Numeric.SpecFunctions:incompleteBetaApprox from math-functions-0.1.5.2, B

Percentage Accurate: 96.4% → 99.3%

Time: 5.8s

Alternatives: 12

Speedup: 1.2×

• 41.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

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)) + (a * (log((1.0d0 - z)) - b))))
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)) + (a * (Math.log((1.0 - z)) - b))));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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)) + (a * (log((1.0d0 - z)) - b))))
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)) + (a * (Math.log((1.0 - z)) - b))));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot e^{\mathsf{fma}\left(-a, b, \left(\log z - t\right) \cdot y\right)}\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-24}:\\ \;\;\;\;e^{\mathsf{fma}\left(\left(-z\right) - b, a, \left(-t\right) \cdot y\right)} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (exp (fma (- a) b (* (- (log z) t) y))))))
   (if (<= y -1.3e-14)
     t_1
     (if (<= y 2e-24) (* (exp (fma (- (- z) b) a (* (- t) y))) x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * exp(fma(-a, b, ((log(z) - t) * y)));
	double tmp;
	if (y <= -1.3e-14) {
		tmp = t_1;
	} else if (y <= 2e-24) {
		tmp = exp(fma((-z - b), a, (-t * y))) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * exp(fma(Float64(-a), b, Float64(Float64(log(z) - t) * y))))
	tmp = 0.0
	if (y <= -1.3e-14)
		tmp = t_1;
	elseif (y <= 2e-24)
		tmp = Float64(exp(fma(Float64(Float64(-z) - b), a, Float64(Float64(-t) * y))) * x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[Exp[N[((-a) * b + N[(N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.3e-14], t$95$1, If[LessEqual[y, 2e-24], N[(N[Exp[N[(N[((-z) - b), $MachinePrecision] * a + N[((-t) * y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.29999999999999998e-14 or 1.99999999999999985e-24 < y

   1. Initial program 97.9%

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

   2. Taylor expanded in z around 0

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

      1. associate-*r* N/A

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

      2. lower-fma.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lift-log.f64 N/A

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

      8. lift--.f64 98.2

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

   4. Applied rewrites 98.2%

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

   if -1.29999999999999998e-14 < y < 1.99999999999999985e-24

   1. Initial program 94.7%

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

   2. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in t around inf

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

      1. mul-1-neg N/A

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

      2. lift-neg.f64 99.9

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

   7. Applied rewrites 99.9%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 99.9

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

   9. Applied rewrites 99.9%

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

Alternative 2: 99.0% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

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)) + (a * (-z - b))))
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)) + (a * (-z - b))));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.4%

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

2. Taylor expanded in z around 0

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

   1. mul-1-neg N/A

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

   2. lower-neg.f64 99.3

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

4. Applied rewrites 99.3%

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

Alternative 3: 93.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := e^{\left(\log z - t\right) \cdot y} \cdot x\\ \mathbf{if}\;y \leq -2.25 \cdot 10^{-13}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+117}:\\ \;\;\;\;e^{\mathsf{fma}\left(\left(-z\right) - b, a, \left(-t\right) \cdot y\right)} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (exp (* (- (log z) t) y)) x)))
   (if (<= y -2.25e-13)
     t_1
     (if (<= y 2.3e+117) (* (exp (fma (- (- z) b) a (* (- t) y))) x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = exp(((log(z) - t) * y)) * x;
	double tmp;
	if (y <= -2.25e-13) {
		tmp = t_1;
	} else if (y <= 2.3e+117) {
		tmp = exp(fma((-z - b), a, (-t * y))) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(exp(Float64(Float64(log(z) - t) * y)) * x)
	tmp = 0.0
	if (y <= -2.25e-13)
		tmp = t_1;
	elseif (y <= 2.3e+117)
		tmp = Float64(exp(fma(Float64(Float64(-z) - b), a, Float64(Float64(-t) * y))) * x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[Exp[N[(N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision] * y), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[y, -2.25e-13], t$95$1, If[LessEqual[y, 2.3e+117], N[(N[Exp[N[(N[((-z) - b), $MachinePrecision] * a + N[((-t) * y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.25e-13 or 2.29999999999999988e117 < y

