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

Percentage Accurate: 99.8% → 99.8%

Time: 6.3s

Alternatives: 14

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
}

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, c, i)
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), intent (in) :: c
    real(8), intent (in) :: i
    code = (((((x * log(y)) + z) + t) + a) + ((b - 0.5d0) * log(c))) + (y * i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (((((x * Math.log(y)) + z) + t) + a) + ((b - 0.5) * Math.log(c))) + (y * i);
}

Python

def code(x, y, z, t, a, b, c, i):
	return (((((x * math.log(y)) + z) + t) + a) + ((b - 0.5) * math.log(c))) + (y * i)

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + z) + t) + a) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
}

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, c, i)
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), intent (in) :: c
    real(8), intent (in) :: i
    code = (((((x * log(y)) + z) + t) + a) + ((b - 0.5d0) * log(c))) + (y * i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (((((x * Math.log(y)) + z) + t) + a) + ((b - 0.5) * Math.log(c))) + (y * i);
}

Python

def code(x, y, z, t, a, b, c, i):
	return (((((x * math.log(y)) + z) + t) + a) + ((b - 0.5) * math.log(c))) + (y * i)

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + z) + t) + a) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
}

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, c, i)
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), intent (in) :: c
    real(8), intent (in) :: i
    code = (((((x * log(y)) + z) + t) + a) + ((b - 0.5d0) * log(c))) + (y * i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (((((x * Math.log(y)) + z) + t) + a) + ((b - 0.5) * Math.log(c))) + (y * i);
}

Python

def code(x, y, z, t, a, b, c, i):
	return (((((x * math.log(y)) + z) + t) + a) + ((b - 0.5) * math.log(c))) + (y * i)

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + z) + t) + a) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
2. Add Preprocessing

Alternative 2: 95.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - 0.5, \left(\frac{z}{x} + \log y\right) \cdot x + t\right)\right)\\ \mathbf{if}\;x \leq -6.2 \cdot 10^{+179}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+112}:\\ \;\;\;\;\mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - 0.5, z + \left(t + a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (fma y i (fma (log c) (- b 0.5) (+ (* (+ (/ z x) (log y)) x) t)))))
   (if (<= x -6.2e+179)
     t_1
     (if (<= x 3.2e+112)
       (fma y i (fma (log c) (- b 0.5) (+ z (+ t a))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fma(y, i, fma(log(c), (b - 0.5), ((((z / x) + log(y)) * x) + t)));
	double tmp;
	if (x <= -6.2e+179) {
		tmp = t_1;
	} else if (x <= 3.2e+112) {
		tmp = fma(y, i, fma(log(c), (b - 0.5), (z + (t + a))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fma(y, i, fma(log(c), Float64(b - 0.5), Float64(Float64(Float64(Float64(z / x) + log(y)) * x) + t)))
	tmp = 0.0
	if (x <= -6.2e+179)
		tmp = t_1;
	elseif (x <= 3.2e+112)
		tmp = fma(y, i, fma(log(c), Float64(b - 0.5), Float64(z + Float64(t + a))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(y * i + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + N[(N[(N[(N[(z / x), $MachinePrecision] + N[Log[y], $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.2e+179], t$95$1, If[LessEqual[x, 3.2e+112], N[(y * i + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + N[(z + N[(t + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -6.2e179 or 3.19999999999999986e112 < x

   1. Initial program 99.6%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in z around inf

      \[\leadsto \left(\left(\left(\color{blue}{z \cdot \left(1 + \frac{x \cdot \log y}{z}\right)} + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\left(\left(\left(1 + \frac{x \cdot \log y}{z}\right) \cdot \color{blue}{z} + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(1 + \frac{x \cdot \log y}{z}\right) \cdot \color{blue}{z} + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      3. +-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-fma.f64 N/A

         \[\leadsto \left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      6. lower-/.f64 N/A

         \[\leadsto \left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      7. lift-log.f64 69.0

         \[\leadsto \left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Applied rewrites 69.0%

      \[\leadsto \left(\left(\left(\color{blue}{\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z} + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   5. Taylor expanded in x around inf

      \[\leadsto \left(\left(\left(\color{blue}{x \cdot \left(\log y + \frac{z}{x}\right)} + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]
   6. Step-by-step derivation

      1. *-commutative N/A

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

      2. *-commutative N/A

         \[\leadsto \left(\left(\left(\left(\log y + \frac{z}{x}\right) \cdot \color{blue}{x} + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      3. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\log y + \frac{z}{x}\right) \cdot \color{blue}{x} + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      4. +-commutative N/A

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

      5. lower-+.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift-log.f64 99.5

         \[\leadsto \left(\left(\left(\left(\frac{z}{x} + \log y\right) \cdot x + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   7. Applied rewrites 99.5%

      \[\leadsto \left(\left(\left(\color{blue}{\left(\frac{z}{x} + \log y\right) \cdot x} + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   8. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(\left(\frac{z}{x} + \log y\right) \cdot x + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i} \]

      2. lift-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(\frac{z}{x} + \log y\right) \cdot x + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + \color{blue}{y \cdot i} \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{y \cdot i + \left(\left(\left(\left(\frac{z}{x} + \log y\right) \cdot x + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right)} \]

      4. lower-fma.f64 99.5

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \left(\left(\left(\frac{z}{x} + \log y\right) \cdot x + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right)} \]

      5. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\left(\left(\left(\frac{z}{x} + \log y\right) \cdot x + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c}\right) \]

      6. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \left(\left(\left(\frac{z}{x} + \log y\right) \cdot x + t\right) + a\right) + \color{blue}{\left(b - \frac{1}{2}\right)} \cdot \log c\right) \]

      7. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \left(\left(\left(\frac{z}{x} + \log y\right) \cdot x + t\right) + a\right) + \color{blue}{\left(b - \frac{1}{2}\right) \cdot \log c}\right) \]

      8. lift-log.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \left(\left(\left(\frac{z}{x} + \log y\right) \cdot x + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \color{blue}{\log c}\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\left(b - \frac{1}{2}\right) \cdot \log c + \left(\left(\left(\frac{z}{x} + \log y\right) \cdot x + t\right) + a\right)}\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\log c \cdot \left(b - \frac{1}{2}\right)} + \left(\left(\left(\frac{z}{x} + \log y\right) \cdot x + t\right) + a\right)\right) \]

   9. Applied rewrites 99.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - 0.5, \left(\frac{z}{x} + \log y\right) \cdot x + \left(a + t\right)\right)\right)} \]

