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

Percentage Accurate: 98.3% → 98.3%

Time: 6.2s

Alternatives: 15

Speedup: 1.0×

• 46.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.3%

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

Alternative 2: 93.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}\\ \mathbf{if}\;t \leq -3400:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 85:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} \cdot e^{\log z \cdot y - b}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (exp (- (* (log a) (- t 1.0)) b))) y)))
   (if (<= t -3400.0)
     t_1
     (if (<= t 85.0)
       (/ (* x (* (/ 1.0 a) (exp (- (* (log z) y) b)))) y)
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * exp(((log(a) * (t - 1.0)) - b))) / y;
	double tmp;
	if (t <= -3400.0) {
		tmp = t_1;
	} else if (t <= 85.0) {
		tmp = (x * ((1.0 / a) * exp(((log(z) * y) - b)))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * exp(((log(a) * (t - 1.0d0)) - b))) / y
    if (t <= (-3400.0d0)) then
        tmp = t_1
    else if (t <= 85.0d0) then
        tmp = (x * ((1.0d0 / a) * exp(((log(z) * y) - b)))) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * Math.exp(((Math.log(a) * (t - 1.0)) - b))) / y;
	double tmp;
	if (t <= -3400.0) {
		tmp = t_1;
	} else if (t <= 85.0) {
		tmp = (x * ((1.0 / a) * Math.exp(((Math.log(z) * y) - b)))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * math.exp(((math.log(a) * (t - 1.0)) - b))) / y
	tmp = 0
	if t <= -3400.0:
		tmp = t_1
	elif t <= 85.0:
		tmp = (x * ((1.0 / a) * math.exp(((math.log(z) * y) - b)))) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * exp(Float64(Float64(log(a) * Float64(t - 1.0)) - b))) / y)
	tmp = 0.0
	if (t <= -3400.0)
		tmp = t_1;
	elseif (t <= 85.0)
		tmp = Float64(Float64(x * Float64(Float64(1.0 / a) * exp(Float64(Float64(log(z) * y) - b)))) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * exp(((log(a) * (t - 1.0)) - b))) / y;
	tmp = 0.0;
	if (t <= -3400.0)
		tmp = t_1;
	elseif (t <= 85.0)
		tmp = (x * ((1.0 / a) * exp(((log(z) * y) - b)))) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[Exp[N[(N[(N[Log[a], $MachinePrecision] * N[(t - 1.0), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t, -3400.0], t$95$1, If[LessEqual[t, 85.0], N[(N[(x * N[(N[(1.0 / a), $MachinePrecision] * N[Exp[N[(N[(N[Log[z], $MachinePrecision] * y), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -3400 or 85 < t

   1. Initial program 98.3%

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

   2. Taylor expanded in y around 0

      \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot \left(t - 1\right)} - b}}{y} \]
   3. 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 80.1

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

   4. Applied rewrites 80.1%

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

   if -3400 < t < 85

   1. Initial program 98.3%

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

   2. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

      2. exp-sum N/A

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

      3. *-commutative N/A

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

      4. pow-to-exp N/A

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

      5. inv-pow N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower-exp.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift-log.f64 80.8

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

   4. Applied rewrites 80.8%

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

Alternative 3: 93.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}\\ \mathbf{if}\;t \leq -3400:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-20}:\\ \;\;\;\;x \cdot \frac{\frac{1}{a} \cdot e^{\log z \cdot y - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (exp (- (* (log a) (- t 1.0)) b))) y)))
   (if (<= t -3400.0)
     t_1
     (if (<= t 6.8e-20)
       (* x (/ (* (/ 1.0 a) (exp (- (* (log z) y) b))) y))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * exp(((log(a) * (t - 1.0)) - b))) / y;
	double tmp;
	if (t <= -3400.0) {
		tmp = t_1;
	} else if (t <= 6.8e-20) {
		tmp = x * (((1.0 / a) * exp(((log(z) * y) - b))) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * exp(((log(a) * (t - 1.0d0)) - b))) / y
    if (t <= (-3400.0d0)) then
        tmp = t_1
    else if (t <= 6.8d-20) then
        tmp = x * (((1.0d0 / a) * exp(((log(z) * y) - b))) / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * Math.exp(((Math.log(a) * (t - 1.0)) - b))) / y;
	double tmp;
	if (t <= -3400.0) {
		tmp = t_1;
	} else if (t <= 6.8e-20) {
		tmp = x * (((1.0 / a) * Math.exp(((Math.log(z) * y) - b))) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * math.exp(((math.log(a) * (t - 1.0)) - b))) / y
	tmp = 0
	if t <= -3400.0:
		tmp = t_1
	elif t <= 6.8e-20:
		tmp = x * (((1.0 / a) * math.exp(((math.log(z) * y) - b))) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * exp(Float64(Float64(log(a) * Float64(t - 1.0)) - b))) / y)
	tmp = 0.0
	if (t <= -3400.0)
		tmp = t_1;
	elseif (t <= 6.8e-20)
		tmp = Float64(x * Float64(Float64(Float64(1.0 / a) * exp(Float64(Float64(log(z) * y) - b))) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * exp(((log(a) * (t - 1.0)) - b))) / y;
	tmp = 0.0;
	if (t <= -3400.0)
		tmp = t_1;
	elseif (t <= 6.8e-20)
		tmp = x * (((1.0 / a) * exp(((log(z) * y) - b))) / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[Exp[N[(N[(N[Log[a], $MachinePrecision] * N[(t - 1.0), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t, -3400.0], t$95$1, If[LessEqual[t, 6.8e-20], N[(x * N[(N[(N[(1.0 / a), $MachinePrecision] * N[Exp[N[(N[(N[Log[z], $MachinePrecision] * y), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -3400 or 6.7999999999999994e-20 < t