   1. Initial program 97.9%

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

   2. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-exp.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-log.f64 N/A

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

      7. lift--.f64 89.0

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

   4. Applied rewrites 89.0%

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

   if -2.25e-13 < y < 2.29999999999999988e117

   1. Initial program 95.4%

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

   2. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in t around inf

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

      1. mul-1-neg N/A

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

      2. lift-neg.f64 95.8

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

   7. Applied rewrites 95.8%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 95.8

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

   9. Applied rewrites 95.8%

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

Alternative 4: 89.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := e^{\left(\log z - t\right) \cdot y} \cdot x\\ \mathbf{if}\;y \leq -2.25 \cdot 10^{-13}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+117}:\\ \;\;\;\;x \cdot e^{\mathsf{fma}\left(-a, b, \left(-t\right) \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (exp (* (- (log z) t) y)) x)))
   (if (<= y -2.25e-13)
     t_1
     (if (<= y 2.3e+117) (* x (exp (fma (- a) b (* (- t) y)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = exp(((log(z) - t) * y)) * x;
	double tmp;
	if (y <= -2.25e-13) {
		tmp = t_1;
	} else if (y <= 2.3e+117) {
		tmp = x * exp(fma(-a, b, (-t * y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(exp(Float64(Float64(log(z) - t) * y)) * x)
	tmp = 0.0
	if (y <= -2.25e-13)
		tmp = t_1;
	elseif (y <= 2.3e+117)
		tmp = Float64(x * exp(fma(Float64(-a), b, Float64(Float64(-t) * y))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[Exp[N[(N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision] * y), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[y, -2.25e-13], t$95$1, If[LessEqual[y, 2.3e+117], N[(x * N[Exp[N[((-a) * b + N[((-t) * y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.25e-13 or 2.29999999999999988e117 < y

   1. Initial program 97.9%

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

   2. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-exp.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-log.f64 N/A

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

      7. lift--.f64 89.0

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

   4. Applied rewrites 89.0%

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

   if -2.25e-13 < y < 2.29999999999999988e117

   1. Initial program 95.4%

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

   2. Taylor expanded in z around 0

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

      1. associate-*r* N/A

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

      2. lower-fma.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lift-log.f64 N/A

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

      8. lift--.f64 94.7

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

   4. Applied rewrites 94.7%

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

   5. Taylor expanded in t around inf

      \[\leadsto x \cdot e^{\mathsf{fma}\left(-a, b, \left(-1 \cdot t\right) \cdot y\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. lift-neg.f64 90.5

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

   7. Applied rewrites 90.5%

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

Alternative 5: 84.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot e^{\mathsf{fma}\left(-a, b, \left(-t\right) \cdot y\right)}\\ \mathbf{if}\;t \leq -1.45 \cdot 10^{-133}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-253}:\\ \;\;\;\;{z}^{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (exp (fma (- a) b (* (- t) y))))))
   (if (<= t -1.45e-133) t_1 (if (<= t 6.2e-253) (* (pow z y) x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * exp(fma(-a, b, (-t * y)));
	double tmp;
	if (t <= -1.45e-133) {
		tmp = t_1;
	} else if (t <= 6.2e-253) {
		tmp = pow(z, y) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * exp(fma(Float64(-a), b, Float64(Float64(-t) * y))))
	tmp = 0.0
	if (t <= -1.45e-133)
		tmp = t_1;
	elseif (t <= 6.2e-253)
		tmp = Float64((z ^ y) * x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[Exp[N[((-a) * b + N[((-t) * y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.45e-133], t$95$1, If[LessEqual[t, 6.2e-253], N[(N[Power[z, y], $MachinePrecision] * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.4499999999999999e-133 or 6.19999999999999991e-253 < t

   1. Initial program 96.3%

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

   2. Taylor expanded in z around 0

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

      1. associate-*r* N/A

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

      2. lower-fma.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lift-log.f64 N/A

