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

Percentage Accurate: 98.5% → 98.5%

Time: 16.3s

Alternatives: 18

Speedup: 1.0×

• 47.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.5% accurate, 1.0× speedup

Math

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

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 97.6%

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

3. Final simplification 97.6%

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

Alternative 2: 89.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t + -1 \leq -1 \cdot 10^{+121} \lor \neg \left(t + -1 \leq 1.55 \cdot 10^{+33}\right):\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (+ t -1.0) -1e+121) (not (<= (+ t -1.0) 1.55e+33)))
   (* x (/ (pow a t) y))
   (/ (* x (exp (- (- (* y (log z)) (log a)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t + -1.0) <= -1e+121) || !((t + -1.0) <= 1.55e+33)) {
		tmp = x * (pow(a, t) / y);
	} else {
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (((t + (-1.0d0)) <= (-1d+121)) .or. (.not. ((t + (-1.0d0)) <= 1.55d+33))) then
        tmp = x * ((a ** t) / y)
    else
        tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t + -1.0) <= -1e+121) || !((t + -1.0) <= 1.55e+33)) {
		tmp = x * (Math.pow(a, t) / y);
	} else {
		tmp = (x * Math.exp((((y * Math.log(z)) - Math.log(a)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((t + -1.0) <= -1e+121) or not ((t + -1.0) <= 1.55e+33):
		tmp = x * (math.pow(a, t) / y)
	else:
		tmp = (x * math.exp((((y * math.log(z)) - math.log(a)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(t + -1.0) <= -1e+121) || !(Float64(t + -1.0) <= 1.55e+33))
		tmp = Float64(x * Float64((a ^ t) / y));
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) - log(a)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((t + -1.0) <= -1e+121) || ~(((t + -1.0) <= 1.55e+33)))
		tmp = x * ((a ^ t) / y);
	else
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(t + -1.0), $MachinePrecision], -1e+121], N[Not[LessEqual[N[(t + -1.0), $MachinePrecision], 1.55e+33]], $MachinePrecision]], N[(x * N[(N[Power[a, t], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] - N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 t #s(literal 1 binary64)) < -1.00000000000000004e121 or 1.55e33 < (-.f64 t #s(literal 1 binary64))

   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. Add Preprocessing

   3. Taylor expanded in b around 0 95.4%

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

      1. exp-sum 72.7%

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

      2. exp-to-pow 72.7%

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

      3. sub-neg 72.7%

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

      4. metadata-eval 72.7%

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

      5. *-commutative 72.7%

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

      6. exp-to-pow 72.7%

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

   5. Simplified 72.7%

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

   6. Taylor expanded in y around 0 87.9%

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

      1. associate-/l* 87.9%

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

      2. exp-to-pow 87.9%

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

      3. sub-neg 87.9%

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

      4. metadata-eval 87.9%

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

      5. +-commutative 87.9%

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

   8. Simplified 87.9%

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

   9. Taylor expanded in t around inf 87.9%

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

   if -1.00000000000000004e121 < (-.f64 t #s(literal 1 binary64)) < 1.55e33

   1. Initial program 95.9%

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

   3. Taylor expanded in t around 0 91.9%

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

      1. +-commutative 91.9%

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

      2. mul-1-neg 91.9%

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

      3. unsub-neg 91.9%

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

   5. Simplified 91.9%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t + -1 \leq -1 \cdot 10^{+121} \lor \neg \left(t + -1 \leq 1.55 \cdot 10^{+33}\right):\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 81.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{if}\;y \leq -3.9 \cdot 10^{+153}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.62 \cdot 10^{-304}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+123}:\\ \;\;\;\;e^{\left(t + -1\right) \cdot \log a - b} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ (* x (pow z y)) a) y)))
   (if (<= y -3.9e+153)
     t_1
     (if (<= y 1.62e-304)
       (/ (* x (/ (pow a (+ t -1.0)) (exp b))) y)
       (if (<= y 1.15e+123)
         (* (exp (- (* (+ t -1.0) (log a)) b)) (/ x y))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * pow(z, y)) / a) / y;
	double tmp;
	if (y <= -3.9e+153) {
		tmp = t_1;
	} else if (y <= 1.62e-304) {
		tmp = (x * (pow(a, (t + -1.0)) / exp(b))) / y;
	} else if (y <= 1.15e+123) {
		tmp = exp((((t + -1.0) * log(a)) - b)) * (x / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((x * (z ** y)) / a) / y
    if (y <= (-3.9d+153)) then
        tmp = t_1
    else if (y <= 1.62d-304) then
        tmp = (x * ((a ** (t + (-1.0d0))) / exp(b))) / y
    else if (y <= 1.15d+123) then
        tmp = exp((((t + (-1.0d0)) * log(a)) - b)) * (x / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * Math.pow(z, y)) / a) / y;
	double tmp;
	if (y <= -3.9e+153) {
		tmp = t_1;
	} else if (y <= 1.62e-304) {
		tmp = (x * (Math.pow(a, (t + -1.0)) / Math.exp(b))) / y;
	} else if (y <= 1.15e+123) {
		tmp = Math.exp((((t + -1.0) * Math.log(a)) - b)) * (x / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x * math.pow(z, y)) / a) / y
	tmp = 0
	if y <= -3.9e+153:
		tmp = t_1
	elif y <= 1.62e-304:
		tmp = (x * (math.pow(a, (t + -1.0)) / math.exp(b))) / y
	elif y <= 1.15e+123:
		tmp = math.exp((((t + -1.0) * math.log(a)) - b)) * (x / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x * (z ^ y)) / a) / y)
	tmp = 0.0
	if (y <= -3.9e+153)
		tmp = t_1;
	elseif (y <= 1.62e-304)
		tmp = Float64(Float64(x * Float64((a ^ Float64(t + -1.0)) / exp(b))) / y);
	elseif (y <= 1.15e+123)
		tmp = Float64(exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b)) * Float64(x / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x * (z ^ y)) / a) / y;
	tmp = 0.0;
	if (y <= -3.9e+153)
		tmp = t_1;
	elseif (y <= 1.62e-304)
		tmp = (x * ((a ^ (t + -1.0)) / exp(b))) / y;
	elseif (y <= 1.15e+123)
		tmp = exp((((t + -1.0) * log(a)) - b)) * (x / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -3.9e+153], t$95$1, If[LessEqual[y, 1.62e-304], N[(N[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 1.15e+123], N[(N[Exp[N[(N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.89999999999999983e153 or 1.14999999999999995e123 < 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. Add Preprocessing