   1. Initial program 98.3%

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

   2. Taylor expanded in y around 0

      \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot \left(t - 1\right)} - b}}{y} \]
   3. 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 80.1

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

   4. Applied rewrites 80.1%

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

   if -3400 < t < 6.7999999999999994e-20

   1. Initial program 98.3%

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

   2. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

   4. Applied rewrites 80.7%

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

Alternative 4: 88.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{if}\;y \leq -2.1 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+162}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (/ (pow z y) a)) y)))
   (if (<= y -2.1e+40)
     t_1
     (if (<= y 2.8e+162) (/ (* x (exp (- (* (log a) (- t 1.0)) b))) y) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * (pow(z, y) / a)) / y;
	double tmp;
	if (y <= -2.1e+40) {
		tmp = t_1;
	} else if (y <= 2.8e+162) {
		tmp = (x * exp(((log(a) * (t - 1.0)) - b))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * ((z ** y) / a)) / y
    if (y <= (-2.1d+40)) then
        tmp = t_1
    else if (y <= 2.8d+162) then
        tmp = (x * exp(((log(a) * (t - 1.0d0)) - b))) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * (Math.pow(z, y) / a)) / y;
	double tmp;
	if (y <= -2.1e+40) {
		tmp = t_1;
	} else if (y <= 2.8e+162) {
		tmp = (x * Math.exp(((Math.log(a) * (t - 1.0)) - b))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * (math.pow(z, y) / a)) / y
	tmp = 0
	if y <= -2.1e+40:
		tmp = t_1
	elif y <= 2.8e+162:
		tmp = (x * math.exp(((math.log(a) * (t - 1.0)) - b))) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * Float64((z ^ y) / a)) / y)
	tmp = 0.0
	if (y <= -2.1e+40)
		tmp = t_1;
	elseif (y <= 2.8e+162)
		tmp = Float64(Float64(x * exp(Float64(Float64(log(a) * Float64(t - 1.0)) - b))) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * ((z ^ y) / a)) / y;
	tmp = 0.0;
	if (y <= -2.1e+40)
		tmp = t_1;
	elseif (y <= 2.8e+162)
		tmp = (x * exp(((log(a) * (t - 1.0)) - b))) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -2.1e+40], t$95$1, If[LessEqual[y, 2.8e+162], N[(N[(x * N[Exp[N[(N[(N[Log[a], $MachinePrecision] * N[(t - 1.0), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.1000000000000001e40 or 2.79999999999999991e162 < y

   1. Initial program 98.3%

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

   2. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

      2. exp-sum N/A

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

      3. *-commutative N/A

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

      4. pow-to-exp N/A

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

      5. inv-pow N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower-exp.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift-log.f64 80.8

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

   4. Applied rewrites 80.8%

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

   5. Taylor expanded in b around 0

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

      1. lower-/.f64 N/A

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

      2. lower-pow.f64 60.3

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

   7. Applied rewrites 60.3%

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

   if -2.1000000000000001e40 < y < 2.79999999999999991e162

   1. Initial program 98.3%

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

   2. Taylor expanded in y around 0

      \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot \left(t - 1\right)} - b}}{y} \]
   3. 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 80.1

