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

Percentage Accurate: 98.4% → 98.4%

Time: 9.3s

Alternatives: 15

Speedup: 1.0×

• 48.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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 99.5%

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

Alternative 2: 45.8% accurate, 0.4× speedup

Math

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

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))
     (* (pow a -1.0) (/ x y))
     (if (<= t_1 0.0)
       (/
        (*
         x
         (/ (/ 1.0 a) (fma (fma (fma 0.16666666666666666 b 0.5) b 1.0) b 1.0)))
        y)
       (/ (* x (pow a -1.0)) 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 = pow(a, -1.0) * (x / y);
	} else if (t_1 <= 0.0) {
		tmp = (x * ((1.0 / a) / fma(fma(fma(0.16666666666666666, b, 0.5), b, 1.0), b, 1.0))) / y;
	} else {
		tmp = (x * pow(a, -1.0)) / 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((a ^ -1.0) * Float64(x / y));
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(x * Float64(Float64(1.0 / a) / fma(fma(fma(0.16666666666666666, b, 0.5), b, 1.0), b, 1.0))) / y);
	else
		tmp = Float64(Float64(x * (a ^ -1.0)) / 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[Power[a, -1.0], $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(N[(x * N[(N[(1.0 / a), $MachinePrecision] / N[(N[(N[(0.16666666666666666 * b + 0.5), $MachinePrecision] * b + 1.0), $MachinePrecision] * b + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Power[a, -1.0], $MachinePrecision]), $MachinePrecision] / y), $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

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. exp-sum N/A

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

      6. lower-*.f64 N/A

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

      7. exp-prod N/A

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

      8. lower-pow.f64 N/A

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

      9. rem-exp-log N/A

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

      10. lower--.f64 N/A

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

      11. *-commutative N/A

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

      12. exp-to-pow N/A

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

      13. lower-pow.f64 N/A

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

      14. lower-/.f64 64.1

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

   5. Applied rewrites 64.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 59.6%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 25.1%

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

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

   1. Initial program 99.7%

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

   3. Taylor expanded in t around 0

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

      1. exp-diff N/A

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

      2. lower-/.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

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

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

      6. distribute-lft-neg-in N/A

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

      7. distribute-rgt-neg-in N/A

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

      8. metadata-eval N/A

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

      9. *-rgt-identity N/A

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

      10. exp-diff N/A

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

      11. lower-/.f64 N/A

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

      12. *-commutative N/A

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

      13. exp-to-pow N/A

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

      14. lower-pow.f64 N/A

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

      15. rem-exp-log N/A

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

      16. lower-exp.f64 71.1

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

   5. Applied rewrites 71.1%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 60.8%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 46.2%

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

   12. Taylor expanded in b around 0

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

   14. Applied rewrites 63.9%

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

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

   1. Initial program 98.9%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

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

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

      4. distribute-lft-neg-in N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. metadata-eval N/A

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

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

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

      8. *-commutative N/A

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

      9. distribute-lft-neg-in N/A

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

      10. distribute-rgt-neg-in N/A

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

      11. metadata-eval N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-log.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 N/A

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

      17. rem-exp-log N/A

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

      18. lower-log.f64 N/A

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

      19. rem-exp-log 83.7

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

   5. Applied rewrites 83.7%

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

   6. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. *-commutative N/A

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

      3. exp-to-pow N/A

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

      4. lower-*.f64 N/A

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

      5. lower-pow.f64 N/A

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

      6. exp-to-pow 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

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

      8. lower--.f64 78.5

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

   8. Applied rewrites 78.5%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 59.8%

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

   12. Taylor expanded in t around 0

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

   14. Applied rewrites 33.5%

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

4. Final simplification 45.9%

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

Alternative 3: 89.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+120}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)} \cdot x}{y}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+105}:\\ \;\;\;\;\frac{x \cdot e^{\mathsf{fma}\left(\log z, y, -\log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{{a}^{t} \cdot x}{y}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -3.2e+120)
   (/ (* (pow a (- t 1.0)) x) y)
   (if (<= t 7.5e+105)
     (/ (* x (exp (- (fma (log z) y (- (log a))) b))) y)
     (/ (/ (* (pow a t) x) y) a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.2e+120) {
		tmp = (pow(a, (t - 1.0)) * x) / y;
	} else if (t <= 7.5e+105) {
		tmp = (x * exp((fma(log(z), y, -log(a)) - b))) / y;
	} else {
		tmp = ((pow(a, t) * x) / y) / a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -3.2e+120)
		tmp = Float64(Float64((a ^ Float64(t - 1.0)) * x) / y);
	elseif (t <= 7.5e+105)
		tmp = Float64(Float64(x * exp(Float64(fma(log(z), y, Float64(-log(a))) - b))) / y);
	else
		tmp = Float64(Float64(Float64((a ^ t) * x) / y) / a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -3.2e+120], N[(N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 7.5e+105], N[(N[(x * N[Exp[N[(N[(N[Log[z], $MachinePrecision] * y + (-N[Log[a], $MachinePrecision])), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(N[(N[Power[a, t], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision] / a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.19999999999999982e120

