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

Percentage Accurate: 98.4% → 98.4%

Time: 10.2s

Alternatives: 21

Speedup: 1.0×

• 46.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.8%

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

Alternative 2: 51.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-117} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(\frac{x}{a} \cdot 0.5\right) \cdot b - \frac{x}{a}, b, \frac{x}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(b \cdot a, 0.16666666666666666, 0.5 \cdot a\right), b, a\right), b, a\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)))
   (if (or (<= t_1 -5e-117) (not (<= t_1 0.0)))
     (/ (fma (- (* (* (/ x a) 0.5) b) (/ x a)) b (/ x a)) y)
     (/
      (/ x (fma (fma (fma (* b a) 0.16666666666666666 (* 0.5 a)) b a) b a))
      y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * exp((((y * log(z)) + ((t - 1.0) * log(a))) - b))) / y;
	double tmp;
	if ((t_1 <= -5e-117) || !(t_1 <= 0.0)) {
		tmp = fma(((((x / a) * 0.5) * b) - (x / a)), b, (x / a)) / y;
	} else {
		tmp = (x / fma(fma(fma((b * a), 0.16666666666666666, (0.5 * a)), b, a), b, a)) / y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) + Float64(Float64(t - 1.0) * log(a))) - b))) / y)
	tmp = 0.0
	if ((t_1 <= -5e-117) || !(t_1 <= 0.0))
		tmp = Float64(fma(Float64(Float64(Float64(Float64(x / a) * 0.5) * b) - Float64(x / a)), b, Float64(x / a)) / y);
	else
		tmp = Float64(Float64(x / fma(fma(fma(Float64(b * a), 0.16666666666666666, Float64(0.5 * a)), b, a), b, a)) / y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] + N[(N[(t - 1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-117], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(N[(N[(N[(N[(x / a), $MachinePrecision] * 0.5), $MachinePrecision] * b), $MachinePrecision] - N[(x / a), $MachinePrecision]), $MachinePrecision] * b + N[(x / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / N[(N[(N[(N[(b * a), $MachinePrecision] * 0.16666666666666666 + N[(0.5 * a), $MachinePrecision]), $MachinePrecision] * b + a), $MachinePrecision] * b + a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (exp.f64 (-.f64 (+.f64 (*.f64 y (log.f64 z)) (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))) b))) y) < -5e-117 or 0.0 < (/.f64 (*.f64 x (exp.f64 (-.f64 (+.f64 (*.f64 y (log.f64 z)) (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))) b))) y)

   1. Initial program 98.6%

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

   3. Taylor expanded in y around 0

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

      1. exp-diff N/A

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

      2. associate-*r/ N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. exp-to-pow N/A

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

      6. lower-pow.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-exp.f64 63.1

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

   5. Applied rewrites 63.1%

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

   7. Applied rewrites 68.8%

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

   8. Taylor expanded in t around 0

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

   10. Applied rewrites 59.0%

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

   11. Taylor expanded in b around 0

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

   13. Applied rewrites 46.4%

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

   if -5e-117 < (/.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 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

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

      1. exp-diff N/A

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

      2. associate-*r/ N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. exp-to-pow N/A

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

      6. lower-pow.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-exp.f64 62.6

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

   5. Applied rewrites 62.6%

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

   7. Applied rewrites 66.5%

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

   8. Taylor expanded in t around 0

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

   10. Applied rewrites 65.2%

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

   11. Taylor expanded in b around 0

       \[\leadsto \frac{\frac{x}{a + b \cdot \color{blue}{\left(a + b \cdot \left(\frac{1}{6} \cdot \left(a \cdot b\right) + \frac{1}{2} \cdot a\right)\right)}}}{y} \]
   12. Step-by-step derivation

   13. Applied rewrites 63.1%

       \[\leadsto \frac{\frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(b \cdot a, 0.16666666666666666, 0.5 \cdot a\right), b, a\right), b, a\right)}}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \leq -5 \cdot 10^{-117} \lor \neg \left(\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \leq 0\right):\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(\frac{x}{a} \cdot 0.5\right) \cdot b - \frac{x}{a}, b, \frac{x}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(b \cdot a, 0.16666666666666666, 0.5 \cdot a\right), b, a\right), b, a\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 48.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(-x, b, x\right)}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(b \cdot a, 0.16666666666666666, 0.5 \cdot a\right), b, a\right), b, a\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 0.0)))
     (/ (/ (fma (- x) b x) a) y)
     (/
      (/ x (fma (fma (fma (* b a) 0.16666666666666666 (* 0.5 a)) b a) b a))
      y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * exp((((y * log(z)) + ((t - 1.0) * log(a))) - b))) / y;
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 0.0)) {
		tmp = (fma(-x, b, x) / a) / y;
	} else {
		tmp = (x / fma(fma(fma((b * a), 0.16666666666666666, (0.5 * a)), b, a), b, a)) / y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) + Float64(Float64(t - 1.0) * log(a))) - b))) / y)
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 0.0))
		tmp = Float64(Float64(fma(Float64(-x), b, x) / a) / y);
	else
		tmp = Float64(Float64(x / fma(fma(fma(Float64(b * a), 0.16666666666666666, Float64(0.5 * a)), b, a), b, a)) / y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] + N[(N[(t - 1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(N[((-x) * b + x), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / N[(N[(N[(N[(b * a), $MachinePrecision] * 0.16666666666666666 + N[(0.5 * a), $MachinePrecision]), $MachinePrecision] * b + a), $MachinePrecision] * b + a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (exp.f64 (-.f64 (+.f64 (*.f64 y (log.f64 z)) (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))) b))) y) < -inf.0 or 0.0 < (/.f64 (*.f64 x (exp.f64 (-.f64 (+.f64 (*.f64 y (log.f64 z)) (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))) b))) y)

   1. Initial program 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

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

      1. exp-diff N/A

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

      2. associate-*r/ N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. exp-to-pow N/A

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

      6. lower-pow.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-exp.f64 60.8

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

   5. Applied rewrites 60.8%

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

   7. Applied rewrites 66.7%

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

   8. Taylor expanded in t around 0

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

   10. Applied rewrites 56.6%

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

   11. Taylor expanded in b around 0

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

   13. Applied rewrites 34.6%

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

   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) < 0.0

   1. Initial program 98.4%

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

   3. Taylor expanded in y around 0

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

      1. exp-diff N/A

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

      2. associate-*r/ N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. exp-to-pow N/A

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

      6. lower-pow.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-exp.f64 64.7

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

   5. Applied rewrites 64.7%

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

   7. Applied rewrites 68.5%

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

   8. Taylor expanded in t around 0

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

   10. Applied rewrites 66.8%

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

   11. Taylor expanded in b around 0

       \[\leadsto \frac{\frac{x}{a + b \cdot \color{blue}{\left(a + b \cdot \left(\frac{1}{6} \cdot \left(a \cdot b\right) + \frac{1}{2} \cdot a\right)\right)}}}{y} \]
   12. Step-by-step derivation