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

   4. Applied rewrites 80.1%

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

Alternative 5: 76.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - 1\right) \cdot \log a\\ t_2 := \frac{x \cdot e^{\log a \cdot t}}{y}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+49}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 360:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{elif}\;t\_1 \leq 10000000000:\\ \;\;\;\;\frac{x \cdot \frac{e^{-b}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- t 1.0) (log a))) (t_2 (/ (* x (exp (* (log a) t))) y)))
   (if (<= t_1 -5e+49)
     t_2
     (if (<= t_1 360.0)
       (/ (* x (/ (pow z y) a)) y)
       (if (<= t_1 10000000000.0) (/ (* x (/ (exp (- b)) a)) y) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - 1.0) * log(a);
	double t_2 = (x * exp((log(a) * t))) / y;
	double tmp;
	if (t_1 <= -5e+49) {
		tmp = t_2;
	} else if (t_1 <= 360.0) {
		tmp = (x * (pow(z, y) / a)) / y;
	} else if (t_1 <= 10000000000.0) {
		tmp = (x * (exp(-b) / a)) / 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 = (t - 1.0d0) * log(a)
    t_2 = (x * exp((log(a) * t))) / y
    if (t_1 <= (-5d+49)) then
        tmp = t_2
    else if (t_1 <= 360.0d0) then
        tmp = (x * ((z ** y) / a)) / y
    else if (t_1 <= 10000000000.0d0) then
        tmp = (x * (exp(-b) / a)) / y
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - 1.0) * Math.log(a);
	double t_2 = (x * Math.exp((Math.log(a) * t))) / y;
	double tmp;
	if (t_1 <= -5e+49) {
		tmp = t_2;
	} else if (t_1 <= 360.0) {
		tmp = (x * (Math.pow(z, y) / a)) / y;
	} else if (t_1 <= 10000000000.0) {
		tmp = (x * (Math.exp(-b) / a)) / y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - 1.0) * math.log(a)
	t_2 = (x * math.exp((math.log(a) * t))) / y
	tmp = 0
	if t_1 <= -5e+49:
		tmp = t_2
	elif t_1 <= 360.0:
		tmp = (x * (math.pow(z, y) / a)) / y
	elif t_1 <= 10000000000.0:
		tmp = (x * (math.exp(-b) / a)) / y
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - 1.0) * log(a))
	t_2 = Float64(Float64(x * exp(Float64(log(a) * t))) / y)
	tmp = 0.0
	if (t_1 <= -5e+49)
		tmp = t_2;
	elseif (t_1 <= 360.0)
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	elseif (t_1 <= 10000000000.0)
		tmp = Float64(Float64(x * Float64(exp(Float64(-b)) / a)) / y);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - 1.0) * log(a);
	t_2 = (x * exp((log(a) * t))) / y;
	tmp = 0.0;
	if (t_1 <= -5e+49)
		tmp = t_2;
	elseif (t_1 <= 360.0)
		tmp = (x * ((z ^ y) / a)) / y;
	elseif (t_1 <= 10000000000.0)
		tmp = (x * (exp(-b) / a)) / y;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - 1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[Exp[N[(N[Log[a], $MachinePrecision] * t), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+49], t$95$2, If[LessEqual[t$95$1, 360.0], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t$95$1, 10000000000.0], N[(N[(x * N[(N[Exp[(-b)], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -5.0000000000000004e49 or 1e10 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))

   1. Initial program 98.3%

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

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-log.f64 48.2

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

   4. Applied rewrites 48.2%

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

   if -5.0000000000000004e49 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 360

   1. Initial program 98.3%

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

   2. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

      2. exp-sum N/A

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

      3. *-commutative N/A

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

      4. pow-to-exp N/A

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

      5. inv-pow N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower-exp.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift-log.f64 80.8

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

   4. Applied rewrites 80.8%

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

   5. Taylor expanded in b around 0

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

      1. lower-/.f64 N/A

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

      2. lower-pow.f64 60.3

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

   7. Applied rewrites 60.3%

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

   if 360 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 1e10

   1. Initial program 98.3%

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

   2. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

      2. exp-sum N/A

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

      3. *-commutative N/A

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

      4. pow-to-exp N/A

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

      5. inv-pow N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower-exp.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift-log.f64 80.8

