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

Percentage Accurate: 98.3% → 98.3%

Time: 14.8s

Alternatives: 24

Speedup: 1.0×

• 46.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. Final simplification 97.5%

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

Alternative 2: 48.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b} \cdot x}{y}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{\left(-x\right) \cdot b}{y}, a, \frac{x}{y} \cdot a\right)}{a \cdot a}\\ \mathbf{elif}\;t\_1 \leq 10^{+116}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(0.16666666666666666, b, 0.5\right) \cdot y, b, y\right), b, y\right) \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - b \cdot x}{a \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* (exp (- (+ (* (log a) (- t 1.0)) (* (log z) y)) b)) x) y)))
   (if (<= t_1 (- INFINITY))
     (/ (fma (/ (* (- x) b) y) a (* (/ x y) a)) (* a a))
     (if (<= t_1 1e+116)
       (/ x (* (fma (fma (* (fma 0.16666666666666666 b 0.5) y) b y) b y) a))
       (/ (- x (* b x)) (* a y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (exp((((log(a) * (t - 1.0)) + (log(z) * y)) - b)) * x) / y;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = fma(((-x * b) / y), a, ((x / y) * a)) / (a * a);
	} else if (t_1 <= 1e+116) {
		tmp = x / (fma(fma((fma(0.16666666666666666, b, 0.5) * y), b, y), b, y) * a);
	} else {
		tmp = (x - (b * x)) / (a * y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(exp(Float64(Float64(Float64(log(a) * Float64(t - 1.0)) + Float64(log(z) * y)) - b)) * x) / y)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(fma(Float64(Float64(Float64(-x) * b) / y), a, Float64(Float64(x / y) * a)) / Float64(a * a));
	elseif (t_1 <= 1e+116)
		tmp = Float64(x / Float64(fma(fma(Float64(fma(0.16666666666666666, b, 0.5) * y), b, y), b, y) * a));
	else
		tmp = Float64(Float64(x - Float64(b * x)) / Float64(a * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[Exp[N[(N[(N[(N[Log[a], $MachinePrecision] * N[(t - 1.0), $MachinePrecision]), $MachinePrecision] + N[(N[Log[z], $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(N[(N[((-x) * b), $MachinePrecision] / y), $MachinePrecision] * a + N[(N[(x / y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] / N[(a * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+116], N[(x / N[(N[(N[(N[(N[(0.16666666666666666 * b + 0.5), $MachinePrecision] * y), $MachinePrecision] * b + y), $MachinePrecision] * b + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(b * x), $MachinePrecision]), $MachinePrecision] / N[(a * y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

   5. Applied rewrites 57.7%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 54.1%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 20.9%

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

   13. Applied rewrites 35.8%

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

   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) < 1.00000000000000002e116

   1. Initial program 95.6%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

   5. Applied rewrites 60.6%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 54.4%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 55.2%

       \[\leadsto \frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(y \cdot \mathsf{fma}\left(0.16666666666666666, b, 0.5\right), b, y\right), b, y\right) \cdot a} \]

   if 1.00000000000000002e116 < (/.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 99.3%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

   5. Applied rewrites 79.4%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 67.6%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 32.3%

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

   13. Applied rewrites 47.5%

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

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b} \cdot x}{y} \leq -\infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{\left(-x\right) \cdot b}{y}, a, \frac{x}{y} \cdot a\right)}{a \cdot a}\\ \mathbf{elif}\;\frac{e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b} \cdot x}{y} \leq 10^{+116}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(0.16666666666666666, b, 0.5\right) \cdot y, b, y\right), b, y\right) \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - b \cdot x}{a \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 48.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b} \cdot x}{y}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+101}:\\ \;\;\;\;\frac{\left(1 - b\right) \cdot \frac{x}{y}}{a}\\ \mathbf{elif}\;t\_1 \leq 10^{+116}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(0.16666666666666666, b, 0.5\right) \cdot y, b, y\right), b, y\right) \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - b \cdot x}{a \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* (exp (- (+ (* (log a) (- t 1.0)) (* (log z) y)) b)) x) y)))
   (if (<= t_1 -2e+101)
     (/ (* (- 1.0 b) (/ x y)) a)
     (if (<= t_1 1e+116)
       (/ x (* (fma (fma (* (fma 0.16666666666666666 b 0.5) y) b y) b y) a))
       (/ (- x (* b x)) (* a y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (exp((((log(a) * (t - 1.0)) + (log(z) * y)) - b)) * x) / y;
	double tmp;
	if (t_1 <= -2e+101) {
		tmp = ((1.0 - b) * (x / y)) / a;
	} else if (t_1 <= 1e+116) {
		tmp = x / (fma(fma((fma(0.16666666666666666, b, 0.5) * y), b, y), b, y) * a);
	} else {
		tmp = (x - (b * x)) / (a * y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(exp(Float64(Float64(Float64(log(a) * Float64(t - 1.0)) + Float64(log(z) * y)) - b)) * x) / y)
	tmp = 0.0
	if (t_1 <= -2e+101)
		tmp = Float64(Float64(Float64(1.0 - b) * Float64(x / y)) / a);
	elseif (t_1 <= 1e+116)
		tmp = Float64(x / Float64(fma(fma(Float64(fma(0.16666666666666666, b, 0.5) * y), b, y), b, y) * a));
	else
		tmp = Float64(Float64(x - Float64(b * x)) / Float64(a * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[Exp[N[(N[(N[(N[Log[a], $MachinePrecision] * N[(t - 1.0), $MachinePrecision]), $MachinePrecision] + N[(N[Log[z], $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+101], N[(N[(N[(1.0 - b), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[t$95$1, 1e+116], N[(x / N[(N[(N[(N[(N[(0.16666666666666666 * b + 0.5), $MachinePrecision] * y), $MachinePrecision] * b + y), $MachinePrecision] * b + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(b * x), $MachinePrecision]), $MachinePrecision] / N[(a * y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 x (exp.f64 (-.f64 (+.f64 (*.f64 y (log.f64 z)) (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))) b))) y) < -2e101

   1. Initial program 99.3%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

   5. Applied rewrites 60.8%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 57.5%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 26.0%

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

   13. Applied rewrites 38.5%

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

   if -2e101 < (/.f64 (*.f64 x (exp.f64 (-.f64 (+.f64 (*.f64 y (log.f64 z)) (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))) b))) y) < 1.00000000000000002e116

   1. Initial program 95.8%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

   5. Applied rewrites 59.4%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 53.0%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 54.0%

       \[\leadsto \frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(y \cdot \mathsf{fma}\left(0.16666666666666666, b, 0.5\right), b, y\right), b, y\right) \cdot a} \]

   if 1.00000000000000002e116 < (/.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 99.3%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

   5. Applied rewrites 79.4%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 67.6%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 32.3%

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

   13. Applied rewrites 47.5%

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

4. Final simplification 49.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b} \cdot x}{y} \leq -2 \cdot 10^{+101}:\\ \;\;\;\;\frac{\left(1 - b\right) \cdot \frac{x}{y}}{a}\\ \mathbf{elif}\;\frac{e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b} \cdot x}{y} \leq 10^{+116}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(0.16666666666666666, b, 0.5\right) \cdot y, b, y\right), b, y\right) \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - b \cdot x}{a \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 40.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b} \cdot x}{y}\\ t_2 := \frac{x - b \cdot x}{a \cdot y}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+116}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(b, y, y\right) \cdot a}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* (exp (- (+ (* (log a) (- t 1.0)) (* (log z) y)) b)) x) y))
        (t_2 (/ (- x (* b x)) (* a y))))
   (if (<= t_1 (- INFINITY))
     t_2
     (if (<= t_1 1e+116) (/ x (* (fma b y y) a)) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (exp((((log(a) * (t - 1.0)) + (log(z) * y)) - b)) * x) / y;
	double t_2 = (x - (b * x)) / (a * y);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= 1e+116) {
		tmp = x / (fma(b, y, y) * a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(exp(Float64(Float64(Float64(log(a) * Float64(t - 1.0)) + Float64(log(z) * y)) - b)) * x) / y)
	t_2 = Float64(Float64(x - Float64(b * x)) / Float64(a * y))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_1 <= 1e+116)
		tmp = Float64(x / Float64(fma(b, y, y) * a));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[Exp[N[(N[(N[(N[Log[a], $MachinePrecision] * N[(t - 1.0), $MachinePrecision]), $MachinePrecision] + N[(N[Log[z], $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x - N[(b * x), $MachinePrecision]), $MachinePrecision] / N[(a * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, 1e+116], N[(x / N[(N[(b * y + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

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 1.00000000000000002e116 < (/.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 99.6%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

   5. Applied rewrites 70.6%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 62.1%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 27.7%

