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

Percentage Accurate: 98.6% → 98.6%

Time: 6.3s

Alternatives: 14

Speedup: 1.0×

• 48.4% 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: 98.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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: 98.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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 98.7%

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

Alternative 2: 85.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{-124} \lor \neg \left(b \leq 2.8 \cdot 10^{+16}\right):\\ \;\;\;\;x \cdot \frac{e^{\log a \cdot \left(t - 1\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left({z}^{y} \cdot {a}^{\left(t - 1\right)}\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -3.8e-124) (not (<= b 2.8e+16)))
   (* x (/ (exp (- (* (log a) (- t 1.0)) b)) y))
   (/ (* x (* (pow z y) (pow a (- t 1.0)))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.8e-124) || !(b <= 2.8e+16)) {
		tmp = x * (exp(((log(a) * (t - 1.0)) - b)) / y);
	} else {
		tmp = (x * (pow(z, y) * pow(a, (t - 1.0)))) / y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-3.8d-124)) .or. (.not. (b <= 2.8d+16))) then
        tmp = x * (exp(((log(a) * (t - 1.0d0)) - b)) / y)
    else
        tmp = (x * ((z ** y) * (a ** (t - 1.0d0)))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.8e-124) || !(b <= 2.8e+16)) {
		tmp = x * (Math.exp(((Math.log(a) * (t - 1.0)) - b)) / y);
	} else {
		tmp = (x * (Math.pow(z, y) * Math.pow(a, (t - 1.0)))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -3.8e-124) or not (b <= 2.8e+16):
		tmp = x * (math.exp(((math.log(a) * (t - 1.0)) - b)) / y)
	else:
		tmp = (x * (math.pow(z, y) * math.pow(a, (t - 1.0)))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -3.8e-124) || !(b <= 2.8e+16))
		tmp = Float64(x * Float64(exp(Float64(Float64(log(a) * Float64(t - 1.0)) - b)) / y));
	else
		tmp = Float64(Float64(x * Float64((z ^ y) * (a ^ Float64(t - 1.0)))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -3.8e-124) || ~((b <= 2.8e+16)))
		tmp = x * (exp(((log(a) * (t - 1.0)) - b)) / y);
	else
		tmp = (x * ((z ^ y) * (a ^ (t - 1.0)))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -3.8e-124], N[Not[LessEqual[b, 2.8e+16]], $MachinePrecision]], N[(x * N[(N[Exp[N[(N[(N[Log[a], $MachinePrecision] * N[(t - 1.0), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] * N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.80000000000000012e-124 or 2.8e16 < b

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0

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

      1. lower-*.f64 N/A

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

      2. lift-log.f64 N/A

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

      3. lift--.f64 90.2

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

   5. Applied rewrites 90.2%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 90.8

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

   7. Applied rewrites 90.8%

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

   if -3.80000000000000012e-124 < b < 2.8e16

   1. Initial program 98.2%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. *-commutative N/A

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

      3. pow-to-exp N/A

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

      4. pow-to-exp N/A

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

      5. lower-*.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 84.6

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

   5. Applied rewrites 84.6%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{-124} \lor \neg \left(b \leq 2.8 \cdot 10^{+16}\right):\\ \;\;\;\;x \cdot \frac{e^{\log a \cdot \left(t - 1\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left({z}^{y} \cdot {a}^{\left(t - 1\right)}\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.6 \cdot 10^{+34} \lor \neg \left(b \leq 2.55 \cdot 10^{+95}\right):\\ \;\;\;\;x \cdot \frac{e^{-b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left({z}^{y} \cdot {a}^{\left(t - 1\right)}\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -6.6e+34) (not (<= b 2.55e+95)))
   (* x (/ (exp (- b)) y))
   (/ (* x (* (pow z y) (pow a (- t 1.0)))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -6.6e+34) || !(b <= 2.55e+95)) {
		tmp = x * (exp(-b) / y);
	} else {
		tmp = (x * (pow(z, y) * pow(a, (t - 1.0)))) / y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-6.6d+34)) .or. (.not. (b <= 2.55d+95))) then
        tmp = x * (exp(-b) / y)
    else
        tmp = (x * ((z ** y) * (a ** (t - 1.0d0)))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -6.6e+34) || !(b <= 2.55e+95)) {
		tmp = x * (Math.exp(-b) / y);
	} else {
		tmp = (x * (Math.pow(z, y) * Math.pow(a, (t - 1.0)))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -6.6e+34) or not (b <= 2.55e+95):
		tmp = x * (math.exp(-b) / y)
	else:
		tmp = (x * (math.pow(z, y) * math.pow(a, (t - 1.0)))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -6.6e+34) || !(b <= 2.55e+95))
		tmp = Float64(x * Float64(exp(Float64(-b)) / y));
	else
		tmp = Float64(Float64(x * Float64((z ^ y) * (a ^ Float64(t - 1.0)))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -6.6e+34) || ~((b <= 2.55e+95)))
		tmp = x * (exp(-b) / y);
	else
		tmp = (x * ((z ^ y) * (a ^ (t - 1.0)))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -6.6e+34], N[Not[LessEqual[b, 2.55e+95]], $MachinePrecision]], N[(x * N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] * N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -6.59999999999999976e34 or 2.55000000000000001e95 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 86.1