   10. Taylor expanded in t around inf

       \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - \frac{1}{2}, \left(\frac{z}{x} + \log y\right) \cdot x + \color{blue}{t}\right)\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 90.7%

       \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - 0.5, \left(\frac{z}{x} + \log y\right) \cdot x + \color{blue}{t}\right)\right) \]

   if -6.2e179 < x < 3.19999999999999986e112

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in z around inf

      \[\leadsto \left(\left(\left(\color{blue}{z \cdot \left(1 + \frac{x \cdot \log y}{z}\right)} + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\left(\left(\left(1 + \frac{x \cdot \log y}{z}\right) \cdot \color{blue}{z} + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(1 + \frac{x \cdot \log y}{z}\right) \cdot \color{blue}{z} + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      3. +-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-fma.f64 N/A

         \[\leadsto \left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      6. lower-/.f64 N/A

         \[\leadsto \left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      7. lift-log.f64 96.4

         \[\leadsto \left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Applied rewrites 96.4%

      \[\leadsto \left(\left(\left(\color{blue}{\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z} + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{y \cdot i + \left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{y \cdot i} + \left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) \]

      4. lower-fma.f64 96.4

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right)} \]

      5. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c}\right) \]

      6. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \color{blue}{\left(b - \frac{1}{2}\right)} \cdot \log c\right) \]

      7. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \color{blue}{\left(b - \frac{1}{2}\right) \cdot \log c}\right) \]

      8. lift-log.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \color{blue}{\log c}\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\left(b - \frac{1}{2}\right) \cdot \log c + \left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right)}\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\log c \cdot \left(b - \frac{1}{2}\right)} + \left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right)\right) \]

   6. Applied rewrites 96.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - 0.5, \mathsf{fma}\left(\frac{\log y}{z}, x, 1\right) \cdot z + \left(t + a\right)\right)\right)} \]

   7. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - \frac{1}{2}, z + \left(t + a\right)\right)\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 96.5%

      \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - 0.5, z + \left(t + a\right)\right)\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 91.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;\left(\left(\left(\left(t\_1 + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \leq -40:\\ \;\;\;\;\mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - 0.5, \mathsf{fma}\left(\frac{\log y}{z}, x, 1\right) \cdot z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - 0.5, t\_1 + a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= (+ (+ (+ (+ (+ t_1 z) t) a) (* (- b 0.5) (log c))) (* y i)) -40.0)
     (fma y i (fma (log c) (- b 0.5) (+ (* (fma (/ (log y) z) x 1.0) z) t)))
     (fma y i (fma (log c) (- b 0.5) (+ t_1 a))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * log(y);
	double tmp;
	if ((((((t_1 + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i)) <= -40.0) {
		tmp = fma(y, i, fma(log(c), (b - 0.5), ((fma((log(y) / z), x, 1.0) * z) + t)));
	} else {
		tmp = fma(y, i, fma(log(c), (b - 0.5), (t_1 + a)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(t_1 + z) + t) + a) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i)) <= -40.0)
		tmp = fma(y, i, fma(log(c), Float64(b - 0.5), Float64(Float64(fma(Float64(log(y) / z), x, 1.0) * z) + t)));
	else
		tmp = fma(y, i, fma(log(c), Float64(b - 0.5), Float64(t_1 + a)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(N[(N[(N[(t$95$1 + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], -40.0], N[(y * i + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + N[(N[(N[(N[(N[Log[y], $MachinePrecision] / z), $MachinePrecision] * x + 1.0), $MachinePrecision] * z), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * i + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + N[(t$95$1 + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < -40

   1. Initial program 99.8%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in z around inf

      \[\leadsto \left(\left(\left(\color{blue}{z \cdot \left(1 + \frac{x \cdot \log y}{z}\right)} + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\left(\left(\left(1 + \frac{x \cdot \log y}{z}\right) \cdot \color{blue}{z} + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(1 + \frac{x \cdot \log y}{z}\right) \cdot \color{blue}{z} + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      3. +-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-fma.f64 N/A

         \[\leadsto \left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      6. lower-/.f64 N/A

         \[\leadsto \left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      7. lift-log.f64 89.0

         \[\leadsto \left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Applied rewrites 89.0%

      \[\leadsto \left(\left(\left(\color{blue}{\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z} + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{y \cdot i + \left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{y \cdot i} + \left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) \]

      4. lower-fma.f64 89.0

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right)} \]

      5. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c}\right) \]

      6. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \color{blue}{\left(b - \frac{1}{2}\right)} \cdot \log c\right) \]

      7. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \color{blue}{\left(b - \frac{1}{2}\right) \cdot \log c}\right) \]

      8. lift-log.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \color{blue}{\log c}\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\left(b - \frac{1}{2}\right) \cdot \log c + \left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right)}\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\log c \cdot \left(b - \frac{1}{2}\right)} + \left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right)\right) \]

   6. Applied rewrites 89.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - 0.5, \mathsf{fma}\left(\frac{\log y}{z}, x, 1\right) \cdot z + \left(t + a\right)\right)\right)} \]

   7. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - \frac{1}{2}, \mathsf{fma}\left(\frac{\log y}{z}, x, 1\right) \cdot z + \color{blue}{t}\right)\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 75.2%

      \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - 0.5, \mathsf{fma}\left(\frac{\log y}{z}, x, 1\right) \cdot z + \color{blue}{t}\right)\right) \]

   if -40 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i))

   1. Initial program 99.8%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in t around inf

      \[\leadsto \left(\left(\color{blue}{t \cdot \left(1 + \left(\frac{z}{t} + \frac{x \cdot \log y}{t}\right)\right)} + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\left(\left(1 + \left(\frac{z}{t} + \frac{x \cdot \log y}{t}\right)\right) \cdot \color{blue}{t} + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(1 + \left(\frac{z}{t} + \frac{x \cdot \log y}{t}\right)\right) \cdot \color{blue}{t} + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. div-add-rev N/A

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

      6. lower-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

         \[\leadsto \left(\left(\left(\frac{\mathsf{fma}\left(\log y, x, z\right)}{t} + 1\right) \cdot t + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      10. lift-log.f64 80.9

          \[\leadsto \left(\left(\left(\frac{\mathsf{fma}\left(\log y, x, z\right)}{t} + 1\right) \cdot t + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Applied rewrites 80.9%

      \[\leadsto \left(\left(\color{blue}{\left(\frac{\mathsf{fma}\left(\log y, x, z\right)}{t} + 1\right) \cdot t} + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   5. Taylor expanded in z around inf

      \[\leadsto \left(\left(z + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]
   6. Step-by-step derivation