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

   13. Applied rewrites 42.2%

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

   if -inf.0 < (/.f64 (*.f64 x (exp.f64 (-.f64 (+.f64 (*.f64 y (log.f64 z)) (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))) b))) y) < 1.00000000000000002e116

   1. Initial program 95.6%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

   5. Applied rewrites 60.6%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 54.4%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 45.5%

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

4. Final simplification 43.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b} \cdot x}{y} \leq -\infty:\\ \;\;\;\;\frac{x - b \cdot x}{a \cdot y}\\ \mathbf{elif}\;\frac{e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b} \cdot x}{y} \leq 10^{+116}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(b, y, y\right) \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - b \cdot x}{a \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 36.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b} \cdot x}{y}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-229}:\\ \;\;\;\;\frac{x}{a \cdot y}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+172}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(b, y, y\right) \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{a \cdot y} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* (exp (- (+ (* (log a) (- t 1.0)) (* (log z) y)) b)) x) y)))
   (if (<= t_1 -1e-229)
     (/ x (* a y))
     (if (<= t_1 5e+172) (/ x (* (fma b y y) a)) (* (/ 1.0 (* a y)) x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (exp((((log(a) * (t - 1.0)) + (log(z) * y)) - b)) * x) / y;
	double tmp;
	if (t_1 <= -1e-229) {
		tmp = x / (a * y);
	} else if (t_1 <= 5e+172) {
		tmp = x / (fma(b, y, y) * a);
	} else {
		tmp = (1.0 / (a * y)) * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(exp(Float64(Float64(Float64(log(a) * Float64(t - 1.0)) + Float64(log(z) * y)) - b)) * x) / y)
	tmp = 0.0
	if (t_1 <= -1e-229)
		tmp = Float64(x / Float64(a * y));
	elseif (t_1 <= 5e+172)
		tmp = Float64(x / Float64(fma(b, y, y) * a));
	else
		tmp = Float64(Float64(1.0 / Float64(a * y)) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[Exp[N[(N[(N[(N[Log[a], $MachinePrecision] * N[(t - 1.0), $MachinePrecision]), $MachinePrecision] + N[(N[Log[z], $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-229], N[(x / N[(a * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+172], N[(x / N[(N[(b * y + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / N[(a * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 x (exp.f64 (-.f64 (+.f64 (*.f64 y (log.f64 z)) (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))) b))) y) < -1.00000000000000007e-229

   1. Initial program 99.0%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

   5. Applied rewrites 61.5%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 58.3%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 30.7%

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

   if -1.00000000000000007e-229 < (/.f64 (*.f64 x (exp.f64 (-.f64 (+.f64 (*.f64 y (log.f64 z)) (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))) b))) y) < 5.0000000000000001e172

   1. Initial program 95.8%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

   5. Applied rewrites 59.4%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 53.0%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 44.2%

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

   if 5.0000000000000001e172 < (/.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 99.4%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

   5. Applied rewrites 79.2%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 67.1%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 41.4%

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

   13. Applied rewrites 41.3%

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

4. Final simplification 40.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b} \cdot x}{y} \leq -1 \cdot 10^{-229}:\\ \;\;\;\;\frac{x}{a \cdot y}\\ \mathbf{elif}\;\frac{e^{\left(\log a \cdot \left(t - 1\right) + \log z \cdot y\right) - b} \cdot x}{y} \leq 5 \cdot 10^{+172}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(b, y, y\right) \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{a \cdot y} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log a \cdot \left(t - 1\right)\\ t_2 := e^{b} \cdot y\\ t_3 := \frac{e^{\log a \cdot t - b} \cdot x}{y}\\ \mathbf{if}\;t\_1 \leq -5000000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_1 \leq -150:\\ \;\;\;\;\frac{x}{t\_2 \cdot a}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+63}:\\ \;\;\;\;\frac{\frac{{z}^{y}}{a} \cdot x}{t\_2}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (log a) (- t 1.0)))
        (t_2 (* (exp b) y))
        (t_3 (/ (* (exp (- (* (log a) t) b)) x) y)))
   (if (<= t_1 -5000000.0)
     t_3
     (if (<= t_1 -150.0)
       (/ x (* t_2 a))
       (if (<= t_1 5e+63) (/ (* (/ (pow z y) a) x) t_2) t_3)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = log(a) * (t - 1.0);
	double t_2 = exp(b) * y;
	double t_3 = (exp(((log(a) * t) - b)) * x) / y;
	double tmp;
	if (t_1 <= -5000000.0) {
		tmp = t_3;
	} else if (t_1 <= -150.0) {
		tmp = x / (t_2 * a);
	} else if (t_1 <= 5e+63) {
		tmp = ((pow(z, y) / a) * x) / t_2;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = log(a) * (t - 1.0d0)
    t_2 = exp(b) * y
    t_3 = (exp(((log(a) * t) - b)) * x) / y
    if (t_1 <= (-5000000.0d0)) then
        tmp = t_3
    else if (t_1 <= (-150.0d0)) then
        tmp = x / (t_2 * a)
    else if (t_1 <= 5d+63) then
        tmp = (((z ** y) / a) * x) / t_2
    else
        tmp = t_3
    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.log(a) * (t - 1.0);
	double t_2 = Math.exp(b) * y;
	double t_3 = (Math.exp(((Math.log(a) * t) - b)) * x) / y;
	double tmp;
	if (t_1 <= -5000000.0) {
		tmp = t_3;
	} else if (t_1 <= -150.0) {
		tmp = x / (t_2 * a);
	} else if (t_1 <= 5e+63) {
		tmp = ((Math.pow(z, y) / a) * x) / t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.log(a) * (t - 1.0)
	t_2 = math.exp(b) * y
	t_3 = (math.exp(((math.log(a) * t) - b)) * x) / y
	tmp = 0
	if t_1 <= -5000000.0:
		tmp = t_3
	elif t_1 <= -150.0:
		tmp = x / (t_2 * a)
	elif t_1 <= 5e+63:
		tmp = ((math.pow(z, y) / a) * x) / t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(log(a) * Float64(t - 1.0))
	t_2 = Float64(exp(b) * y)
	t_3 = Float64(Float64(exp(Float64(Float64(log(a) * t) - b)) * x) / y)
	tmp = 0.0
	if (t_1 <= -5000000.0)
		tmp = t_3;
	elseif (t_1 <= -150.0)
		tmp = Float64(x / Float64(t_2 * a));
	elseif (t_1 <= 5e+63)
		tmp = Float64(Float64(Float64((z ^ y) / a) * x) / t_2);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = log(a) * (t - 1.0);
	t_2 = exp(b) * y;
	t_3 = (exp(((log(a) * t) - b)) * x) / y;
	tmp = 0.0;
	if (t_1 <= -5000000.0)
		tmp = t_3;
	elseif (t_1 <= -150.0)
		tmp = x / (t_2 * a);
	elseif (t_1 <= 5e+63)
		tmp = (((z ^ y) / a) * x) / t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[Log[a], $MachinePrecision] * N[(t - 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[Exp[b], $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[Exp[N[(N[(N[Log[a], $MachinePrecision] * t), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t$95$1, -5000000.0], t$95$3, If[LessEqual[t$95$1, -150.0], N[(x / N[(t$95$2 * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+63], N[(N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] * x), $MachinePrecision] / t$95$2), $MachinePrecision], t$95$3]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -5e6 or 5.00000000000000011e63 < (*.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. lower-*.f64 N/A

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

      2. rem-exp-log N/A

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

      3. lower-log.f64 N/A

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

      4. rem-exp-log 91.6

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

   5. Applied rewrites 91.6%

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

   if -5e6 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -150

   1. Initial program 87.7%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

   5. Applied rewrites 69.5%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 80.8%

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

   if -150 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 5.00000000000000011e63

