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

Percentage Accurate: 98.4% → 98.4%

Time: 5.6s

Alternatives: 16

Speedup: 1.0×

• 48.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.4%

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

Alternative 2: 93.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - 1\right) \cdot \log a\\ t_2 := \frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}\\ \mathbf{if}\;t\_1 \leq -4000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 650:\\ \;\;\;\;x \cdot \frac{\frac{1}{a} \cdot e^{\log z \cdot y - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 1.0)) b))) y)))
   (if (<= t_1 -4000.0)
     t_2
     (if (<= t_1 650.0)
       (* x (/ (* (/ 1.0 a) (exp (- (* (log z) y) b))) 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 - 1.0)) - b))) / y;
	double tmp;
	if (t_1 <= -4000.0) {
		tmp = t_2;
	} else if (t_1 <= 650.0) {
		tmp = x * (((1.0 / a) * exp(((log(z) * y) - b))) / 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 - 1.0d0)) - b))) / y
    if (t_1 <= (-4000.0d0)) then
        tmp = t_2
    else if (t_1 <= 650.0d0) then
        tmp = x * (((1.0d0 / a) * exp(((log(z) * y) - b))) / 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 - 1.0)) - b))) / y;
	double tmp;
	if (t_1 <= -4000.0) {
		tmp = t_2;
	} else if (t_1 <= 650.0) {
		tmp = x * (((1.0 / a) * Math.exp(((Math.log(z) * y) - b))) / 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 - 1.0)) - b))) / y
	tmp = 0
	if t_1 <= -4000.0:
		tmp = t_2
	elif t_1 <= 650.0:
		tmp = x * (((1.0 / a) * math.exp(((math.log(z) * y) - b))) / 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(Float64(log(a) * Float64(t - 1.0)) - b))) / y)
	tmp = 0.0
	if (t_1 <= -4000.0)
		tmp = t_2;
	elseif (t_1 <= 650.0)
		tmp = Float64(x * Float64(Float64(Float64(1.0 / a) * exp(Float64(Float64(log(z) * y) - b))) / 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 - 1.0)) - b))) / y;
	tmp = 0.0;
	if (t_1 <= -4000.0)
		tmp = t_2;
	elseif (t_1 <= 650.0)
		tmp = x * (((1.0 / a) * exp(((log(z) * y) - b))) / 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[(N[Log[a], $MachinePrecision] * N[(t - 1.0), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t$95$1, -4000.0], t$95$2, If[LessEqual[t$95$1, 650.0], 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$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -4e3 or 650 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))

   1. Initial program 100.0%

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

   2. 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 88.4

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

   4. Applied rewrites 88.4%

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

   if -4e3 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 650

   1. Initial program 96.6%

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

   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 97.1%

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

Alternative 3: 92.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}\\ \mathbf{if}\;t \leq -4 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 9:\\ \;\;\;\;\frac{x \cdot \frac{e^{0 + \left(\log z \cdot y - b\right)}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (exp (- (* (log a) (- t 1.0)) b))) y)))
   (if (<= t -4e+78)
     t_1
     (if (<= t 9.0) (/ (* x (/ (exp (+ 0.0 (- (* (log z) y) b))) a)) 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 <= -4e+78) {
		tmp = t_1;
	} else if (t <= 9.0) {
		tmp = (x * (exp((0.0 + ((log(z) * y) - b))) / 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(((log(a) * (t - 1.0d0)) - b))) / y
    if (t <= (-4d+78)) then
        tmp = t_1
    else if (t <= 9.0d0) then
        tmp = (x * (exp((0.0d0 + ((log(z) * y) - b))) / 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(((Math.log(a) * (t - 1.0)) - b))) / y;
	double tmp;
	if (t <= -4e+78) {
		tmp = t_1;
	} else if (t <= 9.0) {
		tmp = (x * (Math.exp((0.0 + ((Math.log(z) * y) - b))) / a)) / 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 <= -4e+78:
		tmp = t_1
	elif t <= 9.0:
		tmp = (x * (math.exp((0.0 + ((math.log(z) * y) - b))) / a)) / 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 <= -4e+78)
		tmp = t_1;
	elseif (t <= 9.0)
		tmp = Float64(Float64(x * Float64(exp(Float64(0.0 + Float64(Float64(log(z) * y) - b))) / 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(((log(a) * (t - 1.0)) - b))) / y;
	tmp = 0.0;
	if (t <= -4e+78)
		tmp = t_1;
	elseif (t <= 9.0)
		tmp = (x * (exp((0.0 + ((log(z) * y) - b))) / a)) / 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, -4e+78], t$95$1, If[LessEqual[t, 9.0], N[(N[(x * N[(N[Exp[N[(0.0 + N[(N[(N[Log[z], $MachinePrecision] * y), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.00000000000000003e78 or 9 < t