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

      8. lift--.f64 96.1

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

   4. Applied rewrites 96.1%

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

   5. Taylor expanded in t around inf

      \[\leadsto x \cdot e^{\mathsf{fma}\left(-a, b, \left(-1 \cdot t\right) \cdot y\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. lift-neg.f64 88.0

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

   7. Applied rewrites 88.0%

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

   if -1.4499999999999999e-133 < t < 6.19999999999999991e-253

   1. Initial program 96.8%

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

   2. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-exp.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-log.f64 N/A

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

      7. lift--.f64 66.4

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

   4. Applied rewrites 66.4%

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

   5. Taylor expanded in t around 0

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

      1. lower-pow.f64 66.4

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

   7. Applied rewrites 66.4%

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

Alternative 6: 73.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := {z}^{y} \cdot x\\ \mathbf{if}\;y \leq -2.25 \cdot 10^{-13}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4800:\\ \;\;\;\;e^{\left(-a\right) \cdot b} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (pow z y) x)))
   (if (<= y -2.25e-13) t_1 (if (<= y 4800.0) (* (exp (* (- a) b)) x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = pow(z, y) * x;
	double tmp;
	if (y <= -2.25e-13) {
		tmp = t_1;
	} else if (y <= 4800.0) {
		tmp = exp((-a * b)) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z ** y) * x
    if (y <= (-2.25d-13)) then
        tmp = t_1
    else if (y <= 4800.0d0) then
        tmp = exp((-a * b)) * x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = Math.pow(z, y) * x;
	double tmp;
	if (y <= -2.25e-13) {
		tmp = t_1;
	} else if (y <= 4800.0) {
		tmp = Math.exp((-a * b)) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.pow(z, y) * x
	tmp = 0
	if y <= -2.25e-13:
		tmp = t_1
	elif y <= 4800.0:
		tmp = math.exp((-a * b)) * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64((z ^ y) * x)
	tmp = 0.0
	if (y <= -2.25e-13)
		tmp = t_1;
	elseif (y <= 4800.0)
		tmp = Float64(exp(Float64(Float64(-a) * b)) * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z ^ y) * x;
	tmp = 0.0;
	if (y <= -2.25e-13)
		tmp = t_1;
	elseif (y <= 4800.0)
		tmp = exp((-a * b)) * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[Power[z, y], $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[y, -2.25e-13], t$95$1, If[LessEqual[y, 4800.0], N[(N[Exp[N[((-a) * b), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.25e-13 or 4800 < y

   1. Initial program 98.0%

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

   2. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-exp.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-log.f64 N/A

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

      7. lift--.f64 87.9

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

   4. Applied rewrites 87.9%

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

   5. Taylor expanded in t around 0

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

      1. lower-pow.f64 67.3

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

   7. Applied rewrites 67.3%

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

   if -2.25e-13 < y < 4800

   1. Initial program 94.8%

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

   2. Taylor expanded in b around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 79.8

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

   4. Applied rewrites 79.8%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 79.8

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

   6. Applied rewrites 79.8%

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

Alternative 7: 70.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := e^{\left(-a\right) \cdot b} \cdot x\\ \mathbf{if}\;a \leq -1.85 \cdot 10^{+20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-30}:\\ \;\;\;\;e^{\left(-t\right) \cdot y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (exp (* (- a) b)) x)))
   (if (<= a -1.85e+20) t_1 (if (<= a 1.6e-30) (* (exp (* (- t) y)) x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = exp((-a * b)) * x;
	double tmp;
	if (a <= -1.85e+20) {
		tmp = t_1;
	} else if (a <= 1.6e-30) {
		tmp = exp((-t * y)) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = exp((-a * b)) * x
    if (a <= (-1.85d+20)) then
        tmp = t_1
    else if (a <= 1.6d-30) then
        tmp = exp((-t * y)) * x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = Math.exp((-a * b)) * x;
	double tmp;
	if (a <= -1.85e+20) {
		tmp = t_1;
	} else if (a <= 1.6e-30) {
		tmp = Math.exp((-t * y)) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.exp((-a * b)) * x
	tmp = 0
	if a <= -1.85e+20:
		tmp = t_1
	elif a <= 1.6e-30:
		tmp = math.exp((-t * y)) * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(exp(Float64(Float64(-a) * b)) * x)
	tmp = 0.0
	if (a <= -1.85e+20)
		tmp = t_1;
	elseif (a <= 1.6e-30)
		tmp = Float64(exp(Float64(Float64(-t) * y)) * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = exp((-a * b)) * x;
	tmp = 0.0;
	if (a <= -1.85e+20)
		tmp = t_1;
	elseif (a <= 1.6e-30)
		tmp = exp((-t * y)) * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[Exp[N[((-a) * b), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[a, -1.85e+20], t$95$1, If[LessEqual[a, 1.6e-30], N[(N[Exp[N[((-t) * y), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.85e20 or 1.6e-30 < a