   7. Applied rewrites 69.5%

      \[\leadsto \left(\left(z + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   8. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(z + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i} \]

      2. lift-*.f64 N/A

         \[\leadsto \left(\left(z + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + \color{blue}{y \cdot i} \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{y \cdot i + \left(\left(z + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right)} \]

      4. lower-fma.f64 69.5

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \left(z + a\right) + \left(b - 0.5\right) \cdot \log c\right)} \]

      5. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\left(z + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c}\right) \]

      6. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \left(z + a\right) + \color{blue}{\left(b - \frac{1}{2}\right)} \cdot \log c\right) \]

      7. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \left(z + a\right) + \color{blue}{\left(b - \frac{1}{2}\right) \cdot \log c}\right) \]

      8. lift-log.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \left(z + a\right) + \left(b - \frac{1}{2}\right) \cdot \color{blue}{\log c}\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\left(b - \frac{1}{2}\right) \cdot \log c + \left(z + a\right)}\right) \]

   9. Applied rewrites 69.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - 0.5, z + a\right)\right)} \]

   10. Taylor expanded in x around inf

       \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - \frac{1}{2}, \color{blue}{x \cdot \log y} + a\right)\right) \]
   11. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - \frac{1}{2}, x \cdot \color{blue}{\log y} + a\right)\right) \]

       2. lift-log.f64 69.1

          \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - 0.5, x \cdot \log y + a\right)\right) \]

   12. Applied rewrites 69.1%

       \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - 0.5, \color{blue}{x \cdot \log y} + a\right)\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 77.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+150}:\\ \;\;\;\;\mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - 0.5, z + \left(t + a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - 0.5, x \cdot \log y + a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -6.6e+150)
   (fma y i (fma (log c) (- b 0.5) (+ z (+ t a))))
   (fma y i (fma (log c) (- b 0.5) (+ (* x (log y)) a)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -6.6e+150) {
		tmp = fma(y, i, fma(log(c), (b - 0.5), (z + (t + a))));
	} else {
		tmp = fma(y, i, fma(log(c), (b - 0.5), ((x * log(y)) + a)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -6.6e+150)
		tmp = fma(y, i, fma(log(c), Float64(b - 0.5), Float64(z + Float64(t + a))));
	else
		tmp = fma(y, i, fma(log(c), Float64(b - 0.5), Float64(Float64(x * log(y)) + a)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -6.6e+150], N[(y * i + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + N[(z + N[(t + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * i + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.59999999999999962e150

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in z around inf

      \[\leadsto \left(\left(\left(\color{blue}{z \cdot \left(1 + \frac{x \cdot \log y}{z}\right)} + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\left(\left(\left(1 + \frac{x \cdot \log y}{z}\right) \cdot \color{blue}{z} + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(1 + \frac{x \cdot \log y}{z}\right) \cdot \color{blue}{z} + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      3. +-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-fma.f64 N/A

         \[\leadsto \left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      6. lower-/.f64 N/A

         \[\leadsto \left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      7. lift-log.f64 99.9

         \[\leadsto \left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Applied rewrites 99.9%

      \[\leadsto \left(\left(\left(\color{blue}{\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z} + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{y \cdot i + \left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{y \cdot i} + \left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) \]

      4. lower-fma.f64 99.9

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right)} \]

      5. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c}\right) \]

      6. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \color{blue}{\left(b - \frac{1}{2}\right)} \cdot \log c\right) \]

      7. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \color{blue}{\left(b - \frac{1}{2}\right) \cdot \log c}\right) \]

      8. lift-log.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \color{blue}{\log c}\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\left(b - \frac{1}{2}\right) \cdot \log c + \left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right)}\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\log c \cdot \left(b - \frac{1}{2}\right)} + \left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right)\right) \]

   6. Applied rewrites 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - 0.5, \mathsf{fma}\left(\frac{\log y}{z}, x, 1\right) \cdot z + \left(t + a\right)\right)\right)} \]

   7. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - \frac{1}{2}, z + \left(t + a\right)\right)\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 89.3%

      \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - 0.5, z + \left(t + a\right)\right)\right) \]

   if -6.59999999999999962e150 < z

   1. Initial program 99.8%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in t around inf

      \[\leadsto \left(\left(\color{blue}{t \cdot \left(1 + \left(\frac{z}{t} + \frac{x \cdot \log y}{t}\right)\right)} + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\left(\left(1 + \left(\frac{z}{t} + \frac{x \cdot \log y}{t}\right)\right) \cdot \color{blue}{t} + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(1 + \left(\frac{z}{t} + \frac{x \cdot \log y}{t}\right)\right) \cdot \color{blue}{t} + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. div-add-rev N/A

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

      6. lower-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

         \[\leadsto \left(\left(\left(\frac{\mathsf{fma}\left(\log y, x, z\right)}{t} + 1\right) \cdot t + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      10. lift-log.f64 83.7

          \[\leadsto \left(\left(\left(\frac{\mathsf{fma}\left(\log y, x, z\right)}{t} + 1\right) \cdot t + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Applied rewrites 83.7%

      \[\leadsto \left(\left(\color{blue}{\left(\frac{\mathsf{fma}\left(\log y, x, z\right)}{t} + 1\right) \cdot t} + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   5. Taylor expanded in z around inf

      \[\leadsto \left(\left(z + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]
   6. Step-by-step derivation

   7. Applied rewrites 67.3%

      \[\leadsto \left(\left(z + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   8. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(z + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i} \]

      2. lift-*.f64 N/A

         \[\leadsto \left(\left(z + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + \color{blue}{y \cdot i} \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{y \cdot i + \left(\left(z + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right)} \]

      4. lower-fma.f64 67.3

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \left(z + a\right) + \left(b - 0.5\right) \cdot \log c\right)} \]

      5. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\left(z + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c}\right) \]

      6. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \left(z + a\right) + \color{blue}{\left(b - \frac{1}{2}\right)} \cdot \log c\right) \]

      7. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \left(z + a\right) + \color{blue}{\left(b - \frac{1}{2}\right) \cdot \log c}\right) \]

      8. lift-log.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \left(z + a\right) + \left(b - \frac{1}{2}\right) \cdot \color{blue}{\log c}\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\left(b - \frac{1}{2}\right) \cdot \log c + \left(z + a\right)}\right) \]

