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

Percentage Accurate: 98.3% → 98.3%

Time: 8.3s

Alternatives: 15

Speedup: 1.0×

• 47.3% 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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    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

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

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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.0%

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

Alternative 2: 46.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{x \cdot \frac{1}{a}}{y}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+290}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(0.16666666666666666, b, 0.5\right), b, 1\right), b, 1\right) \cdot a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{1}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)))
   (if (<= t_1 (- INFINITY))
     (/ (* x (/ 1.0 a)) y)
     (if (<= t_1 2e+290)
       (/
        (*
         x
         (/ 1.0 (* (fma (fma (fma 0.16666666666666666 b 0.5) b 1.0) b 1.0) a)))
        y)
       (* x (/ (/ 1.0 a) y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * exp((((y * log(z)) + ((t - 1.0) * log(a))) - b))) / y;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (x * (1.0 / a)) / y;
	} else if (t_1 <= 2e+290) {
		tmp = (x * (1.0 / (fma(fma(fma(0.16666666666666666, b, 0.5), b, 1.0), b, 1.0) * a))) / y;
	} else {
		tmp = x * ((1.0 / a) / y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) + Float64(Float64(t - 1.0) * log(a))) - b))) / y)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(x * Float64(1.0 / a)) / y);
	elseif (t_1 <= 2e+290)
		tmp = Float64(Float64(x * Float64(1.0 / Float64(fma(fma(fma(0.16666666666666666, b, 0.5), b, 1.0), b, 1.0) * a))) / y);
	else
		tmp = Float64(x * Float64(Float64(1.0 / a) / y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] + N[(N[(t - 1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(x * N[(1.0 / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t$95$1, 2e+290], N[(N[(x * N[(1.0 / N[(N[(N[(N[(0.16666666666666666 * b + 0.5), $MachinePrecision] * b + 1.0), $MachinePrecision] * b + 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x * N[(N[(1.0 / a), $MachinePrecision] / 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 b around 0

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

      1. exp-sum N/A

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

      2. *-commutative N/A

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

      3. pow-to-exp N/A

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

      4. pow-to-exp N/A

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

      5. lower-*.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 63.1

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

   5. Applied rewrites 63.1%

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

   6. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lift-pow.f64 65.2

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

   8. Applied rewrites 65.2%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 25.8%

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

   if -inf.0 < (/.f64 (*.f64 x (exp.f64 (-.f64 (+.f64 (*.f64 y (log.f64 z)) (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))) b))) y) < 2.00000000000000012e290

   1. Initial program 98.0%

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

   3. Taylor expanded in y around 0

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

      1. div-exp N/A

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

      2. pow-to-exp N/A

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

      3. lower-/.f64 N/A

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

      4. lower-pow.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lower-exp.f64 70.2

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

   5. Applied rewrites 70.2%

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

   6. Taylor expanded in t around 0

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

      1. inv-pow N/A

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

      2. lower-pow.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift-exp.f64 66.4

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

   8. Applied rewrites 66.4%

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

      1. lift-pow.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-exp.f64 N/A

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

      4. unpow-1 N/A

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

      5. *-commutative N/A

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

      6. lower-/.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-exp.f64 N/A

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

      9. lift-*.f64 66.4

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

   10. Applied rewrites 66.4%

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

   11. Taylor expanded in b around 0

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

       1. +-commutative N/A

          \[\leadsto \frac{x \cdot \frac{1}{\left(b \cdot \left(1 + b \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot b\right)\right) + 1\right) \cdot a}}{y} \]

       2. *-commutative N/A

          \[\leadsto \frac{x \cdot \frac{1}{\left(\left(1 + b \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot b\right)\right) \cdot b + 1\right) \cdot a}}{y} \]

       3. lower-fma.f64 N/A

          \[\leadsto \frac{x \cdot \frac{1}{\mathsf{fma}\left(1 + b \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot b\right), b, 1\right) \cdot a}}{y} \]

       4. +-commutative N/A

          \[\leadsto \frac{x \cdot \frac{1}{\mathsf{fma}\left(b \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot b\right) + 1, b, 1\right) \cdot a}}{y} \]

       5. *-commutative N/A

          \[\leadsto \frac{x \cdot \frac{1}{\mathsf{fma}\left(\left(\frac{1}{2} + \frac{1}{6} \cdot b\right) \cdot b + 1, b, 1\right) \cdot a}}{y} \]

       6. lower-fma.f64 N/A

          \[\leadsto \frac{x \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{2} + \frac{1}{6} \cdot b, b, 1\right), b, 1\right) \cdot a}}{y} \]

       7. +-commutative N/A

          \[\leadsto \frac{x \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{6} \cdot b + \frac{1}{2}, b, 1\right), b, 1\right) \cdot a}}{y} \]

       8. lower-fma.f64 67.6

          \[\leadsto \frac{x \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(0.16666666666666666, b, 0.5\right), b, 1\right), b, 1\right) \cdot a}}{y} \]

   13. Applied rewrites 67.6%

       \[\leadsto \frac{x \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(0.16666666666666666, b, 0.5\right), b, 1\right), b, 1\right) \cdot a}}{y} \]

   if 2.00000000000000012e290 < (/.f64 (*.f64 x (exp.f64 (-.f64 (+.f64 (*.f64 y (log.f64 z)) (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))) b))) y)

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. *-commutative N/A

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

      3. pow-to-exp N/A

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

      4. pow-to-exp N/A

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

      5. lower-*.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 69.4

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

   5. Applied rewrites 69.4%

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

   6. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lift-pow.f64 66.9

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

   8. Applied rewrites 66.9%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 22.2%

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

       1. lift-/.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. associate-/l* N/A