   1. Initial program 93.0%

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

   2. Taylor expanded in b around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 69.4

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

   4. Applied rewrites 69.4%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 69.4

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

   6. Applied rewrites 69.4%

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

   if -1.85e20 < a < 1.6e-30

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 71.2

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

   4. Applied rewrites 71.2%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 71.2

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

   6. Applied rewrites 71.2%

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

Alternative 8: 60.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.26 \cdot 10^{+186}:\\ \;\;\;\;\mathsf{fma}\left(\log z - t, y, 1\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;e^{\left(-a\right) \cdot b} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.26e+186)
   (* (fma (- (log z) t) y 1.0) x)
   (* (exp (* (- a) b)) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.26e+186) {
		tmp = fma((log(z) - t), y, 1.0) * x;
	} else {
		tmp = exp((-a * b)) * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.26e+186)
		tmp = Float64(fma(Float64(log(z) - t), y, 1.0) * x);
	else
		tmp = Float64(exp(Float64(Float64(-a) * b)) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.26e+186], N[(N[(N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision] * y + 1.0), $MachinePrecision] * x), $MachinePrecision], N[(N[Exp[N[((-a) * b), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.26e186

   1. Initial program 97.1%

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

   2. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-exp.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-log.f64 N/A

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

      7. lift--.f64 92.3

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

   4. Applied rewrites 92.3%

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

   5. Taylor expanded in y around 0

      \[\leadsto \left(1 + y \cdot \left(\log z - t\right)\right) \cdot x \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(y \cdot \left(\log z - t\right) + 1\right) \cdot x \]

      2. *-commutative N/A

         \[\leadsto \left(\left(\log z - t\right) \cdot y + 1\right) \cdot x \]

      3. lower-fma.f64 N/A

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

      4. lift-log.f64 N/A

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

      5. lift--.f64 43.8

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

   7. Applied rewrites 43.8%

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

   if -1.26e186 < y

   1. Initial program 96.3%

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

   2. Taylor expanded in b around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 61.8

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

   4. Applied rewrites 61.8%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 61.8

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

   6. Applied rewrites 61.8%

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

Alternative 9: 34.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log z - t\\ \mathbf{if}\;y \cdot t\_1 + a \cdot \left(\log \left(1 - z\right) - b\right) \leq -2 \cdot 10^{+83}:\\ \;\;\;\;\left(y \cdot \left(-t\right)\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, y, 1\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (log z) t)))
   (if (<= (+ (* y t_1) (* a (- (log (- 1.0 z)) b))) -2e+83)
     (* (* y (- t)) x)
     (* (fma t_1 y 1.0) x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = log(z) - t;
	double tmp;
	if (((y * t_1) + (a * (log((1.0 - z)) - b))) <= -2e+83) {
		tmp = (y * -t) * x;
	} else {
		tmp = fma(t_1, y, 1.0) * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(log(z) - t)
	tmp = 0.0
	if (Float64(Float64(y * t_1) + Float64(a * Float64(log(Float64(1.0 - z)) - b))) <= -2e+83)
		tmp = Float64(Float64(y * Float64(-t)) * x);
	else
		tmp = Float64(fma(t_1, y, 1.0) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]}, If[LessEqual[N[(N[(y * t$95$1), $MachinePrecision] + N[(a * N[(N[Log[N[(1.0 - z), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -2e+83], N[(N[(y * (-t)), $MachinePrecision] * x), $MachinePrecision], N[(N[(t$95$1 * y + 1.0), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (*.f64 y (-.f64 (log.f64 z) t)) (*.f64 a (-.f64 (log.f64 (-.f64 #s(literal 1 binary64) z)) b))) < -2.00000000000000006e83

