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

Percentage Accurate: 84.4% → 96.3%

Time: 13.5s

Alternatives: 14

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{-13} \lor \neg \left(z \leq 1.55 \cdot 10^{-231}\right):\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.02e-13) (not (<= z 1.55e-231)))
   (* x (/ (- y z) (- t z)))
   (* (- y z) (/ x (- t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.02e-13) || !(z <= 1.55e-231)) {
		tmp = x * ((y - z) / (t - z));
	} else {
		tmp = (y - z) * (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 <= (-1.02d-13)) .or. (.not. (z <= 1.55d-231))) then
        tmp = x * ((y - z) / (t - z))
    else
        tmp = (y - z) * (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 <= -1.02e-13) || !(z <= 1.55e-231)) {
		tmp = x * ((y - z) / (t - z));
	} else {
		tmp = (y - z) * (x / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.02e-13) or not (z <= 1.55e-231):
		tmp = x * ((y - z) / (t - z))
	else:
		tmp = (y - z) * (x / (t - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.02e-13) || !(z <= 1.55e-231))
		tmp = Float64(x * Float64(Float64(y - z) / Float64(t - z)));
	else
		tmp = Float64(Float64(y - z) * Float64(x / Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.02e-13) || ~((z <= 1.55e-231)))
		tmp = x * ((y - z) / (t - z));
	else
		tmp = (y - z) * (x / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.02e-13], N[Not[LessEqual[z, 1.55e-231]], $MachinePrecision]], N[(x * N[(N[(y - z), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.0199999999999999e-13 or 1.54999999999999994e-231 < z

   1. Initial program 76.5%

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

      1. *-commutative 76.5%

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

      2. associate-*l/ 99.3%

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

      3. *-commutative 99.3%

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

   3. Simplified 99.3%

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

   if -1.0199999999999999e-13 < z < 1.54999999999999994e-231

   1. Initial program 87.3%

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

      1. associate-*l/ 99.1%

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

   3. Simplified 99.1%

      \[\leadsto \color{blue}{\frac{x}{t - z} \cdot \left(y - z\right)} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{-13} \lor \neg \left(z \leq 1.55 \cdot 10^{-231}\right):\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 69.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{t - z}\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{+24}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-232}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{-295}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ y (- t z)))))
   (if (<= z -3.8e+24)
     x
     (if (<= z -1.05e-232)
       t_1
       (if (<= z 1.52e-295)
         (* (- y z) (/ x t))
         (if (<= z 2.6e-100)
           t_1
           (if (<= z 8.5e+49) (* x (/ (- y z) t)) x)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y / (t - z));
	double tmp;
	if (z <= -3.8e+24) {
		tmp = x;
	} else if (z <= -1.05e-232) {
		tmp = t_1;
	} else if (z <= 1.52e-295) {
		tmp = (y - z) * (x / t);
	} else if (z <= 2.6e-100) {
		tmp = t_1;
	} else if (z <= 8.5e+49) {
		tmp = x * ((y - z) / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y / (t - z))
    if (z <= (-3.8d+24)) then
        tmp = x
    else if (z <= (-1.05d-232)) then
        tmp = t_1
    else if (z <= 1.52d-295) then
        tmp = (y - z) * (x / t)
    else if (z <= 2.6d-100) then
        tmp = t_1
    else if (z <= 8.5d+49) then
        tmp = x * ((y - z) / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (y / (t - z));
	double tmp;
	if (z <= -3.8e+24) {
		tmp = x;
	} else if (z <= -1.05e-232) {
		tmp = t_1;
	} else if (z <= 1.52e-295) {
		tmp = (y - z) * (x / t);
	} else if (z <= 2.6e-100) {
		tmp = t_1;
	} else if (z <= 8.5e+49) {
		tmp = x * ((y - z) / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y / (t - z))
	tmp = 0
	if z <= -3.8e+24:
		tmp = x
	elif z <= -1.05e-232:
		tmp = t_1
	elif z <= 1.52e-295:
		tmp = (y - z) * (x / t)
	elif z <= 2.6e-100:
		tmp = t_1
	elif z <= 8.5e+49:
		tmp = x * ((y - z) / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y / Float64(t - z)))
	tmp = 0.0
	if (z <= -3.8e+24)
		tmp = x;
	elseif (z <= -1.05e-232)
		tmp = t_1;
	elseif (z <= 1.52e-295)
		tmp = Float64(Float64(y - z) * Float64(x / t));
	elseif (z <= 2.6e-100)
		tmp = t_1;
	elseif (z <= 8.5e+49)
		tmp = Float64(x * Float64(Float64(y - z) / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y / (t - z));
	tmp = 0.0;
	if (z <= -3.8e+24)
		tmp = x;
	elseif (z <= -1.05e-232)
		tmp = t_1;
	elseif (z <= 1.52e-295)
		tmp = (y - z) * (x / t);
	elseif (z <= 2.6e-100)
		tmp = t_1;
	elseif (z <= 8.5e+49)
		tmp = x * ((y - z) / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.8e+24], x, If[LessEqual[z, -1.05e-232], t$95$1, If[LessEqual[z, 1.52e-295], N[(N[(y - z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e-100], t$95$1, If[LessEqual[z, 8.5e+49], N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], x]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.80000000000000015e24 or 8.4999999999999996e49 < z

