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

Percentage Accurate: 84.4% → 97.2%

Time: 9.0s

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: 84.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 82.5%

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

   1. associate-/l* 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. Add Preprocessing

5. Final simplification 97.2%

   \[\leadsto x \cdot \frac{y - z}{t - z} \]
6. Add Preprocessing

Alternative 2: 59.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-25}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+16}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{+175}:\\ \;\;\;\;\frac{x}{t} \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -8.5e+38)
   x
   (if (<= z 1.3e-25)
     (/ x (/ t y))
     (if (<= z 2.5e+16) x (if (<= z 1.08e+175) (* (/ x t) (- z)) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -8.5e+38) {
		tmp = x;
	} else if (z <= 1.3e-25) {
		tmp = x / (t / y);
	} else if (z <= 2.5e+16) {
		tmp = x;
	} else if (z <= 1.08e+175) {
		tmp = (x / 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 <= (-8.5d+38)) then
        tmp = x
    else if (z <= 1.3d-25) then
        tmp = x / (t / y)
    else if (z <= 2.5d+16) then
        tmp = x
    else if (z <= 1.08d+175) then
        tmp = (x / 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 <= -8.5e+38) {
		tmp = x;
	} else if (z <= 1.3e-25) {
		tmp = x / (t / y);
	} else if (z <= 2.5e+16) {
		tmp = x;
	} else if (z <= 1.08e+175) {
		tmp = (x / t) * -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -8.5e+38:
		tmp = x
	elif z <= 1.3e-25:
		tmp = x / (t / y)
	elif z <= 2.5e+16:
		tmp = x
	elif z <= 1.08e+175:
		tmp = (x / t) * -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -8.5e+38)
		tmp = x;
	elseif (z <= 1.3e-25)
		tmp = Float64(x / Float64(t / y));
	elseif (z <= 2.5e+16)
		tmp = x;
	elseif (z <= 1.08e+175)
		tmp = Float64(Float64(x / t) * Float64(-z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -8.5e+38)
		tmp = x;
	elseif (z <= 1.3e-25)
		tmp = x / (t / y);
	elseif (z <= 2.5e+16)
		tmp = x;
	elseif (z <= 1.08e+175)
		tmp = (x / t) * -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -8.5e+38], x, If[LessEqual[z, 1.3e-25], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e+16], x, If[LessEqual[z, 1.08e+175], N[(N[(x / t), $MachinePrecision] * (-z)), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.4999999999999997e38 or 1.3e-25 < z < 2.5e16 or 1.08e175 < z

   1. Initial program 68.6%

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

      1. associate-/l* 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. Add Preprocessing

   5. Taylor expanded in z around inf 66.1%

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

   if -8.4999999999999997e38 < z < 1.3e-25

   1. Initial program 95.9%

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

      1. associate-/l* 94.3%

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

   3. Simplified 94.3%

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

      1. clear-num 94.3%

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

      2. un-div-inv 94.4%

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

   6. Applied egg-rr 94.4%

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

   7. Taylor expanded in z around 0 67.5%

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

   if 2.5e16 < z < 1.08e175

   1. Initial program 75.5%

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

      1. associate-/l* 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. Add Preprocessing