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

       4. lower-*.f64 N/A

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

       5. lower-/.f64 22.2

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

   13. Applied rewrites 22.2%

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

Alternative 3: 44.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{x \cdot \frac{1}{a}}{y}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+290}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(0.5, b, 1\right), b, 1\right) \cdot a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{1}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)))
   (if (<= t_1 (- INFINITY))
     (/ (* x (/ 1.0 a)) y)
     (if (<= t_1 2e+290)
       (/ (* x (/ 1.0 (* (fma (fma 0.5 b 1.0) b 1.0) a))) y)
       (* x (/ (/ 1.0 a) y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * exp((((y * log(z)) + ((t - 1.0) * log(a))) - b))) / y;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (x * (1.0 / a)) / y;
	} else if (t_1 <= 2e+290) {
		tmp = (x * (1.0 / (fma(fma(0.5, b, 1.0), b, 1.0) * a))) / y;
	} else {
		tmp = x * ((1.0 / a) / y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) + Float64(Float64(t - 1.0) * log(a))) - b))) / y)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(x * Float64(1.0 / a)) / y);
	elseif (t_1 <= 2e+290)
		tmp = Float64(Float64(x * Float64(1.0 / Float64(fma(fma(0.5, b, 1.0), b, 1.0) * a))) / y);
	else
		tmp = Float64(x * Float64(Float64(1.0 / a) / y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] + N[(N[(t - 1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(x * N[(1.0 / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t$95$1, 2e+290], N[(N[(x * N[(1.0 / N[(N[(N[(0.5 * b + 1.0), $MachinePrecision] * b + 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x * N[(N[(1.0 / a), $MachinePrecision] / 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 b around 0

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

      1. exp-sum N/A

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

      2. *-commutative N/A

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

      3. pow-to-exp N/A

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

      4. pow-to-exp N/A

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

      5. lower-*.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 63.1

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

   5. Applied rewrites 63.1%

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

   6. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lift-pow.f64 65.2

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

   8. Applied rewrites 65.2%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 25.8%

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

   if -inf.0 < (/.f64 (*.f64 x (exp.f64 (-.f64 (+.f64 (*.f64 y (log.f64 z)) (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))) b))) y) < 2.00000000000000012e290

   1. Initial program 98.0%

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

   3. Taylor expanded in y around 0

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

      1. div-exp N/A

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

      2. pow-to-exp N/A

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

      3. lower-/.f64 N/A

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

      4. lower-pow.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lower-exp.f64 70.2

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

   5. Applied rewrites 70.2%

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

   6. Taylor expanded in t around 0

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

      1. inv-pow N/A

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

      2. lower-pow.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift-exp.f64 66.4

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

   8. Applied rewrites 66.4%

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

      1. lift-pow.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-exp.f64 N/A

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

      4. unpow-1 N/A

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

      5. *-commutative N/A

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

      6. lower-/.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-exp.f64 N/A

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

      9. lift-*.f64 66.4

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

   10. Applied rewrites 66.4%

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

   11. Taylor expanded in b around 0

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

       1. +-commutative N/A

          \[\leadsto \frac{x \cdot \frac{1}{\left(b \cdot \left(1 + \frac{1}{2} \cdot b\right) + 1\right) \cdot a}}{y} \]

       2. *-commutative N/A

          \[\leadsto \frac{x \cdot \frac{1}{\left(\left(1 + \frac{1}{2} \cdot b\right) \cdot b + 1\right) \cdot a}}{y} \]

       3. lower-fma.f64 N/A

          \[\leadsto \frac{x \cdot \frac{1}{\mathsf{fma}\left(1 + \frac{1}{2} \cdot b, b, 1\right) \cdot a}}{y} \]

       4. +-commutative N/A

          \[\leadsto \frac{x \cdot \frac{1}{\mathsf{fma}\left(\frac{1}{2} \cdot b + 1, b, 1\right) \cdot a}}{y} \]

       5. lower-fma.f64 58.4

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

   13. Applied rewrites 58.4%

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

   if 2.00000000000000012e290 < (/.f64 (*.f64 x (exp.f64 (-.f64 (+.f64 (*.f64 y (log.f64 z)) (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))) b))) y)

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. *-commutative N/A

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

      3. pow-to-exp N/A

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

      4. pow-to-exp N/A

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

      5. lower-*.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 69.4

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

   5. Applied rewrites 69.4%

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

   6. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lift-pow.f64 66.9

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

   8. Applied rewrites 66.9%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 22.2%

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

       1. lift-/.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. associate-/l* N/A

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

       4. lower-*.f64 N/A

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

       5. lower-/.f64 22.2

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

   13. Applied rewrites 22.2%

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

Alternative 4: 37.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{x \cdot \frac{1}{a}}{y}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+290}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\mathsf{fma}\left(b, a, a\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{1}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)))
   (if (<= t_1 (- INFINITY))
     (/ (* x (/ 1.0 a)) y)
     (if (<= t_1 2e+290)
       (/ (* x (/ 1.0 (fma b a a))) y)
       (* x (/ (/ 1.0 a) y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * exp((((y * log(z)) + ((t - 1.0) * log(a))) - b))) / y;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (x * (1.0 / a)) / y;
	} else if (t_1 <= 2e+290) {
		tmp = (x * (1.0 / fma(b, a, a))) / y;
	} else {
		tmp = x * ((1.0 / a) / y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) + Float64(Float64(t - 1.0) * log(a))) - b))) / y)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(x * Float64(1.0 / a)) / y);
	elseif (t_1 <= 2e+290)
		tmp = Float64(Float64(x * Float64(1.0 / fma(b, a, a))) / y);
	else
		tmp = Float64(x * Float64(Float64(1.0 / a) / y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] + N[(N[(t - 1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(x * N[(1.0 / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t$95$1, 2e+290], N[(N[(x * N[(1.0 / N[(b * a + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x * N[(N[(1.0 / a), $MachinePrecision] / 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 b around 0

