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

Percentage Accurate: 98.4% → 98.4%

Time: 18.8s

Alternatives: 17

Speedup: 1.0×

• 21.5% 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: 98.4% 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: 98.4% 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]

Derivation

1. Initial program 98.6%

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

2. Final simplification 98.6%

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

Alternative 2: 92.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -12000 \lor \neg \left(y \leq 7.8 \cdot 10^{+56}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -12000.0) (not (<= y 7.8e+56)))
   (/ (* x (exp (- (- (* y (log z)) (log a)) b))) y)
   (/ (* x (exp (- (* (+ t -1.0) (log a)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -12000.0) || !(y <= 7.8e+56)) {
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	} else {
		tmp = (x * exp((((t + -1.0) * 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 ((y <= (-12000.0d0)) .or. (.not. (y <= 7.8d+56))) then
        tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y
    else
        tmp = (x * exp((((t + (-1.0d0)) * 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 ((y <= -12000.0) || !(y <= 7.8e+56)) {
		tmp = (x * Math.exp((((y * Math.log(z)) - Math.log(a)) - b))) / y;
	} else {
		tmp = (x * Math.exp((((t + -1.0) * Math.log(a)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -12000.0) or not (y <= 7.8e+56):
		tmp = (x * math.exp((((y * math.log(z)) - math.log(a)) - b))) / y
	else:
		tmp = (x * math.exp((((t + -1.0) * math.log(a)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -12000.0) || !(y <= 7.8e+56))
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) - log(a)) - b))) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -12000.0) || ~((y <= 7.8e+56)))
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	else
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -12000.0], N[Not[LessEqual[y, 7.8e+56]], $MachinePrecision]], N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] - N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -12000 or 7.79999999999999989e56 < 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. Taylor expanded in t around 0 92.9%

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

      1. +-commutative 92.9%

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

      2. mul-1-neg 92.9%

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

      3. unsub-neg 92.9%

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

   4. Simplified 92.9%

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

   if -12000 < y < 7.79999999999999989e56

   1. Initial program 97.2%

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

   2. Taylor expanded in y around 0 96.6%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -12000 \lor \neg \left(y \leq 7.8 \cdot 10^{+56}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \]

Alternative 3: 88.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+44} \lor \neg \left(y \leq 1.7 \cdot 10^{+58}\right):\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -5e+44) (not (<= y 1.7e+58)))
   (* x (/ (/ (pow z y) a) y))
   (/ (* x (exp (- (* (+ t -1.0) (log a)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -5e+44) || !(y <= 1.7e+58)) {
		tmp = x * ((pow(z, y) / a) / y);
	} else {
		tmp = (x * exp((((t + -1.0) * 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 ((y <= (-5d+44)) .or. (.not. (y <= 1.7d+58))) then
        tmp = x * (((z ** y) / a) / y)
    else
        tmp = (x * exp((((t + (-1.0d0)) * 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 ((y <= -5e+44) || !(y <= 1.7e+58)) {
		tmp = x * ((Math.pow(z, y) / a) / y);
	} else {
		tmp = (x * Math.exp((((t + -1.0) * Math.log(a)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -5e+44) or not (y <= 1.7e+58):
		tmp = x * ((math.pow(z, y) / a) / y)
	else:
		tmp = (x * math.exp((((t + -1.0) * math.log(a)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -5e+44) || !(y <= 1.7e+58))
		tmp = Float64(x * Float64(Float64((z ^ y) / a) / y));
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -5e+44) || ~((y <= 1.7e+58)))
		tmp = x * (((z ^ y) / a) / y);
	else
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -5e+44], N[Not[LessEqual[y, 1.7e+58]], $MachinePrecision]], N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.9999999999999996e44 or 1.7e58 < 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* 77.9%

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

      3. exp-diff 59.3%

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

      4. associate-/l/ 59.3%

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

      5. exp-sum 46.9%

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

      6. *-commutative 46.9%

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

      7. exp-to-pow 46.9%

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

      8. *-commutative 46.9%

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

      9. exp-to-pow 46.9%

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

      10. sub-neg 46.9%

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

      11. metadata-eval 46.9%

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

   3. Simplified 46.9%

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

   4. Taylor expanded in t around 0 54.9%

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

   5. Taylor expanded in b around 0 67.4%

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

      1. associate-/r/ 88.7%

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

   7. Applied egg-rr 88.7%

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

   if -4.9999999999999996e44 < y < 1.7e58

   1. Initial program 97.5%

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

   2. Taylor expanded in y around 0 94.2%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+44} \lor \neg \left(y \leq 1.7 \cdot 10^{+58}\right):\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \]

Alternative 4: 81.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+49} \lor \neg \left(y \leq 1.45 \cdot 10^{+56}\right):\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4.8e+49) (not (<= y 1.45e+56)))
   (* x (/ (/ (pow z y) a) 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 <= -4.8e+49) || !(y <= 1.45e+56)) {
		tmp = x * ((pow(z, y) / a) / 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 <= (-4.8d+49)) .or. (.not. (y <= 1.45d+56))) then
        tmp = x * (((z ** y) / a) / 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 <= -4.8e+49) || !(y <= 1.45e+56)) {
		tmp = x * ((Math.pow(z, y) / a) / 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 <= -4.8e+49) or not (y <= 1.45e+56):
		tmp = x * ((math.pow(z, y) / a) / 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 <= -4.8e+49) || !(y <= 1.45e+56))
		tmp = Float64(x * Float64(Float64((z ^ y) / a) / 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 <= -4.8e+49) || ~((y <= 1.45e+56)))
		tmp = x * (((z ^ y) / a) / 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, -4.8e+49], N[Not[LessEqual[y, 1.45e+56]], $MachinePrecision]], N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $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 < -4.8e49 or 1.45000000000000004e56 < 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* 77.9%

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

      3. exp-diff 59.3%

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

      4. associate-/l/ 59.3%

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

      5. exp-sum 46.9%

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

      6. *-commutative 46.9%

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

      7. exp-to-pow 46.9%

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

      8. *-commutative 46.9%

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

      9. exp-to-pow 46.9%

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

      10. sub-neg 46.9%

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

      11. metadata-eval 46.9%

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

   3. Simplified 46.9%

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

   4. Taylor expanded in t around 0 54.9%

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

   5. Taylor expanded in b around 0 67.4%

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

      1. associate-/r/ 88.7%

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

   7. Applied egg-rr 88.7%

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

   if -4.8e49 < y < 1.45000000000000004e56

   1. Initial program 97.5%

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

   2. Taylor expanded in y around 0 94.2%

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

      1. associate-/l* 92.6%

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

      2. div-exp 80.0%

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

      3. exp-to-pow 80.6%

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

      4. sub-neg 80.6%

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

      5. metadata-eval 80.6%

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

   4. Simplified 80.6%

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

   5. Taylor expanded in x around 0 80.2%

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

      1. associate-/l/ 80.2%

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

      2. exp-to-pow 81.1%

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

      3. sub-neg 81.1%

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

      4. metadata-eval 81.1%

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

      5. associate-*r/ 82.5%

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

      6. *-rgt-identity 82.5%

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

      7. associate-*r/ 82.4%

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

      8. associate-*l* 80.5%

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

      9. associate-*r/ 80.5%

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

      10. *-rgt-identity 80.5%

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

      11. metadata-eval 80.5%

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

      12. sub-neg 80.5%

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

   7. Simplified 80.5%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+49} \lor \neg \left(y \leq 1.45 \cdot 10^{+56}\right):\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \end{array} \]

