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

Percentage Accurate: 98.3% → 98.3%

Time: 32.5s

Alternatives: 14

Speedup: 1.0×

• 20.9% 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: 98.3% 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: 98.3% 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: 92.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+62} \lor \neg \left(y \leq 4 \cdot 10^{+54}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t - 1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.3e+62) (not (<= y 4e+54)))
   (/ (* x (exp (- (- (* y (log z)) (log a)) b))) y)
   (/ (* x (exp (- (* (- t 1.0) (log a)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.3e+62) || !(y <= 4e+54)) {
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	} else {
		tmp = (x * exp((((t - 1.0) * log(a)) - b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.3d+62)) .or. (.not. (y <= 4d+54))) then
        tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y
    else
        tmp = (x * exp((((t - 1.0d0) * log(a)) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.3e+62) || !(y <= 4e+54)) {
		tmp = (x * Math.exp((((y * Math.log(z)) - Math.log(a)) - b))) / y;
	} else {
		tmp = (x * Math.exp((((t - 1.0) * Math.log(a)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.3e+62) or not (y <= 4e+54):
		tmp = (x * math.exp((((y * math.log(z)) - math.log(a)) - b))) / y
	else:
		tmp = (x * math.exp((((t - 1.0) * math.log(a)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.3e+62) || !(y <= 4e+54))
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) - log(a)) - b))) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t - 1.0) * log(a)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.3e+62) || ~((y <= 4e+54)))
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	else
		tmp = (x * exp((((t - 1.0) * log(a)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.3e+62], N[Not[LessEqual[y, 4e+54]], $MachinePrecision]], N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] - N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[(t - 1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.29999999999999992e62 or 4.0000000000000003e54 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 94.2%

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

      1. +-commutative 94.2%

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

      2. mul-1-neg 94.2%

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

      3. unsub-neg 94.2%

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

   4. Simplified 94.2%

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

   if -1.29999999999999992e62 < y < 4.0000000000000003e54

   1. Initial program 97.6%

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

      1. associate-/l* 96.7%

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

      2. fma-def 96.7%

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

      3. sub-neg 96.7%

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

      4. metadata-eval 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in y around 0 96.4%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+62} \lor \neg \left(y \leq 4 \cdot 10^{+54}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t - 1\right) \cdot \log a - b}}{y}\\ \end{array} \]

Alternative 3: 88.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+137} \lor \neg \left(y \leq 9.5 \cdot 10^{+64}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t - 1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.7e+137) (not (<= y 9.5e+64)))
   (/ (* x (/ (pow z y) a)) y)
   (/ (* x (exp (- (* (- t 1.0) (log a)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.7e+137) || !(y <= 9.5e+64)) {
		tmp = (x * (pow(z, y) / a)) / y;
	} else {
		tmp = (x * exp((((t - 1.0) * log(a)) - b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-2.7d+137)) .or. (.not. (y <= 9.5d+64))) then
        tmp = (x * ((z ** y) / a)) / y
    else
        tmp = (x * exp((((t - 1.0d0) * log(a)) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.7e+137) || !(y <= 9.5e+64)) {
		tmp = (x * (Math.pow(z, y) / a)) / y;
	} else {
		tmp = (x * Math.exp((((t - 1.0) * Math.log(a)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.7e+137) or not (y <= 9.5e+64):
		tmp = (x * (math.pow(z, y) / a)) / y
	else:
		tmp = (x * math.exp((((t - 1.0) * math.log(a)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.7e+137) || !(y <= 9.5e+64))
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t - 1.0) * log(a)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.7e+137) || ~((y <= 9.5e+64)))
		tmp = (x * ((z ^ y) / a)) / y;
	else
		tmp = (x * exp((((t - 1.0) * log(a)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.7e+137], N[Not[LessEqual[y, 9.5e+64]], $MachinePrecision]], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[(t - 1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.70000000000000017e137 or 9.50000000000000028e64 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 94.5%

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

      1. +-commutative 94.5%

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

      2. mul-1-neg 94.5%

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

      3. unsub-neg 94.5%

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

   4. Simplified 94.5%

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

   5. Taylor expanded in b around 0 86.9%

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

      1. *-commutative 86.9%

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

      2. div-exp 86.9%

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

      3. *-commutative 86.9%

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

      4. exp-to-pow 86.9%

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

      5. rem-exp-log 86.9%

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

   7. Simplified 86.9%

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

   if -2.70000000000000017e137 < y < 9.50000000000000028e64

   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* 96.9%

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

      2. fma-def 96.9%

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

      3. sub-neg 96.9%

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

      4. metadata-eval 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in y around 0 95.9%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+137} \lor \neg \left(y \leq 9.5 \cdot 10^{+64}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t - 1\right) \cdot \log a - b}}{y}\\ \end{array} \]

Alternative 4: 77.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+45} \lor \neg \left(y \leq 7.2 \cdot 10^{+65}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)}}{e^{b}} \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.95e+45) (not (<= y 7.2e+65)))
   (/ (* x (/ (pow z y) a)) y)
   (* (/ (pow a (- t 1.0)) (exp b)) (/ x y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.95e+45) || !(y <= 7.2e+65)) {
		tmp = (x * (pow(z, y) / a)) / y;
	} else {
		tmp = (pow(a, (t - 1.0)) / exp(b)) * (x / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.95d+45)) .or. (.not. (y <= 7.2d+65))) then
        tmp = (x * ((z ** y) / a)) / y
    else
        tmp = ((a ** (t - 1.0d0)) / exp(b)) * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.95e+45) || !(y <= 7.2e+65)) {
		tmp = (x * (Math.pow(z, y) / a)) / y;
	} else {
		tmp = (Math.pow(a, (t - 1.0)) / Math.exp(b)) * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.95e+45) or not (y <= 7.2e+65):
		tmp = (x * (math.pow(z, y) / a)) / y
	else:
		tmp = (math.pow(a, (t - 1.0)) / math.exp(b)) * (x / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.95e+45) || !(y <= 7.2e+65))
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	else
		tmp = Float64(Float64((a ^ Float64(t - 1.0)) / exp(b)) * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.95e+45) || ~((y <= 7.2e+65)))
		tmp = (x * ((z ^ y) / a)) / y;
	else
		tmp = ((a ^ (t - 1.0)) / exp(b)) * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.95e+45], N[Not[LessEqual[y, 7.2e+65]], $MachinePrecision]], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.95e45 or 7.19999999999999957e65 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 93.3%

