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

Percentage Accurate: 98.2% → 98.2%

Time: 11.1s

Alternatives: 17

Speedup: 1.0×

• 48.0% 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: 98.2% 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: 98.2% 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 99.0%

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

Alternative 2: 43.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-129} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\frac{x \cdot \mathsf{fma}\left(\frac{b}{a} \cdot 0.5 - {a}^{-1}, b, {a}^{-1}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{-b}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)))
   (if (or (<= t_1 -2e-129) (not (<= t_1 0.0)))
     (/ (* x (fma (- (* (/ b a) 0.5) (pow a -1.0)) b (pow a -1.0))) y)
     (/ (* x (/ (- b) a)) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * exp((((y * log(z)) + ((t - 1.0) * log(a))) - b))) / y;
	double tmp;
	if ((t_1 <= -2e-129) || !(t_1 <= 0.0)) {
		tmp = (x * fma((((b / a) * 0.5) - pow(a, -1.0)), b, pow(a, -1.0))) / y;
	} else {
		tmp = (x * (-b / a)) / y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) + Float64(Float64(t - 1.0) * log(a))) - b))) / y)
	tmp = 0.0
	if ((t_1 <= -2e-129) || !(t_1 <= 0.0))
		tmp = Float64(Float64(x * fma(Float64(Float64(Float64(b / a) * 0.5) - (a ^ -1.0)), b, (a ^ -1.0))) / y);
	else
		tmp = Float64(Float64(x * Float64(Float64(-b) / a)) / y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = 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]}, If[Or[LessEqual[t$95$1, -2e-129], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(x * N[(N[(N[(N[(b / a), $MachinePrecision] * 0.5), $MachinePrecision] - N[Power[a, -1.0], $MachinePrecision]), $MachinePrecision] * b + N[Power[a, -1.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[((-b) / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (exp.f64 (-.f64 (+.f64 (*.f64 y (log.f64 z)) (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))) b))) y) < -1.9999999999999999e-129 or 0.0 < (/.f64 (*.f64 x (exp.f64 (-.f64 (+.f64 (*.f64 y (log.f64 z)) (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))) b))) y)

   1. Initial program 98.7%

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

   3. Taylor expanded in t around 0

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

      1. exp-diff N/A

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

      2. lower-/.f64 N/A

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

      3. +-commutative N/A

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

      4. fp-cancel-sign-sub-inv N/A

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

      5. metadata-eval N/A

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

      6. *-lft-identity N/A

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

      7. exp-diff N/A

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

      8. rem-exp-log N/A

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

      9. lower-/.f64 N/A

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

      10. *-commutative N/A

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

      11. exp-to-pow N/A

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

      12. lower-pow.f64 N/A

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

      13. lower-exp.f64 78.2

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

   5. Applied rewrites 78.2%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 63.1%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 64.0%

       \[\leadsto \frac{x \cdot \mathsf{fma}\left(\frac{b}{a} \cdot 0.5 - \frac{1}{a}, b, \frac{1}{a}\right)}{y} \]

   if -1.9999999999999999e-129 < (/.f64 (*.f64 x (exp.f64 (-.f64 (+.f64 (*.f64 y (log.f64 z)) (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))) b))) y) < 0.0

   1. Initial program 99.2%

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

   3. Taylor expanded in t around 0

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

      1. exp-diff N/A

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

      2. lower-/.f64 N/A

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

      3. +-commutative N/A

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

      4. fp-cancel-sign-sub-inv N/A

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

      5. metadata-eval N/A

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

      6. *-lft-identity N/A

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

      7. exp-diff N/A

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

      8. rem-exp-log N/A

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

      9. lower-/.f64 N/A

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

      10. *-commutative N/A

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

      11. exp-to-pow N/A

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

      12. lower-pow.f64 N/A

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

      13. lower-exp.f64 65.5

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

   5. Applied rewrites 65.5%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 57.4%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 17.8%

       \[\leadsto \frac{x \cdot \frac{\mathsf{fma}\left(-1, b, 1\right)}{a}}{y} \]

   12. Taylor expanded in b around inf

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

   14. Applied rewrites 25.7%

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

4. Final simplification 45.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \leq -2 \cdot 10^{-129} \lor \neg \left(\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \leq 0\right):\\ \;\;\;\;\frac{x \cdot \mathsf{fma}\left(\frac{b}{a} \cdot 0.5 - {a}^{-1}, b, {a}^{-1}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{-b}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 92.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t - 1 \leq -1.0000000000026263:\\ \;\;\;\;\frac{x \cdot e^{\left(-1 + t\right) \cdot \log a - b}}{y}\\ \mathbf{elif}\;t - 1 \leq 5 \cdot 10^{+101}:\\ \;\;\;\;\frac{x \cdot e^{\mathsf{fma}\left(\log z, y, -\log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot t - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (- t 1.0) -1.0000000000026263)
   (/ (* x (exp (- (* (+ -1.0 t) (log a)) b))) y)
   (if (<= (- t 1.0) 5e+101)
     (/ (* x (exp (- (fma (log z) y (- (log a))) b))) y)
     (/ (* x (exp (- (* (log a) t) b))) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t - 1.0) <= -1.0000000000026263) {
		tmp = (x * exp((((-1.0 + t) * log(a)) - b))) / y;
	} else if ((t - 1.0) <= 5e+101) {
		tmp = (x * exp((fma(log(z), y, -log(a)) - b))) / y;
	} else {
		tmp = (x * exp(((log(a) * t) - b))) / y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(t - 1.0) <= -1.0000000000026263)
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(-1.0 + t) * log(a)) - b))) / y);
	elseif (Float64(t - 1.0) <= 5e+101)
		tmp = Float64(Float64(x * exp(Float64(fma(log(z), y, Float64(-log(a))) - b))) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(log(a) * t) - b))) / y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(t - 1.0), $MachinePrecision], -1.0000000000026263], N[(N[(x * N[Exp[N[(N[(N[(-1.0 + t), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[N[(t - 1.0), $MachinePrecision], 5e+101], N[(N[(x * N[Exp[N[(N[(N[Log[z], $MachinePrecision] * y + (-N[Log[a], $MachinePrecision])), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[Log[a], $MachinePrecision] * t), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 t #s(literal 1 binary64)) < -1.0000000000026263

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. distribute-rgt-out-- N/A

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

      2. metadata-eval N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. distribute-rgt-out N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. metadata-eval N/A

