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

Percentage Accurate: 98.7% → 98.7%

Time: 9.0s

Alternatives: 16

Speedup: 1.0×

• 48.0% 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: 98.7% 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: 98.7% 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 97.1%

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

Alternative 2: 59.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - 1\right) \cdot \log a\\ t_2 := x \cdot \frac{{a}^{t}}{y}\\ \mathbf{if}\;t\_1 \leq -610:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -5:\\ \;\;\;\;x \cdot {\left(\mathsf{fma}\left(b, y, y\right) \cdot a\right)}^{-1}\\ \mathbf{elif}\;t\_1 \leq 1000:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 -610.0)
     t_2
     (if (<= t_1 -5.0)
       (* x (pow (* (fma b y y) a) -1.0))
       (if (<= t_1 1000.0) (/ (/ 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 <= -610.0) {
		tmp = t_2;
	} else if (t_1 <= -5.0) {
		tmp = x * pow((fma(b, y, y) * a), -1.0);
	} else if (t_1 <= 1000.0) {
		tmp = (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(x * Float64((a ^ t) / y))
	tmp = 0.0
	if (t_1 <= -610.0)
		tmp = t_2;
	elseif (t_1 <= -5.0)
		tmp = Float64(x * (Float64(fma(b, y, y) * a) ^ -1.0));
	elseif (t_1 <= 1000.0)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = t_2;
	end
	return 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[(x * N[(N[Power[a, t], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -610.0], t$95$2, If[LessEqual[t$95$1, -5.0], N[(x * N[Power[N[(N[(b * y + y), $MachinePrecision] * a), $MachinePrecision], -1.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1000.0], N[(N[(x / 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)) < -610 or 1e3 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. 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 66.4

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

   5. Applied rewrites 66.4%

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

   6. Taylor expanded in y around 0

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

      1. pow-to-exp N/A

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

      2. lift-pow.f64 N/A

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

      3. lift--.f64 69.8

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

   8. Applied rewrites 69.8%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 70.5%

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

   if -610 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -5

   1. Initial program 86.9%

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

   3. Taylor expanded in y around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. div-exp N/A

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

      5. pow-to-exp N/A

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

      6. lower-/.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower-exp.f64 74.6

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

   5. Applied rewrites 74.6%

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

   6. Taylor expanded in t around 0

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

      1. inv-pow N/A

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

      2. lower-pow.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lift-exp.f64 74.6

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

   8. Applied rewrites 74.6%

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

   9. Taylor expanded in b around 0

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

       1. +-commutative N/A

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

       2. lower-fma.f64 53.2

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

   11. Applied rewrites 53.2%

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

   if -5 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 1e3

   1. Initial program 98.8%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. 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 74.6

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

   5. Applied rewrites 74.6%

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

      1. lift--.f64 N/A

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

      2. lift-pow.f64 N/A

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

      3. pow-sub N/A

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

      4. unpow1 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-pow.f64 74.6

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

   7. Applied rewrites 74.6%

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

   8. Taylor expanded in y around 0

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

      1. associate-/r* N/A

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

      2. lower-/.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lift-pow.f64 N/A

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

      6. lift-/.f64 32.7

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

   10. Applied rewrites 32.7%

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

   11. Taylor expanded in t around 0

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

       1. lower-/.f64 32.6

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

   13. Applied rewrites 32.6%

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

Alternative 3: 88.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+46} \lor \neg \left(y \leq 4200000000000\right):\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.1e+46) (not (<= y 4200000000000.0)))
   (* x (/ (/ (pow z y) a) y))
   (/ (* x (exp (- (* (log a) (- t 1.0)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.1e+46) || !(y <= 4200000000000.0)) {
		tmp = x * ((pow(z, y) / a) / y);
	} else {
		tmp = (x * exp(((log(a) * (t - 1.0)) - b))) / y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-2.1d+46)) .or. (.not. (y <= 4200000000000.0d0))) then
        tmp = x * (((z ** y) / a) / y)
    else
        tmp = (x * exp(((log(a) * (t - 1.0d0)) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.1e+46) || !(y <= 4200000000000.0)) {
		tmp = x * ((Math.pow(z, y) / a) / y);
	} else {
		tmp = (x * Math.exp(((Math.log(a) * (t - 1.0)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.1e+46) or not (y <= 4200000000000.0):
		tmp = x * ((math.pow(z, y) / a) / y)
	else:
		tmp = (x * math.exp(((math.log(a) * (t - 1.0)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.1e+46) || !(y <= 4200000000000.0))
		tmp = Float64(x * Float64(Float64((z ^ y) / a) / y));
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(log(a) * Float64(t - 1.0)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.1e+46) || ~((y <= 4200000000000.0)))
		tmp = x * (((z ^ y) / a) / y);
	else
		tmp = (x * exp(((log(a) * (t - 1.0)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.1e+46], N[Not[LessEqual[y, 4200000000000.0]], $MachinePrecision]], N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[Log[a], $MachinePrecision] * N[(t - 1.0), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.1e46 or 4.2e12 < 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

      \[\leadsto \color{blue}{\frac{x \cdot e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}}{y}} \]
   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 74.7

