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

Percentage Accurate: 98.5% → 98.5%

Time: 5.8s

Alternatives: 14

Speedup: 1.0×

• 47.9% 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
3. Add Preprocessing

Alternative 2: 60.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - 1\right) \cdot \log a\\ t_2 := \frac{x \cdot {a}^{t}}{y}\\ \mathbf{if}\;t\_1 \leq -700:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 250:\\ \;\;\;\;x \cdot \frac{\frac{1}{a}}{y}\\ \mathbf{elif}\;t\_1 \leq 700:\\ \;\;\;\;\frac{\frac{x - b \cdot x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- t 1.0) (log a))) (t_2 (/ (* x (pow a t)) y)))
   (if (<= t_1 -700.0)
     t_2
     (if (<= t_1 250.0)
       (* x (/ (/ 1.0 a) y))
       (if (<= t_1 700.0) (/ (/ (- x (* b x)) a) y) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - 1.0) * log(a);
	double t_2 = (x * pow(a, t)) / y;
	double tmp;
	if (t_1 <= -700.0) {
		tmp = t_2;
	} else if (t_1 <= 250.0) {
		tmp = x * ((1.0 / a) / y);
	} else if (t_1 <= 700.0) {
		tmp = ((x - (b * x)) / a) / y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t - 1.0d0) * log(a)
    t_2 = (x * (a ** t)) / y
    if (t_1 <= (-700.0d0)) then
        tmp = t_2
    else if (t_1 <= 250.0d0) then
        tmp = x * ((1.0d0 / a) / y)
    else if (t_1 <= 700.0d0) then
        tmp = ((x - (b * x)) / a) / y
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - 1.0) * Math.log(a);
	double t_2 = (x * Math.pow(a, t)) / y;
	double tmp;
	if (t_1 <= -700.0) {
		tmp = t_2;
	} else if (t_1 <= 250.0) {
		tmp = x * ((1.0 / a) / y);
	} else if (t_1 <= 700.0) {
		tmp = ((x - (b * x)) / a) / y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - 1.0) * math.log(a)
	t_2 = (x * math.pow(a, t)) / y
	tmp = 0
	if t_1 <= -700.0:
		tmp = t_2
	elif t_1 <= 250.0:
		tmp = x * ((1.0 / a) / y)
	elif t_1 <= 700.0:
		tmp = ((x - (b * x)) / a) / y
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - 1.0) * log(a))
	t_2 = Float64(Float64(x * (a ^ t)) / y)
	tmp = 0.0
	if (t_1 <= -700.0)
		tmp = t_2;
	elseif (t_1 <= 250.0)
		tmp = Float64(x * Float64(Float64(1.0 / a) / y));
	elseif (t_1 <= 700.0)
		tmp = Float64(Float64(Float64(x - Float64(b * x)) / 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 * (a ^ t)) / y;
	tmp = 0.0;
	if (t_1 <= -700.0)
		tmp = t_2;
	elseif (t_1 <= 250.0)
		tmp = x * ((1.0 / a) / y);
	elseif (t_1 <= 700.0)
		tmp = ((x - (b * x)) / a) / y;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - 1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t$95$1, -700.0], t$95$2, If[LessEqual[t$95$1, 250.0], N[(x * N[(N[(1.0 / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 700.0], N[(N[(N[(x - N[(b * x), $MachinePrecision]), $MachinePrecision] / a), $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)) < -700 or 700 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))

   1. Initial program 99.9%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. *-commutative N/A

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

      3. pow-to-exp N/A

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

      4. pow-to-exp N/A

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

      5. lower-*.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 66.9

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

   5. Applied rewrites 66.9%

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

   7. Applied rewrites 66.9%

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

   8. Taylor expanded in y around 0

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

      1. pow-to-exp N/A

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

      2. lift-pow.f64 N/A

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

      3. lift--.f64 79.1

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

   10. Applied rewrites 79.1%

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

   11. Taylor expanded in t around inf

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

   13. Applied rewrites 78.5%

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

   if -700 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 250

   1. Initial program 96.1%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. *-commutative N/A

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

      3. pow-to-exp N/A

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

      4. pow-to-exp N/A

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

      5. lower-*.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 69.1

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

   5. Applied rewrites 69.1%

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

   6. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lift-pow.f64 68.5

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

   8. Applied rewrites 68.5%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 36.2%

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

       1. lift-/.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. associate-/l* N/A

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

       4. lower-*.f64 N/A

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

       5. lower-/.f64 39.3

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

   13. Applied rewrites 39.3%

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

   if 250 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 700

   1. Initial program 98.9%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

   5. Applied rewrites 61.9%

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

   6. Taylor expanded in t around 0

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

      1. sub-div N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-pow.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lift-pow.f64 66.2

