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

Percentage Accurate: 99.8% → 99.8%

Time: 9.6s

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: 87.3% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(N[(i * y + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + a), $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. Taylor expanded in t around 0

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

   1. +-commutative N/A

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

   2. lower-+.f64 N/A

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

   3. +-commutative N/A

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

   4. lower-+.f64 N/A

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

   5. lower-fma.f64 N/A

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

   6. +-commutative N/A

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

   7. lower-fma.f64 N/A

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

   8. lift-log.f64 N/A

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

   9. lift--.f64 N/A

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

   10. *-commutative N/A

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

   11. lower-*.f64 N/A

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

   12. lift-log.f64 84.6

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

4. Applied rewrites 84.6%

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

Alternative 3: 86.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \leq -2 \cdot 10^{+61}:\\ \;\;\;\;\left(\left(\mathsf{fma}\left(\log c, b - 0.5, i \cdot y\right) + z\right) + t\right) + a\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(i, y, \mathsf{fma}\left(\log c, b - 0.5, \log y \cdot x\right)\right) + t\right) + a\\ \end{array} \end{array} \]

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))
      -2e+61)
   (+ (+ (+ (fma (log c) (- b 0.5) (* i y)) z) t) a)
   (+ (+ (fma i y (fma (log c) (- b 0.5) (* (log y) x))) 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)) <= -2e+61) {
		tmp = ((fma(log(c), (b - 0.5), (i * y)) + z) + t) + a;
	} else {
		tmp = (fma(i, y, fma(log(c), (b - 0.5), (log(y) * x))) + 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)) <= -2e+61)
		tmp = Float64(Float64(Float64(fma(log(c), Float64(b - 0.5), Float64(i * y)) + z) + t) + a);
	else
		tmp = Float64(Float64(fma(i, y, fma(log(c), Float64(b - 0.5), Float64(log(y) * x))) + 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], -2e+61], N[(N[(N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + N[(i * y), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision], N[(N[(N[(i * y + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision] + a), $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)) < -1.9999999999999999e61

   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 x around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lift-log.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lower-*.f64 84.5

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

   4. Applied rewrites 84.5%

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

   if -1.9999999999999999e61 < (+.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 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. lower-fma.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lift-log.f64 N/A

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

      9. lift--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift-log.f64 84.5

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

   4. Applied rewrites 84.5%

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

Alternative 4: 84.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.9 \cdot 10^{+231}:\\ \;\;\;\;\left(\left(\mathsf{fma}\left(\log c, b - 0.5, i \cdot y\right) + z\right) + t\right) + a\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(x, \log y, \log c \cdot \left(b - 0.5\right)\right) + t\right) + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x 1.9e+231)
   (+ (+ (+ (fma (log c) (- b 0.5) (* i y)) z) t) a)
   (+ (+ (fma x (log y) (* (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 <= 1.9e+231) {
		tmp = ((fma(log(c), (b - 0.5), (i * y)) + z) + t) + a;
	} else {
		tmp = (fma(x, log(y), (log(c) * (b - 0.5))) + t) + a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= 1.9e+231)
		tmp = Float64(Float64(Float64(fma(log(c), Float64(b - 0.5), Float64(i * y)) + z) + t) + a);
	else
		tmp = Float64(Float64(fma(x, log(y), Float64(log(c) * Float64(b - 0.5))) + t) + a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, 1.9e+231], N[(N[(N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + N[(i * y), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision], N[(N[(N[(x * N[Log[y], $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.9e231

   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 x around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lift-log.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lower-*.f64 84.5

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

   4. Applied rewrites 84.5%

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

   if 1.9e231 < x

   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 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. lower-fma.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lift-log.f64 N/A

