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

Percentage Accurate: 98.4% → 98.4%

Time: 21.7s

Alternatives: 21

Speedup: 1.0×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.4% 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 98.5%

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

2. Final simplification 98.5%

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

Alternative 2: 93.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t + -1 \leq -2 \cdot 10^{+64} \lor \neg \left(t + -1 \leq -0.95\right):\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (+ t -1.0) -2e+64) (not (<= (+ t -1.0) -0.95)))
   (/ (* x (exp (- (* (+ t -1.0) (log a)) b))) y)
   (/ (* x (exp (- (- (* y (log z)) (log a)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t + -1.0) <= -2e+64) || !((t + -1.0) <= -0.95)) {
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	} else {
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (((t + (-1.0d0)) <= (-2d+64)) .or. (.not. ((t + (-1.0d0)) <= (-0.95d0)))) then
        tmp = (x * exp((((t + (-1.0d0)) * log(a)) - b))) / y
    else
        tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t + -1.0) <= -2e+64) || !((t + -1.0) <= -0.95)) {
		tmp = (x * Math.exp((((t + -1.0) * Math.log(a)) - b))) / y;
	} else {
		tmp = (x * Math.exp((((y * Math.log(z)) - Math.log(a)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((t + -1.0) <= -2e+64) or not ((t + -1.0) <= -0.95):
		tmp = (x * math.exp((((t + -1.0) * math.log(a)) - b))) / y
	else:
		tmp = (x * math.exp((((y * math.log(z)) - math.log(a)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(t + -1.0) <= -2e+64) || !(Float64(t + -1.0) <= -0.95))
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b))) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) - log(a)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((t + -1.0) <= -2e+64) || ~(((t + -1.0) <= -0.95)))
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	else
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(t + -1.0), $MachinePrecision], -2e+64], N[Not[LessEqual[N[(t + -1.0), $MachinePrecision], -0.95]], $MachinePrecision]], N[(N[(x * N[Exp[N[(N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $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]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 t 1) < -2.00000000000000004e64 or -0.94999999999999996 < (-.f64 t 1)

   1. Initial program 99.1%

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

   2. Taylor expanded in y around 0 94.1%

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

   if -2.00000000000000004e64 < (-.f64 t 1) < -0.94999999999999996

   1. Initial program 98.0%

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

   2. Taylor expanded in t around 0 97.3%

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

      1. +-commutative 97.3%

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

      2. mul-1-neg 97.3%

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

      3. unsub-neg 97.3%

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

   4. Simplified 97.3%

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

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t + -1 \leq -2 \cdot 10^{+64} \lor \neg \left(t + -1 \leq -0.95\right):\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \end{array} \]

Alternative 3: 88.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+66} \lor \neg \left(y \leq 8.5 \cdot 10^{+124}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.2e+66) (not (<= y 8.5e+124)))
   (/ (* x (/ (pow z y) y)) a)
   (/ (* 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 <= -3.2e+66) || !(y <= 8.5e+124)) {
		tmp = (x * (pow(z, y) / y)) / a;
	} 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 <= (-3.2d+66)) .or. (.not. (y <= 8.5d+124))) then
        tmp = (x * ((z ** y) / y)) / a
    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 <= -3.2e+66) || !(y <= 8.5e+124)) {
		tmp = (x * (Math.pow(z, y) / y)) / a;
	} 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 <= -3.2e+66) or not (y <= 8.5e+124):
		tmp = (x * (math.pow(z, y) / y)) / a
	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 <= -3.2e+66) || !(y <= 8.5e+124))
		tmp = Float64(Float64(x * Float64((z ^ y) / y)) / a);
	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 <= -3.2e+66) || ~((y <= 8.5e+124)))
		tmp = (x * ((z ^ y) / y)) / a;
	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, -3.2e+66], N[Not[LessEqual[y, 8.5e+124]], $MachinePrecision]], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / a), $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 < -3.2e66 or 8.4999999999999997e124 < 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. associate-*l/ 86.2%

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

      2. *-commutative 86.2%

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

      3. exp-diff 71.3%

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

      4. exp-sum 58.5%

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

      5. *-commutative 58.5%

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

      6. exp-to-pow 58.5%

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

      7. *-commutative 58.5%

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

      8. exp-to-pow 58.5%

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

      9. sub-neg 58.5%

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

      10. metadata-eval 58.5%

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

   3. Simplified 58.5%

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

   4. Taylor expanded in t around 0 70.3%

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

      1. times-frac 69.2%

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

   6. Simplified 69.2%

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

   7. Taylor expanded in b around 0 78.9%

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

      1. times-frac 77.9%

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

   9. Simplified 77.9%

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

       1. associate-*l/ 84.3%

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

   11. Applied egg-rr 84.3%

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

   if -3.2e66 < y < 8.4999999999999997e124

   1. Initial program 97.6%

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

   2. Taylor expanded in y around 0 94.1%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+66} \lor \neg \left(y \leq 8.5 \cdot 10^{+124}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \]

Alternative 4: 87.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.4 \cdot 10^{-48} \lor \neg \left(b \leq 5.8 \cdot 10^{-32}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left({z}^{y} \cdot \frac{{a}^{t}}{a}\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -3.4e-48) (not (<= b 5.8e-32)))
   (/ (* x (exp (- (* (+ t -1.0) (log a)) b))) y)
   (/ (* x (* (pow z y) (/ (pow a t) a))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.4e-48) || !(b <= 5.8e-32)) {
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	} else {
		tmp = (x * (pow(z, y) * (pow(a, t) / a))) / 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-48)) .or. (.not. (b <= 5.8d-32))) then
        tmp = (x * exp((((t + (-1.0d0)) * log(a)) - b))) / y
    else
        tmp = (x * ((z ** y) * ((a ** t) / a))) / 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-48) || !(b <= 5.8e-32)) {
		tmp = (x * Math.exp((((t + -1.0) * Math.log(a)) - b))) / y;
	} else {
		tmp = (x * (Math.pow(z, y) * (Math.pow(a, t) / a))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -3.4e-48) or not (b <= 5.8e-32):
		tmp = (x * math.exp((((t + -1.0) * math.log(a)) - b))) / y
	else:
		tmp = (x * (math.pow(z, y) * (math.pow(a, t) / a))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -3.4e-48) || !(b <= 5.8e-32))
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b))) / y);
	else
		tmp = Float64(Float64(x * Float64((z ^ y) * Float64((a ^ t) / a))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -3.4e-48) || ~((b <= 5.8e-32)))
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	else
		tmp = (x * ((z ^ y) * ((a ^ t) / a))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -3.4e-48], N[Not[LessEqual[b, 5.8e-32]], $MachinePrecision]], N[(N[(x * N[Exp[N[(N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] * N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.40000000000000028e-48 or 5.79999999999999991e-32 < b

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 91.3%

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

   if -3.40000000000000028e-48 < b < 5.79999999999999991e-32

   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 b around 0 96.8%

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

      1. +-commutative 96.8%

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

      2. exp-sum 88.7%

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

      3. *-commutative 88.7%

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

      4. exp-to-pow 88.7%

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

      5. *-commutative 88.7%

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

      6. exp-to-pow 89.6%

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

      7. sub-neg 89.6%

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

      8. metadata-eval 89.6%

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

   4. Simplified 89.6%

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

      1. unpow-prod-up 89.7%

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

      2. unpow-1 89.7%

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

   6. Applied egg-rr 89.7%

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

      1. associate-*r/ 89.7%

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

      2. *-rgt-identity 89.7%

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

   8. Simplified 89.7%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.4 \cdot 10^{-48} \lor \neg \left(b \leq 5.8 \cdot 10^{-32}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left({z}^{y} \cdot \frac{{a}^{t}}{a}\right)}{y}\\ \end{array} \]