   13. Applied rewrites 64.9%

       \[\leadsto \frac{\frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(b \cdot a, 0.16666666666666666, 0.5 \cdot a\right), b, a\right), b, a\right)}}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 50.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \leq -\infty \lor \neg \left(\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \leq 0\right):\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(-x, b, x\right)}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(b \cdot a, 0.16666666666666666, 0.5 \cdot a\right), b, a\right), b, a\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 80.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - 1\right) \cdot \log a\\ t_2 := \frac{x \cdot e^{\log a \cdot t - b}}{y}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+31}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -430:\\ \;\;\;\;\frac{\frac{x}{e^{b} \cdot a}}{y}\\ \mathbf{elif}\;t\_1 \leq 700:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- t 1.0) (log a)))
        (t_2 (/ (* x (exp (- (* (log a) t) b))) y)))
   (if (<= t_1 -2e+31)
     t_2
     (if (<= t_1 -430.0)
       (/ (/ x (* (exp b) a)) y)
       (if (<= t_1 700.0) (/ (* x (/ (pow z y) a)) y) 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(((log(a) * t) - b))) / y;
	double tmp;
	if (t_1 <= -2e+31) {
		tmp = t_2;
	} else if (t_1 <= -430.0) {
		tmp = (x / (exp(b) * a)) / y;
	} else if (t_1 <= 700.0) {
		tmp = (x * (pow(z, y) / a)) / 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 = (t - 1.0d0) * log(a)
    t_2 = (x * exp(((log(a) * t) - b))) / y
    if (t_1 <= (-2d+31)) then
        tmp = t_2
    else if (t_1 <= (-430.0d0)) then
        tmp = (x / (exp(b) * a)) / y
    else if (t_1 <= 700.0d0) then
        tmp = (x * ((z ** y) / a)) / 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 = (t - 1.0) * Math.log(a);
	double t_2 = (x * Math.exp(((Math.log(a) * t) - b))) / y;
	double tmp;
	if (t_1 <= -2e+31) {
		tmp = t_2;
	} else if (t_1 <= -430.0) {
		tmp = (x / (Math.exp(b) * a)) / y;
	} else if (t_1 <= 700.0) {
		tmp = (x * (Math.pow(z, y) / a)) / y;
	} 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(((math.log(a) * t) - b))) / y
	tmp = 0
	if t_1 <= -2e+31:
		tmp = t_2
	elif t_1 <= -430.0:
		tmp = (x / (math.exp(b) * a)) / y
	elif t_1 <= 700.0:
		tmp = (x * (math.pow(z, y) / a)) / y
	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(log(a) * t) - b))) / y)
	tmp = 0.0
	if (t_1 <= -2e+31)
		tmp = t_2;
	elseif (t_1 <= -430.0)
		tmp = Float64(Float64(x / Float64(exp(b) * a)) / y);
	elseif (t_1 <= 700.0)
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	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(((log(a) * t) - b))) / y;
	tmp = 0.0;
	if (t_1 <= -2e+31)
		tmp = t_2;
	elseif (t_1 <= -430.0)
		tmp = (x / (exp(b) * a)) / y;
	elseif (t_1 <= 700.0)
		tmp = (x * ((z ^ y) / a)) / y;
	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[(N[Log[a], $MachinePrecision] * t), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+31], t$95$2, If[LessEqual[t$95$1, -430.0], N[(N[(x / N[(N[Exp[b], $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t$95$1, 700.0], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -1.9999999999999999e31 or 700 < (*.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. lower-log.f64 94.0

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

   5. Applied rewrites 94.0%

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

   if -1.9999999999999999e31 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -430

   1. Initial program 96.2%

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

   3. Taylor expanded in y around 0

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

      1. exp-diff N/A

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

      2. associate-*r/ N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. exp-to-pow N/A

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

      6. lower-pow.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-exp.f64 57.4

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

   5. Applied rewrites 57.4%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 77.9%

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

   if -430 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 700

   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 b around 0

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

      1. +-commutative N/A

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

      2. exp-sum N/A

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

      3. lower-*.f64 N/A

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

      4. exp-to-pow N/A

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

      5. lower-pow.f64 N/A

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

      6. lower--.f64 N/A

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

      7. *-commutative N/A

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

      8. exp-to-pow N/A

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

      9. lower-pow.f64 83.5

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

   5. Applied rewrites 83.5%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 83.1%

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

Alternative 5: 75.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - 1\right) \cdot \log a\\ t_2 := \frac{{a}^{\left(t - 1\right)}}{y} \cdot x\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+31}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -430:\\ \;\;\;\;\frac{\frac{x}{e^{b} \cdot a}}{y}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+84}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- t 1.0) (log a))) (t_2 (* (/ (pow a (- t 1.0)) y) x)))
   (if (<= t_1 -2e+31)
     t_2
     (if (<= t_1 -430.0)
       (/ (/ x (* (exp b) a)) y)
       (if (<= t_1 2e+84) (/ (* x (/ (pow z y) a)) y) 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 = (pow(a, (t - 1.0)) / y) * x;
	double tmp;
	if (t_1 <= -2e+31) {
		tmp = t_2;
	} else if (t_1 <= -430.0) {
		tmp = (x / (exp(b) * a)) / y;
	} else if (t_1 <= 2e+84) {
		tmp = (x * (pow(z, y) / a)) / 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 = (t - 1.0d0) * log(a)
    t_2 = ((a ** (t - 1.0d0)) / y) * x
    if (t_1 <= (-2d+31)) then
        tmp = t_2
    else if (t_1 <= (-430.0d0)) then
        tmp = (x / (exp(b) * a)) / y
    else if (t_1 <= 2d+84) then
        tmp = (x * ((z ** y) / a)) / 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 = (t - 1.0) * Math.log(a);
	double t_2 = (Math.pow(a, (t - 1.0)) / y) * x;
	double tmp;
	if (t_1 <= -2e+31) {
		tmp = t_2;
	} else if (t_1 <= -430.0) {
		tmp = (x / (Math.exp(b) * a)) / y;
	} else if (t_1 <= 2e+84) {
		tmp = (x * (Math.pow(z, y) / a)) / y;
	} 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 = (math.pow(a, (t - 1.0)) / y) * x
	tmp = 0
	if t_1 <= -2e+31:
		tmp = t_2
	elif t_1 <= -430.0:
		tmp = (x / (math.exp(b) * a)) / y
	elif t_1 <= 2e+84:
		tmp = (x * (math.pow(z, y) / a)) / y
	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((a ^ Float64(t - 1.0)) / y) * x)
	tmp = 0.0
	if (t_1 <= -2e+31)
		tmp = t_2;
	elseif (t_1 <= -430.0)
		tmp = Float64(Float64(x / Float64(exp(b) * a)) / y);
	elseif (t_1 <= 2e+84)
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	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 = ((a ^ (t - 1.0)) / y) * x;
	tmp = 0.0;
	if (t_1 <= -2e+31)
		tmp = t_2;
	elseif (t_1 <= -430.0)
		tmp = (x / (exp(b) * a)) / y;
	elseif (t_1 <= 2e+84)
		tmp = (x * ((z ^ y) / a)) / y;
	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[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+31], t$95$2, If[LessEqual[t$95$1, -430.0], N[(N[(x / N[(N[Exp[b], $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t$95$1, 2e+84], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -1.9999999999999999e31 or 2.00000000000000012e84 < (*.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 b around 0

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

      1. +-commutative N/A

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

      2. exp-sum N/A

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

      3. lower-*.f64 N/A

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

      4. exp-to-pow N/A

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

      5. lower-pow.f64 N/A

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

      6. lower--.f64 N/A

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

      7. *-commutative N/A

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

      8. exp-to-pow N/A

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

      9. lower-pow.f64 74.4

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

   5. Applied rewrites 74.4%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 86.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 86.4

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

   10. Applied rewrites 86.4%

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

   if -1.9999999999999999e31 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -430

   1. Initial program 96.2%

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

   3. Taylor expanded in y around 0

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

      1. exp-diff N/A

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

      2. associate-*r/ N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. exp-to-pow N/A

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

      6. lower-pow.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-exp.f64 57.4

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

   5. Applied rewrites 57.4%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 77.9%

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

   if -430 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 2.00000000000000012e84

