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

Percentage Accurate: 84.0% → 96.9%

Time: 9.4s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.2%

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

   1. *-commutative 85.2%

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

   2. associate-*l/ 97.2%

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

   3. *-commutative 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: 74.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+31} \lor \neg \left(z \leq -1.02 \cdot 10^{-72}\right) \land \left(z \leq -1.2 \cdot 10^{-90} \lor \neg \left(z \leq 5800000000\right)\right):\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -8.2e+31)
         (and (not (<= z -1.02e-72))
              (or (<= z -1.2e-90) (not (<= z 5800000000.0)))))
   (/ x (- 1.0 (/ t z)))
   (* y (/ x (- t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8.2e+31) || (!(z <= -1.02e-72) && ((z <= -1.2e-90) || !(z <= 5800000000.0)))) {
		tmp = x / (1.0 - (t / z));
	} else {
		tmp = y * (x / (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 <= (-8.2d+31)) .or. (.not. (z <= (-1.02d-72))) .and. (z <= (-1.2d-90)) .or. (.not. (z <= 5800000000.0d0))) then
        tmp = x / (1.0d0 - (t / z))
    else
        tmp = y * (x / (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 <= -8.2e+31) || (!(z <= -1.02e-72) && ((z <= -1.2e-90) || !(z <= 5800000000.0)))) {
		tmp = x / (1.0 - (t / z));
	} else {
		tmp = y * (x / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -8.2e+31) or (not (z <= -1.02e-72) and ((z <= -1.2e-90) or not (z <= 5800000000.0))):
		tmp = x / (1.0 - (t / z))
	else:
		tmp = y * (x / (t - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -8.2e+31) || (!(z <= -1.02e-72) && ((z <= -1.2e-90) || !(z <= 5800000000.0))))
		tmp = Float64(x / Float64(1.0 - Float64(t / z)));
	else
		tmp = Float64(y * Float64(x / Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -8.2e+31) || (~((z <= -1.02e-72)) && ((z <= -1.2e-90) || ~((z <= 5800000000.0)))))
		tmp = x / (1.0 - (t / z));
	else
		tmp = y * (x / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -8.2e+31], And[N[Not[LessEqual[z, -1.02e-72]], $MachinePrecision], Or[LessEqual[z, -1.2e-90], N[Not[LessEqual[z, 5800000000.0]], $MachinePrecision]]]], N[(x / N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.2000000000000003e31 or -1.02e-72 < z < -1.2000000000000001e-90 or 5.8e9 < z

   1. Initial program 77.0%

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

      1. *-commutative 77.0%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 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 y around 0 63.9%

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

      1. mul-1-neg 63.9%

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

      2. associate-/l* 83.7%

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

      3. distribute-neg-frac 83.7%

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

      4. div-sub 83.8%

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

      5. *-inverses 83.8%

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

   7. Simplified 83.8%

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

      1. frac-2neg 83.8%

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

      2. div-inv 83.7%

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

      3. remove-double-neg 83.7%

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

      4. sub-neg 83.7%

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

      5. metadata-eval 83.7%

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

      6. distribute-neg-in 83.7%

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

      7. metadata-eval 83.7%

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

   9. Applied egg-rr 83.7%

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

       1. associate-*r/ 83.8%

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

       2. *-rgt-identity 83.8%

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

       3. +-commutative 83.8%

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

       4. unsub-neg 83.8%

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

   11. Simplified 83.8%

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

   if -8.2000000000000003e31 < z < -1.02e-72 or -1.2000000000000001e-90 < z < 5.8e9

   1. Initial program 92.8%

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

      1. *-commutative 92.8%

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

      2. associate-*l/ 94.6%

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

      3. *-commutative 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in y around inf 78.9%

