Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A

Percentage Accurate: 98.5% → 98.5%

Time: 48.2s

Alternatives: 14

Speedup: 1.0×

• 47.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x * exp((((y * log(z)) + ((t - 1.0) * log(a))) - b))) / y;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (x * exp((((y * log(z)) + ((t - 1.0d0) * log(a))) - b))) / y
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x * Math.exp((((y * Math.log(z)) + ((t - 1.0) * Math.log(a))) - b))) / y;
}

Python

def code(x, y, z, t, a, b):
	return (x * math.exp((((y * math.log(z)) + ((t - 1.0) * math.log(a))) - b))) / y

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) + Float64(Float64(t - 1.0) * log(a))) - b))) / y)
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x * exp((((y * log(z)) + ((t - 1.0) * log(a))) - b))) / y;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] + N[(N[(t - 1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]

Initial Program: 98.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x * exp((((y * log(z)) + ((t - 1.0) * log(a))) - b))) / y;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (x * exp((((y * log(z)) + ((t - 1.0d0) * log(a))) - b))) / y
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x * Math.exp((((y * Math.log(z)) + ((t - 1.0) * Math.log(a))) - b))) / y;
}

Python

def code(x, y, z, t, a, b):
	return (x * math.exp((((y * math.log(z)) + ((t - 1.0) * math.log(a))) - b))) / y

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) + Float64(Float64(t - 1.0) * log(a))) - b))) / y)
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x * exp((((y * log(z)) + ((t - 1.0) * log(a))) - b))) / y;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] + N[(N[(t - 1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]

Alternative 1: 98.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot e^{\left(y \cdot \log z + \log a \cdot \left(t + -1\right)\right) - b}}{y} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (/ (* x (exp (- (+ (* y (log z)) (* (log a) (+ t -1.0))) b))) y))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x * exp((((y * log(z)) + (log(a) * (t + -1.0))) - b))) / y;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (x * exp((((y * log(z)) + (log(a) * (t + (-1.0d0)))) - b))) / y
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x * Math.exp((((y * Math.log(z)) + (Math.log(a) * (t + -1.0))) - b))) / y;
}

Python

def code(x, y, z, t, a, b):
	return (x * math.exp((((y * math.log(z)) + (math.log(a) * (t + -1.0))) - b))) / y

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) + Float64(log(a) * Float64(t + -1.0))) - b))) / y)
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x * exp((((y * log(z)) + (log(a) * (t + -1.0))) - b))) / y;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] + N[(N[Log[a], $MachinePrecision] * N[(t + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]

Derivation

1. Initial program 96.5%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Add Preprocessing

3. Final simplification 96.5%

   \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \log a \cdot \left(t + -1\right)\right) - b}}{y} \]
4. Add Preprocessing

Alternative 2: 92.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.85 \cdot 10^{+34} \lor \neg \left(t \leq 2 \cdot 10^{-69}\right):\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t + -1\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2.85e+34) (not (<= t 2e-69)))
   (/ (* x (exp (- (* (log a) (+ t -1.0)) b))) y)
   (* x (/ (exp (- (- (* y (log z)) (log a)) b)) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.85e+34) || !(t <= 2e-69)) {
		tmp = (x * exp(((log(a) * (t + -1.0)) - b))) / y;
	} else {
		tmp = x * (exp((((y * log(z)) - log(a)) - b)) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-2.85d+34)) .or. (.not. (t <= 2d-69))) then
        tmp = (x * exp(((log(a) * (t + (-1.0d0))) - b))) / y
    else
        tmp = x * (exp((((y * log(z)) - log(a)) - b)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.85e+34) || !(t <= 2e-69)) {
		tmp = (x * Math.exp(((Math.log(a) * (t + -1.0)) - b))) / y;
	} else {
		tmp = x * (Math.exp((((y * Math.log(z)) - Math.log(a)) - b)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -2.85e+34) or not (t <= 2e-69):
		tmp = (x * math.exp(((math.log(a) * (t + -1.0)) - b))) / y
	else:
		tmp = x * (math.exp((((y * math.log(z)) - math.log(a)) - b)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2.85e+34) || !(t <= 2e-69))
		tmp = Float64(Float64(x * exp(Float64(Float64(log(a) * Float64(t + -1.0)) - b))) / y);
	else
		tmp = Float64(x * Float64(exp(Float64(Float64(Float64(y * log(z)) - log(a)) - b)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -2.85e+34) || ~((t <= 2e-69)))
		tmp = (x * exp(((log(a) * (t + -1.0)) - b))) / y;
	else
		tmp = x * (exp((((y * log(z)) - log(a)) - b)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2.85e+34], N[Not[LessEqual[t, 2e-69]], $MachinePrecision]], N[(N[(x * N[Exp[N[(N[(N[Log[a], $MachinePrecision] * N[(t + -1.0), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x * N[(N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] - N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.84999999999999987e34 or 1.9999999999999999e-69 < t

   1. Initial program 99.9%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. *-commutative 99.9%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 86.7%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 86.7%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 86.7%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. fma-neg 86.7%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\mathsf{fma}\left(t - 1, \log a, -b\right)}\right)} \cdot \frac{x}{y} \]

      6. sub-neg 86.7%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(\color{blue}{t + \left(-1\right)}, \log a, -b\right)\right)} \cdot \frac{x}{y} \]

      7. metadata-eval 86.7%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(t + \color{blue}{-1}, \log a, -b\right)\right)} \cdot \frac{x}{y} \]

   3. Simplified 86.7%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(t + -1, \log a, -b\right)\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 91.0%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

   if -2.84999999999999987e34 < t < 1.9999999999999999e-69

   1. Initial program 92.1%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. *-commutative 92.1%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 89.5%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 89.5%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 89.5%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. fma-neg 89.5%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\mathsf{fma}\left(t - 1, \log a, -b\right)}\right)} \cdot \frac{x}{y} \]

      6. sub-neg 89.5%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(\color{blue}{t + \left(-1\right)}, \log a, -b\right)\right)} \cdot \frac{x}{y} \]

      7. metadata-eval 89.5%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(t + \color{blue}{-1}, \log a, -b\right)\right)} \cdot \frac{x}{y} \]

   3. Simplified 89.5%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(t + -1, \log a, -b\right)\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 91.9%

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

      1. associate-/l* 94.4%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}{y}} \]

      2. log-pow 88.3%

         \[\leadsto x \cdot \frac{e^{\left(-1 \cdot \log a + \color{blue}{\log \left({z}^{y}\right)}\right) - b}}{y} \]