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

   5. Applied rewrites 74.7%

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

   6. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lift-pow.f64 91.4

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

   8. Applied rewrites 91.4%

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

   if -2.1e46 < y < 4.2e12

   1. Initial program 94.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   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 91.8

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

   5. Applied rewrites 91.8%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+46} \lor \neg \left(y \leq 4200000000000\right):\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{+27}:\\ \;\;\;\;x \cdot \frac{e^{-b}}{y}\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-15}:\\ \;\;\;\;x \cdot \frac{{z}^{y} \cdot {a}^{\left(t - 1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(e^{b} \cdot y\right) \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.15e+27)
   (* x (/ (exp (- b)) y))
   (if (<= b 3e-15)
     (* x (/ (* (pow z y) (pow a (- t 1.0))) y))
     (/ x (* (* (exp b) y) a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.15e+27) {
		tmp = x * (exp(-b) / y);
	} else if (b <= 3e-15) {
		tmp = x * ((pow(z, y) * pow(a, (t - 1.0))) / y);
	} else {
		tmp = x / ((exp(b) * y) * a);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.15d+27)) then
        tmp = x * (exp(-b) / y)
    else if (b <= 3d-15) then
        tmp = x * (((z ** y) * (a ** (t - 1.0d0))) / y)
    else
        tmp = x / ((exp(b) * y) * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.15e+27) {
		tmp = x * (Math.exp(-b) / y);
	} else if (b <= 3e-15) {
		tmp = x * ((Math.pow(z, y) * Math.pow(a, (t - 1.0))) / y);
	} else {
		tmp = x / ((Math.exp(b) * y) * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.15e+27:
		tmp = x * (math.exp(-b) / y)
	elif b <= 3e-15:
		tmp = x * ((math.pow(z, y) * math.pow(a, (t - 1.0))) / y)
	else:
		tmp = x / ((math.exp(b) * y) * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.15e+27)
		tmp = Float64(x * Float64(exp(Float64(-b)) / y));
	elseif (b <= 3e-15)
		tmp = Float64(x * Float64(Float64((z ^ y) * (a ^ Float64(t - 1.0))) / y));
	else
		tmp = Float64(x / Float64(Float64(exp(b) * y) * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.15e+27)
		tmp = x * (exp(-b) / y);
	elseif (b <= 3e-15)
		tmp = x * (((z ^ y) * (a ^ (t - 1.0))) / y);
	else
		tmp = x / ((exp(b) * y) * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.15e+27], N[(x * N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3e-15], N[(x * N[(N[(N[Power[z, y], $MachinePrecision] * N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(N[Exp[b], $MachinePrecision] * y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.15e27

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 85.2

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

   5. Applied rewrites 85.2%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 85.2

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

   7. Applied rewrites 85.2%

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

   if -1.15e27 < b < 3e-15

   1. Initial program 94.6%

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

   3. Taylor expanded in b around 0

      \[\leadsto \color{blue}{\frac{x \cdot e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}}{y}} \]
   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 84.3

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

   5. Applied rewrites 84.3%

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

   if 3e-15 < b

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. div-exp N/A

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

      5. pow-to-exp N/A

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

      6. lower-/.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower-exp.f64 67.3

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

   5. Applied rewrites 67.3%

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

   6. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-exp.f64 84.7

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

   8. Applied rewrites 84.7%

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

Alternative 5: 80.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{+27}:\\ \;\;\;\;x \cdot \frac{e^{-b}}{y}\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-15}:\\ \;\;\;\;x \cdot \left({z}^{y} \cdot \frac{{a}^{\left(t - 1\right)}}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(e^{b} \cdot y\right) \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.15e+27)
   (* x (/ (exp (- b)) y))
   (if (<= b 3e-15)
     (* x (* (pow z y) (/ (pow a (- t 1.0)) y)))
     (/ x (* (* (exp b) y) a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.15e+27) {
		tmp = x * (exp(-b) / y);
	} else if (b <= 3e-15) {
		tmp = x * (pow(z, y) * (pow(a, (t - 1.0)) / y));
	} else {
		tmp = x / ((exp(b) * y) * a);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.15d+27)) then
        tmp = x * (exp(-b) / y)
    else if (b <= 3d-15) then
        tmp = x * ((z ** y) * ((a ** (t - 1.0d0)) / y))
    else
        tmp = x / ((exp(b) * y) * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.15e+27) {
		tmp = x * (Math.exp(-b) / y);
	} else if (b <= 3e-15) {
		tmp = x * (Math.pow(z, y) * (Math.pow(a, (t - 1.0)) / y));
	} else {
		tmp = x / ((Math.exp(b) * y) * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.15e+27:
		tmp = x * (math.exp(-b) / y)
	elif b <= 3e-15:
		tmp = x * (math.pow(z, y) * (math.pow(a, (t - 1.0)) / y))
	else:
		tmp = x / ((math.exp(b) * y) * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.15e+27)
		tmp = Float64(x * Float64(exp(Float64(-b)) / y));
	elseif (b <= 3e-15)
		tmp = Float64(x * Float64((z ^ y) * Float64((a ^ Float64(t - 1.0)) / y)));
	else
		tmp = Float64(x / Float64(Float64(exp(b) * y) * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.15e+27)
		tmp = x * (exp(-b) / y);
	elseif (b <= 3e-15)
		tmp = x * ((z ^ y) * ((a ^ (t - 1.0)) / y));
	else
		tmp = x / ((exp(b) * y) * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.15e+27], N[(x * N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3e-15], N[(x * N[(N[Power[z, y], $MachinePrecision] * N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(N[Exp[b], $MachinePrecision] * y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.15e27

