Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D

Percentage Accurate: 92.9% → 98.0%

Time: 9.8s

Alternatives: 17

Speedup: 1.0×

• 25.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

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 - x)) / t)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 92.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 - x)) / t)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.1 \cdot 10^{-46}:\\ \;\;\;\;x + \frac{z - x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - x}{t}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 3.1e-46) (+ x (/ (- z x) (/ t y))) (fma y (/ (- z x) t) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 3.1e-46) {
		tmp = x + ((z - x) / (t / y));
	} else {
		tmp = fma(y, ((z - x) / t), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 3.1e-46)
		tmp = Float64(x + Float64(Float64(z - x) / Float64(t / y)));
	else
		tmp = fma(y, Float64(Float64(z - x) / t), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 3.1e-46], N[(x + N[(N[(z - x), $MachinePrecision] / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z - x), $MachinePrecision] / t), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.1000000000000001e-46

   1. Initial program 96.7%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 95.6%

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

      1. mul-1-neg 95.6%

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

      2. associate-/l* 94.4%

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

      3. distribute-lft-neg-in 94.4%

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

      4. *-commutative 94.4%

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

      5. associate-*r/ 93.0%

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

      6. distribute-rgt-in 97.1%

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

      7. +-commutative 97.1%

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

      8. sub-neg 97.1%

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

   5. Simplified 97.1%

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

   6. Taylor expanded in y around 0 96.7%

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

      1. associate-*r/ 86.3%

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

      2. *-commutative 86.3%

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

      3. associate-/r/ 97.2%

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

   8. Simplified 97.2%

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

   if 3.1000000000000001e-46 < y

   1. Initial program 89.9%

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

      1. +-commutative 89.9%

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

      2. associate-/l* 99.8%

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

      3. fma-define 99.8%

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

   3. Simplified 99.8%

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

Alternative 2: 73.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-59} \lor \neg \left(x \leq 1.35 \cdot 10^{-89}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -5.8e-59) (not (<= x 1.35e-89)))
   (* x (- 1.0 (/ y t)))
   (/ (* y z) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5.8e-59) || !(x <= 1.35e-89)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = (y * z) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-5.8d-59)) .or. (.not. (x <= 1.35d-89))) then
        tmp = x * (1.0d0 - (y / t))
    else
        tmp = (y * z) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5.8e-59) || !(x <= 1.35e-89)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = (y * z) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -5.8e-59) or not (x <= 1.35e-89):
		tmp = x * (1.0 - (y / t))
	else:
		tmp = (y * z) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -5.8e-59) || !(x <= 1.35e-89))
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = Float64(Float64(y * z) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -5.8e-59) || ~((x <= 1.35e-89)))
		tmp = x * (1.0 - (y / t));
	else
		tmp = (y * z) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -5.8e-59], N[Not[LessEqual[x, 1.35e-89]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.80000000000000033e-59 or 1.34999999999999994e-89 < x

   1. Initial program 93.0%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 82.8%

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

      1. mul-1-neg 82.8%

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

      2. unsub-neg 82.8%

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

   5. Simplified 82.8%

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

   if -5.80000000000000033e-59 < x < 1.34999999999999994e-89

   1. Initial program 96.5%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 81.6%

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

   4. Taylor expanded in z around inf 72.3%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-59} \lor \neg \left(x \leq 1.35 \cdot 10^{-89}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-104}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-100}:\\ \;\;\;\;\frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -8.5e-104)
   (+ x (* z (/ y t)))
   (if (<= t 1.02e-100) (/ (* y (- z x)) t) (+ x (* y (/ z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -8.5e-104) {
		tmp = x + (z * (y / t));
	} else if (t <= 1.02e-100) {
		tmp = (y * (z - x)) / t;
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-8.5d-104)) then
        tmp = x + (z * (y / t))
    else if (t <= 1.02d-100) then
        tmp = (y * (z - x)) / t
    else
        tmp = x + (y * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -8.5e-104) {
		tmp = x + (z * (y / t));
	} else if (t <= 1.02e-100) {
		tmp = (y * (z - x)) / t;
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -8.5e-104:
		tmp = x + (z * (y / t))
	elif t <= 1.02e-100:
		tmp = (y * (z - x)) / t
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -8.5e-104)
		tmp = Float64(x + Float64(z * Float64(y / t)));
	elseif (t <= 1.02e-100)
		tmp = Float64(Float64(y * Float64(z - x)) / t);
	else
		tmp = Float64(x + Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -8.5e-104)
		tmp = x + (z * (y / t));
	elseif (t <= 1.02e-100)
		tmp = (y * (z - x)) / t;
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -8.5e-104], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.02e-100], N[(N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.50000000000000007e-104