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. exp-sum N/A

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

      6. lower-*.f64 N/A

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

      7. exp-prod N/A

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

      8. lower-pow.f64 N/A

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

      9. rem-exp-log N/A

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

      10. lower--.f64 N/A

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

      11. *-commutative N/A

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

      12. exp-to-pow N/A

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

      13. lower-pow.f64 N/A

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

      14. lower-/.f64 61.3

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

   5. Applied rewrites 61.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 93.6%

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

   if -3.19999999999999982e120 < t < 7.5000000000000002e105

   1. Initial program 99.3%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

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

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

      4. distribute-lft-neg-in N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. metadata-eval N/A

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

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

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

      8. *-commutative N/A

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

      9. distribute-lft-neg-in N/A

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

      10. distribute-rgt-neg-in N/A

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

      11. metadata-eval N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-log.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 N/A

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

      17. rem-exp-log N/A

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

      18. lower-log.f64 N/A

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

      19. rem-exp-log 96.4

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

   5. Applied rewrites 96.4%

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

   if 7.5000000000000002e105 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. exp-sum N/A

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

      6. lower-*.f64 N/A

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

      7. exp-prod N/A

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

      8. lower-pow.f64 N/A

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

      9. rem-exp-log N/A

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

      10. lower--.f64 N/A

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

      11. *-commutative N/A

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

      12. exp-to-pow N/A

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

      13. lower-pow.f64 N/A

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

      14. lower-/.f64 60.9

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

   5. Applied rewrites 60.9%

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

   7. Applied rewrites 60.9%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 89.3%

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

Alternative 4: 81.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+119}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)} \cdot x}{y}\\ \mathbf{elif}\;t \leq 6.9 \cdot 10^{+105}:\\ \;\;\;\;\frac{x \cdot \frac{\frac{{z}^{y}}{a}}{e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{{a}^{t} \cdot x}{y}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -6e+119)
   (/ (* (pow a (- t 1.0)) x) y)
   (if (<= t 6.9e+105)
     (/ (* x (/ (/ (pow z y) a) (exp b))) y)
     (/ (/ (* (pow a t) x) y) a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -6e+119) {
		tmp = (pow(a, (t - 1.0)) * x) / y;
	} else if (t <= 6.9e+105) {
		tmp = (x * ((pow(z, y) / a) / exp(b))) / y;
	} else {
		tmp = ((pow(a, t) * x) / y) / a;
	}
	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 (t <= (-6d+119)) then
        tmp = ((a ** (t - 1.0d0)) * x) / y
    else if (t <= 6.9d+105) then
        tmp = (x * (((z ** y) / a) / exp(b))) / y
    else
        tmp = (((a ** t) * x) / y) / a
    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 (t <= -6e+119) {
		tmp = (Math.pow(a, (t - 1.0)) * x) / y;
	} else if (t <= 6.9e+105) {
		tmp = (x * ((Math.pow(z, y) / a) / Math.exp(b))) / y;
	} else {
		tmp = ((Math.pow(a, t) * x) / y) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -6e+119:
		tmp = (math.pow(a, (t - 1.0)) * x) / y
	elif t <= 6.9e+105:
		tmp = (x * ((math.pow(z, y) / a) / math.exp(b))) / y
	else:
		tmp = ((math.pow(a, t) * x) / y) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -6e+119)
		tmp = Float64(Float64((a ^ Float64(t - 1.0)) * x) / y);
	elseif (t <= 6.9e+105)
		tmp = Float64(Float64(x * Float64(Float64((z ^ y) / a) / exp(b))) / y);
	else
		tmp = Float64(Float64(Float64((a ^ t) * x) / y) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -6e+119)
		tmp = ((a ^ (t - 1.0)) * x) / y;
	elseif (t <= 6.9e+105)
		tmp = (x * (((z ^ y) / a) / exp(b))) / y;
	else
		tmp = (((a ^ t) * x) / y) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -6e+119], N[(N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 6.9e+105], N[(N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(N[(N[Power[a, t], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision] / a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.00000000000000002e119

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. exp-sum N/A

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

      6. lower-*.f64 N/A

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

      7. exp-prod N/A

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

      8. lower-pow.f64 N/A

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

      9. rem-exp-log N/A

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

      10. lower--.f64 N/A

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

      11. *-commutative N/A

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

      12. exp-to-pow N/A

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

      13. lower-pow.f64 N/A

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

      14. lower-/.f64 61.3

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

   5. Applied rewrites 61.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 93.6%

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

   if -6.00000000000000002e119 < t < 6.90000000000000036e105

   1. Initial program 99.3%

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

   3. Taylor expanded in t around 0

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

      1. exp-diff N/A

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

      2. lower-/.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

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

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

      6. distribute-lft-neg-in N/A

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

      7. distribute-rgt-neg-in N/A

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

      8. metadata-eval N/A

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

      9. *-rgt-identity N/A

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

      10. exp-diff N/A

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

      11. lower-/.f64 N/A

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

      12. *-commutative N/A

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

      13. exp-to-pow N/A

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

      14. lower-pow.f64 N/A

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

      15. rem-exp-log N/A

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

      16. lower-exp.f64 86.4

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

   5. Applied rewrites 86.4%

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

   if 6.90000000000000036e105 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. exp-sum N/A