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 85.2

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

   5. Applied rewrites 85.2%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 85.2

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

   7. Applied rewrites 85.2%

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

   if -1.15e27 < b < 3e-15

   1. Initial program 94.6%

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

   3. Taylor expanded in b around 0

      \[\leadsto \color{blue}{\frac{x \cdot e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}}{y}} \]
   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 84.3

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

   5. Applied rewrites 84.3%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-pow.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-pow.f64 N/A

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

      6. pow-to-exp N/A

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

      7. associate-/l* N/A

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

      8. lower-*.f64 N/A

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

      9. lift-pow.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. pow-to-exp N/A

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

      12. lift-pow.f64 N/A

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

      13. lift--.f64 81.4

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

   7. Applied rewrites 81.4%

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

   if 3e-15 < b

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. div-exp N/A

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

      5. pow-to-exp N/A

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

      6. lower-/.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower-exp.f64 67.3

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

   5. Applied rewrites 67.3%

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

   6. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-exp.f64 84.7

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

   8. Applied rewrites 84.7%

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

Alternative 6: 75.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{if}\;y \leq -1.55 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-173}:\\ \;\;\;\;x \cdot {\left(\left(e^{b} \cdot y\right) \cdot a\right)}^{-1}\\ \mathbf{elif}\;y \leq 7.1 \cdot 10^{-6}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (/ (pow z y) a) y))))
   (if (<= y -1.55e+18)
     t_1
     (if (<= y 1.6e-173)
       (* x (pow (* (* (exp b) y) a) -1.0))
       (if (<= y 7.1e-6) (/ (* (pow a (- t 1.0)) x) 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 <= -1.55e+18) {
		tmp = t_1;
	} else if (y <= 1.6e-173) {
		tmp = x * pow(((exp(b) * y) * a), -1.0);
	} else if (y <= 7.1e-6) {
		tmp = (pow(a, (t - 1.0)) * x) / 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 <= (-1.55d+18)) then
        tmp = t_1
    else if (y <= 1.6d-173) then
        tmp = x * (((exp(b) * y) * a) ** (-1.0d0))
    else if (y <= 7.1d-6) then
        tmp = ((a ** (t - 1.0d0)) * x) / 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 <= -1.55e+18) {
		tmp = t_1;
	} else if (y <= 1.6e-173) {
		tmp = x * Math.pow(((Math.exp(b) * y) * a), -1.0);
	} else if (y <= 7.1e-6) {
		tmp = (Math.pow(a, (t - 1.0)) * x) / 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 <= -1.55e+18:
		tmp = t_1
	elif y <= 1.6e-173:
		tmp = x * math.pow(((math.exp(b) * y) * a), -1.0)
	elif y <= 7.1e-6:
		tmp = (math.pow(a, (t - 1.0)) * x) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(Float64((z ^ y) / a) / y))
	tmp = 0.0
	if (y <= -1.55e+18)
		tmp = t_1;
	elseif (y <= 1.6e-173)
		tmp = Float64(x * (Float64(Float64(exp(b) * y) * a) ^ -1.0));
	elseif (y <= 7.1e-6)
		tmp = Float64(Float64((a ^ Float64(t - 1.0)) * x) / 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 <= -1.55e+18)
		tmp = t_1;
	elseif (y <= 1.6e-173)
		tmp = x * (((exp(b) * y) * a) ^ -1.0);
	elseif (y <= 7.1e-6)
		tmp = ((a ^ (t - 1.0)) * x) / 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[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.55e+18], t$95$1, If[LessEqual[y, 1.6e-173], N[(x * N[Power[N[(N[(N[Exp[b], $MachinePrecision] * y), $MachinePrecision] * a), $MachinePrecision], -1.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.1e-6], N[(N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.55e18 or 7.0999999999999998e-6 < y

   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

      \[\leadsto \color{blue}{\frac{x \cdot e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}}{y}} \]
   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 71.3

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

   5. Applied rewrites 71.3%

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

   6. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lift-pow.f64 87.4

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

   8. Applied rewrites 87.4%

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

   if -1.55e18 < y < 1.6e-173

   1. Initial program 93.8%

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

   3. Taylor expanded in y around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. div-exp N/A

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

      5. pow-to-exp N/A

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

      6. lower-/.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower-exp.f64 81.3

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

   5. Applied rewrites 81.3%

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

   6. Taylor expanded in t around 0

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

      1. inv-pow N/A

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

      2. lower-pow.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lift-exp.f64 74.7

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

   8. Applied rewrites 74.7%

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

   if 1.6e-173 < y < 7.0999999999999998e-6

   1. Initial program 95.9%

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

   3. Taylor expanded in b around 0

      \[\leadsto \color{blue}{\frac{x \cdot e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}}{y}} \]
   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 74.1