   5. Taylor expanded in x around 0 75.5%

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

      1. remove-double-neg 75.5%

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

      2. distribute-neg-frac2 75.5%

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

      3. *-commutative 75.5%

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

      4. associate-/l* 85.9%

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

      5. distribute-lft-neg-out 85.9%

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

      6. neg-sub0 85.9%

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

      7. associate--r- 85.9%

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

      8. neg-sub0 85.9%

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

      9. +-commutative 85.9%

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

      10. sub-neg 85.9%

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

      11. neg-sub0 85.9%

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

      12. associate--r- 85.9%

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

      13. neg-sub0 85.9%

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

      14. +-commutative 85.9%

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

      15. sub-neg 85.9%

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

      16. *-commutative 85.9%

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

   7. Simplified 85.9%

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

   8. Taylor expanded in z around 0 48.1%

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

      1. associate-*r/ 48.1%

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

      2. neg-mul-1 48.1%

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

   10. Simplified 48.1%

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

   11. Taylor expanded in z around inf 35.7%

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

       1. mul-1-neg 35.7%

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

       2. associate-*l/ 42.1%

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

       3. *-commutative 42.1%

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

   13. Simplified 42.1%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-25}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+16}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{+175}:\\ \;\;\;\;\frac{x}{t} \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 59.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-25}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+16}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{+175}:\\ \;\;\;\;x \cdot \frac{z}{-t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.8e+38)
   x
   (if (<= z 1.3e-25)
     (/ x (/ t y))
     (if (<= z 2.3e+16) x (if (<= z 1.08e+175) (* x (/ z (- t))) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.8e+38) {
		tmp = x;
	} else if (z <= 1.3e-25) {
		tmp = x / (t / y);
	} else if (z <= 2.3e+16) {
		tmp = x;
	} else if (z <= 1.08e+175) {
		tmp = x * (z / -t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2.8d+38)) then
        tmp = x
    else if (z <= 1.3d-25) then
        tmp = x / (t / y)
    else if (z <= 2.3d+16) then
        tmp = x
    else if (z <= 1.08d+175) then
        tmp = x * (z / -t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.8e+38) {
		tmp = x;
	} else if (z <= 1.3e-25) {
		tmp = x / (t / y);
	} else if (z <= 2.3e+16) {
		tmp = x;
	} else if (z <= 1.08e+175) {
		tmp = x * (z / -t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.8e+38:
		tmp = x
	elif z <= 1.3e-25:
		tmp = x / (t / y)
	elif z <= 2.3e+16:
		tmp = x
	elif z <= 1.08e+175:
		tmp = x * (z / -t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.8e+38)
		tmp = x;
	elseif (z <= 1.3e-25)
		tmp = Float64(x / Float64(t / y));
	elseif (z <= 2.3e+16)
		tmp = x;
	elseif (z <= 1.08e+175)
		tmp = Float64(x * Float64(z / Float64(-t)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.8e+38)
		tmp = x;
	elseif (z <= 1.3e-25)
		tmp = x / (t / y);
	elseif (z <= 2.3e+16)
		tmp = x;
	elseif (z <= 1.08e+175)
		tmp = x * (z / -t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.8e+38], x, If[LessEqual[z, 1.3e-25], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.3e+16], x, If[LessEqual[z, 1.08e+175], N[(x * N[(z / (-t)), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.8e38 or 1.3e-25 < z < 2.3e16 or 1.08e175 < z

   1. Initial program 68.6%

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

      1. associate-/l* 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. Add Preprocessing

   5. Taylor expanded in z around inf 66.1%

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

   if -2.8e38 < z < 1.3e-25

   1. Initial program 95.9%

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

      1. associate-/l* 94.3%

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

   3. Simplified 94.3%

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

      1. clear-num 94.3%

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

      2. un-div-inv 94.4%

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

   6. Applied egg-rr 94.4%

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

   7. Taylor expanded in z around 0 67.5%

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

   if 2.3e16 < z < 1.08e175

   1. Initial program 75.5%

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

      1. associate-/l* 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. Add Preprocessing