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

      6. lower-*.f64 N/A

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

      7. exp-prod N/A

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

      8. lower-pow.f64 N/A

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

      9. rem-exp-log N/A

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

      10. lower--.f64 N/A

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

      11. *-commutative N/A

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

      12. exp-to-pow N/A

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

      13. lower-pow.f64 N/A

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

      14. lower-/.f64 60.9

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

   5. Applied rewrites 60.9%

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

   7. Applied rewrites 60.9%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 89.3%

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

Alternative 5: 82.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -270000000000 \lor \neg \left(y \leq 5.8 \cdot 10^{+116}\right):\\ \;\;\;\;\frac{\frac{{z}^{y} \cdot x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{a}^{\left(t - 1\right)}}{e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -270000000000.0) (not (<= y 5.8e+116)))
   (/ (/ (* (pow z y) x) y) a)
   (* x (/ (/ (pow a (- t 1.0)) (exp b)) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -270000000000.0) || !(y <= 5.8e+116)) {
		tmp = ((pow(z, y) * x) / y) / a;
	} else {
		tmp = x * ((pow(a, (t - 1.0)) / exp(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 <= (-270000000000.0d0)) .or. (.not. (y <= 5.8d+116))) then
        tmp = (((z ** y) * x) / y) / a
    else
        tmp = x * (((a ** (t - 1.0d0)) / exp(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 <= -270000000000.0) || !(y <= 5.8e+116)) {
		tmp = ((Math.pow(z, y) * x) / y) / a;
	} else {
		tmp = x * ((Math.pow(a, (t - 1.0)) / Math.exp(b)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -270000000000.0) or not (y <= 5.8e+116):
		tmp = ((math.pow(z, y) * x) / y) / a
	else:
		tmp = x * ((math.pow(a, (t - 1.0)) / math.exp(b)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -270000000000.0) || !(y <= 5.8e+116))
		tmp = Float64(Float64(Float64((z ^ y) * x) / y) / a);
	else
		tmp = Float64(x * Float64(Float64((a ^ Float64(t - 1.0)) / exp(b)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -270000000000.0) || ~((y <= 5.8e+116)))
		tmp = (((z ^ y) * x) / y) / a;
	else
		tmp = x * (((a ^ (t - 1.0)) / exp(b)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -270000000000.0], N[Not[LessEqual[y, 5.8e+116]], $MachinePrecision]], N[(N[(N[(N[Power[z, y], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision] / a), $MachinePrecision], N[(x * N[(N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.7e11 or 5.8000000000000003e116 < 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

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. exp-sum N/A

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

      6. lower-*.f64 N/A

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

      7. exp-prod N/A

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

      8. lower-pow.f64 N/A

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

      9. rem-exp-log N/A

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

      10. lower--.f64 N/A

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

      11. *-commutative N/A

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

      12. exp-to-pow N/A

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

      13. lower-pow.f64 N/A

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

      14. lower-/.f64 61.8

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

   5. Applied rewrites 61.8%

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

   7. Applied rewrites 61.8%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 48.0%

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

   11. Taylor expanded in t around 0

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

   13. Applied rewrites 86.3%

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

   if -2.7e11 < y < 5.8000000000000003e116

   1. Initial program 99.1%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

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

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

      4. distribute-lft-neg-in N/A

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

      5. distribute-rgt-neg-in N/A

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

      6. metadata-eval N/A

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

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

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

      8. *-commutative N/A

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

      9. distribute-lft-neg-in N/A

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

      10. distribute-rgt-neg-in N/A

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

      11. metadata-eval N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-log.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 N/A

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

      17. rem-exp-log N/A

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

      18. lower-log.f64 N/A

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

      19. rem-exp-log 73.3

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

   5. Applied rewrites 73.3%

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

   6. Taylor expanded in y around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. exp-diff N/A

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

      5. lower-/.f64 N/A

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

      6. exp-to-pow N/A

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

      7. lower-pow.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower-exp.f64 85.2