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

      1. +-commutative 93.3%

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

      2. mul-1-neg 93.3%

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

      3. unsub-neg 93.3%

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

   4. Simplified 93.3%

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

   5. Taylor expanded in b around 0 85.7%

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

      1. *-commutative 85.7%

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

      2. div-exp 85.7%

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

      3. *-commutative 85.7%

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

      4. exp-to-pow 85.7%

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

      5. rem-exp-log 85.7%

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

   7. Simplified 85.7%

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

   if -1.95e45 < y < 7.19999999999999957e65

   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/ 90.3%

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

      2. *-commutative 90.3%

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

      3. +-commutative 90.3%

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

      4. associate--l+ 90.3%

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

      5. exp-sum 79.3%

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

      6. *-commutative 79.3%

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

      7. exp-to-pow 80.2%

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

      8. sub-neg 80.2%

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

      9. metadata-eval 80.2%

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

      10. exp-diff 76.2%

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

      11. *-commutative 76.2%

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

      12. exp-to-pow 76.3%

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

   3. Simplified 76.3%

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

   4. Taylor expanded in y around 0 82.7%

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

      1. *-commutative 82.7%

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

      2. *-commutative 82.7%

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

      3. times-frac 79.4%

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

      4. exp-to-pow 80.3%

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

      5. sub-neg 80.3%

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

      6. metadata-eval 80.3%

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

   6. Simplified 80.3%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+45} \lor \neg \left(y \leq 7.2 \cdot 10^{+65}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)}}{e^{b}} \cdot \frac{x}{y}\\ \end{array} \]

Alternative 5: 81.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+46} \lor \neg \left(y \leq 1.66 \cdot 10^{+68}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4.3e+46) (not (<= y 1.66e+68)))
   (/ (* x (/ (pow z y) a)) y)
   (/ (* x (/ (pow a (- t 1.0)) (exp b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4.3e+46) || !(y <= 1.66e+68)) {
		tmp = (x * (pow(z, y) / a)) / y;
	} else {
		tmp = (x * (pow(a, (t - 1.0)) / exp(b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-4.3d+46)) .or. (.not. (y <= 1.66d+68))) then
        tmp = (x * ((z ** y) / a)) / y
    else
        tmp = (x * ((a ** (t - 1.0d0)) / exp(b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4.3e+46) || !(y <= 1.66e+68)) {
		tmp = (x * (Math.pow(z, y) / a)) / y;
	} else {
		tmp = (x * (Math.pow(a, (t - 1.0)) / Math.exp(b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -4.3e+46) or not (y <= 1.66e+68):
		tmp = (x * (math.pow(z, y) / a)) / y
	else:
		tmp = (x * (math.pow(a, (t - 1.0)) / math.exp(b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -4.3e+46) || !(y <= 1.66e+68))
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	else
		tmp = Float64(Float64(x * Float64((a ^ Float64(t - 1.0)) / exp(b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -4.3e+46) || ~((y <= 1.66e+68)))
		tmp = (x * ((z ^ y) / a)) / y;
	else
		tmp = (x * ((a ^ (t - 1.0)) / exp(b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -4.3e+46], N[Not[LessEqual[y, 1.66e+68]], $MachinePrecision]], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.30000000000000005e46 or 1.66e68 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 93.3%

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

      1. +-commutative 93.3%

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

      2. mul-1-neg 93.3%

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

      3. unsub-neg 93.3%

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

   4. Simplified 93.3%

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

   5. Taylor expanded in b around 0 85.7%

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

      1. *-commutative 85.7%

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

      2. div-exp 85.7%

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

      3. *-commutative 85.7%

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

      4. exp-to-pow 85.7%

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

      5. rem-exp-log 85.7%

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

   7. Simplified 85.7%

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

   if -4.30000000000000005e46 < y < 1.66e68

   1. Initial program 97.5%

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

   2. Taylor expanded in y around 0 96.4%

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

      1. div-exp 85.9%

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

      2. exp-to-pow 87.0%

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

      3. sub-neg 87.0%

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

      4. metadata-eval 87.0%

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

   4. Simplified 87.0%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+46} \lor \neg \left(y \leq 1.66 \cdot 10^{+68}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{e^{b}}}{y}\\ \end{array} \]

Alternative 6: 73.7% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.9 \cdot 10^{+44} \lor \neg \left(y \leq 4.4 \cdot 10^{+54}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -5.9e+44) (not (<= y 4.4e+54)))
   (/ (* x (/ (pow z y) a)) y)
   (/ (/ x (* a (exp b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -5.9e+44) || !(y <= 4.4e+54)) {
		tmp = (x * (pow(z, y) / a)) / y;
	} else {
		tmp = (x / (a * exp(b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-5.9d+44)) .or. (.not. (y <= 4.4d+54))) then
        tmp = (x * ((z ** y) / a)) / y
    else
        tmp = (x / (a * exp(b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -5.9e+44) || !(y <= 4.4e+54)) {
		tmp = (x * (Math.pow(z, y) / a)) / y;
	} else {
		tmp = (x / (a * Math.exp(b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -5.9e+44) or not (y <= 4.4e+54):
		tmp = (x * (math.pow(z, y) / a)) / y
	else:
		tmp = (x / (a * math.exp(b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -5.9e+44) || !(y <= 4.4e+54))
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	else
		tmp = Float64(Float64(x / Float64(a * exp(b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -5.9e+44) || ~((y <= 4.4e+54)))
		tmp = (x * ((z ^ y) / a)) / y;
	else
		tmp = (x / (a * exp(b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -5.9e+44], N[Not[LessEqual[y, 4.4e+54]], $MachinePrecision]], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.89999999999999965e44 or 4.3999999999999998e54 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 93.3%

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

      1. +-commutative 93.3%

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

      2. mul-1-neg 93.3%

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

      3. unsub-neg 93.3%

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

   4. Simplified 93.3%

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

   5. Taylor expanded in b around 0 85.7%

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

      1. *-commutative 85.7%

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

      2. div-exp 85.7%

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

      3. *-commutative 85.7%

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

      4. exp-to-pow 85.7%

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

      5. rem-exp-log 85.7%

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

   7. Simplified 85.7%

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

   if -5.89999999999999965e44 < y < 4.3999999999999998e54

   1. Initial program 97.5%

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

   2. Taylor expanded in t around 0 76.0%

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

      1. +-commutative 76.0%

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

      2. mul-1-neg 76.0%

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

      3. unsub-neg 76.0%

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

   4. Simplified 76.0%

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

   5. Taylor expanded in y around 0 74.9%

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

      1. exp-neg 74.9%

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

      2. associate-*r/ 74.9%

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

      3. *-rgt-identity 74.9%

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

      4. +-commutative 74.9%

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

      5. exp-sum 74.9%

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

      6. rem-exp-log 75.9%

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

   7. Simplified 75.9%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.9 \cdot 10^{+44} \lor \neg \left(y \leq 4.4 \cdot 10^{+54}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \end{array} \]

