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

Percentage Accurate: 98.5% → 98.5%

Time: 6.3s

Alternatives: 15

Speedup: 1.0×

• 46.7% 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: 98.5% 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: 98.5% 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 98.5%

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

Alternative 2: 92.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - 1\right) \cdot \log a\\ t_2 := \frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+78}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+97}:\\ \;\;\;\;x \cdot \frac{\frac{1}{a} \cdot e^{\log z \cdot y - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 -1e+78)
     t_2
     (if (<= t_1 4e+97)
       (* 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 <= -1e+78) {
		tmp = t_2;
	} else if (t_1 <= 4e+97) {
		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 <= (-1d+78)) then
        tmp = t_2
    else if (t_1 <= 4d+97) 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 <= -1e+78) {
		tmp = t_2;
	} else if (t_1 <= 4e+97) {
		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 <= -1e+78:
		tmp = t_2
	elif t_1 <= 4e+97:
		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 <= -1e+78)
		tmp = t_2;
	elseif (t_1 <= 4e+97)
		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 <= -1e+78)
		tmp = t_2;
	elseif (t_1 <= 4e+97)
		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, -1e+78], t$95$2, If[LessEqual[t$95$1, 4e+97], 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)) < -1.00000000000000001e78 or 4.0000000000000003e97 < (*.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 91.1

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

   4. Applied rewrites 91.1%

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

   if -1.00000000000000001e78 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 4.0000000000000003e97

   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 93.2%

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

Alternative 3: 92.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{e^{\log z \cdot y - b} \cdot x}{a}}{y}\\ \mathbf{if}\;y \leq -1200:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+15}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ (* (exp (- (* (log z) y) b)) x) a) y)))
   (if (<= y -1200.0)
     t_1
     (if (<= y 1.35e+15) (/ (* 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 = ((exp(((log(z) * y) - b)) * x) / a) / y;
	double tmp;
	if (y <= -1200.0) {
		tmp = t_1;
	} else if (y <= 1.35e+15) {
		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 = ((exp(((log(z) * y) - b)) * x) / a) / y
    if (y <= (-1200.0d0)) then
        tmp = t_1
    else if (y <= 1.35d+15) 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 = ((Math.exp(((Math.log(z) * y) - b)) * x) / a) / y;
	double tmp;
	if (y <= -1200.0) {
		tmp = t_1;
	} else if (y <= 1.35e+15) {
		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 = ((math.exp(((math.log(z) * y) - b)) * x) / a) / y
	tmp = 0
	if y <= -1200.0:
		tmp = t_1
	elif y <= 1.35e+15:
		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(Float64(exp(Float64(Float64(log(z) * y) - b)) * x) / a) / y)
	tmp = 0.0
	if (y <= -1200.0)
		tmp = t_1;
	elseif (y <= 1.35e+15)
		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 = ((exp(((log(z) * y) - b)) * x) / a) / y;
	tmp = 0.0;
	if (y <= -1200.0)
		tmp = t_1;
	elseif (y <= 1.35e+15)
		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[(N[(N[Exp[N[(N[(N[Log[z], $MachinePrecision] * y), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -1200.0], t$95$1, If[LessEqual[y, 1.35e+15], 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 < -1200 or 1.35e15 < 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 t around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

   4. Applied rewrites 67.6%

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

   5. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. exp-diff N/A

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

      5. *-commutative N/A

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

      6. exp-diff N/A

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

      7. lower-exp.f64 N/A

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

      8. lift-log.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. lift--.f64 89.3

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

   7. Applied rewrites 89.3%

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

   if -1200 < y < 1.35e15

   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 96.1

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

   4. Applied rewrites 96.1%

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

Alternative 4: 89.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot e^{\log z \cdot y}}{y}\\ \mathbf{if}\;y \leq -6 \cdot 10^{+114}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+69}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (exp (* (log z) y))) y)))
   (if (<= y -6e+114)
     t_1
     (if (<= y 1.35e+69) (/ (* 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 <= -6e+114) {
		tmp = t_1;
	} else if (y <= 1.35e+69) {
		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 <= (-6d+114)) then
        tmp = t_1
    else if (y <= 1.35d+69) 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 <= -6e+114) {
		tmp = t_1;
	} else if (y <= 1.35e+69) {
		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 <= -6e+114:
		tmp = t_1
	elif y <= 1.35e+69:
		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 <= -6e+114)
		tmp = t_1;
	elseif (y <= 1.35e+69)
		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 <= -6e+114)
		tmp = t_1;
	elseif (y <= 1.35e+69)
		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, -6e+114], t$95$1, If[LessEqual[y, 1.35e+69], 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 < -6.0000000000000001e114 or 1.3499999999999999e69 < 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 85.0