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

      9. lift--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift-log.f64 84.5

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

   4. Applied rewrites 84.5%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lift-log.f64 N/A

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

      3. lift--.f64 69.4

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

   7. Applied rewrites 69.4%

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

   8. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lift-log.f64 N/A

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

      5. div-add-rev N/A

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

      6. lower-/.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lift-log.f64 N/A

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

      9. lift--.f64 N/A

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

      10. lift-*.f64 71.7

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

   10. Applied rewrites 71.7%

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

   11. Taylor expanded in y around 0

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

       1. lower-fma.f64 N/A

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

       2. lift-log.f64 N/A

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

       3. lift-log.f64 N/A

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

       4. lift--.f64 N/A

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

       5. lift-*.f64 62.3

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

   13. Applied rewrites 62.3%

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

Alternative 5: 84.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.45 \cdot 10^{+240}:\\ \;\;\;\;\left(\left(\mathsf{fma}\left(\log c, b - 0.5, i \cdot y\right) + z\right) + t\right) + a\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x 1.45e+240)
   (+ (+ (+ (fma (log c) (- b 0.5) (* i y)) z) t) a)
   (* x (log y))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= 1.45e+240) {
		tmp = ((fma(log(c), (b - 0.5), (i * y)) + z) + t) + a;
	} else {
		tmp = x * log(y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= 1.45e+240)
		tmp = Float64(Float64(Float64(fma(log(c), Float64(b - 0.5), Float64(i * y)) + z) + t) + a);
	else
		tmp = Float64(x * log(y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, 1.45e+240], N[(N[(N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + N[(i * y), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.44999999999999999e240

   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 x around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lift-log.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lower-*.f64 84.5

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

   4. Applied rewrites 84.5%

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

   if 1.44999999999999999e240 < x

   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 x around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lift-log.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lower-*.f64 84.5

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

   4. Applied rewrites 84.5%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lift-log.f64 16.3

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

   7. Applied rewrites 16.3%

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

Alternative 6: 72.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log c \cdot \left(b - 0.5\right)\\ t_2 := \left(\mathsf{fma}\left(i, y, t\_1\right) + t\right) + a\\ t_3 := \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq -5 \cdot 10^{+28}:\\ \;\;\;\;\left(\left(t\_1 + z\right) + t\right) + a\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (log c) (- b 0.5)))
        (t_2 (+ (+ (fma i y t_1) t) a))
        (t_3
         (+
          (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c)))
          (* y i))))
   (if (<= t_3 (- INFINITY))
     t_2
     (if (<= t_3 -5e+28) (+ (+ (+ t_1 z) t) a) t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = log(c) * (b - 0.5);
	double t_2 = (fma(i, y, t_1) + t) + a;
	double t_3 = (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_3 <= -5e+28) {
		tmp = ((t_1 + z) + t) + a;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(log(c) * Float64(b - 0.5))
	t_2 = Float64(Float64(fma(i, y, t_1) + t) + a)
	t_3 = 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_3 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_3 <= -5e+28)
		tmp = Float64(Float64(Float64(t_1 + z) + t) + a);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(i * y + t$95$1), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision]}, Block[{t$95$3 = 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$3, (-Infinity)], t$95$2, If[LessEqual[t$95$3, -5e+28], N[(N[(N[(t$95$1 + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision], t$95$2]]]]]

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)) < -inf.0 or -4.99999999999999957e28 < (+.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 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. lower-fma.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lift-log.f64 N/A

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

      9. lift--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift-log.f64 84.5

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

   4. Applied rewrites 84.5%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lift-log.f64 N/A

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

      3. lift--.f64 69.4

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

   7. Applied rewrites 69.4%

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

   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)) < -4.99999999999999957e28

   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 x around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lift-log.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lower-*.f64 84.5