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

   8. Applied rewrites 85.2%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -270000000000 \lor \neg \left(y \leq 5.8 \cdot 10^{+116}\right):\\ \;\;\;\;\frac{\frac{{z}^{y} \cdot x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{a}^{\left(t - 1\right)}}{e^{b}}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+122} \lor \neg \left(b \leq 4.5 \cdot 10^{-14}\right):\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left({a}^{\left(t - 1\right)} \cdot {z}^{y}\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -3.5e+122) (not (<= b 4.5e-14)))
   (* (/ (exp (- b)) y) x)
   (/ (* x (* (pow a (- t 1.0)) (pow z y))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.5e+122) || !(b <= 4.5e-14)) {
		tmp = (exp(-b) / y) * x;
	} else {
		tmp = (x * (pow(a, (t - 1.0)) * pow(z, y))) / 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 <= (-3.5d+122)) .or. (.not. (b <= 4.5d-14))) then
        tmp = (exp(-b) / y) * x
    else
        tmp = (x * ((a ** (t - 1.0d0)) * (z ** y))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.5e+122) || !(b <= 4.5e-14)) {
		tmp = (Math.exp(-b) / y) * x;
	} else {
		tmp = (x * (Math.pow(a, (t - 1.0)) * Math.pow(z, y))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -3.5e+122) or not (b <= 4.5e-14):
		tmp = (math.exp(-b) / y) * x
	else:
		tmp = (x * (math.pow(a, (t - 1.0)) * math.pow(z, y))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -3.5e+122) || !(b <= 4.5e-14))
		tmp = Float64(Float64(exp(Float64(-b)) / y) * x);
	else
		tmp = Float64(Float64(x * Float64((a ^ Float64(t - 1.0)) * (z ^ y))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -3.5e+122) || ~((b <= 4.5e-14)))
		tmp = (exp(-b) / y) * x;
	else
		tmp = (x * ((a ^ (t - 1.0)) * (z ^ y))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -3.5e+122], N[Not[LessEqual[b, 4.5e-14]], $MachinePrecision]], N[(N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision], N[(N[(x * N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] * N[Power[z, y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.50000000000000014e122 or 4.4999999999999998e-14 < 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

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

      2. lower-neg.f64 84.5

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

   5. Applied rewrites 84.5%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]
   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. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 84.5

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

   7. Applied rewrites 84.5%

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

   if -3.50000000000000014e122 < b < 4.4999999999999998e-14

   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 b around 0

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

      1. +-commutative N/A

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

      2. exp-sum N/A

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

      3. lower-*.f64 N/A

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

      4. exp-prod N/A

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

      5. lower-pow.f64 N/A

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

      6. rem-exp-log N/A

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

      7. lower--.f64 N/A

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

      8. *-commutative N/A

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

      9. exp-to-pow N/A

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

      10. lower-pow.f64 83.8

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

   5. Applied rewrites 83.8%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+122} \lor \neg \left(b \leq 4.5 \cdot 10^{-14}\right):\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left({a}^{\left(t - 1\right)} \cdot {z}^{y}\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{e^{-b}}{y} \cdot x\\ \mathbf{if}\;b \leq -3.5 \cdot 10^{+122}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -9.8 \cdot 10^{-262}:\\ \;\;\;\;\left({a}^{\left(t - 1\right)} \cdot {z}^{y}\right) \cdot \frac{x}{y}\\ \mathbf{elif}\;b \leq 22000:\\ \;\;\;\;\frac{\frac{{z}^{y} \cdot x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ (exp (- b)) y) x)))
   (if (<= b -3.5e+122)
     t_1
     (if (<= b -9.8e-262)
       (* (* (pow a (- t 1.0)) (pow z y)) (/ x y))
       (if (<= b 22000.0) (/ (/ (* (pow z y) x) y) a) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (exp(-b) / y) * x;
	double tmp;
	if (b <= -3.5e+122) {
		tmp = t_1;
	} else if (b <= -9.8e-262) {
		tmp = (pow(a, (t - 1.0)) * pow(z, y)) * (x / y);
	} else if (b <= 22000.0) {
		tmp = ((pow(z, y) * x) / y) / a;
	} else {
		tmp = t_1;
	}
	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 = (exp(-b) / y) * x
    if (b <= (-3.5d+122)) then
        tmp = t_1
    else if (b <= (-9.8d-262)) then
        tmp = ((a ** (t - 1.0d0)) * (z ** y)) * (x / y)
    else if (b <= 22000.0d0) then
        tmp = (((z ** y) * x) / y) / a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (Math.exp(-b) / y) * x;
	double tmp;
	if (b <= -3.5e+122) {
		tmp = t_1;
	} else if (b <= -9.8e-262) {
		tmp = (Math.pow(a, (t - 1.0)) * Math.pow(z, y)) * (x / y);
	} else if (b <= 22000.0) {
		tmp = ((Math.pow(z, y) * x) / y) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (math.exp(-b) / y) * x
	tmp = 0
	if b <= -3.5e+122:
		tmp = t_1
	elif b <= -9.8e-262:
		tmp = (math.pow(a, (t - 1.0)) * math.pow(z, y)) * (x / y)
	elif b <= 22000.0:
		tmp = ((math.pow(z, y) * x) / y) / a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(exp(Float64(-b)) / y) * x)
	tmp = 0.0
	if (b <= -3.5e+122)
		tmp = t_1;
	elseif (b <= -9.8e-262)
		tmp = Float64(Float64((a ^ Float64(t - 1.0)) * (z ^ y)) * Float64(x / y));
	elseif (b <= 22000.0)
		tmp = Float64(Float64(Float64((z ^ y) * x) / y) / a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (exp(-b) / y) * x;
	tmp = 0.0;
	if (b <= -3.5e+122)
		tmp = t_1;
	elseif (b <= -9.8e-262)
		tmp = ((a ^ (t - 1.0)) * (z ^ y)) * (x / y);
	elseif (b <= 22000.0)
		tmp = (((z ^ y) * x) / y) / a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[b, -3.5e+122], t$95$1, If[LessEqual[b, -9.8e-262], N[(N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] * N[Power[z, y], $MachinePrecision]), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 22000.0], N[(N[(N[(N[Power[z, y], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision] / a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.50000000000000014e122 or 22000 < 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