      3. +-commutative 88.3%

         \[\leadsto x \cdot \frac{e^{\color{blue}{\left(\log \left({z}^{y}\right) + -1 \cdot \log a\right)} - b}}{y} \]

      4. mul-1-neg 88.3%

         \[\leadsto x \cdot \frac{e^{\left(\log \left({z}^{y}\right) + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      5. unsub-neg 88.3%

         \[\leadsto x \cdot \frac{e^{\color{blue}{\left(\log \left({z}^{y}\right) - \log a\right)} - b}}{y} \]

      6. log-pow 94.4%

         \[\leadsto x \cdot \frac{e^{\left(\color{blue}{y \cdot \log z} - \log a\right) - b}}{y} \]

   7. Simplified 94.4%

      \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z - \log a\right) - b}}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.85 \cdot 10^{+34} \lor \neg \left(t \leq 2 \cdot 10^{-69}\right):\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t + -1\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+240} \lor \neg \left(y \leq 2.7 \cdot 10^{+88}\right):\\ \;\;\;\;x \cdot \frac{{z}^{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t + -1\right) - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.1e+240) (not (<= y 2.7e+88)))
   (* x (/ (pow z y) y))
   (/ (* x (exp (- (* (log a) (+ t -1.0)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.1e+240) || !(y <= 2.7e+88)) {
		tmp = x * (pow(z, y) / y);
	} else {
		tmp = (x * exp(((log(a) * (t + -1.0)) - b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.1d+240)) .or. (.not. (y <= 2.7d+88))) then
        tmp = x * ((z ** y) / y)
    else
        tmp = (x * exp(((log(a) * (t + (-1.0d0))) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.1e+240) || !(y <= 2.7e+88)) {
		tmp = x * (Math.pow(z, y) / y);
	} else {
		tmp = (x * Math.exp(((Math.log(a) * (t + -1.0)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.1e+240) or not (y <= 2.7e+88):
		tmp = x * (math.pow(z, y) / y)
	else:
		tmp = (x * math.exp(((math.log(a) * (t + -1.0)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.1e+240) || !(y <= 2.7e+88))
		tmp = Float64(x * Float64((z ^ y) / y));
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(log(a) * Float64(t + -1.0)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.1e+240) || ~((y <= 2.7e+88)))
		tmp = x * ((z ^ y) / y);
	else
		tmp = (x * exp(((log(a) * (t + -1.0)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.1e+240], N[Not[LessEqual[y, 2.7e+88]], $MachinePrecision]], N[(x * N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[Log[a], $MachinePrecision] * N[(t + -1.0), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.1000000000000001e240 or 2.70000000000000016e88 < y

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 85.0%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 85.0%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 85.0%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. fma-neg 85.0%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\mathsf{fma}\left(t - 1, \log a, -b\right)}\right)} \cdot \frac{x}{y} \]

      6. sub-neg 85.0%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(\color{blue}{t + \left(-1\right)}, \log a, -b\right)\right)} \cdot \frac{x}{y} \]

      7. metadata-eval 85.0%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(t + \color{blue}{-1}, \log a, -b\right)\right)} \cdot \frac{x}{y} \]

   3. Simplified 85.0%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(t + -1, \log a, -b\right)\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 80.1%

      \[\leadsto e^{\color{blue}{y \cdot \log z}} \cdot \frac{x}{y} \]

   6. Taylor expanded in y around inf 95.1%

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

      1. associate-/l* 95.1%

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

   8. Simplified 95.1%

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

   if -1.1000000000000001e240 < y < 2.70000000000000016e88

   1. Initial program 95.4%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. *-commutative 95.4%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 88.8%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 88.8%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 88.8%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. fma-neg 88.8%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\mathsf{fma}\left(t - 1, \log a, -b\right)}\right)} \cdot \frac{x}{y} \]

      6. sub-neg 88.8%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(\color{blue}{t + \left(-1\right)}, \log a, -b\right)\right)} \cdot \frac{x}{y} \]

      7. metadata-eval 88.8%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(t + \color{blue}{-1}, \log a, -b\right)\right)} \cdot \frac{x}{y} \]

   3. Simplified 88.8%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(t + -1, \log a, -b\right)\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 90.7%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+240} \lor \neg \left(y \leq 2.7 \cdot 10^{+88}\right):\\ \;\;\;\;x \cdot \frac{{z}^{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t + -1\right) - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 80.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+179} \lor \neg \left(y \leq 1.95 \cdot 10^{+18}\right):\\ \;\;\;\;x \cdot \frac{{z}^{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.02e+179) (not (<= y 1.95e+18)))
   (* x (/ (pow z y) y))
   (* x (/ (/ (pow a (+ t -1.0)) (exp b)) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.02e+179) || !(y <= 1.95e+18)) {
		tmp = x * (pow(z, y) / y);
	} else {
		tmp = x * ((pow(a, (t + -1.0)) / exp(b)) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.02d+179)) .or. (.not. (y <= 1.95d+18))) then
        tmp = x * ((z ** y) / y)
    else
        tmp = x * (((a ** (t + (-1.0d0))) / exp(b)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.02e+179) || !(y <= 1.95e+18)) {
		tmp = x * (Math.pow(z, y) / y);
	} else {
		tmp = x * ((Math.pow(a, (t + -1.0)) / Math.exp(b)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.02e+179) or not (y <= 1.95e+18):
		tmp = x * (math.pow(z, y) / y)
	else:
		tmp = x * ((math.pow(a, (t + -1.0)) / math.exp(b)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.02e+179) || !(y <= 1.95e+18))
		tmp = Float64(x * Float64((z ^ y) / y));
	else
		tmp = Float64(x * Float64(Float64((a ^ Float64(t + -1.0)) / exp(b)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.02e+179) || ~((y <= 1.95e+18)))
		tmp = x * ((z ^ y) / y);
	else
		tmp = x * (((a ^ (t + -1.0)) / exp(b)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.02e+179], N[Not[LessEqual[y, 1.95e+18]], $MachinePrecision]], N[(x * N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.0199999999999999e179 or 1.95e18 < y

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 88.7%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 88.7%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 88.7%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. fma-neg 88.7%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\mathsf{fma}\left(t - 1, \log a, -b\right)}\right)} \cdot \frac{x}{y} \]

      6. sub-neg 88.7%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(\color{blue}{t + \left(-1\right)}, \log a, -b\right)\right)} \cdot \frac{x}{y} \]