Alternative 7: 51.2% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+129}:\\ \;\;\;\;\left(b \cdot b\right) \cdot \frac{0.5 \cdot \frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y \cdot a}}{e^{b}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.65e+129)
   (* (* b b) (/ (* 0.5 (/ x a)) y))
   (/ (/ x (* y a)) (exp b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.65e+129) {
		tmp = (b * b) * ((0.5 * (x / a)) / y);
	} else {
		tmp = (x / (y * a)) / exp(b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.65d+129)) then
        tmp = (b * b) * ((0.5d0 * (x / a)) / y)
    else
        tmp = (x / (y * a)) / exp(b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.65e+129) {
		tmp = (b * b) * ((0.5 * (x / a)) / y);
	} else {
		tmp = (x / (y * a)) / Math.exp(b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.65e+129:
		tmp = (b * b) * ((0.5 * (x / a)) / y)
	else:
		tmp = (x / (y * a)) / math.exp(b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.65e+129)
		tmp = Float64(Float64(b * b) * Float64(Float64(0.5 * Float64(x / a)) / y));
	else
		tmp = Float64(Float64(x / Float64(y * a)) / exp(b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.65e+129)
		tmp = (b * b) * ((0.5 * (x / a)) / y);
	else
		tmp = (x / (y * a)) / exp(b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.65e+129], N[(N[(b * b), $MachinePrecision] * N[(N[(0.5 * N[(x / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.64999999999999995e129

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 60.5%

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

      1. +-commutative 60.5%

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

      2. mul-1-neg 60.5%

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

      3. unsub-neg 60.5%

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

   4. Simplified 60.5%

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

   5. Taylor expanded in y around 0 57.5%

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

      1. exp-neg 57.5%

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

      2. associate-*r/ 57.5%

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

      3. *-rgt-identity 57.5%

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

      4. +-commutative 57.5%

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

      5. exp-sum 57.5%

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

      6. rem-exp-log 57.5%

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

      7. associate-/r* 54.3%

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

      8. associate-/r* 54.3%

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

      9. *-commutative 54.3%

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

      10. associate-/r* 52.1%

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

      11. associate-*r* 45.7%

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

      12. associate-/r* 42.5%

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

   7. Simplified 42.5%

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

   8. Taylor expanded in b around 0 17.9%

      \[\leadsto \color{blue}{-1 \cdot \left({b}^{2} \cdot \left(-1 \cdot \frac{x}{a \cdot y} + 0.5 \cdot \frac{x}{a \cdot y}\right)\right) + \left(-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{a \cdot y}\right)} \]
   9. Step-by-step derivation

      1. +-commutative 17.9%

         \[\leadsto \color{blue}{\left(-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{a \cdot y}\right) + -1 \cdot \left({b}^{2} \cdot \left(-1 \cdot \frac{x}{a \cdot y} + 0.5 \cdot \frac{x}{a \cdot y}\right)\right)} \]

      2. +-commutative 17.9%

         \[\leadsto \color{blue}{\left(\frac{x}{a \cdot y} + -1 \cdot \frac{b \cdot x}{a \cdot y}\right)} + -1 \cdot \left({b}^{2} \cdot \left(-1 \cdot \frac{x}{a \cdot y} + 0.5 \cdot \frac{x}{a \cdot y}\right)\right) \]

      3. mul-1-neg 17.9%

         \[\leadsto \left(\frac{x}{a \cdot y} + \color{blue}{\left(-\frac{b \cdot x}{a \cdot y}\right)}\right) + -1 \cdot \left({b}^{2} \cdot \left(-1 \cdot \frac{x}{a \cdot y} + 0.5 \cdot \frac{x}{a \cdot y}\right)\right) \]

      4. unsub-neg 17.9%

         \[\leadsto \color{blue}{\left(\frac{x}{a \cdot y} - \frac{b \cdot x}{a \cdot y}\right)} + -1 \cdot \left({b}^{2} \cdot \left(-1 \cdot \frac{x}{a \cdot y} + 0.5 \cdot \frac{x}{a \cdot y}\right)\right) \]

      5. *-commutative 17.9%

         \[\leadsto \left(\frac{x}{a \cdot y} - \frac{\color{blue}{x \cdot b}}{a \cdot y}\right) + -1 \cdot \left({b}^{2} \cdot \left(-1 \cdot \frac{x}{a \cdot y} + 0.5 \cdot \frac{x}{a \cdot y}\right)\right) \]

      6. times-frac 17.5%

         \[\leadsto \left(\frac{x}{a \cdot y} - \color{blue}{\frac{x}{a} \cdot \frac{b}{y}}\right) + -1 \cdot \left({b}^{2} \cdot \left(-1 \cdot \frac{x}{a \cdot y} + 0.5 \cdot \frac{x}{a \cdot y}\right)\right) \]

      7. mul-1-neg 17.5%

         \[\leadsto \left(\frac{x}{a \cdot y} - \frac{x}{a} \cdot \frac{b}{y}\right) + \color{blue}{\left(-{b}^{2} \cdot \left(-1 \cdot \frac{x}{a \cdot y} + 0.5 \cdot \frac{x}{a \cdot y}\right)\right)} \]

      8. distribute-rgt-neg-in 17.5%

         \[\leadsto \left(\frac{x}{a \cdot y} - \frac{x}{a} \cdot \frac{b}{y}\right) + \color{blue}{{b}^{2} \cdot \left(-\left(-1 \cdot \frac{x}{a \cdot y} + 0.5 \cdot \frac{x}{a \cdot y}\right)\right)} \]

      9. distribute-rgt-out 33.2%

         \[\leadsto \left(\frac{x}{a \cdot y} - \frac{x}{a} \cdot \frac{b}{y}\right) + {b}^{2} \cdot \left(-\color{blue}{\frac{x}{a \cdot y} \cdot \left(-1 + 0.5\right)}\right) \]

      10. metadata-eval 33.2%

          \[\leadsto \left(\frac{x}{a \cdot y} - \frac{x}{a} \cdot \frac{b}{y}\right) + {b}^{2} \cdot \left(-\frac{x}{a \cdot y} \cdot \color{blue}{-0.5}\right) \]

      11. *-commutative 33.2%

          \[\leadsto \left(\frac{x}{a \cdot y} - \frac{x}{a} \cdot \frac{b}{y}\right) + {b}^{2} \cdot \left(-\color{blue}{-0.5 \cdot \frac{x}{a \cdot y}}\right) \]

      12. distribute-lft-neg-in 33.2%

          \[\leadsto \left(\frac{x}{a \cdot y} - \frac{x}{a} \cdot \frac{b}{y}\right) + {b}^{2} \cdot \color{blue}{\left(\left(--0.5\right) \cdot \frac{x}{a \cdot y}\right)} \]

      13. metadata-eval 33.2%

          \[\leadsto \left(\frac{x}{a \cdot y} - \frac{x}{a} \cdot \frac{b}{y}\right) + {b}^{2} \cdot \left(\color{blue}{0.5} \cdot \frac{x}{a \cdot y}\right) \]

   10. Simplified 33.2%

       \[\leadsto \color{blue}{\left(\frac{x}{a \cdot y} - \frac{x}{a} \cdot \frac{b}{y}\right) + b \cdot \left(b \cdot \left(\frac{0.5}{a} \cdot \frac{x}{y}\right)\right)} \]

   11. Taylor expanded in b around inf 57.0%

       \[\leadsto \color{blue}{0.5 \cdot \frac{{b}^{2} \cdot x}{a \cdot y}} \]
   12. Step-by-step derivation

       1. associate-/l* 60.1%

          \[\leadsto 0.5 \cdot \color{blue}{\frac{{b}^{2}}{\frac{a \cdot y}{x}}} \]