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

      1. exp-sum N/A

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

      2. *-commutative N/A

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

      3. pow-to-exp N/A

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

      4. pow-to-exp N/A

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

      5. lower-*.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 63.1

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

   5. Applied rewrites 63.1%

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

   6. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lift-pow.f64 65.2

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

   8. Applied rewrites 65.2%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 25.8%

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

   if -inf.0 < (/.f64 (*.f64 x (exp.f64 (-.f64 (+.f64 (*.f64 y (log.f64 z)) (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))) b))) y) < 2.00000000000000012e290

   1. Initial program 98.0%

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

   3. Taylor expanded in y around 0

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

      1. div-exp N/A

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

      2. pow-to-exp N/A

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

      3. lower-/.f64 N/A

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

      4. lower-pow.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lower-exp.f64 70.2

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

   5. Applied rewrites 70.2%

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

   6. Taylor expanded in t around 0

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

      1. inv-pow N/A

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

      2. lower-pow.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift-exp.f64 66.4

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

   8. Applied rewrites 66.4%

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

   9. Taylor expanded in b around 0

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

       1. +-commutative N/A

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

       2. *-commutative N/A

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

       3. lower-fma.f64 47.0

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

   11. Applied rewrites 47.0%

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

       1. lift-pow.f64 N/A

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

       2. unpow-1 N/A

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

       3. lower-/.f64 47.0

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

   13. Applied rewrites 47.0%

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

   if 2.00000000000000012e290 < (/.f64 (*.f64 x (exp.f64 (-.f64 (+.f64 (*.f64 y (log.f64 z)) (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))) b))) y)

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. *-commutative N/A

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

      3. pow-to-exp N/A

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

      4. pow-to-exp N/A

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

      5. lower-*.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 69.4

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

   5. Applied rewrites 69.4%

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

   6. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lift-pow.f64 66.9

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

   8. Applied rewrites 66.9%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 22.2%

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

       1. lift-/.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. associate-/l* N/A

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

       4. lower-*.f64 N/A

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

       5. lower-/.f64 22.2

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

   13. Applied rewrites 22.2%

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

Alternative 5: 92.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.75 \cdot 10^{+47} \lor \neg \left(y \leq 1.9 \cdot 10^{+34}\right):\\ \;\;\;\;x \cdot \frac{e^{\mathsf{fma}\left(\log z, y, -\log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.75e+47) (not (<= y 1.9e+34)))
   (* x (/ (exp (- (fma (log z) y (- (log a))) b)) y))
   (/ (* x (exp (- (* (log a) (- t 1.0)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.75e+47) || !(y <= 1.9e+34)) {
		tmp = x * (exp((fma(log(z), y, -log(a)) - b)) / y);
	} else {
		tmp = (x * exp(((log(a) * (t - 1.0)) - b))) / y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.75e+47) || !(y <= 1.9e+34))
		tmp = Float64(x * Float64(exp(Float64(fma(log(z), y, Float64(-log(a))) - b)) / y));
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(log(a) * Float64(t - 1.0)) - b))) / y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.75e+47], N[Not[LessEqual[y, 1.9e+34]], $MachinePrecision]], N[(x * N[(N[Exp[N[(N[(N[Log[z], $MachinePrecision] * y + (-N[Log[a], $MachinePrecision])), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[Log[a], $MachinePrecision] * N[(t - 1.0), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.7499999999999999e47 or 1.9000000000000001e34 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lift-log.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lower-neg.f64 N/A

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

      12. lift-log.f64 95.2

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

   5. Applied rewrites 95.2%

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

   if -2.7499999999999999e47 < y < 1.9000000000000001e34

   1. Initial program 98.2%

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

   3. Taylor expanded in y around 0

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

      1. lower-*.f64 N/A

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

      2. lift-log.f64 N/A

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

      3. lift--.f64 96.1

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

   5. Applied rewrites 96.1%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.75 \cdot 10^{+47} \lor \neg \left(y \leq 1.9 \cdot 10^{+34}\right):\\ \;\;\;\;x \cdot \frac{e^{\mathsf{fma}\left(\log z, y, -\log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 88.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+54} \lor \neg \left(y \leq 5.6 \cdot 10^{+51}\right):\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -5.4e+54) (not (<= y 5.6e+51)))
   (* x (/ (/ (pow z y) a) y))
   (/ (* x (exp (- (* (log a) (- t 1.0)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -5.4e+54) || !(y <= 5.6e+51)) {
		tmp = x * ((pow(z, y) / a) / y);
	} else {
		tmp = (x * exp(((log(a) * (t - 1.0)) - b))) / y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-5.4d+54)) .or. (.not. (y <= 5.6d+51))) then
        tmp = x * (((z ** y) / a) / y)
    else
        tmp = (x * exp(((log(a) * (t - 1.0d0)) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -5.4e+54) || !(y <= 5.6e+51)) {
		tmp = x * ((Math.pow(z, y) / a) / y);
	} else {
		tmp = (x * Math.exp(((Math.log(a) * (t - 1.0)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -5.4e+54) or not (y <= 5.6e+51):
		tmp = x * ((math.pow(z, y) / a) / y)
	else:
		tmp = (x * math.exp(((math.log(a) * (t - 1.0)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -5.4e+54) || !(y <= 5.6e+51))
		tmp = Float64(x * Float64(Float64((z ^ y) / a) / y));
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(log(a) * Float64(t - 1.0)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -5.4e+54) || ~((y <= 5.6e+51)))
		tmp = x * (((z ^ y) / a) / y);
	else
		tmp = (x * exp(((log(a) * (t - 1.0)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -5.4e+54], N[Not[LessEqual[y, 5.6e+51]], $MachinePrecision]], N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[Log[a], $MachinePrecision] * N[(t - 1.0), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.40000000000000022e54 or 5.60000000000000009e51 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. *-commutative N/A