      7. metadata-eval 88.7%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(t + \color{blue}{-1}, \log a, -b\right)\right)} \cdot \frac{x}{y} \]

   3. Simplified 88.7%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(t + -1, \log a, -b\right)\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 80.6%

      \[\leadsto e^{\color{blue}{y \cdot \log z}} \cdot \frac{x}{y} \]

   6. Taylor expanded in y around inf 90.9%

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

      1. associate-/l* 90.9%

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

   8. Simplified 90.9%

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

   if -1.0199999999999999e179 < y < 1.95e18

   1. Initial program 94.4%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. *-commutative 94.4%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 87.5%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 87.5%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 87.5%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. fma-neg 87.5%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\mathsf{fma}\left(t - 1, \log a, -b\right)}\right)} \cdot \frac{x}{y} \]

      6. sub-neg 87.5%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(\color{blue}{t + \left(-1\right)}, \log a, -b\right)\right)} \cdot \frac{x}{y} \]

      7. metadata-eval 87.5%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(t + \color{blue}{-1}, \log a, -b\right)\right)} \cdot \frac{x}{y} \]

   3. Simplified 87.5%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(t + -1, \log a, -b\right)\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 92.2%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
   6. Step-by-step derivation

      1. associate-/l* 93.4%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

      2. div-exp 82.1%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      3. exp-to-pow 83.0%

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

      4. sub-neg 83.0%

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

      5. metadata-eval 83.0%

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

   7. Simplified 83.0%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+179} \lor \neg \left(y \leq 1.95 \cdot 10^{+18}\right):\\ \;\;\;\;x \cdot \frac{{z}^{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ t_2 := x \cdot \frac{{z}^{y}}{y}\\ \mathbf{if}\;y \leq -6.6 \cdot 10^{+126}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-275}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-239}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+88}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (pow a (+ t -1.0))) y)) (t_2 (* x (/ (pow z y) y))))
   (if (<= y -6.6e+126)
     t_2
     (if (<= y 1.4e-275)
       t_1
       (if (<= y 3.5e-239)
         (/ x (* a (* y (exp b))))
         (if (<= y 1.8e+88) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * pow(a, (t + -1.0))) / y;
	double t_2 = x * (pow(z, y) / y);
	double tmp;
	if (y <= -6.6e+126) {
		tmp = t_2;
	} else if (y <= 1.4e-275) {
		tmp = t_1;
	} else if (y <= 3.5e-239) {
		tmp = x / (a * (y * exp(b)));
	} else if (y <= 1.8e+88) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * (a ** (t + (-1.0d0)))) / y
    t_2 = x * ((z ** y) / y)
    if (y <= (-6.6d+126)) then
        tmp = t_2
    else if (y <= 1.4d-275) then
        tmp = t_1
    else if (y <= 3.5d-239) then
        tmp = x / (a * (y * exp(b)))
    else if (y <= 1.8d+88) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * Math.pow(a, (t + -1.0))) / y;
	double t_2 = x * (Math.pow(z, y) / y);
	double tmp;
	if (y <= -6.6e+126) {
		tmp = t_2;
	} else if (y <= 1.4e-275) {
		tmp = t_1;
	} else if (y <= 3.5e-239) {
		tmp = x / (a * (y * Math.exp(b)));
	} else if (y <= 1.8e+88) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * math.pow(a, (t + -1.0))) / y
	t_2 = x * (math.pow(z, y) / y)
	tmp = 0
	if y <= -6.6e+126:
		tmp = t_2
	elif y <= 1.4e-275:
		tmp = t_1
	elif y <= 3.5e-239:
		tmp = x / (a * (y * math.exp(b)))
	elif y <= 1.8e+88:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * (a ^ Float64(t + -1.0))) / y)
	t_2 = Float64(x * Float64((z ^ y) / y))
	tmp = 0.0
	if (y <= -6.6e+126)
		tmp = t_2;
	elseif (y <= 1.4e-275)
		tmp = t_1;
	elseif (y <= 3.5e-239)
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	elseif (y <= 1.8e+88)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * (a ^ (t + -1.0))) / y;
	t_2 = x * ((z ^ y) / y);
	tmp = 0.0;
	if (y <= -6.6e+126)
		tmp = t_2;
	elseif (y <= 1.4e-275)
		tmp = t_1;
	elseif (y <= 3.5e-239)
		tmp = x / (a * (y * exp(b)));
	elseif (y <= 1.8e+88)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.6e+126], t$95$2, If[LessEqual[y, 1.4e-275], t$95$1, If[LessEqual[y, 3.5e-239], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.8e+88], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.60000000000000026e126 or 1.8000000000000001e88 < y

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 86.6%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 86.6%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 86.6%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. fma-neg 86.6%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\mathsf{fma}\left(t - 1, \log a, -b\right)}\right)} \cdot \frac{x}{y} \]

      6. sub-neg 86.6%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(\color{blue}{t + \left(-1\right)}, \log a, -b\right)\right)} \cdot \frac{x}{y} \]

      7. metadata-eval 86.6%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(t + \color{blue}{-1}, \log a, -b\right)\right)} \cdot \frac{x}{y} \]

   3. Simplified 86.6%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(t + -1, \log a, -b\right)\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 79.4%

      \[\leadsto e^{\color{blue}{y \cdot \log z}} \cdot \frac{x}{y} \]

   6. Taylor expanded in y around inf 92.8%

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

      1. associate-/l* 92.8%

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

   8. Simplified 92.8%

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

   if -6.60000000000000026e126 < y < 1.39999999999999997e-275 or 3.50000000000000005e-239 < y < 1.8000000000000001e88

   1. Initial program 96.4%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. *-commutative 96.4%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 88.3%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 88.3%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 88.3%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. fma-neg 88.3%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\mathsf{fma}\left(t - 1, \log a, -b\right)}\right)} \cdot \frac{x}{y} \]

      6. sub-neg 88.3%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(\color{blue}{t + \left(-1\right)}, \log a, -b\right)\right)} \cdot \frac{x}{y} \]

      7. metadata-eval 88.3%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(t + \color{blue}{-1}, \log a, -b\right)\right)} \cdot \frac{x}{y} \]

   3. Simplified 88.3%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(t + -1, \log a, -b\right)\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 92.0%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