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

      8. remove-double-neg N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. lower-*.f64 N/A

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

      12. mul-1-neg N/A

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

      13. distribute-neg-in N/A

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

      14. metadata-eval N/A

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

      15. remove-double-neg N/A

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

      16. lower-+.f64 N/A

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

      17. lower-log.f64 94.0

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

   5. Applied rewrites 94.0%

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

   if -1.0000000000026263 < (-.f64 t #s(literal 1 binary64)) < 4.99999999999999989e101

   1. Initial program 98.3%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-log.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-log.f64 97.0

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

   5. Applied rewrites 97.0%

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

   if 4.99999999999999989e101 < (-.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 t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-log.f64 95.1

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

   5. Applied rewrites 95.1%

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

Alternative 4: 92.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t - 1 \leq -1.0000000000026263:\\ \;\;\;\;\frac{x \cdot e^{\left(-1 + t\right) \cdot \log a - b}}{y}\\ \mathbf{elif}\;t - 1 \leq 5 \cdot 10^{+101}:\\ \;\;\;\;x \cdot \frac{e^{\mathsf{fma}\left(\log z, y, -\log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot t - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (- t 1.0) -1.0000000000026263)
   (/ (* x (exp (- (* (+ -1.0 t) (log a)) b))) y)
   (if (<= (- t 1.0) 5e+101)
     (* x (/ (exp (- (fma (log z) y (- (log a))) b)) y))
     (/ (* x (exp (- (* (log a) t) b))) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t - 1.0) <= -1.0000000000026263) {
		tmp = (x * exp((((-1.0 + t) * log(a)) - b))) / y;
	} else if ((t - 1.0) <= 5e+101) {
		tmp = x * (exp((fma(log(z), y, -log(a)) - b)) / y);
	} else {
		tmp = (x * exp(((log(a) * t) - b))) / y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(t - 1.0) <= -1.0000000000026263)
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(-1.0 + t) * log(a)) - b))) / y);
	elseif (Float64(t - 1.0) <= 5e+101)
		tmp = Float64(x * Float64(exp(Float64(fma(log(z), y, Float64(-log(a))) - b)) / y));
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(log(a) * t) - b))) / y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(t - 1.0), $MachinePrecision], -1.0000000000026263], N[(N[(x * N[Exp[N[(N[(N[(-1.0 + t), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[N[(t - 1.0), $MachinePrecision], 5e+101], N[(x * N[(N[Exp[N[(N[(N[Log[z], $MachinePrecision] * y + (-N[Log[a], $MachinePrecision])), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[Log[a], $MachinePrecision] * t), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 t #s(literal 1 binary64)) < -1.0000000000026263

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. distribute-rgt-out-- N/A

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

      2. metadata-eval N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. distribute-rgt-out N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. metadata-eval N/A

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

      8. remove-double-neg N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. lower-*.f64 N/A

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

      12. mul-1-neg N/A

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

      13. distribute-neg-in N/A

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

      14. metadata-eval N/A

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

      15. remove-double-neg N/A

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

      16. lower-+.f64 N/A

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

      17. lower-log.f64 94.0

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

   5. Applied rewrites 94.0%

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

   if -1.0000000000026263 < (-.f64 t #s(literal 1 binary64)) < 4.99999999999999989e101

   1. Initial program 98.3%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower-log.f64 N/A

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

      10. lower-log.f64 98.2

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

   5. Applied rewrites 98.2%

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

   6. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-log.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lower-neg.f64 N/A

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

      12. lower-log.f64 95.9

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

   8. Applied rewrites 95.9%

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

   if 4.99999999999999989e101 < (-.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 t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-log.f64 95.1

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

   5. Applied rewrites 95.1%

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

Alternative 5: 80.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ t_2 := \frac{x \cdot e^{\log a \cdot t - b}}{y}\\ \mathbf{if}\;b \leq -3 \cdot 10^{+21}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -5.6 \cdot 10^{-181}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-60}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t - 1\right)}}{y}\\ \mathbf{elif}\;b \leq 128000000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (/ (pow z y) a)) y))
        (t_2 (/ (* x (exp (- (* (log a) t) b))) y)))
   (if (<= b -3e+21)
     t_2
     (if (<= b -5.6e-181)
       t_1
       (if (<= b 4.5e-60)
         (/ (* x (pow a (- t 1.0))) y)
         (if (<= b 128000000000.0) 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 * exp(((log(a) * t) - b))) / y;
	double tmp;
	if (b <= -3e+21) {
		tmp = t_2;
	} else if (b <= -5.6e-181) {
		tmp = t_1;
	} else if (b <= 4.5e-60) {
		tmp = (x * pow(a, (t - 1.0))) / y;
	} else if (b <= 128000000000.0) {
		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 * exp(((log(a) * t) - b))) / y
    if (b <= (-3d+21)) then
        tmp = t_2
    else if (b <= (-5.6d-181)) then
        tmp = t_1
    else if (b <= 4.5d-60) then
        tmp = (x * (a ** (t - 1.0d0))) / y
    else if (b <= 128000000000.0d0) 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.exp(((Math.log(a) * t) - b))) / y;
	double tmp;
	if (b <= -3e+21) {
		tmp = t_2;
	} else if (b <= -5.6e-181) {
		tmp = t_1;
	} else if (b <= 4.5e-60) {
		tmp = (x * Math.pow(a, (t - 1.0))) / y;
	} else if (b <= 128000000000.0) {
		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.exp(((math.log(a) * t) - b))) / y
	tmp = 0
	if b <= -3e+21:
		tmp = t_2
	elif b <= -5.6e-181:
		tmp = t_1
	elif b <= 4.5e-60:
		tmp = (x * math.pow(a, (t - 1.0))) / y
	elif b <= 128000000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * Float64((z ^ y) / a)) / y)
	t_2 = Float64(Float64(x * exp(Float64(Float64(log(a) * t) - b))) / y)
	tmp = 0.0
	if (b <= -3e+21)
		tmp = t_2;
	elseif (b <= -5.6e-181)
		tmp = t_1;
	elseif (b <= 4.5e-60)
		tmp = Float64(Float64(x * (a ^ Float64(t - 1.0))) / y);
	elseif (b <= 128000000000.0)
		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 * exp(((log(a) * t) - b))) / y;
	tmp = 0.0;
	if (b <= -3e+21)
		tmp = t_2;
	elseif (b <= -5.6e-181)
		tmp = t_1;
	elseif (b <= 4.5e-60)
		tmp = (x * (a ^ (t - 1.0))) / y;
	elseif (b <= 128000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[Exp[N[(N[(N[Log[a], $MachinePrecision] * t), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -3e+21], t$95$2, If[LessEqual[b, -5.6e-181], t$95$1, If[LessEqual[b, 4.5e-60], N[(N[(x * N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 128000000000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3e21 or 1.28e11 < 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. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-log.f64 93.4

