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

Percentage Accurate: 98.3% → 98.4%

Time: 9.8s

Alternatives: 12

Speedup: 1.0×

• 46.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.3%

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

3. Taylor expanded in z around inf

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

   1. associate-/l* N/A

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

   2. lower-*.f64 N/A

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

   3. lower-/.f64 N/A

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

5. Applied rewrites 98.4%

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

Alternative 2: 58.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - 1\right) \cdot \log a\\ t_2 := \frac{{a}^{t} \cdot x}{y}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+26}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 680.5:\\ \;\;\;\;\frac{x}{a \cdot y}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- t 1.0) (log a))) (t_2 (/ (* (pow a t) x) y)))
   (if (<= t_1 -1e+26) t_2 (if (<= t_1 680.5) (/ 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 = (pow(a, t) * x) / y;
	double tmp;
	if (t_1 <= -1e+26) {
		tmp = t_2;
	} else if (t_1 <= 680.5) {
		tmp = x / (a * y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t - 1.0d0) * log(a)
    t_2 = ((a ** t) * x) / y
    if (t_1 <= (-1d+26)) then
        tmp = t_2
    else if (t_1 <= 680.5d0) then
        tmp = x / (a * y)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - 1.0) * Math.log(a);
	double t_2 = (Math.pow(a, t) * x) / y;
	double tmp;
	if (t_1 <= -1e+26) {
		tmp = t_2;
	} else if (t_1 <= 680.5) {
		tmp = x / (a * y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - 1.0) * math.log(a)
	t_2 = (math.pow(a, t) * x) / y
	tmp = 0
	if t_1 <= -1e+26:
		tmp = t_2
	elif t_1 <= 680.5:
		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(Float64((a ^ t) * x) / y)
	tmp = 0.0
	if (t_1 <= -1e+26)
		tmp = t_2;
	elseif (t_1 <= 680.5)
		tmp = Float64(x / Float64(a * y));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - 1.0) * log(a);
	t_2 = ((a ^ t) * x) / y;
	tmp = 0.0;
	if (t_1 <= -1e+26)
		tmp = t_2;
	elseif (t_1 <= 680.5)
		tmp = x / (a * y);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - 1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[Power[a, t], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+26], t$95$2, If[LessEqual[t$95$1, 680.5], N[(x / N[(a * y), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -1.00000000000000005e26 or 680.5 < (*.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 67.6

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

   5. Applied rewrites 67.6%

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

   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 79.6

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

   8. Applied rewrites 79.6%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 78.9%

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

   if -1.00000000000000005e26 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < 680.5

   1. Initial program 96.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   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 72.3

