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

Percentage Accurate: 84.5% → 97.2%

Time: 8.4s

Alternatives: 9

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: 84.5% 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 86.8%

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

   1. associate-/l* 98.1%

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

3. Simplified 98.1%

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

5. Final simplification 98.1%

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

Alternative 2: 60.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{+91}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -0.00116:\\ \;\;\;\;x \cdot \frac{y}{-z}\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-35}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 950000:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.32e+91)
   x
   (if (<= z -0.00116)
     (* x (/ y (- z)))
     (if (<= z -4.7e-35) x (if (<= z 950000.0) (* x (/ y t)) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.32e+91) {
		tmp = x;
	} else if (z <= -0.00116) {
		tmp = x * (y / -z);
	} else if (z <= -4.7e-35) {
		tmp = x;
	} else if (z <= 950000.0) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.32d+91)) then
        tmp = x
    else if (z <= (-0.00116d0)) then
        tmp = x * (y / -z)
    else if (z <= (-4.7d-35)) then
        tmp = x
    else if (z <= 950000.0d0) then
        tmp = x * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.32e+91) {
		tmp = x;
	} else if (z <= -0.00116) {
		tmp = x * (y / -z);
	} else if (z <= -4.7e-35) {
		tmp = x;
	} else if (z <= 950000.0) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.32e+91:
		tmp = x
	elif z <= -0.00116:
		tmp = x * (y / -z)
	elif z <= -4.7e-35:
		tmp = x
	elif z <= 950000.0:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.32e+91)
		tmp = x;
	elseif (z <= -0.00116)
		tmp = Float64(x * Float64(y / Float64(-z)));
	elseif (z <= -4.7e-35)
		tmp = x;
	elseif (z <= 950000.0)
		tmp = Float64(x * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.32e+91)
		tmp = x;
	elseif (z <= -0.00116)
		tmp = x * (y / -z);
	elseif (z <= -4.7e-35)
		tmp = x;
	elseif (z <= 950000.0)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.32e+91], x, If[LessEqual[z, -0.00116], N[(x * N[(y / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.7e-35], x, If[LessEqual[z, 950000.0], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.32000000000000003e91 or -0.00116 < z < -4.7e-35 or 9.5e5 < z