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

   5. Applied rewrites 93.4%

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

   if -3e21 < b < -5.59999999999999973e-181 or 4.50000000000000001e-60 < b < 1.28e11

   1. Initial program 98.6%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. exp-sum N/A

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

      3. lower-*.f64 N/A

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

      4. exp-to-pow N/A

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

      5. lower-pow.f64 N/A

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

      6. lower--.f64 N/A

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

      7. *-commutative N/A

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

      8. exp-to-pow N/A

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

      9. lower-pow.f64 92.6

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

   5. Applied rewrites 92.6%

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

   7. Applied rewrites 92.8%

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

   8. Taylor expanded in t around 0

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

   10. Applied rewrites 87.2%

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

   if -5.59999999999999973e-181 < b < 4.50000000000000001e-60

   1. Initial program 97.7%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. exp-sum N/A

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

      3. lower-*.f64 N/A

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

      4. exp-to-pow N/A

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

      5. lower-pow.f64 N/A

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

      6. lower--.f64 N/A

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

      7. *-commutative N/A

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

      8. exp-to-pow N/A

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

      9. lower-pow.f64 85.3

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

   5. Applied rewrites 85.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 79.5%

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

Alternative 6: 75.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.4 \cdot 10^{+26}:\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{elif}\;b \leq -5.6 \cdot 10^{-181}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{elif}\;b \leq 12500000000:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t - 1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {\left(e^{b} \cdot a\right)}^{-1}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -4.4e+26)
   (* (/ (exp (- b)) y) x)
   (if (<= b -5.6e-181)
     (/ (* x (/ (pow z y) a)) y)
     (if (<= b 12500000000.0)
       (/ (* x (pow a (- t 1.0))) y)
       (/ (* x (pow (* (exp b) a) -1.0)) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4.4e+26) {
		tmp = (exp(-b) / y) * x;
	} else if (b <= -5.6e-181) {
		tmp = (x * (pow(z, y) / a)) / y;
	} else if (b <= 12500000000.0) {
		tmp = (x * pow(a, (t - 1.0))) / y;
	} else {
		tmp = (x * pow((exp(b) * a), -1.0)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-4.4d+26)) then
        tmp = (exp(-b) / y) * x
    else if (b <= (-5.6d-181)) then
        tmp = (x * ((z ** y) / a)) / y
    else if (b <= 12500000000.0d0) then
        tmp = (x * (a ** (t - 1.0d0))) / y
    else
        tmp = (x * ((exp(b) * a) ** (-1.0d0))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4.4e+26) {
		tmp = (Math.exp(-b) / y) * x;
	} else if (b <= -5.6e-181) {
		tmp = (x * (Math.pow(z, y) / a)) / y;
	} else if (b <= 12500000000.0) {
		tmp = (x * Math.pow(a, (t - 1.0))) / y;
	} else {
		tmp = (x * Math.pow((Math.exp(b) * a), -1.0)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -4.4e+26:
		tmp = (math.exp(-b) / y) * x
	elif b <= -5.6e-181:
		tmp = (x * (math.pow(z, y) / a)) / y
	elif b <= 12500000000.0:
		tmp = (x * math.pow(a, (t - 1.0))) / y
	else:
		tmp = (x * math.pow((math.exp(b) * a), -1.0)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -4.4e+26)
		tmp = Float64(Float64(exp(Float64(-b)) / y) * x);
	elseif (b <= -5.6e-181)
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	elseif (b <= 12500000000.0)
		tmp = Float64(Float64(x * (a ^ Float64(t - 1.0))) / y);
	else
		tmp = Float64(Float64(x * (Float64(exp(b) * a) ^ -1.0)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -4.4e+26)
		tmp = (exp(-b) / y) * x;
	elseif (b <= -5.6e-181)
		tmp = (x * ((z ^ y) / a)) / y;
	elseif (b <= 12500000000.0)
		tmp = (x * (a ^ (t - 1.0))) / y;
	else
		tmp = (x * ((exp(b) * a) ^ -1.0)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -4.4e+26], N[(N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[b, -5.6e-181], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 12500000000.0], N[(N[(x * N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Power[N[(N[Exp[b], $MachinePrecision] * a), $MachinePrecision], -1.0], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -4.40000000000000014e26

   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 y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower-log.f64 N/A

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

      10. lower-log.f64 94.5

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

   5. Applied rewrites 94.5%

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

   6. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 85.4

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

   8. Applied rewrites 85.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 85.4

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

   10. Applied rewrites 85.4%

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

   if -4.40000000000000014e26 < b < -5.59999999999999973e-181

   1. Initial program 98.8%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. exp-sum N/A

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

      3. lower-*.f64 N/A

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

      4. exp-to-pow N/A

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

      5. lower-pow.f64 N/A

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

      6. lower--.f64 N/A

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

      7. *-commutative N/A

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

      8. exp-to-pow N/A

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

      9. lower-pow.f64 91.7

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

   5. Applied rewrites 91.7%

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

   7. Applied rewrites 92.1%

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

   8. Taylor expanded in t around 0

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

   10. Applied rewrites 88.8%

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

   if -5.59999999999999973e-181 < b < 1.25e10

   1. Initial program 97.8%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. exp-sum N/A

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

      3. lower-*.f64 N/A

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

      4. exp-to-pow N/A

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

      5. lower-pow.f64 N/A

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

      6. lower--.f64 N/A

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

      7. *-commutative N/A

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

      8. exp-to-pow N/A

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

      9. lower-pow.f64 87.8

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

   5. Applied rewrites 87.8%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 76.3%

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

   if 1.25e10 < 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. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. exp-diff N/A