   3. Taylor expanded in b around 0 98.6%

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

      1. exp-sum 66.7%

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

      2. exp-to-pow 66.7%

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

      3. sub-neg 66.7%

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

      4. metadata-eval 66.7%

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

      5. *-commutative 66.7%

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

      6. exp-to-pow 66.7%

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

   5. Simplified 66.7%

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

   6. Taylor expanded in t around 0 90.4%

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

   if -3.89999999999999983e153 < y < 1.61999999999999994e-304

   1. Initial program 98.1%

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

   3. Taylor expanded in y around 0 92.2%

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

      1. div-exp 84.8%

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

      2. exp-to-pow 85.5%

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

      3. sub-neg 85.5%

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

      4. metadata-eval 85.5%

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

   5. Simplified 85.5%

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

   if 1.61999999999999994e-304 < y < 1.14999999999999995e123

   1. Initial program 95.0%

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

      1. *-commutative 95.0%

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

      2. associate-/l* 92.1%

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

      3. associate--l+ 92.1%

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

      4. fma-define 92.1%

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

      5. sub-neg 92.1%

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

      6. metadata-eval 92.1%

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

   3. Simplified 92.1%

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

   5. Taylor expanded in y around 0 88.6%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+153}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{elif}\;y \leq 1.62 \cdot 10^{-304}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+123}:\\ \;\;\;\;e^{\left(t + -1\right) \cdot \log a - b} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t + -1 \leq -1 \cdot 10^{+121} \lor \neg \left(t + -1 \leq 1.55 \cdot 10^{+33}\right):\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (+ t -1.0) -1e+121) (not (<= (+ t -1.0) 1.55e+33)))
   (* x (/ (pow a t) y))
   (* x (/ (pow z y) (* a (* y (exp b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t + -1.0) <= -1e+121) || !((t + -1.0) <= 1.55e+33)) {
		tmp = x * (pow(a, t) / y);
	} else {
		tmp = x * (pow(z, y) / (a * (y * exp(b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (((t + (-1.0d0)) <= (-1d+121)) .or. (.not. ((t + (-1.0d0)) <= 1.55d+33))) then
        tmp = x * ((a ** t) / y)
    else
        tmp = x * ((z ** y) / (a * (y * exp(b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t + -1.0) <= -1e+121) || !((t + -1.0) <= 1.55e+33)) {
		tmp = x * (Math.pow(a, t) / y);
	} else {
		tmp = x * (Math.pow(z, y) / (a * (y * Math.exp(b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((t + -1.0) <= -1e+121) or not ((t + -1.0) <= 1.55e+33):
		tmp = x * (math.pow(a, t) / y)
	else:
		tmp = x * (math.pow(z, y) / (a * (y * math.exp(b))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(t + -1.0) <= -1e+121) || !(Float64(t + -1.0) <= 1.55e+33))
		tmp = Float64(x * Float64((a ^ t) / y));
	else
		tmp = Float64(x * Float64((z ^ y) / Float64(a * Float64(y * exp(b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((t + -1.0) <= -1e+121) || ~(((t + -1.0) <= 1.55e+33)))
		tmp = x * ((a ^ t) / y);
	else
		tmp = x * ((z ^ y) / (a * (y * exp(b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(t + -1.0), $MachinePrecision], -1e+121], N[Not[LessEqual[N[(t + -1.0), $MachinePrecision], 1.55e+33]], $MachinePrecision]], N[(x * N[(N[Power[a, t], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[Power[z, y], $MachinePrecision] / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 t #s(literal 1 binary64)) < -1.00000000000000004e121 or 1.55e33 < (-.f64 t #s(literal 1 binary64))

   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. Add Preprocessing

   3. Taylor expanded in b around 0 95.4%

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

      1. exp-sum 72.7%

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

      2. exp-to-pow 72.7%

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

      3. sub-neg 72.7%

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

      4. metadata-eval 72.7%

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

      5. *-commutative 72.7%

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

      6. exp-to-pow 72.7%

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

   5. Simplified 72.7%

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

   6. Taylor expanded in y around 0 87.9%

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

      1. associate-/l* 87.9%

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

      2. exp-to-pow 87.9%

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

      3. sub-neg 87.9%

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

      4. metadata-eval 87.9%

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

      5. +-commutative 87.9%

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

   8. Simplified 87.9%

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

   9. Taylor expanded in t around inf 87.9%

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

   if -1.00000000000000004e121 < (-.f64 t #s(literal 1 binary64)) < 1.55e33

   1. Initial program 95.9%

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

      1. associate-/l* 97.4%

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

      2. associate--l+ 97.4%

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

      3. exp-sum 83.4%

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

      4. associate-/l* 81.4%

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

      5. *-commutative 81.4%

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

      6. exp-to-pow 81.4%

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

      7. exp-diff 78.1%

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

      8. *-commutative 78.1%

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

      9. exp-to-pow 79.1%

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

      10. sub-neg 79.1%

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

      11. metadata-eval 79.1%

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

   3. Simplified 79.1%

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

   5. Taylor expanded in t around 0 81.1%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t + -1 \leq -1 \cdot 10^{+121} \lor \neg \left(t + -1 \leq 1.55 \cdot 10^{+33}\right):\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 80.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+152} \lor \neg \left(y \leq 2.8 \cdot 10^{+122}\right):\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4.5e+152) (not (<= y 2.8e+122)))
   (/ (/ (* 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 <= -4.5e+152) || !(y <= 2.8e+122)) {
		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 <= (-4.5d+152)) .or. (.not. (y <= 2.8d+122))) 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 <= -4.5e+152) || !(y <= 2.8e+122)) {
		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 <= -4.5e+152) or not (y <= 2.8e+122):
		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 <= -4.5e+152) || !(y <= 2.8e+122))
		tmp = Float64(Float64(Float64(x * (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 <= -4.5e+152) || ~((y <= 2.8e+122)))
		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, -4.5e+152], N[Not[LessEqual[y, 2.8e+122]], $MachinePrecision]], N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $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 < -4.5000000000000001e152 or 2.8e122 < 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. Add Preprocessing