   1. Initial program 65.8%

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

      1. *-commutative 65.8%

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

      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 69.0%

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

   if -3.80000000000000015e24 < z < -1.05e-232 or 1.5200000000000001e-295 < z < 2.5999999999999998e-100

   1. Initial program 88.7%

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

      1. *-commutative 88.7%

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

      2. associate-*l/ 93.8%

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

      3. *-commutative 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in y around inf 77.8%

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

   if -1.05e-232 < z < 1.5200000000000001e-295

   1. Initial program 95.4%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 99.9%

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

   if 2.5999999999999998e-100 < z < 8.4999999999999996e49

   1. Initial program 93.0%

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

      1. *-commutative 93.0%

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

      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 77.8%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+24}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-232}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{-295}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-100}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 69.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+24}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-229}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-296}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-103}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+50}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.5e+24)
   x
   (if (<= z -9.2e-229)
     (/ x (/ (- t z) y))
     (if (<= z 1.5e-296)
       (* (- y z) (/ x t))
       (if (<= z 5.5e-103)
         (* x (/ y (- t z)))
         (if (<= z 1.4e+50) (* x (/ (- y z) t)) x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.5e+24) {
		tmp = x;
	} else if (z <= -9.2e-229) {
		tmp = x / ((t - z) / y);
	} else if (z <= 1.5e-296) {
		tmp = (y - z) * (x / t);
	} else if (z <= 5.5e-103) {
		tmp = x * (y / (t - z));
	} else if (z <= 1.4e+50) {
		tmp = x * ((y - z) / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-3.5d+24)) then
        tmp = x
    else if (z <= (-9.2d-229)) then
        tmp = x / ((t - z) / y)
    else if (z <= 1.5d-296) then
        tmp = (y - z) * (x / t)
    else if (z <= 5.5d-103) then
        tmp = x * (y / (t - z))
    else if (z <= 1.4d+50) then
        tmp = x * ((y - z) / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.5e+24) {
		tmp = x;
	} else if (z <= -9.2e-229) {
		tmp = x / ((t - z) / y);
	} else if (z <= 1.5e-296) {
		tmp = (y - z) * (x / t);
	} else if (z <= 5.5e-103) {
		tmp = x * (y / (t - z));
	} else if (z <= 1.4e+50) {
		tmp = x * ((y - z) / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.5e+24:
		tmp = x
	elif z <= -9.2e-229:
		tmp = x / ((t - z) / y)
	elif z <= 1.5e-296:
		tmp = (y - z) * (x / t)
	elif z <= 5.5e-103:
		tmp = x * (y / (t - z))
	elif z <= 1.4e+50:
		tmp = x * ((y - z) / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.5e+24)
		tmp = x;
	elseif (z <= -9.2e-229)
		tmp = Float64(x / Float64(Float64(t - z) / y));
	elseif (z <= 1.5e-296)
		tmp = Float64(Float64(y - z) * Float64(x / t));
	elseif (z <= 5.5e-103)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	elseif (z <= 1.4e+50)
		tmp = Float64(x * Float64(Float64(y - z) / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.5e+24)
		tmp = x;
	elseif (z <= -9.2e-229)
		tmp = x / ((t - z) / y);
	elseif (z <= 1.5e-296)
		tmp = (y - z) * (x / t);
	elseif (z <= 5.5e-103)
		tmp = x * (y / (t - z));
	elseif (z <= 1.4e+50)
		tmp = x * ((y - z) / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.5e+24], x, If[LessEqual[z, -9.2e-229], N[(x / N[(N[(t - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e-296], N[(N[(y - z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.5e-103], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e+50], N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], x]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.5000000000000002e24 or 1.3999999999999999e50 < z

   1. Initial program 65.8%

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

      1. *-commutative 65.8%

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

      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 69.0%

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

   if -3.5000000000000002e24 < z < -9.19999999999999983e-229

   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/ 92.6%

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

      3. *-commutative 92.6%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in y around inf 72.6%