Alternative 5: 78.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+59} \lor \neg \left(t \leq 1.72\right):\\ \;\;\;\;\frac{x}{\frac{y}{{a}^{\left(t + -1\right)}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -5.2e+59) (not (<= t 1.72)))
   (/ x (/ y (pow a (+ t -1.0))))
   (* (/ x a) (/ (pow z y) (* y (exp b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -5.2e+59) || !(t <= 1.72)) {
		tmp = x / (y / pow(a, (t + -1.0)));
	} else {
		tmp = (x / a) * (pow(z, y) / (y * exp(b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-5.2d+59)) .or. (.not. (t <= 1.72d0))) then
        tmp = x / (y / (a ** (t + (-1.0d0))))
    else
        tmp = (x / a) * ((z ** y) / (y * exp(b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -5.2e+59) || !(t <= 1.72)) {
		tmp = x / (y / Math.pow(a, (t + -1.0)));
	} else {
		tmp = (x / a) * (Math.pow(z, y) / (y * Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -5.2e+59) or not (t <= 1.72):
		tmp = x / (y / math.pow(a, (t + -1.0)))
	else:
		tmp = (x / a) * (math.pow(z, y) / (y * math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -5.2e+59) || !(t <= 1.72))
		tmp = Float64(x / Float64(y / (a ^ Float64(t + -1.0))));
	else
		tmp = Float64(Float64(x / a) * Float64((z ^ y) / Float64(y * exp(b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -5.2e+59) || ~((t <= 1.72)))
		tmp = x / (y / (a ^ (t + -1.0)));
	else
		tmp = (x / a) * ((z ^ y) / (y * exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -5.2e+59], N[Not[LessEqual[t, 1.72]], $MachinePrecision]], N[(x / N[(y / N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] * N[(N[Power[z, y], $MachinePrecision] / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.19999999999999999e59 or 1.71999999999999997 < t

   1. Initial program 99.2%

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

   2. Taylor expanded in y around 0 93.3%

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

   3. Taylor expanded in b around 0 83.9%

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

      1. associate-/l* 83.9%

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

      2. exp-to-pow 83.9%

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

      3. sub-neg 83.9%

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

      4. metadata-eval 83.9%

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

      5. +-commutative 83.9%

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

   5. Simplified 83.9%

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

   if -5.19999999999999999e59 < t < 1.71999999999999997

   1. Initial program 97.9%

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

      1. associate-*l/ 85.6%

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

      2. *-commutative 85.6%

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

      3. exp-diff 74.2%

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

      4. exp-sum 74.2%

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

      5. *-commutative 74.2%

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

      6. exp-to-pow 74.2%

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

      7. *-commutative 74.2%

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

      8. exp-to-pow 75.0%

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

      9. sub-neg 75.0%

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

      10. metadata-eval 75.0%

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

   3. Simplified 75.0%

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

   4. Taylor expanded in t around 0 83.0%

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

      1. times-frac 80.4%

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

   6. Simplified 80.4%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+59} \lor \neg \left(t \leq 1.72\right):\\ \;\;\;\;\frac{x}{\frac{y}{{a}^{\left(t + -1\right)}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}\\ \end{array} \]

Alternative 6: 81.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+67} \lor \neg \left(y \leq 1850000000\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{\frac{{a}^{t}}{a}}{e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.05e+67) (not (<= y 1850000000.0)))
   (/ (* x (/ (pow z y) y)) a)
   (/ (* x (/ (/ (pow a t) a) (exp b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.05e+67) || !(y <= 1850000000.0)) {
		tmp = (x * (pow(z, y) / y)) / a;
	} else {
		tmp = (x * ((pow(a, t) / 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 <= (-1.05d+67)) .or. (.not. (y <= 1850000000.0d0))) then
        tmp = (x * ((z ** y) / y)) / a
    else
        tmp = (x * (((a ** t) / 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 <= -1.05e+67) || !(y <= 1850000000.0)) {
		tmp = (x * (Math.pow(z, y) / y)) / a;
	} else {
		tmp = (x * ((Math.pow(a, t) / a) / Math.exp(b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.05e+67) or not (y <= 1850000000.0):
		tmp = (x * (math.pow(z, y) / y)) / a
	else:
		tmp = (x * ((math.pow(a, t) / a) / math.exp(b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.05e+67) || !(y <= 1850000000.0))
		tmp = Float64(Float64(x * Float64((z ^ y) / y)) / a);
	else
		tmp = Float64(Float64(x * Float64(Float64((a ^ t) / a) / exp(b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.05e+67) || ~((y <= 1850000000.0)))
		tmp = (x * ((z ^ y) / y)) / a;
	else
		tmp = (x * (((a ^ t) / a) / exp(b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.05e+67], N[Not[LessEqual[y, 1850000000.0]], $MachinePrecision]], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(x * N[(N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.0500000000000001e67 or 1.85e9 < 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. associate-*l/ 86.2%

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

      2. *-commutative 86.2%

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

      3. exp-diff 66.4%

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

      4. exp-sum 53.4%

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

      5. *-commutative 53.4%

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

      6. exp-to-pow 53.4%

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

      7. *-commutative 53.4%

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

      8. exp-to-pow 53.4%

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

      9. sub-neg 53.4%

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

      10. metadata-eval 53.4%

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

   3. Simplified 53.4%

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

   4. Taylor expanded in t around 0 66.5%

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

      1. times-frac 64.7%

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

   6. Simplified 64.7%

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

   7. Taylor expanded in b around 0 74.4%

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

      1. times-frac 72.7%

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

   9. Simplified 72.7%

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

       1. associate-*l/ 80.5%

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

   11. Applied egg-rr 80.5%

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

   if -1.0500000000000001e67 < y < 1.85e9

   1. Initial program 97.3%

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

   2. Taylor expanded in y around 0 95.3%

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

      1. exp-diff 85.3%

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

      2. sub-neg 85.3%

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

      3. metadata-eval 85.3%

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

      4. pow-to-exp 86.0%

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

      5. div-inv 86.0%

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

      6. pow-prod-up 86.0%

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

      7. inv-pow 86.0%

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

      8. associate-*l* 86.0%

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

      9. rec-exp 86.0%

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

   4. Applied egg-rr 86.0%

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

      1. rem-exp-log 85.3%

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

      2. log-rec 85.3%

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

      3. mul-1-neg 85.3%

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

      4. exp-sum 85.3%

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

      5. sub-neg 85.3%

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

      6. exp-diff 85.3%

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

      7. mul-1-neg 85.3%

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

      8. log-rec 85.3%

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

      9. rem-exp-log 86.0%

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

      10. associate-*r/ 86.0%

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

      11. associate-*r/ 86.0%

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

      12. *-rgt-identity 86.0%

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

   6. Simplified 86.0%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+67} \lor \neg \left(y \leq 1850000000\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{\frac{{a}^{t}}{a}}{e^{b}}}{y}\\ \end{array} \]

Alternative 7: 81.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.1 \cdot 10^{+57} \lor \neg \left(t \leq 5.8\right):\\ \;\;\;\;\frac{x}{\frac{y}{{a}^{\left(t + -1\right)}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -5.1e+57) (not (<= t 5.8)))
   (/ x (/ y (pow a (+ t -1.0))))
   (/ (* x (pow z y)) (* a (* y (exp b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -5.1e+57) || !(t <= 5.8)) {
		tmp = x / (y / pow(a, (t + -1.0)));
	} else {
		tmp = (x * pow(z, y)) / (a * (y * exp(b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-5.1d+57)) .or. (.not. (t <= 5.8d0))) then
        tmp = x / (y / (a ** (t + (-1.0d0))))
    else
        tmp = (x * (z ** y)) / (a * (y * exp(b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -5.1e+57) || !(t <= 5.8)) {
		tmp = x / (y / Math.pow(a, (t + -1.0)));
	} else {
		tmp = (x * Math.pow(z, y)) / (a * (y * Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -5.1e+57) or not (t <= 5.8):
		tmp = x / (y / math.pow(a, (t + -1.0)))
	else:
		tmp = (x * math.pow(z, y)) / (a * (y * math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -5.1e+57) || !(t <= 5.8))
		tmp = Float64(x / Float64(y / (a ^ Float64(t + -1.0))));
	else
		tmp = Float64(Float64(x * (z ^ y)) / Float64(a * Float64(y * exp(b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -5.1e+57) || ~((t <= 5.8)))
		tmp = x / (y / (a ^ (t + -1.0)));
	else
		tmp = (x * (z ^ y)) / (a * (y * exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -5.1e+57], N[Not[LessEqual[t, 5.8]], $MachinePrecision]], N[(x / N[(y / N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.10000000000000023e57 or 5.79999999999999982 < t