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

   4. Applied rewrites 85.0%

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

   if -6.0000000000000001e114 < y < 1.3499999999999999e69

   1. Initial program 97.7%

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

   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 91.4

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

   4. Applied rewrites 91.4%

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

Alternative 5: 75.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - 1\right) \cdot \log a\\ t_2 := \frac{e^{-b}}{a}\\ t_3 := \frac{x \cdot e^{\log a \cdot t}}{y}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+78}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_1 \leq 50:\\ \;\;\;\;x \cdot \frac{t\_2}{y}\\ \mathbf{elif}\;t\_1 \leq 304:\\ \;\;\;\;x \cdot \frac{{z}^{y}}{a \cdot y}\\ \mathbf{elif}\;t\_1 \leq 682:\\ \;\;\;\;\frac{x \cdot t\_2}{y}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+59}:\\ \;\;\;\;\frac{x \cdot e^{\log z \cdot y}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- t 1.0) (log a)))
        (t_2 (/ (exp (- b)) a))
        (t_3 (/ (* x (exp (* (log a) t))) y)))
   (if (<= t_1 -1e+78)
     t_3
     (if (<= t_1 50.0)
       (* x (/ t_2 y))
       (if (<= t_1 304.0)
         (* x (/ (pow z y) (* a y)))
         (if (<= t_1 682.0)
           (/ (* x t_2) y)
           (if (<= t_1 5e+59) (/ (* x (exp (* (log z) y))) y) t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - 1.0) * log(a);
	double t_2 = exp(-b) / a;
	double t_3 = (x * exp((log(a) * t))) / y;
	double tmp;
	if (t_1 <= -1e+78) {
		tmp = t_3;
	} else if (t_1 <= 50.0) {
		tmp = x * (t_2 / y);
	} else if (t_1 <= 304.0) {
		tmp = x * (pow(z, y) / (a * y));
	} else if (t_1 <= 682.0) {
		tmp = (x * t_2) / y;
	} else if (t_1 <= 5e+59) {
		tmp = (x * exp((log(z) * y))) / y;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (t - 1.0d0) * log(a)
    t_2 = exp(-b) / a
    t_3 = (x * exp((log(a) * t))) / y
    if (t_1 <= (-1d+78)) then
        tmp = t_3
    else if (t_1 <= 50.0d0) then
        tmp = x * (t_2 / y)
    else if (t_1 <= 304.0d0) then
        tmp = x * ((z ** y) / (a * y))
    else if (t_1 <= 682.0d0) then
        tmp = (x * t_2) / y
    else if (t_1 <= 5d+59) then
        tmp = (x * exp((log(z) * y))) / y
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - 1.0) * Math.log(a);
	double t_2 = Math.exp(-b) / a;
	double t_3 = (x * Math.exp((Math.log(a) * t))) / y;
	double tmp;
	if (t_1 <= -1e+78) {
		tmp = t_3;
	} else if (t_1 <= 50.0) {
		tmp = x * (t_2 / y);
	} else if (t_1 <= 304.0) {
		tmp = x * (Math.pow(z, y) / (a * y));
	} else if (t_1 <= 682.0) {
		tmp = (x * t_2) / y;
	} else if (t_1 <= 5e+59) {
		tmp = (x * Math.exp((Math.log(z) * y))) / y;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - 1.0) * math.log(a)
	t_2 = math.exp(-b) / a
	t_3 = (x * math.exp((math.log(a) * t))) / y
	tmp = 0
	if t_1 <= -1e+78:
		tmp = t_3
	elif t_1 <= 50.0:
		tmp = x * (t_2 / y)
	elif t_1 <= 304.0:
		tmp = x * (math.pow(z, y) / (a * y))
	elif t_1 <= 682.0:
		tmp = (x * t_2) / y
	elif t_1 <= 5e+59:
		tmp = (x * math.exp((math.log(z) * y))) / y
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - 1.0) * log(a))
	t_2 = Float64(exp(Float64(-b)) / a)
	t_3 = Float64(Float64(x * exp(Float64(log(a) * t))) / y)
	tmp = 0.0
	if (t_1 <= -1e+78)
		tmp = t_3;
	elseif (t_1 <= 50.0)
		tmp = Float64(x * Float64(t_2 / y));
	elseif (t_1 <= 304.0)
		tmp = Float64(x * Float64((z ^ y) / Float64(a * y)));
	elseif (t_1 <= 682.0)
		tmp = Float64(Float64(x * t_2) / y);
	elseif (t_1 <= 5e+59)
		tmp = Float64(Float64(x * exp(Float64(log(z) * y))) / y);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - 1.0) * log(a);
	t_2 = exp(-b) / a;
	t_3 = (x * exp((log(a) * t))) / y;
	tmp = 0.0;
	if (t_1 <= -1e+78)
		tmp = t_3;
	elseif (t_1 <= 50.0)
		tmp = x * (t_2 / y);
	elseif (t_1 <= 304.0)
		tmp = x * ((z ^ y) / (a * y));
	elseif (t_1 <= 682.0)
		tmp = (x * t_2) / y;
	elseif (t_1 <= 5e+59)
		tmp = (x * exp((log(z) * y))) / y;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - 1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[Exp[(-b)], $MachinePrecision] / a), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * N[Exp[N[(N[Log[a], $MachinePrecision] * t), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+78], t$95$3, If[LessEqual[t$95$1, 50.0], N[(x * N[(t$95$2 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 304.0], N[(x * N[(N[Power[z, y], $MachinePrecision] / N[(a * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 682.0], N[(N[(x * t$95$2), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t$95$1, 5e+59], N[(N[(x * N[Exp[N[(N[Log[z], $MachinePrecision] * y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$3]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -1.00000000000000001e78 or 4.9999999999999997e59 < (*.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 82.4