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

      1. associate-/l* 77.0%

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

   7. Simplified 77.0%

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

   if -9.19999999999999983e-229 < z < 1.4999999999999999e-296

   1. Initial program 95.4%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 99.9%

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

   if 1.4999999999999999e-296 < z < 5.50000000000000032e-103

   1. Initial program 84.4%

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

      1. *-commutative 84.4%

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

      2. associate-*l/ 95.6%

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

      3. *-commutative 95.6%

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

   3. Simplified 95.6%

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

   5. Taylor expanded in y around inf 82.4%

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

   if 5.50000000000000032e-103 < z < 1.3999999999999999e50

   1. Initial program 93.0%

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

      1. *-commutative 93.0%

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

      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 77.8%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+24}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-229}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-296}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-103}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+50}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z} \cdot \left(z - y\right)\\ \mathbf{if}\;z \leq -6.6 \cdot 10^{+156}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-6}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-103}:\\ \;\;\;\;\frac{y}{\frac{t - z}{x}}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+49}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+161}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x z) (- z y))))
   (if (<= z -6.6e+156)
     x
     (if (<= z -3.8e-6)
       t_1
       (if (<= z 1.6e-103)
         (/ y (/ (- t z) x))
         (if (<= z 6.8e+49)
           (/ (* x (- y z)) t)
           (if (<= z 3.4e+161) t_1 x)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / z) * (z - y);
	double tmp;
	if (z <= -6.6e+156) {
		tmp = x;
	} else if (z <= -3.8e-6) {
		tmp = t_1;
	} else if (z <= 1.6e-103) {
		tmp = y / ((t - z) / x);
	} else if (z <= 6.8e+49) {
		tmp = (x * (y - z)) / t;
	} else if (z <= 3.4e+161) {
		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 / z) * (z - y)
    if (z <= (-6.6d+156)) then
        tmp = x
    else if (z <= (-3.8d-6)) then
        tmp = t_1
    else if (z <= 1.6d-103) then
        tmp = y / ((t - z) / x)
    else if (z <= 6.8d+49) then
        tmp = (x * (y - z)) / t
    else if (z <= 3.4d+161) 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 / z) * (z - y);
	double tmp;
	if (z <= -6.6e+156) {
		tmp = x;
	} else if (z <= -3.8e-6) {
		tmp = t_1;
	} else if (z <= 1.6e-103) {
		tmp = y / ((t - z) / x);
	} else if (z <= 6.8e+49) {
		tmp = (x * (y - z)) / t;
	} else if (z <= 3.4e+161) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / z) * (z - y)
	tmp = 0
	if z <= -6.6e+156:
		tmp = x
	elif z <= -3.8e-6:
		tmp = t_1
	elif z <= 1.6e-103:
		tmp = y / ((t - z) / x)
	elif z <= 6.8e+49:
		tmp = (x * (y - z)) / t
	elif z <= 3.4e+161:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) * Float64(z - y))
	tmp = 0.0
	if (z <= -6.6e+156)
		tmp = x;
	elseif (z <= -3.8e-6)
		tmp = t_1;
	elseif (z <= 1.6e-103)
		tmp = Float64(y / Float64(Float64(t - z) / x));
	elseif (z <= 6.8e+49)
		tmp = Float64(Float64(x * Float64(y - z)) / t);
	elseif (z <= 3.4e+161)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) * (z - y);
	tmp = 0.0;
	if (z <= -6.6e+156)
		tmp = x;
	elseif (z <= -3.8e-6)
		tmp = t_1;
	elseif (z <= 1.6e-103)
		tmp = y / ((t - z) / x);
	elseif (z <= 6.8e+49)
		tmp = (x * (y - z)) / t;
	elseif (z <= 3.4e+161)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.6e+156], x, If[LessEqual[z, -3.8e-6], t$95$1, If[LessEqual[z, 1.6e-103], N[(y / N[(N[(t - z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e+49], N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 3.4e+161], t$95$1, x]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.5999999999999997e156 or 3.39999999999999993e161 < z

   1. Initial program 58.3%

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

      1. *-commutative 58.3%

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

      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 84.5%

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

   if -6.5999999999999997e156 < z < -3.8e-6 or 6.8000000000000001e49 < z < 3.39999999999999993e161

   1. Initial program 81.1%

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

      1. associate-*l/ 93.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in t around 0 67.8%

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

      1. associate-*r/ 67.8%

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

      2. neg-mul-1 67.8%

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

   7. Simplified 67.8%

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

   if -3.8e-6 < z < 1.59999999999999988e-103

   1. Initial program 89.5%

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

      1. *-commutative 89.5%

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

      2. associate-*l/ 90.9%

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

      3. *-commutative 90.9%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in y around inf 75.5%

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

      1. *-commutative 75.5%

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

      2. associate-/l* 81.6%

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

      3. add-cube-cbrt 80.8%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}{\frac{t - z}{x}} \]

      4. *-un-lft-identity 80.8%

         \[\leadsto \frac{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}{\color{blue}{1 \cdot \frac{t - z}{x}}} \]

      5. times-frac 80.8%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{1} \cdot \frac{\sqrt[3]{y}}{\frac{t - z}{x}}} \]

      6. pow2 80.8%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{y}\right)}^{2}}}{1} \cdot \frac{\sqrt[3]{y}}{\frac{t - z}{x}} \]

