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

Percentage Accurate: 99.8% → 99.8%

Time: 9.0s

Alternatives: 17

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: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-+.f64 N/A

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

   4. associate-+r+ N/A

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

   5. lower-+.f64 N/A

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

   6. lift-*.f64 N/A

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

   7. *-commutative N/A

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

   8. lower-fma.f64 99.8

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

   9. lift-+.f64 N/A

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

   10. +-commutative N/A

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

   11. lower-+.f64 99.8

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

   12. lift-+.f64 N/A

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

   13. lift-*.f64 N/A

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

   14. *-commutative N/A

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

   15. lower-fma.f64 99.8

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

3. Applied rewrites 99.8%

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

Alternative 3: 92.8% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(a + N[(z + N[(i * y + N[(x * N[Log[y], $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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. 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. lower-+.f64 N/A

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

   2. lower-+.f64 N/A

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

   3. lower-fma.f64 N/A

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

   4. lower-fma.f64 N/A

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

   5. lower-log.f64 N/A

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

   6. lower-*.f64 N/A

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

   7. lower-log.f64 N/A

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

   8. lower--.f64 84.4

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

4. Applied rewrites 84.4%

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

Alternative 4: 91.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(x, \log y, \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{if}\;x \leq -6.2 \cdot 10^{+106}:\\ \;\;\;\;a + \left(t + \left(z + t\_1\right)\right)\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+150}:\\ \;\;\;\;\left(\mathsf{fma}\left(\log c, b - 0.5, t + z\right) + a\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(i, y, t\_1\right) + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fma x (log y) (* (log c) (- b 0.5)))))
   (if (<= x -6.2e+106)
     (+ a (+ t (+ z t_1)))
     (if (<= x 1.2e+150)
       (+ (+ (fma (log c) (- b 0.5) (+ t z)) a) (* y i))
       (+ (fma i y t_1) t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fma(x, log(y), (log(c) * (b - 0.5)));
	double tmp;
	if (x <= -6.2e+106) {
		tmp = a + (t + (z + t_1));
	} else if (x <= 1.2e+150) {
		tmp = (fma(log(c), (b - 0.5), (t + z)) + a) + (y * i);
	} else {
		tmp = fma(i, y, t_1) + t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fma(x, log(y), Float64(log(c) * Float64(b - 0.5)))
	tmp = 0.0
	if (x <= -6.2e+106)
		tmp = Float64(a + Float64(t + Float64(z + t_1)));
	elseif (x <= 1.2e+150)
		tmp = Float64(Float64(fma(log(c), Float64(b - 0.5), Float64(t + z)) + a) + Float64(y * i));
	else
		tmp = Float64(fma(i, y, t_1) + t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.2e+106], N[(a + N[(t + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.2e+150], N[(N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + N[(t + z), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(N[(i * y + t$95$1), $MachinePrecision] + t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.1999999999999999e106

   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 -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-log.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

   4. Applied rewrites 73.0%

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

   5. Taylor expanded in a around inf

      \[\leadsto -1 \cdot \left(-1 \cdot \color{blue}{a}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 16.0

         \[\leadsto -1 \cdot \left(-1 \cdot a\right) \]

   7. Applied rewrites 16.0%

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

   8. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-log.f64 N/A

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

      8. lower--.f64 77.9

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

   10. Applied rewrites 77.9%

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

   if -6.1999999999999999e106 < x < 1.20000000000000001e150

   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. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-+.f64 N/A

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

      4. associate-+r+ N/A

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

      5. lower-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 99.8

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

      9. lift-+.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 99.8

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

      12. lift-+.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-fma.f64 99.8

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 84.0%

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

   if 1.20000000000000001e150 < 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 a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-log.f64 N/A

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

      8. lower--.f64 84.8

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

   4. Applied rewrites 84.8%

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

   5. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-log.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower--.f64 63.1