   5. Taylor expanded in t around inf 43.4%

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

      1. associate-/l* 52.8%

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

   7. Simplified 52.8%

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

   8. Taylor expanded in y around 0 35.7%

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

      1. mul-1-neg 35.7%

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

      2. associate-/l* 45.0%

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

      3. distribute-rgt-neg-in 45.0%

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

      4. distribute-neg-frac2 45.0%

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

   10. Simplified 45.0%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-25}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+16}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{+175}:\\ \;\;\;\;x \cdot \frac{z}{-t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 59.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-25}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{+175}:\\ \;\;\;\;\frac{x}{\frac{t}{-z}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.9e+39)
   x
   (if (<= z 1.3e-25)
     (/ x (/ t y))
     (if (<= z 8e+15) x (if (<= z 1.08e+175) (/ x (/ t (- z))) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.9e+39) {
		tmp = x;
	} else if (z <= 1.3e-25) {
		tmp = x / (t / y);
	} else if (z <= 8e+15) {
		tmp = x;
	} else if (z <= 1.08e+175) {
		tmp = x / (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 <= (-3.9d+39)) then
        tmp = x
    else if (z <= 1.3d-25) then
        tmp = x / (t / y)
    else if (z <= 8d+15) then
        tmp = x
    else if (z <= 1.08d+175) then
        tmp = x / (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 <= -3.9e+39) {
		tmp = x;
	} else if (z <= 1.3e-25) {
		tmp = x / (t / y);
	} else if (z <= 8e+15) {
		tmp = x;
	} else if (z <= 1.08e+175) {
		tmp = x / (t / -z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.9e+39:
		tmp = x
	elif z <= 1.3e-25:
		tmp = x / (t / y)
	elif z <= 8e+15:
		tmp = x
	elif z <= 1.08e+175:
		tmp = x / (t / -z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.9e+39)
		tmp = x;
	elseif (z <= 1.3e-25)
		tmp = Float64(x / Float64(t / y));
	elseif (z <= 8e+15)
		tmp = x;
	elseif (z <= 1.08e+175)
		tmp = Float64(x / Float64(t / Float64(-z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.9e+39)
		tmp = x;
	elseif (z <= 1.3e-25)
		tmp = x / (t / y);
	elseif (z <= 8e+15)
		tmp = x;
	elseif (z <= 1.08e+175)
		tmp = x / (t / -z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.9e+39], x, If[LessEqual[z, 1.3e-25], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e+15], x, If[LessEqual[z, 1.08e+175], N[(x / N[(t / (-z)), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.9000000000000001e39 or 1.3e-25 < z < 8e15 or 1.08e175 < z

   1. Initial program 68.6%

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

      1. associate-/l* 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. Add Preprocessing

   5. Taylor expanded in z around inf 66.1%

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

   if -3.9000000000000001e39 < z < 1.3e-25

   1. Initial program 95.9%

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

      1. associate-/l* 94.3%

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

   3. Simplified 94.3%

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

      1. clear-num 94.3%

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

      2. un-div-inv 94.4%

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

   6. Applied egg-rr 94.4%

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

   7. Taylor expanded in z around 0 67.5%

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

   if 8e15 < z < 1.08e175

   1. Initial program 75.5%

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

      1. associate-/l* 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. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 99.4%