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

   4. Applied rewrites 84.5%

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

   5. Taylor expanded in y around 0

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

      1. lift-log.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 62.2

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

   7. Applied rewrites 62.2%

      \[\leadsto \left(\left(\log c \cdot \left(b - 0.5\right) + z\right) + t\right) + a \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 71.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\mathsf{fma}\left(i, y, \log c \cdot -0.5\right) + t\right) + a\\ \mathbf{if}\;i \leq -1.1 \cdot 10^{+88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 1.75 \cdot 10^{+65}:\\ \;\;\;\;\left(\left(\log c \cdot \left(b - 0.5\right) + z\right) + t\right) + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (+ (fma i y (* (log c) -0.5)) t) a)))
   (if (<= i -1.1e+88)
     t_1
     (if (<= i 1.75e+65) (+ (+ (+ (* (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(i, y, (log(c) * -0.5)) + t) + a;
	double tmp;
	if (i <= -1.1e+88) {
		tmp = t_1;
	} else if (i <= 1.75e+65) {
		tmp = (((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 = Float64(Float64(fma(i, y, Float64(log(c) * -0.5)) + t) + a)
	tmp = 0.0
	if (i <= -1.1e+88)
		tmp = t_1;
	elseif (i <= 1.75e+65)
		tmp = Float64(Float64(Float64(Float64(log(c) * Float64(b - 0.5)) + z) + 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[(N[(N[(i * y + N[(N[Log[c], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision]}, If[LessEqual[i, -1.1e+88], t$95$1, If[LessEqual[i, 1.75e+65], N[(N[(N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if i < -1.10000000000000004e88 or 1.75e65 < 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 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. lower-fma.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lift-log.f64 N/A

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

      9. lift--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift-log.f64 84.5

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

   4. Applied rewrites 84.5%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lift-log.f64 N/A

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

      3. lift--.f64 69.4

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

   7. Applied rewrites 69.4%

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

   8. Taylor expanded in b around 0

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

   10. Applied rewrites 54.9%

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

   if -1.10000000000000004e88 < i < 1.75e65

   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 x around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lift-log.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lower-*.f64 84.5

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

   4. Applied rewrites 84.5%

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

   5. Taylor expanded in y around 0

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

      1. lift-log.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 62.2

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

   7. Applied rewrites 62.2%

      \[\leadsto \left(\left(\log c \cdot \left(b - 0.5\right) + z\right) + t\right) + a \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 45.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\mathsf{fma}\left(i, y, \log c \cdot -0.5\right) + t\right) + a\\ t_2 := \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{+28}:\\ \;\;\;\;-\left(-z\right)\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+307}:\\ \;\;\;\;\left(\log y \cdot x + t\right) + a\\ \mathbf{else}:\\ \;\;\;\;\left(-a\right) \cdot \left(\left(-\frac{i \cdot y}{a}\right) - 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (+ (fma i y (* (log c) -0.5)) t) a))
        (t_2
         (+
          (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c)))
          (* y i))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -5e+28)
       (- (- z))
       (if (<= t_2 2e+80)
         t_1
         (if (<= t_2 5e+307)
           (+ (+ (* (log y) x) t) a)
           (* (- a) (- (- (/ (* i y) a)) 1.0))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (fma(i, y, (log(c) * -0.5)) + t) + a;
	double t_2 = (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -5e+28) {
		tmp = -(-z);
	} else if (t_2 <= 2e+80) {
		tmp = t_1;
	} else if (t_2 <= 5e+307) {
		tmp = ((log(y) * x) + t) + a;
	} else {
		tmp = -a * (-((i * y) / a) - 1.0);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(fma(i, y, Float64(log(c) * -0.5)) + t) + a)
	t_2 = 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_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -5e+28)
		tmp = Float64(-Float64(-z));
	elseif (t_2 <= 2e+80)
		tmp = t_1;
	elseif (t_2 <= 5e+307)
		tmp = Float64(Float64(Float64(log(y) * x) + t) + a);
	else
		tmp = Float64(Float64(-a) * Float64(Float64(-Float64(Float64(i * y) / a)) - 1.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(i * y + N[(N[Log[c], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision]}, Block[{t$95$2 = 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$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -5e+28], (-(-z)), If[LessEqual[t$95$2, 2e+80], t$95$1, If[LessEqual[t$95$2, 5e+307], N[(N[(N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision], N[((-a) * N[((-N[(N[(i * y), $MachinePrecision] / a), $MachinePrecision]) - 1.0), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 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 -4.99999999999999957e28 < (+.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)) < 2e80

   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 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. lower-fma.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lift-log.f64 N/A

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

      9. lift--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift-log.f64 84.5

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

   4. Applied rewrites 84.5%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lift-log.f64 N/A

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

      3. lift--.f64 69.4

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

   7. Applied rewrites 69.4%

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

   8. Taylor expanded in b around 0

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

   10. Applied rewrites 54.9%

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

   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)) < -4.99999999999999957e28