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

      2. lower-/.f64 N/A

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

      3. +-commutative N/A

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

      4. fp-cancel-sign-sub-inv N/A

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

      5. metadata-eval N/A

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

      6. *-lft-identity N/A

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

      7. exp-diff N/A

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

      8. rem-exp-log N/A

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

      9. lower-/.f64 N/A

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

      10. *-commutative N/A

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

      11. exp-to-pow N/A

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

      12. lower-pow.f64 N/A

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

      13. lower-exp.f64 71.4

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

   5. Applied rewrites 71.4%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 83.6%

      \[\leadsto \frac{x \cdot \frac{1}{\color{blue}{e^{b} \cdot a}}}{y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.4 \cdot 10^{+26}:\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{elif}\;b \leq -5.6 \cdot 10^{-181}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{elif}\;b \leq 12500000000:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t - 1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {\left(e^{b} \cdot a\right)}^{-1}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 88.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+19} \lor \neg \left(y \leq 5.8 \cdot 10^{+147}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(-1 + t\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -5.4e+19) (not (<= y 5.8e+147)))
   (/ (* x (/ (pow z y) a)) y)
   (/ (* x (exp (- (* (+ -1.0 t) (log a)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -5.4e+19) || !(y <= 5.8e+147)) {
		tmp = (x * (pow(z, y) / a)) / y;
	} else {
		tmp = (x * exp((((-1.0 + t) * log(a)) - b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-5.4d+19)) .or. (.not. (y <= 5.8d+147))) then
        tmp = (x * ((z ** y) / a)) / y
    else
        tmp = (x * exp(((((-1.0d0) + t) * log(a)) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -5.4e+19) || !(y <= 5.8e+147)) {
		tmp = (x * (Math.pow(z, y) / a)) / y;
	} else {
		tmp = (x * Math.exp((((-1.0 + t) * Math.log(a)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -5.4e+19) or not (y <= 5.8e+147):
		tmp = (x * (math.pow(z, y) / a)) / y
	else:
		tmp = (x * math.exp((((-1.0 + t) * math.log(a)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -5.4e+19) || !(y <= 5.8e+147))
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(-1.0 + t) * log(a)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -5.4e+19) || ~((y <= 5.8e+147)))
		tmp = (x * ((z ^ y) / a)) / y;
	else
		tmp = (x * exp((((-1.0 + t) * log(a)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -5.4e+19], N[Not[LessEqual[y, 5.8e+147]], $MachinePrecision]], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[(-1.0 + t), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.4e19 or 5.7999999999999997e147 < 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

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

      1. +-commutative N/A

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

      2. exp-sum N/A

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

      3. lower-*.f64 N/A

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

      4. exp-to-pow N/A

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

      5. lower-pow.f64 N/A

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

      6. lower--.f64 N/A

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

      7. *-commutative N/A

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

      8. exp-to-pow N/A

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

      9. lower-pow.f64 70.5

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

   5. Applied rewrites 70.5%

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

   7. Applied rewrites 70.5%

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

   8. Taylor expanded in t around 0

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

   10. Applied rewrites 85.5%

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

   if -5.4e19 < y < 5.7999999999999997e147

   1. Initial program 98.4%

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

   3. Taylor expanded in y around 0

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

      1. distribute-rgt-out-- N/A

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

      2. metadata-eval N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. distribute-rgt-out N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. metadata-eval N/A

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

      8. remove-double-neg N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. lower-*.f64 N/A

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

      12. mul-1-neg N/A

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

      13. distribute-neg-in N/A

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

      14. metadata-eval N/A

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

      15. remove-double-neg N/A

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

      16. lower-+.f64 N/A

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

      17. lower-log.f64 94.0

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

   5. Applied rewrites 94.0%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+19} \lor \neg \left(y \leq 5.8 \cdot 10^{+147}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(-1 + t\right) \cdot \log a - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 87.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.4 \cdot 10^{+26} \lor \neg \left(b \leq 10500000000\right):\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot t - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left({a}^{\left(t - 1\right)} \cdot {z}^{y}\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -4.4e+26) (not (<= b 10500000000.0)))
   (/ (* x (exp (- (* (log a) t) b))) y)
   (/ (* x (* (pow a (- t 1.0)) (pow z y))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -4.4e+26) || !(b <= 10500000000.0)) {
		tmp = (x * exp(((log(a) * t) - b))) / y;
	} else {
		tmp = (x * (pow(a, (t - 1.0)) * pow(z, y))) / 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 <= (-4.4d+26)) .or. (.not. (b <= 10500000000.0d0))) then
        tmp = (x * exp(((log(a) * t) - b))) / y
    else
        tmp = (x * ((a ** (t - 1.0d0)) * (z ** y))) / 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 <= -4.4e+26) || !(b <= 10500000000.0)) {
		tmp = (x * Math.exp(((Math.log(a) * t) - b))) / y;
	} else {
		tmp = (x * (Math.pow(a, (t - 1.0)) * Math.pow(z, y))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -4.4e+26) or not (b <= 10500000000.0):
		tmp = (x * math.exp(((math.log(a) * t) - b))) / y
	else:
		tmp = (x * (math.pow(a, (t - 1.0)) * math.pow(z, y))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -4.4e+26) || !(b <= 10500000000.0))
		tmp = Float64(Float64(x * exp(Float64(Float64(log(a) * t) - b))) / y);
	else
		tmp = Float64(Float64(x * Float64((a ^ Float64(t - 1.0)) * (z ^ y))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -4.4e+26) || ~((b <= 10500000000.0)))
		tmp = (x * exp(((log(a) * t) - b))) / y;
	else
		tmp = (x * ((a ^ (t - 1.0)) * (z ^ y))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -4.4e+26], N[Not[LessEqual[b, 10500000000.0]], $MachinePrecision]], N[(N[(x * N[Exp[N[(N[(N[Log[a], $MachinePrecision] * t), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] * N[Power[z, y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.40000000000000014e26 or 1.05e10 < 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. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-log.f64 92.6