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

   4. Applied rewrites 82.4%

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

   if -1.00000000000000001e78 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 50

   1. Initial program 96.2%

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

   2. 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 94.6%

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

   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 71.1

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

   7. Applied rewrites 71.1%

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

   if 50 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 304

   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 97.5%

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

   5. Taylor expanded in b around 0

      \[\leadsto x \cdot \frac{{z}^{y}}{\color{blue}{a \cdot y}} \]
   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 70.4

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

   7. Applied rewrites 70.4%

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

   if 304 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 682

   1. Initial program 98.9%

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

   2. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

      2. exp-sum N/A

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

      3. *-commutative N/A

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

      4. pow-to-exp N/A

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

      5. inv-pow N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower-exp.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift-log.f64 99.6

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

   4. Applied rewrites 99.6%

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

   5. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-exp.f64 N/A

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

      3. lift-neg.f64 72.9

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

   7. Applied rewrites 72.9%

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

   if 682 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 4.9999999999999997e59

   1. Initial program 99.9%

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

   2. 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 53.8

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

   4. Applied rewrites 53.8%

      \[\leadsto \frac{x \cdot e^{\color{blue}{\log z \cdot y}}}{y} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 6: 75.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - 1\right) \cdot \log a\\ t_2 := \frac{x \cdot e^{\log a \cdot t}}{y}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+78}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 50:\\ \;\;\;\;x \cdot \frac{\frac{e^{-b}}{a}}{y}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+59}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- t 1.0) (log a))) (t_2 (/ (* x (exp (* (log a) t))) y)))
   (if (<= t_1 -1e+78)
     t_2
     (if (<= t_1 50.0)
       (* x (/ (/ (exp (- b)) a) y))
       (if (<= t_1 4e+59) (/ (* x (/ (pow z y) 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 <= -1e+78) {
		tmp = t_2;
	} else if (t_1 <= 50.0) {
		tmp = x * ((exp(-b) / a) / y);
	} else if (t_1 <= 4e+59) {
		tmp = (x * (pow(z, y) / 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 <= (-1d+78)) then
        tmp = t_2
    else if (t_1 <= 50.0d0) then
        tmp = x * ((exp(-b) / a) / y)
    else if (t_1 <= 4d+59) then
        tmp = (x * ((z ** y) / 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 <= -1e+78) {
		tmp = t_2;
	} else if (t_1 <= 50.0) {
		tmp = x * ((Math.exp(-b) / a) / y);
	} else if (t_1 <= 4e+59) {
		tmp = (x * (Math.pow(z, y) / 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 <= -1e+78:
		tmp = t_2
	elif t_1 <= 50.0:
		tmp = x * ((math.exp(-b) / a) / y)
	elif t_1 <= 4e+59:
		tmp = (x * (math.pow(z, y) / 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 <= -1e+78)
		tmp = t_2;
	elseif (t_1 <= 50.0)
		tmp = Float64(x * Float64(Float64(exp(Float64(-b)) / a) / y));
	elseif (t_1 <= 4e+59)
		tmp = Float64(Float64(x * Float64((z ^ y) / 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 <= -1e+78)
		tmp = t_2;
	elseif (t_1 <= 50.0)
		tmp = x * ((exp(-b) / a) / y);
	elseif (t_1 <= 4e+59)
		tmp = (x * ((z ^ y) / 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, -1e+78], t$95$2, If[LessEqual[t$95$1, 50.0], N[(x * N[(N[(N[Exp[(-b)], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+59], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -1.00000000000000001e78 or 3.99999999999999989e59 < (*.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 82.4