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

   8. Applied rewrites 66.2%

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

   9. Taylor expanded in y around 0

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

       1. lower--.f64 N/A

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

       2. lower-*.f64 47.1

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

   11. Applied rewrites 47.1%

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

Alternative 3: 65.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - 1\right) \cdot \log a\\ t_2 := \frac{x \cdot {a}^{t}}{y}\\ \mathbf{if}\;t\_1 \leq -10000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+73}:\\ \;\;\;\;x \cdot \frac{e^{-b}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- t 1.0) (log a))) (t_2 (/ (* x (pow a t)) y)))
   (if (<= t_1 -10000000.0)
     t_2
     (if (<= t_1 1e+73) (* x (/ (exp (- 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 * pow(a, t)) / y;
	double tmp;
	if (t_1 <= -10000000.0) {
		tmp = t_2;
	} else if (t_1 <= 1e+73) {
		tmp = x * (exp(-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 * (a ** t)) / y
    if (t_1 <= (-10000000.0d0)) then
        tmp = t_2
    else if (t_1 <= 1d+73) then
        tmp = x * (exp(-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.pow(a, t)) / y;
	double tmp;
	if (t_1 <= -10000000.0) {
		tmp = t_2;
	} else if (t_1 <= 1e+73) {
		tmp = x * (Math.exp(-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.pow(a, t)) / y
	tmp = 0
	if t_1 <= -10000000.0:
		tmp = t_2
	elif t_1 <= 1e+73:
		tmp = x * (math.exp(-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 * (a ^ t)) / y)
	tmp = 0.0
	if (t_1 <= -10000000.0)
		tmp = t_2;
	elseif (t_1 <= 1e+73)
		tmp = Float64(x * Float64(exp(Float64(-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 * (a ^ t)) / y;
	tmp = 0.0;
	if (t_1 <= -10000000.0)
		tmp = t_2;
	elseif (t_1 <= 1e+73)
		tmp = x * (exp(-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[Power[a, t], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t$95$1, -10000000.0], t$95$2, If[LessEqual[t$95$1, 1e+73], N[(x * N[(N[Exp[(-b)], $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)) < -1e7 or 9.99999999999999983e72 < (*.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. Add Preprocessing

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. *-commutative N/A

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

      3. pow-to-exp N/A

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

      4. pow-to-exp N/A

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

      5. lower-*.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 67.7

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

   5. Applied rewrites 67.7%

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

   7. Applied rewrites 67.7%

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

   8. Taylor expanded in y around 0

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

      1. pow-to-exp N/A

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

      2. lift-pow.f64 N/A

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

      3. lift--.f64 81.2

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

   10. Applied rewrites 81.2%

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

   11. Taylor expanded in t around inf

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

   13. Applied rewrites 81.2%

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

   if -1e7 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 9.99999999999999983e72

   1. Initial program 97.3%

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

   3. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 52.9

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

   5. Applied rewrites 52.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 52.9

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

   7. Applied rewrites 52.9%

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

Alternative 4: 74.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+145}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y}\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-179}:\\ \;\;\;\;\frac{x \cdot {\left(e^{b} \cdot a\right)}^{-1}}{y}\\ \mathbf{elif}\;t \leq 4.2:\\ \;\;\;\;\frac{x \cdot {\left({z}^{\left(-y\right)} \cdot a\right)}^{-1}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t - 1\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -7.2e+145)
   (/ (* x (pow a t)) y)
   (if (<= t -1.3e-179)
     (/ (* x (pow (* (exp b) a) -1.0)) y)
     (if (<= t 4.2)
       (/ (* x (pow (* (pow z (- y)) a) -1.0)) y)
       (/ (* x (pow a (- t 1.0))) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7.2e+145) {
		tmp = (x * pow(a, t)) / y;
	} else if (t <= -1.3e-179) {
		tmp = (x * pow((exp(b) * a), -1.0)) / y;
	} else if (t <= 4.2) {
		tmp = (x * pow((pow(z, -y) * a), -1.0)) / y;
	} else {
		tmp = (x * pow(a, (t - 1.0))) / y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-7.2d+145)) then
        tmp = (x * (a ** t)) / y
    else if (t <= (-1.3d-179)) then
        tmp = (x * ((exp(b) * a) ** (-1.0d0))) / y
    else if (t <= 4.2d0) then
        tmp = (x * (((z ** -y) * a) ** (-1.0d0))) / y
    else
        tmp = (x * (a ** (t - 1.0d0))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7.2e+145) {
		tmp = (x * Math.pow(a, t)) / y;
	} else if (t <= -1.3e-179) {
		tmp = (x * Math.pow((Math.exp(b) * a), -1.0)) / y;
	} else if (t <= 4.2) {
		tmp = (x * Math.pow((Math.pow(z, -y) * a), -1.0)) / y;
	} else {
		tmp = (x * Math.pow(a, (t - 1.0))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -7.2e+145:
		tmp = (x * math.pow(a, t)) / y
	elif t <= -1.3e-179:
		tmp = (x * math.pow((math.exp(b) * a), -1.0)) / y
	elif t <= 4.2:
		tmp = (x * math.pow((math.pow(z, -y) * a), -1.0)) / y
	else:
		tmp = (x * math.pow(a, (t - 1.0))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -7.2e+145)
		tmp = Float64(Float64(x * (a ^ t)) / y);
	elseif (t <= -1.3e-179)
		tmp = Float64(Float64(x * (Float64(exp(b) * a) ^ -1.0)) / y);
	elseif (t <= 4.2)
		tmp = Float64(Float64(x * (Float64((z ^ Float64(-y)) * a) ^ -1.0)) / y);
	else
		tmp = Float64(Float64(x * (a ^ Float64(t - 1.0))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -7.2e+145)
		tmp = (x * (a ^ t)) / y;
	elseif (t <= -1.3e-179)
		tmp = (x * ((exp(b) * a) ^ -1.0)) / y;
	elseif (t <= 4.2)
		tmp = (x * (((z ^ -y) * a) ^ -1.0)) / y;
	else
		tmp = (x * (a ^ (t - 1.0))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -7.2e+145], N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, -1.3e-179], N[(N[(x * N[Power[N[(N[Exp[b], $MachinePrecision] * a), $MachinePrecision], -1.0], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 4.2], N[(N[(x * N[Power[N[(N[Power[z, (-y)], $MachinePrecision] * a), $MachinePrecision], -1.0], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.19999999999999948e145