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

      3. pow-to-exp N/A

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

      4. pow-to-exp N/A

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

      5. lower-*.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 72.1

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

   5. Applied rewrites 72.1%

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

   6. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lift-pow.f64 91.7

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

   8. Applied rewrites 91.7%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 91.7

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

   10. Applied rewrites 91.7%

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

   if -5.40000000000000022e54 < y < 5.60000000000000009e51

   1. Initial program 98.2%

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

   3. Taylor expanded in y around 0

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

      1. lower-*.f64 N/A

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

      2. lift-log.f64 N/A

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

      3. lift--.f64 96.2

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

   5. Applied rewrites 96.2%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+54} \lor \neg \left(y \leq 5.6 \cdot 10^{+51}\right):\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \frac{e^{-b}}{y}\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{+108}:\\ \;\;\;\;\frac{x \cdot \left({z}^{y} \cdot {a}^{\left(t - 1\right)}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(0.16666666666666666, b, 0.5\right), b, 1\right), b, 1\right) \cdot a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.3e+34)
   (* x (/ (exp (- b)) y))
   (if (<= b 2.05e+108)
     (/ (* x (* (pow z y) (pow a (- t 1.0)))) y)
     (/
      (*
       x
       (/ 1.0 (* (fma (fma (fma 0.16666666666666666 b 0.5) b 1.0) b 1.0) a)))
      y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.3e+34) {
		tmp = x * (exp(-b) / y);
	} else if (b <= 2.05e+108) {
		tmp = (x * (pow(z, y) * pow(a, (t - 1.0)))) / y;
	} else {
		tmp = (x * (1.0 / (fma(fma(fma(0.16666666666666666, b, 0.5), b, 1.0), b, 1.0) * a))) / y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.3e+34)
		tmp = Float64(x * Float64(exp(Float64(-b)) / y));
	elseif (b <= 2.05e+108)
		tmp = Float64(Float64(x * Float64((z ^ y) * (a ^ Float64(t - 1.0)))) / y);
	else
		tmp = Float64(Float64(x * Float64(1.0 / Float64(fma(fma(fma(0.16666666666666666, b, 0.5), b, 1.0), b, 1.0) * a))) / y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.3e+34], N[(x * N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.05e+108], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] * N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[(1.0 / N[(N[(N[(N[(0.16666666666666666 * b + 0.5), $MachinePrecision] * b + 1.0), $MachinePrecision] * b + 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.29999999999999999e34

   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 inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 75.4

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

   5. Applied rewrites 75.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 75.4

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

   7. Applied rewrites 75.4%

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

   if -1.29999999999999999e34 < b < 2.05e108

   1. Initial program 98.5%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. *-commutative N/A

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

      3. pow-to-exp N/A

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

      4. pow-to-exp N/A

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

      5. lower-*.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 83.6

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

   5. Applied rewrites 83.6%

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

   if 2.05e108 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. div-exp N/A

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

      2. pow-to-exp N/A

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

      3. lower-/.f64 N/A

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

      4. lower-pow.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lower-exp.f64 71.5

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

   5. Applied rewrites 71.5%

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

   6. Taylor expanded in t around 0

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

      1. inv-pow N/A

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

      2. lower-pow.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift-exp.f64 88.8

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

   8. Applied rewrites 88.8%

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

      1. lift-pow.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-exp.f64 N/A

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

      4. unpow-1 N/A

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

      5. *-commutative N/A

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

      6. lower-/.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-exp.f64 N/A

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

      9. lift-*.f64 88.8

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

   10. Applied rewrites 88.8%

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

   11. Taylor expanded in b around 0

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

       1. +-commutative N/A

          \[\leadsto \frac{x \cdot \frac{1}{\left(b \cdot \left(1 + b \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot b\right)\right) + 1\right) \cdot a}}{y} \]

       2. *-commutative N/A

          \[\leadsto \frac{x \cdot \frac{1}{\left(\left(1 + b \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot b\right)\right) \cdot b + 1\right) \cdot a}}{y} \]

       3. lower-fma.f64 N/A

          \[\leadsto \frac{x \cdot \frac{1}{\mathsf{fma}\left(1 + b \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot b\right), b, 1\right) \cdot a}}{y} \]

       4. +-commutative N/A

          \[\leadsto \frac{x \cdot \frac{1}{\mathsf{fma}\left(b \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot b\right) + 1, b, 1\right) \cdot a}}{y} \]

       5. *-commutative N/A

          \[\leadsto \frac{x \cdot \frac{1}{\mathsf{fma}\left(\left(\frac{1}{2} + \frac{1}{6} \cdot b\right) \cdot b + 1, b, 1\right) \cdot a}}{y} \]

       6. lower-fma.f64 N/A

          \[\leadsto \frac{x \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{2} + \frac{1}{6} \cdot b, b, 1\right), b, 1\right) \cdot a}}{y} \]

       7. +-commutative N/A

          \[\leadsto \frac{x \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{6} \cdot b + \frac{1}{2}, b, 1\right), b, 1\right) \cdot a}}{y} \]

       8. lower-fma.f64 88.8

          \[\leadsto \frac{x \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(0.16666666666666666, b, 0.5\right), b, 1\right), b, 1\right) \cdot a}}{y} \]