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

   4. Applied rewrites 82.4%

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

   if -1.00000000000000001e78 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 50

   1. Initial program 96.2%

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

   2. 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 94.6%

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

   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 71.1

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

   7. Applied rewrites 71.1%

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

   if 50 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 3.99999999999999989e59

   1. Initial program 99.2%

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

   2. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

      2. exp-sum N/A

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

      3. *-commutative N/A

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

      4. pow-to-exp N/A

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

      5. inv-pow N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower-exp.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift-log.f64 96.4

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

   4. Applied rewrites 96.4%

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

   5. Taylor expanded in b around 0

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

      1. lower-/.f64 N/A

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

      2. lower-pow.f64 71.5

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

   7. Applied rewrites 71.5%

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

Alternative 7: 74.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - 1\right) \cdot \log a\\ t_2 := \frac{x \cdot e^{\log a \cdot t}}{y}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+78}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 50:\\ \;\;\;\;x \cdot \frac{\frac{e^{-b}}{a}}{y}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+59}:\\ \;\;\;\;x \cdot \frac{{z}^{y}}{a \cdot y}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 -1e+78)
     t_2
     (if (<= t_1 50.0)
       (* x (/ (/ (exp (- b)) a) y))
       (if (<= t_1 5e+59) (* x (/ (pow z y) (* 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 <= -1e+78) {
		tmp = t_2;
	} else if (t_1 <= 50.0) {
		tmp = x * ((exp(-b) / a) / y);
	} else if (t_1 <= 5e+59) {
		tmp = x * (pow(z, y) / (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 <= (-1d+78)) then
        tmp = t_2
    else if (t_1 <= 50.0d0) then
        tmp = x * ((exp(-b) / a) / y)
    else if (t_1 <= 5d+59) then
        tmp = x * ((z ** y) / (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 <= -1e+78) {
		tmp = t_2;
	} else if (t_1 <= 50.0) {
		tmp = x * ((Math.exp(-b) / a) / y);
	} else if (t_1 <= 5e+59) {
		tmp = x * (Math.pow(z, y) / (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 <= -1e+78:
		tmp = t_2
	elif t_1 <= 50.0:
		tmp = x * ((math.exp(-b) / a) / y)
	elif t_1 <= 5e+59:
		tmp = x * (math.pow(z, y) / (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 <= -1e+78)
		tmp = t_2;
	elseif (t_1 <= 50.0)
		tmp = Float64(x * Float64(Float64(exp(Float64(-b)) / a) / y));
	elseif (t_1 <= 5e+59)
		tmp = Float64(x * Float64((z ^ y) / 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 <= -1e+78)
		tmp = t_2;
	elseif (t_1 <= 50.0)
		tmp = x * ((exp(-b) / a) / y);
	elseif (t_1 <= 5e+59)
		tmp = x * ((z ^ y) / (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, -1e+78], t$95$2, If[LessEqual[t$95$1, 50.0], N[(x * N[(N[(N[Exp[(-b)], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+59], N[(x * N[(N[Power[z, y], $MachinePrecision] / N[(a * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -1.00000000000000001e78 or 4.9999999999999997e59 < (*.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 82.4