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

      2. un-div-inv 99.6%

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

   6. Applied egg-rr 99.6%

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

      1. clear-num 99.4%

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

      2. inv-pow 99.4%

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

   8. Applied egg-rr 99.4%

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

      1. unpow-1 99.4%

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

   10. Simplified 99.4%

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

   11. Taylor expanded in y around 0 66.0%

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

       1. associate-*r/ 66.0%

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

       2. neg-mul-1 66.0%

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

   13. Simplified 66.0%

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

   14. Taylor expanded in t around inf 45.1%

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

       1. associate-*r/ 45.1%

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

       2. neg-mul-1 45.1%

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

   16. Simplified 45.1%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-25}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{+175}:\\ \;\;\;\;\frac{x}{\frac{t}{-z}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 70.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-85} \lor \neg \left(z \leq 1.2 \cdot 10^{-25}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.5e-85) (not (<= z 1.2e-25)))
   (* x (- 1.0 (/ y z)))
   (/ x (/ t y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.5e-85) || !(z <= 1.2e-25)) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = x / (t / y);
	}
	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-85)) .or. (.not. (z <= 1.2d-25))) then
        tmp = x * (1.0d0 - (y / z))
    else
        tmp = x / (t / y)
    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-85) || !(z <= 1.2e-25)) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = x / (t / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.5e-85) or not (z <= 1.2e-25):
		tmp = x * (1.0 - (y / z))
	else:
		tmp = x / (t / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.5e-85) || !(z <= 1.2e-25))
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(x / Float64(t / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.5e-85) || ~((z <= 1.2e-25)))
		tmp = x * (1.0 - (y / z));
	else
		tmp = x / (t / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.5e-85], N[Not[LessEqual[z, 1.2e-25]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.5000000000000001e-85 or 1.20000000000000005e-25 < z

   1. Initial program 73.0%

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

      1. associate-/l* 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. Add Preprocessing

   5. Taylor expanded in t around 0 49.3%

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

      1. mul-1-neg 49.3%

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

      2. associate-/l* 70.7%

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

      3. distribute-rgt-neg-in 70.7%

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

      4. distribute-frac-neg 70.7%

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

      5. neg-sub0 70.7%

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

      6. associate--r- 70.7%

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

      7. neg-sub0 70.7%

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

      8. +-commutative 70.7%

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

      9. sub-neg 70.7%

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

      10. div-sub 70.7%

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

      11. *-inverses 70.7%

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

   7. Simplified 70.7%

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

   if -2.5000000000000001e-85 < z < 1.20000000000000005e-25

   1. Initial program 95.4%

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

      1. associate-/l* 93.7%

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

   3. Simplified 93.7%

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

      1. clear-num 93.6%

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

      2. un-div-inv 93.7%

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

   6. Applied egg-rr 93.7%

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

   7. Taylor expanded in z around 0 72.1%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-85} \lor \neg \left(z \leq 1.2 \cdot 10^{-25}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+38} \lor \neg \left(z \leq 1.3 \cdot 10^{-25}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.8e+38) (not (<= z 1.3e-25)))
   (* x (- 1.0 (/ y z)))
   (* x (/ y (- t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.8e+38) || !(z <= 1.3e-25)) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = x * (y / (t - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-5.8d+38)) .or. (.not. (z <= 1.3d-25))) then
        tmp = x * (1.0d0 - (y / z))
    else
        tmp = x * (y / (t - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.8e+38) || !(z <= 1.3e-25)) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = x * (y / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.8e+38) or not (z <= 1.3e-25):
		tmp = x * (1.0 - (y / z))
	else:
		tmp = x * (y / (t - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.8e+38) || !(z <= 1.3e-25))
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(x * Float64(y / Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5.8e+38) || ~((z <= 1.3e-25)))
		tmp = x * (1.0 - (y / z));
	else
		tmp = x * (y / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.8e+38], N[Not[LessEqual[z, 1.3e-25]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.80000000000000013e38 or 1.3e-25 < z

   1. Initial program 70.2%

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

      1. associate-/l* 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. Add Preprocessing

