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

Percentage Accurate: 98.6% → 98.6%

Time: 15.0s

Alternatives: 20

Speedup: 1.0×

• 47.0% 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: 98.6% 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: 98.6% 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 99.1%

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

3. Final simplification 99.1%

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

Alternative 2: 49.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot e^{\left(y \cdot \log z + \left(t + -1\right) \cdot \log a\right) - b}}{y}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+273}:\\ \;\;\;\;\frac{\mathsf{fma}\left(b, \frac{x \cdot \mathsf{fma}\left(b, 0.5, -1\right)}{a}, \frac{x}{a}\right)}{y}\\ \mathbf{elif}\;t\_1 \leq 10^{+292}:\\ \;\;\;\;\frac{x}{y \cdot \left(\mathsf{fma}\left(b, \mathsf{fma}\left(b, -0.5, -1\right), -1\right) \cdot \left(-a\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(0.5 \cdot \left(y \cdot b\right)\right)\right)}\\ \end{array} \end{array} \]

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 (<= t_1 -1e+273)
     (/ (fma b (/ (* x (fma b 0.5 -1.0)) a) (/ x a)) y)
     (if (<= t_1 1e+292)
       (/ x (* y (* (fma b (fma b -0.5 -1.0) -1.0) (- a))))
       (/ x (* b (* a (* 0.5 (* y b)))))))))

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 <= -1e+273) {
		tmp = fma(b, ((x * fma(b, 0.5, -1.0)) / a), (x / a)) / y;
	} else if (t_1 <= 1e+292) {
		tmp = x / (y * (fma(b, fma(b, -0.5, -1.0), -1.0) * -a));
	} else {
		tmp = x / (b * (a * (0.5 * (y * b))));
	}
	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 <= -1e+273)
		tmp = Float64(fma(b, Float64(Float64(x * fma(b, 0.5, -1.0)) / a), Float64(x / a)) / y);
	elseif (t_1 <= 1e+292)
		tmp = Float64(x / Float64(y * Float64(fma(b, fma(b, -0.5, -1.0), -1.0) * Float64(-a))));
	else
		tmp = Float64(x / Float64(b * Float64(a * Float64(0.5 * Float64(y * b)))));
	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[LessEqual[t$95$1, -1e+273], N[(N[(b * N[(N[(x * N[(b * 0.5 + -1.0), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] + N[(x / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t$95$1, 1e+292], N[(x / N[(y * N[(N[(b * N[(b * -0.5 + -1.0), $MachinePrecision] + -1.0), $MachinePrecision] * (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(b * N[(a * N[(0.5 * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 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) < -9.99999999999999945e272

   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

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. exp-prod N/A

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

      8. lower-pow.f64 N/A

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

      9. rem-exp-log N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. lower-+.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-exp.f64 64.1

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

   5. Applied rewrites 64.1%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 51.5%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 31.9%

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

   12. Taylor expanded in y around 0

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

   14. Applied rewrites 39.7%

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

   if -9.99999999999999945e272 < (/.f64 (*.f64 x (exp.f64 (-.f64 (+.f64 (*.f64 y (log.f64 z)) (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))) b))) y) < 1e292

   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

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. exp-prod N/A

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

      8. lower-pow.f64 N/A

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

      9. rem-exp-log N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. lower-+.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-exp.f64 67.1

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

   5. Applied rewrites 67.1%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 59.5%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 50.6%

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

   12. Taylor expanded in y around -inf

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

   14. Applied rewrites 58.1%

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

   if 1e292 < (/.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 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 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. exp-prod N/A

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

      8. lower-pow.f64 N/A

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

      9. rem-exp-log N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. lower-+.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-exp.f64 58.0

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

   5. Applied rewrites 58.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 60.1%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 25.8%

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

   12. Taylor expanded in b around inf

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

   14. Applied rewrites 35.1%

       \[\leadsto \frac{x}{b \cdot \left(a \cdot \left(0.5 \cdot \color{blue}{\left(y \cdot b\right)}\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot e^{\left(y \cdot \log z + \left(t + -1\right) \cdot \log a\right) - b}}{y} \leq -1 \cdot 10^{+273}:\\ \;\;\;\;\frac{\mathsf{fma}\left(b, \frac{x \cdot \mathsf{fma}\left(b, 0.5, -1\right)}{a}, \frac{x}{a}\right)}{y}\\ \mathbf{elif}\;\frac{x \cdot e^{\left(y \cdot \log z + \left(t + -1\right) \cdot \log a\right) - b}}{y} \leq 10^{+292}:\\ \;\;\;\;\frac{x}{y \cdot \left(\mathsf{fma}\left(b, \mathsf{fma}\left(b, -0.5, -1\right), -1\right) \cdot \left(-a\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(0.5 \cdot \left(y \cdot b\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 47.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot e^{\left(y \cdot \log z + \left(t + -1\right) \cdot \log a\right) - b}}{y}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{0.5 \cdot \left(x \cdot \left(b \cdot b\right)\right)}{y \cdot a}\\ \mathbf{elif}\;t\_1 \leq 10^{+292}:\\ \;\;\;\;\frac{x}{y \cdot \left(\mathsf{fma}\left(b, \mathsf{fma}\left(b, -0.5, -1\right), -1\right) \cdot \left(-a\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(0.5 \cdot \left(y \cdot b\right)\right)\right)}\\ \end{array} \end{array} \]

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 (<= t_1 (- INFINITY))
     (/ (* 0.5 (* x (* b b))) (* y a))
     (if (<= t_1 1e+292)
       (/ x (* y (* (fma b (fma b -0.5 -1.0) -1.0) (- a))))
       (/ x (* b (* a (* 0.5 (* y b)))))))))

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 <= -((double) INFINITY)) {
		tmp = (0.5 * (x * (b * b))) / (y * a);
	} else if (t_1 <= 1e+292) {
		tmp = x / (y * (fma(b, fma(b, -0.5, -1.0), -1.0) * -a));
	} else {
		tmp = x / (b * (a * (0.5 * (y * b))));
	}
	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 <= Float64(-Inf))
		tmp = Float64(Float64(0.5 * Float64(x * Float64(b * b))) / Float64(y * a));
	elseif (t_1 <= 1e+292)
		tmp = Float64(x / Float64(y * Float64(fma(b, fma(b, -0.5, -1.0), -1.0) * Float64(-a))));
	else
		tmp = Float64(x / Float64(b * Float64(a * Float64(0.5 * Float64(y * b)))));
	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[LessEqual[t$95$1, (-Infinity)], N[(N[(0.5 * N[(x * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+292], N[(x / N[(y * N[(N[(b * N[(b * -0.5 + -1.0), $MachinePrecision] + -1.0), $MachinePrecision] * (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(b * N[(a * N[(0.5 * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 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) < -inf.0

   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 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. exp-prod N/A

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

      8. lower-pow.f64 N/A

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

      9. rem-exp-log N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. lower-+.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-exp.f64 63.1

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

   5. Applied rewrites 63.1%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 50.2%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 30.1%

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

   12. Taylor expanded in b around inf

       \[\leadsto \frac{1}{2} \cdot \frac{{b}^{2} \cdot x}{a \cdot \color{blue}{y}} \]
   13. Step-by-step derivation

   14. Applied rewrites 36.1%

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

   if -inf.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) < 1e292

   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 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. exp-prod N/A