   3. Taylor expanded in b around 0 98.6%

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

      1. exp-sum 66.7%

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

      2. exp-to-pow 66.7%

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

      3. sub-neg 66.7%

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

      4. metadata-eval 66.7%

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

      5. *-commutative 66.7%

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

      6. exp-to-pow 66.7%

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

   5. Simplified 66.7%

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

   6. Taylor expanded in t around 0 90.4%

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

   if -4.5000000000000001e152 < y < 2.8e122

   1. Initial program 96.6%

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

   3. Taylor expanded in y around 0 91.9%

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

      1. div-exp 81.6%

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

      2. exp-to-pow 82.3%

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

      3. sub-neg 82.3%

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

      4. metadata-eval 82.3%

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

   5. Simplified 82.3%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+152} \lor \neg \left(y \leq 2.8 \cdot 10^{+122}\right):\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ t_2 := x \cdot \frac{{a}^{t}}{y}\\ \mathbf{if}\;t \leq -6.2 \cdot 10^{+53}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-307}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ (* x (pow z y)) a) y)) (t_2 (* x (/ (pow a t) y))))
   (if (<= t -6.2e+53)
     t_2
     (if (<= t -2.2e-30)
       t_1
       (if (<= t -7e-307)
         (/ x (* a (* y (exp b))))
         (if (<= t 1.55e+33) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * pow(z, y)) / a) / y;
	double t_2 = x * (pow(a, t) / y);
	double tmp;
	if (t <= -6.2e+53) {
		tmp = t_2;
	} else if (t <= -2.2e-30) {
		tmp = t_1;
	} else if (t <= -7e-307) {
		tmp = x / (a * (y * exp(b)));
	} else if (t <= 1.55e+33) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * (z ** y)) / a) / y
    t_2 = x * ((a ** t) / y)
    if (t <= (-6.2d+53)) then
        tmp = t_2
    else if (t <= (-2.2d-30)) then
        tmp = t_1
    else if (t <= (-7d-307)) then
        tmp = x / (a * (y * exp(b)))
    else if (t <= 1.55d+33) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * Math.pow(z, y)) / a) / y;
	double t_2 = x * (Math.pow(a, t) / y);
	double tmp;
	if (t <= -6.2e+53) {
		tmp = t_2;
	} else if (t <= -2.2e-30) {
		tmp = t_1;
	} else if (t <= -7e-307) {
		tmp = x / (a * (y * Math.exp(b)));
	} else if (t <= 1.55e+33) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x * math.pow(z, y)) / a) / y
	t_2 = x * (math.pow(a, t) / y)
	tmp = 0
	if t <= -6.2e+53:
		tmp = t_2
	elif t <= -2.2e-30:
		tmp = t_1
	elif t <= -7e-307:
		tmp = x / (a * (y * math.exp(b)))
	elif t <= 1.55e+33:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x * (z ^ y)) / a) / y)
	t_2 = Float64(x * Float64((a ^ t) / y))
	tmp = 0.0
	if (t <= -6.2e+53)
		tmp = t_2;
	elseif (t <= -2.2e-30)
		tmp = t_1;
	elseif (t <= -7e-307)
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	elseif (t <= 1.55e+33)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x * (z ^ y)) / a) / y;
	t_2 = x * ((a ^ t) / y);
	tmp = 0.0;
	if (t <= -6.2e+53)
		tmp = t_2;
	elseif (t <= -2.2e-30)
		tmp = t_1;
	elseif (t <= -7e-307)
		tmp = x / (a * (y * exp(b)));
	elseif (t <= 1.55e+33)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[Power[a, t], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.2e+53], t$95$2, If[LessEqual[t, -2.2e-30], t$95$1, If[LessEqual[t, -7e-307], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.55e+33], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.20000000000000038e53 or 1.55e33 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 95.1%

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

      1. exp-sum 70.9%

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

      2. exp-to-pow 70.9%

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

      3. sub-neg 70.9%

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

      4. metadata-eval 70.9%

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

      5. *-commutative 70.9%

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

      6. exp-to-pow 70.9%

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

   5. Simplified 70.9%

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

   6. Taylor expanded in y around 0 85.2%

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

      1. associate-/l* 85.2%

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

      2. exp-to-pow 85.2%

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

      3. sub-neg 85.2%

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

      4. metadata-eval 85.2%

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

      5. +-commutative 85.2%

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

   8. Simplified 85.2%

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

   9. Taylor expanded in t around inf 85.2%

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

   if -6.20000000000000038e53 < t < -2.19999999999999983e-30 or -7.0000000000000004e-307 < t < 1.55e33

   1. Initial program 95.8%

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

   3. Taylor expanded in b around 0 78.6%

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

      1. exp-sum 73.2%

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

      2. exp-to-pow 74.2%

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

      3. sub-neg 74.2%

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

      4. metadata-eval 74.2%

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

      5. *-commutative 74.2%

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

      6. exp-to-pow 74.2%

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

   5. Simplified 74.2%

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

   6. Taylor expanded in t around 0 76.4%

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

   if -2.19999999999999983e-30 < t < -7.0000000000000004e-307

   1. Initial program 94.7%

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

      1. associate-/l* 98.4%

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

      2. associate--l+ 98.4%

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

      3. exp-sum 85.1%

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

      4. associate-/l* 85.1%

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

      5. *-commutative 85.1%

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

      6. exp-to-pow 85.1%

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

      7. exp-diff 85.1%

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

      8. *-commutative 85.1%

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

      9. exp-to-pow 86.5%

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

      10. sub-neg 86.5%

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

      11. metadata-eval 86.5%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in t around 0 86.6%