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

      1. associate-*l/ 82.3%

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

      2. *-commutative 82.3%

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

   7. Simplified 82.3%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+31} \lor \neg \left(z \leq -1.02 \cdot 10^{-72}\right) \land \left(z \leq -1.2 \cdot 10^{-90} \lor \neg \left(z \leq 5800000000\right)\right):\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 66.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y - z}{t}\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{+83}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.5:\\ \;\;\;\;y \cdot \left(-\frac{x}{z}\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+76}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (- y z) t))))
   (if (<= z -9.5e+83)
     x
     (if (<= z 1.1e-46)
       t_1
       (if (<= z 7.5) (* y (- (/ x z))) (if (<= z 3.5e+76) t_1 x))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y - z) / t);
	double tmp;
	if (z <= -9.5e+83) {
		tmp = x;
	} else if (z <= 1.1e-46) {
		tmp = t_1;
	} else if (z <= 7.5) {
		tmp = y * -(x / z);
	} else if (z <= 3.5e+76) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y - z) / t)
    if (z <= (-9.5d+83)) then
        tmp = x
    else if (z <= 1.1d-46) then
        tmp = t_1
    else if (z <= 7.5d0) then
        tmp = y * -(x / z)
    else if (z <= 3.5d+76) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((y - z) / t);
	double tmp;
	if (z <= -9.5e+83) {
		tmp = x;
	} else if (z <= 1.1e-46) {
		tmp = t_1;
	} else if (z <= 7.5) {
		tmp = y * -(x / z);
	} else if (z <= 3.5e+76) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y - z) / t)
	tmp = 0
	if z <= -9.5e+83:
		tmp = x
	elif z <= 1.1e-46:
		tmp = t_1
	elif z <= 7.5:
		tmp = y * -(x / z)
	elif z <= 3.5e+76:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y - z) / t))
	tmp = 0.0
	if (z <= -9.5e+83)
		tmp = x;
	elseif (z <= 1.1e-46)
		tmp = t_1;
	elseif (z <= 7.5)
		tmp = Float64(y * Float64(-Float64(x / z)));
	elseif (z <= 3.5e+76)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y - z) / t);
	tmp = 0.0;
	if (z <= -9.5e+83)
		tmp = x;
	elseif (z <= 1.1e-46)
		tmp = t_1;
	elseif (z <= 7.5)
		tmp = y * -(x / z);
	elseif (z <= 3.5e+76)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.5e+83], x, If[LessEqual[z, 1.1e-46], t$95$1, If[LessEqual[z, 7.5], N[(y * (-N[(x / z), $MachinePrecision])), $MachinePrecision], If[LessEqual[z, 3.5e+76], t$95$1, x]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.5000000000000002e83 or 3.5e76 < z

   1. Initial program 72.9%

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

      1. *-commutative 72.9%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 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 70.8%

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

   if -9.5000000000000002e83 < z < 1.1e-46 or 7.5 < z < 3.5e76

   1. Initial program 91.8%

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

      1. *-commutative 91.8%

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

      2. associate-*l/ 95.3%

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

      3. *-commutative 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in t around inf 77.2%

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

   if 1.1e-46 < z < 7.5

   1. Initial program 99.5%

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

      1. *-commutative 99.5%

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

      2. associate-*l/ 99.4%

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

      3. *-commutative 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in y around inf 81.2%

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

   6. Taylor expanded in t around 0 71.5%

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

      1. associate-*r/ 71.5%

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

      2. mul-1-neg 71.5%

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

      3. distribute-rgt-neg-in 71.5%

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

   8. Simplified 71.5%

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

   9. Taylor expanded in x around 0 71.5%

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

       1. mul-1-neg 71.5%

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

       2. associate-*l/ 71.7%

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

       3. *-commutative 71.7%

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

   11. Simplified 71.7%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+83}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-46}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{elif}\;z \leq 7.5:\\ \;\;\;\;y \cdot \left(-\frac{x}{z}\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+76}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 58.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+45}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-100}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-57}:\\ \;\;\;\;\frac{y}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 8.5:\\ \;\;\;\;y \cdot \left(-\frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.8e+45)
   x
   (if (<= z -2.3e-100)
     (* x (/ (- z) t))
     (if (<= z 3.2e-57) (/ y (/ t x)) (if (<= z 8.5) (* y (- (/ x z))) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.8e+45) {
		tmp = x;
	} else if (z <= -2.3e-100) {
		tmp = x * (-z / t);
	} else if (z <= 3.2e-57) {
		tmp = y / (t / x);
	} else if (z <= 8.5) {
		tmp = y * -(x / 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 <= (-3.8d+45)) then
        tmp = x
    else if (z <= (-2.3d-100)) then
        tmp = x * (-z / t)
    else if (z <= 3.2d-57) then
        tmp = y / (t / x)
    else if (z <= 8.5d0) then
        tmp = y * -(x / 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 <= -3.8e+45) {
		tmp = x;
	} else if (z <= -2.3e-100) {
		tmp = x * (-z / t);
	} else if (z <= 3.2e-57) {
		tmp = y / (t / x);
	} else if (z <= 8.5) {
		tmp = y * -(x / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.8e+45:
		tmp = x
	elif z <= -2.3e-100:
		tmp = x * (-z / t)
	elif z <= 3.2e-57:
		tmp = y / (t / x)
	elif z <= 8.5:
		tmp = y * -(x / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.8e+45)
		tmp = x;
	elseif (z <= -2.3e-100)
		tmp = Float64(x * Float64(Float64(-z) / t));
	elseif (z <= 3.2e-57)
		tmp = Float64(y / Float64(t / x));
	elseif (z <= 8.5)
		tmp = Float64(y * Float64(-Float64(x / z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.8e+45)
		tmp = x;
	elseif (z <= -2.3e-100)
		tmp = x * (-z / t);
	elseif (z <= 3.2e-57)
		tmp = y / (t / x);
	elseif (z <= 8.5)
		tmp = y * -(x / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.8e+45], x, If[LessEqual[z, -2.3e-100], N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e-57], N[(y / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5], N[(y * (-N[(x / z), $MachinePrecision])), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.8000000000000002e45 or 8.5 < z