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

   5. Applied rewrites 92.6%

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

   if -4.40000000000000014e26 < b < 1.05e10

   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 b around 0

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

      1. +-commutative N/A

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

      2. exp-sum N/A

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

      3. lower-*.f64 N/A

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

      4. exp-to-pow N/A

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

      5. lower-pow.f64 N/A

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

      6. lower--.f64 N/A

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

      7. *-commutative N/A

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

      8. exp-to-pow N/A

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

      9. lower-pow.f64 88.9

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

   5. Applied rewrites 88.9%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.4 \cdot 10^{+26} \lor \neg \left(b \leq 10500000000\right):\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot t - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left({a}^{\left(t - 1\right)} \cdot {z}^{y}\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 83.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{+21} \lor \neg \left(b \leq 10500000000\right):\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot t - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\left({a}^{\left(t - 1\right)} \cdot {z}^{y}\right) \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -3e+21) (not (<= b 10500000000.0)))
   (/ (* x (exp (- (* (log a) t) b))) y)
   (* (* (pow a (- t 1.0)) (pow z y)) (/ x y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3e+21) || !(b <= 10500000000.0)) {
		tmp = (x * exp(((log(a) * t) - b))) / y;
	} else {
		tmp = (pow(a, (t - 1.0)) * pow(z, y)) * (x / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-3d+21)) .or. (.not. (b <= 10500000000.0d0))) then
        tmp = (x * exp(((log(a) * t) - b))) / y
    else
        tmp = ((a ** (t - 1.0d0)) * (z ** y)) * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3e+21) || !(b <= 10500000000.0)) {
		tmp = (x * Math.exp(((Math.log(a) * t) - b))) / y;
	} else {
		tmp = (Math.pow(a, (t - 1.0)) * Math.pow(z, y)) * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -3e+21) or not (b <= 10500000000.0):
		tmp = (x * math.exp(((math.log(a) * t) - b))) / y
	else:
		tmp = (math.pow(a, (t - 1.0)) * math.pow(z, y)) * (x / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -3e+21) || !(b <= 10500000000.0))
		tmp = Float64(Float64(x * exp(Float64(Float64(log(a) * t) - b))) / y);
	else
		tmp = Float64(Float64((a ^ Float64(t - 1.0)) * (z ^ y)) * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -3e+21) || ~((b <= 10500000000.0)))
		tmp = (x * exp(((log(a) * t) - b))) / y;
	else
		tmp = ((a ^ (t - 1.0)) * (z ^ y)) * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -3e+21], N[Not[LessEqual[b, 10500000000.0]], $MachinePrecision]], N[(N[(x * N[Exp[N[(N[(N[Log[a], $MachinePrecision] * t), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] * N[Power[z, y], $MachinePrecision]), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3e21 or 1.05e10 < 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. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-log.f64 92.6

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

   5. Applied rewrites 92.6%

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

   if -3e21 < b < 1.05e10

   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 b around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. exp-sum N/A

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

      6. lower-*.f64 N/A

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

      7. exp-to-pow N/A

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

      8. lower-pow.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. exp-to-pow N/A

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

      12. lower-pow.f64 N/A

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

      13. lower-/.f64 77.9

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

   5. Applied rewrites 77.9%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{+21} \lor \neg \left(b \leq 10500000000\right):\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot t - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\left({a}^{\left(t - 1\right)} \cdot {z}^{y}\right) \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 75.3% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.4 \cdot 10^{+23} \lor \neg \left(b \leq 12500000000\right):\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -5.4e+23) (not (<= b 12500000000.0)))
   (* (/ (exp (- b)) y) x)
   (/ (* x (/ (pow a t) a)) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -5.4e+23) || !(b <= 12500000000.0)) {
		tmp = (exp(-b) / y) * x;
	} 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 ((b <= (-5.4d+23)) .or. (.not. (b <= 12500000000.0d0))) then
        tmp = (exp(-b) / y) * x
    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 ((b <= -5.4e+23) || !(b <= 12500000000.0)) {
		tmp = (Math.exp(-b) / y) * x;
	} else {
		tmp = (x * (Math.pow(a, t) / a)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -5.4e+23) or not (b <= 12500000000.0):
		tmp = (math.exp(-b) / y) * x
	else:
		tmp = (x * (math.pow(a, t) / a)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -5.4e+23) || !(b <= 12500000000.0))
		tmp = Float64(Float64(exp(Float64(-b)) / y) * x);
	else
		tmp = Float64(Float64(x * Float64((a ^ t) / a)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -5.4e+23) || ~((b <= 12500000000.0)))
		tmp = (exp(-b) / y) * x;
	else
		tmp = (x * ((a ^ t) / a)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -5.4e+23], N[Not[LessEqual[b, 12500000000.0]], $MachinePrecision]], N[(N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision], N[(N[(x * N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5.3999999999999997e23 or 1.25e10 < 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. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower-log.f64 N/A

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

      10. lower-log.f64 96.7

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

   5. Applied rewrites 96.7%

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

   6. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 84.4

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

   8. Applied rewrites 84.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 84.4

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

   10. Applied rewrites 84.4%

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

   if -5.3999999999999997e23 < b < 1.25e10

   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 b around 0

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

      1. +-commutative N/A

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

      2. exp-sum N/A

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

      3. lower-*.f64 N/A

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

      4. exp-to-pow N/A

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

      5. lower-pow.f64 N/A

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

      6. lower--.f64 N/A

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

      7. *-commutative N/A

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

      8. exp-to-pow N/A

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

      9. lower-pow.f64 88.9

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

   5. Applied rewrites 88.9%

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

   7. Applied rewrites 89.0%

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

   8. Taylor expanded in y around 0

      \[\leadsto \frac{x \cdot \frac{{a}^{t}}{a}}{y} \]
   9. Step-by-step derivation

   10. Applied rewrites 74.3%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.4 \cdot 10^{+23} \lor \neg \left(b \leq 12500000000\right):\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 75.3% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{e^{-b}}{y} \cdot x\\ \mathbf{if}\;b \leq -4.4 \cdot 10^{+26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -5.6 \cdot 10^{-181}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{elif}\;b \leq 12500000000:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t - 1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ (exp (- b)) y) x)))
   (if (<= b -4.4e+26)
     t_1
     (if (<= b -5.6e-181)
       (/ (* x (/ (pow z y) a)) y)
       (if (<= b 12500000000.0) (/ (* x (pow a (- t 1.0))) y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (exp(-b) / y) * x;
	double tmp;
	if (b <= -4.4e+26) {
		tmp = t_1;
	} else if (b <= -5.6e-181) {
		tmp = (x * (pow(z, y) / a)) / y;
	} else if (b <= 12500000000.0) {
		tmp = (x * pow(a, (t - 1.0))) / 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 = (exp(-b) / y) * x
    if (b <= (-4.4d+26)) then
        tmp = t_1
    else if (b <= (-5.6d-181)) then
        tmp = (x * ((z ** y) / a)) / y
    else if (b <= 12500000000.0d0) then
        tmp = (x * (a ** (t - 1.0d0))) / 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 = (Math.exp(-b) / y) * x;
	double tmp;
	if (b <= -4.4e+26) {
		tmp = t_1;
	} else if (b <= -5.6e-181) {
		tmp = (x * (Math.pow(z, y) / a)) / y;
	} else if (b <= 12500000000.0) {
		tmp = (x * Math.pow(a, (t - 1.0))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (math.exp(-b) / y) * x
	tmp = 0
	if b <= -4.4e+26:
		tmp = t_1
	elif b <= -5.6e-181:
		tmp = (x * (math.pow(z, y) / a)) / y
	elif b <= 12500000000.0:
		tmp = (x * math.pow(a, (t - 1.0))) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(exp(Float64(-b)) / y) * x)
	tmp = 0.0
	if (b <= -4.4e+26)
		tmp = t_1;
	elseif (b <= -5.6e-181)
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	elseif (b <= 12500000000.0)
		tmp = Float64(Float64(x * (a ^ Float64(t - 1.0))) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (exp(-b) / y) * x;
	tmp = 0.0;
	if (b <= -4.4e+26)
		tmp = t_1;
	elseif (b <= -5.6e-181)
		tmp = (x * ((z ^ y) / a)) / y;
	elseif (b <= 12500000000.0)
		tmp = (x * (a ^ (t - 1.0))) / 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[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[b, -4.4e+26], t$95$1, If[LessEqual[b, -5.6e-181], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 12500000000.0], N[(N[(x * N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.40000000000000014e26 or 1.25e10 < 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. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower-log.f64 N/A