   1. Initial program 99.4%

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

   2. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-exp.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-log.f64 N/A

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

      7. lift--.f64 68.9

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

   4. Applied rewrites 68.9%

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

   5. Taylor expanded in y around 0

      \[\leadsto \left(1 + y \cdot \left(\log z - t\right)\right) \cdot x \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(y \cdot \left(\log z - t\right) + 1\right) \cdot x \]

      2. *-commutative N/A

         \[\leadsto \left(\left(\log z - t\right) \cdot y + 1\right) \cdot x \]

      3. lower-fma.f64 N/A

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

      4. lift-log.f64 N/A

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

      5. lift--.f64 2.6

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

   7. Applied rewrites 2.6%

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

   8. Taylor expanded in t around inf

      \[\leadsto \left(-1 \cdot \left(t \cdot y\right)\right) \cdot x \]
   9. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(t \cdot y\right)\right) \cdot x \]

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

         \[\leadsto \left(\left(\mathsf{neg}\left(t\right)\right) \cdot y\right) \cdot x \]

      3. lift-neg.f64 N/A

         \[\leadsto \left(\left(-t\right) \cdot y\right) \cdot x \]

      4. *-commutative N/A

         \[\leadsto \left(y \cdot \left(-t\right)\right) \cdot x \]

      5. lower-*.f64 14.2

         \[\leadsto \left(y \cdot \left(-t\right)\right) \cdot x \]

   10. Applied rewrites 14.2%

       \[\leadsto \left(y \cdot \left(-t\right)\right) \cdot x \]

   if -2.00000000000000006e83 < (+.f64 (*.f64 y (-.f64 (log.f64 z) t)) (*.f64 a (-.f64 (log.f64 (-.f64 #s(literal 1 binary64) z)) b)))

   1. Initial program 94.9%

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

   2. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-exp.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-log.f64 N/A

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

      7. lift--.f64 73.8

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

   4. Applied rewrites 73.8%

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

   5. Taylor expanded in y around 0

      \[\leadsto \left(1 + y \cdot \left(\log z - t\right)\right) \cdot x \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(y \cdot \left(\log z - t\right) + 1\right) \cdot x \]

      2. *-commutative N/A

         \[\leadsto \left(\left(\log z - t\right) \cdot y + 1\right) \cdot x \]

      3. lower-fma.f64 N/A

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

      4. lift-log.f64 N/A

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

      5. lift--.f64 45.3

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

   7. Applied rewrites 45.3%

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

Alternative 10: 32.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y \cdot \left(-t\right)\right) \cdot x\\ t_2 := y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+83}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+306}:\\ \;\;\;\;\mathsf{fma}\left(\log z, y, 1\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* y (- t)) x))
        (t_2 (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))))
   (if (<= t_2 -2e+83)
     t_1
     (if (<= t_2 1e+306) (* (fma (log z) y 1.0) x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * -t) * x;
	double t_2 = (y * (log(z) - t)) + (a * (log((1.0 - z)) - b));
	double tmp;
	if (t_2 <= -2e+83) {
		tmp = t_1;
	} else if (t_2 <= 1e+306) {
		tmp = fma(log(z), y, 1.0) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * Float64(-t)) * x)
	t_2 = Float64(Float64(y * Float64(log(z) - t)) + Float64(a * Float64(log(Float64(1.0 - z)) - b)))
	tmp = 0.0
	if (t_2 <= -2e+83)
		tmp = t_1;
	elseif (t_2 <= 1e+306)
		tmp = Float64(fma(log(z), y, 1.0) * x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * (-t)), $MachinePrecision] * x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[Log[N[(1.0 - z), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+83], t$95$1, If[LessEqual[t$95$2, 1e+306], N[(N[(N[Log[z], $MachinePrecision] * y + 1.0), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (*.f64 y (-.f64 (log.f64 z) t)) (*.f64 a (-.f64 (log.f64 (-.f64 #s(literal 1 binary64) z)) b))) < -2.00000000000000006e83 or 1.00000000000000002e306 < (+.f64 (*.f64 y (-.f64 (log.f64 z) t)) (*.f64 a (-.f64 (log.f64 (-.f64 #s(literal 1 binary64) z)) b)))