   1. Initial program 75.3%

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

      1. *-commutative 75.3%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 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 63.7%

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

   if -3.8000000000000002e45 < z < -2.29999999999999994e-100

   1. Initial program 96.6%

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

      1. *-commutative 96.6%

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

      2. associate-*l/ 99.6%

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

      3. *-commutative 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 65.0%

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

   6. Taylor expanded in y around 0 45.1%

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

      1. neg-mul-1 45.1%

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

      2. distribute-neg-frac 45.1%

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

   8. Simplified 45.1%

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

   if -2.29999999999999994e-100 < z < 3.2000000000000001e-57

   1. Initial program 91.6%

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

      1. *-commutative 91.6%

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

      2. associate-*l/ 94.1%

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

      3. *-commutative 94.1%

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

   3. Simplified 94.1%

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

   5. Taylor expanded in z around 0 78.3%

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

      1. associate-*r/ 76.8%

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

      2. *-commutative 76.8%

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

      3. associate-/l* 81.3%

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

   7. Applied egg-rr 81.3%

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

   if 3.2000000000000001e-57 < z < 8.5

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*l/ 90.7%

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

      3. *-commutative 90.7%

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

   3. Simplified 90.7%

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

   5. Taylor expanded in y around inf 74.0%

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

   6. Taylor expanded in t around 0 65.3%

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

      1. associate-*r/ 65.3%

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

      2. mul-1-neg 65.3%

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

      3. distribute-rgt-neg-in 65.3%

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

   8. Simplified 65.3%

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

   9. Taylor expanded in x around 0 65.3%

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

       1. mul-1-neg 65.3%

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

       2. associate-*l/ 65.4%

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

       3. *-commutative 65.4%

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

   11. Simplified 65.4%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+45}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-100}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-57}:\\ \;\;\;\;\frac{y}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 8.5:\\ \;\;\;\;y \cdot \left(-\frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 58.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+45}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-100}:\\ \;\;\;\;\frac{z}{\frac{-t}{x}}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-57}:\\ \;\;\;\;\frac{y}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 7.2:\\ \;\;\;\;y \cdot \left(-\frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.8e+45)
   x
   (if (<= z -1.4e-100)
     (/ z (/ (- t) x))
     (if (<= z 5e-57) (/ y (/ t x)) (if (<= z 7.2) (* y (- (/ x z))) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.8e+45) {
		tmp = x;
	} else if (z <= -1.4e-100) {
		tmp = z / (-t / x);
	} else if (z <= 5e-57) {
		tmp = y / (t / x);
	} else if (z <= 7.2) {
		tmp = y * -(x / 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 <= (-3.8d+45)) then
        tmp = x
    else if (z <= (-1.4d-100)) then
        tmp = z / (-t / x)
    else if (z <= 5d-57) then
        tmp = y / (t / x)
    else if (z <= 7.2d0) then
        tmp = y * -(x / 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 <= -3.8e+45) {
		tmp = x;
	} else if (z <= -1.4e-100) {
		tmp = z / (-t / x);
	} else if (z <= 5e-57) {
		tmp = y / (t / x);
	} else if (z <= 7.2) {
		tmp = y * -(x / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.8e+45:
		tmp = x
	elif z <= -1.4e-100:
		tmp = z / (-t / x)
	elif z <= 5e-57:
		tmp = y / (t / x)
	elif z <= 7.2:
		tmp = y * -(x / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.8e+45)
		tmp = x;
	elseif (z <= -1.4e-100)
		tmp = Float64(z / Float64(Float64(-t) / x));
	elseif (z <= 5e-57)
		tmp = Float64(y / Float64(t / x));
	elseif (z <= 7.2)
		tmp = Float64(y * Float64(-Float64(x / z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.8e+45)
		tmp = x;
	elseif (z <= -1.4e-100)
		tmp = z / (-t / x);
	elseif (z <= 5e-57)
		tmp = y / (t / x);
	elseif (z <= 7.2)
		tmp = y * -(x / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.8e+45], x, If[LessEqual[z, -1.4e-100], N[(z / N[((-t) / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e-57], N[(y / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.2], N[(y * (-N[(x / z), $MachinePrecision])), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.8000000000000002e45 or 7.20000000000000018 < z