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

   5. Applied rewrites 74.1%

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

   6. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. pow-to-exp N/A

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

      5. lift-pow.f64 N/A

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

      6. lift--.f64 78.8

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

   8. Applied rewrites 78.8%

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

Alternative 7: 75.0% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{if}\;y \leq -1.55 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-173}:\\ \;\;\;\;\frac{x}{\left(e^{b} \cdot y\right) \cdot a}\\ \mathbf{elif}\;y \leq 7.1 \cdot 10^{-6}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (/ (pow z y) a) y))))
   (if (<= y -1.55e+18)
     t_1
     (if (<= y 1.6e-173)
       (/ x (* (* (exp b) y) a))
       (if (<= y 7.1e-6) (/ (* (pow a (- t 1.0)) x) 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 <= -1.55e+18) {
		tmp = t_1;
	} else if (y <= 1.6e-173) {
		tmp = x / ((exp(b) * y) * a);
	} else if (y <= 7.1e-6) {
		tmp = (pow(a, (t - 1.0)) * x) / 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 <= (-1.55d+18)) then
        tmp = t_1
    else if (y <= 1.6d-173) then
        tmp = x / ((exp(b) * y) * a)
    else if (y <= 7.1d-6) then
        tmp = ((a ** (t - 1.0d0)) * x) / 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 <= -1.55e+18) {
		tmp = t_1;
	} else if (y <= 1.6e-173) {
		tmp = x / ((Math.exp(b) * y) * a);
	} else if (y <= 7.1e-6) {
		tmp = (Math.pow(a, (t - 1.0)) * x) / 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 <= -1.55e+18:
		tmp = t_1
	elif y <= 1.6e-173:
		tmp = x / ((math.exp(b) * y) * a)
	elif y <= 7.1e-6:
		tmp = (math.pow(a, (t - 1.0)) * x) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(Float64((z ^ y) / a) / y))
	tmp = 0.0
	if (y <= -1.55e+18)
		tmp = t_1;
	elseif (y <= 1.6e-173)
		tmp = Float64(x / Float64(Float64(exp(b) * y) * a));
	elseif (y <= 7.1e-6)
		tmp = Float64(Float64((a ^ Float64(t - 1.0)) * x) / 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 <= -1.55e+18)
		tmp = t_1;
	elseif (y <= 1.6e-173)
		tmp = x / ((exp(b) * y) * a);
	elseif (y <= 7.1e-6)
		tmp = ((a ^ (t - 1.0)) * x) / 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[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.55e+18], t$95$1, If[LessEqual[y, 1.6e-173], N[(x / N[(N[(N[Exp[b], $MachinePrecision] * y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.1e-6], N[(N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.55e18 or 7.0999999999999998e-6 < y

   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

      \[\leadsto \color{blue}{\frac{x \cdot e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}}{y}} \]
   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 71.3

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

   5. Applied rewrites 71.3%

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

   6. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lift-pow.f64 87.4

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

   8. Applied rewrites 87.4%

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

   if -1.55e18 < y < 1.6e-173

   1. Initial program 93.8%

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

   3. Taylor expanded in y around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. div-exp N/A

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

      5. pow-to-exp N/A

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

      6. lower-/.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower-exp.f64 81.3

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

   5. Applied rewrites 81.3%

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

   6. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-exp.f64 74.7

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

   8. Applied rewrites 74.7%

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

   if 1.6e-173 < y < 7.0999999999999998e-6

   1. Initial program 95.9%

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

   3. Taylor expanded in b around 0

      \[\leadsto \color{blue}{\frac{x \cdot e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}}{y}} \]
   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 74.1

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

   5. Applied rewrites 74.1%

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

   6. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. pow-to-exp N/A

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

      5. lift-pow.f64 N/A

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

      6. lift--.f64 78.8

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

   8. Applied rewrites 78.8%

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

Alternative 8: 71.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \frac{e^{-b}}{y}\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-141}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{z}^{y}}{y}\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-47}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t - 1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(e^{b} \cdot y\right) \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.15e+18)
   (* x (/ (exp (- b)) y))
   (if (<= b 9.5e-141)
     (* (/ x a) (/ (pow z y) y))
     (if (<= b 1.2e-47)
       (* x (/ (pow a (- t 1.0)) y))
       (/ x (* (* (exp b) y) a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.15e+18) {
		tmp = x * (exp(-b) / y);
	} else if (b <= 9.5e-141) {
		tmp = (x / a) * (pow(z, y) / y);
	} else if (b <= 1.2e-47) {
		tmp = x * (pow(a, (t - 1.0)) / y);
	} else {
		tmp = x / ((exp(b) * y) * a);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.15d+18)) then
        tmp = x * (exp(-b) / y)
    else if (b <= 9.5d-141) then
        tmp = (x / a) * ((z ** y) / y)
    else if (b <= 1.2d-47) then
        tmp = x * ((a ** (t - 1.0d0)) / y)
    else
        tmp = x / ((exp(b) * y) * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.15e+18) {
		tmp = x * (Math.exp(-b) / y);
	} else if (b <= 9.5e-141) {
		tmp = (x / a) * (Math.pow(z, y) / y);
	} else if (b <= 1.2e-47) {
		tmp = x * (Math.pow(a, (t - 1.0)) / y);
	} else {
		tmp = x / ((Math.exp(b) * y) * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.15e+18:
		tmp = x * (math.exp(-b) / y)
	elif b <= 9.5e-141:
		tmp = (x / a) * (math.pow(z, y) / y)
	elif b <= 1.2e-47:
		tmp = x * (math.pow(a, (t - 1.0)) / y)
	else:
		tmp = x / ((math.exp(b) * y) * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.15e+18)
		tmp = Float64(x * Float64(exp(Float64(-b)) / y));
	elseif (b <= 9.5e-141)
		tmp = Float64(Float64(x / a) * Float64((z ^ y) / y));
	elseif (b <= 1.2e-47)
		tmp = Float64(x * Float64((a ^ Float64(t - 1.0)) / y));
	else
		tmp = Float64(x / Float64(Float64(exp(b) * y) * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.15e+18)
		tmp = x * (exp(-b) / y);
	elseif (b <= 9.5e-141)
		tmp = (x / a) * ((z ^ y) / y);
	elseif (b <= 1.2e-47)
		tmp = x * ((a ^ (t - 1.0)) / y);
	else
		tmp = x / ((exp(b) * y) * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.15e+18], N[(x * N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.5e-141], N[(N[(x / a), $MachinePrecision] * N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.2e-47], N[(x * N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(N[Exp[b], $MachinePrecision] * y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.15e18