       2. associate-*r/ 60.1%

          \[\leadsto \color{blue}{\frac{0.5 \cdot {b}^{2}}{\frac{a \cdot y}{x}}} \]

       3. *-commutative 60.1%

          \[\leadsto \frac{\color{blue}{{b}^{2} \cdot 0.5}}{\frac{a \cdot y}{x}} \]

       4. associate-/l* 54.2%

          \[\leadsto \frac{{b}^{2} \cdot 0.5}{\color{blue}{\frac{a}{\frac{x}{y}}}} \]

       5. associate-*r/ 54.2%

          \[\leadsto \color{blue}{{b}^{2} \cdot \frac{0.5}{\frac{a}{\frac{x}{y}}}} \]

       6. unpow2 54.2%

          \[\leadsto \color{blue}{\left(b \cdot b\right)} \cdot \frac{0.5}{\frac{a}{\frac{x}{y}}} \]

       7. associate-/l* 54.2%

          \[\leadsto \left(b \cdot b\right) \cdot \color{blue}{\frac{0.5 \cdot \frac{x}{y}}{a}} \]

       8. associate-*r/ 54.2%

          \[\leadsto \left(b \cdot b\right) \cdot \frac{\color{blue}{\frac{0.5 \cdot x}{y}}}{a} \]

       9. associate-/l/ 60.1%

          \[\leadsto \left(b \cdot b\right) \cdot \color{blue}{\frac{0.5 \cdot x}{a \cdot y}} \]

       10. associate-/r* 57.2%

           \[\leadsto \left(b \cdot b\right) \cdot \color{blue}{\frac{\frac{0.5 \cdot x}{a}}{y}} \]

       11. associate-*r/ 57.2%

           \[\leadsto \left(b \cdot b\right) \cdot \frac{\color{blue}{0.5 \cdot \frac{x}{a}}}{y} \]

   13. Simplified 57.2%

       \[\leadsto \color{blue}{\left(b \cdot b\right) \cdot \frac{0.5 \cdot \frac{x}{a}}{y}} \]

   if -1.64999999999999995e129 < t

   1. Initial program 98.3%

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

   2. Taylor expanded in t around 0 86.2%

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

      1. +-commutative 86.2%

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

      2. mul-1-neg 86.2%

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

      3. unsub-neg 86.2%

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

   4. Simplified 86.2%

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

   5. Taylor expanded in y around 0 67.0%

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

      1. exp-neg 67.0%

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

      2. associate-*r/ 67.0%

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

      3. *-rgt-identity 67.0%

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

      4. +-commutative 67.0%

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

      5. exp-sum 67.0%

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

      6. rem-exp-log 67.7%

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

      7. associate-/r* 63.2%

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

      8. associate-/r* 63.2%

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

      9. *-commutative 63.2%

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

      10. associate-/r* 66.8%

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

      11. associate-*r* 64.1%

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

      12. associate-/r* 61.4%

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

   7. Simplified 61.4%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+129}:\\ \;\;\;\;\left(b \cdot b\right) \cdot \frac{0.5 \cdot \frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y \cdot a}}{e^{b}}\\ \end{array} \]

Alternative 8: 58.9% 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 t around 0 83.0%

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

   1. +-commutative 83.0%

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

   2. mul-1-neg 83.0%

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

   3. unsub-neg 83.0%

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

4. Simplified 83.0%

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

5. Taylor expanded in y around 0 65.8%

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

   1. exp-neg 65.8%

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

   2. associate-*r/ 65.8%

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

   3. *-rgt-identity 65.8%

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

   4. +-commutative 65.8%

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

   5. exp-sum 65.8%

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

   6. rem-exp-log 66.4%

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

7. Simplified 66.4%

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

8. Final simplification 66.4%

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

Alternative 9: 43.3% accurate, 24.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+67}:\\ \;\;\;\;\left(b \cdot b\right) \cdot \frac{0.5 \cdot \frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq -750:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1 - b}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.5e+67)
   (* (* b b) (/ (* 0.5 (/ x a)) y))
   (if (<= b -750.0) (* (/ x y) (/ (- 1.0 b) a)) (/ (/ x (+ a (* a b))) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.5e+67) {
		tmp = (b * b) * ((0.5 * (x / a)) / y);
	} else if (b <= -750.0) {
		tmp = (x / y) * ((1.0 - b) / a);
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-3.5d+67)) then
        tmp = (b * b) * ((0.5d0 * (x / a)) / y)
    else if (b <= (-750.0d0)) then
        tmp = (x / y) * ((1.0d0 - b) / a)
    else
        tmp = (x / (a + (a * b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.5e+67) {
		tmp = (b * b) * ((0.5 * (x / a)) / y);
	} else if (b <= -750.0) {
		tmp = (x / y) * ((1.0 - b) / a);
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3.5e+67:
		tmp = (b * b) * ((0.5 * (x / a)) / y)
	elif b <= -750.0:
		tmp = (x / y) * ((1.0 - b) / a)
	else:
		tmp = (x / (a + (a * b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.5e+67)
		tmp = Float64(Float64(b * b) * Float64(Float64(0.5 * Float64(x / a)) / y));
	elseif (b <= -750.0)
		tmp = Float64(Float64(x / y) * Float64(Float64(1.0 - b) / a));
	else
		tmp = Float64(Float64(x / Float64(a + Float64(a * b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3.5e+67)
		tmp = (b * b) * ((0.5 * (x / a)) / y);
	elseif (b <= -750.0)
		tmp = (x / y) * ((1.0 - b) / a);
	else
		tmp = (x / (a + (a * b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.5e+67], N[(N[(b * b), $MachinePrecision] * N[(N[(0.5 * N[(x / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -750.0], N[(N[(x / y), $MachinePrecision] * N[(N[(1.0 - b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.5e67

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 90.0%

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

      1. +-commutative 90.0%

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

      2. mul-1-neg 90.0%

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

      3. unsub-neg 90.0%

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

   4. Simplified 90.0%

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

   5. Taylor expanded in y around 0 87.9%

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

      1. exp-neg 87.9%

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

      2. associate-*r/ 87.9%

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

      3. *-rgt-identity 87.9%

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

      4. +-commutative 87.9%

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

      5. exp-sum 87.9%

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

      6. rem-exp-log 87.9%

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

      7. associate-/r* 81.8%

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

      8. associate-/r* 81.8%

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

      9. *-commutative 81.8%

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

      10. associate-/r* 87.9%

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

      11. associate-*r* 79.7%

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

      12. associate-/r* 77.7%

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

   7. Simplified 77.7%

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

   8. Taylor expanded in b around 0 39.7%

      \[\leadsto \color{blue}{-1 \cdot \left({b}^{2} \cdot \left(-1 \cdot \frac{x}{a \cdot y} + 0.5 \cdot \frac{x}{a \cdot y}\right)\right) + \left(-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{a \cdot y}\right)} \]
   9. Step-by-step derivation