   1. Initial program 100.0%

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

   2. 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 90.1

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

   4. Applied rewrites 90.1%

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

   if -4.00000000000000003e78 < t < 9

   1. Initial program 97.1%

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

   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 73.0

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

   4. Applied rewrites 73.0%

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

   5. Taylor expanded in t around 0

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   6. 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. *-commutative N/A

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

      3. exp-sum N/A

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

      4. *-commutative N/A

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

      5. pow-to-exp N/A

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

      6. inv-pow N/A

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

      7. associate-*l/ N/A

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

      8. lower-/.f64 N/A

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

   7. Applied rewrites 95.5%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{0 + \left(\log z \cdot y - b\right)}}{a}}}{y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 89.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot e^{\log z \cdot y}}{y}\\ \mathbf{if}\;y \leq -9.2 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+89}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (exp (* (log z) y))) y)))
   (if (<= y -9.2e+52)
     t_1
     (if (<= y 2.5e+89) (/ (* 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 * exp((log(z) * y))) / y;
	double tmp;
	if (y <= -9.2e+52) {
		tmp = t_1;
	} else if (y <= 2.5e+89) {
		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 * exp((log(z) * y))) / y
    if (y <= (-9.2d+52)) then
        tmp = t_1
    else if (y <= 2.5d+89) 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.exp((Math.log(z) * y))) / y;
	double tmp;
	if (y <= -9.2e+52) {
		tmp = t_1;
	} else if (y <= 2.5e+89) {
		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.exp((math.log(z) * y))) / y
	tmp = 0
	if y <= -9.2e+52:
		tmp = t_1
	elif y <= 2.5e+89:
		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 * exp(Float64(log(z) * y))) / y)
	tmp = 0.0
	if (y <= -9.2e+52)
		tmp = t_1;
	elseif (y <= 2.5e+89)
		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 * exp((log(z) * y))) / y;
	tmp = 0.0;
	if (y <= -9.2e+52)
		tmp = t_1;
	elseif (y <= 2.5e+89)
		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[Exp[N[(N[Log[z], $MachinePrecision] * y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -9.2e+52], t$95$1, If[LessEqual[y, 2.5e+89], 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 < -9.1999999999999999e52 or 2.49999999999999992e89 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-log.f64 83.5

