) or (not (z <= 4.2e+34) and (z <= 7.2e+129)):
		tmp = x * (y / (t - z))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.2e+54)
		tmp = x;
	elseif ((z <= 1.7e-9) || (!(z <= 4.2e+34) && (z <= 7.2e+129)))
		tmp = Float64(x * Float64(y / Float64(t - z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5.2e+54)
		tmp = x;
	elseif ((z <= 1.7e-9) || (~((z <= 4.2e+34)) && (z <= 7.2e+129)))
		tmp = x * (y / (t - z));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.2e+54], x, If[Or[LessEqual[z, 1.7e-9], And[N[Not[LessEqual[z, 4.2e+34]], $MachinePrecision], LessEqual[z, 7.2e+129]]], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -5.20000000000000013e54 or 1.6999999999999999e-9 < z < 4.20000000000000035e34 or 7.2000000000000002e129 < z

   1. Initial program 77.5%

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

      1. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 66.8%

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

   if -5.20000000000000013e54 < z < 1.6999999999999999e-9 or 4.20000000000000035e34 < z < 7.2000000000000002e129

   1. Initial program 90.6%

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

      1. associate-*r/ 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in y around inf 77.7%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+54}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-9} \lor \neg \left(z \leq 4.2 \cdot 10^{+34}\right) \land z \leq 7.2 \cdot 10^{+129}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 60.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.82 \cdot 10^{+21}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-14}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+112}:\\ \;\;\;\;x \cdot \frac{-y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.82e+21)
   x
   (if (<= z 2.4e-14)
     (* x (/ y t))
     (if (<= z 6.2e+39) x (if (<= z 1.95e+112) (* x (/ (- y) z)) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.82e+21) {
		tmp = x;
	} else if (z <= 2.4e-14) {
		tmp = x * (y / t);
	} else if (z <= 6.2e+39) {
		tmp = x;
	} else if (z <= 1.95e+112) {
		tmp = x * (-y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.82d+21)) then
        tmp = x
    else if (z <= 2.4d-14) then
        tmp = x * (y / t)
    else if (z <= 6.2d+39) then
        tmp = x
    else if (z <= 1.95d+112) then
        tmp = x * (-y / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.82e+21) {
		tmp = x;
	} else if (z <= 2.4e-14) {
		tmp = x * (y / t);
	} else if (z <= 6.2e+39) {
		tmp = x;
	} else if (z <= 1.95e+112) {
		tmp = x * (-y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.82e+21:
		tmp = x
	elif z <= 2.4e-14:
		tmp = x * (y / t)
	elif z <= 6.2e+39:
		tmp = x
	elif z <= 1.95e+112:
		tmp = x * (-y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.82e+21)
		tmp = x;
	elseif (z <= 2.4e-14)
		tmp = Float64(x * Float64(y / t));
	elseif (z <= 6.2e+39)
		tmp = x;
	elseif (z <= 1.95e+112)
		tmp = Float64(x * Float64(Float64(-y) / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.82e+21)
		tmp = x;
	elseif (z <= 2.4e-14)
		tmp = x * (y / t);
	elseif (z <= 6.2e+39)
		tmp = x;
	elseif (z <= 1.95e+112)
		tmp = x * (-y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.82e+21], x, If[LessEqual[z, 2.4e-14], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.2e+39], x, If[LessEqual[z, 1.95e+112], N[(x * N[((-y) / z), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.82e21 or 2.4e-14 < z < 6.2000000000000005e39 or 1.94999999999999984e112 < z

   1. Initial program 77.8%

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

      1. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 62.7%

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

   if -1.82e21 < z < 2.4e-14

   1. Initial program 92.8%

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

      1. associate-*r/ 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in z around 0 70.1%