Alternative 5: 82.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+51} \lor \neg \left(y \leq 7.3 \cdot 10^{+56}\right):\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{\frac{{a}^{t}}{a}}{e^{b}}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.15e+51) (not (<= y 7.3e+56)))
   (* x (/ (/ (pow z y) a) y))
   (/ x (/ y (/ (/ (pow a t) a) (exp b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.15e+51) || !(y <= 7.3e+56)) {
		tmp = x * ((pow(z, y) / a) / y);
	} else {
		tmp = x / (y / ((pow(a, t) / a) / 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 <= (-2.15d+51)) .or. (.not. (y <= 7.3d+56))) then
        tmp = x * (((z ** y) / a) / y)
    else
        tmp = x / (y / (((a ** t) / a) / 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 <= -2.15e+51) || !(y <= 7.3e+56)) {
		tmp = x * ((Math.pow(z, y) / a) / y);
	} else {
		tmp = x / (y / ((Math.pow(a, t) / a) / Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.15e+51) or not (y <= 7.3e+56):
		tmp = x * ((math.pow(z, y) / a) / y)
	else:
		tmp = x / (y / ((math.pow(a, t) / a) / math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.15e+51) || !(y <= 7.3e+56))
		tmp = Float64(x * Float64(Float64((z ^ y) / a) / y));
	else
		tmp = Float64(x / Float64(y / Float64(Float64((a ^ t) / a) / exp(b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.15e+51) || ~((y <= 7.3e+56)))
		tmp = x * (((z ^ y) / a) / y);
	else
		tmp = x / (y / (((a ^ t) / a) / exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.15e+51], N[Not[LessEqual[y, 7.3e+56]], $MachinePrecision]], N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(y / N[(N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.1499999999999999e51 or 7.3e56 < 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* 77.9%

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

      3. exp-diff 59.3%

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

      4. associate-/l/ 59.3%

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

      5. exp-sum 46.9%

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

      6. *-commutative 46.9%

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

      7. exp-to-pow 46.9%

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

      8. *-commutative 46.9%

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

      9. exp-to-pow 46.9%

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

      10. sub-neg 46.9%

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

      11. metadata-eval 46.9%

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

   3. Simplified 46.9%

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

   4. Taylor expanded in t around 0 54.9%

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

   5. Taylor expanded in b around 0 67.4%

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

      1. associate-/r/ 88.7%

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

   7. Applied egg-rr 88.7%

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

   if -2.1499999999999999e51 < y < 7.3e56

   1. Initial program 97.5%

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

   2. Taylor expanded in y around 0 94.2%

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

      1. associate-/l* 92.6%

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

      2. div-exp 80.0%

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

      3. exp-to-pow 80.6%

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

      4. sub-neg 80.6%

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

      5. metadata-eval 80.6%

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

   4. Simplified 80.6%

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

      1. expm1-log1p-u 80.5%

         \[\leadsto \frac{x}{\frac{y}{\frac{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left({a}^{\left(t + -1\right)}\right)\right)}}{e^{b}}}} \]

      2. expm1-udef 69.0%

         \[\leadsto \frac{x}{\frac{y}{\frac{\color{blue}{e^{\mathsf{log1p}\left({a}^{\left(t + -1\right)}\right)} - 1}}{e^{b}}}} \]

      3. metadata-eval 69.0%

         \[\leadsto \frac{x}{\frac{y}{\frac{e^{\mathsf{log1p}\left({a}^{\left(t + \color{blue}{\left(-1\right)}\right)}\right)} - 1}{e^{b}}}} \]

      4. sub-neg 69.0%

         \[\leadsto \frac{x}{\frac{y}{\frac{e^{\mathsf{log1p}\left({a}^{\color{blue}{\left(t - 1\right)}}\right)} - 1}{e^{b}}}} \]

      5. pow-sub 69.0%

         \[\leadsto \frac{x}{\frac{y}{\frac{e^{\mathsf{log1p}\left(\color{blue}{\frac{{a}^{t}}{{a}^{1}}}\right)} - 1}{e^{b}}}} \]

      6. pow1 69.0%

         \[\leadsto \frac{x}{\frac{y}{\frac{e^{\mathsf{log1p}\left(\frac{{a}^{t}}{\color{blue}{a}}\right)} - 1}{e^{b}}}} \]

   6. Applied egg-rr 69.0%

      \[\leadsto \frac{x}{\frac{y}{\frac{\color{blue}{e^{\mathsf{log1p}\left(\frac{{a}^{t}}{a}\right)} - 1}}{e^{b}}}} \]
   7. Step-by-step derivation

      1. expm1-def 80.7%

         \[\leadsto \frac{x}{\frac{y}{\frac{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{{a}^{t}}{a}\right)\right)}}{e^{b}}}} \]

      2. expm1-log1p 80.8%

         \[\leadsto \frac{x}{\frac{y}{\frac{\color{blue}{\frac{{a}^{t}}{a}}}{e^{b}}}} \]

   8. Simplified 80.8%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+51} \lor \neg \left(y \leq 7.3 \cdot 10^{+56}\right):\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{\frac{{a}^{t}}{a}}{e^{b}}}}\\ \end{array} \]

Alternative 6: 74.8% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{if}\;y \leq -4800:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-114}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+55}:\\ \;\;\;\;\frac{x}{\frac{y}{{a}^{\left(t + -1\right)}}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (/ (pow z y) a) y))))
   (if (<= y -4800.0)
     t_1
     (if (<= y 8e-114)
       (/ (/ x (* a (exp b))) y)
       (if (<= y 2.7e+55) (/ x (/ y (pow a (+ t -1.0)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * ((pow(z, y) / a) / y);
	double tmp;
	if (y <= -4800.0) {
		tmp = t_1;
	} else if (y <= 8e-114) {
		tmp = (x / (a * exp(b))) / y;
	} else if (y <= 2.7e+55) {
		tmp = x / (y / pow(a, (t + -1.0)));
	} else {
		tmp = t_1;
	}
	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) :: tmp
    t_1 = x * (((z ** y) / a) / y)
    if (y <= (-4800.0d0)) then
        tmp = t_1
    else if (y <= 8d-114) then
        tmp = (x / (a * exp(b))) / y
    else if (y <= 2.7d+55) then
        tmp = x / (y / (a ** (t + (-1.0d0))))
    else
        tmp = t_1
    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(z, y) / a) / y);
	double tmp;
	if (y <= -4800.0) {
		tmp = t_1;
	} else if (y <= 8e-114) {
		tmp = (x / (a * Math.exp(b))) / y;
	} else if (y <= 2.7e+55) {
		tmp = x / (y / Math.pow(a, (t + -1.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * ((math.pow(z, y) / a) / y)
	tmp = 0
	if y <= -4800.0:
		tmp = t_1
	elif y <= 8e-114:
		tmp = (x / (a * math.exp(b))) / y
	elif y <= 2.7e+55:
		tmp = x / (y / math.pow(a, (t + -1.0)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(Float64((z ^ y) / a) / y))
	tmp = 0.0
	if (y <= -4800.0)
		tmp = t_1;
	elseif (y <= 8e-114)
		tmp = Float64(Float64(x / Float64(a * exp(b))) / y);
	elseif (y <= 2.7e+55)
		tmp = Float64(x / Float64(y / (a ^ Float64(t + -1.0))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (((z ^ y) / a) / y);
	tmp = 0.0;
	if (y <= -4800.0)
		tmp = t_1;
	elseif (y <= 8e-114)
		tmp = (x / (a * exp(b))) / y;
	elseif (y <= 2.7e+55)
		tmp = x / (y / (a ^ (t + -1.0)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4800.0], t$95$1, If[LessEqual[y, 8e-114], N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 2.7e+55], N[(x / N[(y / N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4800 or 2.69999999999999977e55 < 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* 80.0%