   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 b around 0

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

      1. +-commutative N/A

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

      2. exp-sum N/A

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

      3. lower-*.f64 N/A

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

      4. exp-to-pow N/A

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

      5. lower-pow.f64 N/A

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

      6. lower--.f64 N/A

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

      7. *-commutative N/A

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

      8. exp-to-pow N/A

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

      9. lower-pow.f64 80.3

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

   5. Applied rewrites 80.3%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 80.1%

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

Alternative 6: 73.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - 1\right) \cdot \log a\\ t_2 := \frac{{a}^{\left(t - 1\right)}}{y} \cdot x\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+31}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -430:\\ \;\;\;\;\frac{\frac{x}{e^{b} \cdot a}}{y}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+84}:\\ \;\;\;\;\frac{{z}^{y}}{a} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- t 1.0) (log a))) (t_2 (* (/ (pow a (- t 1.0)) y) x)))
   (if (<= t_1 -2e+31)
     t_2
     (if (<= t_1 -430.0)
       (/ (/ x (* (exp b) a)) y)
       (if (<= t_1 2e+84) (* (/ (pow z y) a) (/ x y)) 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 = (pow(a, (t - 1.0)) / y) * x;
	double tmp;
	if (t_1 <= -2e+31) {
		tmp = t_2;
	} else if (t_1 <= -430.0) {
		tmp = (x / (exp(b) * a)) / y;
	} else if (t_1 <= 2e+84) {
		tmp = (pow(z, y) / a) * (x / 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 = (t - 1.0d0) * log(a)
    t_2 = ((a ** (t - 1.0d0)) / y) * x
    if (t_1 <= (-2d+31)) then
        tmp = t_2
    else if (t_1 <= (-430.0d0)) then
        tmp = (x / (exp(b) * a)) / y
    else if (t_1 <= 2d+84) then
        tmp = ((z ** y) / a) * (x / 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 = (t - 1.0) * Math.log(a);
	double t_2 = (Math.pow(a, (t - 1.0)) / y) * x;
	double tmp;
	if (t_1 <= -2e+31) {
		tmp = t_2;
	} else if (t_1 <= -430.0) {
		tmp = (x / (Math.exp(b) * a)) / y;
	} else if (t_1 <= 2e+84) {
		tmp = (Math.pow(z, y) / a) * (x / y);
	} 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 = (math.pow(a, (t - 1.0)) / y) * x
	tmp = 0
	if t_1 <= -2e+31:
		tmp = t_2
	elif t_1 <= -430.0:
		tmp = (x / (math.exp(b) * a)) / y
	elif t_1 <= 2e+84:
		tmp = (math.pow(z, y) / a) * (x / y)
	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((a ^ Float64(t - 1.0)) / y) * x)
	tmp = 0.0
	if (t_1 <= -2e+31)
		tmp = t_2;
	elseif (t_1 <= -430.0)
		tmp = Float64(Float64(x / Float64(exp(b) * a)) / y);
	elseif (t_1 <= 2e+84)
		tmp = Float64(Float64((z ^ y) / a) * Float64(x / y));
	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 = ((a ^ (t - 1.0)) / y) * x;
	tmp = 0.0;
	if (t_1 <= -2e+31)
		tmp = t_2;
	elseif (t_1 <= -430.0)
		tmp = (x / (exp(b) * a)) / y;
	elseif (t_1 <= 2e+84)
		tmp = ((z ^ y) / a) * (x / y);
	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[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+31], t$95$2, If[LessEqual[t$95$1, -430.0], N[(N[(x / N[(N[Exp[b], $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t$95$1, 2e+84], N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -1.9999999999999999e31 or 2.00000000000000012e84 < (*.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 b around 0

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

      1. +-commutative N/A

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

      2. exp-sum N/A

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

      3. lower-*.f64 N/A

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

      4. exp-to-pow N/A

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

      5. lower-pow.f64 N/A

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

      6. lower--.f64 N/A

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

      7. *-commutative N/A

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

      8. exp-to-pow N/A

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

      9. lower-pow.f64 74.4

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

   5. Applied rewrites 74.4%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 86.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 86.4

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

   10. Applied rewrites 86.4%

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

   if -1.9999999999999999e31 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -430

   1. Initial program 96.2%

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

   3. Taylor expanded in y around 0

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

      1. exp-diff N/A

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

      2. associate-*r/ N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. exp-to-pow N/A

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

      6. lower-pow.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-exp.f64 57.4

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

   5. Applied rewrites 57.4%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 77.9%

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

   if -430 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 2.00000000000000012e84

   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 b around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. exp-sum N/A

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

      6. lower-*.f64 N/A

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

      7. exp-to-pow N/A

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

      8. lower-pow.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. exp-to-pow N/A

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

      12. lower-pow.f64 N/A

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

      13. lower-/.f64 78.5

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

   5. Applied rewrites 78.5%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 79.2%

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

Alternative 7: 75.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - 1\right) \cdot \log a\\ t_2 := \frac{{a}^{\left(t - 1\right)}}{y} \cdot x\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+31}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -200:\\ \;\;\;\;\frac{\frac{x}{e^{b} \cdot a}}{y}\\ \mathbf{elif}\;t\_1 \leq 1000:\\ \;\;\;\;\frac{1 \cdot \left({z}^{y} \cdot x\right)}{a \cdot y}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- t 1.0) (log a))) (t_2 (* (/ (pow a (- t 1.0)) y) x)))
   (if (<= t_1 -2e+31)
     t_2
     (if (<= t_1 -200.0)
       (/ (/ x (* (exp b) a)) y)
       (if (<= t_1 1000.0) (/ (* 1.0 (* (pow z y) x)) (* a y)) 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 = (pow(a, (t - 1.0)) / y) * x;
	double tmp;
	if (t_1 <= -2e+31) {
		tmp = t_2;
	} else if (t_1 <= -200.0) {
		tmp = (x / (exp(b) * a)) / y;
	} else if (t_1 <= 1000.0) {
		tmp = (1.0 * (pow(z, y) * x)) / (a * 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 = (t - 1.0d0) * log(a)
    t_2 = ((a ** (t - 1.0d0)) / y) * x
    if (t_1 <= (-2d+31)) then
        tmp = t_2
    else if (t_1 <= (-200.0d0)) then
        tmp = (x / (exp(b) * a)) / y
    else if (t_1 <= 1000.0d0) then
        tmp = (1.0d0 * ((z ** y) * x)) / (a * 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 = (t - 1.0) * Math.log(a);
	double t_2 = (Math.pow(a, (t - 1.0)) / y) * x;
	double tmp;
	if (t_1 <= -2e+31) {
		tmp = t_2;
	} else if (t_1 <= -200.0) {
		tmp = (x / (Math.exp(b) * a)) / y;
	} else if (t_1 <= 1000.0) {
		tmp = (1.0 * (Math.pow(z, y) * x)) / (a * y);
	} 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 = (math.pow(a, (t - 1.0)) / y) * x
	tmp = 0
	if t_1 <= -2e+31:
		tmp = t_2
	elif t_1 <= -200.0:
		tmp = (x / (math.exp(b) * a)) / y
	elif t_1 <= 1000.0:
		tmp = (1.0 * (math.pow(z, y) * x)) / (a * y)
	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((a ^ Float64(t - 1.0)) / y) * x)
	tmp = 0.0
	if (t_1 <= -2e+31)
		tmp = t_2;
	elseif (t_1 <= -200.0)
		tmp = Float64(Float64(x / Float64(exp(b) * a)) / y);
	elseif (t_1 <= 1000.0)
		tmp = Float64(Float64(1.0 * Float64((z ^ y) * x)) / Float64(a * y));
	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 = ((a ^ (t - 1.0)) / y) * x;
	tmp = 0.0;
	if (t_1 <= -2e+31)
		tmp = t_2;
	elseif (t_1 <= -200.0)
		tmp = (x / (exp(b) * a)) / y;
	elseif (t_1 <= 1000.0)
		tmp = (1.0 * ((z ^ y) * x)) / (a * y);
	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[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+31], t$95$2, If[LessEqual[t$95$1, -200.0], N[(N[(x / N[(N[Exp[b], $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t$95$1, 1000.0], N[(N[(1.0 * N[(N[Power[z, y], $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] / N[(a * y), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -1.9999999999999999e31 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 b around 0

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

      1. +-commutative N/A

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

      2. exp-sum N/A

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

      3. lower-*.f64 N/A

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

      4. exp-to-pow N/A

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

      5. lower-pow.f64 N/A

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

      6. lower--.f64 N/A

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

      7. *-commutative N/A

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

      8. exp-to-pow N/A

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

      9. lower-pow.f64 72.1

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

   5. Applied rewrites 72.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 82.7%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 82.7

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

   10. Applied rewrites 82.7%

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

   if -1.9999999999999999e31 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -200

   1. Initial program 96.7%

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

   3. Taylor expanded in y around 0

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

      1. exp-diff N/A

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

      2. associate-*r/ N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. exp-to-pow N/A

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

      6. lower-pow.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-exp.f64 61.5

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

   5. Applied rewrites 61.5%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 76.8%

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

   if -200 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 1e3

   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 b around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. exp-sum N/A

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

      6. lower-*.f64 N/A

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

      7. exp-to-pow N/A

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

      8. lower-pow.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. exp-to-pow N/A