   1. Initial program 88.3%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 88.2%

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

      1. mul-1-neg 88.2%

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

      2. associate-/l* 92.0%

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

      3. distribute-lft-neg-in 92.0%

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

      4. *-commutative 92.0%

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

      5. associate-*r/ 98.5%

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

      6. distribute-rgt-in 99.8%

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

      7. +-commutative 99.8%

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

      8. sub-neg 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in z around inf 86.4%

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

   if -8.50000000000000007e-104 < t < 1.02e-100

   1. Initial program 98.3%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 91.0%

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

   if 1.02e-100 < t

   1. Initial program 95.3%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 84.0%

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

      1. associate-/l* 86.2%

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

   5. Simplified 86.2%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-104}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-100}:\\ \;\;\;\;\frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{-43}:\\ \;\;\;\;x \cdot \frac{t - y}{t}\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+113}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -3.7e-43)
   (* x (/ (- t y) t))
   (if (<= x 3.1e+113) (+ x (/ (* y z) t)) (* x (- 1.0 (/ y t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.7e-43) {
		tmp = x * ((t - y) / t);
	} else if (x <= 3.1e+113) {
		tmp = x + ((y * z) / t);
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-3.7d-43)) then
        tmp = x * ((t - y) / t)
    else if (x <= 3.1d+113) then
        tmp = x + ((y * z) / t)
    else
        tmp = x * (1.0d0 - (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.7e-43) {
		tmp = x * ((t - y) / t);
	} else if (x <= 3.1e+113) {
		tmp = x + ((y * z) / t);
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -3.7e-43:
		tmp = x * ((t - y) / t)
	elif x <= 3.1e+113:
		tmp = x + ((y * z) / t)
	else:
		tmp = x * (1.0 - (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -3.7e-43)
		tmp = Float64(x * Float64(Float64(t - y) / t));
	elseif (x <= 3.1e+113)
		tmp = Float64(x + Float64(Float64(y * z) / t));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -3.7e-43)
		tmp = x * ((t - y) / t);
	elseif (x <= 3.1e+113)
		tmp = x + ((y * z) / t);
	else
		tmp = x * (1.0 - (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -3.7e-43], N[(x * N[(N[(t - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.1e+113], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.7e-43

   1. Initial program 93.6%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 87.3%

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

      1. mul-1-neg 87.3%

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

      2. unsub-neg 87.3%

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

   5. Simplified 87.3%

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

   6. Taylor expanded in t around 0 87.3%

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

   if -3.7e-43 < x < 3.09999999999999991e113

   1. Initial program 95.4%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 85.0%

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

   if 3.09999999999999991e113 < x

   1. Initial program 92.8%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 90.2%

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

      1. mul-1-neg 90.2%

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

      2. unsub-neg 90.2%

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

   5. Simplified 90.2%

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

Alternative 5: 84.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{-43}:\\ \;\;\;\;x \cdot \frac{t - y}{t}\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+113}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -4.4e-43)
   (* x (/ (- t y) t))
   (if (<= x 9.5e+113) (+ x (/ z (/ t y))) (* x (- 1.0 (/ y t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.4e-43) {
		tmp = x * ((t - y) / t);
	} else if (x <= 9.5e+113) {
		tmp = x + (z / (t / y));
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-4.4d-43)) then
        tmp = x * ((t - y) / t)
    else if (x <= 9.5d+113) then
        tmp = x + (z / (t / y))
    else
        tmp = x * (1.0d0 - (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.4e-43) {
		tmp = x * ((t - y) / t);
	} else if (x <= 9.5e+113) {
		tmp = x + (z / (t / y));
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -4.4e-43:
		tmp = x * ((t - y) / t)
	elif x <= 9.5e+113:
		tmp = x + (z / (t / y))
	else:
		tmp = x * (1.0 - (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -4.4e-43)
		tmp = Float64(x * Float64(Float64(t - y) / t));
	elseif (x <= 9.5e+113)
		tmp = Float64(x + Float64(z / Float64(t / y)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -4.4e-43)
		tmp = x * ((t - y) / t);
	elseif (x <= 9.5e+113)
		tmp = x + (z / (t / y));
	else
		tmp = x * (1.0 - (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -4.4e-43], N[(x * N[(N[(t - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.5e+113], N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.39999999999999994e-43