   1. Initial program 75.0%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 70.7%

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

   if -1.32000000000000003e91 < z < -0.00116

   1. Initial program 86.3%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 99.6%

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

      2. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in y around inf 54.7%

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

      1. associate-*l/ 59.4%

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

      2. *-commutative 59.4%

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

   9. Simplified 59.4%

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

   10. Taylor expanded in t around 0 45.0%

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

       1. mul-1-neg 45.0%

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

       2. associate-/l* 45.0%

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

       3. distribute-rgt-neg-in 45.0%

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

   12. Simplified 45.0%

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

   if -4.7e-35 < z < 9.5e5

   1. Initial program 95.4%

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

      1. associate-/l* 96.5%

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

   3. Simplified 96.5%

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

   5. Taylor expanded in z around 0 64.1%

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

      1. associate-/l* 65.5%

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

   7. Simplified 65.5%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{+91}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -0.00116:\\ \;\;\;\;x \cdot \frac{y}{-z}\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-35}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 950000:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 60.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{+91}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -0.000102:\\ \;\;\;\;\frac{x \cdot y}{-z}\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-34}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 410000:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.32e+91)
   x
   (if (<= z -0.000102)
     (/ (* x y) (- z))
     (if (<= z -1.05e-34) x (if (<= z 410000.0) (* x (/ y t)) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.32e+91) {
		tmp = x;
	} else if (z <= -0.000102) {
		tmp = (x * y) / -z;
	} else if (z <= -1.05e-34) {
		tmp = x;
	} else if (z <= 410000.0) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.32d+91)) then
        tmp = x
    else if (z <= (-0.000102d0)) then
        tmp = (x * y) / -z
    else if (z <= (-1.05d-34)) then
        tmp = x
    else if (z <= 410000.0d0) then
        tmp = x * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.32e+91) {
		tmp = x;
	} else if (z <= -0.000102) {
		tmp = (x * y) / -z;
	} else if (z <= -1.05e-34) {
		tmp = x;
	} else if (z <= 410000.0) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.32e+91:
		tmp = x
	elif z <= -0.000102:
		tmp = (x * y) / -z
	elif z <= -1.05e-34:
		tmp = x
	elif z <= 410000.0:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.32e+91)
		tmp = x;
	elseif (z <= -0.000102)
		tmp = Float64(Float64(x * y) / Float64(-z));
	elseif (z <= -1.05e-34)
		tmp = x;
	elseif (z <= 410000.0)
		tmp = Float64(x * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.32e+91)
		tmp = x;
	elseif (z <= -0.000102)
		tmp = (x * y) / -z;
	elseif (z <= -1.05e-34)
		tmp = x;
	elseif (z <= 410000.0)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.32e+91], x, If[LessEqual[z, -0.000102], N[(N[(x * y), $MachinePrecision] / (-z)), $MachinePrecision], If[LessEqual[z, -1.05e-34], x, If[LessEqual[z, 410000.0], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.32000000000000003e91 or -1.01999999999999999e-4 < z < -1.05e-34 or 4.1e5 < z

   1. Initial program 75.0%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 70.7%

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

   if -1.32000000000000003e91 < z < -1.01999999999999999e-4

   1. Initial program 86.3%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 99.6%

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

      2. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in y around inf 54.7%

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

      1. associate-*l/ 59.4%

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

      2. *-commutative 59.4%

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

   9. Simplified 59.4%

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

   10. Taylor expanded in t around 0 45.0%

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

       1. associate-*r/ 45.0%

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

       2. mul-1-neg 45.0%

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

       3. distribute-rgt-neg-out 45.0%

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

   12. Simplified 45.0%

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

   if -1.05e-34 < z < 4.1e5

   1. Initial program 95.4%

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

      1. associate-/l* 96.5%

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

   3. Simplified 96.5%

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

   5. Taylor expanded in z around 0 64.1%

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

      1. associate-/l* 65.5%

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

   7. Simplified 65.5%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{+91}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -0.000102:\\ \;\;\;\;\frac{x \cdot y}{-z}\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-34}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 410000:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 70.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-89} \lor \neg \left(z \leq 290000\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.2e-89) (not (<= z 290000.0)))
   (* x (- 1.0 (/ y z)))
   (* x (/ y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.2e-89) || !(z <= 290000.0)) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = x * (y / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-3.2d-89)) .or. (.not. (z <= 290000.0d0))) then
        tmp = x * (1.0d0 - (y / z))
    else
        tmp = x * (y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.2e-89) || !(z <= 290000.0)) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = x * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.2e-89) or not (z <= 290000.0):
		tmp = x * (1.0 - (y / z))
	else:
		tmp = x * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.2e-89) || !(z <= 290000.0))
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(x * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.2e-89) || ~((z <= 290000.0)))
		tmp = x * (1.0 - (y / z));
	else
		tmp = x * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.2e-89], N[Not[LessEqual[z, 290000.0]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.19999999999999998e-89 or 2.9e5 < z

   1. Initial program 78.8%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 58.4%

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

      1. mul-1-neg 58.4%

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

      2. associate-/l* 72.7%

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

      3. distribute-rgt-neg-in 72.7%

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

      4. distribute-frac-neg 72.7%

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

      5. neg-sub0 72.7%

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

      6. associate--r- 72.7%

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

      7. neg-sub0 72.7%

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

      8. +-commutative 72.7%

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

      9. sub-neg 72.7%

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

      10. div-sub 72.7%

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

      11. *-inverses 72.7%

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

   7. Simplified 72.7%

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

   if -3.19999999999999998e-89 < z < 2.9e5

   1. Initial program 95.7%

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

      1. associate-/l* 96.1%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in z around 0 68.1%