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

      12. lower-pow.f64 N/A

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

      13. lower-/.f64 83.3

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

   5. Applied rewrites 83.3%

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

   7. Applied rewrites 81.3%

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

   8. Taylor expanded in t around 0

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

   10. Applied rewrites 81.3%

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

Alternative 8: 71.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - 1\right) \cdot \log a\\ t_2 := \frac{{a}^{\left(t - 1\right)}}{y} \cdot x\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+41}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -430:\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{elif}\;t\_1 \leq 1000:\\ \;\;\;\;\frac{1 \cdot \left({z}^{y} \cdot x\right)}{a \cdot y}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- t 1.0) (log a))) (t_2 (* (/ (pow a (- t 1.0)) y) x)))
   (if (<= t_1 -4e+41)
     t_2
     (if (<= t_1 -430.0)
       (* (/ (exp (- b)) y) x)
       (if (<= t_1 1000.0) (/ (* 1.0 (* (pow z y) x)) (* a y)) 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 = (pow(a, (t - 1.0)) / y) * x;
	double tmp;
	if (t_1 <= -4e+41) {
		tmp = t_2;
	} else if (t_1 <= -430.0) {
		tmp = (exp(-b) / y) * x;
	} else if (t_1 <= 1000.0) {
		tmp = (1.0 * (pow(z, y) * x)) / (a * 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 = (t - 1.0d0) * log(a)
    t_2 = ((a ** (t - 1.0d0)) / y) * x
    if (t_1 <= (-4d+41)) then
        tmp = t_2
    else if (t_1 <= (-430.0d0)) then
        tmp = (exp(-b) / y) * x
    else if (t_1 <= 1000.0d0) then
        tmp = (1.0d0 * ((z ** y) * x)) / (a * 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 = (t - 1.0) * Math.log(a);
	double t_2 = (Math.pow(a, (t - 1.0)) / y) * x;
	double tmp;
	if (t_1 <= -4e+41) {
		tmp = t_2;
	} else if (t_1 <= -430.0) {
		tmp = (Math.exp(-b) / y) * x;
	} else if (t_1 <= 1000.0) {
		tmp = (1.0 * (Math.pow(z, y) * x)) / (a * y);
	} 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 = (math.pow(a, (t - 1.0)) / y) * x
	tmp = 0
	if t_1 <= -4e+41:
		tmp = t_2
	elif t_1 <= -430.0:
		tmp = (math.exp(-b) / y) * x
	elif t_1 <= 1000.0:
		tmp = (1.0 * (math.pow(z, y) * x)) / (a * y)
	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((a ^ Float64(t - 1.0)) / y) * x)
	tmp = 0.0
	if (t_1 <= -4e+41)
		tmp = t_2;
	elseif (t_1 <= -430.0)
		tmp = Float64(Float64(exp(Float64(-b)) / y) * x);
	elseif (t_1 <= 1000.0)
		tmp = Float64(Float64(1.0 * Float64((z ^ y) * x)) / Float64(a * y));
	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 = ((a ^ (t - 1.0)) / y) * x;
	tmp = 0.0;
	if (t_1 <= -4e+41)
		tmp = t_2;
	elseif (t_1 <= -430.0)
		tmp = (exp(-b) / y) * x;
	elseif (t_1 <= 1000.0)
		tmp = (1.0 * ((z ^ y) * x)) / (a * y);
	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[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+41], t$95$2, If[LessEqual[t$95$1, -430.0], N[(N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t$95$1, 1000.0], N[(N[(1.0 * N[(N[Power[z, y], $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] / N[(a * y), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -4.00000000000000002e41 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 b around 0

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

      1. +-commutative N/A

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

      2. exp-sum N/A

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

      3. lower-*.f64 N/A

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

      4. exp-to-pow N/A

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

      5. lower-pow.f64 N/A

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

      6. lower--.f64 N/A

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

      7. *-commutative N/A

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

      8. exp-to-pow N/A

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

      9. lower-pow.f64 71.8

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

   5. Applied rewrites 71.8%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 82.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 82.6

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

   10. Applied rewrites 82.6%

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

   if -4.00000000000000002e41 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -430

   1. Initial program 96.3%

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

   3. Taylor expanded in y around 0

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

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

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

      2. metadata-eval N/A

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

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

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

      4. distribute-rgt-out N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. metadata-eval N/A

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

      8. remove-double-neg N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. lower-*.f64 N/A

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

      12. mul-1-neg N/A

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

      13. distribute-neg-in N/A

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

      14. metadata-eval N/A

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

      15. remove-double-neg N/A

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

      16. lower-+.f64 N/A

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

      17. lower-log.f64 76.7

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

   5. Applied rewrites 76.7%

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

   6. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 61.2

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

   8. Applied rewrites 61.2%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 61.2

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

   10. Applied rewrites 61.2%

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

   if -430 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 1e3

   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 b around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. exp-sum N/A

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

      6. lower-*.f64 N/A

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

      7. exp-to-pow N/A

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

      8. lower-pow.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. exp-to-pow N/A

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

      12. lower-pow.f64 N/A

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

      13. lower-/.f64 81.7

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

   5. Applied rewrites 81.7%

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

   7. Applied rewrites 79.3%

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

   8. Taylor expanded in t around 0

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

   10. Applied rewrites 79.1%

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

Alternative 9: 41.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \leq 2 \cdot 10^{+55}:\\ \;\;\;\;\frac{\frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(b \cdot a, 0.5, a\right), b, a\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(-x, b, x\right)}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y) 2e+55)
   (/ (/ x (fma (fma (* b a) 0.5 a) b a)) y)
   (/ (/ (fma (- x) b x) a) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((x * exp((((y * log(z)) + ((t - 1.0) * log(a))) - b))) / y) <= 2e+55) {
		tmp = (x / fma(fma((b * a), 0.5, a), b, a)) / y;
	} else {
		tmp = (fma(-x, b, x) / a) / y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) + Float64(Float64(t - 1.0) * log(a))) - b))) / y) <= 2e+55)
		tmp = Float64(Float64(x / fma(fma(Float64(b * a), 0.5, a), b, a)) / y);
	else
		tmp = Float64(Float64(fma(Float64(-x), b, x) / a) / y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[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], 2e+55], N[(N[(x / N[(N[(N[(b * a), $MachinePrecision] * 0.5 + a), $MachinePrecision] * b + a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(N[((-x) * b + x), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (exp.f64 (-.f64 (+.f64 (*.f64 y (log.f64 z)) (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))) b))) y) < 2.00000000000000002e55

   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

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

      1. exp-diff N/A

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

      2. associate-*r/ N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. exp-to-pow N/A

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

      6. lower-pow.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-exp.f64 63.1

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

   5. Applied rewrites 63.1%

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

   7. Applied rewrites 67.3%

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

   8. Taylor expanded in t around 0

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

   10. Applied rewrites 62.8%

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

   11. Taylor expanded in b around 0

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

   13. Applied rewrites 48.1%

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

   if 2.00000000000000002e55 < (/.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 99.5%

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

   3. Taylor expanded in y around 0

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

      1. exp-diff N/A

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

      2. associate-*r/ N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. exp-to-pow N/A

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

      6. lower-pow.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-exp.f64 62.0

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

   5. Applied rewrites 62.0%

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

   7. Applied rewrites 68.8%

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

   8. Taylor expanded in t around 0

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

   10. Applied rewrites 59.5%

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

   11. Taylor expanded in b around 0

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

   13. Applied rewrites 32.0%

       \[\leadsto \frac{\frac{\mathsf{fma}\left(-x, b, x\right)}{a}}{y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 89.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+43} \lor \neg \left(y \leq 6 \cdot 10^{+135}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(-1 + t\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.02e+43) (not (<= y 6e+135)))
   (/ (* x (/ (pow z y) a)) y)
   (/ (* x (exp (- (* (+ -1.0 t) (log a)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.02e+43) || !(y <= 6e+135)) {
		tmp = (x * (pow(z, y) / a)) / y;
	} else {
		tmp = (x * exp((((-1.0 + t) * log(a)) - b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.02d+43)) .or. (.not. (y <= 6d+135))) then
        tmp = (x * ((z ** y) / a)) / y
    else
        tmp = (x * exp(((((-1.0d0) + t) * log(a)) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.02e+43) || !(y <= 6e+135)) {
		tmp = (x * (Math.pow(z, y) / a)) / y;
	} else {
		tmp = (x * Math.exp((((-1.0 + t) * Math.log(a)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.02e+43) or not (y <= 6e+135):
		tmp = (x * (math.pow(z, y) / a)) / y
	else:
		tmp = (x * math.exp((((-1.0 + t) * math.log(a)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.02e+43) || !(y <= 6e+135))
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(-1.0 + t) * log(a)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.02e+43) || ~((y <= 6e+135)))
		tmp = (x * ((z ^ y) / a)) / y;
	else
		tmp = (x * exp((((-1.0 + t) * log(a)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.02e+43], N[Not[LessEqual[y, 6e+135]], $MachinePrecision]], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[(-1.0 + t), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.02e43 or 6.0000000000000001e135 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. exp-sum N/A