   6. Taylor expanded in b around 0 76.7%

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

   8. Simplified 77.4%

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

   if 1.39999999999999997e-275 < y < 3.50000000000000005e-239

   1. Initial program 62.9%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. *-commutative 62.9%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 95.0%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 95.0%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 95.0%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. fma-neg 95.0%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\mathsf{fma}\left(t - 1, \log a, -b\right)}\right)} \cdot \frac{x}{y} \]

      6. sub-neg 95.0%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(\color{blue}{t + \left(-1\right)}, \log a, -b\right)\right)} \cdot \frac{x}{y} \]

      7. metadata-eval 95.0%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(t + \color{blue}{-1}, \log a, -b\right)\right)} \cdot \frac{x}{y} \]

   3. Simplified 95.0%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(t + -1, \log a, -b\right)\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 95.0%

      \[\leadsto \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}} \cdot \frac{x}{y} \]
   6. Step-by-step derivation

      1. div-exp 94.8%

         \[\leadsto \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}} \cdot \frac{x}{y} \]

      2. exp-to-pow 99.4%

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

      3. sub-neg 99.4%

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

      4. metadata-eval 99.4%

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

   7. Simplified 99.4%

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

   8. Taylor expanded in t around 0 88.2%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{+126}:\\ \;\;\;\;x \cdot \frac{{z}^{y}}{y}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-275}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-239}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+88}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{z}^{y}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 69.9% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+127} \lor \neg \left(y \leq 1.5 \cdot 10^{+18}\right):\\ \;\;\;\;x \cdot \frac{{z}^{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;{a}^{\left(t + -1\right)} \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.1e+127) (not (<= y 1.5e+18)))
   (* x (/ (pow z y) y))
   (* (pow a (+ t -1.0)) (/ x y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.1e+127) || !(y <= 1.5e+18)) {
		tmp = x * (pow(z, y) / y);
	} else {
		tmp = pow(a, (t + -1.0)) * (x / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.1d+127)) .or. (.not. (y <= 1.5d+18))) then
        tmp = x * ((z ** y) / y)
    else
        tmp = (a ** (t + (-1.0d0))) * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.1e+127) || !(y <= 1.5e+18)) {
		tmp = x * (Math.pow(z, y) / y);
	} else {
		tmp = Math.pow(a, (t + -1.0)) * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.1e+127) or not (y <= 1.5e+18):
		tmp = x * (math.pow(z, y) / y)
	else:
		tmp = math.pow(a, (t + -1.0)) * (x / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.1e+127) || !(y <= 1.5e+18))
		tmp = Float64(x * Float64((z ^ y) / y));
	else
		tmp = Float64((a ^ Float64(t + -1.0)) * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.1e+127) || ~((y <= 1.5e+18)))
		tmp = x * ((z ^ y) / y);
	else
		tmp = (a ^ (t + -1.0)) * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.1e+127], N[Not[LessEqual[y, 1.5e+18]], $MachinePrecision]], N[(x * N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.1000000000000001e127 or 1.5e18 < y

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 88.3%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 88.3%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 88.3%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. fma-neg 88.3%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\mathsf{fma}\left(t - 1, \log a, -b\right)}\right)} \cdot \frac{x}{y} \]

      6. sub-neg 88.3%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(\color{blue}{t + \left(-1\right)}, \log a, -b\right)\right)} \cdot \frac{x}{y} \]

      7. metadata-eval 88.3%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(t + \color{blue}{-1}, \log a, -b\right)\right)} \cdot \frac{x}{y} \]

   3. Simplified 88.3%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(t + -1, \log a, -b\right)\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 79.7%

      \[\leadsto e^{\color{blue}{y \cdot \log z}} \cdot \frac{x}{y} \]

   6. Taylor expanded in y around inf 90.4%

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

      1. associate-/l* 90.4%

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

   8. Simplified 90.4%

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

   if -1.1000000000000001e127 < y < 1.5e18

   1. Initial program 94.1%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. *-commutative 94.1%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 87.7%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 87.7%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 87.7%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. fma-neg 87.7%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\mathsf{fma}\left(t - 1, \log a, -b\right)}\right)} \cdot \frac{x}{y} \]

      6. sub-neg 87.7%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(\color{blue}{t + \left(-1\right)}, \log a, -b\right)\right)} \cdot \frac{x}{y} \]

      7. metadata-eval 87.7%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(t + \color{blue}{-1}, \log a, -b\right)\right)} \cdot \frac{x}{y} \]

   3. Simplified 87.7%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(t + -1, \log a, -b\right)\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 91.9%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]

   6. Taylor expanded in b around 0 73.9%

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

      1. *-commutative 73.9%

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

      2. exp-to-pow 74.7%

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

      3. sub-neg 74.7%

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

      4. metadata-eval 74.7%

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

      5. associate-*r/ 69.3%

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

      6. *-commutative 69.3%

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

      7. +-commutative 69.3%

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

   8. Simplified 69.3%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot {a}^{\left(-1 + t\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+127} \lor \neg \left(y \leq 1.5 \cdot 10^{+18}\right):\\ \;\;\;\;x \cdot \frac{{z}^{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;{a}^{\left(t + -1\right)} \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.3% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -20500000 \lor \neg \left(y \leq 8.8 \cdot 10^{+17}\right):\\ \;\;\;\;x \cdot \frac{{z}^{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -20500000.0) (not (<= y 8.8e+17)))
   (* x (/ (pow z y) y))
   (/ x (* a (* y (exp b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -20500000.0) || !(y <= 8.8e+17)) {
		tmp = x * (pow(z, y) / y);
	} else {
		tmp = x / (a * (y * exp(b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-20500000.0d0)) .or. (.not. (y <= 8.8d+17))) then
        tmp = x * ((z ** y) / y)
    else
        tmp = x / (a * (y * exp(b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -20500000.0) || !(y <= 8.8e+17)) {
		tmp = x * (Math.pow(z, y) / y);
	} else {
		tmp = x / (a * (y * Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -20500000.0) or not (y <= 8.8e+17):
		tmp = x * (math.pow(z, y) / y)
	else:
		tmp = x / (a * (y * math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -20500000.0) || !(y <= 8.8e+17))
		tmp = Float64(x * Float64((z ^ y) / y));
	else
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -20500000.0) || ~((y <= 8.8e+17)))
		tmp = x * ((z ^ y) / y);
	else
		tmp = x / (a * (y * exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -20500000.0], N[Not[LessEqual[y, 8.8e+17]], $MachinePrecision]], N[(x * N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.05e7 or 8.8e17 < y