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

   5. Applied rewrites 86.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 86.1

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

   7. Applied rewrites 86.1%

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

   if -6.59999999999999976e34 < b < 2.55000000000000001e95

   1. Initial program 98.0%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. *-commutative N/A

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

      3. pow-to-exp N/A

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

      4. pow-to-exp N/A

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

      5. lower-*.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 81.5

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

   5. Applied rewrites 81.5%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.6 \cdot 10^{+34} \lor \neg \left(b \leq 2.55 \cdot 10^{+95}\right):\\ \;\;\;\;x \cdot \frac{e^{-b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left({z}^{y} \cdot {a}^{\left(t - 1\right)}\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{+34} \lor \neg \left(b \leq 4.9 \cdot 10^{+94}\right):\\ \;\;\;\;x \cdot \frac{e^{-b}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{z}^{y} \cdot {a}^{\left(t - 1\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -6.8e+34) (not (<= b 4.9e+94)))
   (* x (/ (exp (- b)) y))
   (* x (/ (* (pow z y) (pow a (- t 1.0))) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -6.8e+34) || !(b <= 4.9e+94)) {
		tmp = x * (exp(-b) / y);
	} else {
		tmp = x * ((pow(z, y) * pow(a, (t - 1.0))) / y);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-6.8d+34)) .or. (.not. (b <= 4.9d+94))) then
        tmp = x * (exp(-b) / y)
    else
        tmp = x * (((z ** y) * (a ** (t - 1.0d0))) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -6.8e+34) || !(b <= 4.9e+94)) {
		tmp = x * (Math.exp(-b) / y);
	} else {
		tmp = x * ((Math.pow(z, y) * Math.pow(a, (t - 1.0))) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -6.8e+34) or not (b <= 4.9e+94):
		tmp = x * (math.exp(-b) / y)
	else:
		tmp = x * ((math.pow(z, y) * math.pow(a, (t - 1.0))) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -6.8e+34) || !(b <= 4.9e+94))
		tmp = Float64(x * Float64(exp(Float64(-b)) / y));
	else
		tmp = Float64(x * Float64(Float64((z ^ y) * (a ^ Float64(t - 1.0))) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -6.8e+34) || ~((b <= 4.9e+94)))
		tmp = x * (exp(-b) / y);
	else
		tmp = x * (((z ^ y) * (a ^ (t - 1.0))) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -6.8e+34], N[Not[LessEqual[b, 4.9e+94]], $MachinePrecision]], N[(x * N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(N[Power[z, y], $MachinePrecision] * N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -6.7999999999999999e34 or 4.8999999999999999e94 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 86.1

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

   5. Applied rewrites 86.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 86.1

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

   7. Applied rewrites 86.1%

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

   if -6.7999999999999999e34 < b < 4.8999999999999999e94

   1. Initial program 98.0%

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

   3. Taylor expanded in 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. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. exp-sum N/A