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

      10. lower-log.f64 96.7

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

   5. Applied rewrites 96.7%

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

   6. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 84.4

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

   8. Applied rewrites 84.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 84.4

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

   10. Applied rewrites 84.4%

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

   if -4.40000000000000014e26 < b < -5.59999999999999973e-181

   1. Initial program 98.8%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. exp-sum N/A

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

      3. lower-*.f64 N/A

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

      4. exp-to-pow N/A

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

      5. lower-pow.f64 N/A

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

      6. lower--.f64 N/A

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

      7. *-commutative N/A

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

      8. exp-to-pow N/A

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

      9. lower-pow.f64 91.7

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

   5. Applied rewrites 91.7%

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

   7. Applied rewrites 92.1%

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

   8. Taylor expanded in t around 0

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

   10. Applied rewrites 88.8%

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

   if -5.59999999999999973e-181 < b < 1.25e10

   1. Initial program 97.8%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. exp-sum N/A

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

      3. lower-*.f64 N/A

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

      4. exp-to-pow N/A

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

      5. lower-pow.f64 N/A

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

      6. lower--.f64 N/A

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

      7. *-commutative N/A

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

      8. exp-to-pow N/A

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

      9. lower-pow.f64 87.8

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

   5. Applied rewrites 87.8%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 76.3%

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

Alternative 12: 75.3% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.4 \cdot 10^{+23} \lor \neg \left(b \leq 12500000000\right):\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t - 1\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -5.4e+23) (not (<= b 12500000000.0)))
   (* (/ (exp (- b)) y) x)
   (/ (* x (pow a (- t 1.0))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -5.4e+23) || !(b <= 12500000000.0)) {
		tmp = (exp(-b) / y) * x;
	} else {
		tmp = (x * pow(a, (t - 1.0))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-5.4d+23)) .or. (.not. (b <= 12500000000.0d0))) then
        tmp = (exp(-b) / y) * x
    else
        tmp = (x * (a ** (t - 1.0d0))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -5.4e+23) || !(b <= 12500000000.0)) {
		tmp = (Math.exp(-b) / y) * x;
	} else {
		tmp = (x * Math.pow(a, (t - 1.0))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -5.4e+23) or not (b <= 12500000000.0):
		tmp = (math.exp(-b) / y) * x
	else:
		tmp = (x * math.pow(a, (t - 1.0))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -5.4e+23) || !(b <= 12500000000.0))
		tmp = Float64(Float64(exp(Float64(-b)) / y) * x);
	else
		tmp = Float64(Float64(x * (a ^ Float64(t - 1.0))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -5.4e+23) || ~((b <= 12500000000.0)))
		tmp = (exp(-b) / y) * x;
	else
		tmp = (x * (a ^ (t - 1.0))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -5.4e+23], N[Not[LessEqual[b, 12500000000.0]], $MachinePrecision]], N[(N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision], N[(N[(x * N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5.3999999999999997e23 or 1.25e10 < 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. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower-log.f64 N/A

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

      10. lower-log.f64 96.7

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

   5. Applied rewrites 96.7%

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

   6. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 84.4

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

   8. Applied rewrites 84.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 84.4

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

   10. Applied rewrites 84.4%

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

   if -5.3999999999999997e23 < b < 1.25e10

   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 b around 0

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

      1. +-commutative N/A

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

      2. exp-sum N/A

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

      3. lower-*.f64 N/A

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

      4. exp-to-pow N/A

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

      5. lower-pow.f64 N/A

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

      6. lower--.f64 N/A

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

      7. *-commutative N/A

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

      8. exp-to-pow N/A

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

      9. lower-pow.f64 88.9

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

   5. Applied rewrites 88.9%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 74.2%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.4 \cdot 10^{+23} \lor \neg \left(b \leq 12500000000\right):\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t - 1\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 58.2% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{+21} \lor \neg \left(b \leq 1.95\right):\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -3e+21) (not (<= b 1.95)))
   (* (/ (exp (- b)) y) x)
   (/ (* x (/ 1.0 a)) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3e+21) || !(b <= 1.95)) {
		tmp = (exp(-b) / y) * x;
	} else {
		tmp = (x * (1.0 / 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 <= (-3d+21)) .or. (.not. (b <= 1.95d0))) then
        tmp = (exp(-b) / y) * x
    else
        tmp = (x * (1.0d0 / 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 <= -3e+21) || !(b <= 1.95)) {
		tmp = (Math.exp(-b) / y) * x;
	} else {
		tmp = (x * (1.0 / a)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -3e+21) or not (b <= 1.95):
		tmp = (math.exp(-b) / y) * x
	else:
		tmp = (x * (1.0 / a)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -3e+21) || !(b <= 1.95))
		tmp = Float64(Float64(exp(Float64(-b)) / y) * x);
	else
		tmp = Float64(Float64(x * Float64(1.0 / a)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -3e+21) || ~((b <= 1.95)))
		tmp = (exp(-b) / y) * x;
	else
		tmp = (x * (1.0 / a)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -3e+21], N[Not[LessEqual[b, 1.95]], $MachinePrecision]], N[(N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision], N[(N[(x * N[(1.0 / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3e21 or 1.94999999999999996 < 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. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower-log.f64 N/A