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

   7. Applied rewrites 63.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 63.1

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

   9. Applied rewrites 63.1%

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

   10. Taylor expanded in z around 0

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

       1. lower-fma.f64 N/A

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

       2. lower-fma.f64 N/A

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

       3. lower-log.f64 N/A

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

       4. lower-*.f64 N/A

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

       5. lower-log.f64 N/A

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

       6. lower--.f64 69.6

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

   12. Applied rewrites 69.6%

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

Alternative 5: 90.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+151}:\\ \;\;\;\;\left(\mathsf{fma}\left(\log y, x, z\right) - \left(0.5 - b\right) \cdot \log c\right) + t\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+150}:\\ \;\;\;\;\left(\mathsf{fma}\left(\log c, b - 0.5, t + z\right) + a\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(i, y, \mathsf{fma}\left(x, \log y, \log c \cdot \left(b - 0.5\right)\right)\right) + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -2.8e+151)
   (+ (- (fma (log y) x z) (* (- 0.5 b) (log c))) t)
   (if (<= x 1.2e+150)
     (+ (+ (fma (log c) (- b 0.5) (+ t z)) a) (* y i))
     (+ (fma i y (fma x (log y) (* (log c) (- b 0.5)))) t))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -2.8e+151) {
		tmp = (fma(log(y), x, z) - ((0.5 - b) * log(c))) + t;
	} else if (x <= 1.2e+150) {
		tmp = (fma(log(c), (b - 0.5), (t + z)) + a) + (y * i);
	} else {
		tmp = fma(i, y, fma(x, log(y), (log(c) * (b - 0.5)))) + t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -2.8e+151)
		tmp = Float64(Float64(fma(log(y), x, z) - Float64(Float64(0.5 - b) * log(c))) + t);
	elseif (x <= 1.2e+150)
		tmp = Float64(Float64(fma(log(c), Float64(b - 0.5), Float64(t + z)) + a) + Float64(y * i));
	else
		tmp = Float64(fma(i, y, fma(x, log(y), Float64(log(c) * Float64(b - 0.5)))) + t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -2.8e+151], N[(N[(N[(N[Log[y], $MachinePrecision] * x + z), $MachinePrecision] - N[(N[(0.5 - b), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision], If[LessEqual[x, 1.2e+150], N[(N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + N[(t + z), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(N[(i * y + N[(x * N[Log[y], $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.79999999999999987e151

   1. Initial program 99.8%

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

   2. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-log.f64 N/A

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

      8. lower--.f64 84.8

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

   4. Applied rewrites 84.8%

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

   5. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-log.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower--.f64 63.1

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

   7. Applied rewrites 63.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 63.1

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

   9. Applied rewrites 63.1%

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

   if -2.79999999999999987e151 < x < 1.20000000000000001e150

   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. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-+.f64 N/A

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

      4. associate-+r+ N/A

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

      5. lower-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 99.8

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

      9. lift-+.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 99.8

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

      12. lift-+.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-fma.f64 99.8

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 84.0%

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

   if 1.20000000000000001e150 < 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 a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-log.f64 N/A

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

      8. lower--.f64 84.8

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

   4. Applied rewrites 84.8%

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

   5. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-log.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower--.f64 63.1

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

   7. Applied rewrites 63.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 63.1

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

   9. Applied rewrites 63.1%

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

   10. Taylor expanded in z around 0

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

       1. lower-fma.f64 N/A

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

       2. lower-fma.f64 N/A

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

       3. lower-log.f64 N/A

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

       4. lower-*.f64 N/A

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

       5. lower-log.f64 N/A

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

       6. lower--.f64 69.6

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

   12. Applied rewrites 69.6%

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

Alternative 6: 90.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+151}:\\ \;\;\;\;\left(\mathsf{fma}\left(\log y, x, z\right) - \left(0.5 - b\right) \cdot \log c\right) + t\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+233}:\\ \;\;\;\;\left(\mathsf{fma}\left(\log c, b - 0.5, t + z\right) + a\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \left(x \cdot \mathsf{fma}\left(-1, \log y, -1 \cdot \frac{i \cdot y}{x}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -2.8e+151)
   (+ (- (fma (log y) x z) (* (- 0.5 b) (log c))) t)
   (if (<= x 7.5e+233)
     (+ (+ (fma (log c) (- b 0.5) (+ t z)) a) (* y i))
     (* -1.0 (* x (fma -1.0 (log y) (* -1.0 (/ (* i y) x))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -2.8e+151) {
		tmp = (fma(log(y), x, z) - ((0.5 - b) * log(c))) + t;
	} else if (x <= 7.5e+233) {
		tmp = (fma(log(c), (b - 0.5), (t + z)) + a) + (y * i);
	} else {
		tmp = -1.0 * (x * fma(-1.0, log(y), (-1.0 * ((i * y) / x))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -2.8e+151)
		tmp = Float64(Float64(fma(log(y), x, z) - Float64(Float64(0.5 - b) * log(c))) + t);
	elseif (x <= 7.5e+233)
		tmp = Float64(Float64(fma(log(c), Float64(b - 0.5), Float64(t + z)) + a) + Float64(y * i));
	else
		tmp = Float64(-1.0 * Float64(x * fma(-1.0, log(y), Float64(-1.0 * Float64(Float64(i * y) / x)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -2.8e+151], N[(N[(N[(N[Log[y], $MachinePrecision] * x + z), $MachinePrecision] - N[(N[(0.5 - b), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision], If[LessEqual[x, 7.5e+233], N[(N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + N[(t + z), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(-1.0 * N[(x * N[(-1.0 * N[Log[y], $MachinePrecision] + N[(-1.0 * N[(N[(i * y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.79999999999999987e151