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

      3. exp-diff 60.0%

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

      4. associate-/l/ 60.0%

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

      5. exp-sum 46.4%

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

      6. *-commutative 46.4%

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

      7. exp-to-pow 46.4%

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

      8. *-commutative 46.4%

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

      9. exp-to-pow 46.4%

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

      10. sub-neg 46.4%

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

      11. metadata-eval 46.4%

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

   3. Simplified 46.4%

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

   4. Taylor expanded in t around 0 55.3%

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

   5. Taylor expanded in b around 0 66.6%

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

      1. associate-/r/ 85.8%

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

   7. Applied egg-rr 85.8%

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

   if -4800 < y < 8.0000000000000004e-114

   1. Initial program 96.8%

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

   2. Taylor expanded in t around 0 76.6%

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

      1. +-commutative 76.6%

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

      2. mul-1-neg 76.6%

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

      3. unsub-neg 76.6%

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

   4. Simplified 76.6%

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

   5. Taylor expanded in y around 0 76.6%

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

      1. exp-neg 76.6%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      2. associate-*r/ 76.6%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot 1}{e^{b + \log a}}}}{y} \]

      3. *-rgt-identity 76.6%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. +-commutative 76.6%

         \[\leadsto \frac{\frac{x}{e^{\color{blue}{\log a + b}}}}{y} \]

      5. exp-sum 76.6%

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

      6. rem-exp-log 77.7%

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

   7. Simplified 77.7%

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

   if 8.0000000000000004e-114 < y < 2.69999999999999977e55

   1. Initial program 98.8%

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

   2. Taylor expanded in y around 0 96.1%

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

      1. associate-/l* 96.3%

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

      2. div-exp 92.9%

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

      3. exp-to-pow 93.4%

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

      4. sub-neg 93.4%

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

      5. metadata-eval 93.4%

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

   4. Simplified 93.4%

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

   5. Taylor expanded in b around 0 86.2%

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

      1. exp-to-pow 86.7%

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

   7. Simplified 86.7%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4800:\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-114}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+55}:\\ \;\;\;\;\frac{x}{\frac{y}{{a}^{\left(t + -1\right)}}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \end{array} \]

Alternative 7: 75.4% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8500 \lor \neg \left(y \leq 0.66\right):\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -8500.0) (not (<= y 0.66)))
   (* x (/ (/ (pow z y) a) y))
   (/ (/ x (* a (exp b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -8500.0) || !(y <= 0.66)) {
		tmp = x * ((pow(z, y) / a) / y);
	} else {
		tmp = (x / (a * 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 <= (-8500.0d0)) .or. (.not. (y <= 0.66d0))) then
        tmp = x * (((z ** y) / a) / y)
    else
        tmp = (x / (a * 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 <= -8500.0) || !(y <= 0.66)) {
		tmp = x * ((Math.pow(z, y) / a) / y);
	} else {
		tmp = (x / (a * Math.exp(b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -8500.0) or not (y <= 0.66):
		tmp = x * ((math.pow(z, y) / a) / y)
	else:
		tmp = (x / (a * math.exp(b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -8500.0) || !(y <= 0.66))
		tmp = Float64(x * Float64(Float64((z ^ y) / a) / y));
	else
		tmp = Float64(Float64(x / Float64(a * exp(b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -8500.0) || ~((y <= 0.66)))
		tmp = x * (((z ^ y) / a) / y);
	else
		tmp = (x / (a * exp(b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -8500.0], N[Not[LessEqual[y, 0.66]], $MachinePrecision]], N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8500 or 0.660000000000000031 < y

   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* 81.4%

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

      3. exp-diff 62.9%

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

      4. associate-/l/ 62.9%

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

      5. exp-sum 47.3%

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

      6. *-commutative 47.3%

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

      7. exp-to-pow 47.3%

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

      8. *-commutative 47.3%

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

      9. exp-to-pow 47.4%

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

      10. sub-neg 47.4%

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

      11. metadata-eval 47.4%

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

   3. Simplified 47.4%

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

   4. Taylor expanded in t around 0 55.7%

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

   5. Taylor expanded in b around 0 66.2%

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

      1. associate-/r/ 84.0%

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

   7. Applied egg-rr 84.0%

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

   if -8500 < y < 0.660000000000000031

   1. Initial program 97.1%

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

   2. Taylor expanded in t around 0 76.2%

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

      1. +-commutative 76.2%

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

      2. mul-1-neg 76.2%

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

      3. unsub-neg 76.2%

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

   4. Simplified 76.2%

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

   5. Taylor expanded in y around 0 76.2%

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

      1. exp-neg 76.2%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      2. associate-*r/ 76.2%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot 1}{e^{b + \log a}}}}{y} \]

      3. *-rgt-identity 76.2%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. +-commutative 76.2%

         \[\leadsto \frac{\frac{x}{e^{\color{blue}{\log a + b}}}}{y} \]

      5. exp-sum 76.2%

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

      6. rem-exp-log 77.2%

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

   7. Simplified 77.2%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8500 \lor \neg \left(y \leq 0.66\right):\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \end{array} \]

Alternative 8: 57.2% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.4 \cdot 10^{-17} \lor \neg \left(b \leq 8.5 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{a - \frac{a}{x} \cdot \left(x \cdot b\right)}{a \cdot \frac{a}{x}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -3.4e-17) (not (<= b 8.5e-7)))
   (/ x (* a (* y (exp b))))
   (/ (/ (- a (* (/ a x) (* x b))) (* a (/ a x))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.4e-17) || !(b <= 8.5e-7)) {
		tmp = x / (a * (y * exp(b)));
	} else {
		tmp = ((a - ((a / x) * (x * b))) / (a * (a / 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 ((b <= (-3.4d-17)) .or. (.not. (b <= 8.5d-7))) then
        tmp = x / (a * (y * exp(b)))
    else
        tmp = ((a - ((a / x) * (x * b))) / (a * (a / 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 ((b <= -3.4e-17) || !(b <= 8.5e-7)) {
		tmp = x / (a * (y * Math.exp(b)));
	} else {
		tmp = ((a - ((a / x) * (x * b))) / (a * (a / x))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -3.4e-17) or not (b <= 8.5e-7):
		tmp = x / (a * (y * math.exp(b)))
	else:
		tmp = ((a - ((a / x) * (x * b))) / (a * (a / x))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -3.4e-17) || !(b <= 8.5e-7))
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	else
		tmp = Float64(Float64(Float64(a - Float64(Float64(a / x) * Float64(x * b))) / Float64(a * Float64(a / x))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -3.4e-17) || ~((b <= 8.5e-7)))
		tmp = x / (a * (y * exp(b)));
	else
		tmp = ((a - ((a / x) * (x * b))) / (a * (a / x))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -3.4e-17], N[Not[LessEqual[b, 8.5e-7]], $MachinePrecision]], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(a - N[(N[(a / x), $MachinePrecision] * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.3999999999999998e-17 or 8.50000000000000014e-7 < 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. associate-*l/ 85.9%

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

      2. *-commutative 85.9%

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

      3. +-commutative 85.9%

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

      4. associate--l+ 85.9%

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

      5. exp-sum 64.4%

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

      6. *-commutative 64.4%

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

      7. exp-to-pow 64.4%

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

      8. sub-neg 64.4%

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

      9. metadata-eval 64.4%

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

      10. exp-diff 50.4%

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

      11. *-commutative 50.4%

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

      12. exp-to-pow 50.4%

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

   3. Simplified 50.4%

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

   4. Taylor expanded in t around 0 69.8%

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

      1. times-frac 60.1%

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

   6. Simplified 60.1%

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

   7. Taylor expanded in y around 0 78.2%

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

   if -3.3999999999999998e-17 < b < 8.50000000000000014e-7

   1. Initial program 97.0%

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

   2. Taylor expanded in t around 0 76.9%

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

      1. +-commutative 76.9%

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

      2. mul-1-neg 76.9%

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

      3. unsub-neg 76.9%

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

   4. Simplified 76.9%

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

   5. Taylor expanded in y around 0 34.0%

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

      1. exp-neg 34.0%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      2. associate-*r/ 34.0%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot 1}{e^{b + \log a}}}}{y} \]