   1. Initial program 99.0%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

   5. Applied rewrites 89.3%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\log a \cdot \left(t - 1\right) \leq -5000000:\\ \;\;\;\;\frac{e^{\log a \cdot t - b} \cdot x}{y}\\ \mathbf{elif}\;\log a \cdot \left(t - 1\right) \leq -150:\\ \;\;\;\;\frac{x}{\left(e^{b} \cdot y\right) \cdot a}\\ \mathbf{elif}\;\log a \cdot \left(t - 1\right) \leq 5 \cdot 10^{+63}:\\ \;\;\;\;\frac{\frac{{z}^{y}}{a} \cdot x}{e^{b} \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{\log a \cdot t - b} \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log a \cdot \left(t - 1\right)\\ t_2 := \frac{e^{\log a \cdot t - b} \cdot x}{y}\\ \mathbf{if}\;t\_1 \leq -5000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 48:\\ \;\;\;\;\frac{x}{\left(e^{b} \cdot y\right) \cdot a}\\ \mathbf{elif}\;t\_1 \leq 677.45:\\ \;\;\;\;\frac{1}{a \cdot y} \cdot \left({z}^{y} \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (log a) (- t 1.0)))
        (t_2 (/ (* (exp (- (* (log a) t) b)) x) y)))
   (if (<= t_1 -5000000.0)
     t_2
     (if (<= t_1 48.0)
       (/ x (* (* (exp b) y) a))
       (if (<= t_1 677.45) (* (/ 1.0 (* a y)) (* (pow z y) x)) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = log(a) * (t - 1.0);
	double t_2 = (exp(((log(a) * t) - b)) * x) / y;
	double tmp;
	if (t_1 <= -5000000.0) {
		tmp = t_2;
	} else if (t_1 <= 48.0) {
		tmp = x / ((exp(b) * y) * a);
	} else if (t_1 <= 677.45) {
		tmp = (1.0 / (a * y)) * (pow(z, y) * x);
	} 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 = log(a) * (t - 1.0d0)
    t_2 = (exp(((log(a) * t) - b)) * x) / y
    if (t_1 <= (-5000000.0d0)) then
        tmp = t_2
    else if (t_1 <= 48.0d0) then
        tmp = x / ((exp(b) * y) * a)
    else if (t_1 <= 677.45d0) then
        tmp = (1.0d0 / (a * y)) * ((z ** y) * x)
    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.log(a) * (t - 1.0);
	double t_2 = (Math.exp(((Math.log(a) * t) - b)) * x) / y;
	double tmp;
	if (t_1 <= -5000000.0) {
		tmp = t_2;
	} else if (t_1 <= 48.0) {
		tmp = x / ((Math.exp(b) * y) * a);
	} else if (t_1 <= 677.45) {
		tmp = (1.0 / (a * y)) * (Math.pow(z, y) * x);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.log(a) * (t - 1.0)
	t_2 = (math.exp(((math.log(a) * t) - b)) * x) / y
	tmp = 0
	if t_1 <= -5000000.0:
		tmp = t_2
	elif t_1 <= 48.0:
		tmp = x / ((math.exp(b) * y) * a)
	elif t_1 <= 677.45:
		tmp = (1.0 / (a * y)) * (math.pow(z, y) * x)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(log(a) * Float64(t - 1.0))
	t_2 = Float64(Float64(exp(Float64(Float64(log(a) * t) - b)) * x) / y)
	tmp = 0.0
	if (t_1 <= -5000000.0)
		tmp = t_2;
	elseif (t_1 <= 48.0)
		tmp = Float64(x / Float64(Float64(exp(b) * y) * a));
	elseif (t_1 <= 677.45)
		tmp = Float64(Float64(1.0 / Float64(a * y)) * Float64((z ^ y) * x));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = log(a) * (t - 1.0);
	t_2 = (exp(((log(a) * t) - b)) * x) / y;
	tmp = 0.0;
	if (t_1 <= -5000000.0)
		tmp = t_2;
	elseif (t_1 <= 48.0)
		tmp = x / ((exp(b) * y) * a);
	elseif (t_1 <= 677.45)
		tmp = (1.0 / (a * y)) * ((z ^ y) * x);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[Log[a], $MachinePrecision] * N[(t - 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[Exp[N[(N[(N[Log[a], $MachinePrecision] * t), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t$95$1, -5000000.0], t$95$2, If[LessEqual[t$95$1, 48.0], N[(x / N[(N[(N[Exp[b], $MachinePrecision] * y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 677.45], N[(N[(1.0 / N[(a * y), $MachinePrecision]), $MachinePrecision] * N[(N[Power[z, y], $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -5e6 or 677.45000000000005 < (*.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. lower-*.f64 N/A

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

      2. rem-exp-log N/A

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

      3. lower-log.f64 N/A

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

      4. rem-exp-log 90.4

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

   5. Applied rewrites 90.4%

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

   if -5e6 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 48

   1. Initial program 90.5%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

   5. Applied rewrites 77.0%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 80.8%

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

   if 48 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 677.45000000000005

   1. Initial program 98.8%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. associate-*r* N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. exp-to-pow N/A

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

      8. lower-pow.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. exp-prod N/A

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

      11. lower-pow.f64 N/A

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

      12. rem-exp-log N/A

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

      13. lower--.f64 87.5

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

   5. Applied rewrites 87.5%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 87.5%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\log a \cdot \left(t - 1\right) \leq -5000000:\\ \;\;\;\;\frac{e^{\log a \cdot t - b} \cdot x}{y}\\ \mathbf{elif}\;\log a \cdot \left(t - 1\right) \leq 48:\\ \;\;\;\;\frac{x}{\left(e^{b} \cdot y\right) \cdot a}\\ \mathbf{elif}\;\log a \cdot \left(t - 1\right) \leq 677.45:\\ \;\;\;\;\frac{1}{a \cdot y} \cdot \left({z}^{y} \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{\log a \cdot t - b} \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 76.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log a \cdot \left(t - 1\right)\\ t_2 := \frac{{a}^{\left(t - 1\right)}}{y} \cdot x\\ \mathbf{if}\;t\_1 \leq -5000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 48:\\ \;\;\;\;\frac{x}{\left(e^{b} \cdot y\right) \cdot a}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+63}:\\ \;\;\;\;\frac{1}{a \cdot y} \cdot \left({z}^{y} \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (log a) (- t 1.0))) (t_2 (* (/ (pow a (- t 1.0)) y) x)))
   (if (<= t_1 -5000000.0)
     t_2
     (if (<= t_1 48.0)
       (/ x (* (* (exp b) y) a))
       (if (<= t_1 5e+63) (* (/ 1.0 (* a y)) (* (pow z y) x)) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = log(a) * (t - 1.0);
	double t_2 = (pow(a, (t - 1.0)) / y) * x;
	double tmp;
	if (t_1 <= -5000000.0) {
		tmp = t_2;
	} else if (t_1 <= 48.0) {
		tmp = x / ((exp(b) * y) * a);
	} else if (t_1 <= 5e+63) {
		tmp = (1.0 / (a * y)) * (pow(z, y) * x);
	} 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 = log(a) * (t - 1.0d0)
    t_2 = ((a ** (t - 1.0d0)) / y) * x
    if (t_1 <= (-5000000.0d0)) then
        tmp = t_2
    else if (t_1 <= 48.0d0) then
        tmp = x / ((exp(b) * y) * a)
    else if (t_1 <= 5d+63) then
        tmp = (1.0d0 / (a * y)) * ((z ** y) * x)
    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.log(a) * (t - 1.0);
	double t_2 = (Math.pow(a, (t - 1.0)) / y) * x;
	double tmp;
	if (t_1 <= -5000000.0) {
		tmp = t_2;
	} else if (t_1 <= 48.0) {
		tmp = x / ((Math.exp(b) * y) * a);
	} else if (t_1 <= 5e+63) {
		tmp = (1.0 / (a * y)) * (Math.pow(z, y) * x);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.log(a) * (t - 1.0)
	t_2 = (math.pow(a, (t - 1.0)) / y) * x
	tmp = 0
	if t_1 <= -5000000.0:
		tmp = t_2
	elif t_1 <= 48.0:
		tmp = x / ((math.exp(b) * y) * a)
	elif t_1 <= 5e+63:
		tmp = (1.0 / (a * y)) * (math.pow(z, y) * x)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(log(a) * Float64(t - 1.0))
	t_2 = Float64(Float64((a ^ Float64(t - 1.0)) / y) * x)
	tmp = 0.0
	if (t_1 <= -5000000.0)
		tmp = t_2;
	elseif (t_1 <= 48.0)
		tmp = Float64(x / Float64(Float64(exp(b) * y) * a));
	elseif (t_1 <= 5e+63)
		tmp = Float64(Float64(1.0 / Float64(a * y)) * Float64((z ^ y) * x));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = log(a) * (t - 1.0);
	t_2 = ((a ^ (t - 1.0)) / y) * x;
	tmp = 0.0;
	if (t_1 <= -5000000.0)
		tmp = t_2;
	elseif (t_1 <= 48.0)
		tmp = x / ((exp(b) * y) * a);
	elseif (t_1 <= 5e+63)
		tmp = (1.0 / (a * y)) * ((z ^ y) * x);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[Log[a], $MachinePrecision] * N[(t - 1.0), $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, -5000000.0], t$95$2, If[LessEqual[t$95$1, 48.0], N[(x / N[(N[(N[Exp[b], $MachinePrecision] * y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+63], N[(N[(1.0 / N[(a * y), $MachinePrecision]), $MachinePrecision] * N[(N[Power[z, y], $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -5e6 or 5.00000000000000011e63 < (*.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