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

   4. Applied rewrites 83.5%

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

   if -9.1999999999999999e52 < y < 2.49999999999999992e89

   1. Initial program 97.4%

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

   2. 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 92.5

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

   4. Applied rewrites 92.5%

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

Alternative 5: 76.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - 1\right) \cdot \log a\\ t_2 := \frac{x \cdot e^{\log a \cdot t}}{y}\\ \mathbf{if}\;t\_1 \leq -4000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 100:\\ \;\;\;\;x \cdot \frac{\frac{e^{-b}}{a}}{y}\\ \mathbf{elif}\;t\_1 \leq 1000:\\ \;\;\;\;\frac{{z}^{y} \cdot x}{a \cdot y}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 -4000.0)
     t_2
     (if (<= t_1 100.0)
       (* x (/ (/ (exp (- b)) a) y))
       (if (<= t_1 1000.0) (/ (* (pow z y) x) (* 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 <= -4000.0) {
		tmp = t_2;
	} else if (t_1 <= 100.0) {
		tmp = x * ((exp(-b) / a) / y);
	} else if (t_1 <= 1000.0) {
		tmp = (pow(z, y) * x) / (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 <= (-4000.0d0)) then
        tmp = t_2
    else if (t_1 <= 100.0d0) then
        tmp = x * ((exp(-b) / a) / y)
    else if (t_1 <= 1000.0d0) then
        tmp = ((z ** y) * x) / (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 <= -4000.0) {
		tmp = t_2;
	} else if (t_1 <= 100.0) {
		tmp = x * ((Math.exp(-b) / a) / y);
	} else if (t_1 <= 1000.0) {
		tmp = (Math.pow(z, y) * x) / (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 <= -4000.0:
		tmp = t_2
	elif t_1 <= 100.0:
		tmp = x * ((math.exp(-b) / a) / y)
	elif t_1 <= 1000.0:
		tmp = (math.pow(z, y) * x) / (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 <= -4000.0)
		tmp = t_2;
	elseif (t_1 <= 100.0)
		tmp = Float64(x * Float64(Float64(exp(Float64(-b)) / a) / y));
	elseif (t_1 <= 1000.0)
		tmp = Float64(Float64((z ^ y) * x) / Float64(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 <= -4000.0)
		tmp = t_2;
	elseif (t_1 <= 100.0)
		tmp = x * ((exp(-b) / a) / y);
	elseif (t_1 <= 1000.0)
		tmp = ((z ^ y) * x) / (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, -4000.0], t$95$2, If[LessEqual[t$95$1, 100.0], N[(x * N[(N[(N[Exp[(-b)], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1000.0], N[(N[(N[Power[z, y], $MachinePrecision] * x), $MachinePrecision] / N[(a * y), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -4e3 or 1e3 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))

   1. Initial program 100.0%

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

   2. 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 79.1

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

   4. Applied rewrites 79.1%

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

   if -4e3 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 100

   1. Initial program 95.3%

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

   2. 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 99.1%

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

   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. lower-exp.f64 N/A

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

      3. lift-neg.f64 74.6

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

   7. Applied rewrites 74.6%

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

   if 100 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 1e3

   1. Initial program 98.8%

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

   2. 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 94.5%

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

   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 73.7

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

   7. Applied rewrites 73.7%

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

Alternative 6: 72.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{e^{-b}}{y}\\ \mathbf{if}\;b \leq -5.8 \cdot 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1650:\\ \;\;\;\;\frac{{z}^{y}}{a \cdot y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (exp (- b)) y))))
   (if (<= b -5.8e+30)
     t_1
     (if (<= b 1650.0) (* (/ (pow z y) (* a y)) x) 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 <= -5.8e+30) {
		tmp = t_1;
	} else if (b <= 1650.0) {
		tmp = (pow(z, y) / (a * y)) * x;
	} 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 <= (-5.8d+30)) then
        tmp = t_1
    else if (b <= 1650.0d0) then
        tmp = ((z ** y) / (a * y)) * x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (Math.exp(-b) / y);
	double tmp;
	if (b <= -5.8e+30) {
		tmp = t_1;
	} else if (b <= 1650.0) {
		tmp = (Math.pow(z, y) / (a * y)) * x;
	} 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 <= -5.8e+30:
		tmp = t_1
	elif b <= 1650.0:
		tmp = (math.pow(z, y) / (a * y)) * x
	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 <= -5.8e+30)
		tmp = t_1;
	elseif (b <= 1650.0)
		tmp = Float64(Float64((z ^ y) / Float64(a * y)) * x);
	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 <= -5.8e+30)
		tmp = t_1;
	elseif (b <= 1650.0)
		tmp = ((z ^ y) / (a * y)) * x;
	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, -5.8e+30], t$95$1, If[LessEqual[b, 1650.0], N[(N[(N[Power[z, y], $MachinePrecision] / N[(a * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -5.7999999999999996e30 or 1650 < b

   1. Initial program 100.0%

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

   2. 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 80.6

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

   4. Applied rewrites 80.6%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]
   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 80.6