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

      1. associate-/l* 68.9%

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

   7. Simplified 68.9%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-89} \lor \neg \left(z \leq 290000\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0034 \lor \neg \left(y \leq 2.1 \cdot 10^{-56}\right):\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -0.0034) (not (<= y 2.1e-56)))
   (* y (/ x (- t z)))
   (* x (/ z (- z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -0.0034) || !(y <= 2.1e-56)) {
		tmp = y * (x / (t - z));
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-0.0034d0)) .or. (.not. (y <= 2.1d-56))) then
        tmp = y * (x / (t - z))
    else
        tmp = x * (z / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -0.0034) || !(y <= 2.1e-56)) {
		tmp = y * (x / (t - z));
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -0.0034) or not (y <= 2.1e-56):
		tmp = y * (x / (t - z))
	else:
		tmp = x * (z / (z - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -0.0034) || !(y <= 2.1e-56))
		tmp = Float64(y * Float64(x / Float64(t - z)));
	else
		tmp = Float64(x * Float64(z / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -0.0034) || ~((y <= 2.1e-56)))
		tmp = y * (x / (t - z));
	else
		tmp = x * (z / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -0.0034], N[Not[LessEqual[y, 2.1e-56]], $MachinePrecision]], N[(y * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.00339999999999999981 or 2.10000000000000006e-56 < y

   1. Initial program 88.9%

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

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

      1. clear-num 97.5%

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

      2. un-div-inv 97.6%

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

   6. Applied egg-rr 97.6%

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

   7. Taylor expanded in y around inf 75.2%

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

      1. associate-*l/ 74.2%

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

      2. *-commutative 74.2%

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

   9. Simplified 74.2%

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

   if -0.00339999999999999981 < y < 2.10000000000000006e-56

   1. Initial program 84.6%

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

      1. associate-/l* 98.6%

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

   3. Simplified 98.6%

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

   5. Taylor expanded in y around 0 71.3%

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

      1. mul-1-neg 71.3%

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

      2. distribute-neg-frac2 71.3%

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

      3. neg-sub0 71.3%

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

      4. associate--r- 71.3%

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

      5. neg-sub0 71.3%

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

      6. +-commutative 71.3%

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

      7. sub-neg 71.3%

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

      8. associate-/l* 84.4%

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

   7. Simplified 84.4%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0034 \lor \neg \left(y \leq 2.1 \cdot 10^{-56}\right):\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00335 \lor \neg \left(y \leq 6 \cdot 10^{-56}\right):\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -0.00335) (not (<= y 6e-56)))
   (/ x (/ (- t z) y))
   (* x (/ z (- z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -0.00335) || !(y <= 6e-56)) {
		tmp = x / ((t - z) / y);
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-0.00335d0)) .or. (.not. (y <= 6d-56))) then
        tmp = x / ((t - z) / y)
    else
        tmp = x * (z / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -0.00335) || !(y <= 6e-56)) {
		tmp = x / ((t - z) / y);
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -0.00335) or not (y <= 6e-56):
		tmp = x / ((t - z) / y)
	else:
		tmp = x * (z / (z - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -0.00335) || !(y <= 6e-56))
		tmp = Float64(x / Float64(Float64(t - z) / y));
	else
		tmp = Float64(x * Float64(z / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -0.00335) || ~((y <= 6e-56)))
		tmp = x / ((t - z) / y);
	else
		tmp = x * (z / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -0.00335], N[Not[LessEqual[y, 6e-56]], $MachinePrecision]], N[(x / N[(N[(t - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.00335000000000000011 or 5.99999999999999979e-56 < y