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

   6. Taylor expanded in y around 0 84.2%

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

Alternative 7: 74.1% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{+118}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y}\\ \mathbf{elif}\;t \leq 180000:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{a}^{t}}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.85e+118)
   (* x (/ (pow a t) y))
   (if (<= t 180000.0) (/ x (* a (* y (exp b)))) (* x (/ (/ (pow a t) a) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.85e+118) {
		tmp = x * (pow(a, t) / y);
	} else if (t <= 180000.0) {
		tmp = x / (a * (y * exp(b)));
	} else {
		tmp = x * ((pow(a, t) / a) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.85d+118)) then
        tmp = x * ((a ** t) / y)
    else if (t <= 180000.0d0) then
        tmp = x / (a * (y * exp(b)))
    else
        tmp = x * (((a ** t) / a) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.85e+118) {
		tmp = x * (Math.pow(a, t) / y);
	} else if (t <= 180000.0) {
		tmp = x / (a * (y * Math.exp(b)));
	} else {
		tmp = x * ((Math.pow(a, t) / a) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.85e+118:
		tmp = x * (math.pow(a, t) / y)
	elif t <= 180000.0:
		tmp = x / (a * (y * math.exp(b)))
	else:
		tmp = x * ((math.pow(a, t) / a) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.85e+118)
		tmp = Float64(x * Float64((a ^ t) / y));
	elseif (t <= 180000.0)
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	else
		tmp = Float64(x * Float64(Float64((a ^ t) / a) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.85e+118)
		tmp = x * ((a ^ t) / y);
	elseif (t <= 180000.0)
		tmp = x / (a * (y * exp(b)));
	else
		tmp = x * (((a ^ t) / a) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.85e+118], N[(x * N[(N[Power[a, t], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 180000.0], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.84999999999999993e118

   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. Add Preprocessing

   3. Taylor expanded in b around 0 91.4%

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

      1. exp-sum 76.2%

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

      2. exp-to-pow 76.2%

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

      3. sub-neg 76.2%

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

      4. metadata-eval 76.2%

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

      5. *-commutative 76.2%

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

      6. exp-to-pow 76.2%

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

   5. Simplified 76.2%

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

   6. Taylor expanded in y around 0 85.0%

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

      1. associate-/l* 85.0%

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

      2. exp-to-pow 85.0%

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

      3. sub-neg 85.0%

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

      4. metadata-eval 85.0%

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

      5. +-commutative 85.0%

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

   8. Simplified 85.0%

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

   9. Taylor expanded in t around inf 85.0%

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

   if -1.84999999999999993e118 < t < 1.8e5

   1. Initial program 95.7%

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

      1. associate-/l* 97.3%

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

      2. associate--l+ 97.3%

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

      3. exp-sum 84.2%

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

      4. associate-/l* 82.2%

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

      5. *-commutative 82.2%

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

      6. exp-to-pow 82.2%

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

      7. exp-diff 79.4%

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

      8. *-commutative 79.4%

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

      9. exp-to-pow 80.5%

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

      10. sub-neg 80.5%

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

      11. metadata-eval 80.5%

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

   3. Simplified 80.5%

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

   5. Taylor expanded in t around 0 82.4%

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

   6. Taylor expanded in y around 0 71.3%

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

   if 1.8e5 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 97.0%

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

      1. exp-sum 67.7%

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

      2. exp-to-pow 67.7%

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

      3. sub-neg 67.7%

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

      4. metadata-eval 67.7%

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

      5. *-commutative 67.7%

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

      6. exp-to-pow 67.7%

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

   5. Simplified 67.7%

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

   6. Taylor expanded in y around 0 86.4%

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

      1. associate-/l* 86.4%

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

      2. exp-to-pow 86.4%

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

      3. sub-neg 86.4%

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

      4. metadata-eval 86.4%

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

      5. +-commutative 86.4%

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

   8. Simplified 86.4%

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

      1. +-commutative 86.4%

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

      2. unpow-prod-up 86.4%

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

      3. inv-pow 86.4%

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

   10. Applied egg-rr 86.4%

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

       1. associate-*r/ 86.4%

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

       2. *-rgt-identity 86.4%

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

   12. Simplified 86.4%

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

Alternative 8: 74.1% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{+118} \lor \neg \left(t \leq 1800\right):\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.85e+118) (not (<= t 1800.0)))
   (* x (/ (pow a t) y))
   (/ x (* a (* y (exp b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.85e+118) || !(t <= 1800.0)) {
		tmp = x * (pow(a, t) / y);
	} else {
		tmp = x / (a * (y * exp(b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.85d+118)) .or. (.not. (t <= 1800.0d0))) then
        tmp = x * ((a ** t) / y)
    else
        tmp = x / (a * (y * exp(b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.85e+118) || !(t <= 1800.0)) {
		tmp = x * (Math.pow(a, t) / y);
	} else {
		tmp = x / (a * (y * Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.85e+118) or not (t <= 1800.0):
		tmp = x * (math.pow(a, t) / y)
	else:
		tmp = x / (a * (y * math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.85e+118) || !(t <= 1800.0))
		tmp = Float64(x * Float64((a ^ t) / y));
	else
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.85e+118) || ~((t <= 1800.0)))
		tmp = x * ((a ^ t) / y);
	else
		tmp = x / (a * (y * exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.85e+118], N[Not[LessEqual[t, 1800.0]], $MachinePrecision]], N[(x * N[(N[Power[a, t], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.84999999999999993e118 or 1800 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 94.7%