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

      5. *-commutative N/A

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

      6. pow-to-exp N/A

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

      7. pow-to-exp N/A

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

      8. lower-*.f64 N/A

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

      9. lower-pow.f64 N/A

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

      10. lower-pow.f64 N/A

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

      11. lift--.f64 80.3

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

   5. Applied rewrites 80.3%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{+34} \lor \neg \left(b \leq 4.9 \cdot 10^{+94}\right):\\ \;\;\;\;x \cdot \frac{e^{-b}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{z}^{y} \cdot {a}^{\left(t - 1\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.00095:\\ \;\;\;\;\frac{x \cdot {\left(e^{b} \cdot a\right)}^{-1}}{y}\\ \mathbf{elif}\;b \leq -1.12 \cdot 10^{-128}:\\ \;\;\;\;x \cdot \frac{\frac{{a}^{\left(t - 1\right)}}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(0.16666666666666666, b, 0.5\right), b, 1\right), b, 1\right)}}{y}\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{+16}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{e^{-b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -0.00095)
   (/ (* x (pow (* (exp b) a) -1.0)) y)
   (if (<= b -1.12e-128)
     (*
      x
      (/
       (/
        (pow a (- t 1.0))
        (fma (fma (fma 0.16666666666666666 b 0.5) b 1.0) b 1.0))
       y))
     (if (<= b 4.2e+16) (/ (* x (/ (pow z y) a)) y) (* x (/ (exp (- b)) y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -0.00095) {
		tmp = (x * pow((exp(b) * a), -1.0)) / y;
	} else if (b <= -1.12e-128) {
		tmp = x * ((pow(a, (t - 1.0)) / fma(fma(fma(0.16666666666666666, b, 0.5), b, 1.0), b, 1.0)) / y);
	} else if (b <= 4.2e+16) {
		tmp = (x * (pow(z, y) / a)) / y;
	} else {
		tmp = x * (exp(-b) / y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -0.00095)
		tmp = Float64(Float64(x * (Float64(exp(b) * a) ^ -1.0)) / y);
	elseif (b <= -1.12e-128)
		tmp = Float64(x * Float64(Float64((a ^ Float64(t - 1.0)) / fma(fma(fma(0.16666666666666666, b, 0.5), b, 1.0), b, 1.0)) / y));
	elseif (b <= 4.2e+16)
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	else
		tmp = Float64(x * Float64(exp(Float64(-b)) / y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -0.00095], N[(N[(x * N[Power[N[(N[Exp[b], $MachinePrecision] * a), $MachinePrecision], -1.0], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, -1.12e-128], N[(x * N[(N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] / N[(N[(N[(0.16666666666666666 * b + 0.5), $MachinePrecision] * b + 1.0), $MachinePrecision] * b + 1.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.2e+16], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x * N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -9.49999999999999998e-4

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. div-exp N/A

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

      2. pow-to-exp N/A

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

      3. lower-/.f64 N/A

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

      4. lower-pow.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lower-exp.f64 56.4

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

   5. Applied rewrites 56.4%

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

   6. Taylor expanded in t around 0

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

      1. inv-pow N/A

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

      2. lower-pow.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift-exp.f64 76.9

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

   8. Applied rewrites 76.9%

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

   if -9.49999999999999998e-4 < b < -1.12e-128

   1. Initial program 95.3%

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

   3. Taylor expanded in y around 0

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

      1. div-exp N/A

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

      2. pow-to-exp N/A

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

      3. lower-/.f64 N/A

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

      4. lower-pow.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lower-exp.f64 78.3

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

   5. Applied rewrites 78.3%

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

   6. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 78.3

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

   8. Applied rewrites 78.3%

      \[\leadsto \frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(0.16666666666666666, b, 0.5\right), b, 1\right), \color{blue}{b}, 1\right)}}{y} \]
   9. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{6}, b, \frac{1}{2}\right), b, 1\right), b, 1\right)}}{y}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{x \cdot \frac{{a}^{\left(t - 1\right)}}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{6}, b, \frac{1}{2}\right), b, 1\right), b, 1\right)}}}{y} \]

      3. associate-/l* N/A

         \[\leadsto \color{blue}{x \cdot \frac{\frac{{a}^{\left(t - 1\right)}}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{6}, b, \frac{1}{2}\right), b, 1\right), b, 1\right)}}{y}} \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \frac{\frac{{a}^{\left(t - 1\right)}}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{6}, b, \frac{1}{2}\right), b, 1\right), b, 1\right)}}{y}} \]