   9. Applied rewrites 67.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - 0.5, z + a\right)\right)} \]

   10. Taylor expanded in x around inf

       \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - \frac{1}{2}, \color{blue}{x \cdot \log y} + a\right)\right) \]
   11. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - \frac{1}{2}, x \cdot \color{blue}{\log y} + a\right)\right) \]

       2. lift-log.f64 72.5

          \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - 0.5, x \cdot \log y + a\right)\right) \]

   12. Applied rewrites 72.5%

       \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - 0.5, \color{blue}{x \cdot \log y} + a\right)\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 74.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - 0.5, x \cdot \log y\right)\right)\\ \mathbf{if}\;x \leq -1 \cdot 10^{+184}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+174}:\\ \;\;\;\;\mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - 0.5, z + \left(t + a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fma y i (fma (log c) (- b 0.5) (* x (log y))))))
   (if (<= x -1e+184)
     t_1
     (if (<= x 1.1e+174)
       (fma y i (fma (log c) (- b 0.5) (+ z (+ t a))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fma(y, i, fma(log(c), (b - 0.5), (x * log(y))));
	double tmp;
	if (x <= -1e+184) {
		tmp = t_1;
	} else if (x <= 1.1e+174) {
		tmp = fma(y, i, fma(log(c), (b - 0.5), (z + (t + a))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fma(y, i, fma(log(c), Float64(b - 0.5), Float64(x * log(y))))
	tmp = 0.0
	if (x <= -1e+184)
		tmp = t_1;
	elseif (x <= 1.1e+174)
		tmp = fma(y, i, fma(log(c), Float64(b - 0.5), Float64(z + Float64(t + a))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(y * i + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1e+184], t$95$1, If[LessEqual[x, 1.1e+174], N[(y * i + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + N[(z + N[(t + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.00000000000000002e184 or 1.1000000000000001e174 < x

   1. Initial program 99.5%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in z around inf

      \[\leadsto \left(\left(\left(\color{blue}{z \cdot \left(1 + \frac{x \cdot \log y}{z}\right)} + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\left(\left(\left(1 + \frac{x \cdot \log y}{z}\right) \cdot \color{blue}{z} + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(1 + \frac{x \cdot \log y}{z}\right) \cdot \color{blue}{z} + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      3. +-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-fma.f64 N/A

         \[\leadsto \left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      6. lower-/.f64 N/A

         \[\leadsto \left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      7. lift-log.f64 66.9

         \[\leadsto \left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Applied rewrites 66.9%

      \[\leadsto \left(\left(\left(\color{blue}{\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z} + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{y \cdot i + \left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{y \cdot i} + \left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) \]

      4. lower-fma.f64 66.9

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right)} \]

      5. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c}\right) \]

      6. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \color{blue}{\left(b - \frac{1}{2}\right)} \cdot \log c\right) \]

      7. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \color{blue}{\left(b - \frac{1}{2}\right) \cdot \log c}\right) \]

      8. lift-log.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \color{blue}{\log c}\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\left(b - \frac{1}{2}\right) \cdot \log c + \left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right)}\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\log c \cdot \left(b - \frac{1}{2}\right)} + \left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right)\right) \]

   6. Applied rewrites 67.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - 0.5, \mathsf{fma}\left(\frac{\log y}{z}, x, 1\right) \cdot z + \left(t + a\right)\right)\right)} \]

   7. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - \frac{1}{2}, \color{blue}{x \cdot \log y}\right)\right) \]
   8. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - \frac{1}{2}, x \cdot \color{blue}{\log y}\right)\right) \]

      2. lift-log.f64 78.6

         \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - 0.5, x \cdot \log y\right)\right) \]

   9. Applied rewrites 78.6%

      \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - 0.5, \color{blue}{x \cdot \log y}\right)\right) \]

   if -1.00000000000000002e184 < x < 1.1000000000000001e174

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in z around inf

      \[\leadsto \left(\left(\left(\color{blue}{z \cdot \left(1 + \frac{x \cdot \log y}{z}\right)} + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\left(\left(\left(1 + \frac{x \cdot \log y}{z}\right) \cdot \color{blue}{z} + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(1 + \frac{x \cdot \log y}{z}\right) \cdot \color{blue}{z} + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      3. +-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-fma.f64 N/A

         \[\leadsto \left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      6. lower-/.f64 N/A

         \[\leadsto \left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      7. lift-log.f64 95.1

         \[\leadsto \left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Applied rewrites 95.1%

      \[\leadsto \left(\left(\left(\color{blue}{\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z} + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{y \cdot i + \left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{y \cdot i} + \left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) \]

      4. lower-fma.f64 95.1

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right)} \]

      5. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c}\right) \]

      6. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \color{blue}{\left(b - \frac{1}{2}\right)} \cdot \log c\right) \]

      7. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \color{blue}{\left(b - \frac{1}{2}\right) \cdot \log c}\right) \]

      8. lift-log.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \color{blue}{\log c}\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\left(b - \frac{1}{2}\right) \cdot \log c + \left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right)}\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\log c \cdot \left(b - \frac{1}{2}\right)} + \left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right)\right) \]

   6. Applied rewrites 95.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - 0.5, \mathsf{fma}\left(\frac{\log y}{z}, x, 1\right) \cdot z + \left(t + a\right)\right)\right)} \]

   7. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - \frac{1}{2}, z + \left(t + a\right)\right)\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 95.4%

      \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - 0.5, z + \left(t + a\right)\right)\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 73.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - 0.5, x \cdot \log y\right)\right)\\ \mathbf{if}\;x \leq -1 \cdot 10^{+184}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+174}:\\ \;\;\;\;\mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - 0.5, z + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fma y i (fma (log c) (- b 0.5) (* x (log y))))))
   (if (<= x -1e+184)
     t_1
     (if (<= x 1.1e+174) (fma y i (fma (log c) (- b 0.5) (+ z a))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fma(y, i, fma(log(c), (b - 0.5), (x * log(y))));
	double tmp;
	if (x <= -1e+184) {
		tmp = t_1;
	} else if (x <= 1.1e+174) {
		tmp = fma(y, i, fma(log(c), (b - 0.5), (z + a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fma(y, i, fma(log(c), Float64(b - 0.5), Float64(x * log(y))))
	tmp = 0.0
	if (x <= -1e+184)
		tmp = t_1;
	elseif (x <= 1.1e+174)
		tmp = fma(y, i, fma(log(c), Float64(b - 0.5), Float64(z + a)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(y * i + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1e+184], t$95$1, If[LessEqual[x, 1.1e+174], N[(y * i + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.00000000000000002e184 or 1.1000000000000001e174 < x