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

   if 6.2000000000000005e39 < z < 1.94999999999999984e112

   1. Initial program 83.2%

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

      1. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 60.9%

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

   5. Taylor expanded in t around 0 49.6%

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

      1. associate-*r/ 49.6%

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

      2. neg-mul-1 49.6%

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

   7. Simplified 49.6%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.82 \cdot 10^{+21}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-14}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+112}:\\ \;\;\;\;x \cdot \frac{-y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 74.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z}{z - t}\\ \mathbf{if}\;z \leq -1.22 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-11}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+67}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ z (- z t)))))
   (if (<= z -1.22e-46)
     t_1
     (if (<= z 4.7e-11)
       (* x (/ y (- t z)))
       (if (<= z 4e+67) t_1 (- x (* y (/ x z))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (z / (z - t));
	double tmp;
	if (z <= -1.22e-46) {
		tmp = t_1;
	} else if (z <= 4.7e-11) {
		tmp = x * (y / (t - z));
	} else if (z <= 4e+67) {
		tmp = t_1;
	} else {
		tmp = x - (y * (x / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (z / (z - t))
    if (z <= (-1.22d-46)) then
        tmp = t_1
    else if (z <= 4.7d-11) then
        tmp = x * (y / (t - z))
    else if (z <= 4d+67) then
        tmp = t_1
    else
        tmp = x - (y * (x / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (z / (z - t));
	double tmp;
	if (z <= -1.22e-46) {
		tmp = t_1;
	} else if (z <= 4.7e-11) {
		tmp = x * (y / (t - z));
	} else if (z <= 4e+67) {
		tmp = t_1;
	} else {
		tmp = x - (y * (x / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (z / (z - t))
	tmp = 0
	if z <= -1.22e-46:
		tmp = t_1
	elif z <= 4.7e-11:
		tmp = x * (y / (t - z))
	elif z <= 4e+67:
		tmp = t_1
	else:
		tmp = x - (y * (x / z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(z / Float64(z - t)))
	tmp = 0.0
	if (z <= -1.22e-46)
		tmp = t_1;
	elseif (z <= 4.7e-11)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	elseif (z <= 4e+67)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(y * Float64(x / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (z / (z - t));
	tmp = 0.0;
	if (z <= -1.22e-46)
		tmp = t_1;
	elseif (z <= 4.7e-11)
		tmp = x * (y / (t - z));
	elseif (z <= 4e+67)
		tmp = t_1;
	else
		tmp = x - (y * (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.22e-46], t$95$1, If[LessEqual[z, 4.7e-11], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4e+67], t$95$1, N[(x - N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.22e-46 or 4.69999999999999993e-11 < z < 3.99999999999999993e67

   1. Initial program 86.6%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 78.6%

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

      1. associate-*r/ 78.6%

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

      2. neg-mul-1 78.6%

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

      3. neg-sub0 78.6%

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

      4. associate--r- 78.6%

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

      5. neg-sub0 78.6%

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

   6. Simplified 78.6%

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

   7. Taylor expanded in x around 0 70.0%

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

      1. associate-/l* 59.5%

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

      2. associate-/r/ 78.6%

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

   9. Applied egg-rr 78.6%

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

   if -1.22e-46 < z < 4.69999999999999993e-11

   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 86.6%

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

   if 3.99999999999999993e67 < z

   1. Initial program 65.8%

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

      1. associate-*l/ 69.8%

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

   3. Simplified 69.8%

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

   4. Taylor expanded in t around 0 56.8%

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

      1. associate-*r/ 56.8%

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

      2. neg-mul-1 56.8%

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

   6. Simplified 56.8%

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

   7. Taylor expanded in z around 0 76.4%

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

      1. +-commutative 76.4%

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

      2. mul-1-neg 76.4%

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

      3. unsub-neg 76.4%

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

      4. associate-*r/ 76.8%

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

   9. Simplified 76.8%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{-46}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-11}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+67}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{x}{z}\\ \end{array} \]

Alternative 10: 74.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-46}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{-11}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+67}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5e-46)
   (/ x (- 1.0 (/ t z)))
   (if (<= z 2.65e-11)
     (* x (/ y (- t z)))
     (if (<= z 1.3e+67) (* x (/ z (- z t))) (- x (* y (/ x z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5e-46) {
		tmp = x / (1.0 - (t / z));
	} else if (z <= 2.65e-11) {
		tmp = x * (y / (t - z));
	} else if (z <= 1.3e+67) {
		tmp = x * (z / (z - t));
	} else {
		tmp = x - (y * (x / 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 <= (-5d-46)) then
        tmp = x / (1.0d0 - (t / z))
    else if (z <= 2.65d-11) then
        tmp = x * (y / (t - z))
    else if (z <= 1.3d+67) then
        tmp = x * (z / (z - t))
    else
        tmp = x - (y * (x / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5e-46) {
		tmp = x / (1.0 - (t / z));
	} else if (z <= 2.65e-11) {
		tmp = x * (y / (t - z));
	} else if (z <= 1.3e+67) {
		tmp = x * (z / (z - t));
	} else {
		tmp = x - (y * (x / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5e-46:
		tmp = x / (1.0 - (t / z))
	elif z <= 2.65e-11:
		tmp = x * (y / (t - z))
	elif z <= 1.3e+67:
		tmp = x * (z / (z - t))
	else:
		tmp = x - (y * (x / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5e-46)
		tmp = Float64(x / Float64(1.0 - Float64(t / z)));
	elseif (z <= 2.65e-11)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	elseif (z <= 1.3e+67)
		tmp = Float64(x * Float64(z / Float64(z - t)));
	else
		tmp = Float64(x - Float64(y * Float64(x / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5e-46)
		tmp = x / (1.0 - (t / z));
	elseif (z <= 2.65e-11)
		tmp = x * (y / (t - z));
	elseif (z <= 1.3e+67)
		tmp = x * (z / (z - t));
	else
		tmp = x - (y * (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5e-46], N[(x / N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.65e-11], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e+67], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.99999999999999992e-46