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

   6. Applied rewrites 80.6%

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

   if -5.7999999999999996e30 < b < 1650

   1. Initial program 97.0%

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

   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 72.8%

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

   5. Taylor expanded in b around 0

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

      1. lower-/.f64 N/A

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

      2. lower-pow.f64 N/A

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

      3. lower-*.f64 65.2

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

   7. Applied rewrites 65.2%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 65.2

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

   9. Applied rewrites 65.2%

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

Alternative 7: 72.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{e^{-b}}{y}\\ \mathbf{if}\;b \leq -5.8 \cdot 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 390:\\ \;\;\;\;\frac{{z}^{y} \cdot x}{a \cdot y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (exp (- b)) y))))
   (if (<= b -5.8e+30) t_1 (if (<= b 390.0) (/ (* (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 <= -5.8e+30) {
		tmp = t_1;
	} else if (b <= 390.0) {
		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 <= (-5.8d+30)) then
        tmp = t_1
    else if (b <= 390.0d0) 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 <= -5.8e+30) {
		tmp = t_1;
	} else if (b <= 390.0) {
		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 <= -5.8e+30:
		tmp = t_1
	elif b <= 390.0:
		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 <= -5.8e+30)
		tmp = t_1;
	elseif (b <= 390.0)
		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 <= -5.8e+30)
		tmp = t_1;
	elseif (b <= 390.0)
		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, -5.8e+30], t$95$1, If[LessEqual[b, 390.0], 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 < -5.7999999999999996e30 or 390 < b

   1. Initial program 100.0%

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

   2. 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 80.5

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

   4. Applied rewrites 80.5%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]
   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 80.5

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

   6. Applied rewrites 80.5%

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

   if -5.7999999999999996e30 < b < 390

   1. Initial program 97.0%

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

   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 72.8%

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

   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 65.4

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

   7. Applied rewrites 65.4%

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

Alternative 8: 60.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{\frac{e^{-b}}{a}}{y}\\ \mathbf{if}\;b \leq -4.4 \cdot 10^{-73}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{-52}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\log z \cdot y, x, x\right)}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (/ (exp (- b)) a) y))))
   (if (<= b -4.4e-73)
     t_1
     (if (<= b 4.3e-52) (/ (/ (fma (* (log z) y) x 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) / a) / y);
	double tmp;
	if (b <= -4.4e-73) {
		tmp = t_1;
	} else if (b <= 4.3e-52) {
		tmp = (fma((log(z) * y), x, x) / a) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(Float64(exp(Float64(-b)) / a) / y))
	tmp = 0.0
	if (b <= -4.4e-73)
		tmp = t_1;
	elseif (b <= 4.3e-52)
		tmp = Float64(Float64(fma(Float64(log(z) * y), x, x) / a) / y);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(N[(N[Exp[(-b)], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.4e-73], t$95$1, If[LessEqual[b, 4.3e-52], N[(N[(N[(N[(N[Log[z], $MachinePrecision] * y), $MachinePrecision] * x + x), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -4.4e-73 or 4.3000000000000003e-52 < b

   1. Initial program 99.4%

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

   2. 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 85.9%

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

   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. lower-exp.f64 N/A

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

      3. lift-neg.f64 72.3

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

   7. Applied rewrites 72.3%

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

   if -4.4e-73 < b < 4.3000000000000003e-52

   1. Initial program 97.0%

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

   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 73.1%

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

   5. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

   7. Applied rewrites 42.6%

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

   8. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-log.f64 N/A

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

      6. lift-*.f64 42.6

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

   10. Applied rewrites 42.6%

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

Alternative 9: 59.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{e^{-b}}{y}\\ \mathbf{if}\;b \leq -2.7 \cdot 10^{-55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 16:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(\log z \cdot y, x, x\right)}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (exp (- b)) y))))
   (if (<= b -2.7e-55)
     t_1
     (if (<= b 16.0) (/ (/ (fma (* (log z) y) x 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 <= -2.7e-55) {
		tmp = t_1;
	} else if (b <= 16.0) {
		tmp = (fma((log(z) * y), x, 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 <= -2.7e-55)
		tmp = t_1;
	elseif (b <= 16.0)
		tmp = Float64(Float64(fma(Float64(log(z) * y), x, x) / a) / y);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.7e-55], t$95$1, If[LessEqual[b, 16.0], N[(N[(N[(N[(N[Log[z], $MachinePrecision] * y), $MachinePrecision] * x + x), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.70000000000000004e-55 or 16 < b

   1. Initial program 99.7%

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

   2. 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 74.0

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

   4. Applied rewrites 74.0%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]
   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 74.0