      3. *-rgt-identity 34.0%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. +-commutative 34.0%

         \[\leadsto \frac{\frac{x}{e^{\color{blue}{\log a + b}}}}{y} \]

      5. exp-sum 34.0%

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

      6. rem-exp-log 35.1%

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

   7. Simplified 35.1%

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

   8. Taylor expanded in b around 0 35.1%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]
   9. Step-by-step derivation

      1. +-commutative 35.1%

         \[\leadsto \frac{\color{blue}{\frac{x}{a} + -1 \cdot \frac{b \cdot x}{a}}}{y} \]

      2. clear-num 35.0%

         \[\leadsto \frac{\color{blue}{\frac{1}{\frac{a}{x}}} + -1 \cdot \frac{b \cdot x}{a}}{y} \]

      3. associate-*r/ 35.0%

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

      4. frac-add 42.8%

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

      5. *-un-lft-identity 42.8%

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

      6. *-commutative 42.8%

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

   10. Applied egg-rr 42.8%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.4 \cdot 10^{-17} \lor \neg \left(b \leq 8.5 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{a - \frac{a}{x} \cdot \left(x \cdot b\right)}{a \cdot \frac{a}{x}}}{y}\\ \end{array} \]

Alternative 9: 39.9% accurate, 14.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{-12}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} - \frac{b}{a}\right) + \frac{b}{\frac{\frac{a}{x}}{b}}}{y}\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-5}:\\ \;\;\;\;\frac{\frac{a - \frac{a}{x} \cdot \left(x \cdot b\right)}{a \cdot \frac{a}{x}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2e-12)
   (/ (+ (* x (- (/ 1.0 a) (/ b a))) (/ b (/ (/ a x) b))) y)
   (if (<= b 7e-5)
     (/ (/ (- a (* (/ a x) (* x b))) (* a (/ a x))) y)
     (/ x (* y (+ a (* a b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2e-12) {
		tmp = ((x * ((1.0 / a) - (b / a))) + (b / ((a / x) / b))) / y;
	} else if (b <= 7e-5) {
		tmp = ((a - ((a / x) * (x * b))) / (a * (a / x))) / y;
	} else {
		tmp = x / (y * (a + (a * 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 <= (-2d-12)) then
        tmp = ((x * ((1.0d0 / a) - (b / a))) + (b / ((a / x) / b))) / y
    else if (b <= 7d-5) then
        tmp = ((a - ((a / x) * (x * b))) / (a * (a / x))) / y
    else
        tmp = x / (y * (a + (a * 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 <= -2e-12) {
		tmp = ((x * ((1.0 / a) - (b / a))) + (b / ((a / x) / b))) / y;
	} else if (b <= 7e-5) {
		tmp = ((a - ((a / x) * (x * b))) / (a * (a / x))) / y;
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2e-12:
		tmp = ((x * ((1.0 / a) - (b / a))) + (b / ((a / x) / b))) / y
	elif b <= 7e-5:
		tmp = ((a - ((a / x) * (x * b))) / (a * (a / x))) / y
	else:
		tmp = x / (y * (a + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2e-12)
		tmp = Float64(Float64(Float64(x * Float64(Float64(1.0 / a) - Float64(b / a))) + Float64(b / Float64(Float64(a / x) / b))) / y);
	elseif (b <= 7e-5)
		tmp = Float64(Float64(Float64(a - Float64(Float64(a / x) * Float64(x * b))) / Float64(a * Float64(a / x))) / y);
	else
		tmp = Float64(x / Float64(y * Float64(a + Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2e-12)
		tmp = ((x * ((1.0 / a) - (b / a))) + (b / ((a / x) / b))) / y;
	elseif (b <= 7e-5)
		tmp = ((a - ((a / x) * (x * b))) / (a * (a / x))) / y;
	else
		tmp = x / (y * (a + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2e-12], N[(N[(N[(x * N[(N[(1.0 / a), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b / N[(N[(a / x), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 7e-5], N[(N[(N[(a - N[(N[(a / x), $MachinePrecision] * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.99999999999999996e-12

   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. Taylor expanded in t around 0 92.5%

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

      1. +-commutative 92.5%

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

      2. mul-1-neg 92.5%

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

      3. unsub-neg 92.5%

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

   4. Simplified 92.5%

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

   5. Taylor expanded in y around 0 79.3%

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

      1. exp-neg 79.3%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      2. associate-*r/ 79.3%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot 1}{e^{b + \log a}}}}{y} \]

      3. *-rgt-identity 79.3%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. +-commutative 79.3%

         \[\leadsto \frac{\frac{x}{e^{\color{blue}{\log a + b}}}}{y} \]

      5. exp-sum 79.3%

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

      6. rem-exp-log 79.3%

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

   7. Simplified 79.3%

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

   8. Taylor expanded in b around 0 13.5%

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

   9. Taylor expanded in b around 0 66.3%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \left(\frac{x}{a} + \frac{{b}^{2} \cdot x}{a}\right)}}{y} \]
   10. Step-by-step derivation

       1. associate-+r+ 66.3%

          \[\leadsto \frac{\color{blue}{\left(-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}\right) + \frac{{b}^{2} \cdot x}{a}}}{y} \]

       2. associate-/l* 66.3%

          \[\leadsto \frac{\left(-1 \cdot \color{blue}{\frac{b}{\frac{a}{x}}} + \frac{x}{a}\right) + \frac{{b}^{2} \cdot x}{a}}{y} \]

       3. associate-/r/ 67.8%

          \[\leadsto \frac{\left(-1 \cdot \color{blue}{\left(\frac{b}{a} \cdot x\right)} + \frac{x}{a}\right) + \frac{{b}^{2} \cdot x}{a}}{y} \]

       4. associate-*r* 67.8%

          \[\leadsto \frac{\left(\color{blue}{\left(-1 \cdot \frac{b}{a}\right) \cdot x} + \frac{x}{a}\right) + \frac{{b}^{2} \cdot x}{a}}{y} \]

       5. *-lft-identity 67.8%

          \[\leadsto \frac{\left(\left(-1 \cdot \frac{b}{a}\right) \cdot x + \frac{\color{blue}{1 \cdot x}}{a}\right) + \frac{{b}^{2} \cdot x}{a}}{y} \]

       6. associate-*l/ 67.8%

          \[\leadsto \frac{\left(\left(-1 \cdot \frac{b}{a}\right) \cdot x + \color{blue}{\frac{1}{a} \cdot x}\right) + \frac{{b}^{2} \cdot x}{a}}{y} \]

       7. distribute-rgt-in 67.8%

          \[\leadsto \frac{\color{blue}{x \cdot \left(-1 \cdot \frac{b}{a} + \frac{1}{a}\right)} + \frac{{b}^{2} \cdot x}{a}}{y} \]

       8. +-commutative 67.8%

          \[\leadsto \frac{x \cdot \color{blue}{\left(\frac{1}{a} + -1 \cdot \frac{b}{a}\right)} + \frac{{b}^{2} \cdot x}{a}}{y} \]

       9. mul-1-neg 67.8%

          \[\leadsto \frac{x \cdot \left(\frac{1}{a} + \color{blue}{\left(-\frac{b}{a}\right)}\right) + \frac{{b}^{2} \cdot x}{a}}{y} \]

       10. unsub-neg 67.8%

           \[\leadsto \frac{x \cdot \color{blue}{\left(\frac{1}{a} - \frac{b}{a}\right)} + \frac{{b}^{2} \cdot x}{a}}{y} \]

       11. associate-/l* 55.7%

           \[\leadsto \frac{x \cdot \left(\frac{1}{a} - \frac{b}{a}\right) + \color{blue}{\frac{{b}^{2}}{\frac{a}{x}}}}{y} \]