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

   4. Applied rewrites 82.4%

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

   if -1.00000000000000001e78 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 50

   1. Initial program 96.2%

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

   2. 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 94.6%

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

   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 71.1

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

   7. Applied rewrites 71.1%

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

   if 50 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 4.9999999999999997e59

   1. Initial program 99.2%

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

   2. 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 93.5%

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

   5. Taylor expanded in b around 0

      \[\leadsto x \cdot \frac{{z}^{y}}{\color{blue}{a \cdot y}} \]
   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 69.9

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

   7. Applied rewrites 69.9%

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

Alternative 8: 71.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := e^{-b}\\ \mathbf{if}\;b \leq -3.05 \cdot 10^{+53}:\\ \;\;\;\;x \cdot \frac{t\_1}{y}\\ \mathbf{elif}\;b \leq 0.22:\\ \;\;\;\;\frac{{z}^{y} \cdot x}{a \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{t\_1}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (exp (- b))))
   (if (<= b -3.05e+53)
     (* x (/ t_1 y))
     (if (<= b 0.22) (/ (* (pow z y) x) (* a y)) (/ (* x (/ t_1 a)) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = exp(-b);
	double tmp;
	if (b <= -3.05e+53) {
		tmp = x * (t_1 / y);
	} else if (b <= 0.22) {
		tmp = (pow(z, y) * x) / (a * y);
	} else {
		tmp = (x * (t_1 / 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) :: t_1
    real(8) :: tmp
    t_1 = exp(-b)
    if (b <= (-3.05d+53)) then
        tmp = x * (t_1 / y)
    else if (b <= 0.22d0) then
        tmp = ((z ** y) * x) / (a * y)
    else
        tmp = (x * (t_1 / 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 t_1 = Math.exp(-b);
	double tmp;
	if (b <= -3.05e+53) {
		tmp = x * (t_1 / y);
	} else if (b <= 0.22) {
		tmp = (Math.pow(z, y) * x) / (a * y);
	} else {
		tmp = (x * (t_1 / a)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.exp(-b)
	tmp = 0
	if b <= -3.05e+53:
		tmp = x * (t_1 / y)
	elif b <= 0.22:
		tmp = (math.pow(z, y) * x) / (a * y)
	else:
		tmp = (x * (t_1 / a)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = exp(Float64(-b))
	tmp = 0.0
	if (b <= -3.05e+53)
		tmp = Float64(x * Float64(t_1 / y));
	elseif (b <= 0.22)
		tmp = Float64(Float64((z ^ y) * x) / Float64(a * y));
	else
		tmp = Float64(Float64(x * Float64(t_1 / a)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = exp(-b);
	tmp = 0.0;
	if (b <= -3.05e+53)
		tmp = x * (t_1 / y);
	elseif (b <= 0.22)
		tmp = ((z ^ y) * x) / (a * y);
	else
		tmp = (x * (t_1 / a)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[Exp[(-b)], $MachinePrecision]}, If[LessEqual[b, -3.05e+53], N[(x * N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 0.22], N[(N[(N[Power[z, y], $MachinePrecision] * x), $MachinePrecision] / N[(a * y), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(t$95$1 / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.0500000000000001e53

   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 80.7

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

   4. Applied rewrites 80.7%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]
   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 80.7

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

   6. Applied rewrites 80.7%

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

   if -3.0500000000000001e53 < b < 0.220000000000000001

   1. Initial program 97.2%

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

   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 72.3%

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

   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 64.6

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

   7. Applied rewrites 64.6%

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

   if 0.220000000000000001 < b

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

      2. exp-sum N/A

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

      3. *-commutative N/A

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

      4. pow-to-exp N/A

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

      5. inv-pow N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower-exp.f64 N/A