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

      8. lower-pow.f64 N/A

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

      9. rem-exp-log N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. lower-+.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-exp.f64 67.6

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

   5. Applied rewrites 67.6%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 60.1%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 51.3%

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

   12. Taylor expanded in y around -inf

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

   14. Applied rewrites 58.7%

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

   if 1e292 < (/.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 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 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. exp-prod N/A

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

      8. lower-pow.f64 N/A

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

      9. rem-exp-log N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. lower-+.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-exp.f64 58.0

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

   5. Applied rewrites 58.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 60.1%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 25.8%

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

   12. Taylor expanded in b around inf

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

   14. Applied rewrites 35.1%

       \[\leadsto \frac{x}{b \cdot \left(a \cdot \left(0.5 \cdot \color{blue}{\left(y \cdot b\right)}\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 47.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot e^{\left(y \cdot \log z + \left(t + -1\right) \cdot \log a\right) - b}}{y} \leq -\infty:\\ \;\;\;\;\frac{0.5 \cdot \left(x \cdot \left(b \cdot b\right)\right)}{y \cdot a}\\ \mathbf{elif}\;\frac{x \cdot e^{\left(y \cdot \log z + \left(t + -1\right) \cdot \log a\right) - b}}{y} \leq 10^{+292}:\\ \;\;\;\;\frac{x}{y \cdot \left(\mathsf{fma}\left(b, \mathsf{fma}\left(b, -0.5, -1\right), -1\right) \cdot \left(-a\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(0.5 \cdot \left(y \cdot b\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 46.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot e^{\left(y \cdot \log z + \left(t + -1\right) \cdot \log a\right) - b}}{y}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{0.5 \cdot \left(x \cdot \left(b \cdot b\right)\right)}{y \cdot a}\\ \mathbf{elif}\;t\_1 \leq 10^{+292}:\\ \;\;\;\;\frac{x}{a \cdot \mathsf{fma}\left(b, \mathsf{fma}\left(y, b \cdot 0.5, y\right), y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(0.5 \cdot \left(y \cdot b\right)\right)\right)}\\ \end{array} \end{array} \]

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 (<= t_1 (- INFINITY))
     (/ (* 0.5 (* x (* b b))) (* y a))
     (if (<= t_1 1e+292)
       (/ x (* a (fma b (fma y (* b 0.5) y) y)))
       (/ x (* b (* a (* 0.5 (* y b)))))))))

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 <= -((double) INFINITY)) {
		tmp = (0.5 * (x * (b * b))) / (y * a);
	} else if (t_1 <= 1e+292) {
		tmp = x / (a * fma(b, fma(y, (b * 0.5), y), y));
	} else {
		tmp = x / (b * (a * (0.5 * (y * b))));
	}
	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 <= Float64(-Inf))
		tmp = Float64(Float64(0.5 * Float64(x * Float64(b * b))) / Float64(y * a));
	elseif (t_1 <= 1e+292)
		tmp = Float64(x / Float64(a * fma(b, fma(y, Float64(b * 0.5), y), y)));
	else
		tmp = Float64(x / Float64(b * Float64(a * Float64(0.5 * Float64(y * b)))));
	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[LessEqual[t$95$1, (-Infinity)], N[(N[(0.5 * N[(x * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+292], N[(x / N[(a * N[(b * N[(y * N[(b * 0.5), $MachinePrecision] + y), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(b * N[(a * N[(0.5 * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 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) < -inf.0

   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 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. exp-prod N/A

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

      8. lower-pow.f64 N/A

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

      9. rem-exp-log N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. lower-+.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-exp.f64 63.1

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

   5. Applied rewrites 63.1%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 50.2%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 30.1%

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

   12. Taylor expanded in b around inf

       \[\leadsto \frac{1}{2} \cdot \frac{{b}^{2} \cdot x}{a \cdot \color{blue}{y}} \]
   13. Step-by-step derivation

   14. Applied rewrites 36.1%

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

   if -inf.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) < 1e292

   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 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. exp-prod N/A

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

      8. lower-pow.f64 N/A

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

      9. rem-exp-log N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. lower-+.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-exp.f64 67.6

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

   5. Applied rewrites 67.6%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 60.1%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 53.6%

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

   if 1e292 < (/.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 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 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. exp-prod N/A

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

      8. lower-pow.f64 N/A

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

      9. rem-exp-log N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. lower-+.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-exp.f64 58.0

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

   5. Applied rewrites 58.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 60.1%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 25.8%

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

   12. Taylor expanded in b around inf

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

   14. Applied rewrites 35.1%

       \[\leadsto \frac{x}{b \cdot \left(a \cdot \left(0.5 \cdot \color{blue}{\left(y \cdot b\right)}\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 44.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot e^{\left(y \cdot \log z + \left(t + -1\right) \cdot \log a\right) - b}}{y} \leq -\infty:\\ \;\;\;\;\frac{0.5 \cdot \left(x \cdot \left(b \cdot b\right)\right)}{y \cdot a}\\ \mathbf{elif}\;\frac{x \cdot e^{\left(y \cdot \log z + \left(t + -1\right) \cdot \log a\right) - b}}{y} \leq 10^{+292}:\\ \;\;\;\;\frac{x}{a \cdot \mathsf{fma}\left(b, \mathsf{fma}\left(y, b \cdot 0.5, y\right), y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(0.5 \cdot \left(y \cdot b\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 37.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot e^{\left(y \cdot \log z + \left(t + -1\right) \cdot \log a\right) - b}}{y}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-296}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{x}{a \cdot \mathsf{fma}\left(y, b, y\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \end{array} \end{array} \]

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 (<= t_1 -5e-296)
     (/ x (* y a))
     (if (<= t_1 0.0) (/ x (* a (fma y b y))) (* x (/ 1.0 (* y a)))))))

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 <= -5e-296) {
		tmp = x / (y * a);
	} else if (t_1 <= 0.0) {
		tmp = x / (a * fma(y, b, y));
	} else {
		tmp = x * (1.0 / (y * a));
	}
	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 <= -5e-296)
		tmp = Float64(x / Float64(y * a));
	elseif (t_1 <= 0.0)
		tmp = Float64(x / Float64(a * fma(y, b, y)));
	else
		tmp = Float64(x * Float64(1.0 / Float64(y * a)));
	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[LessEqual[t$95$1, -5e-296], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(x / N[(a * N[(y * b + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 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) < -5.0000000000000003e-296

   1. Initial program 99.1%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. exp-prod N/A

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

      8. lower-pow.f64 N/A

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

      9. rem-exp-log N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. lower-+.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-exp.f64 67.9

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

   5. Applied rewrites 67.9%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 56.7%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 35.8%

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

   if -5.0000000000000003e-296 < (/.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 y around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. exp-prod N/A

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

      8. lower-pow.f64 N/A

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

      9. rem-exp-log N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. lower-+.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-exp.f64 63.8

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

   5. Applied rewrites 63.8%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 55.6%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 38.9%

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

   if 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 99.1%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. exp-prod N/A

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

      8. lower-pow.f64 N/A

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

      9. rem-exp-log N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. lower-+.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-exp.f64 60.2

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

   5. Applied rewrites 60.2%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 61.5%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 38.4%