   1. Initial program 99.5%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in z around inf

      \[\leadsto \left(\left(\left(\color{blue}{z \cdot \left(1 + \frac{x \cdot \log y}{z}\right)} + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\left(\left(\left(1 + \frac{x \cdot \log y}{z}\right) \cdot \color{blue}{z} + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(1 + \frac{x \cdot \log y}{z}\right) \cdot \color{blue}{z} + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      3. +-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-fma.f64 N/A

         \[\leadsto \left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      6. lower-/.f64 N/A

         \[\leadsto \left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      7. lift-log.f64 66.9

         \[\leadsto \left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Applied rewrites 66.9%

      \[\leadsto \left(\left(\left(\color{blue}{\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z} + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{y \cdot i + \left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{y \cdot i} + \left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) \]

      4. lower-fma.f64 66.9

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right)} \]

      5. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c}\right) \]

      6. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \color{blue}{\left(b - \frac{1}{2}\right)} \cdot \log c\right) \]

      7. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \color{blue}{\left(b - \frac{1}{2}\right) \cdot \log c}\right) \]

      8. lift-log.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \color{blue}{\log c}\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\left(b - \frac{1}{2}\right) \cdot \log c + \left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right)}\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\log c \cdot \left(b - \frac{1}{2}\right)} + \left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right)\right) \]

   6. Applied rewrites 67.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - 0.5, \mathsf{fma}\left(\frac{\log y}{z}, x, 1\right) \cdot z + \left(t + a\right)\right)\right)} \]

   7. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - \frac{1}{2}, \color{blue}{x \cdot \log y}\right)\right) \]
   8. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - \frac{1}{2}, x \cdot \color{blue}{\log y}\right)\right) \]

      2. lift-log.f64 78.6

         \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - 0.5, x \cdot \log y\right)\right) \]

   9. Applied rewrites 78.6%

      \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - 0.5, \color{blue}{x \cdot \log y}\right)\right) \]

   if -1.00000000000000002e184 < x < 1.1000000000000001e174

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in t around inf

      \[\leadsto \left(\left(\color{blue}{t \cdot \left(1 + \left(\frac{z}{t} + \frac{x \cdot \log y}{t}\right)\right)} + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\left(\left(1 + \left(\frac{z}{t} + \frac{x \cdot \log y}{t}\right)\right) \cdot \color{blue}{t} + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(1 + \left(\frac{z}{t} + \frac{x \cdot \log y}{t}\right)\right) \cdot \color{blue}{t} + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. div-add-rev N/A

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

      6. lower-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

         \[\leadsto \left(\left(\left(\frac{\mathsf{fma}\left(\log y, x, z\right)}{t} + 1\right) \cdot t + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      10. lift-log.f64 86.0

          \[\leadsto \left(\left(\left(\frac{\mathsf{fma}\left(\log y, x, z\right)}{t} + 1\right) \cdot t + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Applied rewrites 86.0%

      \[\leadsto \left(\left(\color{blue}{\left(\frac{\mathsf{fma}\left(\log y, x, z\right)}{t} + 1\right) \cdot t} + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   5. Taylor expanded in z around inf

      \[\leadsto \left(\left(z + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]
   6. Step-by-step derivation

   7. Applied rewrites 77.7%

      \[\leadsto \left(\left(z + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   8. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(z + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i} \]

      2. lift-*.f64 N/A

         \[\leadsto \left(\left(z + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + \color{blue}{y \cdot i} \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{y \cdot i + \left(\left(z + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right)} \]

      4. lower-fma.f64 77.7

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \left(z + a\right) + \left(b - 0.5\right) \cdot \log c\right)} \]

      5. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\left(z + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c}\right) \]

      6. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \left(z + a\right) + \color{blue}{\left(b - \frac{1}{2}\right)} \cdot \log c\right) \]

      7. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \left(z + a\right) + \color{blue}{\left(b - \frac{1}{2}\right) \cdot \log c}\right) \]

      8. lift-log.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \left(z + a\right) + \left(b - \frac{1}{2}\right) \cdot \color{blue}{\log c}\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\left(b - \frac{1}{2}\right) \cdot \log c + \left(z + a\right)}\right) \]

   9. Applied rewrites 77.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - 0.5, z + a\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 72.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log y \cdot x\\ \mathbf{if}\;x \leq -2.7 \cdot 10^{+186}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{+215}:\\ \;\;\;\;\mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - 0.5, z + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (log y) x)))
   (if (<= x -2.7e+186)
     t_1
     (if (<= x 2.25e+215) (fma y i (fma (log c) (- b 0.5) (+ z a))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = log(y) * x;
	double tmp;
	if (x <= -2.7e+186) {
		tmp = t_1;
	} else if (x <= 2.25e+215) {
		tmp = fma(y, i, fma(log(c), (b - 0.5), (z + a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(log(y) * x)
	tmp = 0.0
	if (x <= -2.7e+186)
		tmp = t_1;
	elseif (x <= 2.25e+215)
		tmp = fma(y, i, fma(log(c), Float64(b - 0.5), Float64(z + a)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -2.7e+186], t$95$1, If[LessEqual[x, 2.25e+215], N[(y * i + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.6999999999999999e186 or 2.2500000000000001e215 < x

   1. Initial program 99.5%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \log y} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \log y \cdot \color{blue}{x} \]

      2. lower-*.f64 N/A

         \[\leadsto \log y \cdot \color{blue}{x} \]

      3. lift-log.f64 58.6

         \[\leadsto \log y \cdot x \]

   4. Applied rewrites 58.6%

      \[\leadsto \color{blue}{\log y \cdot x} \]

   if -2.6999999999999999e186 < x < 2.2500000000000001e215

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in t around inf

      \[\leadsto \left(\left(\color{blue}{t \cdot \left(1 + \left(\frac{z}{t} + \frac{x \cdot \log y}{t}\right)\right)} + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\left(\left(1 + \left(\frac{z}{t} + \frac{x \cdot \log y}{t}\right)\right) \cdot \color{blue}{t} + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(1 + \left(\frac{z}{t} + \frac{x \cdot \log y}{t}\right)\right) \cdot \color{blue}{t} + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. div-add-rev N/A