   1. Initial program 75.3%

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

      1. *-commutative 75.3%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 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 63.7%

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

   if -3.8000000000000002e45 < z < -1.39999999999999998e-100

   1. Initial program 96.6%

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

      1. *-commutative 96.6%

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

      2. associate-*l/ 99.6%

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

      3. *-commutative 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 65.0%

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

   6. Taylor expanded in y around 0 45.1%

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

      1. neg-mul-1 45.1%

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

      2. distribute-neg-frac 45.1%

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

   8. Simplified 45.1%

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

      1. *-commutative 45.1%

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

      2. div-inv 45.2%

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

      3. associate-*l* 45.2%

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

      4. add-sqr-sqrt 45.1%

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

      5. sqrt-unprod 45.2%

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

      6. sqr-neg 45.2%

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

      7. sqrt-unprod 0.0%

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

      8. add-sqr-sqrt 13.8%

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

      9. associate-/r/ 13.8%

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

      10. div-inv 13.8%

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

      11. frac-2neg 13.8%

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

      12. add-sqr-sqrt 13.8%

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

      13. sqrt-unprod 13.8%

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

      14. sqr-neg 13.8%

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

      15. sqrt-unprod 0.0%

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

      16. add-sqr-sqrt 45.2%

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

      17. distribute-neg-frac 45.2%

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

   10. Applied egg-rr 45.2%

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

   if -1.39999999999999998e-100 < z < 5.0000000000000002e-57

   1. Initial program 91.6%

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

      1. *-commutative 91.6%

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

      2. associate-*l/ 94.1%

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

      3. *-commutative 94.1%

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

   3. Simplified 94.1%

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

   5. Taylor expanded in z around 0 78.3%

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

      1. associate-*r/ 76.8%

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

      2. *-commutative 76.8%

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

      3. associate-/l* 81.3%

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

   7. Applied egg-rr 81.3%

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

   if 5.0000000000000002e-57 < z < 7.20000000000000018

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*l/ 90.7%

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

      3. *-commutative 90.7%

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

   3. Simplified 90.7%

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

   5. Taylor expanded in y around inf 74.0%

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

   6. Taylor expanded in t around 0 65.3%

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

      1. associate-*r/ 65.3%

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

      2. mul-1-neg 65.3%

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

      3. distribute-rgt-neg-in 65.3%

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

   8. Simplified 65.3%

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

   9. Taylor expanded in x around 0 65.3%

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

       1. mul-1-neg 65.3%

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

       2. associate-*l/ 65.4%

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

       3. *-commutative 65.4%

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

   11. Simplified 65.4%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+45}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-100}:\\ \;\;\;\;\frac{z}{\frac{-t}{x}}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-57}:\\ \;\;\;\;\frac{y}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 7.2:\\ \;\;\;\;y \cdot \left(-\frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 58.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+45}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-100}:\\ \;\;\;\;\frac{-x}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-57}:\\ \;\;\;\;\frac{y}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 6.5:\\ \;\;\;\;y \cdot \left(-\frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.8e+45)
   x
   (if (<= z -2.3e-100)
     (/ (- x) (/ t z))
     (if (<= z 3.8e-57) (/ y (/ t x)) (if (<= z 6.5) (* y (- (/ x z))) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.8e+45) {
		tmp = x;
	} else if (z <= -2.3e-100) {
		tmp = -x / (t / z);
	} else if (z <= 3.8e-57) {
		tmp = y / (t / x);
	} else if (z <= 6.5) {
		tmp = y * -(x / 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 <= (-3.8d+45)) then
        tmp = x
    else if (z <= (-2.3d-100)) then
        tmp = -x / (t / z)
    else if (z <= 3.8d-57) then
        tmp = y / (t / x)
    else if (z <= 6.5d0) then
        tmp = y * -(x / 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 <= -3.8e+45) {
		tmp = x;
	} else if (z <= -2.3e-100) {
		tmp = -x / (t / z);
	} else if (z <= 3.8e-57) {
		tmp = y / (t / x);
	} else if (z <= 6.5) {
		tmp = y * -(x / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.8e+45:
		tmp = x
	elif z <= -2.3e-100:
		tmp = -x / (t / z)
	elif z <= 3.8e-57:
		tmp = y / (t / x)
	elif z <= 6.5:
		tmp = y * -(x / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.8e+45)
		tmp = x;
	elseif (z <= -2.3e-100)
		tmp = Float64(Float64(-x) / Float64(t / z));
	elseif (z <= 3.8e-57)
		tmp = Float64(y / Float64(t / x));
	elseif (z <= 6.5)
		tmp = Float64(y * Float64(-Float64(x / z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.8e+45)
		tmp = x;
	elseif (z <= -2.3e-100)
		tmp = -x / (t / z);
	elseif (z <= 3.8e-57)
		tmp = y / (t / x);
	elseif (z <= 6.5)
		tmp = y * -(x / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.8e+45], x, If[LessEqual[z, -2.3e-100], N[((-x) / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e-57], N[(y / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5], N[(y * (-N[(x / z), $MachinePrecision])), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.8000000000000002e45 or 6.5 < z

   1. Initial program 75.3%

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

      1. *-commutative 75.3%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 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 63.7%