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. *-commutative N/A

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

      3. pow-to-exp N/A

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

      4. pow-to-exp N/A

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

      5. lower-*.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 70.8

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

   5. Applied rewrites 70.8%

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

   7. Applied rewrites 70.8%

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

   8. Taylor expanded in y around 0

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

      1. pow-to-exp N/A

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

      2. lift-pow.f64 N/A

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

      3. lift--.f64 88.1

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

   10. Applied rewrites 88.1%

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

   11. Taylor expanded in t around inf

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

   13. Applied rewrites 88.1%

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

   if -7.19999999999999948e145 < t < -1.30000000000000003e-179

   1. Initial program 98.4%

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

   3. Taylor expanded in y around 0

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

      1. div-exp N/A

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

      2. pow-to-exp N/A

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

      3. lower-/.f64 N/A

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

      4. lower-pow.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lower-exp.f64 70.2

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

   5. Applied rewrites 70.2%

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

   6. Taylor expanded in t around 0

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

      1. inv-pow N/A

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

      2. lower-pow.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift-exp.f64 66.8

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

   8. Applied rewrites 66.8%

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

   if -1.30000000000000003e-179 < t < 4.20000000000000018

   1. Initial program 96.8%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. *-commutative N/A

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

      3. pow-to-exp N/A

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

      4. pow-to-exp N/A

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

      5. lower-*.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 71.7

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

   5. Applied rewrites 71.7%

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

   7. Applied rewrites 71.7%

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

   8. Taylor expanded in t around 0

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

      1. inv-pow N/A

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

      2. lower-pow.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

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

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

      7. *-commutative N/A

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

      8. pow-to-exp N/A

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

      9. lower-pow.f64 N/A

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

      10. lift-neg.f64 71.3

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

   10. Applied rewrites 71.3%

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

   if 4.20000000000000018 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. *-commutative N/A

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

      3. pow-to-exp N/A

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

      4. pow-to-exp N/A

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

      5. lower-*.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 66.7

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

   5. Applied rewrites 66.7%

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

   6. Taylor expanded in y around 0

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

      1. pow-to-exp N/A

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

      2. lift-pow.f64 N/A

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

      3. lift--.f64 79.1

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

   8. Applied rewrites 79.1%

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

Alternative 5: 89.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{+98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.16 \cdot 10^{+99}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (/ (pow z y) a)) y)))
   (if (<= y -1.3e+98)
     t_1
     (if (<= y 2.16e+99) (/ (* x (exp (- (* (log a) (- t 1.0)) b))) y) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * (pow(z, y) / a)) / y;
	double tmp;
	if (y <= -1.3e+98) {
		tmp = t_1;
	} else if (y <= 2.16e+99) {
		tmp = (x * exp(((log(a) * (t - 1.0)) - b))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * ((z ** y) / a)) / y
    if (y <= (-1.3d+98)) then
        tmp = t_1
    else if (y <= 2.16d+99) then
        tmp = (x * exp(((log(a) * (t - 1.0d0)) - b))) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * (Math.pow(z, y) / a)) / y;
	double tmp;
	if (y <= -1.3e+98) {
		tmp = t_1;
	} else if (y <= 2.16e+99) {
		tmp = (x * Math.exp(((Math.log(a) * (t - 1.0)) - b))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * (math.pow(z, y) / a)) / y
	tmp = 0
	if y <= -1.3e+98:
		tmp = t_1
	elif y <= 2.16e+99:
		tmp = (x * math.exp(((math.log(a) * (t - 1.0)) - b))) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * Float64((z ^ y) / a)) / y)
	tmp = 0.0
	if (y <= -1.3e+98)
		tmp = t_1;
	elseif (y <= 2.16e+99)
		tmp = Float64(Float64(x * exp(Float64(Float64(log(a) * Float64(t - 1.0)) - b))) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * ((z ^ y) / a)) / y;
	tmp = 0.0;
	if (y <= -1.3e+98)
		tmp = t_1;
	elseif (y <= 2.16e+99)
		tmp = (x * exp(((log(a) * (t - 1.0)) - b))) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -1.3e+98], t$95$1, If[LessEqual[y, 2.16e+99], 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 < -1.3e98 or 2.16e99 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. *-commutative N/A

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

      3. pow-to-exp N/A

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

      4. pow-to-exp N/A

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

      5. lower-*.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 68.4

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

   5. Applied rewrites 68.4%

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

   6. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lift-pow.f64 84.8

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

   8. Applied rewrites 84.8%

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

   if -1.3e98 < y < 2.16e99

   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. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. lower-*.f64 N/A