   13. Applied rewrites 88.8%

       \[\leadsto \frac{x \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(0.16666666666666666, b, 0.5\right), b, 1\right), b, 1\right) \cdot a}}{y} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 75.1% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{if}\;y \leq -1.55 \cdot 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-175}:\\ \;\;\;\;\frac{x \cdot \frac{1}{e^{b} \cdot a}}{y}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+34}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{\mathsf{fma}\left(\mathsf{fma}\left(0.5, b, 1\right), b, 1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (/ (pow z y) a) y))))
   (if (<= y -1.55e+59)
     t_1
     (if (<= y 3e-175)
       (/ (* x (/ 1.0 (* (exp b) a))) y)
       (if (<= y 1.85e+34)
         (/ (* x (/ (pow a (- t 1.0)) (fma (fma 0.5 b 1.0) b 1.0))) y)
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * ((pow(z, y) / a) / y);
	double tmp;
	if (y <= -1.55e+59) {
		tmp = t_1;
	} else if (y <= 3e-175) {
		tmp = (x * (1.0 / (exp(b) * a))) / y;
	} else if (y <= 1.85e+34) {
		tmp = (x * (pow(a, (t - 1.0)) / fma(fma(0.5, b, 1.0), b, 1.0))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(Float64((z ^ y) / a) / y))
	tmp = 0.0
	if (y <= -1.55e+59)
		tmp = t_1;
	elseif (y <= 3e-175)
		tmp = Float64(Float64(x * Float64(1.0 / Float64(exp(b) * a))) / y);
	elseif (y <= 1.85e+34)
		tmp = Float64(Float64(x * Float64((a ^ Float64(t - 1.0)) / fma(fma(0.5, b, 1.0), b, 1.0))) / y);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.55e+59], t$95$1, If[LessEqual[y, 3e-175], N[(N[(x * N[(1.0 / N[(N[Exp[b], $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 1.85e+34], N[(N[(x * N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] / N[(N[(0.5 * b + 1.0), $MachinePrecision] * b + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.55000000000000007e59 or 1.85000000000000004e34 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. *-commutative N/A

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

      3. pow-to-exp N/A

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

      4. pow-to-exp N/A

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

      5. lower-*.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 72.6

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

   5. Applied rewrites 72.6%

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

   6. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lift-pow.f64 91.8

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

   8. Applied rewrites 91.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 91.8

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

   10. Applied rewrites 91.8%

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

   if -1.55000000000000007e59 < y < 3e-175

   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 y around 0

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

      1. div-exp N/A

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

      2. pow-to-exp N/A

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

      3. lower-/.f64 N/A

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

      4. lower-pow.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lower-exp.f64 80.0

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

   5. Applied rewrites 80.0%

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

   6. Taylor expanded in t around 0

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

      1. inv-pow N/A

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

      2. lower-pow.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift-exp.f64 78.1

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

   8. Applied rewrites 78.1%

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

      1. lift-pow.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-exp.f64 N/A

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

      4. unpow-1 N/A

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

      5. *-commutative N/A

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

      6. lower-/.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-exp.f64 N/A

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

      9. lift-*.f64 78.1

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

   10. Applied rewrites 78.1%

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

   if 3e-175 < y < 1.85000000000000004e34

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0

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

      1. div-exp N/A

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

      2. pow-to-exp N/A

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

      3. lower-/.f64 N/A

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

      4. lower-pow.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lower-exp.f64 75.7

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

   5. Applied rewrites 75.7%

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

   6. Taylor expanded in b around 0

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

      1. +-commutative N/A

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{b \cdot \left(1 + \frac{1}{2} \cdot b\right) + 1}}{y} \]

      2. *-commutative N/A

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{\left(1 + \frac{1}{2} \cdot b\right) \cdot b + 1}}{y} \]

      3. lower-fma.f64 N/A

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{\mathsf{fma}\left(1 + \frac{1}{2} \cdot b, b, 1\right)}}{y} \]

      4. +-commutative N/A

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{\mathsf{fma}\left(\frac{1}{2} \cdot b + 1, b, 1\right)}}{y} \]

      5. lower-fma.f64 73.6

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

   8. Applied rewrites 73.6%

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

Alternative 9: 75.0% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{{z}^{y}}{a}\\ \mathbf{if}\;y \leq -1.55 \cdot 10^{+59}:\\ \;\;\;\;x \cdot \frac{t\_1}{y}\\ \mathbf{elif}\;y \leq 300000000000:\\ \;\;\;\;\frac{x \cdot \frac{1}{e^{b} \cdot a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot t\_1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (pow z y) a)))
   (if (<= y -1.55e+59)
     (* x (/ t_1 y))
     (if (<= y 300000000000.0)
       (/ (* x (/ 1.0 (* (exp b) a))) y)
       (/ (* x t_1) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = pow(z, y) / a;
	double tmp;
	if (y <= -1.55e+59) {
		tmp = x * (t_1 / y);
	} else if (y <= 300000000000.0) {
		tmp = (x * (1.0 / (exp(b) * a))) / y;
	} else {
		tmp = (x * t_1) / y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    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 = (z ** y) / a
    if (y <= (-1.55d+59)) then
        tmp = x * (t_1 / y)
    else if (y <= 300000000000.0d0) then
        tmp = (x * (1.0d0 / (exp(b) * a))) / y
    else
        tmp = (x * t_1) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = Math.pow(z, y) / a;
	double tmp;
	if (y <= -1.55e+59) {
		tmp = x * (t_1 / y);
	} else if (y <= 300000000000.0) {
		tmp = (x * (1.0 / (Math.exp(b) * a))) / y;
	} else {
		tmp = (x * t_1) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.pow(z, y) / a
	tmp = 0
	if y <= -1.55e+59:
		tmp = x * (t_1 / y)
	elif y <= 300000000000.0:
		tmp = (x * (1.0 / (math.exp(b) * a))) / y
	else:
		tmp = (x * t_1) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64((z ^ y) / a)
	tmp = 0.0
	if (y <= -1.55e+59)
		tmp = Float64(x * Float64(t_1 / y));
	elseif (y <= 300000000000.0)
		tmp = Float64(Float64(x * Float64(1.0 / Float64(exp(b) * a))) / y);
	else
		tmp = Float64(Float64(x * t_1) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z ^ y) / a;
	tmp = 0.0;
	if (y <= -1.55e+59)
		tmp = x * (t_1 / y);
	elseif (y <= 300000000000.0)
		tmp = (x * (1.0 / (exp(b) * a))) / y;
	else
		tmp = (x * t_1) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[y, -1.55e+59], N[(x * N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 300000000000.0], N[(N[(x * N[(1.0 / N[(N[Exp[b], $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * t$95$1), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.55000000000000007e59