   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

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

   4. Applied rewrites 72.9%

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

   5. Taylor expanded in z around inf

      \[\leadsto --1 \cdot z \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto -\left(\mathsf{neg}\left(z\right)\right) \]

      2. lower-neg.f64 16.4

         \[\leadsto -\left(-z\right) \]

   7. Applied rewrites 16.4%

      \[\leadsto -\left(-z\right) \]

   if 2e80 < (+.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)) < 5e307

   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 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. lower-fma.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lift-log.f64 N/A

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

      9. lift--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift-log.f64 84.5

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

   4. Applied rewrites 84.5%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lift-log.f64 N/A

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

      3. lift--.f64 69.4

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

   7. Applied rewrites 69.4%

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

   8. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lift-log.f64 N/A

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

      5. div-add-rev N/A

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

      6. lower-/.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lift-log.f64 N/A

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

      9. lift--.f64 N/A

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

      10. lift-*.f64 71.7

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

   10. Applied rewrites 71.7%

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

   11. Taylor expanded in x around inf

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

       1. lift-log.f64 45.9

          \[\leadsto \left(\log y \cdot x + t\right) + a \]

   13. Applied rewrites 45.9%

       \[\leadsto \left(\log y \cdot x + t\right) + a \]

   if 5e307 < (+.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 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. lower-fma.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lift-log.f64 N/A

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

      9. lift--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift-log.f64 84.6

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

   4. Applied rewrites 84.6%

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

   5. Taylor expanded in a around -inf

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 N/A

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

   7. Applied rewrites 64.9%

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

   8. Taylor expanded in y around inf

      \[\leadsto \left(-a\right) \cdot \left(\left(-\frac{i \cdot y}{a}\right) - 1\right) \]
   9. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lower-*.f64 35.9

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

   10. Applied rewrites 35.9%

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

Alternative 9: 43.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;-\left(-i\right) \cdot y\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{+61}:\\ \;\;\;\;-\left(-z\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+307}:\\ \;\;\;\;\left(\log y \cdot x + t\right) + a\\ \mathbf{else}:\\ \;\;\;\;\left(-a\right) \cdot \left(\left(-\frac{i \cdot y}{a}\right) - 1\right)\\ \end{array} \end{array} \]

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 -2e+61)
       (- (- z))
       (if (<= t_1 5e+307)
         (+ (+ (* (log y) x) t) a)
         (* (- a) (- (- (/ (* i y) a)) 1.0)))))))

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 <= -2e+61) {
		tmp = -(-z);
	} else if (t_1 <= 5e+307) {
		tmp = ((log(y) * x) + t) + a;
	} else {
		tmp = -a * (-((i * y) / a) - 1.0);
	}
	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 <= -2e+61) {
		tmp = -(-z);
	} else if (t_1 <= 5e+307) {
		tmp = ((Math.log(y) * x) + t) + a;
	} else {
		tmp = -a * (-((i * y) / a) - 1.0);
	}
	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 <= -2e+61:
		tmp = -(-z)
	elif t_1 <= 5e+307:
		tmp = ((math.log(y) * x) + t) + a
	else:
		tmp = -a * (-((i * y) / a) - 1.0)
	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(-Float64(Float64(-i) * y));
	elseif (t_1 <= -2e+61)
		tmp = Float64(-Float64(-z));
	elseif (t_1 <= 5e+307)
		tmp = Float64(Float64(Float64(log(y) * x) + t) + a);
	else
		tmp = Float64(Float64(-a) * Float64(Float64(-Float64(Float64(i * y) / a)) - 1.0));
	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 <= -2e+61)
		tmp = -(-z);
	elseif (t_1 <= 5e+307)
		tmp = ((log(y) * x) + t) + a;
	else
		tmp = -a * (-((i * y) / a) - 1.0);
	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, -2e+61], (-(-z)), If[LessEqual[t$95$1, 5e+307], N[(N[(N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision], N[((-a) * N[((-N[(N[(i * y), $MachinePrecision] / a), $MachinePrecision]) - 1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 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 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