      5. lower-/.f64 85.8

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

   10. Applied rewrites 85.8%

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

   if -1.12e-128 < b < 4.2e16

   1. Initial program 98.2%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. *-commutative N/A

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

      3. pow-to-exp N/A

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

      4. pow-to-exp N/A

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

      5. lower-*.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 84.4

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

   5. Applied rewrites 84.4%

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

   6. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lift-pow.f64 77.0

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

   8. Applied rewrites 77.0%

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

   if 4.2e16 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 87.9

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

   5. Applied rewrites 87.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 87.9

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

   7. Applied rewrites 87.9%

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

Alternative 6: 75.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.00095:\\ \;\;\;\;\frac{x \cdot e^{\left(-\log a\right) - b}}{y}\\ \mathbf{elif}\;b \leq -1.12 \cdot 10^{-128}:\\ \;\;\;\;x \cdot \frac{\frac{{a}^{\left(t - 1\right)}}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(0.16666666666666666, b, 0.5\right), b, 1\right), b, 1\right)}}{y}\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{+16}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{e^{-b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -0.00095)
   (/ (* x (exp (- (- (log a)) b))) y)
   (if (<= b -1.12e-128)
     (*
      x
      (/
       (/
        (pow a (- t 1.0))
        (fma (fma (fma 0.16666666666666666 b 0.5) b 1.0) b 1.0))
       y))
     (if (<= b 4.2e+16) (/ (* x (/ (pow z y) a)) y) (* x (/ (exp (- b)) y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -0.00095) {
		tmp = (x * exp((-log(a) - b))) / y;
	} else if (b <= -1.12e-128) {
		tmp = x * ((pow(a, (t - 1.0)) / fma(fma(fma(0.16666666666666666, b, 0.5), b, 1.0), b, 1.0)) / y);
	} else if (b <= 4.2e+16) {
		tmp = (x * (pow(z, y) / a)) / y;
	} else {
		tmp = x * (exp(-b) / y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -0.00095)
		tmp = Float64(Float64(x * exp(Float64(Float64(-log(a)) - b))) / y);
	elseif (b <= -1.12e-128)
		tmp = Float64(x * Float64(Float64((a ^ Float64(t - 1.0)) / fma(fma(fma(0.16666666666666666, b, 0.5), b, 1.0), b, 1.0)) / y));
	elseif (b <= 4.2e+16)
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	else
		tmp = Float64(x * Float64(exp(Float64(-b)) / y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -0.00095], N[(N[(x * N[Exp[N[((-N[Log[a], $MachinePrecision]) - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, -1.12e-128], N[(x * N[(N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] / N[(N[(N[(0.16666666666666666 * b + 0.5), $MachinePrecision] * b + 1.0), $MachinePrecision] * b + 1.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.2e+16], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x * N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -9.49999999999999998e-4

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. lower-*.f64 N/A

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

      2. lift-log.f64 N/A

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

      3. lift--.f64 90.6

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

   5. Applied rewrites 90.6%

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

   6. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. lift-log.f64 76.8

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

   8. Applied rewrites 76.8%

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

   if -9.49999999999999998e-4 < b < -1.12e-128

   1. Initial program 95.3%

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

   3. Taylor expanded in y around 0

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

      1. div-exp N/A

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

      2. pow-to-exp N/A

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

      3. lower-/.f64 N/A

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

      4. lower-pow.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lower-exp.f64 78.3

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

   5. Applied rewrites 78.3%

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

   6. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 78.3

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

   8. Applied rewrites 78.3%

      \[\leadsto \frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(0.16666666666666666, b, 0.5\right), b, 1\right), \color{blue}{b}, 1\right)}}{y} \]
   9. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{6}, b, \frac{1}{2}\right), b, 1\right), b, 1\right)}}{y}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{x \cdot \frac{{a}^{\left(t - 1\right)}}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{6}, b, \frac{1}{2}\right), b, 1\right), b, 1\right)}}}{y} \]

      3. associate-/l* N/A

         \[\leadsto \color{blue}{x \cdot \frac{\frac{{a}^{\left(t - 1\right)}}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{6}, b, \frac{1}{2}\right), b, 1\right), b, 1\right)}}{y}} \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \frac{\frac{{a}^{\left(t - 1\right)}}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{6}, b, \frac{1}{2}\right), b, 1\right), b, 1\right)}}{y}} \]

      5. lower-/.f64 85.8

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

   10. Applied rewrites 85.8%

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

   if -1.12e-128 < b < 4.2e16

   1. Initial program 98.2%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. *-commutative N/A

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

      3. pow-to-exp N/A

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

      4. pow-to-exp N/A

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

      5. lower-*.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 84.4

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

   5. Applied rewrites 84.4%

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

   6. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lift-pow.f64 77.0

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

   8. Applied rewrites 77.0%

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

   if 4.2e16 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 87.9

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

   5. Applied rewrites 87.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 87.9

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

   7. Applied rewrites 87.9%

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

Alternative 7: 75.6% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{e^{-b}}{y}\\ \mathbf{if}\;b \leq -1.95:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.12 \cdot 10^{-128}:\\ \;\;\;\;x \cdot \frac{\frac{{a}^{\left(t - 1\right)}}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(0.16666666666666666, b, 0.5\right), b, 1\right), b, 1\right)}}{y}\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{+16}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (exp (- b)) y))))
   (if (<= b -1.95)
     t_1
     (if (<= b -1.12e-128)
       (*
        x
        (/
         (/
          (pow a (- t 1.0))
          (fma (fma (fma 0.16666666666666666 b 0.5) b 1.0) b 1.0))
         y))
       (if (<= b 4.2e+16) (/ (* x (/ (pow z y) a)) y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (exp(-b) / y);
	double tmp;
	if (b <= -1.95) {
		tmp = t_1;
	} else if (b <= -1.12e-128) {
		tmp = x * ((pow(a, (t - 1.0)) / fma(fma(fma(0.16666666666666666, b, 0.5), b, 1.0), b, 1.0)) / y);
	} else if (b <= 4.2e+16) {
		tmp = (x * (pow(z, y) / a)) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(exp(Float64(-b)) / y))
	tmp = 0.0
	if (b <= -1.95)
		tmp = t_1;
	elseif (b <= -1.12e-128)
		tmp = Float64(x * Float64(Float64((a ^ Float64(t - 1.0)) / fma(fma(fma(0.16666666666666666, b, 0.5), b, 1.0), b, 1.0)) / y));
	elseif (b <= 4.2e+16)
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.95], t$95$1, If[LessEqual[b, -1.12e-128], N[(x * N[(N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] / N[(N[(N[(0.16666666666666666 * b + 0.5), $MachinePrecision] * b + 1.0), $MachinePrecision] * b + 1.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.2e+16], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.94999999999999996 or 4.2e16 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 82.0