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

      1. exp-sum 71.3%

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

      2. exp-to-pow 71.3%

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

      3. sub-neg 71.3%

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

      4. metadata-eval 71.3%

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

      5. *-commutative 71.3%

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

      6. exp-to-pow 71.3%

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

   5. Simplified 71.3%

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

   6. Taylor expanded in y around 0 85.8%

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

      1. associate-/l* 85.8%

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

      2. exp-to-pow 85.8%

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

      3. sub-neg 85.8%

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

      4. metadata-eval 85.8%

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

      5. +-commutative 85.8%

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

   8. Simplified 85.8%

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

   9. Taylor expanded in t around inf 85.8%

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

   if -1.84999999999999993e118 < t < 1800

   1. Initial program 95.7%

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

      1. associate-/l* 97.3%

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

      2. associate--l+ 97.3%

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

      3. exp-sum 84.2%

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

      4. associate-/l* 82.2%

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

      5. *-commutative 82.2%

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

      6. exp-to-pow 82.2%

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

      7. exp-diff 79.4%

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

      8. *-commutative 79.4%

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

      9. exp-to-pow 80.5%

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

      10. sub-neg 80.5%

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

      11. metadata-eval 80.5%

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

   3. Simplified 80.5%

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

   5. Taylor expanded in t around 0 82.4%

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

   6. Taylor expanded in y around 0 71.3%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{+118} \lor \neg \left(t \leq 1800\right):\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 65.7% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{+17} \lor \neg \left(t \leq 1.55 \cdot 10^{+33}\right):\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.02e+17) (not (<= t 1.55e+33)))
   (* x (/ (pow a t) y))
   (/ x (* y (exp b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.02e+17) || !(t <= 1.55e+33)) {
		tmp = x * (pow(a, t) / y);
	} else {
		tmp = x / (y * exp(b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.02d+17)) .or. (.not. (t <= 1.55d+33))) then
        tmp = x * ((a ** t) / y)
    else
        tmp = x / (y * exp(b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.02e+17) || !(t <= 1.55e+33)) {
		tmp = x * (Math.pow(a, t) / y);
	} else {
		tmp = x / (y * Math.exp(b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.02e+17) or not (t <= 1.55e+33):
		tmp = x * (math.pow(a, t) / y)
	else:
		tmp = x / (y * math.exp(b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.02e+17) || !(t <= 1.55e+33))
		tmp = Float64(x * Float64((a ^ t) / y));
	else
		tmp = Float64(x / Float64(y * exp(b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.02e+17) || ~((t <= 1.55e+33)))
		tmp = x * ((a ^ t) / y);
	else
		tmp = x / (y * exp(b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.02e+17], N[Not[LessEqual[t, 1.55e+33]], $MachinePrecision]], N[(x * N[(N[Power[a, t], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.02e17 or 1.55e33 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 95.3%

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

      1. exp-sum 71.3%

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

      2. exp-to-pow 71.3%

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

      3. sub-neg 71.3%

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

      4. metadata-eval 71.3%

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

      5. *-commutative 71.3%

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

      6. exp-to-pow 71.3%

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

   5. Simplified 71.3%

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

   6. Taylor expanded in y around 0 85.0%

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

      1. associate-/l* 85.0%

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

      2. exp-to-pow 85.0%

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

      3. sub-neg 85.0%

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

      4. metadata-eval 85.0%

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

      5. +-commutative 85.0%

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

   8. Simplified 85.0%

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

   9. Taylor expanded in t around inf 85.0%

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

   if -1.02e17 < t < 1.55e33

   1. Initial program 95.3%

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

      1. *-commutative 95.3%

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

      2. associate-/l* 87.3%

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

      3. associate--l+ 87.3%

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

      4. fma-define 87.3%

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

      5. sub-neg 87.3%

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

      6. metadata-eval 87.3%

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

   3. Simplified 87.3%

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

   5. Taylor expanded in b around inf 44.1%

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

      1. neg-mul-1 44.1%

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

   7. Simplified 44.1%

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

      1. exp-neg 44.1%

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

      2. frac-times 49.5%

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

      3. *-un-lft-identity 49.5%

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

      4. *-commutative 49.5%

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

   9. Applied egg-rr 49.5%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{+17} \lor \neg \left(t \leq 1.55 \cdot 10^{+33}\right):\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.1% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -180 \lor \neg \left(b \leq 7\right):\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -180.0) (not (<= b 7.0)))
   (/ x (* y (exp b)))
   (* (/ x y) (/ 1.0 a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -180.0) || !(b <= 7.0)) {
		tmp = x / (y * exp(b));
	} else {
		tmp = (x / y) * (1.0 / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-180.0d0)) .or. (.not. (b <= 7.0d0))) then
        tmp = x / (y * exp(b))
    else
        tmp = (x / y) * (1.0d0 / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -180.0) || !(b <= 7.0)) {
		tmp = x / (y * Math.exp(b));
	} else {
		tmp = (x / y) * (1.0 / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -180.0) or not (b <= 7.0):
		tmp = x / (y * math.exp(b))
	else:
		tmp = (x / y) * (1.0 / a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -180.0) || !(b <= 7.0))
		tmp = Float64(x / Float64(y * exp(b)));
	else
		tmp = Float64(Float64(x / y) * Float64(1.0 / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -180.0) || ~((b <= 7.0)))
		tmp = x / (y * exp(b));
	else
		tmp = (x / y) * (1.0 / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -180.0], N[Not[LessEqual[b, 7.0]], $MachinePrecision]], N[(x / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[(1.0 / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -180 or 7 < b