   1. Initial program 93.6%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 87.3%

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

      1. mul-1-neg 87.3%

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

      2. unsub-neg 87.3%

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

   5. Simplified 87.3%

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

   6. Taylor expanded in t around 0 87.3%

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

   if -4.39999999999999994e-43 < x < 9.5000000000000001e113

   1. Initial program 95.4%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 93.9%

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

      1. mul-1-neg 93.9%

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

      2. associate-/l* 84.4%

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

      3. distribute-lft-neg-in 84.4%

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

      4. *-commutative 84.4%

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

      5. associate-*r/ 87.3%

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

      6. distribute-rgt-in 91.9%

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

      7. +-commutative 91.9%

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

      8. sub-neg 91.9%

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

   5. Simplified 91.9%

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

   6. Taylor expanded in y around 0 95.4%

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

      1. associate-*r/ 93.5%

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

      2. *-commutative 93.5%

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

      3. associate-/r/ 91.9%

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

   8. Simplified 91.9%

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

   9. Taylor expanded in z around inf 83.9%

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

   if 9.5000000000000001e113 < x

   1. Initial program 92.8%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 90.2%

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

      1. mul-1-neg 90.2%

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

      2. unsub-neg 90.2%

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

   5. Simplified 90.2%

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

Alternative 6: 84.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{-43}:\\ \;\;\;\;x \cdot \frac{t - y}{t}\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+113}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -3.7e-43)
   (* x (/ (- t y) t))
   (if (<= x 3e+113) (+ x (* z (/ y t))) (* x (- 1.0 (/ y t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.7e-43) {
		tmp = x * ((t - y) / t);
	} else if (x <= 3e+113) {
		tmp = x + (z * (y / t));
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-3.7d-43)) then
        tmp = x * ((t - y) / t)
    else if (x <= 3d+113) then
        tmp = x + (z * (y / t))
    else
        tmp = x * (1.0d0 - (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.7e-43) {
		tmp = x * ((t - y) / t);
	} else if (x <= 3e+113) {
		tmp = x + (z * (y / t));
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -3.7e-43:
		tmp = x * ((t - y) / t)
	elif x <= 3e+113:
		tmp = x + (z * (y / t))
	else:
		tmp = x * (1.0 - (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -3.7e-43)
		tmp = Float64(x * Float64(Float64(t - y) / t));
	elseif (x <= 3e+113)
		tmp = Float64(x + Float64(z * Float64(y / t)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -3.7e-43)
		tmp = x * ((t - y) / t);
	elseif (x <= 3e+113)
		tmp = x + (z * (y / t));
	else
		tmp = x * (1.0 - (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -3.7e-43], N[(x * N[(N[(t - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3e+113], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.7e-43