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 85.5

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

   5. Applied rewrites 85.5%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 85.5

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

   7. Applied rewrites 85.5%

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

   if -1.15e18 < b < 9.49999999999999996e-141

   1. Initial program 95.3%

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

   3. Taylor expanded in 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 84.2

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

   5. Applied rewrites 84.2%

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

   6. Taylor expanded in t around 0

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

      1. times-frac N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift-pow.f64 70.8

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

   8. Applied rewrites 70.8%

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

   if 9.49999999999999996e-141 < b < 1.2e-47

   1. Initial program 90.2%

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

   3. Taylor expanded in b around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. exp-sum N/A

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

      5. *-commutative N/A

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

      6. pow-to-exp N/A

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

      7. pow-to-exp N/A

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

      8. lower-*.f64 N/A

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

      9. lower-pow.f64 N/A

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

      10. lower-pow.f64 N/A

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

      11. lift--.f64 80.3

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

   5. Applied rewrites 80.3%

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

   6. Taylor expanded in y around 0

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

      1. pow-to-exp N/A

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

      2. lift-pow.f64 N/A

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

      3. lift--.f64 81.0

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

   8. Applied rewrites 81.0%

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

   if 1.2e-47 < 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 y around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. div-exp N/A

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

      5. pow-to-exp N/A

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

      6. lower-/.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower-exp.f64 66.8

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

   5. Applied rewrites 66.8%

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

   6. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-exp.f64 82.9

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

   8. Applied rewrites 82.9%

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

Alternative 9: 74.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.8 \cdot 10^{+25}:\\ \;\;\;\;x \cdot \frac{e^{-b}}{y}\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-15}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(e^{b} \cdot y\right) \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -4.8e+25)
   (* x (/ (exp (- b)) y))
   (if (<= b 3e-15) (/ (* x (/ (pow a t) a)) y) (/ x (* (* (exp b) y) a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4.8e+25) {
		tmp = x * (exp(-b) / y);
	} else if (b <= 3e-15) {
		tmp = (x * (pow(a, t) / a)) / y;
	} else {
		tmp = x / ((exp(b) * y) * a);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-4.8d+25)) then
        tmp = x * (exp(-b) / y)
    else if (b <= 3d-15) then
        tmp = (x * ((a ** t) / a)) / y
    else
        tmp = x / ((exp(b) * y) * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4.8e+25) {
		tmp = x * (Math.exp(-b) / y);
	} else if (b <= 3e-15) {
		tmp = (x * (Math.pow(a, t) / a)) / y;
	} else {
		tmp = x / ((Math.exp(b) * y) * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -4.8e+25:
		tmp = x * (math.exp(-b) / y)
	elif b <= 3e-15:
		tmp = (x * (math.pow(a, t) / a)) / y
	else:
		tmp = x / ((math.exp(b) * y) * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -4.8e+25)
		tmp = Float64(x * Float64(exp(Float64(-b)) / y));
	elseif (b <= 3e-15)
		tmp = Float64(Float64(x * Float64((a ^ t) / a)) / y);
	else
		tmp = Float64(x / Float64(Float64(exp(b) * y) * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -4.8e+25)
		tmp = x * (exp(-b) / y);
	elseif (b <= 3e-15)
		tmp = (x * ((a ^ t) / a)) / y;
	else
		tmp = x / ((exp(b) * y) * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -4.8e+25], N[(x * N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3e-15], N[(N[(x * N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(N[(N[Exp[b], $MachinePrecision] * y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.79999999999999992e25

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 85.2

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

   5. Applied rewrites 85.2%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 85.2

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

   7. Applied rewrites 85.2%

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

   if -4.79999999999999992e25 < b < 3e-15

   1. Initial program 94.6%

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

   3. Taylor expanded in b around 0

      \[\leadsto \color{blue}{\frac{x \cdot e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}}{y}} \]
   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 84.3