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

   4. Applied rewrites 80.8%

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

   5. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lift-neg.f64 N/A

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

      3. lower-exp.f64 59.5

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

   7. Applied rewrites 59.5%

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

Alternative 6: 75.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - 1\right) \cdot \log a\\ t_2 := \frac{e^{-b}}{a}\\ t_3 := \frac{x \cdot e^{\log a \cdot t}}{y}\\ \mathbf{if}\;t\_1 \leq -695:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_1 \leq -345:\\ \;\;\;\;x \cdot \frac{t\_2}{y}\\ \mathbf{elif}\;t\_1 \leq 360:\\ \;\;\;\;\frac{{z}^{y} \cdot x}{a \cdot y}\\ \mathbf{elif}\;t\_1 \leq 10000000000:\\ \;\;\;\;\frac{x \cdot t\_2}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- t 1.0) (log a)))
        (t_2 (/ (exp (- b)) a))
        (t_3 (/ (* x (exp (* (log a) t))) y)))
   (if (<= t_1 -695.0)
     t_3
     (if (<= t_1 -345.0)
       (* x (/ t_2 y))
       (if (<= t_1 360.0)
         (/ (* (pow z y) x) (* a y))
         (if (<= t_1 10000000000.0) (/ (* x t_2) y) t_3))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - 1.0) * log(a);
	double t_2 = exp(-b) / a;
	double t_3 = (x * exp((log(a) * t))) / y;
	double tmp;
	if (t_1 <= -695.0) {
		tmp = t_3;
	} else if (t_1 <= -345.0) {
		tmp = x * (t_2 / y);
	} else if (t_1 <= 360.0) {
		tmp = (pow(z, y) * x) / (a * y);
	} else if (t_1 <= 10000000000.0) {
		tmp = (x * t_2) / y;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = (t - 1.0d0) * log(a)
    t_2 = exp(-b) / a
    t_3 = (x * exp((log(a) * t))) / y
    if (t_1 <= (-695.0d0)) then
        tmp = t_3
    else if (t_1 <= (-345.0d0)) then
        tmp = x * (t_2 / y)
    else if (t_1 <= 360.0d0) then
        tmp = ((z ** y) * x) / (a * y)
    else if (t_1 <= 10000000000.0d0) then
        tmp = (x * t_2) / y
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - 1.0) * Math.log(a);
	double t_2 = Math.exp(-b) / a;
	double t_3 = (x * Math.exp((Math.log(a) * t))) / y;
	double tmp;
	if (t_1 <= -695.0) {
		tmp = t_3;
	} else if (t_1 <= -345.0) {
		tmp = x * (t_2 / y);
	} else if (t_1 <= 360.0) {
		tmp = (Math.pow(z, y) * x) / (a * y);
	} else if (t_1 <= 10000000000.0) {
		tmp = (x * t_2) / y;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - 1.0) * math.log(a)
	t_2 = math.exp(-b) / a
	t_3 = (x * math.exp((math.log(a) * t))) / y
	tmp = 0
	if t_1 <= -695.0:
		tmp = t_3
	elif t_1 <= -345.0:
		tmp = x * (t_2 / y)
	elif t_1 <= 360.0:
		tmp = (math.pow(z, y) * x) / (a * y)
	elif t_1 <= 10000000000.0:
		tmp = (x * t_2) / y
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - 1.0) * log(a))
	t_2 = Float64(exp(Float64(-b)) / a)
	t_3 = Float64(Float64(x * exp(Float64(log(a) * t))) / y)
	tmp = 0.0
	if (t_1 <= -695.0)
		tmp = t_3;
	elseif (t_1 <= -345.0)
		tmp = Float64(x * Float64(t_2 / y));
	elseif (t_1 <= 360.0)
		tmp = Float64(Float64((z ^ y) * x) / Float64(a * y));
	elseif (t_1 <= 10000000000.0)
		tmp = Float64(Float64(x * t_2) / y);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - 1.0) * log(a);
	t_2 = exp(-b) / a;
	t_3 = (x * exp((log(a) * t))) / y;
	tmp = 0.0;
	if (t_1 <= -695.0)
		tmp = t_3;
	elseif (t_1 <= -345.0)
		tmp = x * (t_2 / y);
	elseif (t_1 <= 360.0)
		tmp = ((z ^ y) * x) / (a * y);
	elseif (t_1 <= 10000000000.0)
		tmp = (x * t_2) / y;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - 1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[Exp[(-b)], $MachinePrecision] / a), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * N[Exp[N[(N[Log[a], $MachinePrecision] * t), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t$95$1, -695.0], t$95$3, If[LessEqual[t$95$1, -345.0], N[(x * N[(t$95$2 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 360.0], N[(N[(N[Power[z, y], $MachinePrecision] * x), $MachinePrecision] / N[(a * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 10000000000.0], N[(N[(x * t$95$2), $MachinePrecision] / y), $MachinePrecision], t$95$3]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -695 or 1e10 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))

   1. Initial program 98.3%

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

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-log.f64 48.2

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

   4. Applied rewrites 48.2%

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

   if -695 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -345

   1. Initial program 98.3%

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

   2. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

   4. Applied rewrites 80.7%

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

   5. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lift-neg.f64 N/A

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

      3. lower-exp.f64 59.1

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

   7. Applied rewrites 59.1%

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

   if -345 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 360

   1. Initial program 98.3%

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

   2. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

   4. Applied rewrites 80.7%

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

   5. Taylor expanded in b around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-pow.f64 N/A

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

      5. lower-*.f64 54.8

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

   7. Applied rewrites 54.8%

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

   if 360 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 1e10

   1. Initial program 98.3%

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

   2. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

      2. exp-sum N/A

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

      3. *-commutative N/A

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

      4. pow-to-exp N/A

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

      5. inv-pow N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower-exp.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift-log.f64 80.8