      1. +-commutative 39.7%

         \[\leadsto \color{blue}{\left(-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{a \cdot y}\right) + -1 \cdot \left({b}^{2} \cdot \left(-1 \cdot \frac{x}{a \cdot y} + 0.5 \cdot \frac{x}{a \cdot y}\right)\right)} \]

      2. +-commutative 39.7%

         \[\leadsto \color{blue}{\left(\frac{x}{a \cdot y} + -1 \cdot \frac{b \cdot x}{a \cdot y}\right)} + -1 \cdot \left({b}^{2} \cdot \left(-1 \cdot \frac{x}{a \cdot y} + 0.5 \cdot \frac{x}{a \cdot y}\right)\right) \]

      3. mul-1-neg 39.7%

         \[\leadsto \left(\frac{x}{a \cdot y} + \color{blue}{\left(-\frac{b \cdot x}{a \cdot y}\right)}\right) + -1 \cdot \left({b}^{2} \cdot \left(-1 \cdot \frac{x}{a \cdot y} + 0.5 \cdot \frac{x}{a \cdot y}\right)\right) \]

      4. unsub-neg 39.7%

         \[\leadsto \color{blue}{\left(\frac{x}{a \cdot y} - \frac{b \cdot x}{a \cdot y}\right)} + -1 \cdot \left({b}^{2} \cdot \left(-1 \cdot \frac{x}{a \cdot y} + 0.5 \cdot \frac{x}{a \cdot y}\right)\right) \]

      5. *-commutative 39.7%

         \[\leadsto \left(\frac{x}{a \cdot y} - \frac{\color{blue}{x \cdot b}}{a \cdot y}\right) + -1 \cdot \left({b}^{2} \cdot \left(-1 \cdot \frac{x}{a \cdot y} + 0.5 \cdot \frac{x}{a \cdot y}\right)\right) \]

      6. times-frac 39.5%

         \[\leadsto \left(\frac{x}{a \cdot y} - \color{blue}{\frac{x}{a} \cdot \frac{b}{y}}\right) + -1 \cdot \left({b}^{2} \cdot \left(-1 \cdot \frac{x}{a \cdot y} + 0.5 \cdot \frac{x}{a \cdot y}\right)\right) \]

      7. mul-1-neg 39.5%

         \[\leadsto \left(\frac{x}{a \cdot y} - \frac{x}{a} \cdot \frac{b}{y}\right) + \color{blue}{\left(-{b}^{2} \cdot \left(-1 \cdot \frac{x}{a \cdot y} + 0.5 \cdot \frac{x}{a \cdot y}\right)\right)} \]

      8. distribute-rgt-neg-in 39.5%

         \[\leadsto \left(\frac{x}{a \cdot y} - \frac{x}{a} \cdot \frac{b}{y}\right) + \color{blue}{{b}^{2} \cdot \left(-\left(-1 \cdot \frac{x}{a \cdot y} + 0.5 \cdot \frac{x}{a \cdot y}\right)\right)} \]

      9. distribute-rgt-out 66.1%

         \[\leadsto \left(\frac{x}{a \cdot y} - \frac{x}{a} \cdot \frac{b}{y}\right) + {b}^{2} \cdot \left(-\color{blue}{\frac{x}{a \cdot y} \cdot \left(-1 + 0.5\right)}\right) \]

      10. metadata-eval 66.1%

          \[\leadsto \left(\frac{x}{a \cdot y} - \frac{x}{a} \cdot \frac{b}{y}\right) + {b}^{2} \cdot \left(-\frac{x}{a \cdot y} \cdot \color{blue}{-0.5}\right) \]

      11. *-commutative 66.1%

          \[\leadsto \left(\frac{x}{a \cdot y} - \frac{x}{a} \cdot \frac{b}{y}\right) + {b}^{2} \cdot \left(-\color{blue}{-0.5 \cdot \frac{x}{a \cdot y}}\right) \]

      12. distribute-lft-neg-in 66.1%

          \[\leadsto \left(\frac{x}{a \cdot y} - \frac{x}{a} \cdot \frac{b}{y}\right) + {b}^{2} \cdot \color{blue}{\left(\left(--0.5\right) \cdot \frac{x}{a \cdot y}\right)} \]

      13. metadata-eval 66.1%

          \[\leadsto \left(\frac{x}{a \cdot y} - \frac{x}{a} \cdot \frac{b}{y}\right) + {b}^{2} \cdot \left(\color{blue}{0.5} \cdot \frac{x}{a \cdot y}\right) \]

   10. Simplified 56.6%

       \[\leadsto \color{blue}{\left(\frac{x}{a \cdot y} - \frac{x}{a} \cdot \frac{b}{y}\right) + b \cdot \left(b \cdot \left(\frac{0.5}{a} \cdot \frac{x}{y}\right)\right)} \]

   11. Taylor expanded in b around inf 72.0%

       \[\leadsto \color{blue}{0.5 \cdot \frac{{b}^{2} \cdot x}{a \cdot y}} \]
   12. Step-by-step derivation

       1. associate-/l* 66.2%

          \[\leadsto 0.5 \cdot \color{blue}{\frac{{b}^{2}}{\frac{a \cdot y}{x}}} \]

       2. associate-*r/ 66.2%

          \[\leadsto \color{blue}{\frac{0.5 \cdot {b}^{2}}{\frac{a \cdot y}{x}}} \]

       3. *-commutative 66.2%

          \[\leadsto \frac{\color{blue}{{b}^{2} \cdot 0.5}}{\frac{a \cdot y}{x}} \]

       4. associate-/l* 64.2%

          \[\leadsto \frac{{b}^{2} \cdot 0.5}{\color{blue}{\frac{a}{\frac{x}{y}}}} \]

       5. associate-*r/ 64.2%

          \[\leadsto \color{blue}{{b}^{2} \cdot \frac{0.5}{\frac{a}{\frac{x}{y}}}} \]

       6. unpow2 64.2%

          \[\leadsto \color{blue}{\left(b \cdot b\right)} \cdot \frac{0.5}{\frac{a}{\frac{x}{y}}} \]

       7. associate-/l* 64.2%

          \[\leadsto \left(b \cdot b\right) \cdot \color{blue}{\frac{0.5 \cdot \frac{x}{y}}{a}} \]

       8. associate-*r/ 64.2%

          \[\leadsto \left(b \cdot b\right) \cdot \frac{\color{blue}{\frac{0.5 \cdot x}{y}}}{a} \]

       9. associate-/l/ 66.2%

          \[\leadsto \left(b \cdot b\right) \cdot \color{blue}{\frac{0.5 \cdot x}{a \cdot y}} \]

       10. associate-/r* 70.3%

           \[\leadsto \left(b \cdot b\right) \cdot \color{blue}{\frac{\frac{0.5 \cdot x}{a}}{y}} \]

       11. associate-*r/ 70.3%

           \[\leadsto \left(b \cdot b\right) \cdot \frac{\color{blue}{0.5 \cdot \frac{x}{a}}}{y} \]