   1. Initial program 99.2%

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

   2. Taylor expanded in y around 0 93.3%

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

   3. Taylor expanded in b around 0 84.1%

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

      1. associate-/l* 84.1%

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

      2. exp-to-pow 84.1%

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

      3. sub-neg 84.1%

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

      4. metadata-eval 84.1%

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

      5. +-commutative 84.1%

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

   5. Simplified 84.1%

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

   if -5.10000000000000023e57 < t < 5.79999999999999982

   1. Initial program 97.9%

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

      1. associate-*l/ 85.5%

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

      2. *-commutative 85.5%

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

      3. exp-diff 74.0%

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

      4. exp-sum 74.0%

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

      5. *-commutative 74.0%

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

      6. exp-to-pow 74.0%

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

      7. *-commutative 74.0%

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

      8. exp-to-pow 74.8%

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

      9. sub-neg 74.8%

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

      10. metadata-eval 74.8%

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

   3. Simplified 74.8%

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

   4. Taylor expanded in t around 0 83.6%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.1 \cdot 10^{+57} \lor \neg \left(t \leq 5.8\right):\\ \;\;\;\;\frac{x}{\frac{y}{{a}^{\left(t + -1\right)}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]

Alternative 8: 74.5% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{a \cdot e^{b}}}{y}\\ t_2 := \frac{x}{\frac{y}{{a}^{\left(t + -1\right)}}}\\ \mathbf{if}\;t \leq -2.15 \cdot 10^{-44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -4.7 \cdot 10^{-265}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-204}:\\ \;\;\;\;\frac{{z}^{y}}{y} \cdot \frac{x}{a}\\ \mathbf{elif}\;t \leq 2.6:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ x (* a (exp b))) y)) (t_2 (/ x (/ y (pow a (+ t -1.0))))))
   (if (<= t -2.15e-44)
     t_2
     (if (<= t -4.7e-265)
       t_1
       (if (<= t 1.05e-204)
         (* (/ (pow z y) y) (/ x a))
         (if (<= t 2.6) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / (a * exp(b))) / y;
	double t_2 = x / (y / pow(a, (t + -1.0)));
	double tmp;
	if (t <= -2.15e-44) {
		tmp = t_2;
	} else if (t <= -4.7e-265) {
		tmp = t_1;
	} else if (t <= 1.05e-204) {
		tmp = (pow(z, y) / y) * (x / a);
	} else if (t <= 2.6) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x / (a * exp(b))) / y
    t_2 = x / (y / (a ** (t + (-1.0d0))))
    if (t <= (-2.15d-44)) then
        tmp = t_2
    else if (t <= (-4.7d-265)) then
        tmp = t_1
    else if (t <= 1.05d-204) then
        tmp = ((z ** y) / y) * (x / a)
    else if (t <= 2.6d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / (a * Math.exp(b))) / y;
	double t_2 = x / (y / Math.pow(a, (t + -1.0)));
	double tmp;
	if (t <= -2.15e-44) {
		tmp = t_2;
	} else if (t <= -4.7e-265) {
		tmp = t_1;
	} else if (t <= 1.05e-204) {
		tmp = (Math.pow(z, y) / y) * (x / a);
	} else if (t <= 2.6) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / (a * math.exp(b))) / y
	t_2 = x / (y / math.pow(a, (t + -1.0)))
	tmp = 0
	if t <= -2.15e-44:
		tmp = t_2
	elif t <= -4.7e-265:
		tmp = t_1
	elif t <= 1.05e-204:
		tmp = (math.pow(z, y) / y) * (x / a)
	elif t <= 2.6:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / Float64(a * exp(b))) / y)
	t_2 = Float64(x / Float64(y / (a ^ Float64(t + -1.0))))
	tmp = 0.0
	if (t <= -2.15e-44)
		tmp = t_2;
	elseif (t <= -4.7e-265)
		tmp = t_1;
	elseif (t <= 1.05e-204)
		tmp = Float64(Float64((z ^ y) / y) * Float64(x / a));
	elseif (t <= 2.6)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x / (a * exp(b))) / y;
	t_2 = x / (y / (a ^ (t + -1.0)));
	tmp = 0.0;
	if (t <= -2.15e-44)
		tmp = t_2;
	elseif (t <= -4.7e-265)
		tmp = t_1;
	elseif (t <= 1.05e-204)
		tmp = ((z ^ y) / y) * (x / a);
	elseif (t <= 2.6)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(y / N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.15e-44], t$95$2, If[LessEqual[t, -4.7e-265], t$95$1, If[LessEqual[t, 1.05e-204], N[(N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.6], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.15000000000000007e-44 or 2.60000000000000009 < t

   1. Initial program 99.2%

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

   2. Taylor expanded in y around 0 89.9%

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

   3. Taylor expanded in b around 0 79.8%

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

      1. associate-/l* 80.5%

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

      2. exp-to-pow 80.6%

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

      3. sub-neg 80.6%

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

      4. metadata-eval 80.6%

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

      5. +-commutative 80.6%

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

   5. Simplified 80.6%

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

   if -2.15000000000000007e-44 < t < -4.69999999999999986e-265 or 1.05000000000000005e-204 < t < 2.60000000000000009

   1. Initial program 97.7%

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

   2. Taylor expanded in y around 0 76.0%

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

      1. exp-diff 76.0%

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

      2. exp-to-pow 76.8%

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

      3. sub-neg 76.8%

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

      4. metadata-eval 76.8%

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

   4. Simplified 76.8%

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

   5. Taylor expanded in t around 0 76.0%

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

   if -4.69999999999999986e-265 < t < 1.05000000000000005e-204

   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. Step-by-step derivation

      1. associate-*l/ 87.1%

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

      2. *-commutative 87.1%

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

      3. exp-diff 78.3%

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

      4. exp-sum 78.4%

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

      5. *-commutative 78.4%

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

      6. exp-to-pow 78.4%

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

      7. *-commutative 78.4%

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

      8. exp-to-pow 79.3%

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

      9. sub-neg 79.3%

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

      10. metadata-eval 79.3%

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

   3. Simplified 79.3%

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

   4. Taylor expanded in t around 0 85.4%

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

      1. times-frac 80.9%

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

   6. Simplified 80.9%

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

   7. Taylor expanded in b around 0 79.9%

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

      1. times-frac 75.4%

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

   9. Simplified 75.4%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{-44}:\\ \;\;\;\;\frac{x}{\frac{y}{{a}^{\left(t + -1\right)}}}\\ \mathbf{elif}\;t \leq -4.7 \cdot 10^{-265}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-204}:\\ \;\;\;\;\frac{{z}^{y}}{y} \cdot \frac{x}{a}\\ \mathbf{elif}\;t \leq 2.6:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{{a}^{\left(t + -1\right)}}}\\ \end{array} \]