   7. Applied egg-rr 80.8%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{y}\right)}^{2}}{1} \cdot \frac{\sqrt[3]{y}}{\frac{t - z}{x}}} \]
   8. Step-by-step derivation

      1. /-rgt-identity 80.8%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{y}\right)}^{2}} \cdot \frac{\sqrt[3]{y}}{\frac{t - z}{x}} \]

      2. associate-*r/ 80.8%

         \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{y}\right)}^{2} \cdot \sqrt[3]{y}}{\frac{t - z}{x}}} \]

      3. unpow2 80.8%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)} \cdot \sqrt[3]{y}}{\frac{t - z}{x}} \]

      4. rem-3cbrt-lft 81.6%

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

   9. Simplified 81.6%

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

   if 1.59999999999999988e-103 < z < 6.8000000000000001e49

   1. Initial program 93.0%

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

      1. *-commutative 93.0%

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

      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 77.9%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+156}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-6}:\\ \;\;\;\;\frac{x}{z} \cdot \left(z - y\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-103}:\\ \;\;\;\;\frac{y}{\frac{t - z}{x}}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+49}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+161}:\\ \;\;\;\;\frac{x}{z} \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 67.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{t - z}\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{+24}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+49}:\\ \;\;\;\;\frac{-x}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+160}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ y (- t z)))))
   (if (<= z -3.8e+24)
     x
     (if (<= z 1.4e-36)
       t_1
       (if (<= z 2.7e+49) (/ (- x) (/ t z)) (if (<= z 7.8e+160) t_1 x))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y / (t - z));
	double tmp;
	if (z <= -3.8e+24) {
		tmp = x;
	} else if (z <= 1.4e-36) {
		tmp = t_1;
	} else if (z <= 2.7e+49) {
		tmp = -x / (t / z);
	} else if (z <= 7.8e+160) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y / (t - z))
    if (z <= (-3.8d+24)) then
        tmp = x
    else if (z <= 1.4d-36) then
        tmp = t_1
    else if (z <= 2.7d+49) then
        tmp = -x / (t / z)
    else if (z <= 7.8d+160) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (y / (t - z));
	double tmp;
	if (z <= -3.8e+24) {
		tmp = x;
	} else if (z <= 1.4e-36) {
		tmp = t_1;
	} else if (z <= 2.7e+49) {
		tmp = -x / (t / z);
	} else if (z <= 7.8e+160) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y / (t - z))
	tmp = 0
	if z <= -3.8e+24:
		tmp = x
	elif z <= 1.4e-36:
		tmp = t_1
	elif z <= 2.7e+49:
		tmp = -x / (t / z)
	elif z <= 7.8e+160:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y / Float64(t - z)))
	tmp = 0.0
	if (z <= -3.8e+24)
		tmp = x;
	elseif (z <= 1.4e-36)
		tmp = t_1;
	elseif (z <= 2.7e+49)
		tmp = Float64(Float64(-x) / Float64(t / z));
	elseif (z <= 7.8e+160)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y / (t - z));
	tmp = 0.0;
	if (z <= -3.8e+24)
		tmp = x;
	elseif (z <= 1.4e-36)
		tmp = t_1;
	elseif (z <= 2.7e+49)
		tmp = -x / (t / z);
	elseif (z <= 7.8e+160)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.8e+24], x, If[LessEqual[z, 1.4e-36], t$95$1, If[LessEqual[z, 2.7e+49], N[((-x) / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.8e+160], t$95$1, x]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.80000000000000015e24 or 7.80000000000000014e160 < z

   1. Initial program 63.3%

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

      1. *-commutative 63.3%

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

      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 74.6%

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

   if -3.80000000000000015e24 < z < 1.4000000000000001e-36 or 2.7000000000000001e49 < z < 7.80000000000000014e160

   1. Initial program 89.1%

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

      1. *-commutative 89.1%

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

      2. associate-*l/ 92.7%

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

      3. *-commutative 92.7%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in y around inf 73.9%