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

   13. Applied rewrites 38.4%

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

4. Final simplification 37.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot e^{\left(y \cdot \log z + \left(t + -1\right) \cdot \log a\right) - b}}{y} \leq -5 \cdot 10^{-296}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{elif}\;\frac{x \cdot e^{\left(y \cdot \log z + \left(t + -1\right) \cdot \log a\right) - b}}{y} \leq 0:\\ \;\;\;\;\frac{x}{a \cdot \mathsf{fma}\left(y, b, y\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + -1\right) \cdot \log a\\ t_2 := \frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{if}\;t\_1 \leq -660:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -140:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;t\_1 \leq 2000:\\ \;\;\;\;x \cdot \frac{{z}^{y}}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (+ t -1.0) (log a))) (t_2 (/ (* x (pow a (+ t -1.0))) y)))
   (if (<= t_1 -660.0)
     t_2
     (if (<= t_1 -140.0)
       (/ x (* a (* y (exp b))))
       (if (<= t_1 2000.0) (* x (/ (pow z y) (* y a))) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + -1.0) * log(a);
	double t_2 = (x * pow(a, (t + -1.0))) / y;
	double tmp;
	if (t_1 <= -660.0) {
		tmp = t_2;
	} else if (t_1 <= -140.0) {
		tmp = x / (a * (y * exp(b)));
	} else if (t_1 <= 2000.0) {
		tmp = x * (pow(z, y) / (y * a));
	} 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 = (t + (-1.0d0)) * log(a)
    t_2 = (x * (a ** (t + (-1.0d0)))) / y
    if (t_1 <= (-660.0d0)) then
        tmp = t_2
    else if (t_1 <= (-140.0d0)) then
        tmp = x / (a * (y * exp(b)))
    else if (t_1 <= 2000.0d0) then
        tmp = x * ((z ** y) / (y * a))
    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 = (t + -1.0) * Math.log(a);
	double t_2 = (x * Math.pow(a, (t + -1.0))) / y;
	double tmp;
	if (t_1 <= -660.0) {
		tmp = t_2;
	} else if (t_1 <= -140.0) {
		tmp = x / (a * (y * Math.exp(b)));
	} else if (t_1 <= 2000.0) {
		tmp = x * (Math.pow(z, y) / (y * a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t + -1.0) * math.log(a)
	t_2 = (x * math.pow(a, (t + -1.0))) / y
	tmp = 0
	if t_1 <= -660.0:
		tmp = t_2
	elif t_1 <= -140.0:
		tmp = x / (a * (y * math.exp(b)))
	elif t_1 <= 2000.0:
		tmp = x * (math.pow(z, y) / (y * a))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t + -1.0) * log(a))
	t_2 = Float64(Float64(x * (a ^ Float64(t + -1.0))) / y)
	tmp = 0.0
	if (t_1 <= -660.0)
		tmp = t_2;
	elseif (t_1 <= -140.0)
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	elseif (t_1 <= 2000.0)
		tmp = Float64(x * Float64((z ^ y) / Float64(y * a)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t + -1.0) * log(a);
	t_2 = (x * (a ^ (t + -1.0))) / y;
	tmp = 0.0;
	if (t_1 <= -660.0)
		tmp = t_2;
	elseif (t_1 <= -140.0)
		tmp = x / (a * (y * exp(b)));
	elseif (t_1 <= 2000.0)
		tmp = x * ((z ^ y) / (y * a));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t$95$1, -660.0], t$95$2, If[LessEqual[t$95$1, -140.0], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2000.0], N[(x * N[(N[Power[z, y], $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -660 or 2e3 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))

   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 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. exp-prod N/A

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

      8. lower-pow.f64 N/A

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

      9. rem-exp-log N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. lower-+.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-exp.f64 67.3

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

   5. Applied rewrites 67.3%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 81.9%

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

   if -660 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -140

   1. Initial program 96.6%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. exp-prod N/A

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

      8. lower-pow.f64 N/A

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

      9. rem-exp-log N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. lower-+.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-exp.f64 66.9

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

   5. Applied rewrites 66.9%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 76.2%

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

   if -140 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 2e3

   1. Initial program 99.3%

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

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{x \cdot e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}{y}} \]
   4. 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. exp-diff N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. mul-1-neg N/A

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

      8. unsub-neg N/A

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

      9. exp-diff N/A

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

      10. lower-/.f64 N/A

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

      11. *-commutative N/A

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

      12. exp-to-pow N/A

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

      13. lower-pow.f64 N/A

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

      14. rem-exp-log N/A

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

      15. lower-*.f64 N/A

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

      16. lower-exp.f64 88.1

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

   5. Applied rewrites 88.1%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 81.3%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(t + -1\right) \cdot \log a \leq -660:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;\left(t + -1\right) \cdot \log a \leq -140:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;\left(t + -1\right) \cdot \log a \leq 2000:\\ \;\;\;\;x \cdot \frac{{z}^{y}}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + -1\right) \cdot \log a\\ t_2 := \frac{x \cdot e^{t \cdot \log a - b}}{y}\\ \mathbf{if}\;t\_1 \leq -620:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 1000:\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y \cdot e^{b}}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (+ t -1.0) (log a)))
        (t_2 (/ (* x (exp (- (* t (log a)) b))) y)))
   (if (<= t_1 -620.0)
     t_2
     (if (<= t_1 1000.0) (* x (/ (/ (pow z y) a) (* y (exp b)))) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + -1.0) * log(a);
	double t_2 = (x * exp(((t * log(a)) - b))) / y;
	double tmp;
	if (t_1 <= -620.0) {
		tmp = t_2;
	} else if (t_1 <= 1000.0) {
		tmp = x * ((pow(z, y) / a) / (y * exp(b)));
	} 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 = (t + (-1.0d0)) * log(a)
    t_2 = (x * exp(((t * log(a)) - b))) / y
    if (t_1 <= (-620.0d0)) then
        tmp = t_2
    else if (t_1 <= 1000.0d0) then
        tmp = x * (((z ** y) / a) / (y * exp(b)))
    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 = (t + -1.0) * Math.log(a);
	double t_2 = (x * Math.exp(((t * Math.log(a)) - b))) / y;
	double tmp;
	if (t_1 <= -620.0) {
		tmp = t_2;
	} else if (t_1 <= 1000.0) {
		tmp = x * ((Math.pow(z, y) / a) / (y * Math.exp(b)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t + -1.0) * math.log(a)
	t_2 = (x * math.exp(((t * math.log(a)) - b))) / y
	tmp = 0
	if t_1 <= -620.0:
		tmp = t_2
	elif t_1 <= 1000.0:
		tmp = x * ((math.pow(z, y) / a) / (y * math.exp(b)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t + -1.0) * log(a))
	t_2 = Float64(Float64(x * exp(Float64(Float64(t * log(a)) - b))) / y)
	tmp = 0.0
	if (t_1 <= -620.0)
		tmp = t_2;
	elseif (t_1 <= 1000.0)
		tmp = Float64(x * Float64(Float64((z ^ y) / a) / Float64(y * exp(b))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t + -1.0) * log(a);
	t_2 = (x * exp(((t * log(a)) - b))) / y;
	tmp = 0.0;
	if (t_1 <= -620.0)
		tmp = t_2;
	elseif (t_1 <= 1000.0)
		tmp = x * (((z ^ y) / a) / (y * exp(b)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[Exp[N[(N[(t * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t$95$1, -620.0], t$95$2, If[LessEqual[t$95$1, 1000.0], N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -620 or 1e3 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))