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

   5. Applied rewrites 72.3%

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

   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 66.4

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

   8. Applied rewrites 66.4%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-pow.f64 N/A

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

      5. frac-times N/A

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

      6. lower-/.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lift-pow.f64 N/A

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

      10. lower-*.f64 65.7

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

   10. Applied rewrites 65.7%

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

   11. Taylor expanded in y around 0

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

   13. Applied rewrites 39.6%

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

Alternative 3: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.3%

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

Alternative 4: 88.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+177}:\\ \;\;\;\;\frac{\frac{{z}^{y} \cdot x}{a}}{y}\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+130}:\\ \;\;\;\;x \cdot \frac{e^{\log a \cdot \left(t - 1\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -5.2e+177)
   (/ (/ (* (pow z y) x) a) y)
   (if (<= y 3.9e+130)
     (* x (/ (exp (- (* (log a) (- t 1.0)) b)) y))
     (* x (/ (/ (pow z y) a) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -5.2e+177) {
		tmp = ((pow(z, y) * x) / a) / y;
	} else if (y <= 3.9e+130) {
		tmp = x * (exp(((log(a) * (t - 1.0)) - b)) / y);
	} else {
		tmp = x * ((pow(z, y) / a) / y);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-5.2d+177)) then
        tmp = (((z ** y) * x) / a) / y
    else if (y <= 3.9d+130) then
        tmp = x * (exp(((log(a) * (t - 1.0d0)) - b)) / y)
    else
        tmp = x * (((z ** y) / a) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -5.2e+177) {
		tmp = ((Math.pow(z, y) * x) / a) / y;
	} else if (y <= 3.9e+130) {
		tmp = x * (Math.exp(((Math.log(a) * (t - 1.0)) - b)) / y);
	} else {
		tmp = x * ((Math.pow(z, y) / a) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -5.2e+177:
		tmp = ((math.pow(z, y) * x) / a) / y
	elif y <= 3.9e+130:
		tmp = x * (math.exp(((math.log(a) * (t - 1.0)) - b)) / y)
	else:
		tmp = x * ((math.pow(z, y) / a) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -5.2e+177)
		tmp = Float64(Float64(Float64((z ^ y) * x) / a) / y);
	elseif (y <= 3.9e+130)
		tmp = Float64(x * Float64(exp(Float64(Float64(log(a) * Float64(t - 1.0)) - b)) / y));
	else
		tmp = Float64(x * Float64(Float64((z ^ y) / a) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -5.2e+177)
		tmp = (((z ^ y) * x) / a) / y;
	elseif (y <= 3.9e+130)
		tmp = x * (exp(((log(a) * (t - 1.0)) - b)) / y);
	else
		tmp = x * (((z ^ y) / a) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -5.2e+177], N[(N[(N[(N[Power[z, y], $MachinePrecision] * x), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 3.9e+130], N[(x * N[(N[Exp[N[(N[(N[Log[a], $MachinePrecision] * N[(t - 1.0), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.19999999999999959e177

   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 71.7

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

   5. Applied rewrites 71.7%

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

   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 82.0

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

   8. Applied rewrites 82.0%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-pow.f64 N/A

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

      5. frac-times N/A

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

      6. associate-/r* N/A

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

      7. lower-/.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lift-pow.f64 91.1

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

   10. Applied rewrites 91.1%

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

   if -5.19999999999999959e177 < y < 3.9000000000000002e130

   1. Initial program 97.7%

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

   3. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

   5. Applied rewrites 97.9%

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

   6. Taylor expanded in y around 0

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

      1. lower-*.f64 N/A

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

      2. lift-log.f64 N/A

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

      3. lift--.f64 88.5

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

   8. Applied rewrites 88.5%

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

   if 3.9000000000000002e130 < 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 69.2

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

   5. Applied rewrites 69.2%

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

   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%

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

Alternative 5: 82.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{e^{-b}}{y}\\ \mathbf{if}\;b \leq -3.8 \cdot 10^{+114}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{+39}:\\ \;\;\;\;x \cdot \frac{{z}^{y} \cdot {a}^{\left(t - 1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (exp (- b)) y))))
   (if (<= b -3.8e+114)
     t_1
     (if (<= b 7.2e+39) (* x (/ (* (pow z y) (pow a (- t 1.0))) y)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (exp(-b) / y);
	double tmp;
	if (b <= -3.8e+114) {
		tmp = t_1;
	} else if (b <= 7.2e+39) {
		tmp = x * ((pow(z, y) * pow(a, (t - 1.0))) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (exp(-b) / y)
    if (b <= (-3.8d+114)) then
        tmp = t_1
    else if (b <= 7.2d+39) then
        tmp = x * (((z ** y) * (a ** (t - 1.0d0))) / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (Math.exp(-b) / y);
	double tmp;
	if (b <= -3.8e+114) {
		tmp = t_1;
	} else if (b <= 7.2e+39) {
		tmp = x * ((Math.pow(z, y) * Math.pow(a, (t - 1.0))) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (math.exp(-b) / y)
	tmp = 0
	if b <= -3.8e+114:
		tmp = t_1
	elif b <= 7.2e+39:
		tmp = x * ((math.pow(z, y) * math.pow(a, (t - 1.0))) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(exp(Float64(-b)) / y))
	tmp = 0.0
	if (b <= -3.8e+114)
		tmp = t_1;
	elseif (b <= 7.2e+39)
		tmp = Float64(x * Float64(Float64((z ^ y) * (a ^ Float64(t - 1.0))) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (exp(-b) / y);
	tmp = 0.0;
	if (b <= -3.8e+114)
		tmp = t_1;
	elseif (b <= 7.2e+39)
		tmp = x * (((z ^ y) * (a ^ (t - 1.0))) / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.8e+114], t$95$1, If[LessEqual[b, 7.2e+39], N[(x * N[(N[(N[Power[z, y], $MachinePrecision] * N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -3.8000000000000001e114 or 7.19999999999999969e39 < 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 83.7