   5. Taylor expanded in t around 0 49.9%

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

      1. mul-1-neg 49.9%

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

      2. associate-/l* 73.5%

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

      3. distribute-rgt-neg-in 73.5%

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

      4. distribute-frac-neg 73.5%

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

      5. neg-sub0 73.5%

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

      6. associate--r- 73.5%

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

      7. neg-sub0 73.5%

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

      8. +-commutative 73.5%

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

      9. sub-neg 73.5%

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

      10. div-sub 73.6%

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

      11. *-inverses 73.6%

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

   7. Simplified 73.6%

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

   if -5.80000000000000013e38 < z < 1.3e-25

   1. Initial program 95.9%

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

      1. associate-/l* 94.3%

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

   3. Simplified 94.3%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 81.1%

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

      1. associate-/l* 79.6%

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

   7. Simplified 79.6%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+38} \lor \neg \left(z \leq 1.3 \cdot 10^{-25}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-74} \lor \neg \left(z \leq 6.5 \cdot 10^{-69}\right):\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.8e-74) (not (<= z 6.5e-69)))
   (* x (/ z (- z t)))
   (* x (/ y (- t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.8e-74) || !(z <= 6.5e-69)) {
		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 <= (-5.8d-74)) .or. (.not. (z <= 6.5d-69))) 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 <= -5.8e-74) || !(z <= 6.5e-69)) {
		tmp = x * (z / (z - t));
	} else {
		tmp = x * (y / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.8e-74) or not (z <= 6.5e-69):
		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 <= -5.8e-74) || !(z <= 6.5e-69))
		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 <= -5.8e-74) || ~((z <= 6.5e-69)))
		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, -5.8e-74], N[Not[LessEqual[z, 6.5e-69]], $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 < -5.8e-74 or 6.49999999999999951e-69 < z

   1. Initial program 74.1%

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

      1. associate-/l* 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. Add Preprocessing

   5. Taylor expanded in y around 0 58.8%

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

      1. mul-1-neg 58.8%

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

      2. distribute-neg-frac2 58.8%

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

      3. neg-sub0 58.8%

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

      4. associate--r- 58.8%

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

      5. neg-sub0 58.8%

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

      6. +-commutative 58.8%

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

      7. sub-neg 58.8%

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

      8. associate-/l* 77.1%

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

   7. Simplified 77.1%

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

   if -5.8e-74 < z < 6.49999999999999951e-69

   1. Initial program 95.1%

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

      1. associate-/l* 93.4%

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

   3. Simplified 93.4%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 86.7%

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

      1. associate-/l* 85.0%

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

   7. Simplified 85.0%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-74} \lor \neg \left(z \leq 6.5 \cdot 10^{-69}\right):\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{-75}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-69}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -9.6e-75)
   (* x (/ z (- z t)))
   (if (<= z 6.5e-69) (* x (/ y (- t z))) (/ x (- 1.0 (/ t z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -9.6e-75) {
		tmp = x * (z / (z - t));
	} else if (z <= 6.5e-69) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x / (1.0 - (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 <= (-9.6d-75)) then
        tmp = x * (z / (z - t))
    else if (z <= 6.5d-69) then
        tmp = x * (y / (t - z))
    else
        tmp = x / (1.0d0 - (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 <= -9.6e-75) {
		tmp = x * (z / (z - t));
	} else if (z <= 6.5e-69) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x / (1.0 - (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -9.6e-75:
		tmp = x * (z / (z - t))
	elif z <= 6.5e-69:
		tmp = x * (y / (t - z))
	else:
		tmp = x / (1.0 - (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -9.6e-75)
		tmp = Float64(x * Float64(z / Float64(z - t)));
	elseif (z <= 6.5e-69)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	else
		tmp = Float64(x / Float64(1.0 - Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -9.6e-75)
		tmp = x * (z / (z - t));
	elseif (z <= 6.5e-69)
		tmp = x * (y / (t - z));
	else
		tmp = x / (1.0 - (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -9.6e-75], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e-69], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.60000000000000077e-75

   1. Initial program 75.0%

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

      1. associate-/l* 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. Add Preprocessing