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

   5. Applied rewrites 84.3%

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

      1. lift--.f64 N/A

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

      2. lift-pow.f64 N/A

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

      3. pow-sub N/A

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

      4. unpow1 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-pow.f64 84.3

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

   7. Applied rewrites 84.3%

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

   8. Taylor expanded in y around 0

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

      1. associate-/r* N/A

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

      2. lower-/.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lift-pow.f64 N/A

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

      6. lift-/.f64 61.2

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

   10. Applied rewrites 61.2%

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

   if 3e-15 < b

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. div-exp N/A

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

      5. pow-to-exp N/A

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

      6. lower-/.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower-exp.f64 67.3

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

   5. Applied rewrites 67.3%

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

   6. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-exp.f64 84.7

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

   8. Applied rewrites 84.7%

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

Alternative 10: 74.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.8 \cdot 10^{+25}:\\ \;\;\;\;x \cdot \frac{e^{-b}}{y}\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-15}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(e^{b} \cdot y\right) \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -4.8e+25)
   (* x (/ (exp (- b)) y))
   (if (<= b 3e-15) (/ (* (pow a (- t 1.0)) x) y) (/ x (* (* (exp b) y) a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4.8e+25) {
		tmp = x * (exp(-b) / y);
	} else if (b <= 3e-15) {
		tmp = (pow(a, (t - 1.0)) * x) / y;
	} else {
		tmp = x / ((exp(b) * y) * a);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-4.8d+25)) then
        tmp = x * (exp(-b) / y)
    else if (b <= 3d-15) then
        tmp = ((a ** (t - 1.0d0)) * x) / y
    else
        tmp = x / ((exp(b) * y) * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4.8e+25) {
		tmp = x * (Math.exp(-b) / y);
	} else if (b <= 3e-15) {
		tmp = (Math.pow(a, (t - 1.0)) * x) / y;
	} else {
		tmp = x / ((Math.exp(b) * y) * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -4.8e+25:
		tmp = x * (math.exp(-b) / y)
	elif b <= 3e-15:
		tmp = (math.pow(a, (t - 1.0)) * x) / y
	else:
		tmp = x / ((math.exp(b) * y) * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -4.8e+25)
		tmp = Float64(x * Float64(exp(Float64(-b)) / y));
	elseif (b <= 3e-15)
		tmp = Float64(Float64((a ^ Float64(t - 1.0)) * x) / y);
	else
		tmp = Float64(x / Float64(Float64(exp(b) * y) * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -4.8e+25)
		tmp = x * (exp(-b) / y);
	elseif (b <= 3e-15)
		tmp = ((a ^ (t - 1.0)) * x) / y;
	else
		tmp = x / ((exp(b) * y) * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -4.8e+25], N[(x * N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3e-15], N[(N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(N[(N[Exp[b], $MachinePrecision] * y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.79999999999999992e25

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 85.2

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

   5. Applied rewrites 85.2%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 85.2

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

   7. Applied rewrites 85.2%

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

   if -4.79999999999999992e25 < b < 3e-15

   1. Initial program 94.6%

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

   3. Taylor expanded in b around 0

      \[\leadsto \color{blue}{\frac{x \cdot e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}}{y}} \]
   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 84.3

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

   5. Applied rewrites 84.3%

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

   6. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. pow-to-exp N/A

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

      5. lift-pow.f64 N/A

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

      6. lift--.f64 61.2

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

   8. Applied rewrites 61.2%

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

   if 3e-15 < b

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. div-exp N/A

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

      5. pow-to-exp N/A

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

      6. lower-/.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower-exp.f64 67.3

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

   5. Applied rewrites 67.3%

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

   6. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-exp.f64 84.7

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

   8. Applied rewrites 84.7%

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

Alternative 11: 75.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.8 \cdot 10^{+25} \lor \neg \left(b \leq 14500\right):\\ \;\;\;\;x \cdot \frac{e^{-b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)} \cdot x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -4.8e+25) (not (<= b 14500.0)))
   (* x (/ (exp (- b)) y))
   (/ (* (pow a (- t 1.0)) x) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -4.8e+25) || !(b <= 14500.0)) {
		tmp = x * (exp(-b) / y);
	} else {
		tmp = (pow(a, (t - 1.0)) * x) / y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-4.8d+25)) .or. (.not. (b <= 14500.0d0))) then
        tmp = x * (exp(-b) / y)
    else
        tmp = ((a ** (t - 1.0d0)) * x) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -4.8e+25) || !(b <= 14500.0)) {
		tmp = x * (Math.exp(-b) / y);
	} else {
		tmp = (Math.pow(a, (t - 1.0)) * x) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -4.8e+25) or not (b <= 14500.0):
		tmp = x * (math.exp(-b) / y)
	else:
		tmp = (math.pow(a, (t - 1.0)) * x) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -4.8e+25) || !(b <= 14500.0))
		tmp = Float64(x * Float64(exp(Float64(-b)) / y));
	else
		tmp = Float64(Float64((a ^ Float64(t - 1.0)) * x) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -4.8e+25) || ~((b <= 14500.0)))
		tmp = x * (exp(-b) / y);
	else
		tmp = ((a ^ (t - 1.0)) * x) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -4.8e+25], N[Not[LessEqual[b, 14500.0]], $MachinePrecision]], N[(x * N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.79999999999999992e25 or 14500 < 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 84.6

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

   5. Applied rewrites 84.6%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]
   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 84.6