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

   4. Applied rewrites 80.8%

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

   5. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lift-neg.f64 N/A

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

      3. lower-exp.f64 59.5

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

   7. Applied rewrites 59.5%

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

Alternative 7: 72.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - 1\right) \cdot \log a\\ t_2 := \frac{x \cdot e^{\log a \cdot t}}{y}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+49}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 360:\\ \;\;\;\;\frac{{z}^{y}}{a} \cdot \frac{x}{y}\\ \mathbf{elif}\;t\_1 \leq 10000000000:\\ \;\;\;\;\frac{x \cdot \frac{e^{-b}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- t 1.0) (log a))) (t_2 (/ (* x (exp (* (log a) t))) y)))
   (if (<= t_1 -5e+49)
     t_2
     (if (<= t_1 360.0)
       (* (/ (pow z y) a) (/ x y))
       (if (<= t_1 10000000000.0) (/ (* x (/ (exp (- b)) a)) y) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - 1.0) * log(a);
	double t_2 = (x * exp((log(a) * t))) / y;
	double tmp;
	if (t_1 <= -5e+49) {
		tmp = t_2;
	} else if (t_1 <= 360.0) {
		tmp = (pow(z, y) / a) * (x / y);
	} else if (t_1 <= 10000000000.0) {
		tmp = (x * (exp(-b) / a)) / 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 = (t - 1.0d0) * log(a)
    t_2 = (x * exp((log(a) * t))) / y
    if (t_1 <= (-5d+49)) then
        tmp = t_2
    else if (t_1 <= 360.0d0) then
        tmp = ((z ** y) / a) * (x / y)
    else if (t_1 <= 10000000000.0d0) then
        tmp = (x * (exp(-b) / a)) / y
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - 1.0) * Math.log(a);
	double t_2 = (x * Math.exp((Math.log(a) * t))) / y;
	double tmp;
	if (t_1 <= -5e+49) {
		tmp = t_2;
	} else if (t_1 <= 360.0) {
		tmp = (Math.pow(z, y) / a) * (x / y);
	} else if (t_1 <= 10000000000.0) {
		tmp = (x * (Math.exp(-b) / a)) / y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - 1.0) * math.log(a)
	t_2 = (x * math.exp((math.log(a) * t))) / y
	tmp = 0
	if t_1 <= -5e+49:
		tmp = t_2
	elif t_1 <= 360.0:
		tmp = (math.pow(z, y) / a) * (x / y)
	elif t_1 <= 10000000000.0:
		tmp = (x * (math.exp(-b) / a)) / y
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - 1.0) * log(a))
	t_2 = Float64(Float64(x * exp(Float64(log(a) * t))) / y)
	tmp = 0.0
	if (t_1 <= -5e+49)
		tmp = t_2;
	elseif (t_1 <= 360.0)
		tmp = Float64(Float64((z ^ y) / a) * Float64(x / y));
	elseif (t_1 <= 10000000000.0)
		tmp = Float64(Float64(x * Float64(exp(Float64(-b)) / a)) / y);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - 1.0) * log(a);
	t_2 = (x * exp((log(a) * t))) / y;
	tmp = 0.0;
	if (t_1 <= -5e+49)
		tmp = t_2;
	elseif (t_1 <= 360.0)
		tmp = ((z ^ y) / a) * (x / y);
	elseif (t_1 <= 10000000000.0)
		tmp = (x * (exp(-b) / a)) / y;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - 1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[Exp[N[(N[Log[a], $MachinePrecision] * t), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+49], t$95$2, If[LessEqual[t$95$1, 360.0], N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 10000000000.0], N[(N[(x * N[(N[Exp[(-b)], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -5.0000000000000004e49 or 1e10 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))

   1. Initial program 98.3%

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

   2. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-log.f64 48.2

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

   4. Applied rewrites 48.2%

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

   if -5.0000000000000004e49 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 360

   1. Initial program 98.3%

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

   2. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

   4. Applied rewrites 80.7%

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

   5. Taylor expanded in b around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-pow.f64 N/A

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

      5. lower-*.f64 54.8

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

   7. Applied rewrites 54.8%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-pow.f64 N/A

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

      5. times-frac N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lift-pow.f64 N/A

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

      9. lower-/.f64 55.2

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

   9. Applied rewrites 55.2%

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

   if 360 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 1e10

   1. Initial program 98.3%

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

   2. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

      2. exp-sum N/A

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

      3. *-commutative N/A

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

      4. pow-to-exp N/A

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

      5. inv-pow N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower-exp.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift-log.f64 80.8