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

   4. Applied rewrites 72.9%

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

   5. Taylor expanded in y around inf

      \[\leadsto --1 \cdot \left(i \cdot y\right) \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto -\left(-1 \cdot i\right) \cdot y \]

      2. lower-*.f64 N/A

         \[\leadsto -\left(-1 \cdot i\right) \cdot y \]

      3. mul-1-neg N/A

         \[\leadsto -\left(\mathsf{neg}\left(i\right)\right) \cdot y \]

      4. lower-neg.f64 24.0

         \[\leadsto -\left(-i\right) \cdot y \]

   7. Applied rewrites 24.0%

      \[\leadsto -\left(-i\right) \cdot y \]

   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)) < -1.9999999999999999e61

   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

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

   4. Applied rewrites 72.9%

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

   5. Taylor expanded in z around inf

      \[\leadsto --1 \cdot z \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto -\left(\mathsf{neg}\left(z\right)\right) \]

      2. lower-neg.f64 16.4

         \[\leadsto -\left(-z\right) \]

   7. Applied rewrites 16.4%

      \[\leadsto -\left(-z\right) \]

   if -1.9999999999999999e61 < (+.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)) < 5e307

   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 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. lower-fma.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lift-log.f64 N/A

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

      9. lift--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift-log.f64 84.5

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

   4. Applied rewrites 84.5%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lift-log.f64 N/A

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

      3. lift--.f64 69.4

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

   7. Applied rewrites 69.4%

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

   8. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lift-log.f64 N/A

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

      5. div-add-rev N/A

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

      6. lower-/.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lift-log.f64 N/A

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

      9. lift--.f64 N/A

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

      10. lift-*.f64 71.7

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

   10. Applied rewrites 71.7%

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

   11. Taylor expanded in x around inf

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

       1. lift-log.f64 45.9

          \[\leadsto \left(\log y \cdot x + t\right) + a \]

   13. Applied rewrites 45.9%

       \[\leadsto \left(\log y \cdot x + t\right) + a \]

   if 5e307 < (+.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 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. lower-fma.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lift-log.f64 N/A

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

      9. lift--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift-log.f64 84.6

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

   4. Applied rewrites 84.6%

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

   5. Taylor expanded in a around -inf

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 N/A

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

   7. Applied rewrites 64.9%

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

   8. Taylor expanded in y around inf

      \[\leadsto \left(-a\right) \cdot \left(\left(-\frac{i \cdot y}{a}\right) - 1\right) \]
   9. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lower-*.f64 35.9

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

   10. Applied rewrites 35.9%

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

Alternative 10: 32.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;-\left(-i\right) \cdot y\\ \mathbf{elif}\;t\_1 \leq -50:\\ \;\;\;\;-\left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-a\right) \cdot \left(\left(-\frac{i \cdot y}{a}\right) - 1\right)\\ \end{array} \end{array} \]

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 -50.0) (- (- z)) (* (- a) (- (- (/ (* i y) a)) 1.0))))))

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 <= -50.0) {
		tmp = -(-z);
	} else {
		tmp = -a * (-((i * y) / a) - 1.0);
	}
	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 <= -50.0) {
		tmp = -(-z);
	} else {
		tmp = -a * (-((i * y) / a) - 1.0);
	}
	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 <= -50.0:
		tmp = -(-z)
	else:
		tmp = -a * (-((i * y) / a) - 1.0)
	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(-Float64(Float64(-i) * y));
	elseif (t_1 <= -50.0)
		tmp = Float64(-Float64(-z));
	else
		tmp = Float64(Float64(-a) * Float64(Float64(-Float64(Float64(i * y) / a)) - 1.0));
	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 <= -50.0)
		tmp = -(-z);
	else
		tmp = -a * (-((i * y) / a) - 1.0);
	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, -50.0], (-(-z)), N[((-a) * N[((-N[(N[(i * y), $MachinePrecision] / a), $MachinePrecision]) - 1.0), $MachinePrecision]), $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 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