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

   if -3.8000000000000002e45 < z < -2.29999999999999994e-100

   1. Initial program 96.6%

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

      1. *-commutative 96.6%

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

      2. associate-*l/ 99.6%

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

      3. *-commutative 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 65.0%

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

   6. Taylor expanded in y around 0 45.3%

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

      1. mul-1-neg 45.3%

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

      2. associate-/l* 45.3%

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

      3. distribute-neg-frac 45.3%

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

   8. Simplified 45.3%

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

   if -2.29999999999999994e-100 < z < 3.7999999999999997e-57

   1. Initial program 91.6%

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

      1. *-commutative 91.6%

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

      2. associate-*l/ 94.1%

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

      3. *-commutative 94.1%

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

   3. Simplified 94.1%

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

   5. Taylor expanded in z around 0 78.3%

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

      1. associate-*r/ 76.8%

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

      2. *-commutative 76.8%

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

      3. associate-/l* 81.3%

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

   7. Applied egg-rr 81.3%

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

   if 3.7999999999999997e-57 < z < 6.5

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*l/ 90.7%

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

      3. *-commutative 90.7%

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

   3. Simplified 90.7%

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

   5. Taylor expanded in y around inf 74.0%

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

   6. Taylor expanded in t around 0 65.3%

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

      1. associate-*r/ 65.3%

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

      2. mul-1-neg 65.3%

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

      3. distribute-rgt-neg-in 65.3%

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

   8. Simplified 65.3%

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

   9. Taylor expanded in x around 0 65.3%

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

       1. mul-1-neg 65.3%

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

       2. associate-*l/ 65.4%

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

       3. *-commutative 65.4%

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

   11. Simplified 65.4%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+45}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-100}:\\ \;\;\;\;\frac{-x}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-57}:\\ \;\;\;\;\frac{y}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 6.5:\\ \;\;\;\;y \cdot \left(-\frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+82}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-95}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{elif}\;z \leq 8300000000:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.1e+82)
   x
   (if (<= z -2.6e-95)
     (* x (/ (- y z) t))
     (if (<= z 8300000000.0) (* y (/ x (- t z))) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.1e+82) {
		tmp = x;
	} else if (z <= -2.6e-95) {
		tmp = x * ((y - z) / t);
	} else if (z <= 8300000000.0) {
		tmp = y * (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 <= (-3.1d+82)) then
        tmp = x
    else if (z <= (-2.6d-95)) then
        tmp = x * ((y - z) / t)
    else if (z <= 8300000000.0d0) then
        tmp = y * (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 <= -3.1e+82) {
		tmp = x;
	} else if (z <= -2.6e-95) {
		tmp = x * ((y - z) / t);
	} else if (z <= 8300000000.0) {
		tmp = y * (x / (t - z));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.1e+82:
		tmp = x
	elif z <= -2.6e-95:
		tmp = x * ((y - z) / t)
	elif z <= 8300000000.0:
		tmp = y * (x / (t - z))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.1e+82)
		tmp = x;
	elseif (z <= -2.6e-95)
		tmp = Float64(x * Float64(Float64(y - z) / t));
	elseif (z <= 8300000000.0)
		tmp = Float64(y * Float64(x / Float64(t - z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.1e+82)
		tmp = x;
	elseif (z <= -2.6e-95)
		tmp = x * ((y - z) / t);
	elseif (z <= 8300000000.0)