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

   5. Applied rewrites 82.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 82.0

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

   7. Applied rewrites 82.0%

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

   if -1.94999999999999996 < b < -1.12e-128

   1. Initial program 95.1%

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

   3. Taylor expanded in y around 0

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

      1. div-exp N/A

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

      2. pow-to-exp N/A

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

      3. lower-/.f64 N/A

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

      4. lower-pow.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lower-exp.f64 79.2

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

   5. Applied rewrites 79.2%

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

   6. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 78.7

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

   8. Applied rewrites 78.7%

      \[\leadsto \frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(0.16666666666666666, b, 0.5\right), b, 1\right), \color{blue}{b}, 1\right)}}{y} \]
   9. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{6}, b, \frac{1}{2}\right), b, 1\right), b, 1\right)}}{y}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{x \cdot \frac{{a}^{\left(t - 1\right)}}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{6}, b, \frac{1}{2}\right), b, 1\right), b, 1\right)}}}{y} \]

      3. associate-/l* N/A

         \[\leadsto \color{blue}{x \cdot \frac{\frac{{a}^{\left(t - 1\right)}}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{6}, b, \frac{1}{2}\right), b, 1\right), b, 1\right)}}{y}} \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \frac{\frac{{a}^{\left(t - 1\right)}}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{6}, b, \frac{1}{2}\right), b, 1\right), b, 1\right)}}{y}} \]

      5. lower-/.f64 82.3

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

   10. Applied rewrites 82.3%

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

   if -1.12e-128 < b < 4.2e16

   1. Initial program 98.2%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. *-commutative N/A

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

      3. pow-to-exp N/A

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

      4. pow-to-exp N/A

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

      5. lower-*.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 84.4

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

   5. Applied rewrites 84.4%

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

   6. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lift-pow.f64 77.0

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

   8. Applied rewrites 77.0%

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

Alternative 8: 75.5% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{e^{-b}}{y}\\ \mathbf{if}\;b \leq -2.1 \cdot 10^{+32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.12 \cdot 10^{-128}:\\ \;\;\;\;x \cdot \frac{\frac{{a}^{\left(t - 1\right)}}{\mathsf{fma}\left(\mathsf{fma}\left(0.5, b, 1\right), b, 1\right)}}{y}\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{+16}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (exp (- b)) y))))
   (if (<= b -2.1e+32)
     t_1
     (if (<= b -1.12e-128)
       (* x (/ (/ (pow a (- t 1.0)) (fma (fma 0.5 b 1.0) b 1.0)) y))
       (if (<= b 4.2e+16) (/ (* x (/ (pow z y) a)) y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (exp(-b) / y);
	double tmp;
	if (b <= -2.1e+32) {
		tmp = t_1;
	} else if (b <= -1.12e-128) {
		tmp = x * ((pow(a, (t - 1.0)) / fma(fma(0.5, b, 1.0), b, 1.0)) / y);
	} else if (b <= 4.2e+16) {
		tmp = (x * (pow(z, y) / a)) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(exp(Float64(-b)) / y))
	tmp = 0.0
	if (b <= -2.1e+32)
		tmp = t_1;
	elseif (b <= -1.12e-128)
		tmp = Float64(x * Float64(Float64((a ^ Float64(t - 1.0)) / fma(fma(0.5, b, 1.0), b, 1.0)) / y));
	elseif (b <= 4.2e+16)
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.1e+32], t$95$1, If[LessEqual[b, -1.12e-128], N[(x * N[(N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] / N[(N[(0.5 * b + 1.0), $MachinePrecision] * b + 1.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.2e+16], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.1000000000000001e32 or 4.2e16 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 83.4

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

   5. Applied rewrites 83.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 83.4

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

   7. Applied rewrites 83.4%

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

   if -2.1000000000000001e32 < b < -1.12e-128

   1. Initial program 96.2%

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

   3. Taylor expanded in y around 0

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

      1. div-exp N/A

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

      2. pow-to-exp N/A

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

      3. lower-/.f64 N/A

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

      4. lower-pow.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lower-exp.f64 74.1