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

   5. Applied rewrites 83.7%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 83.7

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

   7. Applied rewrites 83.7%

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

   if -3.8000000000000001e114 < b < 7.19999999999999969e39

   1. Initial program 97.2%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. 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 82.0

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

   5. Applied rewrites 82.0%

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

Alternative 6: 74.1% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := {a}^{\left(t - 1\right)}\\ t_2 := x \cdot \frac{e^{-b}}{y}\\ \mathbf{if}\;b \leq -1.3 \cdot 10^{+28}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -7 \cdot 10^{-112}:\\ \;\;\;\;x \cdot \frac{t\_1}{y}\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{-217}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{z}^{y}}{y}\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+39}:\\ \;\;\;\;\frac{t\_1 \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (pow a (- t 1.0))) (t_2 (* x (/ (exp (- b)) y))))
   (if (<= b -1.3e+28)
     t_2
     (if (<= b -7e-112)
       (* x (/ t_1 y))
       (if (<= b 2.7e-217)
         (* (/ x a) (/ (pow z y) y))
         (if (<= b 2.5e+39) (/ (* t_1 x) 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 * (exp(-b) / y);
	double tmp;
	if (b <= -1.3e+28) {
		tmp = t_2;
	} else if (b <= -7e-112) {
		tmp = x * (t_1 / y);
	} else if (b <= 2.7e-217) {
		tmp = (x / a) * (pow(z, y) / y);
	} else if (b <= 2.5e+39) {
		tmp = (t_1 * x) / 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 * (exp(-b) / y)
    if (b <= (-1.3d+28)) then
        tmp = t_2
    else if (b <= (-7d-112)) then
        tmp = x * (t_1 / y)
    else if (b <= 2.7d-217) then
        tmp = (x / a) * ((z ** y) / y)
    else if (b <= 2.5d+39) then
        tmp = (t_1 * x) / 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 * (Math.exp(-b) / y);
	double tmp;
	if (b <= -1.3e+28) {
		tmp = t_2;
	} else if (b <= -7e-112) {
		tmp = x * (t_1 / y);
	} else if (b <= 2.7e-217) {
		tmp = (x / a) * (Math.pow(z, y) / y);
	} else if (b <= 2.5e+39) {
		tmp = (t_1 * x) / 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 * (math.exp(-b) / y)
	tmp = 0
	if b <= -1.3e+28:
		tmp = t_2
	elif b <= -7e-112:
		tmp = x * (t_1 / y)
	elif b <= 2.7e-217:
		tmp = (x / a) * (math.pow(z, y) / y)
	elif b <= 2.5e+39:
		tmp = (t_1 * x) / 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(x * Float64(exp(Float64(-b)) / y))
	tmp = 0.0
	if (b <= -1.3e+28)
		tmp = t_2;
	elseif (b <= -7e-112)
		tmp = Float64(x * Float64(t_1 / y));
	elseif (b <= 2.7e-217)
		tmp = Float64(Float64(x / a) * Float64((z ^ y) / y));
	elseif (b <= 2.5e+39)
		tmp = Float64(Float64(t_1 * x) / 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 * (exp(-b) / y);
	tmp = 0.0;
	if (b <= -1.3e+28)
		tmp = t_2;
	elseif (b <= -7e-112)
		tmp = x * (t_1 / y);
	elseif (b <= 2.7e-217)
		tmp = (x / a) * ((z ^ y) / y);
	elseif (b <= 2.5e+39)
		tmp = (t_1 * x) / 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[(x * N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.3e+28], t$95$2, If[LessEqual[b, -7e-112], N[(x * N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.7e-217], N[(N[(x / a), $MachinePrecision] * N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.5e+39], N[(N[(t$95$1 * x), $MachinePrecision] / y), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.3000000000000001e28 or 2.50000000000000008e39 < 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 80.8

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

   5. Applied rewrites 80.8%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]
   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 80.8