   1. Initial program 93.6%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 87.3%

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

      1. mul-1-neg 87.3%

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

      2. unsub-neg 87.3%

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

   5. Simplified 87.3%

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

   6. Taylor expanded in t around 0 87.3%

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

   if -3.7e-43 < x < 3e113

   1. Initial program 95.4%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 93.9%

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

      1. mul-1-neg 93.9%

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

      2. associate-/l* 84.4%

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

      3. distribute-lft-neg-in 84.4%

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

      4. *-commutative 84.4%

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

      5. associate-*r/ 87.3%

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

      6. distribute-rgt-in 91.9%

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

      7. +-commutative 91.9%

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

      8. sub-neg 91.9%

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

   5. Simplified 91.9%

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

   6. Taylor expanded in z around inf 83.9%

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

   if 3e113 < x

   1. Initial program 92.8%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 90.2%

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

      1. mul-1-neg 90.2%

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

      2. unsub-neg 90.2%

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

   5. Simplified 90.2%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{-43}:\\ \;\;\;\;x \cdot \frac{t - y}{t}\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+113}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{-43}:\\ \;\;\;\;x \cdot \frac{t - y}{t}\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+113}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -4.2e-43)
   (* x (/ (- t y) t))
   (if (<= x 3.5e+113) (+ x (* y (/ z t))) (* x (- 1.0 (/ y t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.2e-43) {
		tmp = x * ((t - y) / t);
	} else if (x <= 3.5e+113) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-4.2d-43)) then
        tmp = x * ((t - y) / t)
    else if (x <= 3.5d+113) then
        tmp = x + (y * (z / t))
    else
        tmp = x * (1.0d0 - (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.2e-43) {
		tmp = x * ((t - y) / t);
	} else if (x <= 3.5e+113) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -4.2e-43:
		tmp = x * ((t - y) / t)
	elif x <= 3.5e+113:
		tmp = x + (y * (z / t))
	else:
		tmp = x * (1.0 - (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -4.2e-43)
		tmp = Float64(x * Float64(Float64(t - y) / t));
	elseif (x <= 3.5e+113)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -4.2e-43)
		tmp = x * ((t - y) / t);
	elseif (x <= 3.5e+113)
		tmp = x + (y * (z / t));
	else
		tmp = x * (1.0 - (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -4.2e-43], N[(x * N[(N[(t - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.5e+113], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.2000000000000001e-43

   1. Initial program 93.6%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 87.3%

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

      1. mul-1-neg 87.3%

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

      2. unsub-neg 87.3%

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

   5. Simplified 87.3%

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

   6. Taylor expanded in t around 0 87.3%

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

   if -4.2000000000000001e-43 < x < 3.5000000000000001e113

   1. Initial program 95.4%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 85.0%

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

      1. associate-/l* 82.9%

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

   5. Simplified 82.9%

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

   if 3.5000000000000001e113 < x

   1. Initial program 92.8%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 90.2%

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

      1. mul-1-neg 90.2%

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

      2. unsub-neg 90.2%

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

   5. Simplified 90.2%

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

Alternative 8: 76.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{-39}:\\ \;\;\;\;x \cdot \frac{t - y}{t}\\ \mathbf{elif}\;x \leq 270:\\ \;\;\;\;\left(z - x\right) \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -7.8e-39)
   (* x (/ (- t y) t))
   (if (<= x 270.0) (* (- z x) (/ y t)) (* x (- 1.0 (/ y t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -7.8e-39) {
		tmp = x * ((t - y) / t);
	} else if (x <= 270.0) {
		tmp = (z - x) * (y / t);
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-7.8d-39)) then
        tmp = x * ((t - y) / t)
    else if (x <= 270.0d0) then
        tmp = (z - x) * (y / t)
    else
        tmp = x * (1.0d0 - (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -7.8e-39) {
		tmp = x * ((t - y) / t);
	} else if (x <= 270.0) {
		tmp = (z - x) * (y / t);
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -7.8e-39:
		tmp = x * ((t - y) / t)
	elif x <= 270.0:
		tmp = (z - x) * (y / t)
	else:
		tmp = x * (1.0 - (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -7.8e-39)
		tmp = Float64(x * Float64(Float64(t - y) / t));
	elseif (x <= 270.0)
		tmp = Float64(Float64(z - x) * Float64(y / t));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -7.8e-39)
		tmp = x * ((t - y) / t);
	elseif (x <= 270.0)
		tmp = (z - x) * (y / t);
	else
		tmp = x * (1.0 - (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -7.8e-39], N[(x * N[(N[(t - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 270.0], N[(N[(z - x), $MachinePrecision] * N[(y / t), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.80000000000000059e-39