       12. unpow2 55.7%

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

       13. associate-/l* 57.5%

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

   11. Simplified 57.5%

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

   if -1.99999999999999996e-12 < b < 6.9999999999999994e-5

   1. Initial program 97.0%

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

   2. Taylor expanded in t around 0 77.3%

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

      1. +-commutative 77.3%

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

      2. mul-1-neg 77.3%

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

      3. unsub-neg 77.3%

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

   4. Simplified 77.3%

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

   5. Taylor expanded in y around 0 35.1%

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

      1. exp-neg 35.1%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      2. associate-*r/ 35.1%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot 1}{e^{b + \log a}}}}{y} \]

      3. *-rgt-identity 35.1%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. +-commutative 35.1%

         \[\leadsto \frac{\frac{x}{e^{\color{blue}{\log a + b}}}}{y} \]

      5. exp-sum 35.1%

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

      6. rem-exp-log 36.1%

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

   7. Simplified 36.1%

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

   8. Taylor expanded in b around 0 36.1%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]
   9. Step-by-step derivation

      1. +-commutative 36.1%

         \[\leadsto \frac{\color{blue}{\frac{x}{a} + -1 \cdot \frac{b \cdot x}{a}}}{y} \]

      2. clear-num 36.1%

         \[\leadsto \frac{\color{blue}{\frac{1}{\frac{a}{x}}} + -1 \cdot \frac{b \cdot x}{a}}{y} \]

      3. associate-*r/ 36.1%

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

      4. frac-add 43.7%

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

      5. *-un-lft-identity 43.7%

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

      6. *-commutative 43.7%

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

   10. Applied egg-rr 43.7%

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

   if 6.9999999999999994e-5 < 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. Taylor expanded in t around 0 86.8%

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

      1. +-commutative 86.8%

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

      2. mul-1-neg 86.8%

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

      3. unsub-neg 86.8%

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

   4. Simplified 86.8%

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

   5. Taylor expanded in y around 0 76.5%

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

      1. exp-neg 76.5%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      2. associate-*r/ 76.5%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot 1}{e^{b + \log a}}}}{y} \]

      3. *-rgt-identity 76.5%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. +-commutative 76.5%

         \[\leadsto \frac{\frac{x}{e^{\color{blue}{\log a + b}}}}{y} \]

      5. exp-sum 76.5%

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

      6. rem-exp-log 76.5%

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

   7. Simplified 76.5%

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

   8. Taylor expanded in b around 0 30.3%

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

   9. Taylor expanded in x around 0 31.8%

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

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{-12}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} - \frac{b}{a}\right) + \frac{b}{\frac{\frac{a}{x}}{b}}}{y}\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-5}:\\ \;\;\;\;\frac{\frac{a - \frac{a}{x} \cdot \left(x \cdot b\right)}{a \cdot \frac{a}{x}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \]

Alternative 10: 41.3% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 8.6 \cdot 10^{-167}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} - \frac{b}{a}\right) + \frac{b}{\frac{\frac{a}{x}}{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 8.6e-167)
   (/ (+ (* x (- (/ 1.0 a) (/ b a))) (/ b (/ (/ a x) b))) y)
   (/ x (* y (+ a (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 8.6e-167) {
		tmp = ((x * ((1.0 / a) - (b / a))) + (b / ((a / x) / b))) / y;
	} else {
		tmp = x / (y * (a + (a * 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-167) then
        tmp = ((x * ((1.0d0 / a) - (b / a))) + (b / ((a / x) / b))) / y
    else
        tmp = x / (y * (a + (a * 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-167) {
		tmp = ((x * ((1.0 / a) - (b / a))) + (b / ((a / x) / b))) / y;
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 8.6e-167:
		tmp = ((x * ((1.0 / a) - (b / a))) + (b / ((a / x) / b))) / y
	else:
		tmp = x / (y * (a + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 8.6e-167)
		tmp = Float64(Float64(Float64(x * Float64(Float64(1.0 / a) - Float64(b / a))) + Float64(b / Float64(Float64(a / x) / b))) / y);
	else
		tmp = Float64(x / Float64(y * Float64(a + Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 8.6e-167)
		tmp = ((x * ((1.0 / a) - (b / a))) + (b / ((a / x) / b))) / y;
	else
		tmp = x / (y * (a + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 8.6e-167], N[(N[(N[(x * N[(N[(1.0 / a), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b / N[(N[(a / x), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 8.5999999999999995e-167

   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. Taylor expanded in t around 0 84.3%

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

      1. +-commutative 84.3%

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

      2. mul-1-neg 84.3%

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

      3. unsub-neg 84.3%

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

   4. Simplified 84.3%

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

   5. Taylor expanded in y around 0 55.0%

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

      1. exp-neg 55.0%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      2. associate-*r/ 55.0%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot 1}{e^{b + \log a}}}}{y} \]

      3. *-rgt-identity 55.0%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. +-commutative 55.0%

         \[\leadsto \frac{\frac{x}{e^{\color{blue}{\log a + b}}}}{y} \]

      5. exp-sum 55.0%

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

      6. rem-exp-log 55.6%

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

   7. Simplified 55.6%

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

   8. Taylor expanded in b around 0 26.8%

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

   9. Taylor expanded in b around 0 50.0%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \left(\frac{x}{a} + \frac{{b}^{2} \cdot x}{a}\right)}}{y} \]
   10. Step-by-step derivation

       1. associate-+r+ 50.0%

          \[\leadsto \frac{\color{blue}{\left(-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}\right) + \frac{{b}^{2} \cdot x}{a}}}{y} \]

       2. associate-/l* 48.6%

          \[\leadsto \frac{\left(-1 \cdot \color{blue}{\frac{b}{\frac{a}{x}}} + \frac{x}{a}\right) + \frac{{b}^{2} \cdot x}{a}}{y} \]

       3. associate-/r/ 50.6%

          \[\leadsto \frac{\left(-1 \cdot \color{blue}{\left(\frac{b}{a} \cdot x\right)} + \frac{x}{a}\right) + \frac{{b}^{2} \cdot x}{a}}{y} \]

       4. associate-*r* 50.6%

          \[\leadsto \frac{\left(\color{blue}{\left(-1 \cdot \frac{b}{a}\right) \cdot x} + \frac{x}{a}\right) + \frac{{b}^{2} \cdot x}{a}}{y} \]

       5. *-lft-identity 50.6%

          \[\leadsto \frac{\left(\left(-1 \cdot \frac{b}{a}\right) \cdot x + \frac{\color{blue}{1 \cdot x}}{a}\right) + \frac{{b}^{2} \cdot x}{a}}{y} \]

       6. associate-*l/ 50.6%

          \[\leadsto \frac{\left(\left(-1 \cdot \frac{b}{a}\right) \cdot x + \color{blue}{\frac{1}{a} \cdot x}\right) + \frac{{b}^{2} \cdot x}{a}}{y} \]

       7. distribute-rgt-in 50.6%

          \[\leadsto \frac{\color{blue}{x \cdot \left(-1 \cdot \frac{b}{a} + \frac{1}{a}\right)} + \frac{{b}^{2} \cdot x}{a}}{y} \]

       8. +-commutative 50.6%

          \[\leadsto \frac{x \cdot \color{blue}{\left(\frac{1}{a} + -1 \cdot \frac{b}{a}\right)} + \frac{{b}^{2} \cdot x}{a}}{y} \]

       9. mul-1-neg 50.6%

          \[\leadsto \frac{x \cdot \left(\frac{1}{a} + \color{blue}{\left(-\frac{b}{a}\right)}\right) + \frac{{b}^{2} \cdot x}{a}}{y} \]

       10. unsub-neg 50.6%

           \[\leadsto \frac{x \cdot \color{blue}{\left(\frac{1}{a} - \frac{b}{a}\right)} + \frac{{b}^{2} \cdot x}{a}}{y} \]