   5. Taylor expanded in y around 0 60.9%

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

      1. mul-1-neg 60.9%

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

      2. distribute-neg-frac2 60.9%

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

      3. neg-sub0 60.9%

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

      4. associate--r- 60.9%

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

      5. neg-sub0 60.9%

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

      6. +-commutative 60.9%

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

      7. sub-neg 60.9%

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

      8. associate-/l* 78.0%

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

   7. Simplified 78.0%

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

   if -9.60000000000000077e-75 < z < 6.49999999999999951e-69

   1. Initial program 95.1%

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

      1. associate-/l* 93.4%

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

   3. Simplified 93.4%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 86.7%

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

      1. associate-/l* 85.0%

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

   7. Simplified 85.0%

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

   if 6.49999999999999951e-69 < z

   1. Initial program 73.2%

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

      1. remove-double-neg 73.2%

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

      2. distribute-lft-neg-out 73.2%

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

      3. distribute-neg-frac 73.2%

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

      4. distribute-neg-frac2 73.2%

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

      5. distribute-lft-neg-out 73.2%

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

      6. distribute-rgt-neg-in 73.2%

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

      7. sub-neg 73.2%

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

      8. distribute-neg-in 73.2%

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

      9. remove-double-neg 73.2%

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

      10. +-commutative 73.2%

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

      11. sub-neg 73.2%

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

      12. sub-neg 73.2%

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

      13. distribute-neg-in 73.2%

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

      14. remove-double-neg 73.2%

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

      15. +-commutative 73.2%

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

      16. sub-neg 73.2%

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

   3. Simplified 73.2%

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

      1. div-inv 72.9%

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

      2. *-commutative 72.9%

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

      3. associate-*l* 81.9%

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

   6. Applied egg-rr 81.9%

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

   7. Taylor expanded in y around 0 57.0%

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

      1. associate-*l/ 60.4%

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

      2. associate-/r/ 76.3%

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

      3. div-sub 76.3%

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

      4. *-inverses 76.3%

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

   9. Simplified 76.3%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{-75}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-69}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-74}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-66}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.8e-74)
   (* x (/ z (- z t)))
   (if (<= z 3.9e-66) (/ x (/ (- t z) y)) (/ x (- 1.0 (/ t z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.8e-74) {
		tmp = x * (z / (z - t));
	} else if (z <= 3.9e-66) {
		tmp = x / ((t - z) / y);
	} else {
		tmp = x / (1.0 - (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 <= (-5.8d-74)) then
        tmp = x * (z / (z - t))
    else if (z <= 3.9d-66) then
        tmp = x / ((t - z) / y)
    else
        tmp = x / (1.0d0 - (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 <= -5.8e-74) {
		tmp = x * (z / (z - t));
	} else if (z <= 3.9e-66) {
		tmp = x / ((t - z) / y);
	} else {
		tmp = x / (1.0 - (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.8e-74:
		tmp = x * (z / (z - t))
	elif z <= 3.9e-66:
		tmp = x / ((t - z) / y)
	else:
		tmp = x / (1.0 - (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.8e-74)
		tmp = Float64(x * Float64(z / Float64(z - t)));
	elseif (z <= 3.9e-66)
		tmp = Float64(x / Float64(Float64(t - z) / y));
	else
		tmp = Float64(x / Float64(1.0 - Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5.8e-74)
		tmp = x * (z / (z - t));
	elseif (z <= 3.9e-66)
		tmp = x / ((t - z) / y);
	else
		tmp = x / (1.0 - (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.8e-74], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.9e-66], N[(x / N[(N[(t - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.8e-74

   1. Initial program 75.0%

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

      1. associate-/l* 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. Add Preprocessing