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

   7. Applied rewrites 80.8%

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

   if -1.3000000000000001e28 < b < -6.99999999999999988e-112

   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 83.4

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

   5. Applied rewrites 83.4%

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

   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 70.3

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

   8. Applied rewrites 70.3%

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

   if -6.99999999999999988e-112 < b < 2.70000000000000016e-217

   1. Initial program 96.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   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 85.9

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

   5. Applied rewrites 85.9%

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

   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 67.2

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

   8. Applied rewrites 67.2%

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

   if 2.70000000000000016e-217 < b < 2.50000000000000008e39

   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 81.4

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

   5. Applied rewrites 81.4%

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

   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 69.4

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

   8. Applied rewrites 69.4%

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

Alternative 7: 75.3% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{e^{-b}}{y}\\ \mathbf{if}\;b \leq -2.8 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (exp (- b)) y))))
   (if (<= b -2.8e+22)
     t_1
     (if (<= b 9.5e+38) (* x (/ (/ (pow z y) a) y)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (exp(-b) / y);
	double tmp;
	if (b <= -2.8e+22) {
		tmp = t_1;
	} else if (b <= 9.5e+38) {
		tmp = x * ((pow(z, y) / a) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (exp(-b) / y)
    if (b <= (-2.8d+22)) then
        tmp = t_1
    else if (b <= 9.5d+38) then
        tmp = x * (((z ** y) / a) / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (Math.exp(-b) / y);
	double tmp;
	if (b <= -2.8e+22) {
		tmp = t_1;
	} else if (b <= 9.5e+38) {
		tmp = x * ((Math.pow(z, y) / a) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (math.exp(-b) / y)
	tmp = 0
	if b <= -2.8e+22:
		tmp = t_1
	elif b <= 9.5e+38:
		tmp = x * ((math.pow(z, y) / a) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(exp(Float64(-b)) / y))
	tmp = 0.0
	if (b <= -2.8e+22)
		tmp = t_1;
	elseif (b <= 9.5e+38)
		tmp = Float64(x * Float64(Float64((z ^ y) / a) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (exp(-b) / y);
	tmp = 0.0;
	if (b <= -2.8e+22)
		tmp = t_1;
	elseif (b <= 9.5e+38)
		tmp = x * (((z ^ y) / a) / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.8e+22], t$95$1, If[LessEqual[b, 9.5e+38], N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.8e22 or 9.4999999999999995e38 < 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 80.7

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

   5. Applied rewrites 80.7%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 80.7

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

   7. Applied rewrites 80.7%

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

   if -2.8e22 < b < 9.4999999999999995e38

   1. Initial program 96.9%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. 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 83.9

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

   5. Applied rewrites 83.9%

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

   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 70.8

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

   8. Applied rewrites 70.8%

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

Alternative 8: 75.0% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{e^{-b}}{y}\\ \mathbf{if}\;b \leq -2.7 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{-217}:\\ \;\;\;\;\frac{\frac{{z}^{y} \cdot x}{a}}{y}\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+39}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (exp (- b)) y))))
   (if (<= b -2.7e+22)
     t_1
     (if (<= b 2.7e-217)
       (/ (/ (* (pow z y) x) a) y)
       (if (<= b 2.5e+39) (/ (* (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 * (exp(-b) / y);
	double tmp;
	if (b <= -2.7e+22) {
		tmp = t_1;
	} else if (b <= 2.7e-217) {
		tmp = ((pow(z, y) * x) / a) / y;
	} else if (b <= 2.5e+39) {
		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 * (exp(-b) / y)
    if (b <= (-2.7d+22)) then
        tmp = t_1
    else if (b <= 2.7d-217) then
        tmp = (((z ** y) * x) / a) / y
    else if (b <= 2.5d+39) 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.exp(-b) / y);
	double tmp;
	if (b <= -2.7e+22) {
		tmp = t_1;
	} else if (b <= 2.7e-217) {
		tmp = ((Math.pow(z, y) * x) / a) / y;
	} else if (b <= 2.5e+39) {
		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.exp(-b) / y)
	tmp = 0
	if b <= -2.7e+22:
		tmp = t_1
	elif b <= 2.7e-217:
		tmp = ((math.pow(z, y) * x) / a) / y
	elif b <= 2.5e+39:
		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(exp(Float64(-b)) / y))
	tmp = 0.0
	if (b <= -2.7e+22)
		tmp = t_1;
	elseif (b <= 2.7e-217)
		tmp = Float64(Float64(Float64((z ^ y) * x) / a) / y);
	elseif (b <= 2.5e+39)
		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 * (exp(-b) / y);
	tmp = 0.0;
	if (b <= -2.7e+22)
		tmp = t_1;
	elseif (b <= 2.7e-217)
		tmp = (((z ^ y) * x) / a) / y;
	elseif (b <= 2.5e+39)
		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[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.7e+22], t$95$1, If[LessEqual[b, 2.7e-217], N[(N[(N[(N[Power[z, y], $MachinePrecision] * x), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 2.5e+39], 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 b < -2.7000000000000002e22 or 2.50000000000000008e39 < 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 80.8