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

      9. lower--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift-log.f64 90.2

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

   4. Applied rewrites 90.2%

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

   5. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-exp.f64 N/A

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

      3. lift-neg.f64 79.2

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

   7. Applied rewrites 79.2%

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

Alternative 9: 59.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(t - 1\right) \cdot \log a \leq -1 \cdot 10^{+90}:\\ \;\;\;\;x \cdot \frac{\frac{\left(b \cdot b\right) \cdot 0.5}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{e^{-b}}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* (- t 1.0) (log a)) -1e+90)
   (* x (/ (/ (* (* b b) 0.5) a) y))
   (* x (/ (/ (exp (- b)) a) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t - 1.0) * log(a)) <= -1e+90) {
		tmp = x * ((((b * b) * 0.5) / a) / y);
	} else {
		tmp = x * ((exp(-b) / 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 (((t - 1.0d0) * log(a)) <= (-1d+90)) then
        tmp = x * ((((b * b) * 0.5d0) / a) / y)
    else
        tmp = x * ((exp(-b) / 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 (((t - 1.0) * Math.log(a)) <= -1e+90) {
		tmp = x * ((((b * b) * 0.5) / a) / y);
	} else {
		tmp = x * ((Math.exp(-b) / a) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((t - 1.0) * math.log(a)) <= -1e+90:
		tmp = x * ((((b * b) * 0.5) / a) / y)
	else:
		tmp = x * ((math.exp(-b) / a) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(t - 1.0) * log(a)) <= -1e+90)
		tmp = Float64(x * Float64(Float64(Float64(Float64(b * b) * 0.5) / a) / y));
	else
		tmp = Float64(x * Float64(Float64(exp(Float64(-b)) / a) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((t - 1.0) * log(a)) <= -1e+90)
		tmp = x * ((((b * b) * 0.5) / a) / y);
	else
		tmp = x * ((exp(-b) / a) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(t - 1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision], -1e+90], N[(x * N[(N[(N[(N[(b * b), $MachinePrecision] * 0.5), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(N[Exp[(-b)], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -9.99999999999999966e89

   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 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 54.5%

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

   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 41.3

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

   7. Applied rewrites 41.3%

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

   8. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 22.5

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

   10. Applied rewrites 22.5%

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

   11. Taylor expanded in b around inf

       \[\leadsto x \cdot \frac{\frac{\frac{1}{2} \cdot {b}^{2}}{a}}{y} \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto x \cdot \frac{\frac{{b}^{2} \cdot \frac{1}{2}}{a}}{y} \]

       2. lower-*.f64 N/A

          \[\leadsto x \cdot \frac{\frac{{b}^{2} \cdot \frac{1}{2}}{a}}{y} \]

       3. unpow2 N/A

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

       4. lower-*.f64 44.7

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

   13. Applied rewrites 44.7%

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

   if -9.99999999999999966e89 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))

   1. Initial program 98.2%

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

   2. 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 86.6%

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

   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 62.8

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

   7. Applied rewrites 62.8%

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

Alternative 10: 58.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{e^{-b}}{y}\\ \mathbf{if}\;b \leq -1.7 \cdot 10^{+20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 11:\\ \;\;\;\;\frac{x}{a \cdot y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (exp (- b)) y))))
   (if (<= b -1.7e+20) t_1 (if (<= b 11.0) (/ 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 <= -1.7e+20) {
		tmp = t_1;
	} else if (b <= 11.0) {
		tmp = 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 <= (-1.7d+20)) then
        tmp = t_1
    else if (b <= 11.0d0) then
        tmp = 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 <= -1.7e+20) {
		tmp = t_1;
	} else if (b <= 11.0) {
		tmp = 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 <= -1.7e+20:
		tmp = t_1
	elif b <= 11.0:
		tmp = 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 <= -1.7e+20)
		tmp = t_1;
	elseif (b <= 11.0)
		tmp = Float64(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 <= -1.7e+20)
		tmp = t_1;
	elseif (b <= 11.0)
		tmp = 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, -1.7e+20], t$95$1, If[LessEqual[b, 11.0], N[(x / N[(a * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.7e20 or 11 < 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 78.9

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

   4. Applied rewrites 78.9%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]
   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 78.9

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

   6. Applied rewrites 78.9%

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

   if -1.7e20 < b < 11

   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 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 71.9%