Alternative 9: 75.4% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{y}{{a}^{\left(t + -1\right)}}}\\ \mathbf{if}\;t \leq -5.2:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-119}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{y}}{a}\\ \mathbf{elif}\;t \leq 3.5:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (/ y (pow a (+ t -1.0))))))
   (if (<= t -5.2)
     t_1
     (if (<= t 1.9e-119)
       (/ (* x (/ (pow z y) y)) a)
       (if (<= t 3.5) (/ (/ x (* a (exp b))) y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y / pow(a, (t + -1.0)));
	double tmp;
	if (t <= -5.2) {
		tmp = t_1;
	} else if (t <= 1.9e-119) {
		tmp = (x * (pow(z, y) / y)) / a;
	} else if (t <= 3.5) {
		tmp = (x / (a * exp(b))) / y;
	} 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 / (y / (a ** (t + (-1.0d0))))
    if (t <= (-5.2d0)) then
        tmp = t_1
    else if (t <= 1.9d-119) then
        tmp = (x * ((z ** y) / y)) / a
    else if (t <= 3.5d0) then
        tmp = (x / (a * exp(b))) / y
    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 / (y / Math.pow(a, (t + -1.0)));
	double tmp;
	if (t <= -5.2) {
		tmp = t_1;
	} else if (t <= 1.9e-119) {
		tmp = (x * (Math.pow(z, y) / y)) / a;
	} else if (t <= 3.5) {
		tmp = (x / (a * Math.exp(b))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (y / math.pow(a, (t + -1.0)))
	tmp = 0
	if t <= -5.2:
		tmp = t_1
	elif t <= 1.9e-119:
		tmp = (x * (math.pow(z, y) / y)) / a
	elif t <= 3.5:
		tmp = (x / (a * math.exp(b))) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(y / (a ^ Float64(t + -1.0))))
	tmp = 0.0
	if (t <= -5.2)
		tmp = t_1;
	elseif (t <= 1.9e-119)
		tmp = Float64(Float64(x * Float64((z ^ y) / y)) / a);
	elseif (t <= 3.5)
		tmp = Float64(Float64(x / Float64(a * exp(b))) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (y / (a ^ (t + -1.0)));
	tmp = 0.0;
	if (t <= -5.2)
		tmp = t_1;
	elseif (t <= 1.9e-119)
		tmp = (x * ((z ^ y) / y)) / a;
	elseif (t <= 3.5)
		tmp = (x / (a * exp(b))) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(y / N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.2], t$95$1, If[LessEqual[t, 1.9e-119], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[t, 3.5], N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.20000000000000018 or 3.5 < t

   1. Initial program 99.3%

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

   2. Taylor expanded in y around 0 93.1%

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

   3. Taylor expanded in b around 0 82.4%

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

      1. associate-/l* 82.4%

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

      2. exp-to-pow 82.4%

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

      3. sub-neg 82.4%

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

      4. metadata-eval 82.4%

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

      5. +-commutative 82.4%

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

   5. Simplified 82.4%

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

   if -5.20000000000000018 < t < 1.89999999999999987e-119

   1. Initial program 97.7%

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

      1. associate-*l/ 86.5%

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

      2. *-commutative 86.5%

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

      3. exp-diff 76.7%

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

      4. exp-sum 76.7%

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

      5. *-commutative 76.7%

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

      6. exp-to-pow 76.7%

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

      7. *-commutative 76.7%

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

      8. exp-to-pow 77.5%

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

      9. sub-neg 77.5%

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

      10. metadata-eval 77.5%

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

   3. Simplified 77.5%

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

   4. Taylor expanded in t around 0 83.4%

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

      1. times-frac 79.9%

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

   6. Simplified 79.9%

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

   7. Taylor expanded in b around 0 69.3%

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

      1. times-frac 68.8%

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

   9. Simplified 68.8%

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

       1. associate-*l/ 75.1%

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

   11. Applied egg-rr 75.1%

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

   if 1.89999999999999987e-119 < t < 3.5

   1. Initial program 98.0%

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

   2. Taylor expanded in y around 0 78.9%

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

      1. exp-diff 78.9%

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

      2. exp-to-pow 80.3%

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

      3. sub-neg 80.3%

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

      4. metadata-eval 80.3%

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

   4. Simplified 80.3%

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

   5. Taylor expanded in t around 0 77.4%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2:\\ \;\;\;\;\frac{x}{\frac{y}{{a}^{\left(t + -1\right)}}}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-119}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{y}}{a}\\ \mathbf{elif}\;t \leq 3.5:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{{a}^{\left(t + -1\right)}}}\\ \end{array} \]

Alternative 10: 73.1% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -230 \lor \neg \left(b \leq 9.2 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{{z}^{y}}{y} \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -230.0) (not (<= b 9.2e-15)))
   (/ x (* a (* y (exp b))))
   (* (/ (pow z y) y) (/ x a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -230.0) || !(b <= 9.2e-15)) {
		tmp = x / (a * (y * exp(b)));
	} else {
		tmp = (pow(z, y) / y) * (x / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-230.0d0)) .or. (.not. (b <= 9.2d-15))) then
        tmp = x / (a * (y * exp(b)))
    else
        tmp = ((z ** y) / y) * (x / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -230.0) || !(b <= 9.2e-15)) {
		tmp = x / (a * (y * Math.exp(b)));
	} else {
		tmp = (Math.pow(z, y) / y) * (x / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -230.0) or not (b <= 9.2e-15):
		tmp = x / (a * (y * math.exp(b)))
	else:
		tmp = (math.pow(z, y) / y) * (x / a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -230.0) || !(b <= 9.2e-15))
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	else
		tmp = Float64(Float64((z ^ y) / y) * Float64(x / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -230.0) || ~((b <= 9.2e-15)))
		tmp = x / (a * (y * exp(b)));
	else
		tmp = ((z ^ y) / y) * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -230.0], N[Not[LessEqual[b, 9.2e-15]], $MachinePrecision]], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -230 or 9.19999999999999961e-15 < 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/ 85.8%

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

      2. *-commutative 85.8%

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

      3. exp-diff 57.5%

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

      4. exp-sum 50.4%

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

      5. *-commutative 50.4%

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

      6. exp-to-pow 50.4%

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

      7. *-commutative 50.4%

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

      8. exp-to-pow 50.4%

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

      9. sub-neg 50.4%

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

      10. metadata-eval 50.4%

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

   3. Simplified 50.4%

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

   4. Taylor expanded in t around 0 67.9%

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

      1. times-frac 61.5%

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

   6. Simplified 61.5%

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

   7. Taylor expanded in y around 0 83.7%

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

   if -230 < b < 9.19999999999999961e-15

   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. Step-by-step derivation

      1. associate-*l/ 83.7%

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

      2. *-commutative 83.7%

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

      3. exp-diff 83.7%

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

      4. exp-sum 72.1%

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

      5. *-commutative 72.1%

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

      6. exp-to-pow 72.1%

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

      7. *-commutative 72.1%

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

      8. exp-to-pow 72.9%

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

      9. sub-neg 72.9%

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

      10. metadata-eval 72.9%

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

   3. Simplified 72.9%

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

   4. Taylor expanded in t around 0 65.1%

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

      1. times-frac 66.2%

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

   6. Simplified 66.2%

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

   7. Taylor expanded in b around 0 65.1%

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

      1. times-frac 66.2%

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

   9. Simplified 66.2%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -230 \lor \neg \left(b \leq 9.2 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{{z}^{y}}{y} \cdot \frac{x}{a}\\ \end{array} \]

Alternative 11: 59.9% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \frac{x}{a \cdot \left(y \cdot e^{b}\right)} \end{array} \]

FPCore

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

C

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

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 / (a * (y * exp(b)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.5%

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

   1. associate-*l/ 84.7%

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

   2. *-commutative 84.7%

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

   3. exp-diff 70.7%

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

   4. exp-sum 61.3%

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

   5. *-commutative 61.3%

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

   6. exp-to-pow 61.3%

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

   7. *-commutative 61.3%

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

   8. exp-to-pow 61.7%

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

   9. sub-neg 61.7%

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

   10. metadata-eval 61.7%

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

3. Simplified 61.7%

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

4. Taylor expanded in t around 0 66.4%

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

   1. times-frac 63.9%

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

6. Simplified 63.9%

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

7. Taylor expanded in y around 0 59.6%

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

8. Final simplification 59.6%

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

Alternative 12: 59.9% accurate, 2.9× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x / (a * exp(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 / (a * exp(b))) / y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.5%