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

      2. lower-neg.f64 85.0

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

   5. Applied rewrites 85.0%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]
   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. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 85.0

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

   7. Applied rewrites 85.0%

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

   if -3.50000000000000014e122 < b < -9.8000000000000005e-262

   1. Initial program 99.1%

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

   3. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. exp-sum N/A

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

      6. lower-*.f64 N/A

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

      7. exp-prod N/A

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

      8. lower-pow.f64 N/A

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

      9. rem-exp-log N/A

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

      10. lower--.f64 N/A

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

      11. *-commutative N/A

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

      12. exp-to-pow N/A

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

      13. lower-pow.f64 N/A

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

      14. lower-/.f64 79.5

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

   5. Applied rewrites 79.5%

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

   if -9.8000000000000005e-262 < b < 22000

   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 b around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. exp-sum N/A

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

      6. lower-*.f64 N/A

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

      7. exp-prod N/A

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

      8. lower-pow.f64 N/A

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

      9. rem-exp-log N/A

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

      10. lower--.f64 N/A

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

      11. *-commutative N/A

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

      12. exp-to-pow N/A

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

      13. lower-pow.f64 N/A

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

      14. lower-/.f64 74.5

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

   5. Applied rewrites 74.5%

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

   7. Applied rewrites 74.6%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 72.1%

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

   11. Taylor expanded in t around 0

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

   13. Applied rewrites 82.9%

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

Alternative 8: 74.2% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+122} \lor \neg \left(b \leq 22000\right):\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{{z}^{y} \cdot x}{y}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -3.5e+122) (not (<= b 22000.0)))
   (* (/ (exp (- b)) y) x)
   (/ (/ (* (pow z y) x) y) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.5e+122) || !(b <= 22000.0)) {
		tmp = (exp(-b) / y) * x;
	} else {
		tmp = ((pow(z, y) * x) / y) / a;
	}
	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 <= (-3.5d+122)) .or. (.not. (b <= 22000.0d0))) then
        tmp = (exp(-b) / y) * x
    else
        tmp = (((z ** y) * x) / y) / a
    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 <= -3.5e+122) || !(b <= 22000.0)) {
		tmp = (Math.exp(-b) / y) * x;
	} else {
		tmp = ((Math.pow(z, y) * x) / y) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -3.5e+122) or not (b <= 22000.0):
		tmp = (math.exp(-b) / y) * x
	else:
		tmp = ((math.pow(z, y) * x) / y) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -3.5e+122) || !(b <= 22000.0))
		tmp = Float64(Float64(exp(Float64(-b)) / y) * x);
	else
		tmp = Float64(Float64(Float64((z ^ y) * x) / y) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -3.5e+122) || ~((b <= 22000.0)))
		tmp = (exp(-b) / y) * x;
	else
		tmp = (((z ^ y) * x) / y) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -3.5e+122], N[Not[LessEqual[b, 22000.0]], $MachinePrecision]], N[(N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision], N[(N[(N[(N[Power[z, y], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.50000000000000014e122 or 22000 < 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

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

      2. lower-neg.f64 85.0

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

   5. Applied rewrites 85.0%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]
   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. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 85.0

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

   7. Applied rewrites 85.0%

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

   if -3.50000000000000014e122 < b < 22000

   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 b around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. exp-sum N/A