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

   if 1.4000000000000001e-36 < z < 2.7000000000000001e49

   1. Initial program 93.6%

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

      1. *-commutative 93.6%

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

      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 t around inf 80.2%

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

   6. Taylor expanded in y around 0 75.5%

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

      1. mul-1-neg 75.5%

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

      2. associate-/l* 75.4%

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

      3. distribute-neg-frac 75.4%

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

   8. Simplified 75.4%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+24}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-36}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+49}:\\ \;\;\;\;\frac{-x}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+160}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 69.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-103}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.3e+23)
   x
   (if (<= z 1.5e-103)
     (* x (/ y (- t z)))
     (if (<= z 8.5e+49) (* x (/ (- y z) t)) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.3e+23) {
		tmp = x;
	} else if (z <= 1.5e-103) {
		tmp = x * (y / (t - z));
	} else if (z <= 8.5e+49) {
		tmp = x * ((y - z) / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2.3d+23)) then
        tmp = x
    else if (z <= 1.5d-103) then
        tmp = x * (y / (t - z))
    else if (z <= 8.5d+49) then
        tmp = x * ((y - z) / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.3e+23) {
		tmp = x;
	} else if (z <= 1.5e-103) {
		tmp = x * (y / (t - z));
	} else if (z <= 8.5e+49) {
		tmp = x * ((y - z) / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.3e+23:
		tmp = x
	elif z <= 1.5e-103:
		tmp = x * (y / (t - z))
	elif z <= 8.5e+49:
		tmp = x * ((y - z) / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.3e+23)
		tmp = x;
	elseif (z <= 1.5e-103)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	elseif (z <= 8.5e+49)
		tmp = Float64(x * Float64(Float64(y - z) / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.3e+23)
		tmp = x;
	elseif (z <= 1.5e-103)
		tmp = x * (y / (t - z));
	elseif (z <= 8.5e+49)
		tmp = x * ((y - z) / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.3e+23], x, If[LessEqual[z, 1.5e-103], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e+49], N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.3e23 or 8.4999999999999996e49 < z

   1. Initial program 65.8%

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

      1. *-commutative 65.8%

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

      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 69.0%

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

   if -2.3e23 < z < 1.5e-103

   1. Initial program 89.8%

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

      1. *-commutative 89.8%

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

      2. associate-*l/ 91.1%

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

      3. *-commutative 91.1%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in y around inf 77.7%

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

   if 1.5e-103 < z < 8.4999999999999996e49

   1. Initial program 93.0%

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

      1. *-commutative 93.0%

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

      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 77.8%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-103}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+24}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-100}:\\ \;\;\;\;\frac{y}{\frac{t - z}{x}}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.8e+24)
   x
   (if (<= z 5.6e-100)
     (/ y (/ (- t z) x))
     (if (<= z 3.8e+49) (* x (/ (- y z) t)) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.8e+24) {
		tmp = x;
	} else if (z <= 5.6e-100) {
		tmp = y / ((t - z) / x);
	} else if (z <= 3.8e+49) {
		tmp = x * ((y - z) / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-3.8d+24)) then
        tmp = x
    else if (z <= 5.6d-100) then
        tmp = y / ((t - z) / x)
    else if (z <= 3.8d+49) then
        tmp = x * ((y - z) / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.8e+24) {
		tmp = x;
	} else if (z <= 5.6e-100) {
		tmp = y / ((t - z) / x);
	} else if (z <= 3.8e+49) {
		tmp = x * ((y - z) / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.8e+24:
		tmp = x
	elif z <= 5.6e-100:
		tmp = y / ((t - z) / x)
	elif z <= 3.8e+49:
		tmp = x * ((y - z) / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.8e+24)
		tmp = x;
	elseif (z <= 5.6e-100)
		tmp = Float64(y / Float64(Float64(t - z) / x));
	elseif (z <= 3.8e+49)
		tmp = Float64(x * Float64(Float64(y - z) / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.8e+24)
		tmp = x;
	elseif (z <= 5.6e-100)
		tmp = y / ((t - z) / x);
	elseif (z <= 3.8e+49)
		tmp = x * ((y - z) / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.8e+24], x, If[LessEqual[z, 5.6e-100], N[(y / N[(N[(t - z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e+49], N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.80000000000000015e24 or 3.7999999999999999e49 < z

   1. Initial program 65.8%

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

      1. *-commutative 65.8%

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

      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 69.0%

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

   if -3.80000000000000015e24 < z < 5.59999999999999991e-100

   1. Initial program 89.8%

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

      1. *-commutative 89.8%

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

      2. associate-*l/ 91.1%

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

      3. *-commutative 91.1%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in y around inf 75.3%

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

      1. *-commutative 75.3%

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

      2. associate-/l* 81.3%

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

      3. add-cube-cbrt 80.5%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}{\frac{t - z}{x}} \]

      4. *-un-lft-identity 80.5%

         \[\leadsto \frac{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}{\color{blue}{1 \cdot \frac{t - z}{x}}} \]

      5. times-frac 80.5%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{1} \cdot \frac{\sqrt[3]{y}}{\frac{t - z}{x}}} \]

      6. pow2 80.5%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{y}\right)}^{2}}}{1} \cdot \frac{\sqrt[3]{y}}{\frac{t - z}{x}} \]

   7. Applied egg-rr 80.5%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{y}\right)}^{2}}{1} \cdot \frac{\sqrt[3]{y}}{\frac{t - z}{x}}} \]
   8. Step-by-step derivation

      1. /-rgt-identity 80.5%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{y}\right)}^{2}} \cdot \frac{\sqrt[3]{y}}{\frac{t - z}{x}} \]