   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. rem-exp-log N/A

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

      4. lower-log.f64 N/A

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

      5. rem-exp-log 90.2

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

   5. Applied rewrites 90.2%

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

   if -620 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 1e3

   1. Initial program 98.2%

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

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{x \cdot e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}{y}} \]
   4. 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. exp-diff N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. mul-1-neg N/A

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

      8. unsub-neg N/A

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

      9. exp-diff N/A

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

      10. lower-/.f64 N/A

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

      11. *-commutative N/A

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

      12. exp-to-pow N/A

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

      13. lower-pow.f64 N/A

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

      14. rem-exp-log N/A

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

      15. lower-*.f64 N/A

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

      16. lower-exp.f64 88.5

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

   5. Applied rewrites 88.5%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(t + -1\right) \cdot \log a \leq -620:\\ \;\;\;\;\frac{x \cdot e^{t \cdot \log a - b}}{y}\\ \mathbf{elif}\;\left(t + -1\right) \cdot \log a \leq 1000:\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y \cdot e^{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{t \cdot \log a - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot e^{y \cdot \log z - b}}{y}\\ \mathbf{if}\;y \leq -1700:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{-210}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y \cdot e^{b}}\\ \mathbf{elif}\;y \leq 185000:\\ \;\;\;\;\frac{x \cdot e^{t \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (exp (- (* y (log z)) b))) y)))
   (if (<= y -1700.0)
     t_1
     (if (<= y -4.3e-210)
       (/ (* x (pow a (+ t -1.0))) (* y (exp b)))
       (if (<= y 185000.0) (/ (* x (exp (- (* t (log a)) b))) y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * exp(((y * log(z)) - b))) / y;
	double tmp;
	if (y <= -1700.0) {
		tmp = t_1;
	} else if (y <= -4.3e-210) {
		tmp = (x * pow(a, (t + -1.0))) / (y * exp(b));
	} else if (y <= 185000.0) {
		tmp = (x * exp(((t * log(a)) - b))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * exp(((y * log(z)) - b))) / y
    if (y <= (-1700.0d0)) then
        tmp = t_1
    else if (y <= (-4.3d-210)) then
        tmp = (x * (a ** (t + (-1.0d0)))) / (y * exp(b))
    else if (y <= 185000.0d0) then
        tmp = (x * exp(((t * log(a)) - b))) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * Math.exp(((y * Math.log(z)) - b))) / y;
	double tmp;
	if (y <= -1700.0) {
		tmp = t_1;
	} else if (y <= -4.3e-210) {
		tmp = (x * Math.pow(a, (t + -1.0))) / (y * Math.exp(b));
	} else if (y <= 185000.0) {
		tmp = (x * Math.exp(((t * Math.log(a)) - b))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * math.exp(((y * math.log(z)) - b))) / y
	tmp = 0
	if y <= -1700.0:
		tmp = t_1
	elif y <= -4.3e-210:
		tmp = (x * math.pow(a, (t + -1.0))) / (y * math.exp(b))
	elif y <= 185000.0:
		tmp = (x * math.exp(((t * math.log(a)) - b))) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * exp(Float64(Float64(y * log(z)) - b))) / y)
	tmp = 0.0
	if (y <= -1700.0)
		tmp = t_1;
	elseif (y <= -4.3e-210)
		tmp = Float64(Float64(x * (a ^ Float64(t + -1.0))) / Float64(y * exp(b)));
	elseif (y <= 185000.0)
		tmp = Float64(Float64(x * exp(Float64(Float64(t * log(a)) - b))) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * exp(((y * log(z)) - b))) / y;
	tmp = 0.0;
	if (y <= -1700.0)
		tmp = t_1;
	elseif (y <= -4.3e-210)
		tmp = (x * (a ^ (t + -1.0))) / (y * exp(b));
	elseif (y <= 185000.0)
		tmp = (x * exp(((t * log(a)) - b))) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[Exp[N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -1700.0], t$95$1, If[LessEqual[y, -4.3e-210], N[(N[(x * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 185000.0], N[(N[(x * N[Exp[N[(N[(t * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1700 or 185000 < 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 y around inf

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

      1. lower-*.f64 N/A

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

      2. lower-log.f64 91.7

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

   5. Applied rewrites 91.7%

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

   if -1700 < y < -4.3000000000000001e-210

   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 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. exp-prod N/A

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

      8. lower-pow.f64 N/A

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

      9. rem-exp-log N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. lower-+.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-exp.f64 92.3

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

   5. Applied rewrites 92.3%

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

   if -4.3000000000000001e-210 < y < 185000

   1. Initial program 98.2%

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

   3. Taylor expanded in t around 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. rem-exp-log N/A

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

      4. lower-log.f64 N/A

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

      5. rem-exp-log 87.7

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

   5. Applied rewrites 87.7%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1700:\\ \;\;\;\;\frac{x \cdot e^{y \cdot \log z - b}}{y}\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{-210}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y \cdot e^{b}}\\ \mathbf{elif}\;y \leq 185000:\\ \;\;\;\;\frac{x \cdot e^{t \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{y \cdot \log z - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 84.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot e^{y \cdot \log z - b}}{y}\\ \mathbf{if}\;y \leq -3 \cdot 10^{-6}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.35 \cdot 10^{-173}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;y \leq 185000:\\ \;\;\;\;\frac{x \cdot e^{t \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (exp (- (* y (log z)) b))) y)))
   (if (<= y -3e-6)
     t_1
     (if (<= y -2.35e-173)
       (/ (* x (pow a (+ t -1.0))) y)
       (if (<= y 185000.0) (/ (* x (exp (- (* t (log a)) b))) y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * exp(((y * log(z)) - b))) / y;
	double tmp;
	if (y <= -3e-6) {
		tmp = t_1;
	} else if (y <= -2.35e-173) {
		tmp = (x * pow(a, (t + -1.0))) / y;
	} else if (y <= 185000.0) {
		tmp = (x * exp(((t * log(a)) - b))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * exp(((y * log(z)) - b))) / y
    if (y <= (-3d-6)) then
        tmp = t_1
    else if (y <= (-2.35d-173)) then
        tmp = (x * (a ** (t + (-1.0d0)))) / y
    else if (y <= 185000.0d0) then
        tmp = (x * exp(((t * log(a)) - b))) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * Math.exp(((y * Math.log(z)) - b))) / y;
	double tmp;
	if (y <= -3e-6) {
		tmp = t_1;
	} else if (y <= -2.35e-173) {
		tmp = (x * Math.pow(a, (t + -1.0))) / y;
	} else if (y <= 185000.0) {
		tmp = (x * Math.exp(((t * Math.log(a)) - b))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * math.exp(((y * math.log(z)) - b))) / y
	tmp = 0
	if y <= -3e-6:
		tmp = t_1
	elif y <= -2.35e-173:
		tmp = (x * math.pow(a, (t + -1.0))) / y
	elif y <= 185000.0:
		tmp = (x * math.exp(((t * math.log(a)) - b))) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * exp(Float64(Float64(y * log(z)) - b))) / y)
	tmp = 0.0
	if (y <= -3e-6)
		tmp = t_1;
	elseif (y <= -2.35e-173)
		tmp = Float64(Float64(x * (a ^ Float64(t + -1.0))) / y);
	elseif (y <= 185000.0)
		tmp = Float64(Float64(x * exp(Float64(Float64(t * log(a)) - b))) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * exp(((y * log(z)) - b))) / y;
	tmp = 0.0;
	if (y <= -3e-6)
		tmp = t_1;
	elseif (y <= -2.35e-173)
		tmp = (x * (a ^ (t + -1.0))) / y;
	elseif (y <= 185000.0)
		tmp = (x * exp(((t * log(a)) - b))) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[Exp[N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -3e-6], t$95$1, If[LessEqual[y, -2.35e-173], N[(N[(x * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 185000.0], N[(N[(x * N[Exp[N[(N[(t * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.0000000000000001e-6 or 185000 < 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 y around inf