   1. Initial program 93.3%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 88.1%

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

      1. mul-1-neg 88.1%

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

      2. unsub-neg 88.1%

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

   5. Simplified 88.1%

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

   6. Taylor expanded in t around 0 88.1%

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

   if -7.80000000000000059e-39 < x < 270

   1. Initial program 96.3%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 78.4%

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

   4. Taylor expanded in z around 0 78.4%

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

      1. mul-1-neg 96.3%

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

      2. associate-/l* 84.8%

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

      3. distribute-lft-neg-in 84.8%

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

      4. *-commutative 84.8%

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

      5. associate-*r/ 87.3%

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

      6. distribute-rgt-in 90.9%

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

      7. +-commutative 90.9%

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

      8. sub-neg 90.9%

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

   6. Simplified 73.5%

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

   if 270 < x

   1. Initial program 92.0%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 84.4%

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

      1. mul-1-neg 84.4%

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

      2. unsub-neg 84.4%

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

   5. Simplified 84.4%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{-39}:\\ \;\;\;\;x \cdot \frac{t - y}{t}\\ \mathbf{elif}\;x \leq 270:\\ \;\;\;\;\left(z - x\right) \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 73.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{-59}:\\ \;\;\;\;x \cdot \frac{t - y}{t}\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-88}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -4.2e-59)
   (* x (/ (- t y) t))
   (if (<= x 2.2e-88) (/ (* y z) t) (* x (- 1.0 (/ y t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.2e-59) {
		tmp = x * ((t - y) / t);
	} else if (x <= 2.2e-88) {
		tmp = (y * z) / t;
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-4.2d-59)) then
        tmp = x * ((t - y) / t)
    else if (x <= 2.2d-88) then
        tmp = (y * z) / t
    else
        tmp = x * (1.0d0 - (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.2e-59) {
		tmp = x * ((t - y) / t);
	} else if (x <= 2.2e-88) {
		tmp = (y * z) / t;
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -4.2e-59:
		tmp = x * ((t - y) / t)
	elif x <= 2.2e-88:
		tmp = (y * z) / t
	else:
		tmp = x * (1.0 - (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -4.2e-59)
		tmp = Float64(x * Float64(Float64(t - y) / t));
	elseif (x <= 2.2e-88)
		tmp = Float64(Float64(y * z) / t);
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -4.2e-59)
		tmp = x * ((t - y) / t);
	elseif (x <= 2.2e-88)
		tmp = (y * z) / t;
	else
		tmp = x * (1.0 - (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -4.2e-59], N[(x * N[(N[(t - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.2e-88], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.19999999999999993e-59

   1. Initial program 93.8%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 86.0%

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

      1. mul-1-neg 86.0%

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

      2. unsub-neg 86.0%

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

   5. Simplified 86.0%

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

   6. Taylor expanded in t around 0 86.1%

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

   if -4.19999999999999993e-59 < x < 2.20000000000000005e-88

   1. Initial program 96.5%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 81.6%

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

   4. Taylor expanded in z around inf 72.3%

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

   if 2.20000000000000005e-88 < x

   1. Initial program 92.2%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 79.5%

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

      1. mul-1-neg 79.5%

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

      2. unsub-neg 79.5%

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

   5. Simplified 79.5%

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

Alternative 10: 50.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{-42}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 190:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -3.8e-42) x (if (<= x 190.0) (/ (* y z) t) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.8e-42) {
		tmp = x;
	} else if (x <= 190.0) {
		tmp = (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 (x <= (-3.8d-42)) then
        tmp = x
    else if (x <= 190.0d0) then
        tmp = (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 (x <= -3.8e-42) {
		tmp = x;
	} else if (x <= 190.0) {
		tmp = (y * z) / t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -3.8e-42:
		tmp = x
	elif x <= 190.0:
		tmp = (y * z) / t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -3.8e-42)
		tmp = x;
	elseif (x <= 190.0)
		tmp = 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 (x <= -3.8e-42)
		tmp = x;
	elseif (x <= 190.0)
		tmp = (y * z) / t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -3.8e-42], x, If[LessEqual[x, 190.0], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -3.80000000000000017e-42 or 190 < x

   1. Initial program 92.8%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 48.2%

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

   if -3.80000000000000017e-42 < x < 190

   1. Initial program 96.2%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 78.3%

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

   4. Taylor expanded in z around inf 68.0%

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

Alternative 11: 51.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{-41}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 940:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.3e-41) x (if (<= x 940.0) (/ z (/ t y)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.3e-41) {
		tmp = x;
	} else if (x <= 940.0) {
		tmp = z / (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 (x <= (-1.3d-41)) then
        tmp = x
    else if (x <= 940.0d0) then
        tmp = z / (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 (x <= -1.3e-41) {
		tmp = x;
	} else if (x <= 940.0) {
		tmp = z / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.3e-41:
		tmp = x
	elif x <= 940.0:
		tmp = z / (t / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.3e-41)
		tmp = x;
	elseif (x <= 940.0)
		tmp = Float64(z / Float64(t / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.3e-41)
		tmp = x;
	elseif (x <= 940.0)
		tmp = z / (t / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.3e-41], x, If[LessEqual[x, 940.0], N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3e-41 or 940 < x