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

   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 65.2

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

   7. Applied rewrites 65.2%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 38.5%

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

Alternative 11: 56.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(t - 1\right) \cdot \log a \leq -1 \cdot 10^{+90}:\\ \;\;\;\;x \cdot \frac{\frac{\left(b \cdot b\right) \cdot 0.5}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{e^{-b}}{a \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* (- t 1.0) (log a)) -1e+90)
   (* x (/ (/ (* (* b b) 0.5) a) y))
   (* x (/ (exp (- b)) (* a y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t - 1.0) * log(a)) <= -1e+90) {
		tmp = x * ((((b * b) * 0.5) / a) / y);
	} else {
		tmp = x * (exp(-b) / (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 (((t - 1.0d0) * log(a)) <= (-1d+90)) then
        tmp = x * ((((b * b) * 0.5d0) / a) / y)
    else
        tmp = x * (exp(-b) / (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 (((t - 1.0) * Math.log(a)) <= -1e+90) {
		tmp = x * ((((b * b) * 0.5) / a) / y);
	} else {
		tmp = x * (Math.exp(-b) / (a * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((t - 1.0) * math.log(a)) <= -1e+90:
		tmp = x * ((((b * b) * 0.5) / a) / y)
	else:
		tmp = x * (math.exp(-b) / (a * y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(t - 1.0) * log(a)) <= -1e+90)
		tmp = Float64(x * Float64(Float64(Float64(Float64(b * b) * 0.5) / a) / y));
	else
		tmp = Float64(x * Float64(exp(Float64(-b)) / Float64(a * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((t - 1.0) * log(a)) <= -1e+90)
		tmp = x * ((((b * b) * 0.5) / a) / y);
	else
		tmp = x * (exp(-b) / (a * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(t - 1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision], -1e+90], N[(x * N[(N[(N[(N[(b * b), $MachinePrecision] * 0.5), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[Exp[(-b)], $MachinePrecision] / N[(a * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -9.99999999999999966e89

   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 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 54.5%

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

   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 41.3

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

   7. Applied rewrites 41.3%

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

   8. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 22.5

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

   10. Applied rewrites 22.5%

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

   11. Taylor expanded in b around inf

       \[\leadsto x \cdot \frac{\frac{\frac{1}{2} \cdot {b}^{2}}{a}}{y} \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto x \cdot \frac{\frac{{b}^{2} \cdot \frac{1}{2}}{a}}{y} \]

       2. lower-*.f64 N/A

          \[\leadsto x \cdot \frac{\frac{{b}^{2} \cdot \frac{1}{2}}{a}}{y} \]

       3. unpow2 N/A

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

       4. lower-*.f64 44.7

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

   13. Applied rewrites 44.7%

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

   if -9.99999999999999966e89 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))

   1. Initial program 98.2%

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

   2. 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 86.6%

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

   5. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-exp.f64 N/A

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

      3. lift-neg.f64 N/A

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

      4. lower-*.f64 58.6

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

   7. Applied rewrites 58.6%

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

Alternative 12: 40.4% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+43}:\\ \;\;\;\;x \cdot \frac{\frac{\left(b \cdot b\right) \cdot 0.5}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.25e+43) (* x (/ (/ (* (* b b) 0.5) a) y)) (/ x (* a y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.25e+43) {
		tmp = x * ((((b * b) * 0.5) / a) / y);
	} else {
		tmp = x / (a * y);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.25d+43)) then
        tmp = x * ((((b * b) * 0.5d0) / a) / y)
    else
        tmp = x / (a * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.25e+43) {
		tmp = x * ((((b * b) * 0.5) / a) / y);
	} else {
		tmp = x / (a * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.25e+43:
		tmp = x * ((((b * b) * 0.5) / a) / y)
	else:
		tmp = x / (a * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.25e+43)
		tmp = Float64(x * Float64(Float64(Float64(Float64(b * b) * 0.5) / a) / y));
	else
		tmp = Float64(x / Float64(a * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.25e+43)
		tmp = x * ((((b * b) * 0.5) / a) / y);
	else
		tmp = x / (a * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.25e+43], N[(x * N[(N[(N[(N[(b * b), $MachinePrecision] * 0.5), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.2500000000000001e43

   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 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 90.0%

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

   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 80.2

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

   7. Applied rewrites 80.2%

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

   8. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 69.3

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

   10. Applied rewrites 69.3%

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

   11. Taylor expanded in b around inf

       \[\leadsto x \cdot \frac{\frac{\frac{1}{2} \cdot {b}^{2}}{a}}{y} \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto x \cdot \frac{\frac{{b}^{2} \cdot \frac{1}{2}}{a}}{y} \]

       2. lower-*.f64 N/A

          \[\leadsto x \cdot \frac{\frac{{b}^{2} \cdot \frac{1}{2}}{a}}{y} \]