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

      1. lower-*.f64 N/A

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

      2. lower-log.f64 91.8

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

   5. Applied rewrites 91.8%

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

   if -3.0000000000000001e-6 < y < -2.35e-173

   1. Initial program 98.1%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. exp-prod N/A

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

      8. lower-pow.f64 N/A

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

      9. rem-exp-log N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. lower-+.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-exp.f64 90.3

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

   5. Applied rewrites 90.3%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 90.7%

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

   if -2.35e-173 < y < 185000

   1. Initial program 98.2%

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

   3. Taylor expanded in t around 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. rem-exp-log N/A

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

      4. lower-log.f64 N/A

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

      5. rem-exp-log 86.6

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

   5. Applied rewrites 86.6%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-6}:\\ \;\;\;\;\frac{x \cdot e^{y \cdot \log z - b}}{y}\\ \mathbf{elif}\;y \leq -2.35 \cdot 10^{-173}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;y \leq 185000:\\ \;\;\;\;\frac{x \cdot e^{t \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{y \cdot \log z - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 75.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot e^{y \cdot \log z}}{y}\\ \mathbf{if}\;y \leq -3.4 \cdot 10^{+39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-223}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;y \leq 2.3:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (exp (* y (log z)))) y)))
   (if (<= y -3.4e+39)
     t_1
     (if (<= y 9e-223)
       (/ (* x (pow a (+ t -1.0))) y)
       (if (<= y 2.3) (/ x (* a (* y (exp b)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * exp((y * log(z)))) / y;
	double tmp;
	if (y <= -3.4e+39) {
		tmp = t_1;
	} else if (y <= 9e-223) {
		tmp = (x * pow(a, (t + -1.0))) / y;
	} else if (y <= 2.3) {
		tmp = x / (a * (y * exp(b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * exp((y * log(z)))) / y
    if (y <= (-3.4d+39)) then
        tmp = t_1
    else if (y <= 9d-223) then
        tmp = (x * (a ** (t + (-1.0d0)))) / y
    else if (y <= 2.3d0) then
        tmp = x / (a * (y * exp(b)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * Math.exp((y * Math.log(z)))) / y;
	double tmp;
	if (y <= -3.4e+39) {
		tmp = t_1;
	} else if (y <= 9e-223) {
		tmp = (x * Math.pow(a, (t + -1.0))) / y;
	} else if (y <= 2.3) {
		tmp = x / (a * (y * Math.exp(b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * math.exp((y * math.log(z)))) / y
	tmp = 0
	if y <= -3.4e+39:
		tmp = t_1
	elif y <= 9e-223:
		tmp = (x * math.pow(a, (t + -1.0))) / y
	elif y <= 2.3:
		tmp = x / (a * (y * math.exp(b)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * exp(Float64(y * log(z)))) / y)
	tmp = 0.0
	if (y <= -3.4e+39)
		tmp = t_1;
	elseif (y <= 9e-223)
		tmp = Float64(Float64(x * (a ^ Float64(t + -1.0))) / y);
	elseif (y <= 2.3)
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * exp((y * log(z)))) / y;
	tmp = 0.0;
	if (y <= -3.4e+39)
		tmp = t_1;
	elseif (y <= 9e-223)
		tmp = (x * (a ^ (t + -1.0))) / y;
	elseif (y <= 2.3)
		tmp = x / (a * (y * exp(b)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[Exp[N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -3.4e+39], t$95$1, If[LessEqual[y, 9e-223], N[(N[(x * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 2.3], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.3999999999999999e39 or 2.2999999999999998 < 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 y around inf

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

      1. lower-*.f64 N/A

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

      2. lower-log.f64 90.9

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

   5. Applied rewrites 90.9%

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

   6. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower-log.f64 84.9

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

   8. Applied rewrites 84.9%

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

   if -3.3999999999999999e39 < y < 8.99999999999999935e-223

   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 y around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. exp-prod N/A

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

      8. lower-pow.f64 N/A

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

      9. rem-exp-log N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. lower-+.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-exp.f64 82.7

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

   5. Applied rewrites 82.7%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 81.0%

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

   if 8.99999999999999935e-223 < y < 2.2999999999999998

   1. Initial program 96.5%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. exp-prod N/A

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

      8. lower-pow.f64 N/A

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

      9. rem-exp-log N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. lower-+.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-exp.f64 75.0

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

   5. Applied rewrites 75.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 79.5%

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

Alternative 11: 81.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{if}\;t \leq -6 \cdot 10^{+94}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+103}:\\ \;\;\;\;\frac{x \cdot e^{y \cdot \log z - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (pow a (+ t -1.0))) y)))
   (if (<= t -6e+94)
     t_1
     (if (<= t 2.6e+103) (/ (* x (exp (- (* y (log z)) b))) y) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * pow(a, (t + -1.0))) / y;
	double tmp;
	if (t <= -6e+94) {
		tmp = t_1;
	} else if (t <= 2.6e+103) {
		tmp = (x * exp(((y * log(z)) - b))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * (a ** (t + (-1.0d0)))) / y
    if (t <= (-6d+94)) then
        tmp = t_1
    else if (t <= 2.6d+103) then
        tmp = (x * exp(((y * log(z)) - b))) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * Math.pow(a, (t + -1.0))) / y;
	double tmp;
	if (t <= -6e+94) {
		tmp = t_1;
	} else if (t <= 2.6e+103) {
		tmp = (x * Math.exp(((y * Math.log(z)) - b))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * math.pow(a, (t + -1.0))) / y
	tmp = 0
	if t <= -6e+94:
		tmp = t_1
	elif t <= 2.6e+103:
		tmp = (x * math.exp(((y * math.log(z)) - b))) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * (a ^ Float64(t + -1.0))) / y)
	tmp = 0.0
	if (t <= -6e+94)
		tmp = t_1;
	elseif (t <= 2.6e+103)
		tmp = Float64(Float64(x * exp(Float64(Float64(y * log(z)) - b))) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * (a ^ (t + -1.0))) / y;
	tmp = 0.0;
	if (t <= -6e+94)
		tmp = t_1;
	elseif (t <= 2.6e+103)
		tmp = (x * exp(((y * log(z)) - b))) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t, -6e+94], t$95$1, If[LessEqual[t, 2.6e+103], N[(N[(x * N[Exp[N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -6.0000000000000001e94 or 2.6000000000000002e103 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. exp-prod N/A

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

      8. lower-pow.f64 N/A

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

      9. rem-exp-log N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. lower-+.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-exp.f64 72.2