   1. Initial program 98.1%

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

   2. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-exp.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-log.f64 N/A

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

      7. lift--.f64 68.2

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

   4. Applied rewrites 68.2%

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

   5. Taylor expanded in y around 0

      \[\leadsto \left(1 + y \cdot \left(\log z - t\right)\right) \cdot x \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(y \cdot \left(\log z - t\right) + 1\right) \cdot x \]

      2. *-commutative N/A

         \[\leadsto \left(\left(\log z - t\right) \cdot y + 1\right) \cdot x \]

      3. lower-fma.f64 N/A

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

      4. lift-log.f64 N/A

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

      5. lift--.f64 17.0

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

   7. Applied rewrites 17.0%

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

   8. Taylor expanded in t around inf

      \[\leadsto \left(-1 \cdot \left(t \cdot y\right)\right) \cdot x \]
   9. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(t \cdot y\right)\right) \cdot x \]

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

         \[\leadsto \left(\left(\mathsf{neg}\left(t\right)\right) \cdot y\right) \cdot x \]

      3. lift-neg.f64 N/A

         \[\leadsto \left(\left(-t\right) \cdot y\right) \cdot x \]

      4. *-commutative N/A

         \[\leadsto \left(y \cdot \left(-t\right)\right) \cdot x \]

      5. lower-*.f64 24.8

         \[\leadsto \left(y \cdot \left(-t\right)\right) \cdot x \]

   10. Applied rewrites 24.8%

       \[\leadsto \left(y \cdot \left(-t\right)\right) \cdot x \]

   if -2.00000000000000006e83 < (+.f64 (*.f64 y (-.f64 (log.f64 z) t)) (*.f64 a (-.f64 (log.f64 (-.f64 #s(literal 1 binary64) z)) b))) < 1.00000000000000002e306

   1. Initial program 95.0%

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

   2. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-exp.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-log.f64 N/A

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

      7. lift--.f64 75.5

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

   4. Applied rewrites 75.5%

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

   5. Taylor expanded in t around 0

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

      1. lower-pow.f64 59.4

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

   7. Applied rewrites 59.4%

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

   8. Taylor expanded in y around 0

      \[\leadsto \left(1 + y \cdot \log z\right) \cdot x \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(y \cdot \log z + 1\right) \cdot x \]

      2. *-commutative N/A

         \[\leadsto \left(\log z \cdot y + 1\right) \cdot x \]