   13. Simplified 70.3%

       \[\leadsto \color{blue}{\left(b \cdot b\right) \cdot \frac{0.5 \cdot \frac{x}{a}}{y}} \]

   if -3.5e67 < b < -750

   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/ 89.5%

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

      2. *-commutative 89.5%

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

      3. +-commutative 89.5%

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

      4. associate--l+ 89.5%

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

      5. exp-sum 68.4%

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

      6. *-commutative 68.4%

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

      7. exp-to-pow 68.4%

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

      8. sub-neg 68.4%

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

      9. metadata-eval 68.4%

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

      10. exp-diff 68.4%

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

      11. *-commutative 68.4%

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

      12. exp-to-pow 68.4%

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

   3. Simplified 68.4%

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

   4. Taylor expanded in y around 0 78.9%

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

      1. *-commutative 78.9%

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

      2. *-commutative 78.9%

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

      3. times-frac 68.4%

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

      4. exp-to-pow 68.4%

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

      5. sub-neg 68.4%

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

      6. metadata-eval 68.4%

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

   6. Simplified 68.4%

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

   7. Taylor expanded in b around 0 69.1%

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

      1. associate-*r* 69.1%

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

      2. neg-mul-1 69.1%

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

      3. distribute-rgt1-in 69.1%

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

      4. sub-neg 69.1%

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

      5. metadata-eval 69.1%

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

      6. +-commutative 69.1%

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

      7. distribute-rgt-out 69.1%

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

      8. neg-mul-1 69.1%

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

      9. log-rec 69.1%

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

      10. +-commutative 69.1%

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

      11. log-rec 69.1%

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

      12. unsub-neg 69.1%

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

      13. log-pow 69.1%

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

      14. log-div 69.1%

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

      15. rem-exp-log 69.1%

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

   9. Simplified 69.1%

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

   10. Taylor expanded in t around 0 44.1%

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

   if -750 < b

   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 81.0%

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

      1. +-commutative 81.0%

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

      2. mul-1-neg 81.0%

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

      3. unsub-neg 81.0%

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

   4. Simplified 81.0%

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

   5. Taylor expanded in y around 0 58.2%

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

      1. exp-neg 58.2%

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

      2. associate-*r/ 58.2%

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

      3. *-rgt-identity 58.2%

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

      4. +-commutative 58.2%

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

      5. exp-sum 58.2%

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

      6. rem-exp-log 59.0%

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

   7. Simplified 59.0%

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

   8. Taylor expanded in b around 0 45.7%

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

4. Final simplification 50.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+67}:\\ \;\;\;\;\left(b \cdot b\right) \cdot \frac{0.5 \cdot \frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq -750:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1 - b}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \]

Alternative 10: 43.9% accurate, 24.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -750:\\ \;\;\;\;\frac{0.5 \cdot \left(x \cdot \left(b \cdot b\right)\right)}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -750.0)
   (/ (* 0.5 (* x (* b b))) (* y a))
   (/ (/ x (+ a (* a b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -750.0) {
		tmp = (0.5 * (x * (b * b))) / (y * a);
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-750.0d0)) then
        tmp = (0.5d0 * (x * (b * b))) / (y * a)
    else
        tmp = (x / (a + (a * b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -750.0) {
		tmp = (0.5 * (x * (b * b))) / (y * a);
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -750.0:
		tmp = (0.5 * (x * (b * b))) / (y * a)
	else:
		tmp = (x / (a + (a * b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -750.0)
		tmp = Float64(Float64(0.5 * Float64(x * Float64(b * b))) / Float64(y * a));
	else
		tmp = Float64(Float64(x / Float64(a + Float64(a * b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -750.0)
		tmp = (0.5 * (x * (b * b))) / (y * a);
	else
		tmp = (x / (a + (a * b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -750.0], N[(N[(0.5 * N[(x * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -750

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 88.4%

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

      1. +-commutative 88.4%

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

      2. mul-1-neg 88.4%

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

      3. unsub-neg 88.4%

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

   4. Simplified 88.4%

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

   5. Taylor expanded in y around 0 87.0%

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

      1. exp-neg 87.0%

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

      2. associate-*r/ 87.0%

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

      3. *-rgt-identity 87.0%

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

      4. +-commutative 87.0%

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

      5. exp-sum 87.0%

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

      6. rem-exp-log 87.0%

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

      7. associate-/r* 81.1%

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

      8. associate-/r* 81.1%

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

      9. *-commutative 81.1%

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

      10. associate-/r* 87.0%

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

      11. associate-*r* 79.6%

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

      12. associate-/r* 75.2%

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

   7. Simplified 75.2%

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

   8. Taylor expanded in b around 0 29.5%

      \[\leadsto \color{blue}{-1 \cdot \left({b}^{2} \cdot \left(-1 \cdot \frac{x}{a \cdot y} + 0.5 \cdot \frac{x}{a \cdot y}\right)\right) + \left(-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{a \cdot y}\right)} \]
   9. Step-by-step derivation

      1. +-commutative 29.5%

         \[\leadsto \color{blue}{\left(-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{a \cdot y}\right) + -1 \cdot \left({b}^{2} \cdot \left(-1 \cdot \frac{x}{a \cdot y} + 0.5 \cdot \frac{x}{a \cdot y}\right)\right)} \]

      2. +-commutative 29.5%

         \[\leadsto \color{blue}{\left(\frac{x}{a \cdot y} + -1 \cdot \frac{b \cdot x}{a \cdot y}\right)} + -1 \cdot \left({b}^{2} \cdot \left(-1 \cdot \frac{x}{a \cdot y} + 0.5 \cdot \frac{x}{a \cdot y}\right)\right) \]

      3. mul-1-neg 29.5%

         \[\leadsto \left(\frac{x}{a \cdot y} + \color{blue}{\left(-\frac{b \cdot x}{a \cdot y}\right)}\right) + -1 \cdot \left({b}^{2} \cdot \left(-1 \cdot \frac{x}{a \cdot y} + 0.5 \cdot \frac{x}{a \cdot y}\right)\right) \]

      4. unsub-neg 29.5%

         \[\leadsto \color{blue}{\left(\frac{x}{a \cdot y} - \frac{b \cdot x}{a \cdot y}\right)} + -1 \cdot \left({b}^{2} \cdot \left(-1 \cdot \frac{x}{a \cdot y} + 0.5 \cdot \frac{x}{a \cdot y}\right)\right) \]

      5. *-commutative 29.5%

         \[\leadsto \left(\frac{x}{a \cdot y} - \frac{\color{blue}{x \cdot b}}{a \cdot y}\right) + -1 \cdot \left({b}^{2} \cdot \left(-1 \cdot \frac{x}{a \cdot y} + 0.5 \cdot \frac{x}{a \cdot y}\right)\right) \]

      6. times-frac 29.4%

         \[\leadsto \left(\frac{x}{a \cdot y} - \color{blue}{\frac{x}{a} \cdot \frac{b}{y}}\right) + -1 \cdot \left({b}^{2} \cdot \left(-1 \cdot \frac{x}{a \cdot y} + 0.5 \cdot \frac{x}{a \cdot y}\right)\right) \]