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-/l* 87.6%

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

      3. associate--l+ 87.6%

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

      4. fma-define 87.6%

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

      5. sub-neg 87.6%

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

      6. metadata-eval 87.6%

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

   3. Simplified 87.6%

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

   5. Taylor expanded in b around inf 65.0%

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

      1. neg-mul-1 65.0%

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

   7. Simplified 65.0%

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

      1. exp-neg 65.0%

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

      2. frac-times 74.7%

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

      3. *-un-lft-identity 74.7%

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

      4. *-commutative 74.7%

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

   9. Applied egg-rr 74.7%

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

   if -180 < b < 7

   1. Initial program 95.7%

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

   3. Taylor expanded in b around 0 95.7%

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

      1. exp-sum 83.1%

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

      2. exp-to-pow 84.1%

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

      3. sub-neg 84.1%

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

      4. metadata-eval 84.1%

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

      5. *-commutative 84.1%

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

      6. exp-to-pow 84.1%

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

   5. Simplified 84.1%

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

   6. Taylor expanded in t around 0 68.6%

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

      1. associate-/l/ 66.8%

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

      2. times-frac 63.3%

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

   8. Applied egg-rr 63.3%

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

   9. Taylor expanded in y around 0 37.7%

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

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -180 \lor \neg \left(b \leq 7\right):\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 41.8% accurate, 15.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{+44}:\\ \;\;\;\;\frac{x \cdot \left(1 + b \cdot \left(b \cdot \left(b \cdot -0.16666666666666666\right) + -1\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -4.5e+44)
   (/ (* x (+ 1.0 (* b (+ (* b (* b -0.16666666666666666)) -1.0)))) y)
   (/ (/ x a) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4.5e+44) {
		tmp = (x * (1.0 + (b * ((b * (b * -0.16666666666666666)) + -1.0)))) / y;
	} 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 <= (-4.5d+44)) then
        tmp = (x * (1.0d0 + (b * ((b * (b * (-0.16666666666666666d0))) + (-1.0d0))))) / y
    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 <= -4.5e+44) {
		tmp = (x * (1.0 + (b * ((b * (b * -0.16666666666666666)) + -1.0)))) / y;
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -4.5e+44:
		tmp = (x * (1.0 + (b * ((b * (b * -0.16666666666666666)) + -1.0)))) / y
	else:
		tmp = (x / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -4.5e+44)
		tmp = Float64(Float64(x * Float64(1.0 + Float64(b * Float64(Float64(b * Float64(b * -0.16666666666666666)) + -1.0)))) / y);
	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 <= -4.5e+44)
		tmp = (x * (1.0 + (b * ((b * (b * -0.16666666666666666)) + -1.0)))) / y;
	else
		tmp = (x / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -4.5e+44], N[(N[(x * N[(1.0 + N[(b * N[(N[(b * N[(b * -0.16666666666666666), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.5e44

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-/l* 86.0%

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

      3. associate--l+ 86.0%

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

      4. fma-define 86.0%

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

      5. sub-neg 86.0%

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

      6. metadata-eval 86.0%

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

   3. Simplified 86.0%

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

   5. Taylor expanded in b around inf 60.9%

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

      1. neg-mul-1 60.9%

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

   7. Simplified 60.9%

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

   8. Taylor expanded in b around 0 56.5%

      \[\leadsto \color{blue}{\left(1 + b \cdot \left(b \cdot \left(0.5 + -0.16666666666666666 \cdot b\right) - 1\right)\right)} \cdot \frac{x}{y} \]

   9. Taylor expanded in x around 0 70.3%

      \[\leadsto \color{blue}{\frac{x \cdot \left(1 + b \cdot \left(b \cdot \left(0.5 + -0.16666666666666666 \cdot b\right) - 1\right)\right)}{y}} \]

   10. Taylor expanded in b around inf 70.3%

       \[\leadsto \frac{x \cdot \left(1 + b \cdot \left(b \cdot \color{blue}{\left(-0.16666666666666666 \cdot b\right)} - 1\right)\right)}{y} \]
   11. Step-by-step derivation

       1. *-commutative 70.3%

          \[\leadsto \frac{x \cdot \left(1 + b \cdot \left(b \cdot \color{blue}{\left(b \cdot -0.16666666666666666\right)} - 1\right)\right)}{y} \]

   12. Simplified 70.3%

       \[\leadsto \frac{x \cdot \left(1 + b \cdot \left(b \cdot \color{blue}{\left(b \cdot -0.16666666666666666\right)} - 1\right)\right)}{y} \]

   if -4.5e44 < b

   1. Initial program 97.1%

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

   3. Taylor expanded in b around 0 84.3%

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

      1. exp-sum 72.1%

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

      2. exp-to-pow 72.7%

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

      3. sub-neg 72.7%

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

      4. metadata-eval 72.7%

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

      5. *-commutative 72.7%

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

      6. exp-to-pow 72.7%

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

   5. Simplified 72.7%

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

   6. Taylor expanded in t around 0 58.8%

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

   7. Taylor expanded in y around 0 32.0%

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

4. Final simplification 38.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{+44}:\\ \;\;\;\;\frac{x \cdot \left(1 + b \cdot \left(b \cdot \left(b \cdot -0.16666666666666666\right) + -1\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 40.2% accurate, 17.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{+50}:\\ \;\;\;\;\frac{x \cdot \left(1 + b \cdot \left(b \cdot 0.5 + -1\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -7e+50) (/ (* x (+ 1.0 (* b (+ (* b 0.5) -1.0)))) y) (/ (/ x a) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7e+50) {
		tmp = (x * (1.0 + (b * ((b * 0.5) + -1.0)))) / y;
	} 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 <= (-7d+50)) then
        tmp = (x * (1.0d0 + (b * ((b * 0.5d0) + (-1.0d0))))) / y
    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 <= -7e+50) {
		tmp = (x * (1.0 + (b * ((b * 0.5) + -1.0)))) / y;
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -7e+50:
		tmp = (x * (1.0 + (b * ((b * 0.5) + -1.0)))) / y
	else:
		tmp = (x / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -7e+50)
		tmp = Float64(Float64(x * Float64(1.0 + Float64(b * Float64(Float64(b * 0.5) + -1.0)))) / y);
	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 <= -7e+50)
		tmp = (x * (1.0 + (b * ((b * 0.5) + -1.0)))) / y;
	else
		tmp = (x / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -7e+50], N[(N[(x * N[(1.0 + N[(b * N[(N[(b * 0.5), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -7.00000000000000012e50