      3. lower-fma.f64 N/A

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

      4. lift-log.f64 38.9

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

   10. Applied rewrites 38.9%

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

Alternative 11: 31.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y \cdot \left(-t\right)\right) \cdot x\\ t_2 := y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+83}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+126}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* y (- t)) x))
        (t_2 (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))))
   (if (<= t_2 -2e+83) t_1 (if (<= t_2 5e+126) x t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * -t) * x;
	double t_2 = (y * (log(z) - t)) + (a * (log((1.0 - z)) - b));
	double tmp;
	if (t_2 <= -2e+83) {
		tmp = t_1;
	} else if (t_2 <= 5e+126) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * -t) * x
    t_2 = (y * (log(z) - t)) + (a * (log((1.0d0 - z)) - b))
    if (t_2 <= (-2d+83)) then
        tmp = t_1
    else if (t_2 <= 5d+126) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * -t) * x;
	double t_2 = (y * (Math.log(z) - t)) + (a * (Math.log((1.0 - z)) - b));
	double tmp;
	if (t_2 <= -2e+83) {
		tmp = t_1;
	} else if (t_2 <= 5e+126) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y * -t) * x
	t_2 = (y * (math.log(z) - t)) + (a * (math.log((1.0 - z)) - b))
	tmp = 0
	if t_2 <= -2e+83:
		tmp = t_1
	elif t_2 <= 5e+126:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * Float64(-t)) * x)
	t_2 = Float64(Float64(y * Float64(log(z) - t)) + Float64(a * Float64(log(Float64(1.0 - z)) - b)))
	tmp = 0.0
	if (t_2 <= -2e+83)
		tmp = t_1;
	elseif (t_2 <= 5e+126)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y * -t) * x;
	t_2 = (y * (log(z) - t)) + (a * (log((1.0 - z)) - b));
	tmp = 0.0;
	if (t_2 <= -2e+83)
		tmp = t_1;
	elseif (t_2 <= 5e+126)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * (-t)), $MachinePrecision] * x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[Log[N[(1.0 - z), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+83], t$95$1, If[LessEqual[t$95$2, 5e+126], x, t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (*.f64 y (-.f64 (log.f64 z) t)) (*.f64 a (-.f64 (log.f64 (-.f64 #s(literal 1 binary64) z)) b))) < -2.00000000000000006e83 or 4.99999999999999977e126 < (+.f64 (*.f64 y (-.f64 (log.f64 z) t)) (*.f64 a (-.f64 (log.f64 (-.f64 #s(literal 1 binary64) z)) b)))

   1. Initial program 98.4%

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

   2. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-exp.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-log.f64 N/A

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

      7. lift--.f64 69.3

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

   4. Applied rewrites 69.3%

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

   5. Taylor expanded in y around 0

      \[\leadsto \left(1 + y \cdot \left(\log z - t\right)\right) \cdot x \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(y \cdot \left(\log z - t\right) + 1\right) \cdot x \]

      2. *-commutative N/A

         \[\leadsto \left(\left(\log z - t\right) \cdot y + 1\right) \cdot x \]

      3. lower-fma.f64 N/A

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

      4. lift-log.f64 N/A

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

      5. lift--.f64 20.0

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

   7. Applied rewrites 20.0%

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

   8. Taylor expanded in t around inf

      \[\leadsto \left(-1 \cdot \left(t \cdot y\right)\right) \cdot x \]
   9. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(t \cdot y\right)\right) \cdot x \]

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

         \[\leadsto \left(\left(\mathsf{neg}\left(t\right)\right) \cdot y\right) \cdot x \]

      3. lift-neg.f64 N/A

         \[\leadsto \left(\left(-t\right) \cdot y\right) \cdot x \]

      4. *-commutative N/A

         \[\leadsto \left(y \cdot \left(-t\right)\right) \cdot x \]

      5. lower-*.f64 22.4

         \[\leadsto \left(y \cdot \left(-t\right)\right) \cdot x \]

   10. Applied rewrites 22.4%

       \[\leadsto \left(y \cdot \left(-t\right)\right) \cdot x \]

   if -2.00000000000000006e83 < (+.f64 (*.f64 y (-.f64 (log.f64 z) t)) (*.f64 a (-.f64 (log.f64 (-.f64 #s(literal 1 binary64) z)) b))) < 4.99999999999999977e126

   1. Initial program 92.8%

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

   2. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-exp.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-log.f64 N/A

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

      7. lift--.f64 77.1

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

   4. Applied rewrites 77.1%

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

   5. Taylor expanded in y around 0

      \[\leadsto x \]
   6. Step-by-step derivation

   7. Applied rewrites 48.0%

      \[\leadsto x \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 19.8% accurate, 42.1× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := x

Derivation

1. Initial program 96.4%

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

2. Taylor expanded in a around 0

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

   1. *-commutative N/A

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

   2. lower-*.f64 N/A

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

   3. lower-exp.f64 N/A

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

   4. *-commutative N/A

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

   5. lower-*.f64 N/A

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

   6. lift-log.f64 N/A

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

   7. lift--.f64 72.2

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

4. Applied rewrites 72.2%

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

5. Taylor expanded in y around 0

   \[\leadsto x \]
6. Step-by-step derivation

7. Applied rewrites 19.8%

   \[\leadsto x \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2025110 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaApprox from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))))