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

      6. lower-*.f64 N/A

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

      7. exp-prod N/A

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

      8. lower-pow.f64 N/A

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

      9. rem-exp-log N/A

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

      10. lower--.f64 N/A

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

      11. *-commutative N/A

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

      12. exp-to-pow N/A

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

      13. lower-pow.f64 N/A

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

      14. lower-/.f64 77.4

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

   5. Applied rewrites 77.4%

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

   7. Applied rewrites 77.5%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 67.6%

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

   11. Taylor expanded in t around 0

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

   13. Applied rewrites 77.7%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+122} \lor \neg \left(b \leq 22000\right):\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{{z}^{y} \cdot x}{y}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 71.7% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.6 \cdot 10^{+69} \lor \neg \left(b \leq 220000\right):\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{{z}^{y}}{y} \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -6.6e+69) (not (<= b 220000.0)))
   (* (/ (exp (- b)) y) x)
   (* (/ (pow z y) y) (/ x a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -6.6e+69) || !(b <= 220000.0)) {
		tmp = (exp(-b) / y) * x;
	} else {
		tmp = (pow(z, y) / y) * (x / a);
	}
	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 <= (-6.6d+69)) .or. (.not. (b <= 220000.0d0))) then
        tmp = (exp(-b) / y) * x
    else
        tmp = ((z ** y) / y) * (x / a)
    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 <= -6.6e+69) || !(b <= 220000.0)) {
		tmp = (Math.exp(-b) / y) * x;
	} else {
		tmp = (Math.pow(z, y) / y) * (x / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -6.6e+69) or not (b <= 220000.0):
		tmp = (math.exp(-b) / y) * x
	else:
		tmp = (math.pow(z, y) / y) * (x / a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -6.6e+69) || !(b <= 220000.0))
		tmp = Float64(Float64(exp(Float64(-b)) / y) * x);
	else
		tmp = Float64(Float64((z ^ y) / y) * Float64(x / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -6.6e+69) || ~((b <= 220000.0)))
		tmp = (exp(-b) / y) * x;
	else
		tmp = ((z ^ y) / y) * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -6.6e+69], N[Not[LessEqual[b, 220000.0]], $MachinePrecision]], N[(N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision], N[(N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -6.5999999999999997e69 or 2.2e5 < 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

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

      2. lower-neg.f64 83.3

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

   5. Applied rewrites 83.3%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]
   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. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 83.3

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

   7. Applied rewrites 83.3%

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

   if -6.5999999999999997e69 < b < 2.2e5

   1. Initial program 99.1%

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

   3. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. exp-sum N/A

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

      6. lower-*.f64 N/A

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

      7. exp-prod N/A

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

      8. lower-pow.f64 N/A

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

      9. rem-exp-log N/A

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

      10. lower--.f64 N/A

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

      11. *-commutative N/A

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

      12. exp-to-pow N/A

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

      13. lower-pow.f64 N/A

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

      14. lower-/.f64 76.7

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

   5. Applied rewrites 76.7%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 72.8%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.6 \cdot 10^{+69} \lor \neg \left(b \leq 220000\right):\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{{z}^{y}}{y} \cdot \frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 72.5% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.4 \cdot 10^{+162} \lor \neg \left(b \leq 3.4 \cdot 10^{-23}\right):\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)} \cdot x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.4e+162) (not (<= b 3.4e-23)))
   (* (/ (exp (- b)) y) x)
   (/ (* (pow a (- t 1.0)) x) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.4e+162) || !(b <= 3.4e-23)) {
		tmp = (exp(-b) / y) * x;
	} else {
		tmp = (pow(a, (t - 1.0)) * x) / 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 <= (-1.4d+162)) .or. (.not. (b <= 3.4d-23))) then
        tmp = (exp(-b) / y) * x
    else
        tmp = ((a ** (t - 1.0d0)) * x) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.4e+162) || !(b <= 3.4e-23)) {
		tmp = (Math.exp(-b) / y) * x;
	} else {
		tmp = (Math.pow(a, (t - 1.0)) * x) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.4e+162) or not (b <= 3.4e-23):
		tmp = (math.exp(-b) / y) * x
	else:
		tmp = (math.pow(a, (t - 1.0)) * x) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.4e+162) || !(b <= 3.4e-23))
		tmp = Float64(Float64(exp(Float64(-b)) / y) * x);
	else
		tmp = Float64(Float64((a ^ Float64(t - 1.0)) * x) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.4e+162) || ~((b <= 3.4e-23)))
		tmp = (exp(-b) / y) * x;
	else
		tmp = ((a ^ (t - 1.0)) * x) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.4e+162], N[Not[LessEqual[b, 3.4e-23]], $MachinePrecision]], N[(N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision], N[(N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.39999999999999995e162 or 3.4000000000000001e-23 < 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

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

      2. lower-neg.f64 85.8

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

   5. Applied rewrites 85.8%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]
   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. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 85.8

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

   7. Applied rewrites 85.8%

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

   if -1.39999999999999995e162 < b < 3.4000000000000001e-23

   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 b around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. exp-sum N/A