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

   4. Applied rewrites 80.8%

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

   5. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lift-neg.f64 N/A

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

      3. lower-exp.f64 59.5

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

   7. Applied rewrites 59.5%

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

Alternative 8: 72.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{e^{-b}}{y}\\ \mathbf{if}\;b \leq -13500000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 780:\\ \;\;\;\;\frac{{z}^{y} \cdot x}{a \cdot y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (exp (- b)) y))))
   (if (<= b -13500000000000.0)
     t_1
     (if (<= b 780.0) (/ (* (pow z y) x) (* 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 <= -13500000000000.0) {
		tmp = t_1;
	} else if (b <= 780.0) {
		tmp = (pow(z, y) * x) / (a * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (exp(-b) / y)
    if (b <= (-13500000000000.0d0)) then
        tmp = t_1
    else if (b <= 780.0d0) then
        tmp = ((z ** y) * x) / (a * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (Math.exp(-b) / y);
	double tmp;
	if (b <= -13500000000000.0) {
		tmp = t_1;
	} else if (b <= 780.0) {
		tmp = (Math.pow(z, y) * x) / (a * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (math.exp(-b) / y)
	tmp = 0
	if b <= -13500000000000.0:
		tmp = t_1
	elif b <= 780.0:
		tmp = (math.pow(z, y) * x) / (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 <= -13500000000000.0)
		tmp = t_1;
	elseif (b <= 780.0)
		tmp = Float64(Float64((z ^ y) * x) / Float64(a * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (exp(-b) / y);
	tmp = 0.0;
	if (b <= -13500000000000.0)
		tmp = t_1;
	elseif (b <= 780.0)
		tmp = ((z ^ y) * x) / (a * y);
	else
		tmp = t_1;
	end
	tmp_2 = 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, -13500000000000.0], t$95$1, If[LessEqual[b, 780.0], N[(N[(N[Power[z, y], $MachinePrecision] * x), $MachinePrecision] / N[(a * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.35e13 or 780 < b

   1. Initial program 98.3%

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

   2. Taylor expanded in b around inf

      \[\leadsto \frac{x \cdot e^{\color{blue}{-1 \cdot b}}}{y} \]
   3. 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 47.6

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

   4. Applied rewrites 47.6%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]
   5. 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 47.6

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

   6. Applied rewrites 47.6%

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

   if -1.35e13 < b < 780

   1. Initial program 98.3%

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

   2. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

   4. Applied rewrites 80.7%

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

   5. Taylor expanded in b around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-pow.f64 N/A

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

      5. lower-*.f64 54.8

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

   7. Applied rewrites 54.8%

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

Alternative 9: 59.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(t - 1\right) \cdot \log a \leq 10^{+248}:\\ \;\;\;\;x \cdot \frac{\frac{e^{-b}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{\mathsf{fma}\left(0.5 \cdot b - 1, b, 1\right)}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* (- t 1.0) (log a)) 1e+248)
   (* x (/ (/ (exp (- b)) a) y))
   (* x (/ (/ (fma (- (* 0.5 b) 1.0) b 1.0) a) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t - 1.0) * log(a)) <= 1e+248) {
		tmp = x * ((exp(-b) / a) / y);
	} else {
		tmp = x * ((fma(((0.5 * b) - 1.0), b, 1.0) / a) / y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(t - 1.0) * log(a)) <= 1e+248)
		tmp = Float64(x * Float64(Float64(exp(Float64(-b)) / a) / y));
	else
		tmp = Float64(x * Float64(Float64(fma(Float64(Float64(0.5 * b) - 1.0), b, 1.0) / a) / y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(t - 1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision], 1e+248], N[(x * N[(N[(N[Exp[(-b)], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(N[(N[(N[(0.5 * b), $MachinePrecision] - 1.0), $MachinePrecision] * b + 1.0), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 1.00000000000000005e248

   1. Initial program 98.3%

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

   2. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

   4. Applied rewrites 80.7%

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

   5. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lift-neg.f64 N/A

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

      3. lower-exp.f64 59.1

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

   7. Applied rewrites 59.1%

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

   if 1.00000000000000005e248 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))