       11. associate-/l* 41.2%

           \[\leadsto \frac{x \cdot \left(\frac{1}{a} - \frac{b}{a}\right) + \color{blue}{\frac{{b}^{2}}{\frac{a}{x}}}}{y} \]

       12. unpow2 41.2%

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

       13. associate-/l* 46.1%

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

   11. Simplified 46.1%

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

   if 8.5999999999999995e-167 < b

   1. Initial program 99.7%

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

   2. Taylor expanded in t around 0 82.8%

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

      1. +-commutative 82.8%

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

      2. mul-1-neg 82.8%

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

      3. unsub-neg 82.8%

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

   4. Simplified 82.8%

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

   5. Taylor expanded in y around 0 60.7%

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

      1. exp-neg 60.7%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      2. associate-*r/ 60.7%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot 1}{e^{b + \log a}}}}{y} \]

      3. *-rgt-identity 60.7%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. +-commutative 60.7%

         \[\leadsto \frac{\frac{x}{e^{\color{blue}{\log a + b}}}}{y} \]

      5. exp-sum 60.7%

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

      6. rem-exp-log 61.0%

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

   7. Simplified 61.0%

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

   8. Taylor expanded in b around 0 31.5%

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

   9. Taylor expanded in x around 0 33.4%

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

4. Final simplification 40.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 8.6 \cdot 10^{-167}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} - \frac{b}{a}\right) + \frac{b}{\frac{\frac{a}{x}}{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \]

Alternative 11: 38.6% accurate, 28.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.115:\\ \;\;\;\;\frac{b}{a} \cdot \frac{-x}{y}\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{-5}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -0.115)
   (* (/ b a) (/ (- x) y))
   (if (<= b 1.55e-5) (/ (/ x a) y) (/ x (* a (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -0.115) {
		tmp = (b / a) * (-x / y);
	} else if (b <= 1.55e-5) {
		tmp = (x / a) / y;
	} 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 <= (-0.115d0)) then
        tmp = (b / a) * (-x / y)
    else if (b <= 1.55d-5) then
        tmp = (x / a) / y
    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 <= -0.115) {
		tmp = (b / a) * (-x / y);
	} else if (b <= 1.55e-5) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -0.115:
		tmp = (b / a) * (-x / y)
	elif b <= 1.55e-5:
		tmp = (x / a) / y
	else:
		tmp = x / (a * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -0.115)
		tmp = Float64(Float64(b / a) * Float64(Float64(-x) / y));
	elseif (b <= 1.55e-5)
		tmp = Float64(Float64(x / a) / y);
	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 <= -0.115)
		tmp = (b / a) * (-x / y);
	elseif (b <= 1.55e-5)
		tmp = (x / a) / y;
	else
		tmp = x / (a * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -0.115], N[(N[(b / a), $MachinePrecision] * N[((-x) / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.55e-5], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -0.115000000000000005

   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. Taylor expanded in t around 0 93.8%

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

      1. +-commutative 93.8%

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

      2. mul-1-neg 93.8%

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

      3. unsub-neg 93.8%

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

   4. Simplified 93.8%

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

   5. Taylor expanded in y around 0 80.1%

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

      1. exp-neg 80.1%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      2. associate-*r/ 80.1%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot 1}{e^{b + \log a}}}}{y} \]

      3. *-rgt-identity 80.1%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. +-commutative 80.1%

         \[\leadsto \frac{\frac{x}{e^{\color{blue}{\log a + b}}}}{y} \]

      5. exp-sum 80.1%

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

      6. rem-exp-log 80.1%

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

   7. Simplified 80.1%

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

   8. Taylor expanded in b around 0 45.7%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]

   9. Taylor expanded in b around inf 40.4%

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

       1. mul-1-neg 40.4%

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

       2. times-frac 40.5%

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

       3. distribute-rgt-neg-in 40.5%

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

   11. Simplified 40.5%

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

   if -0.115000000000000005 < b < 1.55000000000000007e-5

   1. Initial program 97.1%

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

   2. Taylor expanded in t around 0 76.9%

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

      1. +-commutative 76.9%

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

      2. mul-1-neg 76.9%

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

      3. unsub-neg 76.9%

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

   4. Simplified 76.9%

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

   5. Taylor expanded in y around 0 35.4%

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

      1. exp-neg 35.4%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      2. associate-*r/ 35.4%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot 1}{e^{b + \log a}}}}{y} \]

      3. *-rgt-identity 35.4%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. +-commutative 35.4%

         \[\leadsto \frac{\frac{x}{e^{\color{blue}{\log a + b}}}}{y} \]

      5. exp-sum 35.4%

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

      6. rem-exp-log 36.4%

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

   7. Simplified 36.4%

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

   8. Taylor expanded in b around 0 36.4%

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

   if 1.55000000000000007e-5 < 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. Taylor expanded in t around 0 86.8%

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

      1. +-commutative 86.8%

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

      2. mul-1-neg 86.8%

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

      3. unsub-neg 86.8%

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

   4. Simplified 86.8%

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

   5. Taylor expanded in y around 0 76.5%

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

      1. exp-neg 76.5%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      2. associate-*r/ 76.5%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot 1}{e^{b + \log a}}}}{y} \]

      3. *-rgt-identity 76.5%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. +-commutative 76.5%

         \[\leadsto \frac{\frac{x}{e^{\color{blue}{\log a + b}}}}{y} \]

      5. exp-sum 76.5%

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

      6. rem-exp-log 76.5%

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

   7. Simplified 76.5%

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

   8. Taylor expanded in b around 0 30.3%

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

   9. Taylor expanded in b around inf 31.8%

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

4. Final simplification 36.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.115:\\ \;\;\;\;\frac{b}{a} \cdot \frac{-x}{y}\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{-5}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \]

Alternative 12: 38.8% accurate, 28.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.11:\\ \;\;\;\;\frac{\frac{b}{a} \cdot \left(-x\right)}{y}\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-5}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -0.11)
   (/ (* (/ b a) (- x)) y)
   (if (<= b 8.5e-5) (/ (/ x a) y) (/ x (* a (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -0.11) {
		tmp = ((b / a) * -x) / y;
	} else if (b <= 8.5e-5) {
		tmp = (x / a) / y;
	} 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 <= (-0.11d0)) then
        tmp = ((b / a) * -x) / y
    else if (b <= 8.5d-5) then
        tmp = (x / a) / y
    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 <= -0.11) {
		tmp = ((b / a) * -x) / y;
	} else if (b <= 8.5e-5) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -0.11:
		tmp = ((b / a) * -x) / y
	elif b <= 8.5e-5:
		tmp = (x / a) / y
	else:
		tmp = x / (a * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -0.11)
		tmp = Float64(Float64(Float64(b / a) * Float64(-x)) / y);
	elseif (b <= 8.5e-5)
		tmp = Float64(Float64(x / a) / y);
	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 <= -0.11)
		tmp = ((b / a) * -x) / y;
	elseif (b <= 8.5e-5)
		tmp = (x / a) / y;
	else
		tmp = x / (a * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -0.11], N[(N[(N[(b / a), $MachinePrecision] * (-x)), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 8.5e-5], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -0.110000000000000001

   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. Taylor expanded in t around 0 93.8%

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

      1. +-commutative 93.8%

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

      2. mul-1-neg 93.8%

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

      3. unsub-neg 93.8%

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

   4. Simplified 93.8%

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

   5. Taylor expanded in y around 0 80.1%

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

      1. exp-neg 80.1%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      2. associate-*r/ 80.1%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot 1}{e^{b + \log a}}}}{y} \]

      3. *-rgt-identity 80.1%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. +-commutative 80.1%

         \[\leadsto \frac{\frac{x}{e^{\color{blue}{\log a + b}}}}{y} \]