       3. unpow2 N/A

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

       4. lower-*.f64 69.3

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

   13. Applied rewrites 69.3%

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

   if -1.2500000000000001e43 < b

   1. Initial program 98.1%

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

   2. 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 77.9%

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

   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 56.3

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

   7. Applied rewrites 56.3%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 32.1%

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

Alternative 13: 35.0% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 10^{-24}:\\ \;\;\;\;\frac{x \cdot \frac{\left(-b\right) + 1}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 1e-24) (/ (* x (/ (+ (- b) 1.0) a)) y) (/ x (* a y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 1e-24) {
		tmp = (x * ((-b + 1.0) / a)) / y;
	} else {
		tmp = x / (a * y);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= 1d-24) then
        tmp = (x * ((-b + 1.0d0) / a)) / y
    else
        tmp = x / (a * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 1e-24) {
		tmp = (x * ((-b + 1.0) / a)) / y;
	} else {
		tmp = x / (a * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 1e-24:
		tmp = (x * ((-b + 1.0) / a)) / y
	else:
		tmp = x / (a * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 1e-24)
		tmp = Float64(Float64(x * Float64(Float64(Float64(-b) + 1.0) / a)) / y);
	else
		tmp = Float64(x / Float64(a * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 1e-24)
		tmp = (x * ((-b + 1.0) / a)) / y;
	else
		tmp = x / (a * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 1e-24], N[(N[(x * N[(N[((-b) + 1.0), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 9.99999999999999924e-25

   1. Initial program 99.5%

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

   2. 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 81.2%

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

   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 55.8

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

   7. Applied rewrites 55.8%

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

   8. Taylor expanded in b around 0

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

      1. mul-1-neg N/A

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

      2. lift-neg.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 33.4

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

   10. Applied rewrites 33.4%

       \[\leadsto x \cdot \frac{\frac{\left(-b\right) + 1}{a}}{y} \]
   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 36.4

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

   12. Applied rewrites 36.4%

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

   if 9.99999999999999924e-25 < a

   1. Initial program 97.7%

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

   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 80.0%

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

   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 46.7

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

   7. Applied rewrites 46.7%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 33.8%

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

Alternative 14: 33.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(t - 1\right) \cdot \log a \leq -1 \cdot 10^{+24}:\\ \;\;\;\;x \cdot \frac{\frac{-b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* (- t 1.0) (log a)) -1e+24) (* x (/ (/ (- b) a) y)) (/ x (* a y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t - 1.0) * log(a)) <= -1e+24) {
		tmp = x * ((-b / a) / y);
	} else {
		tmp = x / (a * y);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (((t - 1.0d0) * log(a)) <= (-1d+24)) then
        tmp = x * ((-b / a) / y)
    else
        tmp = x / (a * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t - 1.0) * Math.log(a)) <= -1e+24) {
		tmp = x * ((-b / a) / y);
	} else {
		tmp = x / (a * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((t - 1.0) * math.log(a)) <= -1e+24:
		tmp = x * ((-b / a) / y)
	else:
		tmp = x / (a * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(t - 1.0) * log(a)) <= -1e+24)
		tmp = Float64(x * Float64(Float64(Float64(-b) / a) / y));
	else
		tmp = Float64(x / Float64(a * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((t - 1.0) * log(a)) <= -1e+24)
		tmp = x * ((-b / a) / y);
	else
		tmp = x / (a * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(t - 1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision], -1e+24], N[(x * N[(N[((-b) / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -9.9999999999999998e23

   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 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 58.3%

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

   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 42.7

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

   7. Applied rewrites 42.7%

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

   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 19.7

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

   10. Applied rewrites 19.7%

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

   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 29.6

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

   13. Applied rewrites 29.6%

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

   if -9.9999999999999998e23 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))

   1. Initial program 98.0%

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

   2. 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 87.5%

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

   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 59.6

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

   7. Applied rewrites 59.6%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 34.5%

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

Alternative 15: 30.9% accurate, 5.8× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.5%

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

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 80.6%

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

5. Taylor expanded in b around 0

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

   1. lower-/.f64 N/A

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

   2. *-commutative N/A

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

   3. lower-*.f64 N/A

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

   4. lower-pow.f64 N/A

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

   5. lower-*.f64 54.1

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

7. Applied rewrites 54.1%

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

8. Taylor expanded in y around 0

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

10. Applied rewrites 30.9%

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

Reproduce

herbie shell --seed 2025119 
(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))