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 90.5%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 90.5%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 90.5%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. fma-neg 90.5%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\mathsf{fma}\left(t - 1, \log a, -b\right)}\right)} \cdot \frac{x}{y} \]

      6. sub-neg 90.5%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(\color{blue}{t + \left(-1\right)}, \log a, -b\right)\right)} \cdot \frac{x}{y} \]

      7. metadata-eval 90.5%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(t + \color{blue}{-1}, \log a, -b\right)\right)} \cdot \frac{x}{y} \]

   3. Simplified 90.5%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(t + -1, \log a, -b\right)\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 78.0%

      \[\leadsto e^{\color{blue}{y \cdot \log z}} \cdot \frac{x}{y} \]

   6. Taylor expanded in y around inf 86.7%

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

      1. associate-/l* 86.7%

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

   8. Simplified 86.7%

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

   if -2.05e7 < y < 8.8e17

   1. Initial program 93.1%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. *-commutative 93.1%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 85.5%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 85.5%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 85.5%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. fma-neg 85.5%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\mathsf{fma}\left(t - 1, \log a, -b\right)}\right)} \cdot \frac{x}{y} \]

      6. sub-neg 85.5%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(\color{blue}{t + \left(-1\right)}, \log a, -b\right)\right)} \cdot \frac{x}{y} \]

      7. metadata-eval 85.5%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(t + \color{blue}{-1}, \log a, -b\right)\right)} \cdot \frac{x}{y} \]

   3. Simplified 85.5%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(t + -1, \log a, -b\right)\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 85.2%

      \[\leadsto \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}} \cdot \frac{x}{y} \]
   6. Step-by-step derivation

      1. div-exp 75.1%

         \[\leadsto \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}} \cdot \frac{x}{y} \]

      2. exp-to-pow 76.5%

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

      3. sub-neg 76.5%

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

      4. metadata-eval 76.5%

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

   7. Simplified 76.5%

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

   8. Taylor expanded in t around 0 62.3%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -20500000 \lor \neg \left(y \leq 8.8 \cdot 10^{+17}\right):\\ \;\;\;\;x \cdot \frac{{z}^{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 58.2% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-6} \lor \neg \left(y \leq 1020000000000\right):\\ \;\;\;\;x \cdot \frac{{z}^{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.6e-6) (not (<= y 1020000000000.0)))
   (* x (/ (pow z y) y))
   (/ (/ x y) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.6e-6) || !(y <= 1020000000000.0)) {
		tmp = x * (pow(z, y) / y);
	} else {
		tmp = (x / y) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.6d-6)) .or. (.not. (y <= 1020000000000.0d0))) then
        tmp = x * ((z ** y) / y)
    else
        tmp = (x / y) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.6e-6) || !(y <= 1020000000000.0)) {
		tmp = x * (Math.pow(z, y) / y);
	} else {
		tmp = (x / y) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.6e-6) or not (y <= 1020000000000.0):
		tmp = x * (math.pow(z, y) / y)
	else:
		tmp = (x / y) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.6e-6) || !(y <= 1020000000000.0))
		tmp = Float64(x * Float64((z ^ y) / y));
	else
		tmp = Float64(Float64(x / y) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.6e-6) || ~((y <= 1020000000000.0)))
		tmp = x * ((z ^ y) / y);
	else
		tmp = (x / y) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.6e-6], N[Not[LessEqual[y, 1020000000000.0]], $MachinePrecision]], N[(x * N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.5999999999999999e-6 or 1.02e12 < y

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 90.9%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 90.9%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 90.9%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. fma-neg 90.9%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\mathsf{fma}\left(t - 1, \log a, -b\right)}\right)} \cdot \frac{x}{y} \]

      6. sub-neg 90.9%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(\color{blue}{t + \left(-1\right)}, \log a, -b\right)\right)} \cdot \frac{x}{y} \]

      7. metadata-eval 90.9%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(t + \color{blue}{-1}, \log a, -b\right)\right)} \cdot \frac{x}{y} \]

   3. Simplified 90.9%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(t + -1, \log a, -b\right)\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 76.0%

      \[\leadsto e^{\color{blue}{y \cdot \log z}} \cdot \frac{x}{y} \]

   6. Taylor expanded in y around inf 84.4%

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

      1. associate-/l* 84.4%

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

   8. Simplified 84.4%

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

   if -1.5999999999999999e-6 < y < 1.02e12

   1. Initial program 92.8%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. *-commutative 92.8%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 84.8%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 84.8%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 84.8%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. fma-neg 84.8%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\mathsf{fma}\left(t - 1, \log a, -b\right)}\right)} \cdot \frac{x}{y} \]

      6. sub-neg 84.8%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(\color{blue}{t + \left(-1\right)}, \log a, -b\right)\right)} \cdot \frac{x}{y} \]

      7. metadata-eval 84.8%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(t + \color{blue}{-1}, \log a, -b\right)\right)} \cdot \frac{x}{y} \]

   3. Simplified 84.8%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(t + -1, \log a, -b\right)\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 84.4%

      \[\leadsto \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}} \cdot \frac{x}{y} \]
   6. Step-by-step derivation

      1. div-exp 73.9%

         \[\leadsto \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}} \cdot \frac{x}{y} \]

      2. exp-to-pow 75.3%

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

      3. sub-neg 75.3%

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

      4. metadata-eval 75.3%

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

   7. Simplified 75.3%

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

   8. Taylor expanded in t around 0 61.3%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 37.6%

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

   10. Taylor expanded in b around 0 37.1%

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

       1. *-commutative 37.1%

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

       2. associate-/r* 42.0%

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

   12. Simplified 42.0%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-6} \lor \neg \left(y \leq 1020000000000\right):\\ \;\;\;\;x \cdot \frac{{z}^{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 34.6% accurate, 22.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 3.5 \cdot 10^{-143}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 3.5e-143) (/ (/ x a) y) (/ x (* a (+ y (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 3.5e-143) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= 3.5d-143) then
        tmp = (x / a) / y
    else
        tmp = x / (a * (y + (y * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 3.5e-143) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 3.5e-143:
		tmp = (x / a) / y
	else:
		tmp = x / (a * (y + (y * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 3.5e-143)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(y * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 3.5e-143)
		tmp = (x / a) / y;
	else
		tmp = x / (a * (y + (y * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 3.5e-143], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 3.50000000000000005e-143

   1. Initial program 97.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. *-commutative 97.6%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 88.6%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 88.6%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 88.6%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. fma-neg 88.6%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\mathsf{fma}\left(t - 1, \log a, -b\right)}\right)} \cdot \frac{x}{y} \]