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

      6. lower-*.f64 N/A

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

      7. exp-prod N/A

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

      8. lower-pow.f64 N/A

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

      9. rem-exp-log N/A

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

      10. lower--.f64 N/A

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

      11. *-commutative N/A

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

      12. exp-to-pow N/A

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

      13. lower-pow.f64 N/A

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

      14. lower-/.f64 75.0

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

   5. Applied rewrites 75.0%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 67.2%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.4 \cdot 10^{+162} \lor \neg \left(b \leq 3.4 \cdot 10^{-23}\right):\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)} \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 56.7% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1 \lor \neg \left(b \leq 2.45 \cdot 10^{-124}\right):\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\left(b - -1\right) \cdot a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.0) (not (<= b 2.45e-124)))
   (* (/ (exp (- b)) y) x)
   (/ (* x (/ 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 <= -1.0) || !(b <= 2.45e-124)) {
		tmp = (exp(-b) / y) * x;
	} else {
		tmp = (x * (1.0 / ((b - -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 <= (-1.0d0)) .or. (.not. (b <= 2.45d-124))) then
        tmp = (exp(-b) / y) * x
    else
        tmp = (x * (1.0d0 / ((b - (-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 <= -1.0) || !(b <= 2.45e-124)) {
		tmp = (Math.exp(-b) / y) * x;
	} else {
		tmp = (x * (1.0 / ((b - -1.0) * a))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.0) or not (b <= 2.45e-124):
		tmp = (math.exp(-b) / y) * x
	else:
		tmp = (x * (1.0 / ((b - -1.0) * a))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.0) || !(b <= 2.45e-124))
		tmp = Float64(Float64(exp(Float64(-b)) / y) * x);
	else
		tmp = Float64(Float64(x * Float64(1.0 / Float64(Float64(b - -1.0) * a))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.0) || ~((b <= 2.45e-124)))
		tmp = (exp(-b) / y) * x;
	else
		tmp = (x * (1.0 / ((b - -1.0) * a))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.0], N[Not[LessEqual[b, 2.45e-124]], $MachinePrecision]], N[(N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision], N[(N[(x * N[(1.0 / N[(N[(b - -1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1 or 2.44999999999999983e-124 < b

   1. Initial program 99.9%

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

   3. Taylor expanded in 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

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

      2. lower-neg.f64 78.0

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

   5. Applied rewrites 78.0%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]
   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. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 78.0

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

   7. Applied rewrites 78.0%

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

   if -1 < b < 2.44999999999999983e-124

   1. Initial program 98.9%

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

   3. Taylor expanded in t around 0

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

      1. exp-diff N/A

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

      2. lower-/.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

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

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

      6. distribute-lft-neg-in N/A

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

      7. distribute-rgt-neg-in N/A

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

      8. metadata-eval N/A

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

      9. *-rgt-identity N/A

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

      10. exp-diff N/A

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

      11. lower-/.f64 N/A

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

      12. *-commutative N/A

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

      13. exp-to-pow N/A

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

      14. lower-pow.f64 N/A

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

      15. rem-exp-log N/A

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

      16. lower-exp.f64 78.2

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

   5. Applied rewrites 78.2%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 78.2%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 36.9%

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

   13. Applied rewrites 36.9%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1 \lor \neg \left(b \leq 2.45 \cdot 10^{-124}\right):\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\left(b - -1\right) \cdot a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 43.5% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 4.5 \cdot 10^{-23}:\\ \;\;\;\;{a}^{-1} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{\frac{1}{a}}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(0.16666666666666666, b, 0.5\right), b, 1\right), b, 1\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 4.5e-23)
   (* (pow a -1.0) (/ x y))
   (/
    (* x (/ (/ 1.0 a) (fma (fma (fma 0.16666666666666666 b 0.5) b 1.0) b 1.0)))
    y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 4.5e-23) {
		tmp = pow(a, -1.0) * (x / y);
	} else {
		tmp = (x * ((1.0 / a) / fma(fma(fma(0.16666666666666666, b, 0.5), b, 1.0), b, 1.0))) / y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 4.5e-23)
		tmp = Float64((a ^ -1.0) * Float64(x / y));
	else
		tmp = Float64(Float64(x * Float64(Float64(1.0 / a) / fma(fma(fma(0.16666666666666666, b, 0.5), b, 1.0), b, 1.0))) / y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 4.5e-23], N[(N[Power[a, -1.0], $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(1.0 / a), $MachinePrecision] / N[(N[(N[(0.16666666666666666 * b + 0.5), $MachinePrecision] * b + 1.0), $MachinePrecision] * b + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 4.49999999999999975e-23

   1. Initial program 99.3%

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

   3. Taylor expanded in b around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. exp-sum N/A

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

      6. lower-*.f64 N/A

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

      7. exp-prod N/A

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

      8. lower-pow.f64 N/A

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

      9. rem-exp-log N/A

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

      10. lower--.f64 N/A

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

      11. *-commutative N/A

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

      12. exp-to-pow N/A

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

      13. lower-pow.f64 N/A

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

      14. lower-/.f64 72.2

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

   5. Applied rewrites 72.2%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 63.0%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 36.3%

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

   if 4.49999999999999975e-23 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0

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

      1. exp-diff N/A

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

      2. lower-/.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

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

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

      6. distribute-lft-neg-in N/A

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

      7. distribute-rgt-neg-in N/A

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

      8. metadata-eval N/A

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

      9. *-rgt-identity N/A

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

      10. exp-diff N/A

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

      11. lower-/.f64 N/A

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

      12. *-commutative N/A

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

      13. exp-to-pow N/A

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

      14. lower-pow.f64 N/A

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

      15. rem-exp-log N/A

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

      16. lower-exp.f64 71.4

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

   5. Applied rewrites 71.4%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 53.2%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 43.0%