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

      2. lift-log.f64 N/A

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

      3. lift--.f64 91.6

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

   5. Applied rewrites 91.6%

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

Alternative 6: 81.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{e^{-b}}{y}\\ \mathbf{if}\;b \leq -3.9 \cdot 10^{+92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{+84}:\\ \;\;\;\;\frac{x \cdot \left({z}^{y} \cdot {a}^{\left(t - 1\right)}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (exp (- b)) y))))
   (if (<= b -3.9e+92)
     t_1
     (if (<= b 4.2e+84) (/ (* x (* (pow z y) (pow a (- t 1.0)))) 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 <= -3.9e+92) {
		tmp = t_1;
	} else if (b <= 4.2e+84) {
		tmp = (x * (pow(z, y) * pow(a, (t - 1.0)))) / 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 <= (-3.9d+92)) then
        tmp = t_1
    else if (b <= 4.2d+84) then
        tmp = (x * ((z ** y) * (a ** (t - 1.0d0)))) / 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 <= -3.9e+92) {
		tmp = t_1;
	} else if (b <= 4.2e+84) {
		tmp = (x * (Math.pow(z, y) * Math.pow(a, (t - 1.0)))) / 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 <= -3.9e+92:
		tmp = t_1
	elif b <= 4.2e+84:
		tmp = (x * (math.pow(z, y) * math.pow(a, (t - 1.0)))) / 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 <= -3.9e+92)
		tmp = t_1;
	elseif (b <= 4.2e+84)
		tmp = Float64(Float64(x * Float64((z ^ y) * (a ^ Float64(t - 1.0)))) / 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 <= -3.9e+92)
		tmp = t_1;
	elseif (b <= 4.2e+84)
		tmp = (x * ((z ^ y) * (a ^ (t - 1.0)))) / 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, -3.9e+92], t$95$1, If[LessEqual[b, 4.2e+84], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] * N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -3.90000000000000011e92 or 4.20000000000000037e84 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 84.3

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

   5. Applied rewrites 84.3%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 84.3

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

   7. Applied rewrites 84.3%

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

   if -3.90000000000000011e92 < b < 4.20000000000000037e84

   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. Add Preprocessing

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. *-commutative N/A

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

      3. pow-to-exp N/A

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

      4. pow-to-exp N/A

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

      5. lower-*.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 80.6

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

   5. Applied rewrites 80.6%

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

Alternative 7: 81.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{e^{-b}}{y}\\ \mathbf{if}\;b \leq -2.5 \cdot 10^{+101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{+84}:\\ \;\;\;\;x \cdot \frac{{z}^{y} \cdot {a}^{\left(t - 1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (exp (- b)) y))))
   (if (<= b -2.5e+101)
     t_1
     (if (<= b 4.2e+84) (* x (/ (* (pow z y) (pow a (- t 1.0))) y)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (exp(-b) / y);
	double tmp;
	if (b <= -2.5e+101) {
		tmp = t_1;
	} else if (b <= 4.2e+84) {
		tmp = x * ((pow(z, y) * pow(a, (t - 1.0))) / 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 <= (-2.5d+101)) then
        tmp = t_1
    else if (b <= 4.2d+84) then
        tmp = x * (((z ** y) * (a ** (t - 1.0d0))) / 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 <= -2.5e+101) {
		tmp = t_1;
	} else if (b <= 4.2e+84) {
		tmp = x * ((Math.pow(z, y) * Math.pow(a, (t - 1.0))) / 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 <= -2.5e+101:
		tmp = t_1
	elif b <= 4.2e+84:
		tmp = x * ((math.pow(z, y) * math.pow(a, (t - 1.0))) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(exp(Float64(-b)) / y))
	tmp = 0.0
	if (b <= -2.5e+101)
		tmp = t_1;
	elseif (b <= 4.2e+84)
		tmp = Float64(x * Float64(Float64((z ^ y) * (a ^ Float64(t - 1.0))) / 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 <= -2.5e+101)
		tmp = t_1;
	elseif (b <= 4.2e+84)
		tmp = x * (((z ^ y) * (a ^ (t - 1.0))) / 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, -2.5e+101], t$95$1, If[LessEqual[b, 4.2e+84], N[(x * N[(N[(N[Power[z, y], $MachinePrecision] * N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.49999999999999994e101 or 4.20000000000000037e84 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 84.7