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

2. Taylor expanded in y around 0 81.2%

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

   1. exp-diff 70.6%

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

   2. exp-to-pow 71.0%

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

   3. sub-neg 71.0%

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

   4. metadata-eval 71.0%

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

4. Simplified 71.0%

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

5. Taylor expanded in t around 0 61.1%

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

6. Final simplification 61.1%

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

Alternative 13: 39.4% accurate, 14.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.7 \cdot 10^{-8}:\\ \;\;\;\;\frac{y \cdot \left(a \cdot \left(b \cdot \frac{x}{y}\right)\right) - x \cdot a}{a \cdot \left(a \cdot \left(-y\right)\right)}\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+66}:\\ \;\;\;\;\frac{\frac{x}{a}}{y \cdot \left(1 + b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.7e-8)
   (/ (- (* y (* a (* b (/ x y)))) (* x a)) (* a (* a (- y))))
   (if (<= b 5.5e+66) (/ (/ x a) (* y (+ 1.0 b))) (/ x (* y (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.7e-8) {
		tmp = ((y * (a * (b * (x / y)))) - (x * a)) / (a * (a * -y));
	} else if (b <= 5.5e+66) {
		tmp = (x / a) / (y * (1.0 + b));
	} else {
		tmp = x / (y * (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 <= (-3.7d-8)) then
        tmp = ((y * (a * (b * (x / y)))) - (x * a)) / (a * (a * -y))
    else if (b <= 5.5d+66) then
        tmp = (x / a) / (y * (1.0d0 + b))
    else
        tmp = x / (y * (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 <= -3.7e-8) {
		tmp = ((y * (a * (b * (x / y)))) - (x * a)) / (a * (a * -y));
	} else if (b <= 5.5e+66) {
		tmp = (x / a) / (y * (1.0 + b));
	} else {
		tmp = x / (y * (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3.7e-8:
		tmp = ((y * (a * (b * (x / y)))) - (x * a)) / (a * (a * -y))
	elif b <= 5.5e+66:
		tmp = (x / a) / (y * (1.0 + b))
	else:
		tmp = x / (y * (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.7e-8)
		tmp = Float64(Float64(Float64(y * Float64(a * Float64(b * Float64(x / y)))) - Float64(x * a)) / Float64(a * Float64(a * Float64(-y))));
	elseif (b <= 5.5e+66)
		tmp = Float64(Float64(x / a) / Float64(y * Float64(1.0 + b)));
	else
		tmp = Float64(x / Float64(y * Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3.7e-8)
		tmp = ((y * (a * (b * (x / y)))) - (x * a)) / (a * (a * -y));
	elseif (b <= 5.5e+66)
		tmp = (x / a) / (y * (1.0 + b));
	else
		tmp = x / (y * (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.7e-8], N[(N[(N[(y * N[(a * N[(b * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] / N[(a * N[(a * (-y)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.5e+66], N[(N[(x / a), $MachinePrecision] / N[(y * N[(1.0 + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.7e-8

   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/ 86.0%

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

      2. *-commutative 86.0%

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

      3. exp-diff 63.2%

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

      4. exp-sum 56.1%

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

      5. *-commutative 56.1%

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

      6. exp-to-pow 56.1%

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

      7. *-commutative 56.1%

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

      8. exp-to-pow 56.1%

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

      9. sub-neg 56.1%

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

      10. metadata-eval 56.1%

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

   3. Simplified 56.1%

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

   4. Taylor expanded in t around 0 65.1%

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

      1. times-frac 58.1%

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

   6. Simplified 58.1%

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

   7. Taylor expanded in y around 0 81.1%

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

   8. Taylor expanded in b around 0 33.7%

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

      1. +-commutative 33.7%

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

      2. mul-1-neg 33.7%

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

      3. unsub-neg 33.7%

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

      4. times-frac 37.0%

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

   10. Simplified 37.0%

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

       1. frac-2neg 37.0%

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

       2. associate-*l/ 40.4%

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

       3. frac-sub 32.6%

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

       4. *-commutative 32.6%

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

       5. distribute-rgt-neg-in 32.6%

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

       6. *-commutative 32.6%

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

       7. distribute-rgt-neg-in 32.6%

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

   12. Applied egg-rr 32.6%

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

       1. *-commutative 32.6%

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

       2. associate-*l* 44.8%

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

       3. *-commutative 44.8%

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

   14. Simplified 44.8%

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

   if -3.7e-8 < b < 5.5e66

   1. Initial program 97.3%

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

      1. associate-*l/ 83.5%

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

      2. *-commutative 83.5%

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

      3. exp-diff 80.7%

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

      4. exp-sum 70.0%

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

      5. *-commutative 70.0%

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

      6. exp-to-pow 70.0%

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

      7. *-commutative 70.0%

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

      8. exp-to-pow 70.7%

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

      9. sub-neg 70.7%

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

      10. metadata-eval 70.7%

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

   3. Simplified 70.7%

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

   4. Taylor expanded in t around 0 65.0%

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

      1. times-frac 65.3%

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

   6. Simplified 65.3%

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

   7. Taylor expanded in y around 0 38.8%

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

   8. Taylor expanded in b around 0 34.0%

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

      1. distribute-lft-out 35.4%

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

      2. distribute-rgt1-in 35.4%

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

   10. Simplified 35.4%

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

       1. *-un-lft-identity 35.4%

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

       2. associate-/r* 38.7%

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

       3. *-commutative 38.7%

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

   12. Applied egg-rr 38.7%

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

   if 5.5e66 < 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/ 86.4%

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

      2. *-commutative 86.4%

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

      3. exp-diff 54.2%

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

      4. exp-sum 45.8%

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

      5. *-commutative 45.8%

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

      6. exp-to-pow 45.8%

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

      7. *-commutative 45.8%

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

      8. exp-to-pow 45.8%

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

      9. sub-neg 45.8%

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

      10. metadata-eval 45.8%

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

   3. Simplified 45.8%

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

   4. Taylor expanded in t around 0 71.3%

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

      1. times-frac 66.2%

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

   6. Simplified 66.2%

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

   7. Taylor expanded in y around 0 88.3%

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

   8. Taylor expanded in b around 0 45.8%

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

      1. distribute-lft-out 45.8%

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

      2. distribute-rgt1-in 45.8%

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

   10. Simplified 45.8%

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

   11. Taylor expanded in b around inf 45.8%

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

       1. associate-*r* 50.6%

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

   13. Simplified 50.6%

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

4. Final simplification 42.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.7 \cdot 10^{-8}:\\ \;\;\;\;\frac{y \cdot \left(a \cdot \left(b \cdot \frac{x}{y}\right)\right) - x \cdot a}{a \cdot \left(a \cdot \left(-y\right)\right)}\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+66}:\\ \;\;\;\;\frac{\frac{x}{a}}{y \cdot \left(1 + b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \]

Alternative 14: 39.4% accurate, 24.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.56 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \left(-\frac{b}{y \cdot a}\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+66}:\\ \;\;\;\;\frac{\frac{x}{a}}{y \cdot \left(1 + b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.56e-6)
   (* x (- (/ b (* y a))))
   (if (<= b 5.5e+66) (/ (/ x a) (* y (+ 1.0 b))) (/ x (* y (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.56e-6) {
		tmp = x * -(b / (y * a));
	} else if (b <= 5.5e+66) {
		tmp = (x / a) / (y * (1.0 + b));
	} else {
		tmp = x / (y * (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 <= (-1.56d-6)) then
        tmp = x * -(b / (y * a))
    else if (b <= 5.5d+66) then
        tmp = (x / a) / (y * (1.0d0 + b))
    else
        tmp = x / (y * (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 <= -1.56e-6) {
		tmp = x * -(b / (y * a));
	} else if (b <= 5.5e+66) {
		tmp = (x / a) / (y * (1.0 + b));
	} else {
		tmp = x / (y * (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.56e-6:
		tmp = x * -(b / (y * a))
	elif b <= 5.5e+66:
		tmp = (x / a) / (y * (1.0 + b))
	else:
		tmp = x / (y * (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.56e-6)
		tmp = Float64(x * Float64(-Float64(b / Float64(y * a))));
	elseif (b <= 5.5e+66)
		tmp = Float64(Float64(x / a) / Float64(y * Float64(1.0 + b)));
	else
		tmp = Float64(x / Float64(y * Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.56e-6)
		tmp = x * -(b / (y * a));
	elseif (b <= 5.5e+66)
		tmp = (x / a) / (y * (1.0 + b));
	else
		tmp = x / (y * (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.56e-6], N[(x * (-N[(b / N[(y * a), $MachinePrecision]), $MachinePrecision])), $MachinePrecision], If[LessEqual[b, 5.5e+66], N[(N[(x / a), $MachinePrecision] / N[(y * N[(1.0 + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.5600000000000001e-6