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

   5. Applied rewrites 74.1%

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

   6. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 73.3

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

   8. Applied rewrites 73.3%

      \[\leadsto \frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{\mathsf{fma}\left(\mathsf{fma}\left(0.5, b, 1\right), \color{blue}{b}, 1\right)}}{y} \]
   9. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 76.1

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

   10. Applied rewrites 76.1%

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

   if -1.12e-128 < b < 4.2e16

   1. Initial program 98.2%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. *-commutative N/A

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

      3. pow-to-exp N/A

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

      4. pow-to-exp N/A

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

      5. lower-*.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 84.4

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

   5. Applied rewrites 84.4%

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

   6. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lift-pow.f64 77.0

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

   8. Applied rewrites 77.0%

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

Alternative 9: 74.7% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.6 \cdot 10^{+90} \lor \neg \left(b \leq 4.2 \cdot 10^{+16}\right):\\ \;\;\;\;x \cdot \frac{e^{-b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -4.6e+90) (not (<= b 4.2e+16)))
   (* x (/ (exp (- b)) y))
   (/ (* x (/ (pow z y) a)) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -4.6e+90) || !(b <= 4.2e+16)) {
		tmp = x * (exp(-b) / y);
	} else {
		tmp = (x * (pow(z, y) / 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 <= (-4.6d+90)) .or. (.not. (b <= 4.2d+16))) then
        tmp = x * (exp(-b) / y)
    else
        tmp = (x * ((z ** y) / 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 <= -4.6e+90) || !(b <= 4.2e+16)) {
		tmp = x * (Math.exp(-b) / y);
	} else {
		tmp = (x * (Math.pow(z, y) / a)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -4.6e+90) or not (b <= 4.2e+16):
		tmp = x * (math.exp(-b) / y)
	else:
		tmp = (x * (math.pow(z, y) / a)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -4.6e+90) || !(b <= 4.2e+16))
		tmp = Float64(x * Float64(exp(Float64(-b)) / y));
	else
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -4.6e+90) || ~((b <= 4.2e+16)))
		tmp = x * (exp(-b) / y);
	else
		tmp = (x * ((z ^ y) / a)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -4.6e+90], N[Not[LessEqual[b, 4.2e+16]], $MachinePrecision]], N[(x * N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.6e90 or 4.2e16 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 85.9

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

   5. Applied rewrites 85.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 85.9

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

   7. Applied rewrites 85.9%

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

   if -4.6e90 < b < 4.2e16

   1. Initial program 97.9%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. *-commutative N/A

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

      3. pow-to-exp N/A

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

      4. pow-to-exp N/A

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

      5. lower-*.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 80.8

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

   5. Applied rewrites 80.8%

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

   6. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lift-pow.f64 72.8

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

   8. Applied rewrites 72.8%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.6 \cdot 10^{+90} \lor \neg \left(b \leq 4.2 \cdot 10^{+16}\right):\\ \;\;\;\;x \cdot \frac{e^{-b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 74.7% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.6 \cdot 10^{+90} \lor \neg \left(b \leq 4.2 \cdot 10^{+16}\right):\\ \;\;\;\;x \cdot \frac{e^{-b}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -4.6e+90) (not (<= b 4.2e+16)))
   (* x (/ (exp (- b)) y))
   (* x (/ (/ (pow z y) a) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -4.6e+90) || !(b <= 4.2e+16)) {
		tmp = x * (exp(-b) / y);
	} else {
		tmp = x * ((pow(z, y) / 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 <= (-4.6d+90)) .or. (.not. (b <= 4.2d+16))) then
        tmp = x * (exp(-b) / y)
    else
        tmp = x * (((z ** y) / 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 <= -4.6e+90) || !(b <= 4.2e+16)) {
		tmp = x * (Math.exp(-b) / y);
	} else {
		tmp = x * ((Math.pow(z, y) / a) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -4.6e+90) or not (b <= 4.2e+16):
		tmp = x * (math.exp(-b) / y)
	else:
		tmp = x * ((math.pow(z, y) / a) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -4.6e+90) || !(b <= 4.2e+16))
		tmp = Float64(x * Float64(exp(Float64(-b)) / y));
	else
		tmp = Float64(x * Float64(Float64((z ^ y) / a) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -4.6e+90) || ~((b <= 4.2e+16)))
		tmp = x * (exp(-b) / y);
	else
		tmp = x * (((z ^ y) / a) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -4.6e+90], N[Not[LessEqual[b, 4.2e+16]], $MachinePrecision]], N[(x * N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.6e90 or 4.2e16 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 85.9