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

   5. Applied rewrites 84.7%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 84.7

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

   7. Applied rewrites 84.7%

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

   if -2.49999999999999994e101 < b < 4.20000000000000037e84

   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. Add Preprocessing

   3. Taylor expanded in b around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. exp-sum N/A

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

      5. *-commutative N/A

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

      6. pow-to-exp N/A

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

      7. pow-to-exp N/A

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

      8. lower-*.f64 N/A

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

      9. lower-pow.f64 N/A

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

      10. lower-pow.f64 N/A

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

      11. lift--.f64 79.9

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

   5. Applied rewrites 79.9%

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

Alternative 8: 74.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+145}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y}\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-179}:\\ \;\;\;\;\frac{x \cdot {\left(e^{b} \cdot a\right)}^{-1}}{y}\\ \mathbf{elif}\;t \leq 4.2:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t - 1\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -7.2e+145)
   (/ (* x (pow a t)) y)
   (if (<= t -1.3e-179)
     (/ (* x (pow (* (exp b) a) -1.0)) y)
     (if (<= t 4.2)
       (/ (* x (/ (pow z y) a)) y)
       (/ (* x (pow a (- t 1.0))) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7.2e+145) {
		tmp = (x * pow(a, t)) / y;
	} else if (t <= -1.3e-179) {
		tmp = (x * pow((exp(b) * a), -1.0)) / y;
	} else if (t <= 4.2) {
		tmp = (x * (pow(z, y) / a)) / y;
	} else {
		tmp = (x * pow(a, (t - 1.0))) / y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-7.2d+145)) then
        tmp = (x * (a ** t)) / y
    else if (t <= (-1.3d-179)) then
        tmp = (x * ((exp(b) * a) ** (-1.0d0))) / y
    else if (t <= 4.2d0) then
        tmp = (x * ((z ** y) / a)) / y
    else
        tmp = (x * (a ** (t - 1.0d0))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7.2e+145) {
		tmp = (x * Math.pow(a, t)) / y;
	} else if (t <= -1.3e-179) {
		tmp = (x * Math.pow((Math.exp(b) * a), -1.0)) / y;
	} else if (t <= 4.2) {
		tmp = (x * (Math.pow(z, y) / a)) / y;
	} else {
		tmp = (x * Math.pow(a, (t - 1.0))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -7.2e+145:
		tmp = (x * math.pow(a, t)) / y
	elif t <= -1.3e-179:
		tmp = (x * math.pow((math.exp(b) * a), -1.0)) / y
	elif t <= 4.2:
		tmp = (x * (math.pow(z, y) / a)) / y
	else:
		tmp = (x * math.pow(a, (t - 1.0))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -7.2e+145)
		tmp = Float64(Float64(x * (a ^ t)) / y);
	elseif (t <= -1.3e-179)
		tmp = Float64(Float64(x * (Float64(exp(b) * a) ^ -1.0)) / y);
	elseif (t <= 4.2)
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	else
		tmp = Float64(Float64(x * (a ^ Float64(t - 1.0))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -7.2e+145)
		tmp = (x * (a ^ t)) / y;
	elseif (t <= -1.3e-179)
		tmp = (x * ((exp(b) * a) ^ -1.0)) / y;
	elseif (t <= 4.2)
		tmp = (x * ((z ^ y) / a)) / y;
	else
		tmp = (x * (a ^ (t - 1.0))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -7.2e+145], N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, -1.3e-179], N[(N[(x * N[Power[N[(N[Exp[b], $MachinePrecision] * a), $MachinePrecision], -1.0], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 4.2], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.19999999999999948e145

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. *-commutative N/A

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

      3. pow-to-exp N/A

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

      4. pow-to-exp N/A

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

      5. lower-*.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 70.8

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

   5. Applied rewrites 70.8%

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

   7. Applied rewrites 70.8%

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

   8. Taylor expanded in y around 0

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

      1. pow-to-exp N/A

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

      2. lift-pow.f64 N/A

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

      3. lift--.f64 88.1

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

   10. Applied rewrites 88.1%

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

   11. Taylor expanded in t around inf

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

   13. Applied rewrites 88.1%

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

   if -7.19999999999999948e145 < t < -1.30000000000000003e-179

   1. Initial program 98.4%

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

   3. Taylor expanded in y around 0

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

      1. div-exp N/A

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

      2. pow-to-exp N/A

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

      3. lower-/.f64 N/A

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

      4. lower-pow.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lower-exp.f64 70.2

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

   5. Applied rewrites 70.2%

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

   6. Taylor expanded in t around 0

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

      1. inv-pow N/A

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

      2. lower-pow.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lift-exp.f64 66.8

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

   8. Applied rewrites 66.8%

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

   if -1.30000000000000003e-179 < t < 4.20000000000000018

   1. Initial program 96.8%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. *-commutative N/A

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

      3. pow-to-exp N/A

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

      4. pow-to-exp N/A

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

      5. lower-*.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 71.7

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

   5. Applied rewrites 71.7%

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

   6. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lift-pow.f64 71.3

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

   8. Applied rewrites 71.3%

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

   if 4.20000000000000018 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. *-commutative N/A