      7. mul-1-neg 29.4%

         \[\leadsto \left(\frac{x}{a \cdot y} - \frac{x}{a} \cdot \frac{b}{y}\right) + \color{blue}{\left(-{b}^{2} \cdot \left(-1 \cdot \frac{x}{a \cdot y} + 0.5 \cdot \frac{x}{a \cdot y}\right)\right)} \]

      8. distribute-rgt-neg-in 29.4%

         \[\leadsto \left(\frac{x}{a \cdot y} - \frac{x}{a} \cdot \frac{b}{y}\right) + \color{blue}{{b}^{2} \cdot \left(-\left(-1 \cdot \frac{x}{a \cdot y} + 0.5 \cdot \frac{x}{a \cdot y}\right)\right)} \]

      9. distribute-rgt-out 55.9%

         \[\leadsto \left(\frac{x}{a \cdot y} - \frac{x}{a} \cdot \frac{b}{y}\right) + {b}^{2} \cdot \left(-\color{blue}{\frac{x}{a \cdot y} \cdot \left(-1 + 0.5\right)}\right) \]

      10. metadata-eval 55.9%

          \[\leadsto \left(\frac{x}{a \cdot y} - \frac{x}{a} \cdot \frac{b}{y}\right) + {b}^{2} \cdot \left(-\frac{x}{a \cdot y} \cdot \color{blue}{-0.5}\right) \]

      11. *-commutative 55.9%

          \[\leadsto \left(\frac{x}{a \cdot y} - \frac{x}{a} \cdot \frac{b}{y}\right) + {b}^{2} \cdot \left(-\color{blue}{-0.5 \cdot \frac{x}{a \cdot y}}\right) \]

      12. distribute-lft-neg-in 55.9%

          \[\leadsto \left(\frac{x}{a \cdot y} - \frac{x}{a} \cdot \frac{b}{y}\right) + {b}^{2} \cdot \color{blue}{\left(\left(--0.5\right) \cdot \frac{x}{a \cdot y}\right)} \]

      13. metadata-eval 55.9%

          \[\leadsto \left(\frac{x}{a \cdot y} - \frac{x}{a} \cdot \frac{b}{y}\right) + {b}^{2} \cdot \left(\color{blue}{0.5} \cdot \frac{x}{a \cdot y}\right) \]

   10. Simplified 54.5%

       \[\leadsto \color{blue}{\left(\frac{x}{a \cdot y} - \frac{x}{a} \cdot \frac{b}{y}\right) + b \cdot \left(b \cdot \left(\frac{0.5}{a} \cdot \frac{x}{y}\right)\right)} \]

   11. Taylor expanded in b around inf 62.8%

       \[\leadsto \color{blue}{0.5 \cdot \frac{{b}^{2} \cdot x}{a \cdot y}} \]
   12. Step-by-step derivation

       1. associate-*r/ 62.8%

          \[\leadsto \color{blue}{\frac{0.5 \cdot \left({b}^{2} \cdot x\right)}{a \cdot y}} \]

       2. *-commutative 62.8%

          \[\leadsto \frac{0.5 \cdot \color{blue}{\left(x \cdot {b}^{2}\right)}}{a \cdot y} \]

       3. unpow2 62.8%

          \[\leadsto \frac{0.5 \cdot \left(x \cdot \color{blue}{\left(b \cdot b\right)}\right)}{a \cdot y} \]

   13. Simplified 62.8%

       \[\leadsto \color{blue}{\frac{0.5 \cdot \left(x \cdot \left(b \cdot b\right)\right)}{a \cdot y}} \]

   if -750 < b

   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 81.0%

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

      1. +-commutative 81.0%

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

      2. mul-1-neg 81.0%

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

      3. unsub-neg 81.0%

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

   4. Simplified 81.0%

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

   5. Taylor expanded in y around 0 58.2%

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

      1. exp-neg 58.2%

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

      2. associate-*r/ 58.2%

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

      3. *-rgt-identity 58.2%

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

      4. +-commutative 58.2%

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

      5. exp-sum 58.2%

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

      6. rem-exp-log 59.0%

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

   7. Simplified 59.0%

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

   8. Taylor expanded in b around 0 45.7%

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

4. Final simplification 50.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -750:\\ \;\;\;\;\frac{0.5 \cdot \left(x \cdot \left(b \cdot b\right)\right)}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \]

Alternative 11: 40.9% accurate, 28.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1250:\\ \;\;\;\;\frac{\frac{b}{y}}{a} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1250.0) (* (/ (/ b y) a) (- x)) (/ (/ x (+ a (* a b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1250.0) {
		tmp = ((b / y) / a) * -x;
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1250.0d0)) then
        tmp = ((b / y) / a) * -x
    else
        tmp = (x / (a + (a * b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1250.0) {
		tmp = ((b / y) / a) * -x;
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1250.0:
		tmp = ((b / y) / a) * -x
	else:
		tmp = (x / (a + (a * b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1250.0)
		tmp = Float64(Float64(Float64(b / y) / a) * Float64(-x));
	else
		tmp = Float64(Float64(x / Float64(a + Float64(a * b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1250.0)
		tmp = ((b / y) / a) * -x;
	else
		tmp = (x / (a + (a * b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1250.0], N[(N[(N[(b / y), $MachinePrecision] / a), $MachinePrecision] * (-x)), $MachinePrecision], N[(N[(x / N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1250

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 88.4%

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

      1. +-commutative 88.4%

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

      2. mul-1-neg 88.4%

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

      3. unsub-neg 88.4%

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

   4. Simplified 88.4%

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

   5. Taylor expanded in y around 0 87.0%

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

      1. exp-neg 87.0%

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

      2. associate-*r/ 87.0%

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

      3. *-rgt-identity 87.0%

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

      4. +-commutative 87.0%

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

      5. exp-sum 87.0%

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

      6. rem-exp-log 87.0%

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

      7. associate-/r* 81.1%

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

      8. associate-/r* 81.1%

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

      9. *-commutative 81.1%

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

      10. associate-/r* 87.0%

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

      11. associate-*r* 79.6%

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

      12. associate-/r* 75.2%

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

   7. Simplified 75.2%

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

   8. Taylor expanded in b around 0 39.0%

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

      1. +-commutative 39.0%

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

      2. mul-1-neg 39.0%

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

      3. unsub-neg 39.0%

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

      4. *-commutative 39.0%

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

      5. times-frac 43.2%

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

   10. Simplified 43.2%

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

   11. Taylor expanded in b around inf 39.0%

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

       1. associate-/l* 40.6%

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

       2. associate-/r/ 42.0%

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

       3. associate-*l* 42.0%

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

       4. mul-1-neg 42.0%

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

       5. *-commutative 42.0%

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

       6. distribute-frac-neg 42.0%

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

       7. *-commutative 42.0%

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

       8. associate-/r* 46.1%

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

   13. Simplified 46.1%

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

   if -1250 < b

   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 81.0%

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

      1. +-commutative 81.0%

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

      2. mul-1-neg 81.0%

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

      3. unsub-neg 81.0%

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

   4. Simplified 81.0%

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

   5. Taylor expanded in y around 0 58.2%

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

      1. exp-neg 58.2%

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

      2. associate-*r/ 58.2%

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

      3. *-rgt-identity 58.2%

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

      4. +-commutative 58.2%

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

      5. exp-sum 58.2%

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

      6. rem-exp-log 59.0%

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

   7. Simplified 59.0%

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

   8. Taylor expanded in b around 0 45.7%

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

4. Final simplification 45.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1250:\\ \;\;\;\;\frac{\frac{b}{y}}{a} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \]