		tmp = y * (x / (t - z));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.1e+82], x, If[LessEqual[z, -2.6e-95], N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8300000000.0], N[(y * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.10000000000000032e82 or 8.3e9 < z

   1. Initial program 73.2%

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

      1. *-commutative 73.2%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 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 67.4%

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

   if -3.10000000000000032e82 < z < -2.60000000000000001e-95

   1. Initial program 94.8%

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

      1. *-commutative 94.8%

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

      2. associate-*l/ 99.7%

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

      3. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around inf 63.1%

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

   if -2.60000000000000001e-95 < z < 8.3e9

   1. Initial program 92.6%

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

      1. *-commutative 92.6%

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

      2. associate-*l/ 94.0%

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

      3. *-commutative 94.0%

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

   3. Simplified 94.0%

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

   5. Taylor expanded in y around inf 80.6%

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

      1. associate-*l/ 83.7%

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

      2. *-commutative 83.7%

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

   7. Simplified 83.7%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+82}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-95}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{elif}\;z \leq 8300000000:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 60.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+45}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-45}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 3.8:\\ \;\;\;\;y \cdot \left(-\frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.8e+45)
   x
   (if (<= z 4.7e-45) (/ x (/ t y)) (if (<= z 3.8) (* y (- (/ x z))) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.8e+45) {
		tmp = x;
	} else if (z <= 4.7e-45) {
		tmp = x / (t / y);
	} else if (z <= 3.8) {
		tmp = y * -(x / 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 <= (-3.8d+45)) then
        tmp = x
    else if (z <= 4.7d-45) then
        tmp = x / (t / y)
    else if (z <= 3.8d0) then
        tmp = y * -(x / 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 <= -3.8e+45) {
		tmp = x;
	} else if (z <= 4.7e-45) {
		tmp = x / (t / y);
	} else if (z <= 3.8) {
		tmp = y * -(x / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.8e+45:
		tmp = x
	elif z <= 4.7e-45:
		tmp = x / (t / y)
	elif z <= 3.8:
		tmp = y * -(x / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.8e+45)
		tmp = x;
	elseif (z <= 4.7e-45)
		tmp = Float64(x / Float64(t / y));
	elseif (z <= 3.8)
		tmp = Float64(y * Float64(-Float64(x / z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.8e+45)
		tmp = x;
	elseif (z <= 4.7e-45)
		tmp = x / (t / y);
	elseif (z <= 3.8)
		tmp = y * -(x / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.8e+45], x, If[LessEqual[z, 4.7e-45], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8], N[(y * (-N[(x / z), $MachinePrecision])), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.8000000000000002e45 or 3.7999999999999998 < z

   1. Initial program 75.3%

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

      1. *-commutative 75.3%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 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 63.7%

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

   if -3.8000000000000002e45 < z < 4.6999999999999998e-45

   1. Initial program 92.7%

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

      1. *-commutative 92.7%

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

      2. associate-*l/ 94.6%

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

      3. *-commutative 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in z around 0 66.0%

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

      1. associate-/l* 69.8%

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

   7. Simplified 69.8%

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

   if 4.6999999999999998e-45 < z < 3.7999999999999998

   1. Initial program 99.5%

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

      1. *-commutative 99.5%

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

      2. associate-*l/ 99.4%

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

      3. *-commutative 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in y around inf 81.2%