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

   5. Applied rewrites 72.2%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 91.3%

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

   if -6.0000000000000001e94 < t < 2.6000000000000002e103

   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 y around inf

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

      1. lower-*.f64 N/A

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

      2. lower-log.f64 82.4

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

   5. Applied rewrites 82.4%

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

Alternative 12: 58.1% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{e^{-b}}{y}\\ \mathbf{if}\;b \leq -5.4 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -8.4 \cdot 10^{-289}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{-91}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(0.5 \cdot \left(y \cdot b\right)\right)\right)}\\ \mathbf{elif}\;b \leq 27000000:\\ \;\;\;\;\frac{x}{\left(b \cdot b\right) \cdot \mathsf{fma}\left(a, \frac{y}{b} + \frac{y}{b \cdot b}, \left(y \cdot a\right) \cdot 0.5\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (exp (- b)) y))))
   (if (<= b -5.4e+19)
     t_1
     (if (<= b -8.4e-289)
       (* x (/ 1.0 (* y a)))
       (if (<= b 1.02e-91)
         (/ x (* b (* a (* 0.5 (* y b)))))
         (if (<= b 27000000.0)
           (/ x (* (* b b) (fma a (+ (/ y b) (/ y (* b b))) (* (* y a) 0.5))))
           t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (exp(-b) / y);
	double tmp;
	if (b <= -5.4e+19) {
		tmp = t_1;
	} else if (b <= -8.4e-289) {
		tmp = x * (1.0 / (y * a));
	} else if (b <= 1.02e-91) {
		tmp = x / (b * (a * (0.5 * (y * b))));
	} else if (b <= 27000000.0) {
		tmp = x / ((b * b) * fma(a, ((y / b) + (y / (b * b))), ((y * a) * 0.5)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(exp(Float64(-b)) / y))
	tmp = 0.0
	if (b <= -5.4e+19)
		tmp = t_1;
	elseif (b <= -8.4e-289)
		tmp = Float64(x * Float64(1.0 / Float64(y * a)));
	elseif (b <= 1.02e-91)
		tmp = Float64(x / Float64(b * Float64(a * Float64(0.5 * Float64(y * b)))));
	elseif (b <= 27000000.0)
		tmp = Float64(x / Float64(Float64(b * b) * fma(a, Float64(Float64(y / b) + Float64(y / Float64(b * b))), Float64(Float64(y * a) * 0.5))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.4e+19], t$95$1, If[LessEqual[b, -8.4e-289], N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.02e-91], N[(x / N[(b * N[(a * N[(0.5 * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 27000000.0], N[(x / N[(N[(b * b), $MachinePrecision] * N[(a * N[(N[(y / b), $MachinePrecision] + N[(y / N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y * a), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -5.4e19 or 2.7e7 < 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

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

      1. lower-*.f64 N/A

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

      2. lower-log.f64 89.3

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

   5. Applied rewrites 89.3%

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

   6. Taylor expanded in b around inf

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

      1. neg-mul-1 N/A

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

      2. lower-neg.f64 77.9

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

   8. Applied rewrites 77.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 77.9

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

   10. Applied rewrites 77.9%

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

   if -5.4e19 < b < -8.3999999999999991e-289

   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 y around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. exp-prod N/A

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

      8. lower-pow.f64 N/A

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

      9. rem-exp-log N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. lower-+.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-exp.f64 66.0

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

   5. Applied rewrites 66.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 39.4%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 40.7%

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

   13. Applied rewrites 40.8%

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

   if -8.3999999999999991e-289 < b < 1.01999999999999994e-91

   1. Initial program 97.2%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. exp-prod N/A

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

      8. lower-pow.f64 N/A

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

      9. rem-exp-log N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. lower-+.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-exp.f64 66.0

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

   5. Applied rewrites 66.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 34.2%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 34.2%

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

   12. Taylor expanded in b around inf

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

   14. Applied rewrites 52.9%

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

   if 1.01999999999999994e-91 < b < 2.7e7

   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 y around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. exp-prod N/A

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

      8. lower-pow.f64 N/A

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

      9. rem-exp-log N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. lower-+.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-exp.f64 80.4

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

   5. Applied rewrites 80.4%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 46.0%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 50.0%

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

   12. Taylor expanded in b around inf

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

   14. Applied rewrites 57.5%

       \[\leadsto \frac{x}{\left(b \cdot b\right) \cdot \mathsf{fma}\left(a, \frac{y}{b} + \color{blue}{\frac{y}{b \cdot b}}, 0.5 \cdot \left(a \cdot y\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.4 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \frac{e^{-b}}{y}\\ \mathbf{elif}\;b \leq -8.4 \cdot 10^{-289}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{-91}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(0.5 \cdot \left(y \cdot b\right)\right)\right)}\\ \mathbf{elif}\;b \leq 27000000:\\ \;\;\;\;\frac{x}{\left(b \cdot b\right) \cdot \mathsf{fma}\left(a, \frac{y}{b} + \frac{y}{b \cdot b}, \left(y \cdot a\right) \cdot 0.5\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{e^{-b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 74.6% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{if}\;t \leq -9.2 \cdot 10^{+91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6.7:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (pow a (+ t -1.0))) y)))
   (if (<= t -9.2e+91) t_1 (if (<= t 6.7) (/ x (* a (* y (exp b)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * pow(a, (t + -1.0))) / y;
	double tmp;
	if (t <= -9.2e+91) {
		tmp = t_1;
	} else if (t <= 6.7) {
		tmp = x / (a * (y * exp(b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * (a ** (t + (-1.0d0)))) / y
    if (t <= (-9.2d+91)) then
        tmp = t_1
    else if (t <= 6.7d0) then
        tmp = x / (a * (y * exp(b)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * Math.pow(a, (t + -1.0))) / y;
	double tmp;
	if (t <= -9.2e+91) {
		tmp = t_1;
	} else if (t <= 6.7) {
		tmp = x / (a * (y * Math.exp(b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * math.pow(a, (t + -1.0))) / y
	tmp = 0
	if t <= -9.2e+91:
		tmp = t_1
	elif t <= 6.7:
		tmp = x / (a * (y * math.exp(b)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * (a ^ Float64(t + -1.0))) / y)
	tmp = 0.0
	if (t <= -9.2e+91)
		tmp = t_1;
	elseif (t <= 6.7)
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * (a ^ (t + -1.0))) / y;
	tmp = 0.0;
	if (t <= -9.2e+91)
		tmp = t_1;
	elseif (t <= 6.7)
		tmp = x / (a * (y * exp(b)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t, -9.2e+91], t$95$1, If[LessEqual[t, 6.7], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -9.19999999999999965e91 or 6.70000000000000018 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. exp-prod N/A

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

      8. lower-pow.f64 N/A

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

      9. rem-exp-log N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. lower-+.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-exp.f64 71.5

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

   5. Applied rewrites 71.5%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 86.9%

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

   if -9.19999999999999965e91 < t < 6.70000000000000018

   1. Initial program 98.5%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. exp-prod N/A

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

      8. lower-pow.f64 N/A

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

      9. rem-exp-log N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. lower-+.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-exp.f64 59.2