   5. Taylor expanded in y around 0 60.9%

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

      1. mul-1-neg 60.9%

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

      2. distribute-neg-frac2 60.9%

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

      3. neg-sub0 60.9%

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

      4. associate--r- 60.9%

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

      5. neg-sub0 60.9%

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

      6. +-commutative 60.9%

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

      7. sub-neg 60.9%

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

      8. associate-/l* 78.0%

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

   7. Simplified 78.0%

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

   if -5.8e-74 < z < 3.89999999999999983e-66

   1. Initial program 95.1%

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

      1. associate-/l* 93.4%

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

   3. Simplified 93.4%

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

      1. clear-num 93.3%

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

      2. un-div-inv 93.3%

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

   6. Applied egg-rr 93.3%

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

   7. Taylor expanded in y around inf 85.0%

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

   if 3.89999999999999983e-66 < z

   1. Initial program 73.2%

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

      1. remove-double-neg 73.2%

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

      2. distribute-lft-neg-out 73.2%

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

      3. distribute-neg-frac 73.2%

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

      4. distribute-neg-frac2 73.2%

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

      5. distribute-lft-neg-out 73.2%

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

      6. distribute-rgt-neg-in 73.2%

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

      7. sub-neg 73.2%

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

      8. distribute-neg-in 73.2%

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

      9. remove-double-neg 73.2%

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

      10. +-commutative 73.2%

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

      11. sub-neg 73.2%

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

      12. sub-neg 73.2%

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

      13. distribute-neg-in 73.2%

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

      14. remove-double-neg 73.2%

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

      15. +-commutative 73.2%

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

      16. sub-neg 73.2%

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

   3. Simplified 73.2%

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

      1. div-inv 72.9%

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

      2. *-commutative 72.9%

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

      3. associate-*l* 81.9%

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

   6. Applied egg-rr 81.9%

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

   7. Taylor expanded in y around 0 57.0%

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

      1. associate-*l/ 60.4%

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

      2. associate-/r/ 76.3%

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

      3. div-sub 76.3%

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

      4. *-inverses 76.3%

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

   9. Simplified 76.3%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-74}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-66}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 74.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-74}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-67}:\\ \;\;\;\;\frac{x \cdot y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.6e-74)
   (* x (/ z (- z t)))
   (if (<= z 5.1e-67) (/ (* x y) (- t z)) (/ x (- 1.0 (/ t z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.6e-74) {
		tmp = x * (z / (z - t));
	} else if (z <= 5.1e-67) {
		tmp = (x * y) / (t - z);
	} else {
		tmp = x / (1.0 - (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 <= (-3.6d-74)) then
        tmp = x * (z / (z - t))
    else if (z <= 5.1d-67) then
        tmp = (x * y) / (t - z)
    else
        tmp = x / (1.0d0 - (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 <= -3.6e-74) {
		tmp = x * (z / (z - t));
	} else if (z <= 5.1e-67) {
		tmp = (x * y) / (t - z);
	} else {
		tmp = x / (1.0 - (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.6e-74:
		tmp = x * (z / (z - t))
	elif z <= 5.1e-67:
		tmp = (x * y) / (t - z)
	else:
		tmp = x / (1.0 - (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.6e-74)
		tmp = Float64(x * Float64(z / Float64(z - t)));
	elseif (z <= 5.1e-67)
		tmp = Float64(Float64(x * y) / Float64(t - z));
	else
		tmp = Float64(x / Float64(1.0 - Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.6e-74)
		tmp = x * (z / (z - t));
	elseif (z <= 5.1e-67)
		tmp = (x * y) / (t - z);
	else
		tmp = x / (1.0 - (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.6e-74], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.1e-67], N[(N[(x * y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.6000000000000002e-74

   1. Initial program 75.0%

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

      1. associate-/l* 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. Add Preprocessing