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

      6. lower-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

         \[\leadsto \left(\left(\left(\frac{\mathsf{fma}\left(\log y, x, z\right)}{t} + 1\right) \cdot t + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      10. lift-log.f64 85.3

          \[\leadsto \left(\left(\left(\frac{\mathsf{fma}\left(\log y, x, z\right)}{t} + 1\right) \cdot t + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Applied rewrites 85.3%

      \[\leadsto \left(\left(\color{blue}{\left(\frac{\mathsf{fma}\left(\log y, x, z\right)}{t} + 1\right) \cdot t} + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   5. Taylor expanded in z around inf

      \[\leadsto \left(\left(z + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]
   6. Step-by-step derivation

   7. Applied rewrites 76.5%

      \[\leadsto \left(\left(z + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   8. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(z + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i} \]

      2. lift-*.f64 N/A

         \[\leadsto \left(\left(z + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + \color{blue}{y \cdot i} \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{y \cdot i + \left(\left(z + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right)} \]

      4. lower-fma.f64 76.5

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \left(z + a\right) + \left(b - 0.5\right) \cdot \log c\right)} \]

      5. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\left(z + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c}\right) \]

      6. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \left(z + a\right) + \color{blue}{\left(b - \frac{1}{2}\right)} \cdot \log c\right) \]

      7. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \left(z + a\right) + \color{blue}{\left(b - \frac{1}{2}\right) \cdot \log c}\right) \]

      8. lift-log.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \left(z + a\right) + \left(b - \frac{1}{2}\right) \cdot \color{blue}{\log c}\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\left(b - \frac{1}{2}\right) \cdot \log c + \left(z + a\right)}\right) \]

   9. Applied rewrites 76.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - 0.5, z + a\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 61.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \leq -40:\\ \;\;\;\;\mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - 0.5, z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - 0.5, t + a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<=
      (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i))
      -40.0)
   (fma y i (fma (log c) (- b 0.5) z))
   (fma y i (fma (log c) (- b 0.5) (+ t a)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i)) <= -40.0) {
		tmp = fma(y, i, fma(log(c), (b - 0.5), z));
	} else {
		tmp = fma(y, i, fma(log(c), (b - 0.5), (t + a)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + z) + t) + a) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i)) <= -40.0)
		tmp = fma(y, i, fma(log(c), Float64(b - 0.5), z));
	else
		tmp = fma(y, i, fma(log(c), Float64(b - 0.5), Float64(t + a)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], -40.0], N[(y * i + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision], N[(y * i + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + N[(t + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < -40

   1. Initial program 99.8%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in z around inf

      \[\leadsto \left(\left(\left(\color{blue}{z \cdot \left(1 + \frac{x \cdot \log y}{z}\right)} + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\left(\left(\left(1 + \frac{x \cdot \log y}{z}\right) \cdot \color{blue}{z} + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(1 + \frac{x \cdot \log y}{z}\right) \cdot \color{blue}{z} + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      3. +-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-fma.f64 N/A

         \[\leadsto \left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      6. lower-/.f64 N/A

         \[\leadsto \left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      7. lift-log.f64 89.0

         \[\leadsto \left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Applied rewrites 89.0%

      \[\leadsto \left(\left(\left(\color{blue}{\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z} + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{y \cdot i + \left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{y \cdot i} + \left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) \]

      4. lower-fma.f64 89.0

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right)} \]

      5. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c}\right) \]

      6. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \color{blue}{\left(b - \frac{1}{2}\right)} \cdot \log c\right) \]

      7. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \color{blue}{\left(b - \frac{1}{2}\right) \cdot \log c}\right) \]

      8. lift-log.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \color{blue}{\log c}\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\left(b - \frac{1}{2}\right) \cdot \log c + \left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right)}\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\log c \cdot \left(b - \frac{1}{2}\right)} + \left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right)\right) \]

   6. Applied rewrites 89.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - 0.5, \mathsf{fma}\left(\frac{\log y}{z}, x, 1\right) \cdot z + \left(t + a\right)\right)\right)} \]

   7. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - \frac{1}{2}, \color{blue}{z}\right)\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 54.0%

      \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - 0.5, \color{blue}{z}\right)\right) \]

   if -40 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i))

   1. Initial program 99.8%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in t around inf

      \[\leadsto \left(\left(\color{blue}{t} + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]
   3. Step-by-step derivation

   4. Applied rewrites 69.2%

      \[\leadsto \left(\left(\color{blue}{t} + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(t + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{y \cdot i + \left(\left(t + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{y \cdot i} + \left(\left(t + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) \]

      4. lower-fma.f64 69.2

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \left(t + a\right) + \left(b - 0.5\right) \cdot \log c\right)} \]

      5. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\left(t + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c}\right) \]

      6. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \left(t + a\right) + \color{blue}{\left(b - \frac{1}{2}\right)} \cdot \log c\right) \]

      7. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \left(t + a\right) + \color{blue}{\left(b - \frac{1}{2}\right) \cdot \log c}\right) \]

      8. lift-log.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \left(t + a\right) + \left(b - \frac{1}{2}\right) \cdot \color{blue}{\log c}\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\left(b - \frac{1}{2}\right) \cdot \log c + \left(t + a\right)}\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\log c \cdot \left(b - \frac{1}{2}\right)} + \left(t + a\right)\right) \]

      11. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\mathsf{fma}\left(\log c, b - \frac{1}{2}, t + a\right)}\right) \]

      12. lift-log.f64 N/A

          \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\color{blue}{\log c}, b - \frac{1}{2}, t + a\right)\right) \]

      13. lift--.f64 69.2

          \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, \color{blue}{b - 0.5}, t + a\right)\right) \]

   6. Applied rewrites 69.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - 0.5, t + a\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 59.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \leq -40:\\ \;\;\;\;\mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - 0.5, z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - 0.5, a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<=
      (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i))
      -40.0)
   (fma y i (fma (log c) (- b 0.5) z))
   (fma y i (fma (log c) (- b 0.5) a))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i)) <= -40.0) {
		tmp = fma(y, i, fma(log(c), (b - 0.5), z));
	} else {
		tmp = fma(y, i, fma(log(c), (b - 0.5), a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + z) + t) + a) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i)) <= -40.0)
		tmp = fma(y, i, fma(log(c), Float64(b - 0.5), z));
	else
		tmp = fma(y, i, fma(log(c), Float64(b - 0.5), a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], -40.0], N[(y * i + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision], N[(y * i + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < -40