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

   5. Applied rewrites 80.8%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]
   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 80.8

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

   7. Applied rewrites 80.8%

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

   if -2.7000000000000002e22 < b < 2.70000000000000016e-217

   1. Initial program 96.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   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 85.5

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

   5. Applied rewrites 85.5%

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

   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 66.2

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

   8. Applied rewrites 66.2%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-pow.f64 N/A

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

      5. frac-times N/A

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

      6. associate-/r* N/A

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

      7. lower-/.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lift-pow.f64 70.7

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

   10. Applied rewrites 70.7%

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

   if 2.70000000000000016e-217 < b < 2.50000000000000008e39

   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 81.4

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

   5. Applied rewrites 81.4%

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

   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 69.4

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

   8. Applied rewrites 69.4%

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

Alternative 9: 75.1% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{e^{-b}}{y}\\ \mathbf{if}\;b \leq -1.3 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{+39}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t - 1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (exp (- b)) y))))
   (if (<= b -1.3e+28)
     t_1
     (if (<= b 7.2e+39) (* x (/ (pow a (- t 1.0)) y)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (exp(-b) / y);
	double tmp;
	if (b <= -1.3e+28) {
		tmp = t_1;
	} else if (b <= 7.2e+39) {
		tmp = x * (pow(a, (t - 1.0)) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (exp(-b) / y)
    if (b <= (-1.3d+28)) then
        tmp = t_1
    else if (b <= 7.2d+39) then
        tmp = x * ((a ** (t - 1.0d0)) / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (Math.exp(-b) / y);
	double tmp;
	if (b <= -1.3e+28) {
		tmp = t_1;
	} else if (b <= 7.2e+39) {
		tmp = x * (Math.pow(a, (t - 1.0)) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (math.exp(-b) / y)
	tmp = 0
	if b <= -1.3e+28:
		tmp = t_1
	elif b <= 7.2e+39:
		tmp = x * (math.pow(a, (t - 1.0)) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(exp(Float64(-b)) / y))
	tmp = 0.0
	if (b <= -1.3e+28)
		tmp = t_1;
	elseif (b <= 7.2e+39)
		tmp = Float64(x * Float64((a ^ Float64(t - 1.0)) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (exp(-b) / y);
	tmp = 0.0;
	if (b <= -1.3e+28)
		tmp = t_1;
	elseif (b <= 7.2e+39)
		tmp = x * ((a ^ (t - 1.0)) / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.3e+28], t$95$1, If[LessEqual[b, 7.2e+39], N[(x * N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.3000000000000001e28 or 7.19999999999999969e39 < 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 80.8

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

   5. Applied rewrites 80.8%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]
   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 80.8

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

   7. Applied rewrites 80.8%

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

   if -1.3000000000000001e28 < b < 7.19999999999999969e39

   1. Initial program 96.9%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. 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 83.7