   1. Initial program 84.5%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 78.1%

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

      1. associate-*r/ 78.1%

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

      2. neg-mul-1 78.1%

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

      3. neg-sub0 78.1%

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

      4. associate--r- 78.1%

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

      5. neg-sub0 78.1%

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

   6. Simplified 78.1%

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

   7. Taylor expanded in t around 0 78.1%

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

      1. mul-1-neg 78.1%

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

      2. unsub-neg 78.1%

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

   9. Simplified 78.1%

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

   if -4.99999999999999992e-46 < z < 2.6499999999999999e-11

   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 86.6%

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

   if 2.6499999999999999e-11 < z < 1.3e67

   1. Initial program 95.1%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 80.6%

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

      1. associate-*r/ 80.6%

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

      2. neg-mul-1 80.6%

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

      3. neg-sub0 80.6%

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

      4. associate--r- 80.6%

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

      5. neg-sub0 80.6%

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

   6. Simplified 80.6%

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

   7. Taylor expanded in x around 0 80.4%

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

      1. associate-/l* 76.1%

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

      2. associate-/r/ 80.6%

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

   9. Applied egg-rr 80.6%

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

   if 1.3e67 < z

   1. Initial program 65.8%

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

      1. associate-*l/ 69.8%

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

   3. Simplified 69.8%

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

   4. Taylor expanded in t around 0 56.8%

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

      1. associate-*r/ 56.8%

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

      2. neg-mul-1 56.8%

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

   6. Simplified 56.8%

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

   7. Taylor expanded in z around 0 76.4%

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

      1. +-commutative 76.4%

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

      2. mul-1-neg 76.4%

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

      3. unsub-neg 76.4%

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

      4. associate-*r/ 76.8%

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

   9. Simplified 76.8%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-46}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{-11}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+67}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{x}{z}\\ \end{array} \]

Alternative 11: 75.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-45} \lor \neg \left(z \leq 5.8 \cdot 10^{-11}\right):\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.3e-45) (not (<= z 5.8e-11)))
   (* x (/ z (- z t)))
   (* x (/ y (- t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.3e-45) || !(z <= 5.8e-11)) {
		tmp = x * (z / (z - t));
	} else {
		tmp = x * (y / (t - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.3d-45)) .or. (.not. (z <= 5.8d-11))) then
        tmp = x * (z / (z - t))
    else
        tmp = x * (y / (t - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.3e-45) || !(z <= 5.8e-11)) {
		tmp = x * (z / (z - t));
	} else {
		tmp = x * (y / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.3e-45) or not (z <= 5.8e-11):
		tmp = x * (z / (z - t))
	else:
		tmp = x * (y / (t - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.3e-45) || !(z <= 5.8e-11))
		tmp = Float64(x * Float64(z / Float64(z - t)));
	else
		tmp = Float64(x * Float64(y / Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.3e-45) || ~((z <= 5.8e-11)))
		tmp = x * (z / (z - t));
	else
		tmp = x * (y / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.3e-45], N[Not[LessEqual[z, 5.8e-11]], $MachinePrecision]], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.29999999999999993e-45 or 5.8e-11 < z

   1. Initial program 79.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 75.0%

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

      1. associate-*r/ 75.0%

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

      2. neg-mul-1 75.0%

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

      3. neg-sub0 75.0%

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

      4. associate--r- 75.0%

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

      5. neg-sub0 75.0%

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

   6. Simplified 75.0%

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

   7. Taylor expanded in x around 0 62.6%

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

      1. associate-/l* 54.2%

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

      2. associate-/r/ 75.0%

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

   9. Applied egg-rr 75.0%

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

   if -1.29999999999999993e-45 < z < 5.8e-11

   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 86.6%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-45} \lor \neg \left(z \leq 5.8 \cdot 10^{-11}\right):\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \]

Alternative 12: 61.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.28 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-14}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.28e+20) x (if (<= z 2e-14) (* x (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.28e+20) {
		tmp = x;
	} else if (z <= 2e-14) {
		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 <= (-1.28d+20)) then
        tmp = x
    else if (z <= 2d-14) 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 <= -1.28e+20) {
		tmp = x;
	} else if (z <= 2e-14) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.28e+20:
		tmp = x
	elif z <= 2e-14:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.28e+20)
		tmp = x;
	elseif (z <= 2e-14)
		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 <= -1.28e+20)
		tmp = x;
	elseif (z <= 2e-14)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.28e+20], x, If[LessEqual[z, 2e-14], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.28e20 or 2e-14 < z

   1. Initial program 78.5%

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

      1. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 57.6%

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

   if -1.28e20 < z < 2e-14

   1. Initial program 92.8%

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

      1. associate-*r/ 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in z around 0 70.1%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.28 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-14}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 36.0% 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 85.4%

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

   1. associate-*r/ 98.7%

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

3. Simplified 98.7%

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

4. Taylor expanded in z around inf 34.6%

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

5. Final simplification 34.6%

   \[\leadsto x \]

Developer target: 96.8% 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 2023195 
(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)))