      6. sub-neg 88.6%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(\color{blue}{t + \left(-1\right)}, \log a, -b\right)\right)} \cdot \frac{x}{y} \]

      7. metadata-eval 88.6%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(t + \color{blue}{-1}, \log a, -b\right)\right)} \cdot \frac{x}{y} \]

   3. Simplified 88.6%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(t + -1, \log a, -b\right)\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 71.1%

      \[\leadsto \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}} \cdot \frac{x}{y} \]
   6. Step-by-step derivation

      1. div-exp 65.1%

         \[\leadsto \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}} \cdot \frac{x}{y} \]

      2. exp-to-pow 66.0%

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

      3. sub-neg 66.0%

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

      4. metadata-eval 66.0%

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

   7. Simplified 66.0%

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

   8. Taylor expanded in t around 0 51.1%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 32.3%

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

       1. associate-/r* 47.0%

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

   11. Simplified 47.0%

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

   if 3.50000000000000005e-143 < a

   1. Initial program 96.1%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. *-commutative 96.1%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 87.7%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 87.7%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 87.7%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. fma-neg 87.7%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\mathsf{fma}\left(t - 1, \log a, -b\right)}\right)} \cdot \frac{x}{y} \]

      6. sub-neg 87.7%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(\color{blue}{t + \left(-1\right)}, \log a, -b\right)\right)} \cdot \frac{x}{y} \]

      7. metadata-eval 87.7%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(t + \color{blue}{-1}, \log a, -b\right)\right)} \cdot \frac{x}{y} \]

   3. Simplified 87.7%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(t + -1, \log a, -b\right)\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 75.6%

      \[\leadsto \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}} \cdot \frac{x}{y} \]
   6. Step-by-step derivation

      1. div-exp 63.9%

         \[\leadsto \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}} \cdot \frac{x}{y} \]

      2. exp-to-pow 64.5%

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

      3. sub-neg 64.5%

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

      4. metadata-eval 64.5%

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

   7. Simplified 64.5%

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

   8. Taylor expanded in t around 0 55.4%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 37.2%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot y\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 39.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 3.5 \cdot 10^{-143}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 35.1% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 8.6 \cdot 10^{+131}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 8.6e+131) (/ (/ x y) a) (/ x (* a (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 8.6e+131) {
		tmp = (x / y) / a;
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 8.6d+131) then
        tmp = (x / y) / a
    else
        tmp = x / (a * (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 8.6e+131) {
		tmp = (x / y) / a;
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 8.6e+131:
		tmp = (x / y) / a
	else:
		tmp = x / (a * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 8.6e+131)
		tmp = Float64(Float64(x / y) / a);
	else
		tmp = Float64(x / Float64(a * Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 8.6e+131)
		tmp = (x / y) / a;
	else
		tmp = x / (a * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 8.6e+131], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 8.6000000000000003e131

   1. Initial program 96.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. *-commutative 96.0%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 88.0%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 88.0%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 88.0%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. fma-neg 88.0%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\mathsf{fma}\left(t - 1, \log a, -b\right)}\right)} \cdot \frac{x}{y} \]

      6. sub-neg 88.0%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(\color{blue}{t + \left(-1\right)}, \log a, -b\right)\right)} \cdot \frac{x}{y} \]

      7. metadata-eval 88.0%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(t + \color{blue}{-1}, \log a, -b\right)\right)} \cdot \frac{x}{y} \]

   3. Simplified 88.0%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(t + -1, \log a, -b\right)\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 72.5%

      \[\leadsto \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}} \cdot \frac{x}{y} \]
   6. Step-by-step derivation

      1. div-exp 64.5%

         \[\leadsto \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}} \cdot \frac{x}{y} \]

      2. exp-to-pow 65.3%

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

      3. sub-neg 65.3%

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

      4. metadata-eval 65.3%

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

   7. Simplified 65.3%

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

   8. Taylor expanded in t around 0 49.9%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 31.6%

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

   10. Taylor expanded in b around 0 32.7%

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

       1. *-commutative 32.7%

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

       2. associate-/r* 35.0%

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

   12. Simplified 35.0%

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

   if 8.6000000000000003e131 < b

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 87.5%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 87.5%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 87.5%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. fma-neg 87.5%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\mathsf{fma}\left(t - 1, \log a, -b\right)}\right)} \cdot \frac{x}{y} \]

      6. sub-neg 87.5%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(\color{blue}{t + \left(-1\right)}, \log a, -b\right)\right)} \cdot \frac{x}{y} \]

      7. metadata-eval 87.5%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(t + \color{blue}{-1}, \log a, -b\right)\right)} \cdot \frac{x}{y} \]

   3. Simplified 87.5%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(t + -1, \log a, -b\right)\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 87.5%

      \[\leadsto \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}} \cdot \frac{x}{y} \]
   6. Step-by-step derivation

      1. div-exp 62.5%

         \[\leadsto \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}} \cdot \frac{x}{y} \]

      2. exp-to-pow 62.5%

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

      3. sub-neg 62.5%

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

      4. metadata-eval 62.5%

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

   7. Simplified 62.5%

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

   8. Taylor expanded in t around 0 84.6%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 53.3%

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

   10. Taylor expanded in b around inf 53.3%

       \[\leadsto \color{blue}{\frac{x}{a \cdot \left(b \cdot y\right)}} \]
   11. Step-by-step derivation

       1. *-commutative 53.3%

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

   12. Simplified 53.3%

       \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot b\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 37.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 8.6 \cdot 10^{+131}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 31.7% accurate, 31.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 5.6 \cdot 10^{+66}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t 5.6e+66) (/ x (* y a)) (/ x y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 5.6e+66) {
		tmp = x / (y * a);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= 5.6d+66) then
        tmp = x / (y * a)
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 5.6e+66) {
		tmp = x / (y * a);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= 5.6e+66:
		tmp = x / (y * a)
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 5.6e+66)
		tmp = Float64(x / Float64(y * a));
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= 5.6e+66)
		tmp = x / (y * a);
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 5.6e+66], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 5.6000000000000001e66

   1. Initial program 95.4%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. *-commutative 95.4%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 87.2%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 87.2%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 87.2%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. fma-neg 87.2%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\mathsf{fma}\left(t - 1, \log a, -b\right)}\right)} \cdot \frac{x}{y} \]