      5. exp-sum 80.1%

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

      6. rem-exp-log 80.1%

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

   7. Simplified 80.1%

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

   8. Taylor expanded in b around 0 45.7%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]

   9. Taylor expanded in b around inf 45.7%

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

       1. associate-/l* 41.1%

          \[\leadsto \frac{-1 \cdot \color{blue}{\frac{b}{\frac{a}{x}}}}{y} \]

       2. associate-/r/ 47.1%

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

       3. associate-*r* 47.1%

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

       4. *-commutative 47.1%

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

       5. associate-*r/ 47.1%

          \[\leadsto \frac{x \cdot \color{blue}{\frac{-1 \cdot b}{a}}}{y} \]

       6. mul-1-neg 47.1%

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

   11. Simplified 47.1%

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

   if -0.110000000000000001 < b < 8.500000000000001e-5

   1. Initial program 97.1%

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

   2. Taylor expanded in t around 0 76.9%

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

      1. +-commutative 76.9%

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

      2. mul-1-neg 76.9%

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

      3. unsub-neg 76.9%

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

   4. Simplified 76.9%

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

   5. Taylor expanded in y around 0 35.4%

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

      1. exp-neg 35.4%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      2. associate-*r/ 35.4%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot 1}{e^{b + \log a}}}}{y} \]

      3. *-rgt-identity 35.4%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. +-commutative 35.4%

         \[\leadsto \frac{\frac{x}{e^{\color{blue}{\log a + b}}}}{y} \]

      5. exp-sum 35.4%

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

      6. rem-exp-log 36.4%

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

   7. Simplified 36.4%

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

   8. Taylor expanded in b around 0 36.4%

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

   if 8.500000000000001e-5 < 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. Taylor expanded in t around 0 86.8%

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

      1. +-commutative 86.8%

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

      2. mul-1-neg 86.8%

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

      3. unsub-neg 86.8%

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

   4. Simplified 86.8%

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

   5. Taylor expanded in y around 0 76.5%

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

      1. exp-neg 76.5%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      2. associate-*r/ 76.5%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot 1}{e^{b + \log a}}}}{y} \]

      3. *-rgt-identity 76.5%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. +-commutative 76.5%

         \[\leadsto \frac{\frac{x}{e^{\color{blue}{\log a + b}}}}{y} \]

      5. exp-sum 76.5%

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

      6. rem-exp-log 76.5%

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

   7. Simplified 76.5%

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

   8. Taylor expanded in b around 0 30.3%

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

   9. Taylor expanded in b around inf 31.8%

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

4. Final simplification 37.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.11:\\ \;\;\;\;\frac{\frac{b}{a} \cdot \left(-x\right)}{y}\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-5}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \]

Alternative 13: 39.0% accurate, 28.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.0031:\\ \;\;\;\;\frac{\frac{b}{a} \cdot \left(-x\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -0.0031) (/ (* (/ b a) (- x)) y) (/ x (* y (+ a (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -0.0031) {
		tmp = ((b / a) * -x) / y;
	} else {
		tmp = x / (y * (a + (a * 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 <= (-0.0031d0)) then
        tmp = ((b / a) * -x) / y
    else
        tmp = x / (y * (a + (a * 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 <= -0.0031) {
		tmp = ((b / a) * -x) / y;
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -0.0031:
		tmp = ((b / a) * -x) / y
	else:
		tmp = x / (y * (a + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -0.0031)
		tmp = Float64(Float64(Float64(b / a) * Float64(-x)) / y);
	else
		tmp = Float64(x / Float64(y * Float64(a + Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -0.0031)
		tmp = ((b / a) * -x) / y;
	else
		tmp = x / (y * (a + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -0.0031], N[(N[(N[(b / a), $MachinePrecision] * (-x)), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -0.00309999999999999989

   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. Taylor expanded in t around 0 93.8%

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

      1. +-commutative 93.8%

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

      2. mul-1-neg 93.8%

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

      3. unsub-neg 93.8%

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

   4. Simplified 93.8%

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

   5. Taylor expanded in y around 0 80.1%

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

      1. exp-neg 80.1%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      2. associate-*r/ 80.1%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot 1}{e^{b + \log a}}}}{y} \]

      3. *-rgt-identity 80.1%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. +-commutative 80.1%

         \[\leadsto \frac{\frac{x}{e^{\color{blue}{\log a + b}}}}{y} \]

      5. exp-sum 80.1%

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

      6. rem-exp-log 80.1%

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

   7. Simplified 80.1%

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

   8. Taylor expanded in b around 0 45.7%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]

   9. Taylor expanded in b around inf 45.7%

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

       1. associate-/l* 41.1%

          \[\leadsto \frac{-1 \cdot \color{blue}{\frac{b}{\frac{a}{x}}}}{y} \]

       2. associate-/r/ 47.1%

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

       3. associate-*r* 47.1%

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

       4. *-commutative 47.1%

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

       5. associate-*r/ 47.1%

          \[\leadsto \frac{x \cdot \color{blue}{\frac{-1 \cdot b}{a}}}{y} \]

       6. mul-1-neg 47.1%

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

   11. Simplified 47.1%

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

   if -0.00309999999999999989 < b

   1. Initial program 98.1%

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

   2. Taylor expanded in t around 0 80.3%

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

      1. +-commutative 80.3%

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

      2. mul-1-neg 80.3%

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

      3. unsub-neg 80.3%

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

   4. Simplified 80.3%

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

   5. Taylor expanded in y around 0 49.7%

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

      1. exp-neg 49.7%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      2. associate-*r/ 49.7%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot 1}{e^{b + \log a}}}}{y} \]

      3. *-rgt-identity 49.7%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. +-commutative 49.7%

         \[\leadsto \frac{\frac{x}{e^{\color{blue}{\log a + b}}}}{y} \]

      5. exp-sum 49.7%

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

      6. rem-exp-log 50.4%

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

   7. Simplified 50.4%

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

   8. Taylor expanded in b around 0 34.3%

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

   9. Taylor expanded in x around 0 33.7%

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

4. Final simplification 37.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.0031:\\ \;\;\;\;\frac{\frac{b}{a} \cdot \left(-x\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \]

Alternative 14: 39.1% accurate, 28.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.125:\\ \;\;\;\;\frac{\frac{b}{a} \cdot \left(-x\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -0.125) (/ (* (/ b a) (- x)) y) (/ (/ x (+ a (* a b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -0.125) {
		tmp = ((b / a) * -x) / y;
	} else {
		tmp = (x / (a + (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 (b <= (-0.125d0)) then
        tmp = ((b / a) * -x) / y
    else
        tmp = (x / (a + (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 (b <= -0.125) {
		tmp = ((b / a) * -x) / y;
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -0.125:
		tmp = ((b / a) * -x) / y
	else:
		tmp = (x / (a + (a * b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -0.125)
		tmp = Float64(Float64(Float64(b / a) * Float64(-x)) / y);
	else
		tmp = Float64(Float64(x / Float64(a + Float64(a * b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -0.125)
		tmp = ((b / a) * -x) / y;
	else
		tmp = (x / (a + (a * b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -0.125], N[(N[(N[(b / a), $MachinePrecision] * (-x)), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -0.125

   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. Taylor expanded in t around 0 93.8%

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

      1. +-commutative 93.8%

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

      2. mul-1-neg 93.8%

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

      3. unsub-neg 93.8%

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

   4. Simplified 93.8%

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

   5. Taylor expanded in y around 0 80.1%

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

      1. exp-neg 80.1%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      2. associate-*r/ 80.1%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot 1}{e^{b + \log a}}}}{y} \]

      3. *-rgt-identity 80.1%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. +-commutative 80.1%

         \[\leadsto \frac{\frac{x}{e^{\color{blue}{\log a + b}}}}{y} \]

      5. exp-sum 80.1%

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

      6. rem-exp-log 80.1%

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

   7. Simplified 80.1%

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

   8. Taylor expanded in b around 0 45.7%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]

   9. Taylor expanded in b around inf 45.7%

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

       1. associate-/l* 41.1%

          \[\leadsto \frac{-1 \cdot \color{blue}{\frac{b}{\frac{a}{x}}}}{y} \]