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. *-commutative N/A

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

      3. pow-to-exp N/A

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

      4. pow-to-exp N/A

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

      5. lower-*.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 66.7

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

   5. Applied rewrites 66.7%

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

   6. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lift-pow.f64 93.1

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

   8. Applied rewrites 93.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 93.1

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

   10. Applied rewrites 93.1%

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

   if -1.55000000000000007e59 < y < 3e11

   1. Initial program 98.1%

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

   3. Taylor expanded in y around 0

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

      1. div-exp N/A

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

      2. pow-to-exp N/A

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

      3. lower-/.f64 N/A

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

      4. lower-pow.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lower-exp.f64 79.4

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

   5. Applied rewrites 79.4%

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

   6. Taylor expanded in t around 0

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

      1. inv-pow N/A

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

      2. lower-pow.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift-exp.f64 74.4

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

   8. Applied rewrites 74.4%

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

      1. lift-pow.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-exp.f64 N/A

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

      4. unpow-1 N/A

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

      5. *-commutative N/A

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

      6. lower-/.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-exp.f64 N/A

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

      9. lift-*.f64 74.4

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

   10. Applied rewrites 74.4%

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

   if 3e11 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. *-commutative N/A

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

      3. pow-to-exp N/A

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

      4. pow-to-exp N/A

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

      5. lower-*.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 75.1

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

   5. Applied rewrites 75.1%

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

   6. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lift-pow.f64 87.0

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

   8. Applied rewrites 87.0%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 27.2%

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

   12. Taylor expanded in t around 0

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

       1. lower-/.f64 N/A

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

       2. lift-pow.f64 87.0

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

   14. Applied rewrites 87.0%

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

Alternative 10: 74.6% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+35} \lor \neg \left(y \leq 1.85 \cdot 10^{+34}\right):\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -9e+35) (not (<= y 1.85e+34)))
   (* x (/ (/ (pow z y) a) y))
   (/ (* x (/ (pow a t) a)) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -9e+35) || !(y <= 1.85e+34)) {
		tmp = x * ((pow(z, y) / a) / y);
	} else {
		tmp = (x * (pow(a, t) / a)) / y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-9d+35)) .or. (.not. (y <= 1.85d+34))) then
        tmp = x * (((z ** y) / a) / y)
    else
        tmp = (x * ((a ** t) / a)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -9e+35) || !(y <= 1.85e+34)) {
		tmp = x * ((Math.pow(z, y) / a) / y);
	} else {
		tmp = (x * (Math.pow(a, t) / a)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -9e+35) or not (y <= 1.85e+34):
		tmp = x * ((math.pow(z, y) / a) / y)
	else:
		tmp = (x * (math.pow(a, t) / a)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -9e+35) || !(y <= 1.85e+34))
		tmp = Float64(x * Float64(Float64((z ^ y) / a) / y));
	else
		tmp = Float64(Float64(x * Float64((a ^ t) / a)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -9e+35) || ~((y <= 1.85e+34)))
		tmp = x * (((z ^ y) / a) / y);
	else
		tmp = (x * ((a ^ t) / a)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -9e+35], N[Not[LessEqual[y, 1.85e+34]], $MachinePrecision]], N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.9999999999999993e35 or 1.85000000000000004e34 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. *-commutative N/A

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

      3. pow-to-exp N/A

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

      4. pow-to-exp N/A

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

      5. lower-*.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 72.4

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

   5. Applied rewrites 72.4%

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

   6. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lift-pow.f64 91.2

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

   8. Applied rewrites 91.2%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 91.2

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

   10. Applied rewrites 91.2%

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

   if -8.9999999999999993e35 < y < 1.85000000000000004e34

   1. Initial program 98.2%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. *-commutative N/A

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

      3. pow-to-exp N/A

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

      4. pow-to-exp N/A

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

      5. lower-*.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 64.4

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

   5. Applied rewrites 64.4%

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

      1. lift--.f64 N/A

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

      2. lift-pow.f64 N/A

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

      3. pow-sub N/A

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

      4. unpow1 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-pow.f64 64.5

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

   7. Applied rewrites 64.5%

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

   8. Taylor expanded in y around 0

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

      1. lift-pow.f64 N/A

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

      2. lift-/.f64 66.1

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

   10. Applied rewrites 66.1%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+35} \lor \neg \left(y \leq 1.85 \cdot 10^{+34}\right):\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 74.6% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+35} \lor \neg \left(y \leq 1.85 \cdot 10^{+34}\right):\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t - 1\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -9e+35) (not (<= y 1.85e+34)))
   (* x (/ (/ (pow z y) a) y))
   (/ (* x (pow a (- t 1.0))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -9e+35) || !(y <= 1.85e+34)) {
		tmp = x * ((pow(z, y) / a) / y);
	} else {
		tmp = (x * pow(a, (t - 1.0))) / y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-9d+35)) .or. (.not. (y <= 1.85d+34))) then
        tmp = x * (((z ** y) / a) / y)
    else
        tmp = (x * (a ** (t - 1.0d0))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -9e+35) || !(y <= 1.85e+34)) {
		tmp = x * ((Math.pow(z, y) / a) / y);
	} else {
		tmp = (x * Math.pow(a, (t - 1.0))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -9e+35) or not (y <= 1.85e+34):
		tmp = x * ((math.pow(z, y) / a) / y)
	else:
		tmp = (x * math.pow(a, (t - 1.0))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -9e+35) || !(y <= 1.85e+34))
		tmp = Float64(x * Float64(Float64((z ^ y) / a) / y));
	else
		tmp = Float64(Float64(x * (a ^ Float64(t - 1.0))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -9e+35) || ~((y <= 1.85e+34)))
		tmp = x * (((z ^ y) / a) / y);
	else
		tmp = (x * (a ^ (t - 1.0))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -9e+35], N[Not[LessEqual[y, 1.85e+34]], $MachinePrecision]], N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.9999999999999993e35 or 1.85000000000000004e34 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. *-commutative N/A