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

   7. Applied rewrites 84.6%

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

   if -4.79999999999999992e25 < b < 14500

   1. Initial program 94.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   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 84.6

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

   5. Applied rewrites 84.6%

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

   6. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. pow-to-exp N/A

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

      5. lift-pow.f64 N/A

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

      6. lift--.f64 62.0

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

   8. Applied rewrites 62.0%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.8 \cdot 10^{+25} \lor \neg \left(b \leq 14500\right):\\ \;\;\;\;x \cdot \frac{e^{-b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)} \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 65.9% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{+25} \lor \neg \left(b \leq 15500\right):\\ \;\;\;\;x \cdot \frac{e^{-b}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -4.5e+25) (not (<= b 15500.0)))
   (* x (/ (exp (- b)) y))
   (* x (/ (pow a t) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -4.5e+25) || !(b <= 15500.0)) {
		tmp = x * (exp(-b) / y);
	} else {
		tmp = x * (pow(a, t) / y);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-4.5d+25)) .or. (.not. (b <= 15500.0d0))) then
        tmp = x * (exp(-b) / y)
    else
        tmp = x * ((a ** t) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -4.5e+25) || !(b <= 15500.0)) {
		tmp = x * (Math.exp(-b) / y);
	} else {
		tmp = x * (Math.pow(a, t) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -4.5e+25) or not (b <= 15500.0):
		tmp = x * (math.exp(-b) / y)
	else:
		tmp = x * (math.pow(a, t) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -4.5e+25) || !(b <= 15500.0))
		tmp = Float64(x * Float64(exp(Float64(-b)) / y));
	else
		tmp = Float64(x * Float64((a ^ t) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -4.5e+25) || ~((b <= 15500.0)))
		tmp = x * (exp(-b) / y);
	else
		tmp = x * ((a ^ t) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -4.5e+25], N[Not[LessEqual[b, 15500.0]], $MachinePrecision]], N[(x * N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[Power[a, t], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.5000000000000003e25 or 15500 < 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 84.6

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

   5. Applied rewrites 84.6%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]
   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 84.6

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

   7. Applied rewrites 84.6%

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

   if -4.5000000000000003e25 < b < 15500

   1. Initial program 94.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   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 84.6

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

   5. Applied rewrites 84.6%

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

   6. Taylor expanded in y around 0

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

      1. pow-to-exp N/A

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

      2. lift-pow.f64 N/A

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

      3. lift--.f64 61.1

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

   8. Applied rewrites 61.1%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 47.6%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{+25} \lor \neg \left(b \leq 15500\right):\\ \;\;\;\;x \cdot \frac{e^{-b}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 34.7% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 1.15 \cdot 10^{-165}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot {\left(\mathsf{fma}\left(b, y, y\right) \cdot a\right)}^{-1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 1.15e-165) (/ (/ x a) y) (* x (pow (* (fma b y y) a) -1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1.15e-165) {
		tmp = (x / a) / y;
	} else {
		tmp = x * pow((fma(b, y, y) * a), -1.0);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 1.15e-165)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(x * (Float64(fma(b, y, y) * a) ^ -1.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 1.15e-165], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x * N[Power[N[(N[(b * y + y), $MachinePrecision] * a), $MachinePrecision], -1.0], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 1.15e-165

   1. Initial program 97.1%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. 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 72.6

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

   5. Applied rewrites 72.6%

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

      1. lift--.f64 N/A

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

      2. lift-pow.f64 N/A

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

      3. pow-sub N/A

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

      4. unpow1 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-pow.f64 72.6

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

   7. Applied rewrites 72.6%

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

   8. Taylor expanded in y around 0

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

      1. associate-/r* N/A

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

      2. lower-/.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lift-pow.f64 N/A

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

      6. lift-/.f64 49.8

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

   10. Applied rewrites 49.8%

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

   11. Taylor expanded in t around 0

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

       1. lower-/.f64 27.5

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

   13. Applied rewrites 27.5%

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

   if 1.15e-165 < b

   1. Initial program 97.0%

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

   3. Taylor expanded in y around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. div-exp N/A

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

      5. pow-to-exp N/A

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

      6. lower-/.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower-exp.f64 68.6

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

   5. Applied rewrites 68.6%

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

   6. Taylor expanded in t around 0

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

      1. inv-pow N/A

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

      2. lower-pow.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lift-exp.f64 66.9

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

   8. Applied rewrites 66.9%

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

   9. Taylor expanded in b around 0

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

       1. +-commutative N/A

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

       2. lower-fma.f64 36.0

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

   11. Applied rewrites 36.0%

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

Alternative 14: 30.7% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 4 \cdot 10^{-195}:\\ \;\;\;\;x \cdot {\left(y \cdot a\right)}^{-1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x 4e-195) (* x (pow (* y a) -1.0)) (/ (/ x a) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 4e-195) {
		tmp = x * pow((y * a), -1.0);
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= 4d-195) then
        tmp = x * ((y * a) ** (-1.0d0))
    else
        tmp = (x / a) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 4e-195) {
		tmp = x * Math.pow((y * a), -1.0);
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= 4e-195:
		tmp = x * math.pow((y * a), -1.0)
	else:
		tmp = (x / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= 4e-195)
		tmp = Float64(x * (Float64(y * a) ^ -1.0));
	else
		tmp = Float64(Float64(x / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= 4e-195)
		tmp = x * ((y * a) ^ -1.0);
	else
		tmp = (x / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, 4e-195], N[(x * N[Power[N[(y * a), $MachinePrecision], -1.0], $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4.0000000000000004e-195