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

      3. lower-*.f64 N/A

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

      4. exp-to-pow N/A

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

      5. lower-pow.f64 N/A

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

      6. lower--.f64 N/A

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

      7. *-commutative N/A

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

      8. exp-to-pow N/A

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

      9. lower-pow.f64 78.3

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

   5. Applied rewrites 78.3%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 89.3%

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

   if -1.02e43 < y < 6.0000000000000001e135

   1. Initial program 98.0%

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

   3. Taylor expanded in y around 0

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

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

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

      2. metadata-eval N/A

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

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

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

      4. distribute-rgt-out N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. metadata-eval N/A

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

      8. remove-double-neg N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. lower-*.f64 N/A

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

      12. mul-1-neg N/A

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

      13. distribute-neg-in N/A

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

      14. metadata-eval N/A

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

      15. remove-double-neg N/A

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

      16. lower-+.f64 N/A

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

      17. lower-log.f64 95.0

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

   5. Applied rewrites 95.0%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+43} \lor \neg \left(y \leq 6 \cdot 10^{+135}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(-1 + t\right) \cdot \log a - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 87.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -8.2 \cdot 10^{+52} \lor \neg \left(b \leq 7500000000000\right):\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot t - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left({a}^{\left(t - 1\right)} \cdot {z}^{y}\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -8.2e+52) (not (<= b 7500000000000.0)))
   (/ (* x (exp (- (* (log a) t) b))) y)
   (/ (* x (* (pow a (- t 1.0)) (pow z y))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -8.2e+52) || !(b <= 7500000000000.0)) {
		tmp = (x * exp(((log(a) * t) - b))) / y;
	} else {
		tmp = (x * (pow(a, (t - 1.0)) * pow(z, y))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-8.2d+52)) .or. (.not. (b <= 7500000000000.0d0))) then
        tmp = (x * exp(((log(a) * t) - b))) / y
    else
        tmp = (x * ((a ** (t - 1.0d0)) * (z ** y))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -8.2e+52) || !(b <= 7500000000000.0)) {
		tmp = (x * Math.exp(((Math.log(a) * t) - b))) / y;
	} else {
		tmp = (x * (Math.pow(a, (t - 1.0)) * Math.pow(z, y))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -8.2e+52) or not (b <= 7500000000000.0):
		tmp = (x * math.exp(((math.log(a) * t) - b))) / y
	else:
		tmp = (x * (math.pow(a, (t - 1.0)) * math.pow(z, y))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -8.2e+52) || !(b <= 7500000000000.0))
		tmp = Float64(Float64(x * exp(Float64(Float64(log(a) * t) - b))) / y);
	else
		tmp = Float64(Float64(x * Float64((a ^ Float64(t - 1.0)) * (z ^ y))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -8.2e+52) || ~((b <= 7500000000000.0)))
		tmp = (x * exp(((log(a) * t) - b))) / y;
	else
		tmp = (x * ((a ^ (t - 1.0)) * (z ^ y))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -8.2e+52], N[Not[LessEqual[b, 7500000000000.0]], $MachinePrecision]], N[(N[(x * N[Exp[N[(N[(N[Log[a], $MachinePrecision] * t), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] * N[Power[z, y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -8.1999999999999999e52 or 7.5e12 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-log.f64 91.3

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

   5. Applied rewrites 91.3%

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

   if -8.1999999999999999e52 < b < 7.5e12

   1. Initial program 97.6%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. exp-sum N/A

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

      3. lower-*.f64 N/A

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

      4. exp-to-pow N/A

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

      5. lower-pow.f64 N/A

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

      6. lower--.f64 N/A

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

      7. *-commutative N/A

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

      8. exp-to-pow N/A

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

      9. lower-pow.f64 86.6

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

   5. Applied rewrites 86.6%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.2 \cdot 10^{+52} \lor \neg \left(b \leq 7500000000000\right):\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot t - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left({a}^{\left(t - 1\right)} \cdot {z}^{y}\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 83.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.35 \cdot 10^{+52} \lor \neg \left(b \leq 800000000000\right):\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot t - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\left({a}^{\left(t - 1\right)} \cdot {z}^{y}\right) \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -2.35e+52) (not (<= b 800000000000.0)))
   (/ (* x (exp (- (* (log a) t) b))) y)
   (* (* (pow a (- t 1.0)) (pow z y)) (/ x y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.35e+52) || !(b <= 800000000000.0)) {
		tmp = (x * exp(((log(a) * t) - b))) / y;
	} else {
		tmp = (pow(a, (t - 1.0)) * pow(z, y)) * (x / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-2.35d+52)) .or. (.not. (b <= 800000000000.0d0))) then
        tmp = (x * exp(((log(a) * t) - b))) / y
    else
        tmp = ((a ** (t - 1.0d0)) * (z ** y)) * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.35e+52) || !(b <= 800000000000.0)) {
		tmp = (x * Math.exp(((Math.log(a) * t) - b))) / y;
	} else {
		tmp = (Math.pow(a, (t - 1.0)) * Math.pow(z, y)) * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -2.35e+52) or not (b <= 800000000000.0):
		tmp = (x * math.exp(((math.log(a) * t) - b))) / y
	else:
		tmp = (math.pow(a, (t - 1.0)) * math.pow(z, y)) * (x / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -2.35e+52) || !(b <= 800000000000.0))
		tmp = Float64(Float64(x * exp(Float64(Float64(log(a) * t) - b))) / y);
	else
		tmp = Float64(Float64((a ^ Float64(t - 1.0)) * (z ^ y)) * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -2.35e+52) || ~((b <= 800000000000.0)))
		tmp = (x * exp(((log(a) * t) - b))) / y;
	else
		tmp = ((a ^ (t - 1.0)) * (z ^ y)) * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -2.35e+52], N[Not[LessEqual[b, 800000000000.0]], $MachinePrecision]], N[(N[(x * N[Exp[N[(N[(N[Log[a], $MachinePrecision] * t), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] * N[Power[z, y], $MachinePrecision]), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.35e52 or 8e11 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-log.f64 91.3

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

   5. Applied rewrites 91.3%

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

   if -2.35e52 < b < 8e11

   1. Initial program 97.6%

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

   3. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. exp-sum N/A

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

      6. lower-*.f64 N/A

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

      7. exp-to-pow N/A

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

      8. lower-pow.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. exp-to-pow N/A

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

      12. lower-pow.f64 N/A

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

      13. lower-/.f64 82.1

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

   5. Applied rewrites 82.1%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.35 \cdot 10^{+52} \lor \neg \left(b \leq 800000000000\right):\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot t - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\left({a}^{\left(t - 1\right)} \cdot {z}^{y}\right) \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 74.8% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{+37} \lor \neg \left(b \leq 1.55 \cdot 10^{+38}\right):\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t - 1\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.3e+37) (not (<= b 1.55e+38)))
   (* (/ (exp (- b)) y) x)
   (/ (* x (pow a (- t 1.0))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.3e+37) || !(b <= 1.55e+38)) {
		tmp = (exp(-b) / y) * x;
	} else {
		tmp = (x * pow(a, (t - 1.0))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1.3d+37)) .or. (.not. (b <= 1.55d+38))) then
        tmp = (exp(-b) / y) * x
    else
        tmp = (x * (a ** (t - 1.0d0))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.3e+37) || !(b <= 1.55e+38)) {
		tmp = (Math.exp(-b) / y) * x;
	} else {
		tmp = (x * Math.pow(a, (t - 1.0))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.3e+37) or not (b <= 1.55e+38):
		tmp = (math.exp(-b) / y) * x
	else:
		tmp = (x * math.pow(a, (t - 1.0))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.3e+37) || !(b <= 1.55e+38))
		tmp = Float64(Float64(exp(Float64(-b)) / y) * x);
	else
		tmp = Float64(Float64(x * (a ^ Float64(t - 1.0))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.3e+37) || ~((b <= 1.55e+38)))
		tmp = (exp(-b) / y) * x;
	else
		tmp = (x * (a ^ (t - 1.0))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.3e+37], N[Not[LessEqual[b, 1.55e+38]], $MachinePrecision]], N[(N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision], N[(N[(x * N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.3e37 or 1.55000000000000009e38 < 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 0