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

   12. Taylor expanded in b around 0

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

   14. Applied rewrites 67.9%

       \[\leadsto \frac{x \cdot \frac{\frac{1}{a}}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(0.16666666666666666, b, 0.5\right), b, 1\right), \color{blue}{b}, 1\right)}}{y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 41.0% accurate, 5.9× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (/
  (* x (/ (/ 1.0 a) (fma (fma (fma 0.16666666666666666 b 0.5) b 1.0) b 1.0)))
  y))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x * ((1.0 / a) / fma(fma(fma(0.16666666666666666, b, 0.5), b, 1.0), b, 1.0))) / y;
}

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x * Float64(Float64(1.0 / a) / fma(fma(fma(0.16666666666666666, b, 0.5), b, 1.0), b, 1.0))) / y)
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x * N[(N[(1.0 / a), $MachinePrecision] / N[(N[(N[(0.16666666666666666 * b + 0.5), $MachinePrecision] * b + 1.0), $MachinePrecision] * b + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]

Derivation

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 t around 0

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

   1. exp-diff N/A

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

   2. lower-/.f64 N/A

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

   3. +-commutative N/A

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

   4. *-commutative N/A

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

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

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

   6. distribute-lft-neg-in N/A

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

   7. distribute-rgt-neg-in N/A

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

   8. metadata-eval N/A

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

   9. *-rgt-identity N/A

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

   10. exp-diff N/A

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

   11. lower-/.f64 N/A

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

   12. *-commutative N/A

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

   13. exp-to-pow N/A

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

   14. lower-pow.f64 N/A

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

   15. rem-exp-log N/A

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

   16. lower-exp.f64 74.4

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

5. Applied rewrites 74.4%

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

6. Taylor expanded in b around 0

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

8. Applied rewrites 54.5%

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

9. Taylor expanded in y around 0

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

11. Applied rewrites 32.5%

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

12. Taylor expanded in b around 0

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

14. Applied rewrites 40.8%

    \[\leadsto \frac{x \cdot \frac{\frac{1}{a}}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(0.16666666666666666, b, 0.5\right), b, 1\right), \color{blue}{b}, 1\right)}}{y} \]
15. Add Preprocessing

Alternative 14: 39.8% accurate, 6.6× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (/ (* x (/ (/ 1.0 a) (fma (fma 0.5 b 1.0) b 1.0))) y))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x * ((1.0 / a) / fma(fma(0.5, b, 1.0), b, 1.0))) / y;
}

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x * Float64(Float64(1.0 / a) / fma(fma(0.5, b, 1.0), b, 1.0))) / y)
end

Wolfram

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

Derivation

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 t around 0

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

   1. exp-diff N/A

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

   2. lower-/.f64 N/A

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

   3. +-commutative N/A

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

   4. *-commutative N/A

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

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

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

   6. distribute-lft-neg-in N/A

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

   7. distribute-rgt-neg-in N/A

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

   8. metadata-eval N/A

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

   9. *-rgt-identity N/A

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

   10. exp-diff N/A

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

   11. lower-/.f64 N/A

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

   12. *-commutative N/A

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

   13. exp-to-pow N/A

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

   14. lower-pow.f64 N/A

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

   15. rem-exp-log N/A

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

   16. lower-exp.f64 74.4

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

5. Applied rewrites 74.4%

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

6. Taylor expanded in b around 0

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

8. Applied rewrites 54.5%

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

9. Taylor expanded in y around 0

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

11. Applied rewrites 32.5%

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

12. Taylor expanded in b around 0

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

14. Applied rewrites 40.3%

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

Alternative 15: 32.2% accurate, 9.3× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot \frac{1}{\left(b - -1\right) \cdot a}}{y} \end{array} \]

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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 t around 0

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

   1. exp-diff N/A

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

   2. lower-/.f64 N/A

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

   3. +-commutative N/A

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

   4. *-commutative N/A

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

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

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

   6. distribute-lft-neg-in N/A

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

   7. distribute-rgt-neg-in N/A

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

   8. metadata-eval N/A

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

   9. *-rgt-identity N/A

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

   10. exp-diff N/A

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

   11. lower-/.f64 N/A

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

   12. *-commutative N/A

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

   13. exp-to-pow N/A

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

   14. lower-pow.f64 N/A

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

   15. rem-exp-log N/A

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

   16. lower-exp.f64 74.4

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

5. Applied rewrites 74.4%

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

6. Taylor expanded in b around 0

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

8. Applied rewrites 54.5%

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

9. Taylor expanded in y around 0

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

11. Applied rewrites 32.5%

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

13. Applied rewrites 32.8%

    \[\leadsto \frac{x \cdot \frac{1}{\color{blue}{\left(b - -1\right) \cdot a}}}{y} \]
14. Add Preprocessing

Developer Target 1: 71.5% 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 2025017 
(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))