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

   6. Applied rewrites 74.0%

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

   if -2.70000000000000004e-55 < b < 16

   1. Initial program 96.9%

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

   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 72.7%

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

   5. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

   7. Applied rewrites 42.1%

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

   8. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-log.f64 N/A

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

      6. lift-*.f64 41.9

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

   10. Applied rewrites 41.9%

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

Alternative 10: 59.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{e^{-b}}{y}\\ \mathbf{if}\;b \leq -6 \cdot 10^{-57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 76:\\ \;\;\;\;\frac{\mathsf{fma}\left(\log z \cdot y, x, x\right)}{a \cdot y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (exp (- b)) y))))
   (if (<= b -6e-57)
     t_1
     (if (<= b 76.0) (/ (fma (* (log z) y) x 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 <= -6e-57) {
		tmp = t_1;
	} else if (b <= 76.0) {
		tmp = fma((log(z) * y), x, 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 <= -6e-57)
		tmp = t_1;
	elseif (b <= 76.0)
		tmp = Float64(fma(Float64(log(z) * y), x, x) / Float64(a * y));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6e-57], t$95$1, If[LessEqual[b, 76.0], N[(N[(N[(N[Log[z], $MachinePrecision] * y), $MachinePrecision] * x + x), $MachinePrecision] / N[(a * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -6.00000000000000001e-57 or 76 < b

   1. Initial program 99.7%

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

   2. 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 73.9

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

   4. Applied rewrites 73.9%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]
   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 73.9

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

   6. Applied rewrites 73.9%

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

   if -6.00000000000000001e-57 < b < 76

   1. Initial program 96.9%

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

   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 72.7%

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

   5. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

   7. Applied rewrites 42.2%

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

   8. Taylor expanded in b around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-log.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 39.8

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

   10. Applied rewrites 39.8%

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

Alternative 11: 58.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{e^{-b}}{y}\\ \mathbf{if}\;b \leq -28500000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 540:\\ \;\;\;\;x \cdot \frac{\mathsf{fma}\left(\log z, y, 1\right)}{a \cdot y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (exp (- b)) y))))
   (if (<= b -28500000000.0)
     t_1
     (if (<= b 540.0) (* x (/ (fma (log z) y 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 <= -28500000000.0) {
		tmp = t_1;
	} else if (b <= 540.0) {
		tmp = x * (fma(log(z), y, 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 <= -28500000000.0)
		tmp = t_1;
	elseif (b <= 540.0)
		tmp = Float64(x * Float64(fma(log(z), y, 1.0) / Float64(a * y)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -28500000000.0], t$95$1, If[LessEqual[b, 540.0], N[(x * N[(N[(N[Log[z], $MachinePrecision] * y + 1.0), $MachinePrecision] / N[(a * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.85e10 or 540 < b

   1. Initial program 100.0%

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

   2. 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 80.1

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

   4. Applied rewrites 80.1%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]
   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 80.1

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

   6. Applied rewrites 80.1%

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

   if -2.85e10 < b < 540

   1. Initial program 96.9%

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

   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 72.7%

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

   5. Taylor expanded in b around 0

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

      1. lower-/.f64 N/A

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

      2. lower-pow.f64 N/A

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

      3. lower-*.f64 65.6

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

   7. Applied rewrites 65.6%

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

   8. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift-log.f64 39.3

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

   10. Applied rewrites 39.3%

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

Alternative 12: 58.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{e^{-b}}{y}\\ \mathbf{if}\;b \leq -6 \cdot 10^{-57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1:\\ \;\;\;\;\frac{x \cdot \frac{\left(-b\right) + 1}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (exp (- b)) y))))
   (if (<= b -6e-57) t_1 (if (<= b 1.0) (/ (* x (/ (+ (- b) 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 <= -6e-57) {
		tmp = t_1;
	} else if (b <= 1.0) {
		tmp = (x * ((-b + 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 <= (-6d-57)) then
        tmp = t_1
    else if (b <= 1.0d0) then
        tmp = (x * ((-b + 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 <= -6e-57) {
		tmp = t_1;
	} else if (b <= 1.0) {
		tmp = (x * ((-b + 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 <= -6e-57:
		tmp = t_1
	elif b <= 1.0:
		tmp = (x * ((-b + 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 <= -6e-57)
		tmp = t_1;
	elseif (b <= 1.0)
		tmp = Float64(Float64(x * Float64(Float64(Float64(-b) + 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 <= -6e-57)
		tmp = t_1;
	elseif (b <= 1.0)
		tmp = (x * ((-b + 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, -6e-57], t$95$1, If[LessEqual[b, 1.0], N[(N[(x * N[(N[((-b) + 1.0), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -6.00000000000000001e-57 or 1 < b