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

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

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

      2. metadata-eval N/A

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

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

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

      4. distribute-rgt-out N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. metadata-eval N/A

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

      8. remove-double-neg N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. lower-*.f64 N/A

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

      12. mul-1-neg N/A

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

      13. distribute-neg-in N/A

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

      14. metadata-eval N/A

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

      15. remove-double-neg N/A

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

      16. lower-+.f64 N/A

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

      17. lower-log.f64 88.8

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

   5. Applied rewrites 88.8%

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

   6. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 78.4

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

   8. Applied rewrites 78.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 78.4

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

   10. Applied rewrites 78.4%

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

   if -1.3e37 < b < 1.55000000000000009e38

   1. Initial program 97.6%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. exp-sum N/A

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

      3. lower-*.f64 N/A

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

      4. exp-to-pow N/A

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

      5. lower-pow.f64 N/A

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

      6. lower--.f64 N/A

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

      7. *-commutative N/A

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

      8. exp-to-pow N/A

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

      9. lower-pow.f64 87.5

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

   5. Applied rewrites 87.5%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 73.2%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{+37} \lor \neg \left(b \leq 1.55 \cdot 10^{+38}\right):\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t - 1\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 74.8% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{+37} \lor \neg \left(b \leq 1.55 \cdot 10^{+38}\right):\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)}}{y} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.1e+37) (not (<= b 1.55e+38)))
   (* (/ (exp (- b)) y) x)
   (* (/ (pow a (- t 1.0)) y) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.1e+37) || !(b <= 1.55e+38)) {
		tmp = (exp(-b) / y) * x;
	} else {
		tmp = (pow(a, (t - 1.0)) / y) * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1.1d+37)) .or. (.not. (b <= 1.55d+38))) then
        tmp = (exp(-b) / y) * x
    else
        tmp = ((a ** (t - 1.0d0)) / y) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.1e+37) || !(b <= 1.55e+38)) {
		tmp = (Math.exp(-b) / y) * x;
	} else {
		tmp = (Math.pow(a, (t - 1.0)) / y) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.1e+37) or not (b <= 1.55e+38):
		tmp = (math.exp(-b) / y) * x
	else:
		tmp = (math.pow(a, (t - 1.0)) / y) * x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.1e+37) || !(b <= 1.55e+38))
		tmp = Float64(Float64(exp(Float64(-b)) / y) * x);
	else
		tmp = Float64(Float64((a ^ Float64(t - 1.0)) / y) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.1e+37) || ~((b <= 1.55e+38)))
		tmp = (exp(-b) / y) * x;
	else
		tmp = ((a ^ (t - 1.0)) / y) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.1e+37], N[Not[LessEqual[b, 1.55e+38]], $MachinePrecision]], N[(N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision], N[(N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.1e37 or 1.55000000000000009e38 < 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 0

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

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

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

      2. metadata-eval N/A

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

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

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

      4. distribute-rgt-out N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. metadata-eval N/A

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

      8. remove-double-neg N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. lower-*.f64 N/A

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

      12. mul-1-neg N/A

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

      13. distribute-neg-in N/A

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

      14. metadata-eval N/A

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

      15. remove-double-neg N/A

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

      16. lower-+.f64 N/A

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

      17. lower-log.f64 88.8

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

   5. Applied rewrites 88.8%

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

   6. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 78.4

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

   8. Applied rewrites 78.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 78.4

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

   10. Applied rewrites 78.4%

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

   if -1.1e37 < b < 1.55000000000000009e38

   1. Initial program 97.6%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. exp-sum N/A

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

      3. lower-*.f64 N/A

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

      4. exp-to-pow N/A

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

      5. lower-pow.f64 N/A

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

      6. lower--.f64 N/A

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

      7. *-commutative N/A

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

      8. exp-to-pow N/A

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

      9. lower-pow.f64 87.5

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

   5. Applied rewrites 87.5%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 73.2%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 70.4

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

   10. Applied rewrites 70.4%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{+37} \lor \neg \left(b \leq 1.55 \cdot 10^{+38}\right):\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)}}{y} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 72.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.05 \cdot 10^{+17} \lor \neg \left(b \leq 1.55 \cdot 10^{+38}\right):\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;{a}^{\left(t - 1\right)} \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.05e+17) (not (<= b 1.55e+38)))
   (* (/ (exp (- b)) y) x)
   (* (pow a (- t 1.0)) (/ x y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.05e+17) || !(b <= 1.55e+38)) {
		tmp = (exp(-b) / y) * x;
	} else {
		tmp = pow(a, (t - 1.0)) * (x / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1.05d+17)) .or. (.not. (b <= 1.55d+38))) then
        tmp = (exp(-b) / y) * x
    else
        tmp = (a ** (t - 1.0d0)) * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.05e+17) || !(b <= 1.55e+38)) {
		tmp = (Math.exp(-b) / y) * x;
	} else {
		tmp = Math.pow(a, (t - 1.0)) * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.05e+17) or not (b <= 1.55e+38):
		tmp = (math.exp(-b) / y) * x
	else:
		tmp = math.pow(a, (t - 1.0)) * (x / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.05e+17) || !(b <= 1.55e+38))
		tmp = Float64(Float64(exp(Float64(-b)) / y) * x);
	else
		tmp = Float64((a ^ Float64(t - 1.0)) * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.05e+17) || ~((b <= 1.55e+38)))
		tmp = (exp(-b) / y) * x;
	else
		tmp = (a ^ (t - 1.0)) * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.05e+17], N[Not[LessEqual[b, 1.55e+38]], $MachinePrecision]], N[(N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision], N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.05e17 or 1.55000000000000009e38 < 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 0

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

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

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

      2. metadata-eval N/A

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

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

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

      4. distribute-rgt-out N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. metadata-eval N/A

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

      8. remove-double-neg N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. lower-*.f64 N/A

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

      12. mul-1-neg N/A

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

      13. distribute-neg-in N/A

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

      14. metadata-eval N/A

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

      15. remove-double-neg N/A

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

      16. lower-+.f64 N/A

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

      17. lower-log.f64 88.6

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

   5. Applied rewrites 88.6%

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

   6. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 78.6

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

   8. Applied rewrites 78.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 78.6

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

   10. Applied rewrites 78.6%

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

   if -1.05e17 < b < 1.55000000000000009e38

   1. Initial program 97.5%

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

   3. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. exp-sum N/A

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

      6. lower-*.f64 N/A

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

      7. exp-to-pow N/A

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

      8. lower-pow.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. exp-to-pow N/A

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

      12. lower-pow.f64 N/A

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

      13. lower-/.f64 82.2

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

   5. Applied rewrites 82.2%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 69.5%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.05 \cdot 10^{+17} \lor \neg \left(b \leq 1.55 \cdot 10^{+38}\right):\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;{a}^{\left(t - 1\right)} \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 58.3% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{-5} \lor \neg \left(b \leq 2 \cdot 10^{+29}\right):\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(b \cdot a, 0.5, a\right), b, a\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -4.5e-5) (not (<= b 2e+29)))
   (* (/ (exp (- b)) y) x)
   (/ (/ x (fma (fma (* b a) 0.5 a) b a)) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -4.5e-5) || !(b <= 2e+29)) {
		tmp = (exp(-b) / y) * x;
	} else {
		tmp = (x / fma(fma((b * a), 0.5, a), b, a)) / y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -4.5e-5) || !(b <= 2e+29))
		tmp = Float64(Float64(exp(Float64(-b)) / y) * x);
	else
		tmp = Float64(Float64(x / fma(fma(Float64(b * a), 0.5, a), b, a)) / y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -4.5e-5], N[Not[LessEqual[b, 2e+29]], $MachinePrecision]], N[(N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision], N[(N[(x / N[(N[(N[(b * a), $MachinePrecision] * 0.5 + a), $MachinePrecision] * b + a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.50000000000000028e-5 or 1.99999999999999983e29 < 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 0

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

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

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

      2. metadata-eval N/A

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

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

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

      4. distribute-rgt-out N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. metadata-eval N/A

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

      8. remove-double-neg N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. lower-*.f64 N/A