   1. Initial program 98.3%

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

   2. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

   4. Applied rewrites 80.7%

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

   5. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lift-neg.f64 N/A

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

      3. lower-exp.f64 59.1

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

   7. Applied rewrites 59.1%

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

   8. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 40.4

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

   10. Applied rewrites 40.4%

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

Alternative 10: 58.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{e^{-b}}{y}\\ \mathbf{if}\;b \leq -2550000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 520:\\ \;\;\;\;x \cdot \frac{\frac{1}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (exp (- b)) y))))
   (if (<= b -2550000000000.0)
     t_1
     (if (<= b 520.0) (* x (/ (/ 1.0 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 <= -2550000000000.0) {
		tmp = t_1;
	} else if (b <= 520.0) {
		tmp = x * ((1.0 / a) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (exp(-b) / y)
    if (b <= (-2550000000000.0d0)) then
        tmp = t_1
    else if (b <= 520.0d0) then
        tmp = x * ((1.0d0 / a) / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (Math.exp(-b) / y);
	double tmp;
	if (b <= -2550000000000.0) {
		tmp = t_1;
	} else if (b <= 520.0) {
		tmp = x * ((1.0 / a) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (math.exp(-b) / y)
	tmp = 0
	if b <= -2550000000000.0:
		tmp = t_1
	elif b <= 520.0:
		tmp = x * ((1.0 / 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 <= -2550000000000.0)
		tmp = t_1;
	elseif (b <= 520.0)
		tmp = Float64(x * Float64(Float64(1.0 / a) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (exp(-b) / y);
	tmp = 0.0;
	if (b <= -2550000000000.0)
		tmp = t_1;
	elseif (b <= 520.0)
		tmp = x * ((1.0 / a) / y);
	else
		tmp = t_1;
	end
	tmp_2 = 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, -2550000000000.0], t$95$1, If[LessEqual[b, 520.0], N[(x * N[(N[(1.0 / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.55e12 or 520 < b

   1. Initial program 98.3%

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

   2. Taylor expanded in b around inf

      \[\leadsto \frac{x \cdot e^{\color{blue}{-1 \cdot b}}}{y} \]
   3. 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 47.6

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

   4. Applied rewrites 47.6%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]
   5. 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 47.6

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

   6. Applied rewrites 47.6%

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

   if -2.55e12 < b < 520

   1. Initial program 98.3%

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

   2. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

   4. Applied rewrites 80.7%

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

   5. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lift-neg.f64 N/A

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

      3. lower-exp.f64 59.1

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

   7. Applied rewrites 59.1%

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

   8. Taylor expanded in b around 0

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

      1. lower-/.f64 32.1

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

   10. Applied rewrites 32.1%

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

Alternative 11: 36.7% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 6.4 \cdot 10^{-200}:\\ \;\;\;\;x \cdot \frac{\frac{\left(-b\right) + 1}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 6.4e-200) (* x (/ (/ (+ (- b) 1.0) a) y)) (/ (/ x a) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 6.4e-200) {
		tmp = x * (((-b + 1.0) / a) / y);
	} else {
		tmp = (x / 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 <= 6.4d-200) then
        tmp = x * (((-b + 1.0d0) / a) / y)
    else
        tmp = (x / a) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 6.4e-200) {
		tmp = x * (((-b + 1.0) / a) / y);
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 6.4e-200:
		tmp = x * (((-b + 1.0) / a) / y)
	else:
		tmp = (x / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 6.4e-200)
		tmp = Float64(x * Float64(Float64(Float64(Float64(-b) + 1.0) / a) / y));
	else
		tmp = Float64(Float64(x / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 6.4e-200)
		tmp = x * (((-b + 1.0) / a) / y);
	else
		tmp = (x / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 6.4e-200], N[(x * N[(N[(N[((-b) + 1.0), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 6.39999999999999965e-200

   1. Initial program 98.3%

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

   2. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

   4. Applied rewrites 80.7%

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

   5. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lift-neg.f64 N/A

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

      3. lower-exp.f64 59.1

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

   7. Applied rewrites 59.1%

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

   8. Taylor expanded in b around 0

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

      1. mul-1-neg N/A

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

      2. lift-neg.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 33.2

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

   10. Applied rewrites 33.2%

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

   if 6.39999999999999965e-200 < b

   1. Initial program 98.3%

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

   2. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

   4. Applied rewrites 80.7%

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

   5. Taylor expanded in b around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-pow.f64 N/A

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

      5. lower-*.f64 54.8

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

   7. Applied rewrites 54.8%

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

   8. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lift-*.f64 32.2

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

   10. Applied rewrites 32.2%

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

       1. lift-*.f64 N/A

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

       2. lift-/.f64 N/A

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

       3. associate-/r* N/A

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

       4. lower-/.f64 N/A

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

       5. lower-/.f64 32.3

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

   12. Applied rewrites 32.3%

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

Alternative 12: 32.3% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 8.5 \cdot 10^{-201}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{1}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 8.5e-201) (/ (/ x 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 (y <= 8.5e-201) {
		tmp = (x / 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 (y <= 8.5d-201) then
        tmp = (x / 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 (y <= 8.5e-201) {
		tmp = (x / a) / y;
	} else {
		tmp = x * ((1.0 / a) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 8.5e-201:
		tmp = (x / a) / y
	else:
		tmp = x * ((1.0 / a) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 8.5e-201)
		tmp = Float64(Float64(x / 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 (y <= 8.5e-201)
		tmp = (x / a) / y;
	else
		tmp = x * ((1.0 / a) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 8.5e-201], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x * N[(N[(1.0 / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 8.5000000000000007e-201