   1. Initial program 88.9%

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

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

      1. clear-num 97.5%

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

      2. un-div-inv 97.6%

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

   6. Applied egg-rr 97.6%

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

   7. Taylor expanded in y around inf 80.9%

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

   if -0.00335000000000000011 < y < 5.99999999999999979e-56

   1. Initial program 84.6%

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

      1. associate-/l* 98.6%

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

   3. Simplified 98.6%

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

   5. Taylor expanded in y around 0 71.3%

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

      1. mul-1-neg 71.3%

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

      2. distribute-neg-frac2 71.3%

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

      3. neg-sub0 71.3%

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

      4. associate--r- 71.3%

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

      5. neg-sub0 71.3%

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

      6. +-commutative 71.3%

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

      7. sub-neg 71.3%

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

      8. associate-/l* 84.4%

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

   7. Simplified 84.4%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00335 \lor \neg \left(y \leq 6 \cdot 10^{-56}\right):\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-89}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-18}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.9e-89)
   (* x (- 1.0 (/ y z)))
   (if (<= z 1.1e-18) (* x (/ y t)) (* x (/ z (- z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.9e-89) {
		tmp = x * (1.0 - (y / z));
	} else if (z <= 1.1e-18) {
		tmp = x * (y / t);
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.9d-89)) then
        tmp = x * (1.0d0 - (y / z))
    else if (z <= 1.1d-18) then
        tmp = x * (y / t)
    else
        tmp = x * (z / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.9e-89) {
		tmp = x * (1.0 - (y / z));
	} else if (z <= 1.1e-18) {
		tmp = x * (y / t);
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.9e-89:
		tmp = x * (1.0 - (y / z))
	elif z <= 1.1e-18:
		tmp = x * (y / t)
	else:
		tmp = x * (z / (z - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.9e-89)
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	elseif (z <= 1.1e-18)
		tmp = Float64(x * Float64(y / t));
	else
		tmp = Float64(x * Float64(z / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.9e-89)
		tmp = x * (1.0 - (y / z));
	elseif (z <= 1.1e-18)
		tmp = x * (y / t);
	else
		tmp = x * (z / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.9e-89], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.1e-18], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.9000000000000001e-89

   1. Initial program 80.8%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 60.2%

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

      1. mul-1-neg 60.2%

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

      2. associate-/l* 70.3%

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

      3. distribute-rgt-neg-in 70.3%

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

      4. distribute-frac-neg 70.3%

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

      5. neg-sub0 70.3%

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

      6. associate--r- 70.3%

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

      7. neg-sub0 70.3%

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

      8. +-commutative 70.3%

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

      9. sub-neg 70.3%

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

      10. div-sub 70.4%

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

      11. *-inverses 70.4%

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

   7. Simplified 70.4%

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

   if -1.9000000000000001e-89 < z < 1.0999999999999999e-18

   1. Initial program 96.2%

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

      1. associate-/l* 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in z around 0 71.6%

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

      1. associate-/l* 71.6%

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

   7. Simplified 71.6%

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

   if 1.0999999999999999e-18 < z

   1. Initial program 77.5%

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

      1. associate-/l* 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in y around 0 66.5%

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

      1. mul-1-neg 66.5%

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

      2. distribute-neg-frac2 66.5%

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

      3. neg-sub0 66.5%

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

      4. associate--r- 66.5%

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

      5. neg-sub0 66.5%

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

      6. +-commutative 66.5%

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

      7. sub-neg 66.5%

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

      8. associate-/l* 83.7%

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

   7. Simplified 83.7%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-89}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-18}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-34}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 43000:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.2e-34) x (if (<= z 43000.0) (* x (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.2e-34) {
		tmp = x;
	} else if (z <= 43000.0) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.2d-34)) then
        tmp = x
    else if (z <= 43000.0d0) then
        tmp = x * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.2e-34) {
		tmp = x;
	} else if (z <= 43000.0) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.2e-34:
		tmp = x
	elif z <= 43000.0:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.2e-34)
		tmp = x;
	elseif (z <= 43000.0)
		tmp = Float64(x * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.2e-34)
		tmp = x;
	elseif (z <= 43000.0)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.2e-34], x, If[LessEqual[z, 43000.0], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.19999999999999996e-34 or 43000 < z

   1. Initial program 77.0%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 62.2%

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

   if -1.19999999999999996e-34 < z < 43000

   1. Initial program 95.4%

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

      1. associate-/l* 96.5%

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

   3. Simplified 96.5%

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

   5. Taylor expanded in z around 0 64.1%

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

      1. associate-/l* 65.5%

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

   7. Simplified 65.5%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-34}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 43000:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 34.1% 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 86.8%

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

   1. associate-/l* 98.1%

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

3. Simplified 98.1%

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

5. Taylor expanded in z around inf 34.1%

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

6. Final simplification 34.1%

   \[\leadsto x \]
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 2024130 
(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)))