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

      1. exp-sum N/A

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

      2. associate-*r* N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. exp-to-pow N/A

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

      8. lower-pow.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. exp-prod N/A

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

      11. lower-pow.f64 N/A

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

      12. rem-exp-log N/A

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

      13. lower--.f64 75.3

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

   5. Applied rewrites 75.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 87.4%

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

   if -5e6 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 48

   1. Initial program 90.5%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

   5. Applied rewrites 77.0%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 80.8%

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

   if 48 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 5.00000000000000011e63

   1. Initial program 99.0%

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

   3. Taylor expanded in 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. exp-sum N/A

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

      2. associate-*r* N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. exp-to-pow N/A

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

      8. lower-pow.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. exp-prod N/A

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

      11. lower-pow.f64 N/A

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

      12. rem-exp-log N/A

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

      13. lower--.f64 80.0

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

   5. Applied rewrites 80.0%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 81.4%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\log a \cdot \left(t - 1\right) \leq -5000000:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)}}{y} \cdot x\\ \mathbf{elif}\;\log a \cdot \left(t - 1\right) \leq 48:\\ \;\;\;\;\frac{x}{\left(e^{b} \cdot y\right) \cdot a}\\ \mathbf{elif}\;\log a \cdot \left(t - 1\right) \leq 5 \cdot 10^{+63}:\\ \;\;\;\;\frac{1}{a \cdot y} \cdot \left({z}^{y} \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)}}{y} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log a \cdot \left(t - 1\right)\\ t_2 := \frac{{a}^{\left(t - 1\right)}}{y} \cdot x\\ \mathbf{if}\;t\_1 \leq -5000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 50:\\ \;\;\;\;\frac{x}{\left(e^{b} \cdot y\right) \cdot a}\\ \mathbf{elif}\;t\_1 \leq 10^{+46}:\\ \;\;\;\;\frac{x}{a \cdot y} \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (log a) (- t 1.0))) (t_2 (* (/ (pow a (- t 1.0)) y) x)))
   (if (<= t_1 -5000000.0)
     t_2
     (if (<= t_1 50.0)
       (/ x (* (* (exp b) y) a))
       (if (<= t_1 1e+46) (* (/ x (* a y)) (pow z y)) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = log(a) * (t - 1.0);
	double t_2 = (pow(a, (t - 1.0)) / y) * x;
	double tmp;
	if (t_1 <= -5000000.0) {
		tmp = t_2;
	} else if (t_1 <= 50.0) {
		tmp = x / ((exp(b) * y) * a);
	} else if (t_1 <= 1e+46) {
		tmp = (x / (a * y)) * pow(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 = log(a) * (t - 1.0d0)
    t_2 = ((a ** (t - 1.0d0)) / y) * x
    if (t_1 <= (-5000000.0d0)) then
        tmp = t_2
    else if (t_1 <= 50.0d0) then
        tmp = x / ((exp(b) * y) * a)
    else if (t_1 <= 1d+46) then
        tmp = (x / (a * y)) * (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.log(a) * (t - 1.0);
	double t_2 = (Math.pow(a, (t - 1.0)) / y) * x;
	double tmp;
	if (t_1 <= -5000000.0) {
		tmp = t_2;
	} else if (t_1 <= 50.0) {
		tmp = x / ((Math.exp(b) * y) * a);
	} else if (t_1 <= 1e+46) {
		tmp = (x / (a * y)) * Math.pow(z, y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.log(a) * (t - 1.0)
	t_2 = (math.pow(a, (t - 1.0)) / y) * x
	tmp = 0
	if t_1 <= -5000000.0:
		tmp = t_2
	elif t_1 <= 50.0:
		tmp = x / ((math.exp(b) * y) * a)
	elif t_1 <= 1e+46:
		tmp = (x / (a * y)) * math.pow(z, y)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(log(a) * Float64(t - 1.0))
	t_2 = Float64(Float64((a ^ Float64(t - 1.0)) / y) * x)
	tmp = 0.0
	if (t_1 <= -5000000.0)
		tmp = t_2;
	elseif (t_1 <= 50.0)
		tmp = Float64(x / Float64(Float64(exp(b) * y) * a));
	elseif (t_1 <= 1e+46)
		tmp = Float64(Float64(x / Float64(a * y)) * (z ^ y));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = log(a) * (t - 1.0);
	t_2 = ((a ^ (t - 1.0)) / y) * x;
	tmp = 0.0;
	if (t_1 <= -5000000.0)
		tmp = t_2;
	elseif (t_1 <= 50.0)
		tmp = x / ((exp(b) * y) * a);
	elseif (t_1 <= 1e+46)
		tmp = (x / (a * y)) * (z ^ y);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[Log[a], $MachinePrecision] * N[(t - 1.0), $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, -5000000.0], t$95$2, If[LessEqual[t$95$1, 50.0], N[(x / N[(N[(N[Exp[b], $MachinePrecision] * y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+46], N[(N[(x / N[(a * y), $MachinePrecision]), $MachinePrecision] * N[Power[z, 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)) < -5e6 or 9.9999999999999999e45 < (*.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

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

      1. exp-sum N/A

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

      2. associate-*r* N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. exp-to-pow N/A

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

      8. lower-pow.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. exp-prod N/A

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

      11. lower-pow.f64 N/A

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

      12. rem-exp-log N/A

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

      13. lower--.f64 74.7

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

   5. Applied rewrites 74.7%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 86.3%

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

   if -5e6 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 50

   1. Initial program 90.7%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

   5. Applied rewrites 77.4%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 79.5%

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

   if 50 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 9.9999999999999999e45

   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 t around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

   5. Applied rewrites 86.3%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 78.6%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\log a \cdot \left(t - 1\right) \leq -5000000:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)}}{y} \cdot x\\ \mathbf{elif}\;\log a \cdot \left(t - 1\right) \leq 50:\\ \;\;\;\;\frac{x}{\left(e^{b} \cdot y\right) \cdot a}\\ \mathbf{elif}\;\log a \cdot \left(t - 1\right) \leq 10^{+46}:\\ \;\;\;\;\frac{x}{a \cdot y} \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)}}{y} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 75.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log a \cdot \left(t - 1\right)\\ t_2 := \frac{{a}^{\left(t - 1\right)}}{y} \cdot x\\ \mathbf{if}\;t\_1 \leq -5000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+46}:\\ \;\;\;\;\frac{x}{\left(e^{b} \cdot y\right) \cdot a}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (log a) (- t 1.0))) (t_2 (* (/ (pow a (- t 1.0)) y) x)))
   (if (<= t_1 -5000000.0)
     t_2
     (if (<= t_1 1e+46) (/ x (* (* (exp b) y) a)) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = log(a) * (t - 1.0);
	double t_2 = (pow(a, (t - 1.0)) / y) * x;
	double tmp;
	if (t_1 <= -5000000.0) {
		tmp = t_2;
	} else if (t_1 <= 1e+46) {
		tmp = x / ((exp(b) * y) * a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = log(a) * (t - 1.0d0)
    t_2 = ((a ** (t - 1.0d0)) / y) * x
    if (t_1 <= (-5000000.0d0)) then
        tmp = t_2
    else if (t_1 <= 1d+46) then
        tmp = x / ((exp(b) * y) * a)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = Math.log(a) * (t - 1.0);
	double t_2 = (Math.pow(a, (t - 1.0)) / y) * x;
	double tmp;
	if (t_1 <= -5000000.0) {
		tmp = t_2;
	} else if (t_1 <= 1e+46) {
		tmp = x / ((Math.exp(b) * y) * a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.log(a) * (t - 1.0)
	t_2 = (math.pow(a, (t - 1.0)) / y) * x
	tmp = 0
	if t_1 <= -5000000.0:
		tmp = t_2
	elif t_1 <= 1e+46:
		tmp = x / ((math.exp(b) * y) * a)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(log(a) * Float64(t - 1.0))
	t_2 = Float64(Float64((a ^ Float64(t - 1.0)) / y) * x)
	tmp = 0.0
	if (t_1 <= -5000000.0)
		tmp = t_2;
	elseif (t_1 <= 1e+46)
		tmp = Float64(x / Float64(Float64(exp(b) * y) * a));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = log(a) * (t - 1.0);
	t_2 = ((a ^ (t - 1.0)) / y) * x;
	tmp = 0.0;
	if (t_1 <= -5000000.0)
		tmp = t_2;
	elseif (t_1 <= 1e+46)
		tmp = x / ((exp(b) * y) * a);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[Log[a], $MachinePrecision] * N[(t - 1.0), $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, -5000000.0], t$95$2, If[LessEqual[t$95$1, 1e+46], N[(x / N[(N[(N[Exp[b], $MachinePrecision] * y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -5e6 or 9.9999999999999999e45 < (*.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