   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/ 86.0%

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

      2. *-commutative 86.0%

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

      3. exp-diff 63.2%

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

      4. exp-sum 56.1%

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

      5. *-commutative 56.1%

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

      6. exp-to-pow 56.1%

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

      7. *-commutative 56.1%

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

      8. exp-to-pow 56.1%

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

      9. sub-neg 56.1%

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

      10. metadata-eval 56.1%

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

   3. Simplified 56.1%

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

   4. Taylor expanded in t around 0 65.1%

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

      1. times-frac 58.1%

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

   6. Simplified 58.1%

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

   7. Taylor expanded in y around 0 81.1%

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

   8. Taylor expanded in b around 0 33.7%

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

      1. +-commutative 33.7%

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

      2. mul-1-neg 33.7%

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

      3. unsub-neg 33.7%

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

      4. times-frac 37.0%

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

   10. Simplified 37.0%

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

   11. Taylor expanded in b around inf 33.7%

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

       1. associate-*r/ 33.7%

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

       2. *-commutative 33.7%

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

       3. neg-mul-1 33.7%

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

       4. distribute-lft-neg-in 33.7%

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

       5. *-commutative 33.7%

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

       6. associate-*r/ 37.2%

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

       7. *-commutative 37.2%

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

   13. Simplified 37.2%

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

   if -1.5600000000000001e-6 < b < 5.5e66

   1. Initial program 97.3%

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

      1. associate-*l/ 83.5%

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

      2. *-commutative 83.5%

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

      3. exp-diff 80.7%

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

      4. exp-sum 70.0%

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

      5. *-commutative 70.0%

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

      6. exp-to-pow 70.0%

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

      7. *-commutative 70.0%

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

      8. exp-to-pow 70.7%

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

      9. sub-neg 70.7%

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

      10. metadata-eval 70.7%

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

   3. Simplified 70.7%

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

   4. Taylor expanded in t around 0 65.0%

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

      1. times-frac 65.3%

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

   6. Simplified 65.3%

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

   7. Taylor expanded in y around 0 38.8%

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

   8. Taylor expanded in b around 0 34.0%

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

      1. distribute-lft-out 35.4%

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

      2. distribute-rgt1-in 35.4%

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

   10. Simplified 35.4%

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

       1. *-un-lft-identity 35.4%

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

       2. associate-/r* 38.7%

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

       3. *-commutative 38.7%

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

   12. Applied egg-rr 38.7%

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

   if 5.5e66 < 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/ 86.4%

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

      2. *-commutative 86.4%

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

      3. exp-diff 54.2%

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

      4. exp-sum 45.8%

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

      5. *-commutative 45.8%

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

      6. exp-to-pow 45.8%

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

      7. *-commutative 45.8%

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

      8. exp-to-pow 45.8%

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

      9. sub-neg 45.8%

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

      10. metadata-eval 45.8%

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

   3. Simplified 45.8%

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

   4. Taylor expanded in t around 0 71.3%

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

      1. times-frac 66.2%

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

   6. Simplified 66.2%

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

   7. Taylor expanded in y around 0 88.3%

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

   8. Taylor expanded in b around 0 45.8%

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

      1. distribute-lft-out 45.8%

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

      2. distribute-rgt1-in 45.8%

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

   10. Simplified 45.8%

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

   11. Taylor expanded in b around inf 45.8%

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

       1. associate-*r* 50.6%

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

   13. Simplified 50.6%

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

4. Final simplification 41.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.56 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \left(-\frac{b}{y \cdot a}\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+66}:\\ \;\;\;\;\frac{\frac{x}{a}}{y \cdot \left(1 + b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \]

Alternative 15: 39.1% accurate, 24.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 5.5 \cdot 10^{-28}:\\ \;\;\;\;\frac{\frac{x}{a} - x \cdot \frac{b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 5.5e-28) (/ (- (/ x a) (* x (/ b a))) y) (/ x (* y (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 5.5e-28) {
		tmp = ((x / a) - (x * (b / a))) / y;
	} else {
		tmp = x / (y * (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 <= 5.5d-28) then
        tmp = ((x / a) - (x * (b / a))) / y
    else
        tmp = x / (y * (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 <= 5.5e-28) {
		tmp = ((x / a) - (x * (b / a))) / y;
	} else {
		tmp = x / (y * (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 5.5e-28:
		tmp = ((x / a) - (x * (b / a))) / y
	else:
		tmp = x / (y * (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 5.5e-28)
		tmp = Float64(Float64(Float64(x / a) - Float64(x * Float64(b / a))) / y);
	else
		tmp = Float64(x / Float64(y * Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 5.5e-28)
		tmp = ((x / a) - (x * (b / a))) / y;
	else
		tmp = x / (y * (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 5.5e-28], N[(N[(N[(x / a), $MachinePrecision] - N[(x * N[(b / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 5.49999999999999967e-28

   1. Initial program 97.8%

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

      1. associate-*l/ 83.6%

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

      2. *-commutative 83.6%

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

      3. exp-diff 76.2%

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

      4. exp-sum 66.6%

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

      5. *-commutative 66.6%

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

      6. exp-to-pow 66.6%

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

      7. *-commutative 66.6%

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

      8. exp-to-pow 67.3%

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

      9. sub-neg 67.3%

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

      10. metadata-eval 67.3%

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

   3. Simplified 67.3%

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

   4. Taylor expanded in t around 0 66.1%

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

      1. times-frac 64.6%

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

   6. Simplified 64.6%

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

   7. Taylor expanded in y around 0 51.6%

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

   8. Taylor expanded in b around 0 34.6%

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

      1. +-commutative 34.6%

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

      2. mul-1-neg 34.6%

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

      3. unsub-neg 34.6%

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

      4. times-frac 32.9%

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

   10. Simplified 32.9%

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

       1. associate-/r* 34.9%

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

       2. associate-*r/ 39.0%

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

       3. sub-div 40.1%

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

   12. Applied egg-rr 40.1%

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

   if 5.49999999999999967e-28 < 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/ 87.3%

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

      2. *-commutative 87.3%

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

      3. exp-diff 58.2%

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

      4. exp-sum 49.4%

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

      5. *-commutative 49.4%

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

      6. exp-to-pow 49.4%

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

      7. *-commutative 49.4%

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

      8. exp-to-pow 49.4%

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

      9. sub-neg 49.4%

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

      10. metadata-eval 49.4%

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

   3. Simplified 49.4%

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

   4. Taylor expanded in t around 0 67.3%

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

      1. times-frac 62.2%

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

   6. Simplified 62.2%

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

   7. Taylor expanded in y around 0 77.7%

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

   8. Taylor expanded in b around 0 39.9%

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

      1. distribute-lft-out 39.9%

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

      2. distribute-rgt1-in 39.9%

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

   10. Simplified 39.9%

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

   11. Taylor expanded in b around inf 39.9%

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

       1. associate-*r* 43.5%

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

   13. Simplified 43.5%

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

4. Final simplification 41.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 5.5 \cdot 10^{-28}:\\ \;\;\;\;\frac{\frac{x}{a} - x \cdot \frac{b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \]