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

   5. Applied rewrites 85.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 85.9

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

   7. Applied rewrites 85.9%

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

   if -4.6e90 < b < 4.2e16

   1. Initial program 97.9%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. *-commutative N/A

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

      3. pow-to-exp N/A

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

      4. pow-to-exp N/A

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

      5. lower-*.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 80.8

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

   5. Applied rewrites 80.8%

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

   6. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lift-pow.f64 72.8

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

   8. Applied rewrites 72.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 70.9

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

   10. Applied rewrites 70.9%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.6 \cdot 10^{+90} \lor \neg \left(b \leq 4.2 \cdot 10^{+16}\right):\\ \;\;\;\;x \cdot \frac{e^{-b}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 75.5% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.62 \cdot 10^{+31} \lor \neg \left(b \leq 4.5 \cdot 10^{+16}\right):\\ \;\;\;\;x \cdot \frac{e^{-b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t - 1\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.62e+31) (not (<= b 4.5e+16)))
   (* x (/ (exp (- b)) y))
   (/ (* x (pow a (- t 1.0))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.62e+31) || !(b <= 4.5e+16)) {
		tmp = x * (exp(-b) / y);
	} else {
		tmp = (x * pow(a, (t - 1.0))) / y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1.62d+31)) .or. (.not. (b <= 4.5d+16))) then
        tmp = x * (exp(-b) / y)
    else
        tmp = (x * (a ** (t - 1.0d0))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.62e+31) || !(b <= 4.5e+16)) {
		tmp = x * (Math.exp(-b) / y);
	} else {
		tmp = (x * Math.pow(a, (t - 1.0))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.62e+31) or not (b <= 4.5e+16):
		tmp = x * (math.exp(-b) / y)
	else:
		tmp = (x * math.pow(a, (t - 1.0))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.62e+31) || !(b <= 4.5e+16))
		tmp = Float64(x * Float64(exp(Float64(-b)) / y));
	else
		tmp = Float64(Float64(x * (a ^ Float64(t - 1.0))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.62e+31) || ~((b <= 4.5e+16)))
		tmp = x * (exp(-b) / y);
	else
		tmp = (x * (a ^ (t - 1.0))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.62e+31], N[Not[LessEqual[b, 4.5e+16]], $MachinePrecision]], N[(x * N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.6199999999999999e31 or 4.5e16 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 83.4

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

   5. Applied rewrites 83.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 83.4

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

   7. Applied rewrites 83.4%

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

   if -1.6199999999999999e31 < b < 4.5e16

   1. Initial program 97.8%

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

   3. Taylor expanded in y around 0

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

      1. div-exp N/A

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

      2. pow-to-exp N/A

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

      3. lower-/.f64 N/A

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

      4. lower-pow.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lower-exp.f64 68.6

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

   5. Applied rewrites 68.6%

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

   6. Taylor expanded in b around 0

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

      1. pow-to-exp N/A

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

      2. lift-pow.f64 N/A

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

      3. lift--.f64 68.6

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

   8. Applied rewrites 68.6%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.62 \cdot 10^{+31} \lor \neg \left(b \leq 4.5 \cdot 10^{+16}\right):\\ \;\;\;\;x \cdot \frac{e^{-b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t - 1\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 59.1% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.95 \lor \neg \left(b \leq 2.7 \cdot 10^{+16}\right):\\ \;\;\;\;x \cdot \frac{e^{-b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.95) (not (<= b 2.7e+16)))
   (* x (/ (exp (- b)) y))
   (/ (* x (/ 1.0 a)) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.95) || !(b <= 2.7e+16)) {
		tmp = x * (exp(-b) / y);
	} else {
		tmp = (x * (1.0 / a)) / y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1.95d0)) .or. (.not. (b <= 2.7d+16))) then
        tmp = x * (exp(-b) / y)
    else
        tmp = (x * (1.0d0 / a)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.95) || !(b <= 2.7e+16)) {
		tmp = x * (Math.exp(-b) / y);
	} else {
		tmp = (x * (1.0 / a)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.95) or not (b <= 2.7e+16):
		tmp = x * (math.exp(-b) / y)
	else:
		tmp = (x * (1.0 / a)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.95) || !(b <= 2.7e+16))
		tmp = Float64(x * Float64(exp(Float64(-b)) / y));
	else
		tmp = Float64(Float64(x * Float64(1.0 / a)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.95) || ~((b <= 2.7e+16)))
		tmp = x * (exp(-b) / y);
	else
		tmp = (x * (1.0 / a)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.95], N[Not[LessEqual[b, 2.7e+16]], $MachinePrecision]], N[(x * N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(1.0 / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.94999999999999996 or 2.7e16 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 82.0