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

   5. Applied rewrites 83.7%

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

   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 70.4

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

   8. Applied rewrites 70.4%

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

Alternative 10: 75.1% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{e^{-b}}{y}\\ \mathbf{if}\;b \leq -1.3 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+39}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (exp (- b)) y))))
   (if (<= b -1.3e+27)
     t_1
     (if (<= b 2.5e+39) (/ (* (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 * (exp(-b) / y);
	double tmp;
	if (b <= -1.3e+27) {
		tmp = t_1;
	} else if (b <= 2.5e+39) {
		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 * (exp(-b) / y)
    if (b <= (-1.3d+27)) then
        tmp = t_1
    else if (b <= 2.5d+39) 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.exp(-b) / y);
	double tmp;
	if (b <= -1.3e+27) {
		tmp = t_1;
	} else if (b <= 2.5e+39) {
		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.exp(-b) / y)
	tmp = 0
	if b <= -1.3e+27:
		tmp = t_1
	elif b <= 2.5e+39:
		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(exp(Float64(-b)) / y))
	tmp = 0.0
	if (b <= -1.3e+27)
		tmp = t_1;
	elseif (b <= 2.5e+39)
		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 * (exp(-b) / y);
	tmp = 0.0;
	if (b <= -1.3e+27)
		tmp = t_1;
	elseif (b <= 2.5e+39)
		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[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.3e+27], t$95$1, If[LessEqual[b, 2.5e+39], N[(N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.30000000000000004e27 or 2.50000000000000008e39 < 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 80.8

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

   5. Applied rewrites 80.8%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]
   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 80.8

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

   7. Applied rewrites 80.8%

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

   if -1.30000000000000004e27 < b < 2.50000000000000008e39

   1. Initial program 96.9%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. 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 83.7

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

   5. Applied rewrites 83.7%

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

   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 70.4

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

   8. Applied rewrites 70.4%

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

Alternative 11: 65.2% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{e^{-b}}{y}\\ \mathbf{if}\;b \leq -1.05 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+39}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (exp (- b)) y))))
   (if (<= b -1.05e+35) t_1 (if (<= b 2.5e+39) (* x (/ (pow a t) y)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (exp(-b) / y);
	double tmp;
	if (b <= -1.05e+35) {
		tmp = t_1;
	} else if (b <= 2.5e+39) {
		tmp = x * (pow(a, t) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (exp(-b) / y)
    if (b <= (-1.05d+35)) then
        tmp = t_1
    else if (b <= 2.5d+39) then
        tmp = x * ((a ** t) / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (Math.exp(-b) / y);
	double tmp;
	if (b <= -1.05e+35) {
		tmp = t_1;
	} else if (b <= 2.5e+39) {
		tmp = x * (Math.pow(a, t) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (math.exp(-b) / y)
	tmp = 0
	if b <= -1.05e+35:
		tmp = t_1
	elif b <= 2.5e+39:
		tmp = x * (math.pow(a, t) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(exp(Float64(-b)) / y))
	tmp = 0.0
	if (b <= -1.05e+35)
		tmp = t_1;
	elseif (b <= 2.5e+39)
		tmp = Float64(x * Float64((a ^ t) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (exp(-b) / y);
	tmp = 0.0;
	if (b <= -1.05e+35)
		tmp = t_1;
	elseif (b <= 2.5e+39)
		tmp = x * ((a ^ t) / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.05e+35], t$95$1, If[LessEqual[b, 2.5e+39], N[(x * N[(N[Power[a, t], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.0499999999999999e35 or 2.50000000000000008e39 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 81.0

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

   5. Applied rewrites 81.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 81.0

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

   7. Applied rewrites 81.0%

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

   if -1.0499999999999999e35 < b < 2.50000000000000008e39

   1. Initial program 96.9%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. 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 83.7

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

   5. Applied rewrites 83.7%

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

   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 70.4

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

   8. Applied rewrites 70.4%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 52.5%

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

Alternative 12: 32.4% 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 98.3%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
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 70.0

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

5. Applied rewrites 70.0%

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

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 55.5

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

8. Applied rewrites 55.5%

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

   1. lift-*.f64 N/A

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

   2. lift-/.f64 N/A

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

   3. lift-/.f64 N/A

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

   4. lift-pow.f64 N/A

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

   5. frac-times N/A

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

   6. lower-/.f64 N/A

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

   7. *-commutative N/A

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

   8. lower-*.f64 N/A

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

   9. lift-pow.f64 N/A

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

   10. lower-*.f64 55.2

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

10. Applied rewrites 55.2%

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

11. Taylor expanded in y around 0

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

13. Applied rewrites 32.4%

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

Developer Target 1: 72.7% 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 2025088 
(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))