Alternative 16: 39.3% accurate, 28.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \left(-\frac{b}{y \cdot a}\right)\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{+67}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.1e-6)
   (* x (- (/ b (* y a))))
   (if (<= b 1.95e+67) (* (/ x a) (/ 1.0 y)) (/ x (* y (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.1e-6) {
		tmp = x * -(b / (y * a));
	} else if (b <= 1.95e+67) {
		tmp = (x / a) * (1.0 / y);
	} else {
		tmp = x / (y * (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 <= (-1.1d-6)) then
        tmp = x * -(b / (y * a))
    else if (b <= 1.95d+67) then
        tmp = (x / a) * (1.0d0 / y)
    else
        tmp = x / (y * (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 <= -1.1e-6) {
		tmp = x * -(b / (y * a));
	} else if (b <= 1.95e+67) {
		tmp = (x / a) * (1.0 / y);
	} else {
		tmp = x / (y * (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.1e-6:
		tmp = x * -(b / (y * a))
	elif b <= 1.95e+67:
		tmp = (x / a) * (1.0 / y)
	else:
		tmp = x / (y * (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.1e-6)
		tmp = Float64(x * Float64(-Float64(b / Float64(y * a))));
	elseif (b <= 1.95e+67)
		tmp = Float64(Float64(x / a) * Float64(1.0 / y));
	else
		tmp = Float64(x / Float64(y * Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.1e-6)
		tmp = x * -(b / (y * a));
	elseif (b <= 1.95e+67)
		tmp = (x / a) * (1.0 / y);
	else
		tmp = x / (y * (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.1e-6], N[(x * (-N[(b / N[(y * a), $MachinePrecision]), $MachinePrecision])), $MachinePrecision], If[LessEqual[b, 1.95e+67], N[(N[(x / a), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.1000000000000001e-6

   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/ 86.0%

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

      2. *-commutative 86.0%

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

      3. exp-diff 63.2%

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

      4. exp-sum 56.1%

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

      5. *-commutative 56.1%

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

      6. exp-to-pow 56.1%

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

      7. *-commutative 56.1%

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

      8. exp-to-pow 56.1%

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

      9. sub-neg 56.1%

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

      10. metadata-eval 56.1%

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

   3. Simplified 56.1%

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

   4. Taylor expanded in t around 0 65.1%

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

      1. times-frac 58.1%

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

   6. Simplified 58.1%

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

   7. Taylor expanded in y around 0 81.1%

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

   8. Taylor expanded in b around 0 33.7%

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

      1. +-commutative 33.7%

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

      2. mul-1-neg 33.7%

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

      3. unsub-neg 33.7%

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

      4. times-frac 37.0%

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

   10. Simplified 37.0%

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

   11. Taylor expanded in b around inf 33.7%

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

       1. associate-*r/ 33.7%

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

       2. *-commutative 33.7%

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

       3. neg-mul-1 33.7%

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

       4. distribute-lft-neg-in 33.7%

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

       5. *-commutative 33.7%

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

       6. associate-*r/ 37.2%

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

       7. *-commutative 37.2%

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

   13. Simplified 37.2%

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

   if -1.1000000000000001e-6 < b < 1.95000000000000003e67

   1. Initial program 97.3%

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

      1. associate-*l/ 83.6%

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

      2. *-commutative 83.6%

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

      3. exp-diff 80.1%

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

      4. exp-sum 69.5%

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

      5. *-commutative 69.5%

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

      6. exp-to-pow 69.5%

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

      7. *-commutative 69.5%

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

      8. exp-to-pow 70.2%

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

      9. sub-neg 70.2%

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

      10. metadata-eval 70.2%

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

   3. Simplified 70.2%

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

   4. Taylor expanded in t around 0 64.5%

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

      1. times-frac 64.9%

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

   6. Simplified 64.9%

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

   7. Taylor expanded in b around 0 63.9%

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

      1. times-frac 64.9%

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

   9. Simplified 64.9%

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

   10. Taylor expanded in y around 0 37.9%

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

   if 1.95000000000000003e67 < 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/ 86.2%

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

      2. *-commutative 86.2%

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

      3. exp-diff 55.2%

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

      4. exp-sum 46.6%

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

      5. *-commutative 46.6%

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

      6. exp-to-pow 46.6%

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

      7. *-commutative 46.6%

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

      8. exp-to-pow 46.6%

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

      9. sub-neg 46.6%

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

      10. metadata-eval 46.6%

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

   3. Simplified 46.6%

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

   4. Taylor expanded in t around 0 72.5%

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

      1. times-frac 67.3%

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

   6. Simplified 67.3%

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

   7. Taylor expanded in y around 0 89.8%

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

   8. Taylor expanded in b around 0 46.5%

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

      1. distribute-lft-out 46.5%

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

      2. distribute-rgt1-in 46.5%

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

   10. Simplified 46.5%

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

   11. Taylor expanded in b around inf 46.5%

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

       1. associate-*r* 51.5%

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

   13. Simplified 51.5%

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

4. Final simplification 40.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \left(-\frac{b}{y \cdot a}\right)\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{+67}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \]

Alternative 17: 30.5% accurate, 34.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 8.5 \cdot 10^{-77}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 8.5e-77) (/ (/ x y) a) (* (/ x a) (/ 1.0 y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 8.5e-77) {
		tmp = (x / y) / a;
	} else {
		tmp = (x / a) * (1.0 / 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 (z <= 8.5d-77) then
        tmp = (x / y) / a
    else
        tmp = (x / a) * (1.0d0 / 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 (z <= 8.5e-77) {
		tmp = (x / y) / a;
	} else {
		tmp = (x / a) * (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= 8.5e-77:
		tmp = (x / y) / a
	else:
		tmp = (x / a) * (1.0 / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 8.5e-77)
		tmp = Float64(Float64(x / y) / a);
	else
		tmp = Float64(Float64(x / a) * Float64(1.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= 8.5e-77)
		tmp = (x / y) / a;
	else
		tmp = (x / a) * (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 8.5e-77], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision], N[(N[(x / a), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 8.4999999999999998e-77

   1. Initial program 99.4%

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

      1. associate-*l/ 87.2%

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

      2. *-commutative 87.2%

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

      3. exp-diff 70.7%

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

      4. exp-sum 63.0%

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

      5. *-commutative 63.0%

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

      6. exp-to-pow 63.0%

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

      7. *-commutative 63.0%

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

      8. exp-to-pow 63.0%

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

      9. sub-neg 63.0%

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

      10. metadata-eval 63.0%

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

   3. Simplified 63.0%

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

   4. Taylor expanded in t around 0 62.9%

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

      1. times-frac 59.5%

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

   6. Simplified 59.5%

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

   7. Taylor expanded in b around 0 48.8%

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

      1. times-frac 46.5%

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

   9. Simplified 46.5%

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

       1. associate-*l/ 51.8%

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

   11. Applied egg-rr 51.8%

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

   12. Taylor expanded in y around 0 27.0%

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

   if 8.4999999999999998e-77 < z

   1. Initial program 97.9%

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

      1. associate-*l/ 83.1%

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

      2. *-commutative 83.1%

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

      3. exp-diff 70.6%

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

      4. exp-sum 60.2%

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

      5. *-commutative 60.2%

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

      6. exp-to-pow 60.2%

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

      7. *-commutative 60.2%

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

      8. exp-to-pow 60.9%

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

      9. sub-neg 60.9%

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

      10. metadata-eval 60.9%

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

   3. Simplified 60.9%

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

   4. Taylor expanded in t around 0 68.8%

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

      1. times-frac 66.9%

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

   6. Simplified 66.9%

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

   7. Taylor expanded in b around 0 56.5%

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

      1. times-frac 57.7%

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

   9. Simplified 57.7%

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

   10. Taylor expanded in y around 0 35.8%

       \[\leadsto \frac{x}{a} \cdot \color{blue}{\frac{1}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 32.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 8.5 \cdot 10^{-77}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{1}{y}\\ \end{array} \]

Alternative 18: 34.6% accurate, 34.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 1.15 \cdot 10^{+85}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 1.15e+85) (* (/ x a) (/ 1.0 y)) (/ x (* a (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1.15e+85) {
		tmp = (x / a) * (1.0 / 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 <= 1.15d+85) then
        tmp = (x / a) * (1.0d0 / 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 <= 1.15e+85) {
		tmp = (x / a) * (1.0 / y);
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 1.15e+85:
		tmp = (x / a) * (1.0 / y)
	else:
		tmp = x / (a * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 1.15e+85)
		tmp = Float64(Float64(x / a) * Float64(1.0 / 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 <= 1.15e+85)
		tmp = (x / a) * (1.0 / y);
	else
		tmp = x / (a * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 1.15e+85], N[(N[(x / a), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 1.1499999999999999e85