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

      3. pow-to-exp N/A

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

      4. pow-to-exp N/A

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

      5. lower-*.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 72.4

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

   5. Applied rewrites 72.4%

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

   6. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lift-pow.f64 91.2

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

   8. Applied rewrites 91.2%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 91.2

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

   10. Applied rewrites 91.2%

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

   if -8.9999999999999993e35 < y < 1.85000000000000004e34

   1. Initial program 98.2%

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

   3. Taylor expanded in y around 0

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

      1. div-exp N/A

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

      2. pow-to-exp N/A

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

      3. lower-/.f64 N/A

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

      4. lower-pow.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lower-exp.f64 79.7

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

   5. Applied rewrites 79.7%

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

   6. Taylor expanded in b around 0

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

      1. pow-to-exp N/A

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

      2. lift-pow.f64 N/A

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

      3. lift--.f64 66.0

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

   8. Applied rewrites 66.0%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+35} \lor \neg \left(y \leq 1.85 \cdot 10^{+34}\right):\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t - 1\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 73.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.0018:\\ \;\;\;\;x \cdot \frac{e^{-b}}{y}\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{+108}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t - 1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(0.16666666666666666, b, 0.5\right), b, 1\right), b, 1\right) \cdot a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -0.0018)
   (* x (/ (exp (- b)) y))
   (if (<= b 2.05e+108)
     (/ (* x (pow a (- t 1.0))) y)
     (/
      (*
       x
       (/ 1.0 (* (fma (fma (fma 0.16666666666666666 b 0.5) b 1.0) b 1.0) a)))
      y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -0.0018) {
		tmp = x * (exp(-b) / y);
	} else if (b <= 2.05e+108) {
		tmp = (x * pow(a, (t - 1.0))) / y;
	} else {
		tmp = (x * (1.0 / (fma(fma(fma(0.16666666666666666, b, 0.5), b, 1.0), b, 1.0) * a))) / y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -0.0018)
		tmp = Float64(x * Float64(exp(Float64(-b)) / y));
	elseif (b <= 2.05e+108)
		tmp = Float64(Float64(x * (a ^ Float64(t - 1.0))) / y);
	else
		tmp = Float64(Float64(x * Float64(1.0 / Float64(fma(fma(fma(0.16666666666666666, b, 0.5), b, 1.0), b, 1.0) * a))) / y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -0.0018], N[(x * N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.05e+108], N[(N[(x * N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[(1.0 / N[(N[(N[(N[(0.16666666666666666 * b + 0.5), $MachinePrecision] * b + 1.0), $MachinePrecision] * b + 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -0.0018

   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 inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 73.1

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

   5. Applied rewrites 73.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 73.1

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

   7. Applied rewrites 73.1%

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

   if -0.0018 < b < 2.05e108

   1. Initial program 98.4%

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

   3. Taylor expanded in y around 0

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

      1. div-exp N/A

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

      2. pow-to-exp N/A

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

      3. lower-/.f64 N/A

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

      4. lower-pow.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lower-exp.f64 63.6

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

   5. Applied rewrites 63.6%

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

   6. Taylor expanded in b around 0

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

      1. pow-to-exp N/A

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

      2. lift-pow.f64 N/A

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

      3. lift--.f64 63.4

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

   8. Applied rewrites 63.4%

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

   if 2.05e108 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. div-exp N/A

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

      2. pow-to-exp N/A

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

      3. lower-/.f64 N/A

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

      4. lower-pow.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lower-exp.f64 71.5

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

   5. Applied rewrites 71.5%

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

   6. Taylor expanded in t around 0

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

      1. inv-pow N/A

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

      2. lower-pow.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift-exp.f64 88.8

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

   8. Applied rewrites 88.8%

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

      1. lift-pow.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-exp.f64 N/A

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

      4. unpow-1 N/A

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

      5. *-commutative N/A

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

      6. lower-/.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-exp.f64 N/A

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

      9. lift-*.f64 88.8

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

   10. Applied rewrites 88.8%

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

   11. Taylor expanded in b around 0

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

       1. +-commutative N/A

          \[\leadsto \frac{x \cdot \frac{1}{\left(b \cdot \left(1 + b \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot b\right)\right) + 1\right) \cdot a}}{y} \]

       2. *-commutative N/A

          \[\leadsto \frac{x \cdot \frac{1}{\left(\left(1 + b \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot b\right)\right) \cdot b + 1\right) \cdot a}}{y} \]

       3. lower-fma.f64 N/A

          \[\leadsto \frac{x \cdot \frac{1}{\mathsf{fma}\left(1 + b \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot b\right), b, 1\right) \cdot a}}{y} \]

       4. +-commutative N/A

          \[\leadsto \frac{x \cdot \frac{1}{\mathsf{fma}\left(b \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot b\right) + 1, b, 1\right) \cdot a}}{y} \]

       5. *-commutative N/A

          \[\leadsto \frac{x \cdot \frac{1}{\mathsf{fma}\left(\left(\frac{1}{2} + \frac{1}{6} \cdot b\right) \cdot b + 1, b, 1\right) \cdot a}}{y} \]

       6. lower-fma.f64 N/A

          \[\leadsto \frac{x \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{2} + \frac{1}{6} \cdot b, b, 1\right), b, 1\right) \cdot a}}{y} \]

       7. +-commutative N/A

          \[\leadsto \frac{x \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{6} \cdot b + \frac{1}{2}, b, 1\right), b, 1\right) \cdot a}}{y} \]

       8. lower-fma.f64 88.8

          \[\leadsto \frac{x \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(0.16666666666666666, b, 0.5\right), b, 1\right), b, 1\right) \cdot a}}{y} \]