Alternative 12: 35.9% accurate, 31.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -64000:\\ \;\;\;\;\frac{\frac{b}{y}}{a} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -64000.0) (* (/ (/ b y) a) (- x)) (/ (/ x a) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -64000.0) {
		tmp = ((b / y) / a) * -x;
	} else {
		tmp = (x / 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 <= (-64000.0d0)) then
        tmp = ((b / y) / a) * -x
    else
        tmp = (x / 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 <= -64000.0) {
		tmp = ((b / y) / a) * -x;
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -64000.0:
		tmp = ((b / y) / a) * -x
	else:
		tmp = (x / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -64000.0)
		tmp = Float64(Float64(Float64(b / y) / a) * Float64(-x));
	else
		tmp = Float64(Float64(x / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -64000.0)
		tmp = ((b / y) / a) * -x;
	else
		tmp = (x / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -64000.0], N[(N[(N[(b / y), $MachinePrecision] / a), $MachinePrecision] * (-x)), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -64000

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 88.2%

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

      1. +-commutative 88.2%

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

      2. mul-1-neg 88.2%

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

      3. unsub-neg 88.2%

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

   4. Simplified 88.2%

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

   5. Taylor expanded in y around 0 86.8%

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

      1. exp-neg 86.8%

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

      2. associate-*r/ 86.8%

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

      3. *-rgt-identity 86.8%

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

      4. +-commutative 86.8%

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

      5. exp-sum 86.8%

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

      6. rem-exp-log 86.8%

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

      7. associate-/r* 80.8%

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

      8. associate-/r* 80.8%

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

      9. *-commutative 80.8%

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

      10. associate-/r* 86.8%

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

      11. associate-*r* 80.8%

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

      12. associate-/r* 76.3%

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

   7. Simplified 76.3%

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

   8. Taylor expanded in b around 0 39.6%

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

      1. +-commutative 39.6%

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

      2. mul-1-neg 39.6%

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

      3. unsub-neg 39.6%

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

      4. *-commutative 39.6%

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

      5. times-frac 43.8%

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

   10. Simplified 43.8%

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

   11. Taylor expanded in b around inf 39.6%

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

       1. associate-/l* 41.2%

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

       2. associate-/r/ 42.6%

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

       3. associate-*l* 42.6%

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

       4. mul-1-neg 42.6%

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

       5. *-commutative 42.6%

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

       6. distribute-frac-neg 42.6%

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

       7. *-commutative 42.6%

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

       8. associate-/r* 46.7%

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

   13. Simplified 46.7%

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

   if -64000 < b

   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 81.1%

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

      1. +-commutative 81.1%

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

      2. mul-1-neg 81.1%

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

      3. unsub-neg 81.1%

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

   4. Simplified 81.1%

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

   5. Taylor expanded in b around 0 66.1%

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

      1. *-commutative 66.1%

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

      2. div-exp 66.1%

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

      3. *-commutative 66.1%

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

      4. exp-to-pow 66.2%

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

      5. rem-exp-log 67.0%

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

   7. Simplified 67.0%

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

   8. Taylor expanded in y around 0 41.0%

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

4. Final simplification 42.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -64000:\\ \;\;\;\;\frac{\frac{b}{y}}{a} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \]

Alternative 13: 31.3% accurate, 44.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.2 \cdot 10^{-40}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -6.2e-40) (/ x (* y a)) (/ (/ x a) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.2e-40) {
		tmp = x / (y * a);
	} else {
		tmp = (x / 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 <= (-6.2d-40)) then
        tmp = x / (y * a)
    else
        tmp = (x / 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 <= -6.2e-40) {
		tmp = x / (y * a);
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -6.2e-40:
		tmp = x / (y * a)
	else:
		tmp = (x / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -6.2e-40)
		tmp = Float64(x / Float64(y * a));
	else
		tmp = Float64(Float64(x / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -6.2e-40)
		tmp = x / (y * a);
	else
		tmp = (x / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -6.2e-40], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -6.20000000000000021e-40

   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 t around 0 86.3%

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

      1. +-commutative 86.3%

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

      2. mul-1-neg 86.3%

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

      3. unsub-neg 86.3%

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

   4. Simplified 86.3%

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

   5. Taylor expanded in y around 0 79.0%

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

      1. exp-neg 79.0%

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

      2. associate-*r/ 79.0%

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

      3. *-rgt-identity 79.0%

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

      4. +-commutative 79.0%

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

      5. exp-sum 79.0%

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

      6. rem-exp-log 79.2%

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

      7. associate-/r* 75.3%

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

      8. associate-/r* 75.3%

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

      9. *-commutative 75.3%

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

      10. associate-/r* 79.2%

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

      11. associate-*r* 74.1%

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

      12. associate-/r* 70.3%

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

   7. Simplified 70.3%

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

   8. Taylor expanded in b around 0 33.6%

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

   if -6.20000000000000021e-40 < b

   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. Taylor expanded in t around 0 81.5%

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

      1. +-commutative 81.5%

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

      2. mul-1-neg 81.5%

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

      3. unsub-neg 81.5%

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

   4. Simplified 81.5%

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

   5. Taylor expanded in b around 0 65.4%

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

      1. *-commutative 65.4%

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

      2. div-exp 65.4%

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

      3. *-commutative 65.4%

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

      4. exp-to-pow 65.4%

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

      5. rem-exp-log 66.3%

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

   7. Simplified 66.3%

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

   8. Taylor expanded in y around 0 41.1%

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

4. Final simplification 38.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.2 \cdot 10^{-40}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \]

Alternative 14: 30.9% 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. Taylor expanded in t around 0 83.0%

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

   1. +-commutative 83.0%

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

   2. mul-1-neg 83.0%

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

   3. unsub-neg 83.0%

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

4. Simplified 83.0%

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

5. Taylor expanded in y around 0 65.8%

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

   1. exp-neg 65.8%

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

   2. associate-*r/ 65.8%

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

   3. *-rgt-identity 65.8%

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

   4. +-commutative 65.8%

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

   5. exp-sum 65.8%

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

   6. rem-exp-log 66.4%

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

   7. associate-/r* 62.1%

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

   8. associate-/r* 62.1%

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

   9. *-commutative 62.1%

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

   10. associate-/r* 65.0%

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

   11. associate-*r* 61.8%

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

   12. associate-/r* 59.0%

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

7. Simplified 59.0%

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

8. Taylor expanded in b around 0 35.8%

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

9. Final simplification 35.8%

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

Developer target: 72.6% 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 2023275 
(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))