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

      12. mul-1-neg N/A

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

      13. distribute-neg-in N/A

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

      14. metadata-eval N/A

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

      15. remove-double-neg N/A

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

      16. lower-+.f64 N/A

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

      17. lower-log.f64 88.0

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

   5. Applied rewrites 88.0%

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

   6. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 76.7

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

   8. Applied rewrites 76.7%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 76.7

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

   10. Applied rewrites 76.7%

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

   if -4.50000000000000028e-5 < b < 1.99999999999999983e29

   1. Initial program 97.3%

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

   3. Taylor expanded in y around 0

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

      1. exp-diff N/A

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

      2. associate-*r/ N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. exp-to-pow N/A

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

      6. lower-pow.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-exp.f64 72.4

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

   5. Applied rewrites 72.4%

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

   7. Applied rewrites 72.6%

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

   8. Taylor expanded in t around 0

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

   10. Applied rewrites 47.1%

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

   11. Taylor expanded in b around 0

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

   13. Applied rewrites 47.1%

       \[\leadsto \frac{\frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(b \cdot a, 0.5, a\right), b, a\right)}}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{-5} \lor \neg \left(b \leq 2 \cdot 10^{+29}\right):\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(b \cdot a, 0.5, a\right), b, a\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 58.3% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := e^{-b}\\ \mathbf{if}\;b \leq -4.5 \cdot 10^{-5}:\\ \;\;\;\;\frac{t\_1}{y} \cdot x\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+29}:\\ \;\;\;\;\frac{\frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(b \cdot a, 0.5, a\right), b, a\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot t\_1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (exp (- b))))
   (if (<= b -4.5e-5)
     (* (/ t_1 y) x)
     (if (<= b 2e+29)
       (/ (/ x (fma (fma (* b a) 0.5 a) b a)) y)
       (/ (* x t_1) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = exp(-b);
	double tmp;
	if (b <= -4.5e-5) {
		tmp = (t_1 / y) * x;
	} else if (b <= 2e+29) {
		tmp = (x / fma(fma((b * a), 0.5, a), b, a)) / y;
	} else {
		tmp = (x * t_1) / y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = exp(Float64(-b))
	tmp = 0.0
	if (b <= -4.5e-5)
		tmp = Float64(Float64(t_1 / y) * x);
	elseif (b <= 2e+29)
		tmp = Float64(Float64(x / fma(fma(Float64(b * a), 0.5, a), b, a)) / y);
	else
		tmp = Float64(Float64(x * t_1) / y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[Exp[(-b)], $MachinePrecision]}, If[LessEqual[b, -4.5e-5], N[(N[(t$95$1 / y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[b, 2e+29], N[(N[(x / N[(N[(N[(b * a), $MachinePrecision] * 0.5 + a), $MachinePrecision] * b + a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * t$95$1), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.50000000000000028e-5

   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

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

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

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

      2. metadata-eval N/A

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

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

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

      4. distribute-rgt-out N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. metadata-eval N/A

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

      8. remove-double-neg N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. lower-*.f64 N/A

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

      12. mul-1-neg N/A

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

      13. distribute-neg-in N/A

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

      14. metadata-eval N/A

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

      15. remove-double-neg N/A

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

      16. lower-+.f64 N/A

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

      17. lower-log.f64 85.6

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

   5. Applied rewrites 85.6%

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

   6. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 74.2

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

   8. Applied rewrites 74.2%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 74.2

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

   10. Applied rewrites 74.2%

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

   if -4.50000000000000028e-5 < b < 1.99999999999999983e29

   1. Initial program 97.3%

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

   3. Taylor expanded in y around 0

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

      1. exp-diff N/A

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

      2. associate-*r/ N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. exp-to-pow N/A

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

      6. lower-pow.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-exp.f64 72.4

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

   5. Applied rewrites 72.4%

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

   7. Applied rewrites 72.6%

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

   8. Taylor expanded in t around 0

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

   10. Applied rewrites 47.1%

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

   11. Taylor expanded in b around 0

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

   13. Applied rewrites 47.1%

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

   if 1.99999999999999983e29 < 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 0

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

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

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

      2. metadata-eval N/A

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

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

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

      4. distribute-rgt-out N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. metadata-eval N/A

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

      8. remove-double-neg N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. lower-*.f64 N/A

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

      12. mul-1-neg N/A

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

      13. distribute-neg-in N/A

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

      14. metadata-eval N/A

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

      15. remove-double-neg N/A

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

      16. lower-+.f64 N/A

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

      17. lower-log.f64 89.9

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

   5. Applied rewrites 89.9%

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

   6. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 78.5

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

   8. Applied rewrites 78.5%

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

Alternative 18: 39.8% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.2 \cdot 10^{+31}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(-x, b, x\right)}{a}}{y}\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-144}:\\ \;\;\;\;{a}^{-1} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{\mathsf{fma}\left(b, a, a\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.2e+31)
   (/ (/ (fma (- x) b x) a) y)
   (if (<= b 3.2e-144) (* (pow a -1.0) (/ x y)) (/ (/ x (fma b a a)) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.2e+31) {
		tmp = (fma(-x, b, x) / a) / y;
	} else if (b <= 3.2e-144) {
		tmp = pow(a, -1.0) * (x / y);
	} else {
		tmp = (x / fma(b, a, a)) / y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.2e+31)
		tmp = Float64(Float64(fma(Float64(-x), b, x) / a) / y);
	elseif (b <= 3.2e-144)
		tmp = Float64((a ^ -1.0) * Float64(x / y));
	else
		tmp = Float64(Float64(x / fma(b, a, a)) / y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.2e+31], N[(N[(N[((-x) * b + x), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 3.2e-144], N[(N[Power[a, -1.0], $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(b * a + a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.2000000000000001e31

   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

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

      1. exp-diff N/A

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

      2. associate-*r/ N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. exp-to-pow N/A

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

      6. lower-pow.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-exp.f64 50.1

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

   5. Applied rewrites 50.1%

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

   7. Applied rewrites 64.2%

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

   8. Taylor expanded in t around 0

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

   10. Applied rewrites 76.4%

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

   11. Taylor expanded in b around 0

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

   13. Applied rewrites 29.4%

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

   if -3.2000000000000001e31 < b < 3.19999999999999973e-144

   1. Initial program 97.5%

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

   3. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. exp-sum N/A

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

      6. lower-*.f64 N/A

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

      7. exp-to-pow N/A

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

      8. lower-pow.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. exp-to-pow N/A

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

      12. lower-pow.f64 N/A

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

      13. lower-/.f64 83.6

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

   5. Applied rewrites 83.6%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 77.7%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 50.2%

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

   if 3.19999999999999973e-144 < b

   1. Initial program 99.4%

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

   3. Taylor expanded in y around 0

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

      1. exp-diff N/A

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

      2. associate-*r/ N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. exp-to-pow N/A

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

      6. lower-pow.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-exp.f64 62.1

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

   5. Applied rewrites 62.1%

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

   7. Applied rewrites 66.9%

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

   8. Taylor expanded in t around 0

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

   10. Applied rewrites 69.9%

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

   11. Taylor expanded in b around 0

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

   13. Applied rewrites 45.9%

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

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.2 \cdot 10^{+31}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(-x, b, x\right)}{a}}{y}\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-144}:\\ \;\;\;\;{a}^{-1} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{\mathsf{fma}\left(b, a, a\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 35.8% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 3.2 \cdot 10^{-144}:\\ \;\;\;\;{a}^{-1} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{\mathsf{fma}\left(b, a, a\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 3.2e-144) (* (pow a -1.0) (/ x y)) (/ (/ x (fma b a a)) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 3.2e-144) {
		tmp = pow(a, -1.0) * (x / y);
	} else {
		tmp = (x / fma(b, a, a)) / y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 3.2e-144)
		tmp = Float64((a ^ -1.0) * Float64(x / y));
	else
		tmp = Float64(Float64(x / fma(b, a, a)) / y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 3.2e-144], N[(N[Power[a, -1.0], $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(b * a + a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 3.19999999999999973e-144

   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 b around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. exp-sum N/A

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

      6. lower-*.f64 N/A

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

      7. exp-to-pow N/A

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

      8. lower-pow.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. exp-to-pow N/A

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

      12. lower-pow.f64 N/A

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

      13. lower-/.f64 73.2

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

   5. Applied rewrites 73.2%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 68.8%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 37.9%