   13. Applied rewrites 88.8%

       \[\leadsto \frac{x \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(0.16666666666666666, b, 0.5\right), b, 1\right), b, 1\right) \cdot a}}{y} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 13: 57.0% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -230 \lor \neg \left(b \leq 1.6 \cdot 10^{-95}\right):\\ \;\;\;\;x \cdot \frac{e^{-b}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{1}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -230.0) (not (<= b 1.6e-95)))
   (* x (/ (exp (- b)) y))
   (* x (/ (/ 1.0 a) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -230.0) || !(b <= 1.6e-95)) {
		tmp = x * (exp(-b) / y);
	} else {
		tmp = x * ((1.0 / a) / y);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-230.0d0)) .or. (.not. (b <= 1.6d-95))) then
        tmp = x * (exp(-b) / y)
    else
        tmp = x * ((1.0d0 / a) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -230.0) || !(b <= 1.6e-95)) {
		tmp = x * (Math.exp(-b) / y);
	} else {
		tmp = x * ((1.0 / a) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -230.0) or not (b <= 1.6e-95):
		tmp = x * (math.exp(-b) / y)
	else:
		tmp = x * ((1.0 / a) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -230.0) || !(b <= 1.6e-95))
		tmp = Float64(x * Float64(exp(Float64(-b)) / y));
	else
		tmp = Float64(x * Float64(Float64(1.0 / a) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -230.0) || ~((b <= 1.6e-95)))
		tmp = x * (exp(-b) / y);
	else
		tmp = x * ((1.0 / a) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -230.0], N[Not[LessEqual[b, 1.6e-95]], $MachinePrecision]], N[(x * N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(1.0 / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -230 or 1.5999999999999999e-95 < 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 b around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 70.0

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

   5. Applied rewrites 70.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 70.0

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

   7. Applied rewrites 70.0%

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

   if -230 < b < 1.5999999999999999e-95

   1. Initial program 97.8%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. *-commutative N/A

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

      3. pow-to-exp N/A

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

      4. pow-to-exp N/A

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

      5. lower-*.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 85.8

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

   5. Applied rewrites 85.8%

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

   6. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lift-pow.f64 79.7

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

   8. Applied rewrites 79.7%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 42.4%

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

       1. lift-/.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. associate-/l* N/A

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

       4. lower-*.f64 N/A

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

       5. lower-/.f64 43.3

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

   13. Applied rewrites 43.3%

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

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -230 \lor \neg \left(b \leq 1.6 \cdot 10^{-95}\right):\\ \;\;\;\;x \cdot \frac{e^{-b}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{1}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 32.3% accurate, 9.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 10^{-102}:\\ \;\;\;\;\frac{x \cdot \frac{1}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{1}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 1e-102) (/ (* x (/ 1.0 a)) y) (* x (/ (/ 1.0 a) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 1e-102) {
		tmp = (x * (1.0 / a)) / y;
	} else {
		tmp = x * ((1.0 / a) / y);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= 1d-102) then
        tmp = (x * (1.0d0 / a)) / y
    else
        tmp = x * ((1.0d0 / a) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 1e-102) {
		tmp = (x * (1.0 / a)) / y;
	} else {
		tmp = x * ((1.0 / a) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 1e-102:
		tmp = (x * (1.0 / a)) / y
	else:
		tmp = x * ((1.0 / a) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 1e-102)
		tmp = Float64(Float64(x * Float64(1.0 / a)) / y);
	else
		tmp = Float64(x * Float64(Float64(1.0 / a) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 1e-102)
		tmp = (x * (1.0 / a)) / y;
	else
		tmp = x * ((1.0 / a) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 1e-102], N[(N[(x * N[(1.0 / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x * N[(N[(1.0 / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 9.99999999999999933e-103

   1. Initial program 99.5%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. *-commutative N/A

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

      3. pow-to-exp N/A

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

      4. pow-to-exp N/A

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

      5. lower-*.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 70.0

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

   5. Applied rewrites 70.0%

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

   6. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lift-pow.f64 64.1

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

   8. Applied rewrites 64.1%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 34.8%

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

   if 9.99999999999999933e-103 < a

   1. Initial program 98.8%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. *-commutative N/A

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

      3. pow-to-exp N/A

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

      4. pow-to-exp N/A

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

      5. lower-*.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 67.3

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

   5. Applied rewrites 67.3%

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

   6. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lift-pow.f64 61.6

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

   8. Applied rewrites 61.6%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 26.3%

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

       1. lift-/.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. associate-/l* N/A

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

       4. lower-*.f64 N/A

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

       5. lower-/.f64 29.1

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

   13. Applied rewrites 29.1%

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

Alternative 15: 31.2% accurate, 12.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x * ((1.0d0 / a) / y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.0%

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

3. Taylor expanded in b around 0

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

   1. exp-sum N/A

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

   2. *-commutative N/A

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

   3. pow-to-exp N/A

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

   4. pow-to-exp N/A

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

   5. lower-*.f64 N/A

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

   6. lower-pow.f64 N/A

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

   7. lower-pow.f64 N/A

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

   8. lift--.f64 68.3

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

5. Applied rewrites 68.3%

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

6. Taylor expanded in t around 0

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

   1. lower-/.f64 N/A

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

   2. lift-pow.f64 62.5

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

8. Applied rewrites 62.5%

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

9. Taylor expanded in y around 0

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

11. Applied rewrites 29.3%

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

    1. lift-/.f64 N/A

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

    2. lift-*.f64 N/A

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

    3. associate-/l* N/A

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

    4. lower-*.f64 N/A

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

    5. lower-/.f64 29.3

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

13. Applied rewrites 29.3%

    \[\leadsto \color{blue}{x \cdot \frac{\frac{1}{a}}{y}} \]
14. Add Preprocessing

Developer Target 1: 71.8% 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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    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 2025040 
(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))