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

      1. exp-sum N/A

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

      2. associate-*r* N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. exp-to-pow N/A

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

      8. lower-pow.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. exp-prod N/A

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

      11. lower-pow.f64 N/A

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

      12. rem-exp-log N/A

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

      13. lower--.f64 74.7

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

   5. Applied rewrites 74.7%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 86.3%

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

   if -5e6 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 9.9999999999999999e45

   1. Initial program 95.2%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

   5. Applied rewrites 82.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 73.6%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\log a \cdot \left(t - 1\right) \leq -5000000:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)}}{y} \cdot x\\ \mathbf{elif}\;\log a \cdot \left(t - 1\right) \leq 10^{+46}:\\ \;\;\;\;\frac{x}{\left(e^{b} \cdot y\right) \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)}}{y} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 72.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log a \cdot \left(t - 1\right)\\ t_2 := \frac{{a}^{\left(t - 1\right)}}{y} \cdot x\\ \mathbf{if}\;t\_1 \leq -5000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+46}:\\ \;\;\;\;\frac{x}{\left(a \cdot y\right) \cdot e^{b}}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (log a) (- t 1.0))) (t_2 (* (/ (pow a (- t 1.0)) y) x)))
   (if (<= t_1 -5000000.0)
     t_2
     (if (<= t_1 1e+46) (/ x (* (* a y) (exp b))) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = log(a) * (t - 1.0);
	double t_2 = (pow(a, (t - 1.0)) / y) * x;
	double tmp;
	if (t_1 <= -5000000.0) {
		tmp = t_2;
	} else if (t_1 <= 1e+46) {
		tmp = x / ((a * y) * exp(b));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = log(a) * (t - 1.0d0)
    t_2 = ((a ** (t - 1.0d0)) / y) * x
    if (t_1 <= (-5000000.0d0)) then
        tmp = t_2
    else if (t_1 <= 1d+46) then
        tmp = x / ((a * y) * exp(b))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = Math.log(a) * (t - 1.0);
	double t_2 = (Math.pow(a, (t - 1.0)) / y) * x;
	double tmp;
	if (t_1 <= -5000000.0) {
		tmp = t_2;
	} else if (t_1 <= 1e+46) {
		tmp = x / ((a * y) * Math.exp(b));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.log(a) * (t - 1.0)
	t_2 = (math.pow(a, (t - 1.0)) / y) * x
	tmp = 0
	if t_1 <= -5000000.0:
		tmp = t_2
	elif t_1 <= 1e+46:
		tmp = x / ((a * y) * math.exp(b))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(log(a) * Float64(t - 1.0))
	t_2 = Float64(Float64((a ^ Float64(t - 1.0)) / y) * x)
	tmp = 0.0
	if (t_1 <= -5000000.0)
		tmp = t_2;
	elseif (t_1 <= 1e+46)
		tmp = Float64(x / Float64(Float64(a * y) * exp(b)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = log(a) * (t - 1.0);
	t_2 = ((a ^ (t - 1.0)) / y) * x;
	tmp = 0.0;
	if (t_1 <= -5000000.0)
		tmp = t_2;
	elseif (t_1 <= 1e+46)
		tmp = x / ((a * y) * exp(b));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[Log[a], $MachinePrecision] * N[(t - 1.0), $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, -5000000.0], t$95$2, If[LessEqual[t$95$1, 1e+46], N[(x / N[(N[(a * y), $MachinePrecision] * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -5e6 or 9.9999999999999999e45 < (*.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

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

      1. exp-sum N/A

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

      2. associate-*r* N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. exp-to-pow N/A

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

      8. lower-pow.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. exp-prod N/A

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

      11. lower-pow.f64 N/A

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

      12. rem-exp-log N/A

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

      13. lower--.f64 74.7

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

   5. Applied rewrites 74.7%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 86.3%

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

   if -5e6 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 9.9999999999999999e45

   1. Initial program 95.2%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

   5. Applied rewrites 82.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 73.6%

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

   10. Applied rewrites 70.7%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\log a \cdot \left(t - 1\right) \leq -5000000:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)}}{y} \cdot x\\ \mathbf{elif}\;\log a \cdot \left(t - 1\right) \leq 10^{+46}:\\ \;\;\;\;\frac{x}{\left(a \cdot y\right) \cdot e^{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)}}{y} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 83.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{e^{\log a \cdot t - b} \cdot x}{y}\\ t_2 := \frac{{z}^{y}}{a}\\ \mathbf{if}\;t \leq -5.6 \cdot 10^{+36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-238}:\\ \;\;\;\;\frac{\left(e^{-b} \cdot t\_2\right) \cdot x}{y}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-20}:\\ \;\;\;\;\frac{x}{y} \cdot t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* (exp (- (* (log a) t) b)) x) y)) (t_2 (/ (pow z y) a)))
   (if (<= t -5.6e+36)
     t_1
     (if (<= t 1.15e-238)
       (/ (* (* (exp (- b)) t_2) x) y)
       (if (<= t 1.8e-20) (* (/ x y) t_2) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (exp(((log(a) * t) - b)) * x) / y;
	double t_2 = pow(z, y) / a;
	double tmp;
	if (t <= -5.6e+36) {
		tmp = t_1;
	} else if (t <= 1.15e-238) {
		tmp = ((exp(-b) * t_2) * x) / y;
	} else if (t <= 1.8e-20) {
		tmp = (x / y) * t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (exp(((log(a) * t) - b)) * x) / y
    t_2 = (z ** y) / a
    if (t <= (-5.6d+36)) then
        tmp = t_1
    else if (t <= 1.15d-238) then
        tmp = ((exp(-b) * t_2) * x) / y
    else if (t <= 1.8d-20) then
        tmp = (x / y) * t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (Math.exp(((Math.log(a) * t) - b)) * x) / y;
	double t_2 = Math.pow(z, y) / a;
	double tmp;
	if (t <= -5.6e+36) {
		tmp = t_1;
	} else if (t <= 1.15e-238) {
		tmp = ((Math.exp(-b) * t_2) * x) / y;
	} else if (t <= 1.8e-20) {
		tmp = (x / y) * t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (math.exp(((math.log(a) * t) - b)) * x) / y
	t_2 = math.pow(z, y) / a
	tmp = 0
	if t <= -5.6e+36:
		tmp = t_1
	elif t <= 1.15e-238:
		tmp = ((math.exp(-b) * t_2) * x) / y
	elif t <= 1.8e-20:
		tmp = (x / y) * t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(exp(Float64(Float64(log(a) * t) - b)) * x) / y)
	t_2 = Float64((z ^ y) / a)
	tmp = 0.0
	if (t <= -5.6e+36)
		tmp = t_1;
	elseif (t <= 1.15e-238)
		tmp = Float64(Float64(Float64(exp(Float64(-b)) * t_2) * x) / y);
	elseif (t <= 1.8e-20)
		tmp = Float64(Float64(x / y) * t_2);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (exp(((log(a) * t) - b)) * x) / y;
	t_2 = (z ^ y) / a;
	tmp = 0.0;
	if (t <= -5.6e+36)
		tmp = t_1;
	elseif (t <= 1.15e-238)
		tmp = ((exp(-b) * t_2) * x) / y;
	elseif (t <= 1.8e-20)
		tmp = (x / y) * t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[Exp[N[(N[(N[Log[a], $MachinePrecision] * t), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[t, -5.6e+36], t$95$1, If[LessEqual[t, 1.15e-238], N[(N[(N[(N[Exp[(-b)], $MachinePrecision] * t$95$2), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 1.8e-20], N[(N[(x / y), $MachinePrecision] * t$95$2), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.6000000000000001e36 or 1.79999999999999987e-20 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. rem-exp-log N/A