   1. Initial program 99.7%

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

   2. 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 73.7

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

   4. Applied rewrites 73.7%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]
   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 73.7

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

   6. Applied rewrites 73.7%

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

   if -6.00000000000000001e-57 < b < 1

   1. Initial program 96.9%

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

   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 72.8%

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

   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. lower-exp.f64 N/A

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

      3. lift-neg.f64 39.6

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

   7. Applied rewrites 39.6%

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

   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 39.4

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

   10. Applied rewrites 39.4%

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

       1. lift-*.f64 N/A

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

       2. lift-/.f64 N/A

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

       3. associate-*r/ N/A

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

       4. lower-/.f64 N/A

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

       5. lower-*.f64 40.2

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

   12. Applied rewrites 40.2%

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

Alternative 13: 58.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot \frac{e^{-b}}{a}}{y} \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x * (exp(-b) / 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 * (exp(-b) / a)) / y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.4%

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

2. 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 80.4

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

4. Applied rewrites 80.4%

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

5. Taylor expanded in t around 0

   \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
6. 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. *-commutative N/A

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

   3. exp-sum N/A

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

   4. *-commutative N/A

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

   5. pow-to-exp N/A

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

   6. inv-pow N/A

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

   7. associate-*l/ N/A

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

   8. lower-/.f64 N/A

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

7. Applied rewrites 80.8%

   \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{0 + \left(\log z \cdot y - b\right)}}{a}}}{y} \]

8. Taylor expanded in y around 0

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

   1. mul-1-neg N/A

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

   2. lift-neg.f64 59.4

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

10. Applied rewrites 59.4%

    \[\leadsto \frac{x \cdot \frac{e^{-b}}{a}}{y} \]
11. Add Preprocessing

Alternative 14: 36.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\\ t_2 := \frac{x \cdot \frac{\left(-b\right) + 1}{a}}{y}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+26}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;x \cdot \frac{\frac{-b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))
        (t_2 (/ (* x (/ (+ (- b) 1.0) a)) y)))
   (if (<= t_1 -2e+26) t_2 (if (<= t_1 0.0) (* x (/ (/ (- b) a) y)) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * exp((((y * log(z)) + ((t - 1.0) * log(a))) - b))) / y;
	double t_2 = (x * ((-b + 1.0) / a)) / y;
	double tmp;
	if (t_1 <= -2e+26) {
		tmp = t_2;
	} else if (t_1 <= 0.0) {
		tmp = x * ((-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 = (x * exp((((y * log(z)) + ((t - 1.0d0) * log(a))) - b))) / y
    t_2 = (x * ((-b + 1.0d0) / a)) / y
    if (t_1 <= (-2d+26)) then
        tmp = t_2
    else if (t_1 <= 0.0d0) then
        tmp = x * ((-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 = (x * Math.exp((((y * Math.log(z)) + ((t - 1.0) * Math.log(a))) - b))) / y;
	double t_2 = (x * ((-b + 1.0) / a)) / y;
	double tmp;
	if (t_1 <= -2e+26) {
		tmp = t_2;
	} else if (t_1 <= 0.0) {
		tmp = x * ((-b / a) / y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * math.exp((((y * math.log(z)) + ((t - 1.0) * math.log(a))) - b))) / y
	t_2 = (x * ((-b + 1.0) / a)) / y
	tmp = 0
	if t_1 <= -2e+26:
		tmp = t_2
	elif t_1 <= 0.0:
		tmp = x * ((-b / a) / y)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) + Float64(Float64(t - 1.0) * log(a))) - b))) / y)
	t_2 = Float64(Float64(x * Float64(Float64(Float64(-b) + 1.0) / a)) / y)
	tmp = 0.0
	if (t_1 <= -2e+26)
		tmp = t_2;
	elseif (t_1 <= 0.0)
		tmp = Float64(x * Float64(Float64(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 = (x * exp((((y * log(z)) + ((t - 1.0) * log(a))) - b))) / y;
	t_2 = (x * ((-b + 1.0) / a)) / y;
	tmp = 0.0;
	if (t_1 <= -2e+26)
		tmp = t_2;
	elseif (t_1 <= 0.0)
		tmp = x * ((-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[(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]}, Block[{t$95$2 = N[(N[(x * N[(N[((-b) + 1.0), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+26], t$95$2, If[LessEqual[t$95$1, 0.0], N[(x * N[(N[((-b) / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (exp.f64 (-.f64 (+.f64 (*.f64 y (log.f64 z)) (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))) b))) y) < -2.0000000000000001e26 or -0.0 < (/.f64 (*.f64 x (exp.f64 (-.f64 (+.f64 (*.f64 y (log.f64 z)) (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))) b))) y)