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

   4. Applied rewrites 72.9%

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

   5. Taylor expanded in y around inf

      \[\leadsto --1 \cdot \left(i \cdot y\right) \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto -\left(-1 \cdot i\right) \cdot y \]

      2. lower-*.f64 N/A

         \[\leadsto -\left(-1 \cdot i\right) \cdot y \]

      3. mul-1-neg N/A

         \[\leadsto -\left(\mathsf{neg}\left(i\right)\right) \cdot y \]

      4. lower-neg.f64 24.0

         \[\leadsto -\left(-i\right) \cdot y \]

   7. Applied rewrites 24.0%

      \[\leadsto -\left(-i\right) \cdot y \]

   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)) < -50

   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

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

   4. Applied rewrites 72.9%

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

   5. Taylor expanded in z around inf

      \[\leadsto --1 \cdot z \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto -\left(\mathsf{neg}\left(z\right)\right) \]

      2. lower-neg.f64 16.4

         \[\leadsto -\left(-z\right) \]

   7. Applied rewrites 16.4%

      \[\leadsto -\left(-z\right) \]

   if -50 < (+.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 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. lower-fma.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lift-log.f64 N/A

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

      9. lift--.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift-log.f64 84.6

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

   4. Applied rewrites 84.6%

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

   5. Taylor expanded in a around -inf

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 N/A

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

   7. Applied rewrites 64.9%

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

   8. Taylor expanded in y around inf

      \[\leadsto \left(-a\right) \cdot \left(\left(-\frac{i \cdot y}{a}\right) - 1\right) \]
   9. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lower-*.f64 35.9

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

   10. Applied rewrites 35.9%

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

Alternative 11: 29.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-i\right) \cdot y\\ t_2 := \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;-t\_1\\ \mathbf{elif}\;t\_2 \leq -50:\\ \;\;\;\;-\left(-z\right)\\ \mathbf{elif}\;t\_2 \leq 10^{+308}:\\ \;\;\;\;-\left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;-\frac{t\_1}{z} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (- i) y))
        (t_2
         (+
          (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c)))
          (* y i))))
   (if (<= t_2 (- INFINITY))
     (- t_1)
     (if (<= t_2 -50.0)
       (- (- z))
       (if (<= t_2 1e+308) (- (- a)) (- (* (/ t_1 z) z)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -i * y;
	double t_2 = (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = -t_1;
	} else if (t_2 <= -50.0) {
		tmp = -(-z);
	} else if (t_2 <= 1e+308) {
		tmp = -(-a);
	} else {
		tmp = -((t_1 / z) * z);
	}
	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 = -i * y;
	double t_2 = (((((x * Math.log(y)) + z) + t) + a) + ((b - 0.5) * Math.log(c))) + (y * i);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = -t_1;
	} else if (t_2 <= -50.0) {
		tmp = -(-z);
	} else if (t_2 <= 1e+308) {
		tmp = -(-a);
	} else {
		tmp = -((t_1 / z) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = -i * y
	t_2 = (((((x * math.log(y)) + z) + t) + a) + ((b - 0.5) * math.log(c))) + (y * i)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = -t_1
	elif t_2 <= -50.0:
		tmp = -(-z)
	elif t_2 <= 1e+308:
		tmp = -(-a)
	else:
		tmp = -((t_1 / z) * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(-i) * y)
	t_2 = 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_2 <= Float64(-Inf))
		tmp = Float64(-t_1);
	elseif (t_2 <= -50.0)
		tmp = Float64(-Float64(-z));
	elseif (t_2 <= 1e+308)
		tmp = Float64(-Float64(-a));
	else
		tmp = Float64(-Float64(Float64(t_1 / z) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = -i * y;
	t_2 = (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = -t_1;
	elseif (t_2 <= -50.0)
		tmp = -(-z);
	elseif (t_2 <= 1e+308)
		tmp = -(-a);
	else
		tmp = -((t_1 / z) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[((-i) * y), $MachinePrecision]}, Block[{t$95$2 = 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$2, (-Infinity)], (-t$95$1), If[LessEqual[t$95$2, -50.0], (-(-z)), If[LessEqual[t$95$2, 1e+308], (-(-a)), (-N[(N[(t$95$1 / z), $MachinePrecision] * z), $MachinePrecision])]]]]]