      6. sub-neg 87.2%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(\color{blue}{t + \left(-1\right)}, \log a, -b\right)\right)} \cdot \frac{x}{y} \]

      7. metadata-eval 87.2%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(t + \color{blue}{-1}, \log a, -b\right)\right)} \cdot \frac{x}{y} \]

   3. Simplified 87.2%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(t + -1, \log a, -b\right)\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 73.4%

      \[\leadsto \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}} \cdot \frac{x}{y} \]
   6. Step-by-step derivation

      1. div-exp 64.6%

         \[\leadsto \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}} \cdot \frac{x}{y} \]

      2. exp-to-pow 65.5%

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

      3. sub-neg 65.5%

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

      4. metadata-eval 65.5%

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

   7. Simplified 65.5%

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

   8. Taylor expanded in t around 0 61.7%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 38.8%

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

   if 5.6000000000000001e66 < t

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 90.3%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 90.3%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 90.3%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. fma-neg 90.3%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\mathsf{fma}\left(t - 1, \log a, -b\right)}\right)} \cdot \frac{x}{y} \]

      6. sub-neg 90.3%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(\color{blue}{t + \left(-1\right)}, \log a, -b\right)\right)} \cdot \frac{x}{y} \]

      7. metadata-eval 90.3%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(t + \color{blue}{-1}, \log a, -b\right)\right)} \cdot \frac{x}{y} \]

   3. Simplified 90.3%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(t + -1, \log a, -b\right)\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 51.2%

      \[\leadsto e^{\color{blue}{y \cdot \log z}} \cdot \frac{x}{y} \]

   6. Taylor expanded in y around 0 18.0%

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

4. Final simplification 33.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 5.6 \cdot 10^{+66}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 32.2% accurate, 31.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 10^{-142}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 1e-142) (/ (/ x a) y) (/ x (* y a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 1e-142) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= 1d-142) then
        tmp = (x / a) / y
    else
        tmp = x / (y * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 1e-142) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 1e-142:
		tmp = (x / a) / y
	else:
		tmp = x / (y * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 1e-142)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(x / Float64(y * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 1e-142)
		tmp = (x / a) / y;
	else
		tmp = x / (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 1e-142], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 1e-142

   1. Initial program 97.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. *-commutative 97.6%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 88.9%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 88.9%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 88.9%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. fma-neg 88.9%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\mathsf{fma}\left(t - 1, \log a, -b\right)}\right)} \cdot \frac{x}{y} \]

      6. sub-neg 88.9%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(\color{blue}{t + \left(-1\right)}, \log a, -b\right)\right)} \cdot \frac{x}{y} \]

      7. metadata-eval 88.9%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(t + \color{blue}{-1}, \log a, -b\right)\right)} \cdot \frac{x}{y} \]

   3. Simplified 88.9%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(t + -1, \log a, -b\right)\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 72.0%

      \[\leadsto \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}} \cdot \frac{x}{y} \]
   6. Step-by-step derivation

      1. div-exp 66.1%

         \[\leadsto \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}} \cdot \frac{x}{y} \]

      2. exp-to-pow 67.0%

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

      3. sub-neg 67.0%

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

      4. metadata-eval 67.0%

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

   7. Simplified 67.0%

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

   8. Taylor expanded in t around 0 51.1%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 31.5%

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

       1. associate-/r* 45.7%

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

   11. Simplified 45.7%

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

   if 1e-142 < a

   1. Initial program 96.1%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. *-commutative 96.1%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 87.6%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 87.6%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 87.6%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. fma-neg 87.6%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\mathsf{fma}\left(t - 1, \log a, -b\right)}\right)} \cdot \frac{x}{y} \]

      6. sub-neg 87.6%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(\color{blue}{t + \left(-1\right)}, \log a, -b\right)\right)} \cdot \frac{x}{y} \]

      7. metadata-eval 87.6%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(t + \color{blue}{-1}, \log a, -b\right)\right)} \cdot \frac{x}{y} \]

   3. Simplified 87.6%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(t + -1, \log a, -b\right)\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 75.3%

      \[\leadsto \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}} \cdot \frac{x}{y} \]
   6. Step-by-step derivation

      1. div-exp 63.6%

         \[\leadsto \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}} \cdot \frac{x}{y} \]

      2. exp-to-pow 64.2%

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

      3. sub-neg 64.2%

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

      4. metadata-eval 64.2%

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

   7. Simplified 64.2%

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

   8. Taylor expanded in t around 0 55.4%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 32.2%

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

4. Final simplification 35.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 10^{-142}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 31.2% accurate, 31.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 2 \cdot 10^{-64}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 2e-64) (/ (/ x a) y) (/ (/ x y) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 2e-64) {
		tmp = (x / a) / y;
	} else {
		tmp = (x / y) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= 2d-64) then
        tmp = (x / a) / y
    else
        tmp = (x / y) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 2e-64) {
		tmp = (x / a) / y;
	} else {
		tmp = (x / y) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 2e-64:
		tmp = (x / a) / y
	else:
		tmp = (x / y) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 2e-64)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(Float64(x / y) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 2e-64)
		tmp = (x / a) / y;
	else
		tmp = (x / y) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 2e-64], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 1.99999999999999993e-64

   1. Initial program 97.8%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. *-commutative 97.8%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 86.7%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 86.7%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 86.7%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. fma-neg 86.7%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\mathsf{fma}\left(t - 1, \log a, -b\right)}\right)} \cdot \frac{x}{y} \]

      6. sub-neg 86.7%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(\color{blue}{t + \left(-1\right)}, \log a, -b\right)\right)} \cdot \frac{x}{y} \]

      7. metadata-eval 86.7%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(t + \color{blue}{-1}, \log a, -b\right)\right)} \cdot \frac{x}{y} \]

   3. Simplified 86.7%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(t + -1, \log a, -b\right)\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 71.6%

      \[\leadsto \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}} \cdot \frac{x}{y} \]
   6. Step-by-step derivation

      1. div-exp 62.7%

         \[\leadsto \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}} \cdot \frac{x}{y} \]

      2. exp-to-pow 63.7%

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

      3. sub-neg 63.7%

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

      4. metadata-eval 63.7%

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

   7. Simplified 63.7%

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

   8. Taylor expanded in t around 0 51.7%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 31.3%

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

       1. associate-/r* 42.2%

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

   11. Simplified 42.2%

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

   if 1.99999999999999993e-64 < a

   1. Initial program 95.8%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. *-commutative 95.8%

         \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

      2. associate-/l* 88.6%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. associate--l+ 88.6%