       2. associate-/r/ 47.1%

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

       3. associate-*r* 47.1%

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

       4. *-commutative 47.1%

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

       5. associate-*r/ 47.1%

          \[\leadsto \frac{x \cdot \color{blue}{\frac{-1 \cdot b}{a}}}{y} \]

       6. mul-1-neg 47.1%

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

   11. Simplified 47.1%

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

   if -0.125 < b

   1. Initial program 98.1%

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

   2. Taylor expanded in t around 0 80.3%

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

      1. +-commutative 80.3%

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

      2. mul-1-neg 80.3%

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

      3. unsub-neg 80.3%

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

   4. Simplified 80.3%

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

   5. Taylor expanded in y around 0 49.7%

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

      1. exp-neg 49.7%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      2. associate-*r/ 49.7%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot 1}{e^{b + \log a}}}}{y} \]

      3. *-rgt-identity 49.7%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. +-commutative 49.7%

         \[\leadsto \frac{\frac{x}{e^{\color{blue}{\log a + b}}}}{y} \]

      5. exp-sum 49.7%

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

      6. rem-exp-log 50.4%

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

   7. Simplified 50.4%

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

   8. Taylor expanded in b around 0 34.3%

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

4. Final simplification 37.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.125:\\ \;\;\;\;\frac{\frac{b}{a} \cdot \left(-x\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \]

Alternative 15: 38.9% accurate, 28.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 5 \cdot 10^{-171}:\\ \;\;\;\;\frac{\frac{x - x \cdot b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 5e-171) (/ (/ (- x (* x b)) a) y) (/ x (* y (+ a (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 5e-171) {
		tmp = ((x - (x * b)) / a) / y;
	} else {
		tmp = x / (y * (a + (a * 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 <= 5d-171) then
        tmp = ((x - (x * b)) / a) / y
    else
        tmp = x / (y * (a + (a * 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 <= 5e-171) {
		tmp = ((x - (x * b)) / a) / y;
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 5e-171:
		tmp = ((x - (x * b)) / a) / y
	else:
		tmp = x / (y * (a + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 5e-171)
		tmp = Float64(Float64(Float64(x - Float64(x * b)) / a) / y);
	else
		tmp = Float64(x / Float64(y * Float64(a + Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 5e-171)
		tmp = ((x - (x * b)) / a) / y;
	else
		tmp = x / (y * (a + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 5e-171], N[(N[(N[(x - N[(x * b), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 4.99999999999999992e-171

   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. Taylor expanded in t around 0 84.3%

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

      1. +-commutative 84.3%

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

      2. mul-1-neg 84.3%

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

      3. unsub-neg 84.3%

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

   4. Simplified 84.3%

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

   5. Taylor expanded in y around 0 55.0%

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

      1. exp-neg 55.0%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      2. associate-*r/ 55.0%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot 1}{e^{b + \log a}}}}{y} \]

      3. *-rgt-identity 55.0%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. +-commutative 55.0%

         \[\leadsto \frac{\frac{x}{e^{\color{blue}{\log a + b}}}}{y} \]

      5. exp-sum 55.0%

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

      6. rem-exp-log 55.6%

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

   7. Simplified 55.6%

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

   8. Taylor expanded in b around 0 41.0%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]

   9. Taylor expanded in a around 0 41.0%

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

       1. mul-1-neg 41.0%

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

       2. *-commutative 41.0%

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

       3. unsub-neg 41.0%

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

   11. Simplified 41.0%

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

   if 4.99999999999999992e-171 < b

   1. Initial program 99.7%

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

   2. Taylor expanded in t around 0 82.8%

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

      1. +-commutative 82.8%

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

      2. mul-1-neg 82.8%

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

      3. unsub-neg 82.8%

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

   4. Simplified 82.8%

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

   5. Taylor expanded in y around 0 60.7%

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

      1. exp-neg 60.7%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      2. associate-*r/ 60.7%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot 1}{e^{b + \log a}}}}{y} \]

      3. *-rgt-identity 60.7%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. +-commutative 60.7%

         \[\leadsto \frac{\frac{x}{e^{\color{blue}{\log a + b}}}}{y} \]

      5. exp-sum 60.7%

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

      6. rem-exp-log 61.0%

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

   7. Simplified 61.0%

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

   8. Taylor expanded in b around 0 31.5%

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

   9. Taylor expanded in x around 0 33.4%

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

4. Final simplification 37.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 5 \cdot 10^{-171}:\\ \;\;\;\;\frac{\frac{x - x \cdot b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \]

Alternative 16: 34.8% accurate, 34.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 2.6 \cdot 10^{+86}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 2.6e+86) (/ 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 <= 2.6e+86) {
		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 <= 2.6d+86) 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 <= 2.6e+86) {
		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 <= 2.6e+86:
		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 <= 2.6e+86)
		tmp = Float64(x / Float64(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 <= 2.6e+86)
		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, 2.6e+86], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 2.5999999999999998e86

   1. Initial program 98.3%

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

      1. associate-*l/ 86.9%

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

      2. *-commutative 86.9%

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

      3. +-commutative 86.9%

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

      4. associate--l+ 86.9%

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

      5. exp-sum 68.8%

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

      6. *-commutative 68.8%

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

      7. exp-to-pow 69.4%

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

      8. sub-neg 69.4%

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

      9. metadata-eval 69.4%

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

      10. exp-diff 62.7%

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

      11. *-commutative 62.7%

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

      12. exp-to-pow 62.7%

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

   3. Simplified 62.7%

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

   4. Taylor expanded in t around 0 68.9%

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

      1. times-frac 66.0%

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

   6. Simplified 66.0%

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

   7. Taylor expanded in y around 0 51.4%

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

   8. Taylor expanded in b around 0 32.1%

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

   if 2.5999999999999998e86 < 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. Taylor expanded in t around 0 89.3%

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

      1. +-commutative 89.3%

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

      2. mul-1-neg 89.3%

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

      3. unsub-neg 89.3%

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

   4. Simplified 89.3%

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

   5. Taylor expanded in y around 0 82.9%

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

      1. exp-neg 82.9%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{e^{b + \log a}}}}{y} \]

      2. associate-*r/ 82.9%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot 1}{e^{b + \log a}}}}{y} \]

      3. *-rgt-identity 82.9%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. +-commutative 82.9%

         \[\leadsto \frac{\frac{x}{e^{\color{blue}{\log a + b}}}}{y} \]

      5. exp-sum 82.9%

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

      6. rem-exp-log 82.9%

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

   7. Simplified 82.9%

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

   8. Taylor expanded in b around 0 30.3%

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

   9. Taylor expanded in b around inf 34.5%

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

4. Final simplification 32.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 2.6 \cdot 10^{+86}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \]

Alternative 17: 30.2% accurate, 63.0× speedup

Math

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

FPCore

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

C

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

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 * a)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.6%

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

   1. associate-*l/ 86.1%

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

   2. *-commutative 86.1%

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

   3. +-commutative 86.1%

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

   4. associate--l+ 86.1%

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

   5. exp-sum 68.2%

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

   6. *-commutative 68.2%

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

   7. exp-to-pow 68.6%

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

   8. sub-neg 68.6%

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

   9. metadata-eval 68.6%

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

   10. exp-diff 61.2%

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

   11. *-commutative 61.2%

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

   12. exp-to-pow 61.2%

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

3. Simplified 61.2%

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

4. Taylor expanded in t around 0 69.8%

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

   1. times-frac 65.5%

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

6. Simplified 65.5%

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

7. Taylor expanded in y around 0 57.0%

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

8. Taylor expanded in b around 0 29.0%

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

9. Final simplification 29.0%

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

Developer target: 72.3% 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 2023271 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (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))