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

   5. Applied rewrites 59.2%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 67.6%

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

Alternative 14: 75.1% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{e^{-b}}{y}\\ \mathbf{if}\;b \leq -6.7 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1300000000:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (exp (- b)) y))))
   (if (<= b -6.7e+19)
     t_1
     (if (<= b 1300000000.0) (/ (* 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 = x * (exp(-b) / y);
	double tmp;
	if (b <= -6.7e+19) {
		tmp = t_1;
	} else if (b <= 1300000000.0) {
		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 = x * (exp(-b) / y)
    if (b <= (-6.7d+19)) then
        tmp = t_1
    else if (b <= 1300000000.0d0) 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 = x * (Math.exp(-b) / y);
	double tmp;
	if (b <= -6.7e+19) {
		tmp = t_1;
	} else if (b <= 1300000000.0) {
		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 = x * (math.exp(-b) / y)
	tmp = 0
	if b <= -6.7e+19:
		tmp = t_1
	elif b <= 1300000000.0:
		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(x * Float64(exp(Float64(-b)) / y))
	tmp = 0.0
	if (b <= -6.7e+19)
		tmp = t_1;
	elseif (b <= 1300000000.0)
		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 = x * (exp(-b) / y);
	tmp = 0.0;
	if (b <= -6.7e+19)
		tmp = t_1;
	elseif (b <= 1300000000.0)
		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[(x * N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.7e+19], t$95$1, If[LessEqual[b, 1300000000.0], N[(N[(x * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -6.7e19 or 1.3e9 < 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

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

      1. lower-*.f64 N/A

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

      2. lower-log.f64 89.3

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

   5. Applied rewrites 89.3%

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

   6. Taylor expanded in b around inf

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

      1. neg-mul-1 N/A

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

      2. lower-neg.f64 77.9

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

   8. Applied rewrites 77.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 77.9

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

   10. Applied rewrites 77.9%

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

   if -6.7e19 < b < 1.3e9

   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

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. exp-prod N/A

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

      8. lower-pow.f64 N/A

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

      9. rem-exp-log N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. lower-+.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-exp.f64 68.7

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

   5. Applied rewrites 68.7%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 71.7%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.7 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \frac{e^{-b}}{y}\\ \mathbf{elif}\;b \leq 1300000000:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{e^{-b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 72.5% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{e^{-b}}{y}\\ \mathbf{if}\;b \leq -6.6 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1100000000:\\ \;\;\;\;{a}^{\left(t + -1\right)} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (exp (- b)) y))))
   (if (<= b -6.6e+19)
     t_1
     (if (<= b 1100000000.0) (* (pow a (+ t -1.0)) (/ x y)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (exp(-b) / y);
	double tmp;
	if (b <= -6.6e+19) {
		tmp = t_1;
	} else if (b <= 1100000000.0) {
		tmp = pow(a, (t + -1.0)) * (x / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (exp(-b) / y)
    if (b <= (-6.6d+19)) then
        tmp = t_1
    else if (b <= 1100000000.0d0) then
        tmp = (a ** (t + (-1.0d0))) * (x / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (Math.exp(-b) / y);
	double tmp;
	if (b <= -6.6e+19) {
		tmp = t_1;
	} else if (b <= 1100000000.0) {
		tmp = Math.pow(a, (t + -1.0)) * (x / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (math.exp(-b) / y)
	tmp = 0
	if b <= -6.6e+19:
		tmp = t_1
	elif b <= 1100000000.0:
		tmp = math.pow(a, (t + -1.0)) * (x / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(exp(Float64(-b)) / y))
	tmp = 0.0
	if (b <= -6.6e+19)
		tmp = t_1;
	elseif (b <= 1100000000.0)
		tmp = Float64((a ^ Float64(t + -1.0)) * Float64(x / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (exp(-b) / y);
	tmp = 0.0;
	if (b <= -6.6e+19)
		tmp = t_1;
	elseif (b <= 1100000000.0)
		tmp = (a ^ (t + -1.0)) * (x / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.6e+19], t$95$1, If[LessEqual[b, 1100000000.0], N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -6.6e19 or 1.1e9 < 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

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

      1. lower-*.f64 N/A

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

      2. lower-log.f64 89.3

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

   5. Applied rewrites 89.3%

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

   6. Taylor expanded in b around inf

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

      1. neg-mul-1 N/A

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

      2. lower-neg.f64 77.9

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

   8. Applied rewrites 77.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 77.9

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

   10. Applied rewrites 77.9%

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

   if -6.6e19 < b < 1.1e9

   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

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. exp-prod N/A

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

      8. lower-pow.f64 N/A

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

      9. rem-exp-log N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. lower-+.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-exp.f64 68.7

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

   5. Applied rewrites 68.7%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 39.2%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 62.9%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.6 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \frac{e^{-b}}{y}\\ \mathbf{elif}\;b \leq 1100000000:\\ \;\;\;\;{a}^{\left(t + -1\right)} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{e^{-b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 43.2% accurate, 8.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.16 \cdot 10^{-153}:\\ \;\;\;\;\frac{0.5 \cdot \left(x \cdot \left(b \cdot b\right)\right)}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(0.5 \cdot \left(y \cdot b\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.16e-153)
   (/ (* 0.5 (* x (* b b))) (* y a))
   (/ x (* b (* a (* 0.5 (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.16e-153) {
		tmp = (0.5 * (x * (b * b))) / (y * a);
	} else {
		tmp = x / (b * (a * (0.5 * (y * b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.16d-153)) then
        tmp = (0.5d0 * (x * (b * b))) / (y * a)
    else
        tmp = x / (b * (a * (0.5d0 * (y * b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.16e-153) {
		tmp = (0.5 * (x * (b * b))) / (y * a);
	} else {
		tmp = x / (b * (a * (0.5 * (y * b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.16e-153:
		tmp = (0.5 * (x * (b * b))) / (y * a)
	else:
		tmp = x / (b * (a * (0.5 * (y * b))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.16e-153)
		tmp = Float64(Float64(0.5 * Float64(x * Float64(b * b))) / Float64(y * a));
	else
		tmp = Float64(x / Float64(b * Float64(a * Float64(0.5 * Float64(y * b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.16e-153)
		tmp = (0.5 * (x * (b * b))) / (y * a);
	else
		tmp = x / (b * (a * (0.5 * (y * b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.16e-153], N[(N[(0.5 * N[(x * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(x / N[(b * N[(a * N[(0.5 * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.16e-153

   1. Initial program 99.5%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. exp-prod N/A

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

      8. lower-pow.f64 N/A

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

      9. rem-exp-log N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. lower-+.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-exp.f64 62.2

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

   5. Applied rewrites 62.2%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 60.1%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 40.4%

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

   12. Taylor expanded in b around inf

       \[\leadsto \frac{1}{2} \cdot \frac{{b}^{2} \cdot x}{a \cdot \color{blue}{y}} \]
   13. Step-by-step derivation

   14. Applied rewrites 44.4%

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

   if -1.16e-153 < b

   1. Initial program 98.9%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. exp-prod N/A

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

      8. lower-pow.f64 N/A

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

      9. rem-exp-log N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. lower-+.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-exp.f64 65.5

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

   5. Applied rewrites 65.5%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 55.7%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 44.4%

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

   12. Taylor expanded in b around inf

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

   14. Applied rewrites 45.3%

       \[\leadsto \frac{x}{b \cdot \left(a \cdot \left(0.5 \cdot \color{blue}{\left(y \cdot b\right)}\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 45.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.16 \cdot 10^{-153}:\\ \;\;\;\;\frac{0.5 \cdot \left(x \cdot \left(b \cdot b\right)\right)}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(0.5 \cdot \left(y \cdot b\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 42.2% accurate, 8.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.4 \cdot 10^{-158}:\\ \;\;\;\;\frac{0.5 \cdot \left(x \cdot \left(b \cdot b\right)\right)}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \mathsf{fma}\left(y, b, y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.4e-158)
   (/ (* 0.5 (* x (* b b))) (* y a))
   (/ x (* a (fma y b y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.4e-158) {
		tmp = (0.5 * (x * (b * b))) / (y * a);
	} else {
		tmp = x / (a * fma(y, b, y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.4e-158)
		tmp = Float64(Float64(0.5 * Float64(x * Float64(b * b))) / Float64(y * a));
	else
		tmp = Float64(x / Float64(a * fma(y, b, y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.4e-158], N[(N[(0.5 * N[(x * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * b + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.3999999999999999e-158