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

      3. lower-log.f64 N/A

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

      4. rem-exp-log 91.4

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

   5. Applied rewrites 91.4%

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

   if -5.6000000000000001e36 < t < 1.15000000000000002e-238

   1. Initial program 95.5%

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

   3. Taylor expanded in t around 0

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

      1. sub-neg N/A

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

      2. exp-sum N/A

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

      3. mul-1-neg N/A

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

      4. lower-*.f64 N/A

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

      5. +-commutative N/A

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

      6. mul-1-neg N/A

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

      7. unsub-neg N/A

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

      8. exp-diff N/A

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

      9. lower-/.f64 N/A

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

      10. *-commutative N/A

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

      11. exp-to-pow N/A

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

      12. lower-pow.f64 N/A

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

      13. rem-exp-log N/A

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

      14. mul-1-neg N/A

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

      15. lower-exp.f64 N/A

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

      16. lower-neg.f64 88.3

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

   5. Applied rewrites 88.3%

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

   if 1.15000000000000002e-238 < t < 1.79999999999999987e-20

   1. Initial program 94.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lift-exp.f64 N/A

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

      6. lift--.f64 N/A

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

      7. exp-diff N/A

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

      8. div-inv N/A

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

      9. associate-*l* N/A

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

      10. lower-*.f64 N/A

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

   4. Applied rewrites 80.4%

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

   5. Taylor expanded in b around 0

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

      1. lower-/.f64 89.2

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

   7. Applied rewrites 89.2%

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

   8. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-pow.f64 89.2

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

   10. Applied rewrites 89.2%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{+36}:\\ \;\;\;\;\frac{e^{\log a \cdot t - b} \cdot x}{y}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-238}:\\ \;\;\;\;\frac{\left(e^{-b} \cdot \frac{{z}^{y}}{a}\right) \cdot x}{y}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-20}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{{z}^{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{\log a \cdot t - b} \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 80.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{e^{\log a \cdot t - b} \cdot x}{y}\\ \mathbf{if}\;t \leq -2.7 \cdot 10^{+151}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-216}:\\ \;\;\;\;\frac{e^{\log z \cdot y - b} \cdot x}{y}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-20}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{{z}^{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* (exp (- (* (log a) t) b)) x) y)))
   (if (<= t -2.7e+151)
     t_1
     (if (<= t 8.5e-216)
       (/ (* (exp (- (* (log z) y) b)) x) y)
       (if (<= t 1.8e-20) (* (/ x y) (/ (pow z y) a)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (exp(((log(a) * t) - b)) * x) / y;
	double tmp;
	if (t <= -2.7e+151) {
		tmp = t_1;
	} else if (t <= 8.5e-216) {
		tmp = (exp(((log(z) * y) - b)) * x) / y;
	} else if (t <= 1.8e-20) {
		tmp = (x / y) * (pow(z, y) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (exp(((log(a) * t) - b)) * x) / y
    if (t <= (-2.7d+151)) then
        tmp = t_1
    else if (t <= 8.5d-216) then
        tmp = (exp(((log(z) * y) - b)) * x) / y
    else if (t <= 1.8d-20) then
        tmp = (x / y) * ((z ** y) / a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (Math.exp(((Math.log(a) * t) - b)) * x) / y;
	double tmp;
	if (t <= -2.7e+151) {
		tmp = t_1;
	} else if (t <= 8.5e-216) {
		tmp = (Math.exp(((Math.log(z) * y) - b)) * x) / y;
	} else if (t <= 1.8e-20) {
		tmp = (x / y) * (Math.pow(z, y) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (math.exp(((math.log(a) * t) - b)) * x) / y
	tmp = 0
	if t <= -2.7e+151:
		tmp = t_1
	elif t <= 8.5e-216:
		tmp = (math.exp(((math.log(z) * y) - b)) * x) / y
	elif t <= 1.8e-20:
		tmp = (x / y) * (math.pow(z, y) / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(exp(Float64(Float64(log(a) * t) - b)) * x) / y)
	tmp = 0.0
	if (t <= -2.7e+151)
		tmp = t_1;
	elseif (t <= 8.5e-216)
		tmp = Float64(Float64(exp(Float64(Float64(log(z) * y) - b)) * x) / y);
	elseif (t <= 1.8e-20)
		tmp = Float64(Float64(x / y) * Float64((z ^ y) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (exp(((log(a) * t) - b)) * x) / y;
	tmp = 0.0;
	if (t <= -2.7e+151)
		tmp = t_1;
	elseif (t <= 8.5e-216)
		tmp = (exp(((log(z) * y) - b)) * x) / y;
	elseif (t <= 1.8e-20)
		tmp = (x / y) * ((z ^ y) / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[Exp[N[(N[(N[Log[a], $MachinePrecision] * t), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t, -2.7e+151], t$95$1, If[LessEqual[t, 8.5e-216], N[(N[(N[Exp[N[(N[(N[Log[z], $MachinePrecision] * y), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 1.8e-20], N[(N[(x / y), $MachinePrecision] * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.7000000000000001e151 or 1.79999999999999987e-20 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. rem-exp-log N/A

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

      3. lower-log.f64 N/A

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

      4. rem-exp-log 95.0

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

   5. Applied rewrites 95.0%

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

   if -2.7000000000000001e151 < t < 8.50000000000000003e-216

   1. Initial program 96.8%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-log.f64 82.1

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

   5. Applied rewrites 82.1%

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

   if 8.50000000000000003e-216 < t < 1.79999999999999987e-20

   1. Initial program 93.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lift-exp.f64 N/A

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

      6. lift--.f64 N/A

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

      7. exp-diff N/A

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

      8. div-inv N/A

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

      9. associate-*l* N/A

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

      10. lower-*.f64 N/A

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

   4. Applied rewrites 80.9%

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

   5. Taylor expanded in b around 0

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

      1. lower-/.f64 90.5

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

   7. Applied rewrites 90.5%

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

   8. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-pow.f64 90.5

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

   10. Applied rewrites 90.5%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+151}:\\ \;\;\;\;\frac{e^{\log a \cdot t - b} \cdot x}{y}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-216}:\\ \;\;\;\;\frac{e^{\log z \cdot y - b} \cdot x}{y}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-20}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{{z}^{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{\log a \cdot t - b} \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 84.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{e^{\log a \cdot t - b} \cdot x}{y}\\ \mathbf{if}\;b \leq -1 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 650:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)}}{y} \cdot \left({z}^{y} \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* (exp (- (* (log a) t) b)) x) y)))
   (if (<= b -1e+50)
     t_1
     (if (<= b 650.0) (* (/ (pow a (- t 1.0)) y) (* (pow z y) x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (exp(((log(a) * t) - b)) * x) / y;
	double tmp;
	if (b <= -1e+50) {
		tmp = t_1;
	} else if (b <= 650.0) {
		tmp = (pow(a, (t - 1.0)) / y) * (pow(z, y) * x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (exp(((log(a) * t) - b)) * x) / y
    if (b <= (-1d+50)) then
        tmp = t_1
    else if (b <= 650.0d0) then
        tmp = ((a ** (t - 1.0d0)) / y) * ((z ** y) * x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (Math.exp(((Math.log(a) * t) - b)) * x) / y;
	double tmp;
	if (b <= -1e+50) {
		tmp = t_1;
	} else if (b <= 650.0) {
		tmp = (Math.pow(a, (t - 1.0)) / y) * (Math.pow(z, y) * x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (math.exp(((math.log(a) * t) - b)) * x) / y
	tmp = 0
	if b <= -1e+50:
		tmp = t_1
	elif b <= 650.0:
		tmp = (math.pow(a, (t - 1.0)) / y) * (math.pow(z, y) * x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(exp(Float64(Float64(log(a) * t) - b)) * x) / y)
	tmp = 0.0
	if (b <= -1e+50)
		tmp = t_1;
	elseif (b <= 650.0)
		tmp = Float64(Float64((a ^ Float64(t - 1.0)) / y) * Float64((z ^ y) * x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (exp(((log(a) * t) - b)) * x) / y;
	tmp = 0.0;
	if (b <= -1e+50)
		tmp = t_1;
	elseif (b <= 650.0)
		tmp = ((a ^ (t - 1.0)) / y) * ((z ^ y) * x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[Exp[N[(N[(N[Log[a], $MachinePrecision] * t), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -1e+50], t$95$1, If[LessEqual[b, 650.0], N[(N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision] * N[(N[Power[z, y], $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.0000000000000001e50 or 650 < 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. lower-*.f64 N/A

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

      2. rem-exp-log N/A

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

      3. lower-log.f64 N/A

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

      4. rem-exp-log 90.7

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

   5. Applied rewrites 90.7%

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

   if -1.0000000000000001e50 < b < 650

   1. Initial program 95.4%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. associate-*r* N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. exp-to-pow N/A