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

   5. Applied rewrites 82.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 82.0

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

   7. Applied rewrites 82.0%

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

   if -1.94999999999999996 < b < 2.7e16

   1. Initial program 97.6%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. *-commutative N/A

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

      3. pow-to-exp N/A

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

      4. pow-to-exp N/A

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

      5. lower-*.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 83.0

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

   5. Applied rewrites 83.0%

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

   6. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lift-pow.f64 73.3

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

   8. Applied rewrites 73.3%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 40.6%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.95 \lor \neg \left(b \leq 2.7 \cdot 10^{+16}\right):\\ \;\;\;\;x \cdot \frac{e^{-b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 31.6% accurate, 9.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 1.5 \cdot 10^{+213}:\\ \;\;\;\;\frac{x \cdot \frac{1}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{1}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 1.5e+213) (/ (* x (/ 1.0 a)) y) (* x (/ (/ 1.0 a) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 1.5e+213) {
		tmp = (x * (1.0 / a)) / y;
	} else {
		tmp = x * ((1.0 / a) / y);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= 1.5d+213) then
        tmp = (x * (1.0d0 / a)) / y
    else
        tmp = x * ((1.0d0 / a) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 1.5e+213) {
		tmp = (x * (1.0 / a)) / y;
	} else {
		tmp = x * ((1.0 / a) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 1.5e+213:
		tmp = (x * (1.0 / a)) / y
	else:
		tmp = x * ((1.0 / a) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 1.5e+213)
		tmp = Float64(Float64(x * Float64(1.0 / a)) / y);
	else
		tmp = Float64(x * Float64(Float64(1.0 / a) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 1.5e+213)
		tmp = (x * (1.0 / a)) / y;
	else
		tmp = x * ((1.0 / a) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 1.5e+213], N[(N[(x * N[(1.0 / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x * N[(N[(1.0 / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 1.5000000000000001e213

   1. Initial program 99.4%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. *-commutative N/A

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

      3. pow-to-exp N/A

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

      4. pow-to-exp N/A

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

      5. lower-*.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 67.8

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

   5. Applied rewrites 67.8%

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

   6. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lift-pow.f64 58.7

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

   8. Applied rewrites 58.7%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 30.8%

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

   if 1.5000000000000001e213 < a

   1. Initial program 95.6%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. *-commutative N/A

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

      3. pow-to-exp N/A

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

      4. pow-to-exp N/A

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

      5. lower-*.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 66.0

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

   5. Applied rewrites 66.0%

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

   6. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lift-pow.f64 59.6

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

   8. Applied rewrites 59.6%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 35.0%

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

       1. lift-/.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. associate-/l* N/A

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

       4. lower-*.f64 N/A

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

       5. lower-/.f64 46.3

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

   13. Applied rewrites 46.3%

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

Alternative 14: 30.3% accurate, 12.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.7%

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

3. Taylor expanded in b around 0

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

   1. exp-sum N/A

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

   2. *-commutative N/A

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

   3. pow-to-exp N/A

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

   4. pow-to-exp N/A

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

   5. lower-*.f64 N/A

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

   6. lower-pow.f64 N/A

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

   7. lower-pow.f64 N/A

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

   8. lift--.f64 67.5

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

5. Applied rewrites 67.5%

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

6. Taylor expanded in t around 0

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

   1. lower-/.f64 N/A

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

   2. lift-pow.f64 58.9

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

8. Applied rewrites 58.9%

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

9. Taylor expanded in y around 0

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

11. Applied rewrites 31.5%

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

    1. lift-/.f64 N/A

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

    2. lift-*.f64 N/A

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

    3. associate-/l* N/A

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

    4. lower-*.f64 N/A

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

    5. lower-/.f64 30.4

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

13. Applied rewrites 30.4%

    \[\leadsto \color{blue}{x \cdot \frac{\frac{1}{a}}{y}} \]
14. Add Preprocessing

Developer Target 1: 71.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := {a}^{\left(t - 1\right)}\\ t_2 := \frac{x \cdot \frac{t\_1}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \mathbf{if}\;t < -0.8845848504127471:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 852031.2288374073:\\ \;\;\;\;\frac{\frac{x}{y} \cdot t\_1}{e^{b - \log z \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (pow a (- t 1.0)))
        (t_2 (/ (* x (/ t_1 y)) (- (+ b 1.0) (* y (log z))))))
   (if (< t -0.8845848504127471)
     t_2
     (if (< t 852031.2288374073)
       (/ (* (/ x y) t_1) (exp (- b (* (log z) y))))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = pow(a, (t - 1.0));
	double t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * log(z)));
	double tmp;
	if (t < -0.8845848504127471) {
		tmp = t_2;
	} else if (t < 852031.2288374073) {
		tmp = ((x / y) * t_1) / exp((b - (log(z) * y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

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 2025064 
(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))