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

      3. pow-to-exp N/A

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

      4. pow-to-exp N/A

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

      5. lower-*.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 66.7

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

   5. Applied rewrites 66.7%

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

   6. Taylor expanded in y around 0

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

      1. pow-to-exp N/A

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

      2. lift-pow.f64 N/A

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

      3. lift--.f64 79.1

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

   8. Applied rewrites 79.1%

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

Alternative 9: 74.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+145}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y}\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-179}:\\ \;\;\;\;\frac{x \cdot e^{\left(-\log a\right) - b}}{y}\\ \mathbf{elif}\;t \leq 4.2:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t - 1\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -7.2e+145)
   (/ (* x (pow a t)) y)
   (if (<= t -1.3e-179)
     (/ (* x (exp (- (- (log a)) b))) y)
     (if (<= t 4.2)
       (/ (* x (/ (pow z y) a)) y)
       (/ (* x (pow a (- t 1.0))) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7.2e+145) {
		tmp = (x * pow(a, t)) / y;
	} else if (t <= -1.3e-179) {
		tmp = (x * exp((-log(a) - b))) / y;
	} else if (t <= 4.2) {
		tmp = (x * (pow(z, y) / a)) / y;
	} else {
		tmp = (x * pow(a, (t - 1.0))) / y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-7.2d+145)) then
        tmp = (x * (a ** t)) / y
    else if (t <= (-1.3d-179)) then
        tmp = (x * exp((-log(a) - b))) / y
    else if (t <= 4.2d0) then
        tmp = (x * ((z ** y) / a)) / y
    else
        tmp = (x * (a ** (t - 1.0d0))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7.2e+145) {
		tmp = (x * Math.pow(a, t)) / y;
	} else if (t <= -1.3e-179) {
		tmp = (x * Math.exp((-Math.log(a) - b))) / y;
	} else if (t <= 4.2) {
		tmp = (x * (Math.pow(z, y) / a)) / y;
	} else {
		tmp = (x * Math.pow(a, (t - 1.0))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -7.2e+145:
		tmp = (x * math.pow(a, t)) / y
	elif t <= -1.3e-179:
		tmp = (x * math.exp((-math.log(a) - b))) / y
	elif t <= 4.2:
		tmp = (x * (math.pow(z, y) / a)) / y
	else:
		tmp = (x * math.pow(a, (t - 1.0))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -7.2e+145)
		tmp = Float64(Float64(x * (a ^ t)) / y);
	elseif (t <= -1.3e-179)
		tmp = Float64(Float64(x * exp(Float64(Float64(-log(a)) - b))) / y);
	elseif (t <= 4.2)
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	else
		tmp = Float64(Float64(x * (a ^ Float64(t - 1.0))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -7.2e+145)
		tmp = (x * (a ^ t)) / y;
	elseif (t <= -1.3e-179)
		tmp = (x * exp((-log(a) - b))) / y;
	elseif (t <= 4.2)
		tmp = (x * ((z ^ y) / a)) / y;
	else
		tmp = (x * (a ^ (t - 1.0))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -7.2e+145], N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, -1.3e-179], N[(N[(x * N[Exp[N[((-N[Log[a], $MachinePrecision]) - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 4.2], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.19999999999999948e145

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. *-commutative N/A

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

      3. pow-to-exp N/A

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

      4. pow-to-exp N/A

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

      5. lower-*.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 70.8

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

   5. Applied rewrites 70.8%

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

   7. Applied rewrites 70.8%

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

   8. Taylor expanded in y around 0

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

      1. pow-to-exp N/A

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

      2. lift-pow.f64 N/A

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

      3. lift--.f64 88.1

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

   10. Applied rewrites 88.1%

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

   11. Taylor expanded in t around inf

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

   13. Applied rewrites 88.1%

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

   if -7.19999999999999948e145 < t < -1.30000000000000003e-179

   1. Initial program 98.4%

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

   3. Taylor expanded in y around 0

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

      1. lower-*.f64 N/A

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

      2. lift-log.f64 N/A

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

      3. lift--.f64 79.2

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

   5. Applied rewrites 79.2%

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

   6. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. lift-log.f64 66.2

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

   8. Applied rewrites 66.2%

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

   if -1.30000000000000003e-179 < t < 4.20000000000000018

   1. Initial program 96.8%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. *-commutative N/A

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

      3. pow-to-exp N/A

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

      4. pow-to-exp N/A

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

      5. lower-*.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 71.7

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

   5. Applied rewrites 71.7%

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

   6. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lift-pow.f64 71.3

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

   8. Applied rewrites 71.3%

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

   if 4.20000000000000018 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. *-commutative N/A

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

      3. pow-to-exp N/A

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

      4. pow-to-exp N/A

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

      5. lower-*.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 66.7

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

   5. Applied rewrites 66.7%

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

   6. Taylor expanded in y around 0

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

      1. pow-to-exp N/A

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

      2. lift-pow.f64 N/A

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

      3. lift--.f64 79.1

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

   8. Applied rewrites 79.1%

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

Alternative 10: 73.7% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{if}\;y \leq -7.2 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+16}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t - 1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (/ (pow z y) a)) y)))
   (if (<= y -7.2e+96)
     t_1
     (if (<= y 4.2e+16) (/ (* x (pow a (- t 1.0))) y) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * (pow(z, y) / a)) / y;
	double tmp;
	if (y <= -7.2e+96) {
		tmp = t_1;
	} else if (y <= 4.2e+16) {
		tmp = (x * pow(a, (t - 1.0))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * ((z ** y) / a)) / y
    if (y <= (-7.2d+96)) then
        tmp = t_1
    else if (y <= 4.2d+16) then
        tmp = (x * (a ** (t - 1.0d0))) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * (Math.pow(z, y) / a)) / y;
	double tmp;
	if (y <= -7.2e+96) {
		tmp = t_1;
	} else if (y <= 4.2e+16) {
		tmp = (x * Math.pow(a, (t - 1.0))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * (math.pow(z, y) / a)) / y
	tmp = 0
	if y <= -7.2e+96:
		tmp = t_1
	elif y <= 4.2e+16:
		tmp = (x * math.pow(a, (t - 1.0))) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * Float64((z ^ y) / a)) / y)
	tmp = 0.0
	if (y <= -7.2e+96)
		tmp = t_1;
	elseif (y <= 4.2e+16)
		tmp = Float64(Float64(x * (a ^ Float64(t - 1.0))) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * ((z ^ y) / a)) / y;
	tmp = 0.0;
	if (y <= -7.2e+96)
		tmp = t_1;
	elseif (y <= 4.2e+16)
		tmp = (x * (a ^ (t - 1.0))) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -7.2e+96], t$95$1, If[LessEqual[y, 4.2e+16], N[(N[(x * N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -7.20000000000000026e96 or 4.2e16 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. *-commutative N/A