   1. Initial program 99.8%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in z around inf

      \[\leadsto \left(\left(\left(\color{blue}{z \cdot \left(1 + \frac{x \cdot \log y}{z}\right)} + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\left(\left(\left(1 + \frac{x \cdot \log y}{z}\right) \cdot \color{blue}{z} + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(1 + \frac{x \cdot \log y}{z}\right) \cdot \color{blue}{z} + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      3. +-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-fma.f64 N/A

         \[\leadsto \left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      6. lower-/.f64 N/A

         \[\leadsto \left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      7. lift-log.f64 89.0

         \[\leadsto \left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Applied rewrites 89.0%

      \[\leadsto \left(\left(\left(\color{blue}{\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z} + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{y \cdot i + \left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{y \cdot i} + \left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) \]

      4. lower-fma.f64 89.0

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right)} \]

      5. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c}\right) \]

      6. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \color{blue}{\left(b - \frac{1}{2}\right)} \cdot \log c\right) \]

      7. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \color{blue}{\left(b - \frac{1}{2}\right) \cdot \log c}\right) \]

      8. lift-log.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \color{blue}{\log c}\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\left(b - \frac{1}{2}\right) \cdot \log c + \left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right)}\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\log c \cdot \left(b - \frac{1}{2}\right)} + \left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right)\right) \]

   6. Applied rewrites 89.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - 0.5, \mathsf{fma}\left(\frac{\log y}{z}, x, 1\right) \cdot z + \left(t + a\right)\right)\right)} \]

   7. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - \frac{1}{2}, \color{blue}{z}\right)\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 54.0%

      \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - 0.5, \color{blue}{z}\right)\right) \]

   if -40 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i))

   1. Initial program 99.8%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in z around inf

      \[\leadsto \left(\left(\left(\color{blue}{z \cdot \left(1 + \frac{x \cdot \log y}{z}\right)} + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\left(\left(\left(1 + \frac{x \cdot \log y}{z}\right) \cdot \color{blue}{z} + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(\left(1 + \frac{x \cdot \log y}{z}\right) \cdot \color{blue}{z} + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      3. +-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-fma.f64 N/A

         \[\leadsto \left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      6. lower-/.f64 N/A

         \[\leadsto \left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      7. lift-log.f64 89.4

         \[\leadsto \left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Applied rewrites 89.4%

      \[\leadsto \left(\left(\left(\color{blue}{\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z} + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{y \cdot i + \left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right)} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{y \cdot i} + \left(\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) \]

      4. lower-fma.f64 89.4

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right)} \]

      5. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c}\right) \]

      6. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \color{blue}{\left(b - \frac{1}{2}\right)} \cdot \log c\right) \]

      7. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \color{blue}{\left(b - \frac{1}{2}\right) \cdot \log c}\right) \]

      8. lift-log.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \color{blue}{\log c}\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\left(b - \frac{1}{2}\right) \cdot \log c + \left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right)}\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\log c \cdot \left(b - \frac{1}{2}\right)} + \left(\left(\mathsf{fma}\left(x, \frac{\log y}{z}, 1\right) \cdot z + t\right) + a\right)\right) \]

   6. Applied rewrites 89.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - 0.5, \mathsf{fma}\left(\frac{\log y}{z}, x, 1\right) \cdot z + \left(t + a\right)\right)\right)} \]

   7. Taylor expanded in a around inf

      \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - \frac{1}{2}, \color{blue}{a}\right)\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 54.5%

      \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - 0.5, \color{blue}{a}\right)\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 54.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log y \cdot x\\ \mathbf{if}\;x \leq -2.7 \cdot 10^{+186}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+215}:\\ \;\;\;\;\mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, -0.5, z + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (log y) x)))
   (if (<= x -2.7e+186)
     t_1
     (if (<= x 1.5e+215) (fma y i (fma (log c) -0.5 (+ z a))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = log(y) * x;
	double tmp;
	if (x <= -2.7e+186) {
		tmp = t_1;
	} else if (x <= 1.5e+215) {
		tmp = fma(y, i, fma(log(c), -0.5, (z + a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(log(y) * x)
	tmp = 0.0
	if (x <= -2.7e+186)
		tmp = t_1;
	elseif (x <= 1.5e+215)
		tmp = fma(y, i, fma(log(c), -0.5, Float64(z + a)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -2.7e+186], t$95$1, If[LessEqual[x, 1.5e+215], N[(y * i + N[(N[Log[c], $MachinePrecision] * -0.5 + N[(z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.6999999999999999e186 or 1.5e215 < x

   1. Initial program 99.5%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \log y} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \log y \cdot \color{blue}{x} \]

      2. lower-*.f64 N/A

         \[\leadsto \log y \cdot \color{blue}{x} \]

      3. lift-log.f64 58.6

         \[\leadsto \log y \cdot x \]

   4. Applied rewrites 58.6%

      \[\leadsto \color{blue}{\log y \cdot x} \]

   if -2.6999999999999999e186 < x < 1.5e215

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in t around inf

      \[\leadsto \left(\left(\color{blue}{t \cdot \left(1 + \left(\frac{z}{t} + \frac{x \cdot \log y}{t}\right)\right)} + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\left(\left(1 + \left(\frac{z}{t} + \frac{x \cdot \log y}{t}\right)\right) \cdot \color{blue}{t} + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(\left(1 + \left(\frac{z}{t} + \frac{x \cdot \log y}{t}\right)\right) \cdot \color{blue}{t} + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. div-add-rev N/A

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

      6. lower-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

         \[\leadsto \left(\left(\left(\frac{\mathsf{fma}\left(\log y, x, z\right)}{t} + 1\right) \cdot t + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]

      10. lift-log.f64 85.4

          \[\leadsto \left(\left(\left(\frac{\mathsf{fma}\left(\log y, x, z\right)}{t} + 1\right) \cdot t + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Applied rewrites 85.4%

      \[\leadsto \left(\left(\color{blue}{\left(\frac{\mathsf{fma}\left(\log y, x, z\right)}{t} + 1\right) \cdot t} + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   5. Taylor expanded in z around inf

      \[\leadsto \left(\left(z + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \]
   6. Step-by-step derivation

   7. Applied rewrites 76.5%

      \[\leadsto \left(\left(z + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   8. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(z + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i} \]

      2. lift-*.f64 N/A

         \[\leadsto \left(\left(z + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + \color{blue}{y \cdot i} \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{y \cdot i + \left(\left(z + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right)} \]

      4. lower-fma.f64 76.5

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \left(z + a\right) + \left(b - 0.5\right) \cdot \log c\right)} \]