         \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      4. fma-define 88.6%

         \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

      5. fma-neg 88.6%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\mathsf{fma}\left(t - 1, \log a, -b\right)}\right)} \cdot \frac{x}{y} \]

      6. sub-neg 88.6%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(\color{blue}{t + \left(-1\right)}, \log a, -b\right)\right)} \cdot \frac{x}{y} \]

      7. metadata-eval 88.6%

         \[\leadsto e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(t + \color{blue}{-1}, \log a, -b\right)\right)} \cdot \frac{x}{y} \]

   3. Simplified 88.6%

      \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(t + -1, \log a, -b\right)\right)} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 75.9%

      \[\leadsto \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}} \cdot \frac{x}{y} \]
   6. Step-by-step derivation

      1. div-exp 65.1%

         \[\leadsto \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}} \cdot \frac{x}{y} \]

      2. exp-to-pow 65.6%

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

      3. sub-neg 65.6%

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

      4. metadata-eval 65.6%

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

   7. Simplified 65.6%

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

   8. Taylor expanded in t around 0 55.7%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 37.4%

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

   10. Taylor expanded in b around 0 32.4%

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

       1. *-commutative 32.4%

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

       2. associate-/r* 33.1%

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

   12. Simplified 33.1%

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

4. Final simplification 36.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 2 \cdot 10^{-64}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 16.2% accurate, 105.0× speedup

Math

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

FPCore

(FPCore (x y z t a b) :precision binary64 (/ x y))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x / y), $MachinePrecision]

Derivation

1. Initial program 96.5%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Step-by-step derivation

   1. *-commutative 96.5%

      \[\leadsto \frac{\color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot x}}{y} \]

   2. associate-/l* 87.9%

      \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

   3. associate--l+ 87.9%

      \[\leadsto e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

   4. fma-define 87.9%

      \[\leadsto e^{\color{blue}{\mathsf{fma}\left(y, \log z, \left(t - 1\right) \cdot \log a - b\right)}} \cdot \frac{x}{y} \]

   5. fma-neg 87.9%

      \[\leadsto e^{\mathsf{fma}\left(y, \log z, \color{blue}{\mathsf{fma}\left(t - 1, \log a, -b\right)}\right)} \cdot \frac{x}{y} \]

   6. sub-neg 87.9%

      \[\leadsto e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(\color{blue}{t + \left(-1\right)}, \log a, -b\right)\right)} \cdot \frac{x}{y} \]

   7. metadata-eval 87.9%

      \[\leadsto e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(t + \color{blue}{-1}, \log a, -b\right)\right)} \cdot \frac{x}{y} \]

3. Simplified 87.9%

   \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log z, \mathsf{fma}\left(t + -1, \log a, -b\right)\right)} \cdot \frac{x}{y}} \]
4. Add Preprocessing

5. Taylor expanded in y around inf 46.6%

   \[\leadsto e^{\color{blue}{y \cdot \log z}} \cdot \frac{x}{y} \]

6. Taylor expanded in y around 0 13.9%

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

7. Final simplification 13.9%

   \[\leadsto \frac{x}{y} \]
8. Add Preprocessing

Developer target: 71.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := {a}^{\left(t - 1\right)}\\ t_2 := \frac{x \cdot \frac{t\_1}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \mathbf{if}\;t < -0.8845848504127471:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 852031.2288374073:\\ \;\;\;\;\frac{\frac{x}{y} \cdot t\_1}{e^{b - \log z \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (pow a (- t 1.0)))
        (t_2 (/ (* x (/ t_1 y)) (- (+ b 1.0) (* y (log z))))))
   (if (< t -0.8845848504127471)
     t_2
     (if (< t 852031.2288374073)
       (/ (* (/ x y) t_1) (exp (- b (* (log z) y))))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = pow(a, (t - 1.0));
	double t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * log(z)));
	double tmp;
	if (t < -0.8845848504127471) {
		tmp = t_2;
	} else if (t < 852031.2288374073) {
		tmp = ((x / y) * t_1) / exp((b - (log(z) * y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a ** (t - 1.0d0)
    t_2 = (x * (t_1 / y)) / ((b + 1.0d0) - (y * log(z)))
    if (t < (-0.8845848504127471d0)) then
        tmp = t_2
    else if (t < 852031.2288374073d0) then
        tmp = ((x / y) * t_1) / exp((b - (log(z) * y)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = Math.pow(a, (t - 1.0));
	double t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * Math.log(z)));
	double tmp;
	if (t < -0.8845848504127471) {
		tmp = t_2;
	} else if (t < 852031.2288374073) {
		tmp = ((x / y) * t_1) / Math.exp((b - (Math.log(z) * y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.pow(a, (t - 1.0))
	t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * math.log(z)))
	tmp = 0
	if t < -0.8845848504127471:
		tmp = t_2
	elif t < 852031.2288374073:
		tmp = ((x / y) * t_1) / math.exp((b - (math.log(z) * y)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = a ^ Float64(t - 1.0)
	t_2 = Float64(Float64(x * Float64(t_1 / y)) / Float64(Float64(b + 1.0) - Float64(y * log(z))))
	tmp = 0.0
	if (t < -0.8845848504127471)
		tmp = t_2;
	elseif (t < 852031.2288374073)
		tmp = Float64(Float64(Float64(x / y) * t_1) / exp(Float64(b - Float64(log(z) * y))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a ^ (t - 1.0);
	t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * log(z)));
	tmp = 0.0;
	if (t < -0.8845848504127471)
		tmp = t_2;
	elseif (t < 852031.2288374073)
		tmp = ((x / y) * t_1) / exp((b - (log(z) * y)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision] / N[(N[(b + 1.0), $MachinePrecision] - N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -0.8845848504127471], t$95$2, If[Less[t, 852031.2288374073], N[(N[(N[(x / y), $MachinePrecision] * t$95$1), $MachinePrecision] / N[Exp[N[(b - N[(N[Log[z], $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024046 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A"
  :precision binary64

  :alt
  (if (< t -0.8845848504127471) (/ (* x (/ (pow a (- t 1.0)) y)) (- (+ b 1.0) (* y (log z)))) (if (< t 852031.2288374073) (/ (* (/ x y) (pow a (- t 1.0))) (exp (- b (* (log z) y)))) (/ (* x (/ (pow a (- t 1.0)) y)) (- (+ b 1.0) (* y (log z))))))

  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))