Derivation

1. Split input into 4 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 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

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

   4. Applied rewrites 72.9%

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

   5. Taylor expanded in y around inf

      \[\leadsto --1 \cdot \left(i \cdot y\right) \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto -\left(-1 \cdot i\right) \cdot y \]

      2. lower-*.f64 N/A

         \[\leadsto -\left(-1 \cdot i\right) \cdot y \]

      3. mul-1-neg N/A

         \[\leadsto -\left(\mathsf{neg}\left(i\right)\right) \cdot y \]

      4. lower-neg.f64 24.0

         \[\leadsto -\left(-i\right) \cdot y \]

   7. Applied rewrites 24.0%

      \[\leadsto -\left(-i\right) \cdot y \]

   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)) < -50

   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

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

   4. Applied rewrites 72.9%

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

   5. Taylor expanded in z around inf

      \[\leadsto --1 \cdot z \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto -\left(\mathsf{neg}\left(z\right)\right) \]

      2. lower-neg.f64 16.4

         \[\leadsto -\left(-z\right) \]

   7. Applied rewrites 16.4%

      \[\leadsto -\left(-z\right) \]

   if -50 < (+.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)) < 1e308

   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

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

   4. Applied rewrites 72.9%

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

   5. Taylor expanded in a around inf

      \[\leadsto --1 \cdot a \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto -\left(\mathsf{neg}\left(a\right)\right) \]

      2. lower-neg.f64 17.1

         \[\leadsto -\left(-a\right) \]

   7. Applied rewrites 17.1%

      \[\leadsto -\left(-a\right) \]

   if 1e308 < (+.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

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

   4. Applied rewrites 72.9%

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

   5. Taylor expanded in y around inf

      \[\leadsto -\left(-1 \cdot \frac{i \cdot y}{z}\right) \cdot z \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

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

      2. mul-1-neg N/A

         \[\leadsto -\frac{\mathsf{neg}\left(i \cdot y\right)}{z} \cdot z \]

      3. lower-/.f64 N/A

         \[\leadsto -\frac{\mathsf{neg}\left(i \cdot y\right)}{z} \cdot z \]

      4. mul-1-neg N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

      7. mul-1-neg N/A

         \[\leadsto -\frac{\left(\mathsf{neg}\left(i\right)\right) \cdot y}{z} \cdot z \]

      8. lower-neg.f64 20.4

         \[\leadsto -\frac{\left(-i\right) \cdot y}{z} \cdot z \]

   7. Applied rewrites 20.4%

      \[\leadsto -\frac{\left(-i\right) \cdot y}{z} \cdot z \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 12: 28.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -\left(-i\right) \cdot y\\ t_2 := \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -50:\\ \;\;\;\;-\left(-z\right)\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+305}:\\ \;\;\;\;-\left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (- (* (- i) y)))
        (t_2
         (+
          (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c)))
          (* y i))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -50.0) (- (- z)) (if (<= t_2 5e+305) (- (- 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 = -(-i * y);
	double t_2 = (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -50.0) {
		tmp = -(-z);
	} else if (t_2 <= 5e+305) {
		tmp = -(-a);
	} else {
		tmp = t_1;
	}
	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 = -(-i * y);
	double t_2 = (((((x * Math.log(y)) + z) + t) + a) + ((b - 0.5) * Math.log(c))) + (y * i);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -50.0) {
		tmp = -(-z);
	} else if (t_2 <= 5e+305) {
		tmp = -(-a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = -(-i * y)
	t_2 = (((((x * math.log(y)) + z) + t) + a) + ((b - 0.5) * math.log(c))) + (y * i)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -50.0:
		tmp = -(-z)
	elif t_2 <= 5e+305:
		tmp = -(-a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(-Float64(Float64(-i) * y))
	t_2 = 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_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -50.0)
		tmp = Float64(-Float64(-z));
	elseif (t_2 <= 5e+305)
		tmp = Float64(-Float64(-a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = -(-i * y);
	t_2 = (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -50.0)
		tmp = -(-z);
	elseif (t_2 <= 5e+305)
		tmp = -(-a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = (-N[((-i) * y), $MachinePrecision])}, Block[{t$95$2 = 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$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -50.0], (-(-z)), If[LessEqual[t$95$2, 5e+305], (-(-a)), t$95$1]]]]]