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

      10. lower-log.f64 96.8

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

   5. Applied rewrites 96.8%

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

   6. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 83.2

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

   8. Applied rewrites 83.2%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 83.2

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

   10. Applied rewrites 83.2%

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

   if -3e21 < b < 1.94999999999999996

   1. Initial program 98.0%

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

   3. Taylor expanded in t around 0

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

      1. exp-diff N/A

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

      2. lower-/.f64 N/A

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

      3. +-commutative N/A

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

      4. fp-cancel-sign-sub-inv N/A

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

      5. metadata-eval N/A

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

      6. *-lft-identity N/A

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

      7. exp-diff N/A

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

      8. rem-exp-log N/A

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

      9. lower-/.f64 N/A

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

      10. *-commutative N/A

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

      11. exp-to-pow N/A

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

      12. lower-pow.f64 N/A

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

      13. lower-exp.f64 72.5

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

   5. Applied rewrites 72.5%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 39.3%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 41.5%

       \[\leadsto \frac{x \cdot \frac{\mathsf{fma}\left(-1, b, 1\right)}{a}}{y} \]

   12. Taylor expanded in b around 0

       \[\leadsto \frac{x \cdot \frac{1}{a}}{y} \]
   13. Step-by-step derivation

   14. Applied rewrites 41.5%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{+21} \lor \neg \left(b \leq 1.95\right):\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 39.7% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.3 \cdot 10^{+27}:\\ \;\;\;\;\frac{x \cdot \frac{\frac{b \cdot b - 1}{b + 1}}{-a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.3e+27)
   (/ (* x (/ (/ (- (* b b) 1.0) (+ b 1.0)) (- a))) y)
   (/ (* x (/ 1.0 a)) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.3e+27) {
		tmp = (x * ((((b * b) - 1.0) / (b + 1.0)) / -a)) / y;
	} else {
		tmp = (x * (1.0 / 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 <= (-2.3d+27)) then
        tmp = (x * ((((b * b) - 1.0d0) / (b + 1.0d0)) / -a)) / y
    else
        tmp = (x * (1.0d0 / 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 <= -2.3e+27) {
		tmp = (x * ((((b * b) - 1.0) / (b + 1.0)) / -a)) / y;
	} else {
		tmp = (x * (1.0 / a)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.3e+27:
		tmp = (x * ((((b * b) - 1.0) / (b + 1.0)) / -a)) / y
	else:
		tmp = (x * (1.0 / a)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.3e+27)
		tmp = Float64(Float64(x * Float64(Float64(Float64(Float64(b * b) - 1.0) / Float64(b + 1.0)) / Float64(-a))) / y);
	else
		tmp = Float64(Float64(x * Float64(1.0 / a)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.3e+27)
		tmp = (x * ((((b * b) - 1.0) / (b + 1.0)) / -a)) / y;
	else
		tmp = (x * (1.0 / a)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.3e+27], N[(N[(x * N[(N[(N[(N[(b * b), $MachinePrecision] - 1.0), $MachinePrecision] / N[(b + 1.0), $MachinePrecision]), $MachinePrecision] / (-a)), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[(1.0 / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.3000000000000001e27

   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 t around 0

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

      1. exp-diff N/A

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

      2. lower-/.f64 N/A

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

      3. +-commutative N/A

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

      4. fp-cancel-sign-sub-inv N/A

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

      5. metadata-eval N/A

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

      6. *-lft-identity N/A

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

      7. exp-diff N/A

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

      8. rem-exp-log N/A

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

      9. lower-/.f64 N/A

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

      10. *-commutative N/A

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

      11. exp-to-pow N/A

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

      12. lower-pow.f64 N/A

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

      13. lower-exp.f64 72.3

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

   5. Applied rewrites 72.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 85.4%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 57.1%

       \[\leadsto \frac{x \cdot \frac{\mathsf{fma}\left(-1, b, 1\right)}{a}}{y} \]
   12. Step-by-step derivation

   13. Applied rewrites 67.7%

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

   if -2.3000000000000001e27 < b

   1. Initial program 98.7%

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

   3. Taylor expanded in t around 0

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

      1. exp-diff N/A

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

      2. lower-/.f64 N/A

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

      3. +-commutative N/A

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

      4. fp-cancel-sign-sub-inv N/A

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

      5. metadata-eval N/A

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

      6. *-lft-identity N/A

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

      7. exp-diff N/A

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

      8. rem-exp-log N/A

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

      9. lower-/.f64 N/A

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

      10. *-commutative N/A

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

      11. exp-to-pow N/A

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

      12. lower-pow.f64 N/A

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

      13. lower-exp.f64 72.1

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

   5. Applied rewrites 72.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 53.7%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 29.5%

       \[\leadsto \frac{x \cdot \frac{\mathsf{fma}\left(-1, b, 1\right)}{a}}{y} \]

   12. Taylor expanded in b around 0

       \[\leadsto \frac{x \cdot \frac{1}{a}}{y} \]
   13. Step-by-step derivation

   14. Applied rewrites 32.6%

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

4. Final simplification 40.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.3 \cdot 10^{+27}:\\ \;\;\;\;\frac{x \cdot \frac{\frac{b \cdot b - 1}{b + 1}}{-a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 35.6% accurate, 8.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.9 \cdot 10^{+22}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(-1, b, 1\right)}{a}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.9e+22) (* (/ (/ (fma -1.0 b 1.0) a) y) x) (/ (* x (/ 1.0 a)) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.9e+22) {
		tmp = ((fma(-1.0, b, 1.0) / a) / y) * x;
	} else {
		tmp = (x * (1.0 / a)) / y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.9e+22)
		tmp = Float64(Float64(Float64(fma(-1.0, b, 1.0) / a) / y) * x);
	else
		tmp = Float64(Float64(x * Float64(1.0 / a)) / y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.9e+22], N[(N[(N[(N[(-1.0 * b + 1.0), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision], N[(N[(x * N[(1.0 / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.9000000000000002e22