   1. Initial program 98.3%

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

   2. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

   4. Applied rewrites 80.7%

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

   5. Taylor expanded in b around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-pow.f64 N/A

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

      5. lower-*.f64 54.8

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

   7. Applied rewrites 54.8%

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

   8. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lift-*.f64 32.2

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

   10. Applied rewrites 32.2%

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

       1. lift-*.f64 N/A

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

       2. lift-/.f64 N/A

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

       3. associate-/r* N/A

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

       4. lower-/.f64 N/A

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

       5. lower-/.f64 32.3

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

   12. Applied rewrites 32.3%

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

   if 8.5000000000000007e-201 < y

   1. Initial program 98.3%

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

   2. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

   4. Applied rewrites 80.7%

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

   5. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lift-neg.f64 N/A

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

      3. lower-exp.f64 59.1

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

   7. Applied rewrites 59.1%

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

   8. Taylor expanded in b around 0

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

      1. lower-/.f64 32.1

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

   10. Applied rewrites 32.1%

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

Alternative 13: 32.2% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 8.2 \cdot 10^{-201}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{a \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 8.2e-201) (/ (/ x 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 (y <= 8.2e-201) {
		tmp = (x / 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 (y <= 8.2d-201) then
        tmp = (x / 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 (y <= 8.2e-201) {
		tmp = (x / a) / y;
	} else {
		tmp = x * (1.0 / (a * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 8.2e-201:
		tmp = (x / a) / y
	else:
		tmp = x * (1.0 / (a * y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 8.2e-201)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(x * Float64(1.0 / Float64(a * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 8.2e-201)
		tmp = (x / a) / y;
	else
		tmp = x * (1.0 / (a * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 8.2e-201], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x * N[(1.0 / N[(a * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 8.20000000000000003e-201

   1. Initial program 98.3%

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

   2. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

   4. Applied rewrites 80.7%

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

   5. Taylor expanded in b around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-pow.f64 N/A

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

      5. lower-*.f64 54.8

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

   7. Applied rewrites 54.8%

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

   8. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lift-*.f64 32.2

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

   10. Applied rewrites 32.2%

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

       1. lift-*.f64 N/A

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

       2. lift-/.f64 N/A

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

       3. associate-/r* N/A

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

       4. lower-/.f64 N/A

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

       5. lower-/.f64 32.3

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

   12. Applied rewrites 32.3%

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

   if 8.20000000000000003e-201 < y

   1. Initial program 98.3%

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

   2. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

   4. Applied rewrites 80.7%

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

   5. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lift-neg.f64 N/A

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

      3. lower-exp.f64 N/A

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

      4. lower-*.f64 54.8

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

   7. Applied rewrites 54.8%

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

   8. Taylor expanded in b around 0

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

      1. lower-/.f64 N/A

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

      2. lift-*.f64 32.3

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

   10. Applied rewrites 32.3%

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

Alternative 14: 32.0% accurate, 5.5× speedup

Math

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

FPCore

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

C

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

Fortran

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 / a) / y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.3%

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

2. Taylor expanded in t around 0

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

   1. associate-/l* N/A

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

   2. lower-*.f64 N/A

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

   3. lower-/.f64 N/A

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

4. Applied rewrites 80.7%

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

5. Taylor expanded in b around 0

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

   1. lower-/.f64 N/A

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

   2. *-commutative N/A

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

   3. lower-*.f64 N/A

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

   4. lower-pow.f64 N/A

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

   5. lower-*.f64 54.8

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

7. Applied rewrites 54.8%

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

8. Taylor expanded in y around 0

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

   1. lower-/.f64 N/A

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

   2. lift-*.f64 32.2

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

10. Applied rewrites 32.2%

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

    1. lift-*.f64 N/A

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

    2. lift-/.f64 N/A

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

    3. associate-/r* N/A

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

    4. lower-/.f64 N/A

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

    5. lower-/.f64 32.3

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

12. Applied rewrites 32.3%

    \[\leadsto \frac{\frac{x}{a}}{y} \]
13. Add Preprocessing

Alternative 15: 31.8% accurate, 5.8× speedup

Math

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

FPCore

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

C

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

Fortran

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 / (a * y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.3%

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

2. Taylor expanded in t around 0

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

   1. associate-/l* N/A

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

   2. lower-*.f64 N/A

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

   3. lower-/.f64 N/A

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

4. Applied rewrites 80.7%

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

5. Taylor expanded in b around 0

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

   1. lower-/.f64 N/A

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

   2. *-commutative N/A

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

   3. lower-*.f64 N/A

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

   4. lower-pow.f64 N/A

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

   5. lower-*.f64 54.8

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

7. Applied rewrites 54.8%

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

8. Taylor expanded in y around 0

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

   1. lower-/.f64 N/A

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

   2. lift-*.f64 32.2

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

10. Applied rewrites 32.2%

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

Reproduce

herbie shell --seed 2025139 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A"
  :precision binary64
  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))