   1. Initial program 99.5%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. exp-prod N/A

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

      8. lower-pow.f64 N/A

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

      9. rem-exp-log N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. lower-+.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-exp.f64 61.9

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

   5. Applied rewrites 61.9%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 58.9%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 39.6%

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

   12. Taylor expanded in b around inf

       \[\leadsto \frac{1}{2} \cdot \frac{{b}^{2} \cdot x}{a \cdot \color{blue}{y}} \]
   13. Step-by-step derivation

   14. Applied rewrites 43.5%

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

   if -3.3999999999999999e-158 < b

   1. Initial program 98.9%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. exp-prod N/A

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

      8. lower-pow.f64 N/A

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

      9. rem-exp-log N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. lower-+.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-exp.f64 65.7

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

   5. Applied rewrites 65.7%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 56.4%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 41.5%

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

4. Final simplification 42.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.4 \cdot 10^{-158}:\\ \;\;\;\;\frac{0.5 \cdot \left(x \cdot \left(b \cdot b\right)\right)}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \mathsf{fma}\left(y, b, y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 35.5% accurate, 9.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.4 \cdot 10^{+19}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \mathsf{fma}\left(y, b, y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -5.4e+19) (* (/ x y) (/ 1.0 a)) (/ x (* a (fma y b y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5.4e+19) {
		tmp = (x / y) * (1.0 / a);
	} else {
		tmp = x / (a * fma(y, b, y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -5.4e+19)
		tmp = Float64(Float64(x / y) * Float64(1.0 / a));
	else
		tmp = Float64(x / Float64(a * fma(y, b, y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -5.4e+19], N[(N[(x / y), $MachinePrecision] * N[(1.0 / a), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * b + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5.4e19

   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 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. exp-prod N/A

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

      8. lower-pow.f64 N/A

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

      9. rem-exp-log N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. lower-+.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-exp.f64 63.8

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

   5. Applied rewrites 63.8%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 80.3%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 46.8%

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

   12. Taylor expanded in t around 0

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

   14. Applied rewrites 27.5%

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

   if -5.4e19 < b

   1. Initial program 98.9%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. exp-prod N/A

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

      8. lower-pow.f64 N/A

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

      9. rem-exp-log N/A

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

      10. sub-neg N/A

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

      11. metadata-eval N/A

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

      12. lower-+.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-exp.f64 64.4

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

   5. Applied rewrites 64.4%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 51.0%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 39.6%

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

4. Final simplification 37.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.4 \cdot 10^{+19}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \mathsf{fma}\left(y, b, y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 30.8% accurate, 15.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.1%

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

3. Taylor expanded in y around 0

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

   1. *-commutative N/A

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

   2. exp-diff N/A

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

   3. associate-*l/ N/A

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

   4. associate-/l/ N/A

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

   5. lower-/.f64 N/A

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

   6. lower-*.f64 N/A

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

   7. exp-prod N/A

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

   8. lower-pow.f64 N/A

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

   9. rem-exp-log N/A

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

   10. sub-neg N/A

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

   11. metadata-eval N/A

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

   12. lower-+.f64 N/A

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

   13. lower-*.f64 N/A

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

   14. lower-exp.f64 64.3

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

5. Applied rewrites 64.3%

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

6. Taylor expanded in t around 0

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

8. Applied rewrites 57.3%

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

9. Taylor expanded in b around 0

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

11. Applied rewrites 31.9%

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

13. Applied rewrites 32.3%

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

14. Final simplification 32.3%

    \[\leadsto x \cdot \frac{1}{y \cdot a} \]
15. Add Preprocessing

Alternative 20: 30.7% accurate, 19.8× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y \cdot a} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ x (* y a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x / (y * a);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x / (y * a)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x / (y * a);
}

Python

def code(x, y, z, t, a, b):
	return x / (y * a)

Julia

function code(x, y, z, t, a, b)
	return Float64(x / Float64(y * a))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x / (y * a);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.1%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Add Preprocessing

3. Taylor expanded in y around 0

   \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
4. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \frac{\color{blue}{e^{\log a \cdot \left(t - 1\right) - b} \cdot x}}{y} \]

   2. exp-diff N/A

      \[\leadsto \frac{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}} \cdot x}{y} \]

   3. associate-*l/ N/A

      \[\leadsto \frac{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)} \cdot x}{e^{b}}}}{y} \]

   4. associate-/l/ N/A

      \[\leadsto \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)} \cdot x}{y \cdot e^{b}}} \]

   5. lower-/.f64 N/A

      \[\leadsto \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)} \cdot x}{y \cdot e^{b}}} \]

   6. lower-*.f64 N/A

      \[\leadsto \frac{\color{blue}{e^{\log a \cdot \left(t - 1\right)} \cdot x}}{y \cdot e^{b}} \]

   7. exp-prod N/A

      \[\leadsto \frac{\color{blue}{{\left(e^{\log a}\right)}^{\left(t - 1\right)}} \cdot x}{y \cdot e^{b}} \]

   8. lower-pow.f64 N/A

      \[\leadsto \frac{\color{blue}{{\left(e^{\log a}\right)}^{\left(t - 1\right)}} \cdot x}{y \cdot e^{b}} \]

   9. rem-exp-log N/A

      \[\leadsto \frac{{\color{blue}{a}}^{\left(t - 1\right)} \cdot x}{y \cdot e^{b}} \]

   10. sub-neg N/A

       \[\leadsto \frac{{a}^{\color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}} \cdot x}{y \cdot e^{b}} \]

   11. metadata-eval N/A

       \[\leadsto \frac{{a}^{\left(t + \color{blue}{-1}\right)} \cdot x}{y \cdot e^{b}} \]

   12. lower-+.f64 N/A

       \[\leadsto \frac{{a}^{\color{blue}{\left(t + -1\right)}} \cdot x}{y \cdot e^{b}} \]

   13. lower-*.f64 N/A

       \[\leadsto \frac{{a}^{\left(t + -1\right)} \cdot x}{\color{blue}{y \cdot e^{b}}} \]

   14. lower-exp.f64 64.3

       \[\leadsto \frac{{a}^{\left(t + -1\right)} \cdot x}{y \cdot \color{blue}{e^{b}}} \]

5. Applied rewrites 64.3%

   \[\leadsto \color{blue}{\frac{{a}^{\left(t + -1\right)} \cdot x}{y \cdot e^{b}}} \]

6. Taylor expanded in t around 0

   \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y \cdot e^{b}\right)}} \]
7. Step-by-step derivation

8. Applied rewrites 57.3%

   \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y \cdot e^{b}\right)}} \]

9. Taylor expanded in b around 0

   \[\leadsto \frac{x}{a \cdot y} \]
10. Step-by-step derivation

11. Applied rewrites 31.9%

    \[\leadsto \frac{x}{y \cdot a} \]
12. Add Preprocessing

Developer Target 1: 71.4% 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 2024221 
(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))