   1. Initial program 99.0%

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

   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 83.1%

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

   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. lower-exp.f64 N/A

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

      3. lift-neg.f64 58.5

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

   7. Applied rewrites 58.5%

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

   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 40.8

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

   10. Applied rewrites 40.8%

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

       1. lift-*.f64 N/A

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

       2. lift-/.f64 N/A

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

       3. associate-*r/ N/A

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

       4. lower-/.f64 N/A

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

       5. lower-*.f64 43.4

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

   12. Applied rewrites 43.4%

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

   if -2.0000000000000001e26 < (/.f64 (*.f64 x (exp.f64 (-.f64 (+.f64 (*.f64 y (log.f64 z)) (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))) b))) y) < -0.0

   1. Initial program 97.6%

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

   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 77.8%

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

   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. lower-exp.f64 N/A

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

      3. lift-neg.f64 59.7

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

   7. Applied rewrites 59.7%

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

   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 22.8

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

   10. Applied rewrites 22.8%

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

   11. Taylor expanded in b around inf

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

       1. mul-1-neg N/A

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

       2. lift-neg.f64 27.4

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

   13. Applied rewrites 27.4%

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

Alternative 15: 32.4% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.2 \cdot 10^{-300}:\\ \;\;\;\;x \cdot \frac{\frac{-b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{a \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.2e-300) (* x (/ (/ (- b) 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 (b <= -1.2e-300) {
		tmp = x * ((-b / 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 (b <= (-1.2d-300)) then
        tmp = x * ((-b / 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 (b <= -1.2e-300) {
		tmp = x * ((-b / a) / y);
	} else {
		tmp = x * (1.0 / (a * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.2e-300:
		tmp = x * ((-b / a) / y)
	else:
		tmp = x * (1.0 / (a * y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.2e-300)
		tmp = Float64(x * Float64(Float64(Float64(-b) / 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 (b <= -1.2e-300)
		tmp = x * ((-b / a) / y);
	else
		tmp = x * (1.0 / (a * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.2e-300], N[(x * N[(N[((-b) / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 / N[(a * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.2e-300

   1. Initial program 98.4%

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

   2. 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 80.8%

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

   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. lower-exp.f64 N/A

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

      3. lift-neg.f64 60.3

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

   7. Applied rewrites 60.3%

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

   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 42.3

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

   10. Applied rewrites 42.3%

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

   11. Taylor expanded in b around inf

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

       1. mul-1-neg N/A

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

       2. lift-neg.f64 35.7

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

   13. Applied rewrites 35.7%

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

   if -1.2e-300 < b

   1. Initial program 98.4%

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

   2. 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

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

      1. lower-/.f64 N/A

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

      2. lower-pow.f64 N/A

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

      3. lower-*.f64 51.9

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

   7. Applied rewrites 51.9%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 29.2%

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

Alternative 16: 31.2% accurate, 4.2× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.4%

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

2. 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

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

   1. lower-/.f64 N/A

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

   2. lower-pow.f64 N/A

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

   3. lower-*.f64 54.1

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

7. Applied rewrites 54.1%

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

8. Taylor expanded in y around 0

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

10. Applied rewrites 31.2%

    \[\leadsto x \cdot \frac{1}{a \cdot y} \]
11. Add Preprocessing

Reproduce

herbie shell --seed 2025110 
(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))