   5. Taylor expanded in y around 0 60.9%

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

      1. mul-1-neg 60.9%

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

      2. distribute-neg-frac2 60.9%

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

      3. neg-sub0 60.9%

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

      4. associate--r- 60.9%

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

      5. neg-sub0 60.9%

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

      6. +-commutative 60.9%

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

      7. sub-neg 60.9%

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

      8. associate-/l* 78.0%

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

   7. Simplified 78.0%

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

   if -3.6000000000000002e-74 < z < 5.09999999999999982e-67

   1. Initial program 95.1%

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

      1. associate-/l* 93.4%

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

   3. Simplified 93.4%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 86.7%

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

   if 5.09999999999999982e-67 < z

   1. Initial program 73.2%

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

      1. remove-double-neg 73.2%

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

      2. distribute-lft-neg-out 73.2%

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

      3. distribute-neg-frac 73.2%

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

      4. distribute-neg-frac2 73.2%

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

      5. distribute-lft-neg-out 73.2%

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

      6. distribute-rgt-neg-in 73.2%

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

      7. sub-neg 73.2%

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

      8. distribute-neg-in 73.2%

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

      9. remove-double-neg 73.2%

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

      10. +-commutative 73.2%

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

      11. sub-neg 73.2%

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

      12. sub-neg 73.2%

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

      13. distribute-neg-in 73.2%

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

      14. remove-double-neg 73.2%

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

      15. +-commutative 73.2%

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

      16. sub-neg 73.2%

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

   3. Simplified 73.2%

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

      1. div-inv 72.9%

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

      2. *-commutative 72.9%

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

      3. associate-*l* 81.9%

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

   6. Applied egg-rr 81.9%

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

   7. Taylor expanded in y around 0 57.0%

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

      1. associate-*l/ 60.4%

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

      2. associate-/r/ 76.3%

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

      3. div-sub 76.3%

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

      4. *-inverses 76.3%

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

   9. Simplified 76.3%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-74}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-67}:\\ \;\;\;\;\frac{x \cdot y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 61.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{-25}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.3e+38) x (if (<= z 1.16e-25) (* x (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.3e+38) {
		tmp = x;
	} else if (z <= 1.16e-25) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-5.3d+38)) then
        tmp = x
    else if (z <= 1.16d-25) then
        tmp = x * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.3e+38) {
		tmp = x;
	} else if (z <= 1.16e-25) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.3e+38:
		tmp = x
	elif z <= 1.16e-25:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.3e+38)
		tmp = x;
	elseif (z <= 1.16e-25)
		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 <= -5.3e+38)
		tmp = x;
	elseif (z <= 1.16e-25)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.3e+38], x, If[LessEqual[z, 1.16e-25], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -5.30000000000000024e38 or 1.1599999999999999e-25 < z

   1. Initial program 70.2%

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

      1. associate-/l* 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. Add Preprocessing

   5. Taylor expanded in z around inf 57.0%

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

   if -5.30000000000000024e38 < z < 1.1599999999999999e-25

   1. Initial program 95.9%

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

      1. associate-/l* 94.3%

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

   3. Simplified 94.3%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 67.5%

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

      1. associate-/l* 67.5%

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

   7. Simplified 67.5%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{-25}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 61.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-25}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.32e+39) x (if (<= z 1.3e-25) (/ x (/ t y)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.32e+39) {
		tmp = x;
	} else if (z <= 1.3e-25) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.32d+39)) then
        tmp = x
    else if (z <= 1.3d-25) then
        tmp = x / (t / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.32e+39) {
		tmp = x;
	} else if (z <= 1.3e-25) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.32e+39:
		tmp = x
	elif z <= 1.3e-25:
		tmp = x / (t / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.32e+39)
		tmp = x;
	elseif (z <= 1.3e-25)
		tmp = Float64(x / Float64(t / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.32e+39)
		tmp = x;
	elseif (z <= 1.3e-25)
		tmp = x / (t / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.32e+39], x, If[LessEqual[z, 1.3e-25], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.32e39 or 1.3e-25 < z

   1. Initial program 70.2%

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

      1. associate-/l* 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. Add Preprocessing

   5. Taylor expanded in z around inf 57.0%

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

   if -1.32e39 < z < 1.3e-25

   1. Initial program 95.9%

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

      1. associate-/l* 94.3%

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

   3. Simplified 94.3%

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

      1. clear-num 94.3%

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

      2. un-div-inv 94.4%

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

   6. Applied egg-rr 94.4%

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

   7. Taylor expanded in z around 0 67.5%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-25}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 35.6% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 82.5%

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

   1. associate-/l* 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. Add Preprocessing

5. Taylor expanded in z around inf 34.2%

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

6. Final simplification 34.2%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 97.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024078 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64

  :alt
  (/ x (/ (- t z) (- y z)))

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