      5. lift-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\left(z + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c}\right) \]

      6. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \left(z + a\right) + \color{blue}{\left(b - \frac{1}{2}\right)} \cdot \log c\right) \]

      7. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \left(z + a\right) + \color{blue}{\left(b - \frac{1}{2}\right) \cdot \log c}\right) \]

      8. lift-log.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, i, \left(z + a\right) + \left(b - \frac{1}{2}\right) \cdot \color{blue}{\log c}\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\left(b - \frac{1}{2}\right) \cdot \log c + \left(z + a\right)}\right) \]

   9. Applied rewrites 76.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - 0.5, z + a\right)\right)} \]

   10. Taylor expanded in b around 0

       \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, \color{blue}{\frac{-1}{2}}, z + a\right)\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 60.0%

       \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, \color{blue}{-0.5}, z + a\right)\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 33.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;i \cdot y\\ \mathbf{elif}\;t\_1 \leq -40:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (+
          (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c)))
          (* y i))))
   (if (<= t_1 (- INFINITY)) (* i y) (if (<= t_1 -40.0) z (fma y i a)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = i * y;
	} else if (t_1 <= -40.0) {
		tmp = z;
	} else {
		tmp = fma(y, i, a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + z) + t) + a) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(i * y);
	elseif (t_1 <= -40.0)
		tmp = z;
	else
		tmp = fma(y, i, a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(i * y), $MachinePrecision], If[LessEqual[t$95$1, -40.0], z, N[(y * i + a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < -inf.0

   1. Initial program 100.0%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{i \cdot y} \]
   3. Step-by-step derivation

      1. lower-*.f64 95.1

         \[\leadsto i \cdot \color{blue}{y} \]

   4. Applied rewrites 95.1%

      \[\leadsto \color{blue}{i \cdot y} \]

   if -inf.0 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < -40

   1. Initial program 99.8%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z} \]
   3. Step-by-step derivation

   4. Applied rewrites 19.0%

      \[\leadsto \color{blue}{z} \]

   if -40 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i))

   1. Initial program 99.8%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a} + y \cdot i \]
   3. Step-by-step derivation

   4. Applied rewrites 38.1%

      \[\leadsto \color{blue}{a} + y \cdot i \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{a + y \cdot i} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{y \cdot i + a} \]

      3. lift-*.f64 N/A

         \[\leadsto \color{blue}{y \cdot i} + a \]

      4. lower-fma.f64 38.1

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, a\right)} \]

   6. Applied rewrites 38.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, a\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 12: 28.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;i \cdot y\\ \mathbf{elif}\;t\_1 \leq -40:\\ \;\;\;\;z\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+302}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;i \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (+
          (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c)))
          (* y i))))
   (if (<= t_1 (- INFINITY))
     (* i y)
     (if (<= t_1 -40.0) z (if (<= t_1 5e+302) a (* i y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = i * y;
	} else if (t_1 <= -40.0) {
		tmp = z;
	} else if (t_1 <= 5e+302) {
		tmp = a;
	} else {
		tmp = i * y;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (((((x * Math.log(y)) + z) + t) + a) + ((b - 0.5) * Math.log(c))) + (y * i);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = i * y;
	} else if (t_1 <= -40.0) {
		tmp = z;
	} else if (t_1 <= 5e+302) {
		tmp = a;
	} else {
		tmp = i * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (((((x * math.log(y)) + z) + t) + a) + ((b - 0.5) * math.log(c))) + (y * i)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = i * y
	elif t_1 <= -40.0:
		tmp = z
	elif t_1 <= 5e+302:
		tmp = a
	else:
		tmp = i * y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + z) + t) + a) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(i * y);
	elseif (t_1 <= -40.0)
		tmp = z;
	elseif (t_1 <= 5e+302)
		tmp = a;
	else
		tmp = Float64(i * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = i * y;
	elseif (t_1 <= -40.0)
		tmp = z;
	elseif (t_1 <= 5e+302)
		tmp = a;
	else
		tmp = i * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(i * y), $MachinePrecision], If[LessEqual[t$95$1, -40.0], z, If[LessEqual[t$95$1, 5e+302], a, N[(i * y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < -inf.0 or 5e302 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i))

   1. Initial program 99.6%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{i \cdot y} \]
   3. Step-by-step derivation

      1. lower-*.f64 82.7

         \[\leadsto i \cdot \color{blue}{y} \]

   4. Applied rewrites 82.7%

      \[\leadsto \color{blue}{i \cdot y} \]

   if -inf.0 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < -40

   1. Initial program 99.8%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z} \]
   3. Step-by-step derivation

   4. Applied rewrites 19.0%

      \[\leadsto \color{blue}{z} \]

   if -40 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < 5e302

   1. Initial program 99.8%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a} \]
   3. Step-by-step derivation

   4. Applied rewrites 18.5%

      \[\leadsto \color{blue}{a} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 13: 16.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \leq -40:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<=
      (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i))
      -40.0)
   z
   a))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i)) <= -40.0) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i)
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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((((((x * log(y)) + z) + t) + a) + ((b - 0.5d0) * log(c))) + (y * i)) <= (-40.0d0)) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((((((x * Math.log(y)) + z) + t) + a) + ((b - 0.5) * Math.log(c))) + (y * i)) <= -40.0) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((((((x * math.log(y)) + z) + t) + a) + ((b - 0.5) * math.log(c))) + (y * i)) <= -40.0:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + z) + t) + a) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i)) <= -40.0)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i)) <= -40.0)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], -40.0], z, a]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < -40

   1. Initial program 99.8%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z} \]
   3. Step-by-step derivation

   4. Applied rewrites 16.8%

      \[\leadsto \color{blue}{z} \]

   if -40 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i))

   1. Initial program 99.8%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   2. Taylor expanded in a around inf

      \[\leadsto \color{blue}{a} \]
   3. Step-by-step derivation

   4. Applied rewrites 16.6%

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

Alternative 14: 16.5% accurate, 21.0× speedup

Math

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

FPCore

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

C

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

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, c, i)
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), intent (in) :: c
    real(8), intent (in) :: i
    code = a
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := a

Derivation

1. Initial program 99.8%

   \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

2. Taylor expanded in a around inf

   \[\leadsto \color{blue}{a} \]
3. Step-by-step derivation

4. Applied rewrites 16.5%

   \[\leadsto \color{blue}{a} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025101 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, B"
  :precision binary64
  (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i)))