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 5.00000000000000009e305 < (+.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

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

   4. Applied rewrites 72.9%

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

   5. Taylor expanded in y around inf

      \[\leadsto --1 \cdot \left(i \cdot y\right) \]
   6. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto -\left(-1 \cdot i\right) \cdot y \]

      2. lower-*.f64 N/A

         \[\leadsto -\left(-1 \cdot i\right) \cdot y \]

      3. mul-1-neg N/A

         \[\leadsto -\left(\mathsf{neg}\left(i\right)\right) \cdot y \]

      4. lower-neg.f64 24.0

         \[\leadsto -\left(-i\right) \cdot y \]

   7. Applied rewrites 24.0%

      \[\leadsto -\left(-i\right) \cdot y \]

   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)) < -50

   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

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

   4. Applied rewrites 72.9%

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

   5. Taylor expanded in z around inf

      \[\leadsto --1 \cdot z \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto -\left(\mathsf{neg}\left(z\right)\right) \]

      2. lower-neg.f64 16.4

         \[\leadsto -\left(-z\right) \]

   7. Applied rewrites 16.4%

      \[\leadsto -\left(-z\right) \]

   if -50 < (+.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)) < 5.00000000000000009e305

   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

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

   4. Applied rewrites 72.9%

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

   5. Taylor expanded in a around inf

      \[\leadsto --1 \cdot a \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto -\left(\mathsf{neg}\left(a\right)\right) \]

      2. lower-neg.f64 17.1

         \[\leadsto -\left(-a\right) \]

   7. Applied rewrites 17.1%

      \[\leadsto -\left(-a\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 13: 17.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \leq -50:\\ \;\;\;\;-\left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;-\left(-a\right)\\ \end{array} \end{array} \]

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))
      -50.0)
   (- (- 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)) <= -50.0) {
		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)) <= (-50.0d0)) 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)) <= -50.0) {
		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)) <= -50.0:
		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)) <= -50.0)
		tmp = Float64(-Float64(-z));
	else
		tmp = Float64(-Float64(-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)) <= -50.0)
		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], -50.0], (-(-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)) < -50

   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

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

   4. Applied rewrites 72.9%

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

   5. Taylor expanded in z around inf

      \[\leadsto --1 \cdot z \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto -\left(\mathsf{neg}\left(z\right)\right) \]

      2. lower-neg.f64 16.4

         \[\leadsto -\left(-z\right) \]

   7. Applied rewrites 16.4%

      \[\leadsto -\left(-z\right) \]

   if -50 < (+.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

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

   4. Applied rewrites 72.9%

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

   5. Taylor expanded in a around inf

      \[\leadsto --1 \cdot a \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto -\left(\mathsf{neg}\left(a\right)\right) \]

      2. lower-neg.f64 17.1

         \[\leadsto -\left(-a\right) \]

   7. Applied rewrites 17.1%

      \[\leadsto -\left(-a\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 16.6% accurate, 12.8× speedup

Math

\[\begin{array}{l} \\ -\left(-a\right) \end{array} \]

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 Float64(-Float64(-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 z around -inf

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

   1. mul-1-neg N/A

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

   2. lower-neg.f64 N/A

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

   3. *-commutative N/A

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

   4. lower-*.f64 N/A

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

4. Applied rewrites 72.9%

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

5. Taylor expanded in a around inf

   \[\leadsto --1 \cdot a \]
6. Step-by-step derivation

   1. mul-1-neg N/A

      \[\leadsto -\left(\mathsf{neg}\left(a\right)\right) \]

   2. lower-neg.f64 17.1

      \[\leadsto -\left(-a\right) \]

7. Applied rewrites 17.1%

   \[\leadsto -\left(-a\right) \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2025142 
(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)))