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-/l* 86.0%

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

      3. associate--l+ 86.0%

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

      4. fma-define 86.0%

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

      5. sub-neg 86.0%

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

      6. metadata-eval 86.0%

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

   3. Simplified 86.0%

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

   5. Taylor expanded in b around inf 60.9%

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

      1. neg-mul-1 60.9%

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

   7. Simplified 60.9%

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

   8. Taylor expanded in b around 0 56.5%

      \[\leadsto \color{blue}{\left(1 + b \cdot \left(b \cdot \left(0.5 + -0.16666666666666666 \cdot b\right) - 1\right)\right)} \cdot \frac{x}{y} \]

   9. Taylor expanded in x around 0 70.3%

      \[\leadsto \color{blue}{\frac{x \cdot \left(1 + b \cdot \left(b \cdot \left(0.5 + -0.16666666666666666 \cdot b\right) - 1\right)\right)}{y}} \]

   10. Taylor expanded in b around 0 63.7%

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

       1. *-commutative 63.7%

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

   12. Simplified 63.7%

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

   if -7.00000000000000012e50 < b

   1. Initial program 97.1%

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

   3. Taylor expanded in b around 0 84.3%

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

      1. exp-sum 72.1%

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

      2. exp-to-pow 72.7%

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

      3. sub-neg 72.7%

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

      4. metadata-eval 72.7%

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

      5. *-commutative 72.7%

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

      6. exp-to-pow 72.7%

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

   5. Simplified 72.7%

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

   6. Taylor expanded in t around 0 58.8%

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

   7. Taylor expanded in y around 0 32.0%

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

4. Final simplification 37.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{+50}:\\ \;\;\;\;\frac{x \cdot \left(1 + b \cdot \left(b \cdot 0.5 + -1\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 40.4% accurate, 17.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+45}:\\ \;\;\;\;x \cdot \frac{1 + b \cdot \left(b \cdot 0.5 + -1\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.5e+45)
   (* x (/ (+ 1.0 (* b (+ (* b 0.5) -1.0))) y))
   (/ (/ x a) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.5e+45) {
		tmp = x * ((1.0 + (b * ((b * 0.5) + -1.0))) / y);
	} 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 <= (-3.5d+45)) then
        tmp = x * ((1.0d0 + (b * ((b * 0.5d0) + (-1.0d0)))) / y)
    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 <= -3.5e+45) {
		tmp = x * ((1.0 + (b * ((b * 0.5) + -1.0))) / y);
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3.5e+45:
		tmp = x * ((1.0 + (b * ((b * 0.5) + -1.0))) / y)
	else:
		tmp = (x / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.5e+45)
		tmp = Float64(x * Float64(Float64(1.0 + Float64(b * Float64(Float64(b * 0.5) + -1.0))) / y));
	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 <= -3.5e+45)
		tmp = x * ((1.0 + (b * ((b * 0.5) + -1.0))) / y);
	else
		tmp = (x / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.5e+45], N[(x * N[(N[(1.0 + N[(b * N[(N[(b * 0.5), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.50000000000000023e45

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-/l* 86.0%

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

      3. associate--l+ 86.0%

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

      4. fma-define 86.0%

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

      5. sub-neg 86.0%

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

      6. metadata-eval 86.0%

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

   3. Simplified 86.0%

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

   5. Taylor expanded in b around inf 60.9%

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

      1. neg-mul-1 60.9%

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

   7. Simplified 60.9%

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

   8. Taylor expanded in b around inf 70.2%

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

      1. associate-/l* 70.2%

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

   10. Simplified 70.2%

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

   11. Taylor expanded in b around 0 61.5%

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

   if -3.50000000000000023e45 < b

   1. Initial program 97.1%

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

   3. Taylor expanded in b around 0 84.3%

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

      1. exp-sum 72.1%

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

      2. exp-to-pow 72.7%

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

      3. sub-neg 72.7%

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

      4. metadata-eval 72.7%

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

      5. *-commutative 72.7%

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

      6. exp-to-pow 72.7%

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

   5. Simplified 72.7%

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

   6. Taylor expanded in t around 0 58.8%

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

   7. Taylor expanded in y around 0 32.0%

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

4. Final simplification 36.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+45}:\\ \;\;\;\;x \cdot \frac{1 + b \cdot \left(b \cdot 0.5 + -1\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 34.4% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.75 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \frac{1 - b}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.75e+38) (* x (/ (- 1.0 b) y)) (/ (/ x a) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.75e+38) {
		tmp = x * ((1.0 - b) / y);
	} 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 <= (-2.75d+38)) then
        tmp = x * ((1.0d0 - b) / y)
    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 <= -2.75e+38) {
		tmp = x * ((1.0 - b) / y);
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.75e+38:
		tmp = x * ((1.0 - b) / y)
	else:
		tmp = (x / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.75e+38)
		tmp = Float64(x * Float64(Float64(1.0 - b) / y));
	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 <= -2.75e+38)
		tmp = x * ((1.0 - b) / y);
	else
		tmp = (x / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.75e+38], N[(x * N[(N[(1.0 - b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.7500000000000002e38