   1. Initial program 92.8%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 48.2%

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

   if -1.3e-41 < x < 940

   1. Initial program 96.2%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 78.3%

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

   4. Taylor expanded in z around 0 78.3%

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

      1. mul-1-neg 96.2%

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

      2. associate-/l* 84.6%

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

      3. distribute-lft-neg-in 84.6%

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

      4. *-commutative 84.6%

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

      5. associate-*r/ 87.2%

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

      6. distribute-rgt-in 90.8%

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

      7. +-commutative 90.8%

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

      8. sub-neg 90.8%

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

   6. Simplified 73.3%

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

   7. Taylor expanded in z around inf 66.4%

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

      1. *-commutative 66.4%

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

      2. clear-num 66.3%

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

      3. div-inv 66.5%

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

   9. Applied egg-rr 66.5%

      \[\leadsto \color{blue}{\frac{z}{\frac{t}{y}}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 51.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{-40}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 12500:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.9e-40) x (if (<= x 12500.0) (* z (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.9e-40) {
		tmp = x;
	} else if (x <= 12500.0) {
		tmp = z * (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 (x <= (-1.9d-40)) then
        tmp = x
    else if (x <= 12500.0d0) then
        tmp = z * (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 (x <= -1.9e-40) {
		tmp = x;
	} else if (x <= 12500.0) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.9e-40:
		tmp = x
	elif x <= 12500.0:
		tmp = z * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.9e-40)
		tmp = x;
	elseif (x <= 12500.0)
		tmp = Float64(z * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.9e-40)
		tmp = x;
	elseif (x <= 12500.0)
		tmp = z * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.9e-40], x, If[LessEqual[x, 12500.0], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.8999999999999999e-40 or 12500 < x

   1. Initial program 92.8%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 48.2%

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

   if -1.8999999999999999e-40 < x < 12500

   1. Initial program 96.2%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 78.3%

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

   4. Taylor expanded in z around 0 78.3%

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

      1. mul-1-neg 96.2%

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

      2. associate-/l* 84.6%

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

      3. distribute-lft-neg-in 84.6%

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

      4. *-commutative 84.6%

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

      5. associate-*r/ 87.2%

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

      6. distribute-rgt-in 90.8%

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

      7. +-commutative 90.8%

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

      8. sub-neg 90.8%

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

   6. Simplified 73.3%

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

   7. Taylor expanded in z around inf 66.4%

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

4. Final simplification 57.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{-40}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 12500:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 50.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-41}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 78:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -5.5e-41) x (if (<= x 78.0) (* y (/ z t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -5.5e-41) {
		tmp = x;
	} else if (x <= 78.0) {
		tmp = 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 (x <= (-5.5d-41)) then
        tmp = x
    else if (x <= 78.0d0) then
        tmp = 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 (x <= -5.5e-41) {
		tmp = x;
	} else if (x <= 78.0) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -5.5e-41:
		tmp = x
	elif x <= 78.0:
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -5.5e-41)
		tmp = x;
	elseif (x <= 78.0)
		tmp = Float64(y * Float64(z / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -5.5e-41)
		tmp = x;
	elseif (x <= 78.0)
		tmp = y * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -5.5e-41], x, If[LessEqual[x, 78.0], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -5.50000000000000022e-41 or 78 < x