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

      3. pow-to-exp N/A

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

      4. pow-to-exp N/A

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

      5. lower-*.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 67.1

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

   5. Applied rewrites 67.1%

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

   6. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lift-pow.f64 82.0

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

   8. Applied rewrites 82.0%

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

   if -7.20000000000000026e96 < y < 4.2e16

   1. Initial program 97.5%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. *-commutative N/A

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

      3. pow-to-exp N/A

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

      4. pow-to-exp N/A

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

      5. lower-*.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 70.2

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

   5. Applied rewrites 70.2%

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

   6. Taylor expanded in y around 0

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

      1. pow-to-exp N/A

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

      2. lift-pow.f64 N/A

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

      3. lift--.f64 68.1

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

   8. Applied rewrites 68.1%

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

Alternative 11: 75.3% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{e^{-b}}{y}\\ \mathbf{if}\;b \leq -3.8 \cdot 10^{+92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 750:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t - 1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (exp (- b)) y))))
   (if (<= b -3.8e+92)
     t_1
     (if (<= b 750.0) (/ (* x (pow a (- t 1.0))) 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 <= -3.8e+92) {
		tmp = t_1;
	} else if (b <= 750.0) {
		tmp = (x * pow(a, (t - 1.0))) / 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 <= (-3.8d+92)) then
        tmp = t_1
    else if (b <= 750.0d0) then
        tmp = (x * (a ** (t - 1.0d0))) / 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 <= -3.8e+92) {
		tmp = t_1;
	} else if (b <= 750.0) {
		tmp = (x * Math.pow(a, (t - 1.0))) / 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 <= -3.8e+92:
		tmp = t_1
	elif b <= 750.0:
		tmp = (x * math.pow(a, (t - 1.0))) / 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 <= -3.8e+92)
		tmp = t_1;
	elseif (b <= 750.0)
		tmp = Float64(Float64(x * (a ^ Float64(t - 1.0))) / 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 <= -3.8e+92)
		tmp = t_1;
	elseif (b <= 750.0)
		tmp = (x * (a ^ (t - 1.0))) / 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, -3.8e+92], t$95$1, If[LessEqual[b, 750.0], N[(N[(x * N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -3.8e92 or 750 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 81.9

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

   5. Applied rewrites 81.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 81.9

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

   7. Applied rewrites 81.9%

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

   if -3.8e92 < b < 750

   1. Initial program 97.4%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. *-commutative N/A

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

      3. pow-to-exp N/A

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

      4. pow-to-exp N/A

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

      5. lower-*.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 82.8

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

   5. Applied rewrites 82.8%

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

   6. Taylor expanded in y around 0

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

      1. pow-to-exp N/A

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

      2. lift-pow.f64 N/A

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

      3. lift--.f64 70.5

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

   8. Applied rewrites 70.5%

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

Alternative 12: 35.4% accurate, 9.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 6 \cdot 10^{-37}:\\ \;\;\;\;\frac{\frac{x - b \cdot x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{1}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 6e-37) (/ (/ (- x (* b x)) a) y) (* x (/ (/ 1.0 a) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 6e-37) {
		tmp = ((x - (b * x)) / a) / y;
	} else {
		tmp = x * ((1.0 / a) / y);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 6d-37) then
        tmp = ((x - (b * x)) / a) / y
    else
        tmp = x * ((1.0d0 / a) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 6e-37) {
		tmp = ((x - (b * x)) / a) / y;
	} else {
		tmp = x * ((1.0 / a) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 6e-37:
		tmp = ((x - (b * x)) / a) / y
	else:
		tmp = x * ((1.0 / a) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 6e-37)
		tmp = Float64(Float64(Float64(x - Float64(b * x)) / a) / y);
	else
		tmp = Float64(x * Float64(Float64(1.0 / a) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 6e-37)
		tmp = ((x - (b * x)) / a) / y;
	else
		tmp = x * ((1.0 / a) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 6e-37], N[(N[(N[(x - N[(b * x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], N[(x * N[(N[(1.0 / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 6e-37

   1. Initial program 98.0%

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

   3. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

   5. Applied rewrites 63.5%

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

   6. Taylor expanded in t around 0

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

      1. sub-div N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-pow.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lift-pow.f64 61.0

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

   8. Applied rewrites 61.0%

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

   9. Taylor expanded in y around 0

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

       1. lower--.f64 N/A

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

       2. lower-*.f64 40.9

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

   11. Applied rewrites 40.9%

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

   if 6e-37 < b

   1. Initial program 99.6%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. *-commutative N/A

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

      3. pow-to-exp N/A

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

      4. pow-to-exp N/A

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

      5. lower-*.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 54.2

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

   5. Applied rewrites 54.2%

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

   6. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lift-pow.f64 46.6

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

   8. Applied rewrites 46.6%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 22.5%

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

       1. lift-/.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. associate-/l* N/A