      2. associate-*r/ 80.5%

         \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{y}\right)}^{2} \cdot \sqrt[3]{y}}{\frac{t - z}{x}}} \]

      3. unpow2 80.5%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)} \cdot \sqrt[3]{y}}{\frac{t - z}{x}} \]

      4. rem-3cbrt-lft 81.3%

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

   9. Simplified 81.3%

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

   if 5.59999999999999991e-100 < z < 3.7999999999999999e49

   1. Initial program 93.0%

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

      1. *-commutative 93.0%

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

      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 77.8%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+24}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-100}:\\ \;\;\;\;\frac{y}{\frac{t - z}{x}}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 68.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-117}:\\ \;\;\;\;\frac{y}{\frac{t - z}{x}}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+50}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -8.5e+23)
   x
   (if (<= z 3.5e-117)
     (/ y (/ (- t z) x))
     (if (<= z 1.35e+50) (/ (* x (- y z)) t) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -8.5e+23) {
		tmp = x;
	} else if (z <= 3.5e-117) {
		tmp = y / ((t - z) / x);
	} else if (z <= 1.35e+50) {
		tmp = (x * (y - z)) / t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-8.5d+23)) then
        tmp = x
    else if (z <= 3.5d-117) then
        tmp = y / ((t - z) / x)
    else if (z <= 1.35d+50) then
        tmp = (x * (y - z)) / t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -8.5e+23) {
		tmp = x;
	} else if (z <= 3.5e-117) {
		tmp = y / ((t - z) / x);
	} else if (z <= 1.35e+50) {
		tmp = (x * (y - z)) / t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -8.5e+23:
		tmp = x
	elif z <= 3.5e-117:
		tmp = y / ((t - z) / x)
	elif z <= 1.35e+50:
		tmp = (x * (y - z)) / t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -8.5e+23)
		tmp = x;
	elseif (z <= 3.5e-117)
		tmp = Float64(y / Float64(Float64(t - z) / x));
	elseif (z <= 1.35e+50)
		tmp = Float64(Float64(x * Float64(y - z)) / t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -8.5e+23)
		tmp = x;
	elseif (z <= 3.5e-117)
		tmp = y / ((t - z) / x);
	elseif (z <= 1.35e+50)
		tmp = (x * (y - z)) / t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -8.5e+23], x, If[LessEqual[z, 3.5e-117], N[(y / N[(N[(t - z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.35e+50], N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.5000000000000001e23 or 1.35e50 < z

   1. Initial program 65.8%

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

      1. *-commutative 65.8%

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

      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 69.0%

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

   if -8.5000000000000001e23 < z < 3.4999999999999998e-117

   1. Initial program 89.8%

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

      1. *-commutative 89.8%

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

      2. associate-*l/ 91.1%

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

      3. *-commutative 91.1%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in y around inf 75.3%

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

      1. *-commutative 75.3%

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

      2. associate-/l* 81.3%

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

      3. add-cube-cbrt 80.5%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}{\frac{t - z}{x}} \]

      4. *-un-lft-identity 80.5%

         \[\leadsto \frac{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}{\color{blue}{1 \cdot \frac{t - z}{x}}} \]

      5. times-frac 80.5%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{1} \cdot \frac{\sqrt[3]{y}}{\frac{t - z}{x}}} \]

      6. pow2 80.5%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{y}\right)}^{2}}}{1} \cdot \frac{\sqrt[3]{y}}{\frac{t - z}{x}} \]

   7. Applied egg-rr 80.5%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{y}\right)}^{2}}{1} \cdot \frac{\sqrt[3]{y}}{\frac{t - z}{x}}} \]
   8. Step-by-step derivation

      1. /-rgt-identity 80.5%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{y}\right)}^{2}} \cdot \frac{\sqrt[3]{y}}{\frac{t - z}{x}} \]

      2. associate-*r/ 80.5%

         \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{y}\right)}^{2} \cdot \sqrt[3]{y}}{\frac{t - z}{x}}} \]

      3. unpow2 80.5%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)} \cdot \sqrt[3]{y}}{\frac{t - z}{x}} \]