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-/l* 86.4%

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

      3. associate--l+ 86.4%

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

      4. fma-define 86.4%

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

      5. sub-neg 86.4%

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

      6. metadata-eval 86.4%

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

   3. Simplified 86.4%

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

   5. Taylor expanded in b around inf 59.5%

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

      1. neg-mul-1 59.5%

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

   7. Simplified 59.5%

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

   8. Taylor expanded in b around inf 68.7%

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

      1. associate-/l* 68.7%

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

   10. Simplified 68.7%

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

   11. Taylor expanded in b around 0 34.0%

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

       1. neg-mul-1 34.0%

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

       2. unsub-neg 34.0%

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

   13. Simplified 34.0%

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

   if -2.7500000000000002e38 < b

   1. Initial program 97.1%

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

   3. Taylor expanded in b around 0 84.2%

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

      1. exp-sum 71.9%

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

      2. exp-to-pow 72.6%

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

      3. sub-neg 72.6%

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

      4. metadata-eval 72.6%

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

      5. *-commutative 72.6%

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

      6. exp-to-pow 72.6%

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

   5. Simplified 72.6%

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

   6. Taylor expanded in t around 0 58.6%

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

   7. Taylor expanded in y around 0 32.1%

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

Alternative 15: 33.3% accurate, 28.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.1 \cdot 10^{+41}:\\ \;\;\;\;b \cdot \frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -6.1e+41) (* b (/ x (- y))) (/ (/ x a) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.1e+41) {
		tmp = b * (x / -y);
	} 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 <= (-6.1d+41)) then
        tmp = b * (x / -y)
    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 <= -6.1e+41) {
		tmp = b * (x / -y);
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -6.1e+41:
		tmp = b * (x / -y)
	else:
		tmp = (x / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -6.1e+41)
		tmp = Float64(b * Float64(x / Float64(-y)));
	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 <= -6.1e+41)
		tmp = b * (x / -y);
	else
		tmp = (x / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -6.1e+41], N[(b * N[(x / (-y)), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -6.09999999999999998e41

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-/l* 86.4%

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

      3. associate--l+ 86.4%

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

      4. fma-define 86.4%

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

      5. sub-neg 86.4%

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

      6. metadata-eval 86.4%

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

   3. Simplified 86.4%

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

   5. Taylor expanded in b around inf 59.5%

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

      1. neg-mul-1 59.5%

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

   7. Simplified 59.5%

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

   8. Taylor expanded in b around 0 33.9%

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

      1. neg-mul-1 34.0%

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

      2. unsub-neg 34.0%

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

   10. Simplified 33.9%

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

   11. Taylor expanded in b around inf 31.8%

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

       1. mul-1-neg 31.8%

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

       2. associate-/l* 33.9%

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

       3. distribute-lft-neg-in 33.9%

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

   13. Simplified 33.9%

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

   if -6.09999999999999998e41 < b

   1. Initial program 97.1%

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

   3. Taylor expanded in b around 0 84.2%

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

      1. exp-sum 71.9%

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

      2. exp-to-pow 72.6%

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

      3. sub-neg 72.6%

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

      4. metadata-eval 72.6%

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

      5. *-commutative 72.6%

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

      6. exp-to-pow 72.6%

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

   5. Simplified 72.6%

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

   6. Taylor expanded in t around 0 58.6%

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

   7. Taylor expanded in y around 0 32.1%

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

4. Final simplification 32.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.1 \cdot 10^{+41}:\\ \;\;\;\;b \cdot \frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 32.3% accurate, 31.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 5.5 \cdot 10^{+135}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 5.5e+135) (/ (/ x a) y) (/ x (* y a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 5.5e+135) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= 5.5d+135) then
        tmp = (x / a) / y
    else
        tmp = x / (y * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 5.5e+135) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 5.5e+135:
		tmp = (x / a) / y
	else:
		tmp = x / (y * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 5.5e+135)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(x / Float64(y * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 5.5e+135)
		tmp = (x / a) / y;
	else
		tmp = x / (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 5.5e+135], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 5.4999999999999999e135

   1. Initial program 99.4%

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

   3. Taylor expanded in b around 0 84.6%

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

      1. exp-sum 73.5%

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

      2. exp-to-pow 74.0%

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

      3. sub-neg 74.0%

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

      4. metadata-eval 74.0%

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

      5. *-commutative 74.0%

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

      6. exp-to-pow 74.0%

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

   5. Simplified 74.0%

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

   6. Taylor expanded in t around 0 61.7%

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

   7. Taylor expanded in y around 0 31.1%

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

   if 5.4999999999999999e135 < a

   1. Initial program 94.0%

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

   3. Taylor expanded in b around 0 75.7%

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

      1. exp-sum 58.0%

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

      2. exp-to-pow 58.6%

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

      3. sub-neg 58.6%

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

      4. metadata-eval 58.6%

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

      5. *-commutative 58.6%

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

      6. exp-to-pow 58.6%

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

   5. Simplified 58.6%

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

   6. Taylor expanded in t around 0 46.5%

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

   7. Taylor expanded in y around 0 34.4%

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

4. Final simplification 32.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 5.5 \cdot 10^{+135}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 31.3% 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 97.6%

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

3. Taylor expanded in b around 0 81.6%

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

   1. exp-sum 68.3%

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

   2. exp-to-pow 68.9%

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

   3. sub-neg 68.9%

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

   4. metadata-eval 68.9%

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

   5. *-commutative 68.9%

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

   6. exp-to-pow 68.9%

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

5. Simplified 68.9%

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

6. Taylor expanded in t around 0 56.7%

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

7. Taylor expanded in y around 0 30.4%

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

8. Final simplification 30.4%

   \[\leadsto \frac{x}{y \cdot a} \]
9. Add Preprocessing

Alternative 18: 15.5% accurate, 105.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

   1. *-commutative 97.6%

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

   2. associate-/l* 86.1%

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

   3. associate--l+ 86.1%

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

   4. fma-define 86.1%

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

   5. sub-neg 86.1%

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

   6. metadata-eval 86.1%

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

3. Simplified 86.1%

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

5. Taylor expanded in b around inf 38.7%

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

   1. neg-mul-1 38.7%

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

7. Simplified 38.7%

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

8. Taylor expanded in b around 0 16.0%

   \[\leadsto \color{blue}{\frac{x}{y}} \]
9. Add Preprocessing

Developer Target 1: 71.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024181 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -8845848504127471/10000000000000000) (/ (* x (/ (pow a (- t 1)) y)) (- (+ b 1) (* y (log z)))) (if (< t 8520312288374073/10000000000) (/ (* (/ x y) (pow a (- t 1))) (exp (- b (* (log z) y)))) (/ (* x (/ (pow a (- t 1)) y)) (- (+ b 1) (* y (log z)))))))

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