   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 t around 0

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

      1. exp-diff N/A

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

      2. lower-/.f64 N/A

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

      3. +-commutative N/A

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

      4. fp-cancel-sign-sub-inv N/A

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

      5. metadata-eval N/A

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

      6. *-lft-identity N/A

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

      7. exp-diff N/A

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

      8. rem-exp-log N/A

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

      9. lower-/.f64 N/A

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

      10. *-commutative N/A

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

      11. exp-to-pow N/A

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

      12. lower-pow.f64 N/A

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

      13. lower-exp.f64 72.3

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

   5. Applied rewrites 72.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 85.4%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 57.1%

       \[\leadsto \frac{x \cdot \frac{\mathsf{fma}\left(-1, b, 1\right)}{a}}{y} \]
   12. Step-by-step derivation

       1. lift-/.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. associate-/l* N/A

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

       4. *-commutative N/A

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

       5. lower-*.f64 N/A

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

   13. Applied rewrites 58.9%

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

   if -1.9000000000000002e22 < b

   1. Initial program 98.7%

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

   3. Taylor expanded in t around 0

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

      1. exp-diff N/A

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

      2. lower-/.f64 N/A

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

      3. +-commutative N/A

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

      4. fp-cancel-sign-sub-inv N/A

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

      5. metadata-eval N/A

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

      6. *-lft-identity N/A

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

      7. exp-diff N/A

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

      8. rem-exp-log N/A

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

      9. lower-/.f64 N/A

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

      10. *-commutative N/A

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

      11. exp-to-pow N/A

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

      12. lower-pow.f64 N/A

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

      13. lower-exp.f64 72.1

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

   5. Applied rewrites 72.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 53.7%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 29.5%

       \[\leadsto \frac{x \cdot \frac{\mathsf{fma}\left(-1, b, 1\right)}{a}}{y} \]

   12. Taylor expanded in b around 0

       \[\leadsto \frac{x \cdot \frac{1}{a}}{y} \]
   13. Step-by-step derivation

   14. Applied rewrites 32.6%

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

Alternative 16: 35.4% accurate, 9.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.3 \cdot 10^{+27}:\\ \;\;\;\;\frac{x \cdot \frac{-b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.3e+27) (/ (* x (/ (- b) a)) y) (/ (* x (/ 1.0 a)) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.3e+27) {
		tmp = (x * (-b / a)) / y;
	} else {
		tmp = (x * (1.0 / 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 <= (-2.3d+27)) then
        tmp = (x * (-b / a)) / y
    else
        tmp = (x * (1.0d0 / 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 <= -2.3e+27) {
		tmp = (x * (-b / a)) / y;
	} else {
		tmp = (x * (1.0 / a)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.3e+27:
		tmp = (x * (-b / a)) / y
	else:
		tmp = (x * (1.0 / a)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.3e+27)
		tmp = Float64(Float64(x * Float64(Float64(-b) / a)) / y);
	else
		tmp = Float64(Float64(x * Float64(1.0 / a)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.3e+27)
		tmp = (x * (-b / a)) / y;
	else
		tmp = (x * (1.0 / a)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.3e+27], N[(N[(x * N[((-b) / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[(1.0 / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.3000000000000001e27

   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 t around 0

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

      1. exp-diff N/A

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

      2. lower-/.f64 N/A

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

      3. +-commutative N/A

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

      4. fp-cancel-sign-sub-inv N/A

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

      5. metadata-eval N/A

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

      6. *-lft-identity N/A

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

      7. exp-diff N/A

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

      8. rem-exp-log N/A

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

      9. lower-/.f64 N/A

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

      10. *-commutative N/A

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

      11. exp-to-pow N/A

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

      12. lower-pow.f64 N/A

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

      13. lower-exp.f64 72.3

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

   5. Applied rewrites 72.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 85.4%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 57.1%

       \[\leadsto \frac{x \cdot \frac{\mathsf{fma}\left(-1, b, 1\right)}{a}}{y} \]

   12. Taylor expanded in b around inf

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

   14. Applied rewrites 57.1%

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

   if -2.3000000000000001e27 < b

   1. Initial program 98.7%

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

   3. Taylor expanded in t around 0

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

      1. exp-diff N/A

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

      2. lower-/.f64 N/A

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

      3. +-commutative N/A

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

      4. fp-cancel-sign-sub-inv N/A

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

      5. metadata-eval N/A

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

      6. *-lft-identity N/A

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

      7. exp-diff N/A

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

      8. rem-exp-log N/A

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

      9. lower-/.f64 N/A

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

      10. *-commutative N/A

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

      11. exp-to-pow N/A

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

      12. lower-pow.f64 N/A

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

      13. lower-exp.f64 72.1

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

   5. Applied rewrites 72.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 53.7%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 29.5%

       \[\leadsto \frac{x \cdot \frac{\mathsf{fma}\left(-1, b, 1\right)}{a}}{y} \]

   12. Taylor expanded in b around 0

       \[\leadsto \frac{x \cdot \frac{1}{a}}{y} \]
   13. Step-by-step derivation

   14. Applied rewrites 32.6%

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

Alternative 17: 30.8% accurate, 12.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot \frac{1}{a}}{y} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ (* x (/ 1.0 a)) y))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x * (1.0 / a)) / 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 * (1.0d0 / a)) / y
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x * (1.0 / a)) / y;
}

Python

def code(x, y, z, t, a, b):
	return (x * (1.0 / a)) / y

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x * N[(1.0 / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]

Derivation

1. Initial program 99.0%

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

3. Taylor expanded in t around 0

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

   1. exp-diff N/A

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

   2. lower-/.f64 N/A

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

   3. +-commutative N/A

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

   4. fp-cancel-sign-sub-inv N/A

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

   5. metadata-eval N/A

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

   6. *-lft-identity N/A

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

   7. exp-diff N/A

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

   8. rem-exp-log N/A

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

   9. lower-/.f64 N/A

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

   10. *-commutative N/A

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

   11. exp-to-pow N/A

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

   12. lower-pow.f64 N/A

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

   13. lower-exp.f64 72.1

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

5. Applied rewrites 72.1%

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

6. Taylor expanded in y around 0

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

8. Applied rewrites 60.4%

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

9. Taylor expanded in b around 0

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

11. Applied rewrites 35.3%

    \[\leadsto \frac{x \cdot \frac{\mathsf{fma}\left(-1, b, 1\right)}{a}}{y} \]

12. Taylor expanded in b around 0

    \[\leadsto \frac{x \cdot \frac{1}{a}}{y} \]
13. Step-by-step derivation

14. Applied rewrites 32.6%

    \[\leadsto \frac{x \cdot \frac{1}{a}}{y} \]
15. Add Preprocessing

Developer Target 1: 72.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024329 
(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))