      4. rem-3cbrt-lft 81.3%

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

   9. Simplified 81.3%

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

   if 3.4999999999999998e-117 < z < 1.35e50

   1. Initial program 93.0%

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

      1. *-commutative 93.0%

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

      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 77.9%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-117}:\\ \;\;\;\;\frac{y}{\frac{t - z}{x}}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+50}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 61.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-8}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-37}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+50}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.8e-8)
   x
   (if (<= z 3.1e-37) (* y (/ x t)) (if (<= z 1.6e+50) (* x (/ (- z) t)) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.8e-8) {
		tmp = x;
	} else if (z <= 3.1e-37) {
		tmp = y * (x / t);
	} else if (z <= 1.6e+50) {
		tmp = x * (-z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-4.8d-8)) then
        tmp = x
    else if (z <= 3.1d-37) then
        tmp = y * (x / t)
    else if (z <= 1.6d+50) then
        tmp = x * (-z / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.8e-8) {
		tmp = x;
	} else if (z <= 3.1e-37) {
		tmp = y * (x / t);
	} else if (z <= 1.6e+50) {
		tmp = x * (-z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.8e-8:
		tmp = x
	elif z <= 3.1e-37:
		tmp = y * (x / t)
	elif z <= 1.6e+50:
		tmp = x * (-z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.8e-8)
		tmp = x;
	elseif (z <= 3.1e-37)
		tmp = Float64(y * Float64(x / t));
	elseif (z <= 1.6e+50)
		tmp = Float64(x * Float64(Float64(-z) / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.8e-8)
		tmp = x;
	elseif (z <= 3.1e-37)
		tmp = y * (x / t);
	elseif (z <= 1.6e+50)
		tmp = x * (-z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.8e-8], x, If[LessEqual[z, 3.1e-37], N[(y * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e+50], N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.79999999999999997e-8 or 1.59999999999999991e50 < z

   1. Initial program 67.0%

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

      1. *-commutative 67.0%

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

      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 z around inf 67.5%

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

   if -4.79999999999999997e-8 < z < 3.09999999999999993e-37

   1. Initial program 89.8%

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

      1. *-commutative 89.8%

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

      2. associate-*l/ 91.7%

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

      3. *-commutative 91.7%

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

   3. Simplified 91.7%

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

      1. add-cube-cbrt 90.6%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \frac{y - z}{t - z}} \cdot \sqrt[3]{x \cdot \frac{y - z}{t - z}}\right) \cdot \sqrt[3]{x \cdot \frac{y - z}{t - z}}} \]

      2. pow3 90.6%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \frac{y - z}{t - z}}\right)}^{3}} \]

   6. Applied egg-rr 90.6%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \frac{y - z}{t - z}}\right)}^{3}} \]

   7. Taylor expanded in z around 0 58.5%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \frac{x \cdot y}{t}} \]
   8. Step-by-step derivation

      1. pow-base-1 58.5%

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

      2. *-lft-identity 58.5%

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

      3. associate-/l* 61.6%

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

      4. associate-/r/ 63.5%

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

   9. Simplified 63.5%

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

   if 3.09999999999999993e-37 < z < 1.59999999999999991e50

   1. Initial program 93.6%

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

      1. *-commutative 93.6%

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

      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 t around inf 80.2%

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

   6. Taylor expanded in y around 0 75.3%

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

      1. neg-mul-1 75.3%

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

   8. Simplified 75.3%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-8}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-37}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+50}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-8}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-37}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+50}:\\ \;\;\;\;\frac{-x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -6e-8)
   x
   (if (<= z 2.25e-37) (* y (/ x t)) (if (<= z 1.7e+50) (/ (- x) (/ t z)) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6e-8) {
		tmp = x;
	} else if (z <= 2.25e-37) {
		tmp = y * (x / t);
	} else if (z <= 1.7e+50) {
		tmp = -x / (t / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-6d-8)) then
        tmp = x
    else if (z <= 2.25d-37) then
        tmp = y * (x / t)
    else if (z <= 1.7d+50) then
        tmp = -x / (t / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6e-8) {
		tmp = x;
	} else if (z <= 2.25e-37) {
		tmp = y * (x / t);
	} else if (z <= 1.7e+50) {
		tmp = -x / (t / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -6e-8:
		tmp = x
	elif z <= 2.25e-37:
		tmp = y * (x / t)
	elif z <= 1.7e+50:
		tmp = -x / (t / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6e-8)
		tmp = x;
	elseif (z <= 2.25e-37)
		tmp = Float64(y * Float64(x / t));
	elseif (z <= 1.7e+50)
		tmp = Float64(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 <= -6e-8)
		tmp = x;
	elseif (z <= 2.25e-37)
		tmp = y * (x / t);
	elseif (z <= 1.7e+50)
		tmp = -x / (t / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -6e-8], x, If[LessEqual[z, 2.25e-37], N[(y * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e+50], N[((-x) / N[(t / z), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.99999999999999946e-8 or 1.6999999999999999e50 < z

   1. Initial program 67.0%

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

      1. *-commutative 67.0%

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

      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 z around inf 67.5%

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

   if -5.99999999999999946e-8 < z < 2.2500000000000002e-37

   1. Initial program 89.8%

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

      1. *-commutative 89.8%

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

      2. associate-*l/ 91.7%

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

      3. *-commutative 91.7%

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

   3. Simplified 91.7%

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

      1. add-cube-cbrt 90.6%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \frac{y - z}{t - z}} \cdot \sqrt[3]{x \cdot \frac{y - z}{t - z}}\right) \cdot \sqrt[3]{x \cdot \frac{y - z}{t - z}}} \]