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

      8. lower-pow.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. exp-prod N/A

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

      11. lower-pow.f64 N/A

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

      12. rem-exp-log N/A

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

      13. lower--.f64 84.4

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

   5. Applied rewrites 84.4%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{+50}:\\ \;\;\;\;\frac{e^{\log a \cdot t - b} \cdot x}{y}\\ \mathbf{elif}\;b \leq 650:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)}}{y} \cdot \left({z}^{y} \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{\log a \cdot t - b} \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 73.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{e^{-b}}{y} \cdot x\\ \mathbf{if}\;b \leq -1.55 \cdot 10^{+161}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1500000000:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ (exp (- b)) y) x)))
   (if (<= b -1.55e+161)
     t_1
     (if (<= b 1500000000.0) (* (/ (pow a (- t 1.0)) y) x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (exp(-b) / y) * x;
	double tmp;
	if (b <= -1.55e+161) {
		tmp = t_1;
	} else if (b <= 1500000000.0) {
		tmp = (pow(a, (t - 1.0)) / y) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (exp(-b) / y) * x
    if (b <= (-1.55d+161)) then
        tmp = t_1
    else if (b <= 1500000000.0d0) then
        tmp = ((a ** (t - 1.0d0)) / y) * x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (Math.exp(-b) / y) * x;
	double tmp;
	if (b <= -1.55e+161) {
		tmp = t_1;
	} else if (b <= 1500000000.0) {
		tmp = (Math.pow(a, (t - 1.0)) / y) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (math.exp(-b) / y) * x
	tmp = 0
	if b <= -1.55e+161:
		tmp = t_1
	elif b <= 1500000000.0:
		tmp = (math.pow(a, (t - 1.0)) / y) * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(exp(Float64(-b)) / y) * x)
	tmp = 0.0
	if (b <= -1.55e+161)
		tmp = t_1;
	elseif (b <= 1500000000.0)
		tmp = Float64(Float64((a ^ Float64(t - 1.0)) / y) * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (exp(-b) / y) * x;
	tmp = 0.0;
	if (b <= -1.55e+161)
		tmp = t_1;
	elseif (b <= 1500000000.0)
		tmp = ((a ^ (t - 1.0)) / y) * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[b, -1.55e+161], t$95$1, If[LessEqual[b, 1500000000.0], N[(N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.55000000000000003e161 or 1.5e9 < 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. lower-*.f64 N/A

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

      2. rem-exp-log N/A

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

      3. lower-log.f64 N/A

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

      4. rem-exp-log 91.5

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

   5. Applied rewrites 91.5%

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

   6. Taylor expanded in b around inf

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

      1. neg-mul-1 N/A

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

      2. lower-neg.f64 80.9

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

   8. Applied rewrites 80.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 80.9

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

   10. Applied rewrites 80.9%

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

   if -1.55000000000000003e161 < b < 1.5e9

   1. Initial program 96.0%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. associate-*r* N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. exp-to-pow N/A

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

      8. lower-pow.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. exp-prod N/A

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

      11. lower-pow.f64 N/A

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

      12. rem-exp-log N/A

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

      13. lower--.f64 82.5

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

   5. Applied rewrites 82.5%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 72.0%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{+161}:\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{elif}\;b \leq 1500000000:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 59.0% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{e^{-b}}{y} \cdot x\\ \mathbf{if}\;b \leq -6.2 \cdot 10^{-18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 240000:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(0.5, b, 1\right) \cdot y, b, y\right) \cdot a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ (exp (- b)) y) x)))
   (if (<= b -6.2e-18)
     t_1
     (if (<= b 240000.0) (/ x (* (fma (* (fma 0.5 b 1.0) y) b y) a)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (exp(-b) / y) * x;
	double tmp;
	if (b <= -6.2e-18) {
		tmp = t_1;
	} else if (b <= 240000.0) {
		tmp = x / (fma((fma(0.5, b, 1.0) * y), b, y) * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(exp(Float64(-b)) / y) * x)
	tmp = 0.0
	if (b <= -6.2e-18)
		tmp = t_1;
	elseif (b <= 240000.0)
		tmp = Float64(x / Float64(fma(Float64(fma(0.5, b, 1.0) * y), b, y) * a));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[b, -6.2e-18], t$95$1, If[LessEqual[b, 240000.0], N[(x / N[(N[(N[(N[(0.5 * b + 1.0), $MachinePrecision] * y), $MachinePrecision] * b + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -6.20000000000000014e-18 or 2.4e5 < 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. lower-*.f64 N/A

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

      2. rem-exp-log N/A

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

      3. lower-log.f64 N/A

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

      4. rem-exp-log 89.9

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

   5. Applied rewrites 89.9%

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

   6. Taylor expanded in b around inf

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

      1. neg-mul-1 N/A

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

      2. lower-neg.f64 75.3

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

   8. Applied rewrites 75.3%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 75.3

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

   10. Applied rewrites 75.3%

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

   if -6.20000000000000014e-18 < b < 2.4e5

   1. Initial program 95.0%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

   5. Applied rewrites 69.0%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 41.1%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 41.6%

       \[\leadsto \frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(0.5, b, 1\right) \cdot y, b, y\right) \cdot a} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 17: 50.2% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a \cdot y}\\ \mathbf{if}\;b \leq -2.1 \cdot 10^{+25}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-\mathsf{fma}\left(\mathsf{fma}\left(t\_1, 0.16666666666666666, 0\right), b, -0.5 \cdot t\_1\right), b, \frac{-x}{a \cdot y}\right), b, t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(0.16666666666666666, b, 0.5\right) \cdot y, b, y\right), b, y\right) \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* a y))))
   (if (<= b -2.1e+25)
     (fma
      (fma
       (- (fma (fma t_1 0.16666666666666666 0.0) b (* -0.5 t_1)))
       b
       (/ (- x) (* a y)))
      b
      t_1)
     (/ x (* (fma (fma (* (fma 0.16666666666666666 b 0.5) y) b y) b y) a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a * y);
	double tmp;
	if (b <= -2.1e+25) {
		tmp = fma(fma(-fma(fma(t_1, 0.16666666666666666, 0.0), b, (-0.5 * t_1)), b, (-x / (a * y))), b, t_1);
	} else {
		tmp = x / (fma(fma((fma(0.16666666666666666, b, 0.5) * y), b, y), b, y) * a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a * y))
	tmp = 0.0
	if (b <= -2.1e+25)
		tmp = fma(fma(Float64(-fma(fma(t_1, 0.16666666666666666, 0.0), b, Float64(-0.5 * t_1))), b, Float64(Float64(-x) / Float64(a * y))), b, t_1);
	else
		tmp = Float64(x / Float64(fma(fma(Float64(fma(0.16666666666666666, b, 0.5) * y), b, y), b, y) * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.1e+25], N[(N[((-N[(N[(t$95$1 * 0.16666666666666666 + 0.0), $MachinePrecision] * b + N[(-0.5 * t$95$1), $MachinePrecision]), $MachinePrecision]) * b + N[((-x) / N[(a * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * b + t$95$1), $MachinePrecision], N[(x / N[(N[(N[(N[(N[(0.16666666666666666 * b + 0.5), $MachinePrecision] * y), $MachinePrecision] * b + y), $MachinePrecision] * b + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.0999999999999999e25

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

   5. Applied rewrites 62.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 75.0%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 30.9%

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

   12. Taylor expanded in b around 0

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

   14. Applied rewrites 67.4%

       \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-\mathsf{fma}\left(\mathsf{fma}\left(\frac{x}{a \cdot y}, 0.16666666666666666, 0\right), b, \frac{x}{a \cdot y} \cdot -0.5\right), b, \frac{-x}{a \cdot y}\right), b, \frac{x}{a \cdot y}\right) \]

   if -2.0999999999999999e25 < b

   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 t around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

   5. Applied rewrites 66.4%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 52.5%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 46.5%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.1 \cdot 10^{+25}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-\mathsf{fma}\left(\mathsf{fma}\left(\frac{x}{a \cdot y}, 0.16666666666666666, 0\right), b, -0.5 \cdot \frac{x}{a \cdot y}\right), b, \frac{-x}{a \cdot y}\right), b, \frac{x}{a \cdot y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(0.16666666666666666, b, 0.5\right) \cdot y, b, y\right), b, y\right) \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 47.3% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a \cdot y}\\ \mathbf{if}\;b \leq -1.02 \cdot 10^{+90}:\\ \;\;\;\;\mathsf{fma}\left(-\mathsf{fma}\left(-0.5 \cdot t\_1, b, t\_1\right), b, t\_1\right)\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{-284}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{\left(-x\right) \cdot b}{y}, a, \frac{x}{y} \cdot a\right)}{a \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(0.16666666666666666, b, 0.5\right) \cdot y, b, y\right), b, y\right) \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* a y))))
   (if (<= b -1.02e+90)
     (fma (- (fma (* -0.5 t_1) b t_1)) b t_1)
     (if (<= b 4.6e-284)
       (/ (fma (/ (* (- x) b) y) a (* (/ x y) a)) (* a a))
       (/
        x
        (* (fma (fma (* (fma 0.16666666666666666 b 0.5) y) b y) b y) a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a * y);
	double tmp;
	if (b <= -1.02e+90) {
		tmp = fma(-fma((-0.5 * t_1), b, t_1), b, t_1);
	} else if (b <= 4.6e-284) {
		tmp = fma(((-x * b) / y), a, ((x / y) * a)) / (a * a);
	} else {
		tmp = x / (fma(fma((fma(0.16666666666666666, b, 0.5) * y), b, y), b, y) * a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a * y))
	tmp = 0.0
	if (b <= -1.02e+90)
		tmp = fma(Float64(-fma(Float64(-0.5 * t_1), b, t_1)), b, t_1);
	elseif (b <= 4.6e-284)
		tmp = Float64(fma(Float64(Float64(Float64(-x) * b) / y), a, Float64(Float64(x / y) * a)) / Float64(a * a));
	else
		tmp = Float64(x / Float64(fma(fma(Float64(fma(0.16666666666666666, b, 0.5) * y), b, y), b, y) * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.02e+90], N[((-N[(N[(-0.5 * t$95$1), $MachinePrecision] * b + t$95$1), $MachinePrecision]) * b + t$95$1), $MachinePrecision], If[LessEqual[b, 4.6e-284], N[(N[(N[(N[((-x) * b), $MachinePrecision] / y), $MachinePrecision] * a + N[(N[(x / y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] / N[(a * a), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(N[(N[(N[(0.16666666666666666 * b + 0.5), $MachinePrecision] * y), $MachinePrecision] * b + y), $MachinePrecision] * b + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.02000000000000005e90