   1. Initial program 92.8%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 48.2%

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

   if -5.50000000000000022e-41 < x < 78

   1. Initial program 96.2%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 76.5%

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

   4. Taylor expanded in z around inf 65.9%

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

Alternative 14: 95.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+100}:\\ \;\;\;\;x + \frac{z - x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.05e+100) (+ x (/ (- z x) (/ t y))) (+ x (/ (* y (- z x)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.05e+100) {
		tmp = x + ((z - x) / (t / y));
	} else {
		tmp = x + ((y * (z - x)) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.05d+100)) then
        tmp = x + ((z - x) / (t / y))
    else
        tmp = x + ((y * (z - x)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.05e+100) {
		tmp = x + ((z - x) / (t / y));
	} else {
		tmp = x + ((y * (z - x)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.05e+100:
		tmp = x + ((z - x) / (t / y))
	else:
		tmp = x + ((y * (z - x)) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.05e+100)
		tmp = Float64(x + Float64(Float64(z - x) / Float64(t / y)));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(z - x)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.05e+100)
		tmp = x + ((z - x) / (t / y));
	else
		tmp = x + ((y * (z - x)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.05e+100], N[(x + N[(N[(z - x), $MachinePrecision] / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.0499999999999999e100

   1. Initial program 77.6%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 77.4%

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

      1. mul-1-neg 77.4%

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

      2. associate-/l* 87.5%

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

      3. distribute-lft-neg-in 87.5%

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

      4. *-commutative 87.5%

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

      5. associate-*r/ 99.9%

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

      6. distribute-rgt-in 99.9%

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

      7. +-commutative 99.9%

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

      8. sub-neg 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in y around 0 77.6%

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

      1. associate-*r/ 96.4%

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

      2. *-commutative 96.4%

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

      3. associate-/r/ 100.0%

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

   8. Simplified 100.0%

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

   if -1.0499999999999999e100 < t

   1. Initial program 97.4%

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

Alternative 15: 95.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{+99}:\\ \;\;\;\;x + \left(z - x\right) \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -9.2e+99) (+ x (* (- z x) (/ y t))) (+ x (/ (* y (- z x)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -9.2e+99) {
		tmp = x + ((z - x) * (y / t));
	} else {
		tmp = x + ((y * (z - x)) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-9.2d+99)) then
        tmp = x + ((z - x) * (y / t))
    else
        tmp = x + ((y * (z - x)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -9.2e+99) {
		tmp = x + ((z - x) * (y / t));
	} else {
		tmp = x + ((y * (z - x)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -9.2e+99:
		tmp = x + ((z - x) * (y / t))
	else:
		tmp = x + ((y * (z - x)) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -9.2e+99)
		tmp = Float64(x + Float64(Float64(z - x) * Float64(y / t)));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(z - x)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -9.2e+99)
		tmp = x + ((z - x) * (y / t));
	else
		tmp = x + ((y * (z - x)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -9.2e+99], N[(x + N[(N[(z - x), $MachinePrecision] * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.20000000000000077e99

   1. Initial program 77.6%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 77.4%

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

      1. mul-1-neg 77.4%

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

      2. associate-/l* 87.5%

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

      3. distribute-lft-neg-in 87.5%

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

      4. *-commutative 87.5%

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

      5. associate-*r/ 99.9%

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

      6. distribute-rgt-in 99.9%

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

      7. +-commutative 99.9%

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

      8. sub-neg 99.9%

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

   5. Simplified 99.9%

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

   if -9.20000000000000077e99 < t

   1. Initial program 97.4%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{+99}:\\ \;\;\;\;x + \left(z - x\right) \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 97.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 + ((z - x) * (y / t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.5%

   \[x + \frac{y \cdot \left(z - x\right)}{t} \]
2. Add Preprocessing

3. Taylor expanded in z around 0 90.5%

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

   1. mul-1-neg 90.5%

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

   2. associate-/l* 87.1%

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

   3. distribute-lft-neg-in 87.1%

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

   4. *-commutative 87.1%

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

   5. associate-*r/ 87.9%

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

   6. distribute-rgt-in 95.5%

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

   7. +-commutative 95.5%

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

   8. sub-neg 95.5%

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

5. Simplified 95.5%

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

6. Final simplification 95.5%

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

Alternative 17: 37.7% 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 94.5%

   \[x + \frac{y \cdot \left(z - x\right)}{t} \]
2. Add Preprocessing

3. Taylor expanded in y around 0 34.2%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Developer Target 1: 90.8% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

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 - ((x * (y / t)) + (-z * (y / t)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024139 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"
  :precision binary64

  :alt
  (! :herbie-platform default (- x (+ (* x (/ y t)) (* (- z) (/ y t)))))

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