      2. pow3 90.6%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \frac{y - z}{t - z}}\right)}^{3}} \]

   6. Applied egg-rr 90.6%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \frac{y - z}{t - z}}\right)}^{3}} \]

   7. Taylor expanded in z around 0 58.5%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \frac{x \cdot y}{t}} \]
   8. Step-by-step derivation

      1. pow-base-1 58.5%

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

      2. *-lft-identity 58.5%

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

      3. associate-/l* 61.6%

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

      4. associate-/r/ 63.5%

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

   9. Simplified 63.5%

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

   if 2.2500000000000002e-37 < z < 1.6999999999999999e50

   1. Initial program 93.6%

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

      1. *-commutative 93.6%

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

      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 t around inf 80.2%

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

   6. Taylor expanded in y around 0 75.5%

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

      1. mul-1-neg 75.5%

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

      2. associate-/l* 75.4%

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

      3. distribute-neg-frac 75.4%

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

   8. Simplified 75.4%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-8}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-37}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+50}:\\ \;\;\;\;\frac{-x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 62.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -165000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-20}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -165000000.0) x (if (<= z 5.1e-20) (* x (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -165000000.0) {
		tmp = x;
	} else if (z <= 5.1e-20) {
		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 <= (-165000000.0d0)) then
        tmp = x
    else if (z <= 5.1d-20) 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 <= -165000000.0) {
		tmp = x;
	} else if (z <= 5.1e-20) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -165000000.0:
		tmp = x
	elif z <= 5.1e-20:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -165000000.0)
		tmp = x;
	elseif (z <= 5.1e-20)
		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 <= -165000000.0)
		tmp = x;
	elseif (z <= 5.1e-20)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -165000000.0], x, If[LessEqual[z, 5.1e-20], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.65e8 or 5.10000000000000019e-20 < z

   1. Initial program 68.7%

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

      1. *-commutative 68.7%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 63.5%

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

   if -1.65e8 < z < 5.10000000000000019e-20

   1. Initial program 90.2%

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

      1. *-commutative 90.2%

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

      2. associate-*l/ 92.1%

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

      3. *-commutative 92.1%

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

   3. Simplified 92.1%

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

   5. Taylor expanded in z around 0 61.3%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -165000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-20}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 61.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-20}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.05e-7) x (if (<= z 9.6e-20) (* y (/ x t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.05e-7) {
		tmp = x;
	} else if (z <= 9.6e-20) {
		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 <= (-1.05d-7)) then
        tmp = x
    else if (z <= 9.6d-20) 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 <= -1.05e-7) {
		tmp = x;
	} else if (z <= 9.6e-20) {
		tmp = y * (x / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.05e-7:
		tmp = x
	elif z <= 9.6e-20:
		tmp = y * (x / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.05e-7)
		tmp = x;
	elseif (z <= 9.6e-20)
		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 <= -1.05e-7)
		tmp = x;
	elseif (z <= 9.6e-20)
		tmp = y * (x / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.05e-7], x, If[LessEqual[z, 9.6e-20], N[(y * N[(x / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.05e-7 or 9.59999999999999971e-20 < z

   1. Initial program 69.0%

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

      1. *-commutative 69.0%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 63.0%

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

   if -1.05e-7 < z < 9.59999999999999971e-20

   1. Initial program 90.1%

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

      1. *-commutative 90.1%

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

      2. associate-*l/ 92.0%

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

      3. *-commutative 92.0%

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

   3. Simplified 92.0%

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

      1. add-cube-cbrt 90.9%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \frac{y - z}{t - z}} \cdot \sqrt[3]{x \cdot \frac{y - z}{t - z}}\right) \cdot \sqrt[3]{x \cdot \frac{y - z}{t - z}}} \]

      2. pow3 90.9%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \frac{y - z}{t - z}}\right)}^{3}} \]

   6. Applied egg-rr 90.9%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \frac{y - z}{t - z}}\right)}^{3}} \]

   7. Taylor expanded in z around 0 57.9%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \frac{x \cdot y}{t}} \]
   8. Step-by-step derivation

      1. pow-base-1 57.9%

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

      2. *-lft-identity 57.9%

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

      3. associate-/l* 60.9%

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

      4. associate-/r/ 62.7%

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

   9. Simplified 62.7%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-20}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 97.1% 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 80.3%

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

   1. *-commutative 80.3%

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

   2. associate-*l/ 95.6%

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

   3. *-commutative 95.6%

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

3. Simplified 95.6%

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

5. Final simplification 95.6%

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

Alternative 14: 36.0% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 80.3%

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

   1. *-commutative 80.3%

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

   2. associate-*l/ 95.6%

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

   3. *-commutative 95.6%

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

3. Simplified 95.6%

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

5. Taylor expanded in z around inf 35.6%

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

6. Final simplification 35.6%

   \[\leadsto x \]
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 2024021 
(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)))