   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. Step-by-step derivation

      1. associate-*l/ 84.2%

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

      2. *-commutative 84.2%

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

      3. exp-diff 75.3%

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

      4. exp-sum 66.0%

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

      5. *-commutative 66.0%

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

      6. exp-to-pow 66.0%

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

      7. *-commutative 66.0%

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

      8. exp-to-pow 66.5%

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

      9. sub-neg 66.5%

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

      10. metadata-eval 66.5%

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

   3. Simplified 66.5%

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

   4. Taylor expanded in t around 0 65.5%

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

      1. times-frac 63.3%

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

   6. Simplified 63.3%

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

   7. Taylor expanded in b around 0 57.6%

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

      1. times-frac 57.9%

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

   9. Simplified 57.9%

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

   10. Taylor expanded in y around 0 33.0%

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

   if 1.1499999999999999e85 < 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/ 86.8%

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

      2. *-commutative 86.8%

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

      3. exp-diff 52.8%

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

      4. exp-sum 43.4%

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

      5. *-commutative 43.4%

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

      6. exp-to-pow 43.4%

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

      7. *-commutative 43.4%

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

      8. exp-to-pow 43.4%

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

      9. sub-neg 43.4%

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

      10. metadata-eval 43.4%

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

   3. Simplified 43.4%

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

   4. Taylor expanded in t around 0 69.9%

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

      1. times-frac 66.1%

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

   6. Simplified 66.1%

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

   7. Taylor expanded in y around 0 88.9%

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

   8. Taylor expanded in b around 0 48.8%

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

      1. distribute-lft-out 48.8%

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

      2. distribute-rgt1-in 48.8%

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

   10. Simplified 48.8%

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

   11. Taylor expanded in b around inf 48.8%

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

       1. *-commutative 48.8%

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

   13. Simplified 48.8%

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

4. Final simplification 36.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 1.15 \cdot 10^{+85}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \]

Alternative 19: 35.0% accurate, 34.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 2.05 \cdot 10^{+68}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 2.05e+68) (* (/ x a) (/ 1.0 y)) (/ x (* y (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 2.05e+68) {
		tmp = (x / a) * (1.0 / y);
	} else {
		tmp = x / (y * (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 <= 2.05d+68) then
        tmp = (x / a) * (1.0d0 / y)
    else
        tmp = x / (y * (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 <= 2.05e+68) {
		tmp = (x / a) * (1.0 / y);
	} else {
		tmp = x / (y * (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 2.05e+68:
		tmp = (x / a) * (1.0 / y)
	else:
		tmp = x / (y * (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 2.05e+68)
		tmp = Float64(Float64(x / a) * Float64(1.0 / y));
	else
		tmp = Float64(x / Float64(y * Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 2.05e+68)
		tmp = (x / a) * (1.0 / y);
	else
		tmp = x / (y * (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 2.05e+68], N[(N[(x / a), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 2.05e68

   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. Step-by-step derivation

      1. associate-*l/ 84.3%

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

      2. *-commutative 84.3%

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

      3. exp-diff 75.2%

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

      4. exp-sum 65.6%

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

      5. *-commutative 65.6%

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

      6. exp-to-pow 65.6%

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

      7. *-commutative 65.6%

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

      8. exp-to-pow 66.2%

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

      9. sub-neg 66.2%

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

      10. metadata-eval 66.2%

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

   3. Simplified 66.2%

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

   4. Taylor expanded in t around 0 64.7%

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

      1. times-frac 62.9%

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

   6. Simplified 62.9%

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

   7. Taylor expanded in b around 0 59.0%

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

      1. times-frac 58.3%

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

   9. Simplified 58.3%

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

   10. Taylor expanded in y around 0 32.8%

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

   if 2.05e68 < 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/ 86.2%

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

      2. *-commutative 86.2%

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

      3. exp-diff 55.2%

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

      4. exp-sum 46.6%

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

      5. *-commutative 46.6%

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

      6. exp-to-pow 46.6%

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

      7. *-commutative 46.6%

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

      8. exp-to-pow 46.6%

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

      9. sub-neg 46.6%

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

      10. metadata-eval 46.6%

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

   3. Simplified 46.6%

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

   4. Taylor expanded in t around 0 72.5%

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

      1. times-frac 67.3%

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

   6. Simplified 67.3%

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

   7. Taylor expanded in y around 0 89.8%

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

   8. Taylor expanded in b around 0 46.5%

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

      1. distribute-lft-out 46.5%

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

      2. distribute-rgt1-in 46.5%

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

   10. Simplified 46.5%

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

   11. Taylor expanded in b around inf 46.5%

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

       1. associate-*r* 51.5%

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

   13. Simplified 51.5%

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

4. Final simplification 37.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 2.05 \cdot 10^{+68}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \]

Alternative 20: 31.7% accurate, 44.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 1.6 \cdot 10^{-76}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 1.6e-76) (/ (/ x y) a) (/ x (* y a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 1.6e-76) {
		tmp = (x / y) / a;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= 1.6d-76) then
        tmp = (x / y) / a
    else
        tmp = x / (y * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 1.6e-76) {
		tmp = (x / y) / a;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 1.6e-76:
		tmp = (x / y) / a
	else:
		tmp = x / (y * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 1.6e-76)
		tmp = Float64(Float64(x / y) / a);
	else
		tmp = Float64(x / Float64(y * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 1.6e-76)
		tmp = (x / y) / a;
	else
		tmp = x / (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 1.6e-76], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 1.5999999999999999e-76

   1. Initial program 98.5%

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

      1. associate-*l/ 84.0%

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

      2. *-commutative 84.0%

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

      3. exp-diff 79.9%

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

      4. exp-sum 67.6%

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

      5. *-commutative 67.6%

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

      6. exp-to-pow 67.6%

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

      7. *-commutative 67.6%

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

      8. exp-to-pow 68.0%

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

      9. sub-neg 68.0%

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

      10. metadata-eval 68.0%

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

   3. Simplified 68.0%

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

   4. Taylor expanded in t around 0 77.8%

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

      1. times-frac 71.4%

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

   6. Simplified 71.4%

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

   7. Taylor expanded in b around 0 66.8%

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

      1. times-frac 60.6%

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

   9. Simplified 60.6%

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

       1. associate-*l/ 66.8%

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

   11. Applied egg-rr 66.8%

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

   12. Taylor expanded in y around 0 35.0%

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

   if 1.5999999999999999e-76 < a

   1. Initial program 98.5%

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

      1. associate-*l/ 85.2%

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

      2. *-commutative 85.2%

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

      3. exp-diff 65.0%

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

      4. exp-sum 57.5%

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

      5. *-commutative 57.5%

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

      6. exp-to-pow 57.5%

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

      7. *-commutative 57.5%

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

      8. exp-to-pow 57.9%

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

      9. sub-neg 57.9%

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

      10. metadata-eval 57.9%

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

   3. Simplified 57.9%

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

   4. Taylor expanded in t around 0 59.5%

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

      1. times-frac 59.3%

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

   6. Simplified 59.3%

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

   7. Taylor expanded in y around 0 58.7%

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

   8. Taylor expanded in b around 0 29.1%

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

4. Final simplification 31.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.6 \cdot 10^{-76}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \]

Alternative 21: 30.4% 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 98.5%

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

   1. associate-*l/ 84.7%

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

   2. *-commutative 84.7%

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

   3. exp-diff 70.7%

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

   4. exp-sum 61.3%

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

   5. *-commutative 61.3%

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

   6. exp-to-pow 61.3%

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

   7. *-commutative 61.3%

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

   8. exp-to-pow 61.7%

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

   9. sub-neg 61.7%

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

   10. metadata-eval 61.7%

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

3. Simplified 61.7%

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

4. Taylor expanded in t around 0 66.4%

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

   1. times-frac 63.9%

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

6. Simplified 63.9%

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

7. Taylor expanded in y around 0 59.6%

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

8. Taylor expanded in b around 0 28.7%

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

9. Final simplification 28.7%

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

Developer target: 71.7% 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 2023333 
(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))