   1. Initial program 95.6%

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

   3. Taylor expanded in y around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. div-exp N/A

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

      5. pow-to-exp N/A

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

      6. lower-/.f64 N/A

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

      7. lower-pow.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lower-exp.f64 65.9

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

   5. Applied rewrites 65.9%

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

   6. Taylor expanded in t around 0

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

      1. inv-pow N/A

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

      2. lower-pow.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lift-exp.f64 55.0

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

   8. Applied rewrites 55.0%

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

   9. Taylor expanded in b around 0

      \[\leadsto x \cdot {\left(y \cdot a\right)}^{-1} \]
   10. Step-by-step derivation

   11. Applied rewrites 28.7%

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

   if 4.0000000000000004e-195 < x

   1. Initial program 99.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. 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 64.4

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

   5. Applied rewrites 64.4%

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

      1. lift--.f64 N/A

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

      2. lift-pow.f64 N/A

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

      3. pow-sub N/A

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

      4. unpow1 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-pow.f64 64.4

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

   7. Applied rewrites 64.4%

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

   8. Taylor expanded in y around 0

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

      1. associate-/r* N/A

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

      2. lower-/.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lift-pow.f64 N/A

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

      6. lift-/.f64 45.3

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

   10. Applied rewrites 45.3%

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

   11. Taylor expanded in t around 0

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

       1. lower-/.f64 20.2

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

   13. Applied rewrites 20.2%

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

Alternative 15: 30.6% accurate, 11.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 4.9 \cdot 10^{-191}:\\ \;\;\;\;\frac{x}{a \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x 4.9e-191) (/ x (* a y)) (/ (/ x a) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 4.9e-191) {
		tmp = x / (a * y);
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= 4.9d-191) then
        tmp = x / (a * y)
    else
        tmp = (x / a) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 4.9e-191) {
		tmp = x / (a * y);
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= 4.9e-191:
		tmp = x / (a * y)
	else:
		tmp = (x / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= 4.9e-191)
		tmp = Float64(x / Float64(a * y));
	else
		tmp = Float64(Float64(x / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= 4.9e-191)
		tmp = x / (a * y);
	else
		tmp = (x / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, 4.9e-191], N[(x / N[(a * y), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4.9e-191

   1. Initial program 95.6%

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

   3. Taylor expanded in b around 0

      \[\leadsto \color{blue}{\frac{x \cdot e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}}{y}} \]
   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 73.2

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

   5. Applied rewrites 73.2%

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

      1. lift--.f64 N/A

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

      2. lift-pow.f64 N/A

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

      3. pow-sub N/A

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

      4. unpow1 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-pow.f64 73.2

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

   7. Applied rewrites 73.2%

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

   8. Taylor expanded in y around 0

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

      1. associate-/r* N/A

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

      2. lower-/.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lift-pow.f64 N/A

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

      6. lift-/.f64 54.0

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

   10. Applied rewrites 54.0%

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

   11. Taylor expanded in t around 0

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

       1. lower-/.f64 N/A

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

       2. lower-*.f64 28.8

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

   13. Applied rewrites 28.8%

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

   if 4.9e-191 < x

   1. Initial program 99.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. 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 64.4

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

   5. Applied rewrites 64.4%

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

      1. lift--.f64 N/A

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

      2. lift-pow.f64 N/A

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

      3. pow-sub N/A

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

      4. unpow1 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-pow.f64 64.4

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

   7. Applied rewrites 64.4%

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

   8. Taylor expanded in y around 0

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

      1. associate-/r* N/A

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

      2. lower-/.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lift-pow.f64 N/A

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

      6. lift-/.f64 45.3

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

   10. Applied rewrites 45.3%

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

   11. Taylor expanded in t around 0

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

       1. lower-/.f64 20.2

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

   13. Applied rewrites 20.2%

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

Alternative 16: 30.7% accurate, 19.8× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.1%

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

3. Taylor expanded in b around 0

   \[\leadsto \color{blue}{\frac{x \cdot e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}}{y}} \]
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 70.1

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

5. Applied rewrites 70.1%

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

   1. lift--.f64 N/A

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

   2. lift-pow.f64 N/A

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

   3. pow-sub N/A

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

   4. unpow1 N/A

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

   5. lower-/.f64 N/A

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

   6. lower-pow.f64 70.1

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

7. Applied rewrites 70.1%

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

8. Taylor expanded in y around 0

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

   1. associate-/r* N/A

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

   2. lower-/.f64 N/A

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

   3. associate-/l* N/A

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

   4. lower-*.f64 N/A

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

   5. lift-pow.f64 N/A

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

   6. lift-/.f64 50.9

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

10. Applied rewrites 50.9%

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

11. Taylor expanded in t around 0

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

    1. lower-/.f64 N/A

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

    2. lower-*.f64 24.7

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

13. Applied rewrites 24.7%

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

Developer Target 1: 71.5% 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 2025037 
(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))