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

       4. lower-*.f64 N/A

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

       5. lower-/.f64 20.9

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

   13. Applied rewrites 20.9%

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

Alternative 13: 31.6% accurate, 9.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 2.2 \cdot 10^{-161}:\\ \;\;\;\;\frac{x \cdot \frac{1}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{1}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 2.2e-161) (/ (* x (/ 1.0 a)) y) (* x (/ (/ 1.0 a) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 2.2e-161) {
		tmp = (x * (1.0 / a)) / y;
	} else {
		tmp = x * ((1.0 / a) / y);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= 2.2d-161) then
        tmp = (x * (1.0d0 / a)) / y
    else
        tmp = x * ((1.0d0 / a) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 2.2e-161) {
		tmp = (x * (1.0 / a)) / y;
	} else {
		tmp = x * ((1.0 / a) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 2.2e-161:
		tmp = (x * (1.0 / a)) / y
	else:
		tmp = x * ((1.0 / a) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 2.2e-161)
		tmp = Float64(Float64(x * Float64(1.0 / a)) / y);
	else
		tmp = Float64(x * Float64(Float64(1.0 / a) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 2.2e-161)
		tmp = (x * (1.0 / a)) / y;
	else
		tmp = x * ((1.0 / a) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 2.2e-161], N[(N[(x * N[(1.0 / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x * N[(N[(1.0 / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 2.20000000000000002e-161

   1. Initial program 99.5%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. *-commutative N/A

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

      3. pow-to-exp N/A

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

      4. pow-to-exp N/A

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

      5. lower-*.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 71.9

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

   5. Applied rewrites 71.9%

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

   6. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lift-pow.f64 63.8

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

   8. Applied rewrites 63.8%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 36.5%

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

   if 2.20000000000000002e-161 < 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. Add Preprocessing

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. *-commutative N/A

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

      3. pow-to-exp N/A

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

      4. pow-to-exp N/A

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

      5. lower-*.f64 N/A

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

      6. lower-pow.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 68.0

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

   5. Applied rewrites 68.0%

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

   6. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lift-pow.f64 57.7

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

   8. Applied rewrites 57.7%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 29.0%

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

       1. lift-/.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. associate-/l* N/A

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

       4. lower-*.f64 N/A

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

       5. lower-/.f64 30.0

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

   13. Applied rewrites 30.0%

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

Alternative 14: 30.5% accurate, 12.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.5%

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

3. Taylor expanded in b around 0

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

   1. exp-sum N/A

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

   2. *-commutative N/A

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

   3. pow-to-exp N/A

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

   4. pow-to-exp N/A

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

   5. lower-*.f64 N/A

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

   6. lower-pow.f64 N/A

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

   7. lower-pow.f64 N/A

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

   8. lift--.f64 69.0

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

5. Applied rewrites 69.0%

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

6. Taylor expanded in t around 0

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

   1. lower-/.f64 N/A

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

   2. lift-pow.f64 59.2

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

8. Applied rewrites 59.2%

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

9. Taylor expanded in y around 0

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

11. Applied rewrites 30.9%

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

    1. lift-/.f64 N/A

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

    2. lift-*.f64 N/A

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

    3. associate-/l* N/A

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

    4. lower-*.f64 N/A

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

    5. lower-/.f64 30.5

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

13. Applied rewrites 30.5%

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

Developer Target 1: 71.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a ** (t - 1.0d0)
    t_2 = (x * (t_1 / y)) / ((b + 1.0d0) - (y * log(z)))
    if (t < (-0.8845848504127471d0)) then
        tmp = t_2
    else if (t < 852031.2288374073d0) then
        tmp = ((x / y) * t_1) / exp((b - (log(z) * y)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

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

Python

def code(x, y, z, t, a, b):
	t_1 = math.pow(a, (t - 1.0))
	t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * math.log(z)))
	tmp = 0
	if t < -0.8845848504127471:
		tmp = t_2
	elif t < 852031.2288374073:
		tmp = ((x / y) * t_1) / math.exp((b - (math.log(z) * y)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = a ^ Float64(t - 1.0)
	t_2 = Float64(Float64(x * Float64(t_1 / y)) / Float64(Float64(b + 1.0) - Float64(y * log(z))))
	tmp = 0.0
	if (t < -0.8845848504127471)
		tmp = t_2;
	elseif (t < 852031.2288374073)
		tmp = Float64(Float64(Float64(x / y) * t_1) / exp(Float64(b - Float64(log(z) * y))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a ^ (t - 1.0);
	t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * log(z)));
	tmp = 0.0;
	if (t < -0.8845848504127471)
		tmp = t_2;
	elseif (t < 852031.2288374073)
		tmp = ((x / y) * t_1) / exp((b - (log(z) * y)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision] / N[(N[(b + 1.0), $MachinePrecision] - N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -0.8845848504127471], t$95$2, If[Less[t, 852031.2288374073], N[(N[(N[(x / y), $MachinePrecision] * t$95$1), $MachinePrecision] / N[Exp[N[(b - N[(N[Log[z], $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2025089 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -8845848504127471/10000000000000000) (/ (* x (/ (pow a (- t 1)) y)) (- (+ b 1) (* y (log z)))) (if (< t 8520312288374073/10000000000) (/ (* (/ x y) (pow a (- t 1))) (exp (- b (* (log z) y)))) (/ (* x (/ (pow a (- t 1)) y)) (- (+ b 1) (* y (log z)))))))

  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))