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

   6. Taylor expanded in t around 0 71.5%

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

      1. associate-*r/ 71.5%

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

      2. mul-1-neg 71.5%

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

      3. distribute-rgt-neg-in 71.5%

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

   8. Simplified 71.5%

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

   9. Taylor expanded in x around 0 71.5%

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

       1. mul-1-neg 71.5%

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

       2. associate-*l/ 71.7%

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

       3. *-commutative 71.7%

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

   11. Simplified 71.7%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+45}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-45}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 3.8:\\ \;\;\;\;y \cdot \left(-\frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+45}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-16}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.8e+45) x (if (<= z 2.1e-16) (* x (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.8e+45) {
		tmp = x;
	} else if (z <= 2.1e-16) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-3.8d+45)) then
        tmp = x
    else if (z <= 2.1d-16) then
        tmp = x * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.8e+45) {
		tmp = x;
	} else if (z <= 2.1e-16) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.8e+45:
		tmp = x
	elif z <= 2.1e-16:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.8e+45)
		tmp = x;
	elseif (z <= 2.1e-16)
		tmp = Float64(x * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.8e+45)
		tmp = x;
	elseif (z <= 2.1e-16)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.8e+45], x, If[LessEqual[z, 2.1e-16], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -3.8000000000000002e45 or 2.1000000000000001e-16 < z

   1. Initial program 76.9%

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

      1. *-commutative 76.9%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 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 61.3%

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

   if -3.8000000000000002e45 < z < 2.1000000000000001e-16

   1. Initial program 92.8%

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

      1. *-commutative 92.8%

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

      2. associate-*l/ 94.6%

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

      3. *-commutative 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in z around 0 67.6%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+45}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-16}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+45}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-16}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.8e+45) x (if (<= z 3.4e-16) (* y (/ x t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.8e+45) {
		tmp = x;
	} else if (z <= 3.4e-16) {
		tmp = y * (x / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-3.8d+45)) then
        tmp = x
    else if (z <= 3.4d-16) then
        tmp = y * (x / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.8e+45) {
		tmp = x;
	} else if (z <= 3.4e-16) {
		tmp = y * (x / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.8e+45:
		tmp = x
	elif z <= 3.4e-16:
		tmp = y * (x / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.8e+45)
		tmp = x;
	elseif (z <= 3.4e-16)
		tmp = Float64(y * Float64(x / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.8e+45)
		tmp = x;
	elseif (z <= 3.4e-16)
		tmp = y * (x / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.8e+45], x, If[LessEqual[z, 3.4e-16], N[(y * N[(x / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -3.8000000000000002e45 or 3.4e-16 < z

   1. Initial program 76.9%

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

      1. *-commutative 76.9%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 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 61.3%

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

   if -3.8000000000000002e45 < z < 3.4e-16

   1. Initial program 92.8%

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

      1. *-commutative 92.8%

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

      2. associate-*l/ 94.6%

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

      3. *-commutative 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in z around 0 65.8%

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

      1. associate-/l* 69.5%

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

   7. Simplified 69.5%

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

      1. associate-/r/ 69.2%

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

   9. Applied egg-rr 69.2%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+45}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-16}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+45}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.8e+45) x (if (<= z 3.7e-16) (/ x (/ t y)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.8e+45) {
		tmp = x;
	} else if (z <= 3.7e-16) {
		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 <= (-3.8d+45)) then
        tmp = x
    else if (z <= 3.7d-16) 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 <= -3.8e+45) {
		tmp = x;
	} else if (z <= 3.7e-16) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.8e+45:
		tmp = x
	elif z <= 3.7e-16:
		tmp = x / (t / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.8e+45)
		tmp = x;
	elseif (z <= 3.7e-16)
		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 <= -3.8e+45)
		tmp = x;
	elseif (z <= 3.7e-16)
		tmp = x / (t / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.8e+45], x, If[LessEqual[z, 3.7e-16], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -3.8000000000000002e45 or 3.7e-16 < z

   1. Initial program 76.9%

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

      1. *-commutative 76.9%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 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 61.3%

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

   if -3.8000000000000002e45 < z < 3.7e-16

   1. Initial program 92.8%

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

      1. *-commutative 92.8%

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

      2. associate-*l/ 94.6%

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

      3. *-commutative 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in z around 0 65.8%

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

      1. associate-/l* 69.5%

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

   7. Simplified 69.5%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+45}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 34.8% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.2%

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

   1. *-commutative 85.2%

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

   2. associate-*l/ 97.2%

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

   3. *-commutative 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 34.9%

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

6. Final simplification 34.9%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024011 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (/ x (/ (- t z) (- y z)))

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