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

   5. Applied rewrites 63.2%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 78.6%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 64.1%

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

   if -1.02000000000000005e90 < b < 4.6e-284

   1. Initial program 95.7%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

   5. Applied rewrites 68.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 45.1%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 37.4%

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

   13. Applied rewrites 45.3%

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

   if 4.6e-284 < b

   1. Initial program 97.8%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

   5. Applied rewrites 64.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 59.3%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 50.9%

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

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.02 \cdot 10^{+90}:\\ \;\;\;\;\mathsf{fma}\left(-\mathsf{fma}\left(-0.5 \cdot \frac{x}{a \cdot y}, b, \frac{x}{a \cdot y}\right), b, \frac{x}{a \cdot y}\right)\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{-284}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{\left(-x\right) \cdot b}{y}, a, \frac{x}{y} \cdot a\right)}{a \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(0.16666666666666666, b, 0.5\right) \cdot y, b, y\right), b, y\right) \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 43.5% accurate, 8.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{-138}:\\ \;\;\;\;\frac{\left(1 - b\right) \cdot \frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(0.5, b, 1\right) \cdot y, b, y\right) \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -5e-138)
   (/ (* (- 1.0 b) (/ x y)) a)
   (/ x (* (fma (* (fma 0.5 b 1.0) y) b y) a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5e-138) {
		tmp = ((1.0 - b) * (x / y)) / a;
	} else {
		tmp = x / (fma((fma(0.5, b, 1.0) * y), b, y) * a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -5e-138)
		tmp = Float64(Float64(Float64(1.0 - b) * Float64(x / y)) / a);
	else
		tmp = Float64(x / Float64(fma(Float64(fma(0.5, b, 1.0) * y), b, y) * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -5e-138], N[(N[(N[(1.0 - b), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(x / N[(N[(N[(N[(0.5 * b + 1.0), $MachinePrecision] * y), $MachinePrecision] * b + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.99999999999999989e-138

   1. Initial program 97.7%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

   5. Applied rewrites 67.0%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 65.9%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 41.5%

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

   13. Applied rewrites 50.2%

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

   if -4.99999999999999989e-138 < b

   1. Initial program 97.4%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

   5. Applied rewrites 64.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 53.3%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 45.9%

       \[\leadsto \frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(0.5, b, 1\right) \cdot y, b, y\right) \cdot a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 47.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{-138}:\\ \;\;\;\;\frac{\left(1 - b\right) \cdot \frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(\mathsf{fma}\left(0.5, b, 1\right) \cdot y, b, y\right) \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 39.0% accurate, 9.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{-138}:\\ \;\;\;\;\frac{\left(1 - b\right) \cdot \frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(b, y, y\right) \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -5e-138) (/ (* (- 1.0 b) (/ x y)) a) (/ x (* (fma b y y) a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5e-138) {
		tmp = ((1.0 - b) * (x / y)) / a;
	} else {
		tmp = x / (fma(b, y, y) * a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -5e-138)
		tmp = Float64(Float64(Float64(1.0 - b) * Float64(x / y)) / a);
	else
		tmp = Float64(x / Float64(fma(b, y, y) * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -5e-138], N[(N[(N[(1.0 - b), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(x / N[(N[(b * y + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.99999999999999989e-138

   1. Initial program 97.7%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

   5. Applied rewrites 67.0%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 65.9%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 41.5%

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

   13. Applied rewrites 50.2%

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

   if -4.99999999999999989e-138 < b

   1. Initial program 97.4%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

   5. Applied rewrites 64.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 53.3%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 41.1%

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

4. Final simplification 44.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{-138}:\\ \;\;\;\;\frac{\left(1 - b\right) \cdot \frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(b, y, y\right) \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 38.6% accurate, 11.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.1 \cdot 10^{+25}:\\ \;\;\;\;\frac{b}{a \cdot y} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(b, y, y\right) \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.1e+25) (* (/ b (* a y)) (- x)) (/ x (* (fma b y y) a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.1e+25) {
		tmp = (b / (a * y)) * -x;
	} else {
		tmp = x / (fma(b, y, y) * a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.1e+25)
		tmp = Float64(Float64(b / Float64(a * y)) * Float64(-x));
	else
		tmp = Float64(x / Float64(fma(b, y, y) * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.1e+25], N[(N[(b / N[(a * y), $MachinePrecision]), $MachinePrecision] * (-x)), $MachinePrecision], N[(x / N[(N[(b * y + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.0999999999999999e25

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

   5. Applied rewrites 62.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 75.0%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 40.8%

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

   12. Taylor expanded in b around inf

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

   14. Applied rewrites 39.3%

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

   if -2.0999999999999999e25 < b

   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 t around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

   5. Applied rewrites 66.4%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 52.5%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 41.7%

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

4. Final simplification 41.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.1 \cdot 10^{+25}:\\ \;\;\;\;\frac{b}{a \cdot y} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(b, y, y\right) \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 35.5% accurate, 11.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.1 \cdot 10^{+25}:\\ \;\;\;\;\frac{1}{a \cdot y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(a, b, a\right) \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.1e+25) (* (/ 1.0 (* a y)) x) (/ x (* (fma a b a) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.1e+25) {
		tmp = (1.0 / (a * y)) * x;
	} else {
		tmp = x / (fma(a, b, a) * y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.1e+25)
		tmp = Float64(Float64(1.0 / Float64(a * y)) * x);
	else
		tmp = Float64(x / Float64(fma(a, b, a) * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.1e+25], N[(N[(1.0 / N[(a * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(x / N[(N[(a * b + a), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.0999999999999999e25

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

   5. Applied rewrites 62.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 75.0%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 30.9%

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

   13. Applied rewrites 32.4%

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

   if -2.0999999999999999e25 < b

   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 t around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

      5. lower-/.f64 N/A

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

   5. Applied rewrites 66.4%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 52.5%

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

   9. Taylor expanded in b around 0

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

   11. Applied rewrites 40.7%

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

4. Final simplification 38.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.1 \cdot 10^{+25}:\\ \;\;\;\;\frac{1}{a \cdot y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(a, b, a\right) \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 30.7% accurate, 15.3× speedup

Math

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

FPCore

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

C

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

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 = (1.0d0 / (a * y)) * x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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 t around 0

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

   1. *-commutative N/A

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

   2. exp-diff N/A

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

   3. associate-*l/ N/A

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

   4. associate-/l/ N/A

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

   5. lower-/.f64 N/A

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

5. Applied rewrites 65.3%

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

6. Taylor expanded in y around 0

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

8. Applied rewrites 58.0%

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

9. Taylor expanded in b around 0

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

11. Applied rewrites 32.8%

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

13. Applied rewrites 33.1%

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

Alternative 24: 30.7% accurate, 19.8× speedup

Math

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

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(x / Float64(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[(x / N[(a * y), $MachinePrecision]), $MachinePrecision]

Derivation

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 t around 0

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

   1. *-commutative N/A

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

   2. exp-diff N/A

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

   3. associate-*l/ N/A

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

   4. associate-/l/ N/A

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

   5. lower-/.f64 N/A

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

5. Applied rewrites 65.3%

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

6. Taylor expanded in y around 0

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

8. Applied rewrites 58.0%

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

9. Taylor expanded in b around 0

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

11. Applied rewrites 32.8%

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

12. Final simplification 32.8%

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

Developer Target 1: 70.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024235 
(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))