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

   if 3.19999999999999973e-144 < b

   1. Initial program 99.4%

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

   3. Taylor expanded in y around 0

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

      1. exp-diff N/A

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

      2. associate-*r/ N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. exp-to-pow N/A

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

      6. lower-pow.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-exp.f64 62.1

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

   5. Applied rewrites 62.1%

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

   7. Applied rewrites 66.9%

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

   8. Taylor expanded in t around 0

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

   10. Applied rewrites 69.9%

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

   11. Taylor expanded in b around 0

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

   13. Applied rewrites 45.9%

       \[\leadsto \frac{\frac{x}{\mathsf{fma}\left(b, a, a\right)}}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 41.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 3.2 \cdot 10^{-144}:\\ \;\;\;\;{a}^{-1} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{\mathsf{fma}\left(b, a, a\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 31.1% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.16 \cdot 10^{-158}:\\ \;\;\;\;{a}^{-1} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.16e-158) (* (pow a -1.0) (/ x y)) (/ (/ x a) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.16e-158) {
		tmp = pow(a, -1.0) * (x / y);
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.16d-158)) then
        tmp = (a ** (-1.0d0)) * (x / y)
    else
        tmp = (x / a) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.16e-158) {
		tmp = Math.pow(a, -1.0) * (x / y);
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.16e-158:
		tmp = math.pow(a, -1.0) * (x / y)
	else:
		tmp = (x / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.16e-158)
		tmp = Float64((a ^ -1.0) * Float64(x / y));
	else
		tmp = Float64(Float64(x / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.16e-158)
		tmp = (a ^ -1.0) * (x / y);
	else
		tmp = (x / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.16e-158], N[(N[Power[a, -1.0], $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.15999999999999996e-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 b around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. exp-sum N/A

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

      6. lower-*.f64 N/A

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

      7. exp-to-pow N/A

         \[\leadsto \left(\color{blue}{{a}^{\left(t - 1\right)}} \cdot e^{y \cdot \log z}\right) \cdot \frac{x}{y} \]

      8. lower-pow.f64 N/A

         \[\leadsto \left(\color{blue}{{a}^{\left(t - 1\right)}} \cdot e^{y \cdot \log z}\right) \cdot \frac{x}{y} \]

      9. lower--.f64 N/A

         \[\leadsto \left({a}^{\color{blue}{\left(t - 1\right)}} \cdot e^{y \cdot \log z}\right) \cdot \frac{x}{y} \]

      10. *-commutative N/A

          \[\leadsto \left({a}^{\left(t - 1\right)} \cdot e^{\color{blue}{\log z \cdot y}}\right) \cdot \frac{x}{y} \]

      11. exp-to-pow N/A

          \[\leadsto \left({a}^{\left(t - 1\right)} \cdot \color{blue}{{z}^{y}}\right) \cdot \frac{x}{y} \]

      12. lower-pow.f64 N/A

          \[\leadsto \left({a}^{\left(t - 1\right)} \cdot \color{blue}{{z}^{y}}\right) \cdot \frac{x}{y} \]

      13. lower-/.f64 67.1

          \[\leadsto \left({a}^{\left(t - 1\right)} \cdot {z}^{y}\right) \cdot \color{blue}{\frac{x}{y}} \]

   5. Applied rewrites 67.1%

      \[\leadsto \color{blue}{\left({a}^{\left(t - 1\right)} \cdot {z}^{y}\right) \cdot \frac{x}{y}} \]

   6. Taylor expanded in t around 0

      \[\leadsto \frac{{z}^{y}}{a} \cdot \frac{\color{blue}{x}}{y} \]
   7. Step-by-step derivation

   8. Applied rewrites 61.8%

      \[\leadsto \frac{{z}^{y}}{a} \cdot \frac{\color{blue}{x}}{y} \]

   9. Taylor expanded in y around 0

      \[\leadsto \frac{1}{a} \cdot \frac{x}{y} \]
   10. Step-by-step derivation

   11. Applied rewrites 31.3%

       \[\leadsto \frac{1}{a} \cdot \frac{x}{y} \]

   if -1.15999999999999996e-158 < y

   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

      \[\leadsto \frac{\color{blue}{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. exp-diff N/A

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. associate-*r/ N/A

         \[\leadsto \frac{\color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{\color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      4. lower-*.f64 N/A

         \[\leadsto \frac{\frac{\color{blue}{x \cdot e^{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y} \]

      5. exp-to-pow N/A

         \[\leadsto \frac{\frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      6. lower-pow.f64 N/A

         \[\leadsto \frac{\frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      7. lower--.f64 N/A

         \[\leadsto \frac{\frac{x \cdot {a}^{\color{blue}{\left(t - 1\right)}}}{e^{b}}}{y} \]

      8. lower-exp.f64 65.1

         \[\leadsto \frac{\frac{x \cdot {a}^{\left(t - 1\right)}}{\color{blue}{e^{b}}}}{y} \]

   5. Applied rewrites 65.1%

      \[\leadsto \frac{\color{blue}{\frac{x \cdot {a}^{\left(t - 1\right)}}{e^{b}}}}{y} \]
   6. Step-by-step derivation

   7. Applied rewrites 69.8%

      \[\leadsto \frac{\frac{{a}^{t} \cdot x}{\color{blue}{a \cdot e^{b}}}}{y} \]

   8. Taylor expanded in t around 0

      \[\leadsto \frac{\frac{x}{\color{blue}{a \cdot e^{b}}}}{y} \]
   9. Step-by-step derivation

   10. Applied rewrites 65.3%

       \[\leadsto \frac{\frac{x}{\color{blue}{e^{b} \cdot a}}}{y} \]

   11. Taylor expanded in b around 0

       \[\leadsto \frac{\frac{x}{a}}{y} \]
   12. Step-by-step derivation

   13. Applied rewrites 37.9%

       \[\leadsto \frac{\frac{x}{a}}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 35.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.16 \cdot 10^{-158}:\\ \;\;\;\;{a}^{-1} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 31.0% accurate, 14.6× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{x}{a}}{y} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ (/ x a) y))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x / a) / y;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (x / a) / y
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x / a) / y;
}

Python

def code(x, y, z, t, a, b):
	return (x / a) / y

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x / a) / y)
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x / a) / y;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]

Derivation

1. Initial program 98.8%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Add Preprocessing

3. Taylor expanded in y around 0

   \[\leadsto \frac{\color{blue}{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
4. Step-by-step derivation

   1. exp-diff N/A

      \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

   2. associate-*r/ N/A

      \[\leadsto \frac{\color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

   3. lower-/.f64 N/A

      \[\leadsto \frac{\color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

   4. lower-*.f64 N/A

      \[\leadsto \frac{\frac{\color{blue}{x \cdot e^{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y} \]

   5. exp-to-pow N/A

      \[\leadsto \frac{\frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

   6. lower-pow.f64 N/A

      \[\leadsto \frac{\frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

   7. lower--.f64 N/A

      \[\leadsto \frac{\frac{x \cdot {a}^{\color{blue}{\left(t - 1\right)}}}{e^{b}}}{y} \]

   8. lower-exp.f64 62.9

      \[\leadsto \frac{\frac{x \cdot {a}^{\left(t - 1\right)}}{\color{blue}{e^{b}}}}{y} \]

5. Applied rewrites 62.9%

   \[\leadsto \frac{\color{blue}{\frac{x \cdot {a}^{\left(t - 1\right)}}{e^{b}}}}{y} \]
6. Step-by-step derivation

7. Applied rewrites 67.6%

   \[\leadsto \frac{\frac{{a}^{t} \cdot x}{\color{blue}{a \cdot e^{b}}}}{y} \]

8. Taylor expanded in t around 0

   \[\leadsto \frac{\frac{x}{\color{blue}{a \cdot e^{b}}}}{y} \]
9. Step-by-step derivation

10. Applied rewrites 62.0%

    \[\leadsto \frac{\frac{x}{\color{blue}{e^{b} \cdot a}}}{y} \]

11. Taylor expanded in b around 0

    \[\leadsto \frac{\frac{x}{a}}{y} \]
12. Step-by-step derivation

13. Applied rewrites 33.2%

    \[\leadsto \frac{\frac{x}{a}}{y} \]
14. Add Preprocessing

Developer Target 1: 71.9% 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 2024320 
(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))