   1. Initial program 99.8%

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

   2. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-log.f64 N/A

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

      8. lower--.f64 84.8

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

   4. Applied rewrites 84.8%

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

   5. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-log.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower--.f64 63.1

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

   7. Applied rewrites 63.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 63.1

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

   9. Applied rewrites 63.1%

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

   if -2.79999999999999987e151 < x < 7.4999999999999997e233

   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. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-+.f64 N/A

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

      4. associate-+r+ N/A

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

      5. lower-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 99.8

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

      9. lift-+.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 99.8

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

      12. lift-+.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-fma.f64 99.8

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 84.0%

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

   if 7.4999999999999997e233 < 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 -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-log.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

   4. Applied rewrites 73.0%

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

   5. Taylor expanded in y around inf

      \[\leadsto -1 \cdot \left(x \cdot \mathsf{fma}\left(-1, \log y, -1 \cdot \frac{i \cdot y}{x}\right)\right) \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lower-*.f64 35.0

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

   7. Applied rewrites 35.0%

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

Alternative 7: 89.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -1 \cdot \left(x \cdot \mathsf{fma}\left(-1, \log y, -1 \cdot \frac{i \cdot y}{x}\right)\right)\\ \mathbf{if}\;x \leq -8 \cdot 10^{+200}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+233}:\\ \;\;\;\;\left(\mathsf{fma}\left(\log c, b - 0.5, t + z\right) + a\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* -1.0 (* x (fma -1.0 (log y) (* -1.0 (/ (* i y) x)))))))
   (if (<= x -8e+200)
     t_1
     (if (<= x 7.5e+233)
       (+ (+ (fma (log c) (- b 0.5) (+ t z)) a) (* y i))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -1.0 * (x * fma(-1.0, log(y), (-1.0 * ((i * y) / x))));
	double tmp;
	if (x <= -8e+200) {
		tmp = t_1;
	} else if (x <= 7.5e+233) {
		tmp = (fma(log(c), (b - 0.5), (t + z)) + a) + (y * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(-1.0 * Float64(x * fma(-1.0, log(y), Float64(-1.0 * Float64(Float64(i * y) / x)))))
	tmp = 0.0
	if (x <= -8e+200)
		tmp = t_1;
	elseif (x <= 7.5e+233)
		tmp = Float64(Float64(fma(log(c), Float64(b - 0.5), Float64(t + z)) + a) + Float64(y * i));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(-1.0 * N[(x * N[(-1.0 * N[Log[y], $MachinePrecision] + N[(-1.0 * N[(N[(i * y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8e+200], t$95$1, If[LessEqual[x, 7.5e+233], N[(N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + N[(t + z), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -7.9999999999999998e200 or 7.4999999999999997e233 < 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 -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-log.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

   4. Applied rewrites 73.0%

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

   5. Taylor expanded in y around inf

      \[\leadsto -1 \cdot \left(x \cdot \mathsf{fma}\left(-1, \log y, -1 \cdot \frac{i \cdot y}{x}\right)\right) \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lower-*.f64 35.0

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

   7. Applied rewrites 35.0%

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

   if -7.9999999999999998e200 < x < 7.4999999999999997e233

   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. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-+.f64 N/A

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

      4. associate-+r+ N/A

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

      5. lower-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 99.8

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

      9. lift-+.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 99.8

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

      12. lift-+.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-fma.f64 99.8

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 84.0%

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

Alternative 8: 88.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+151}:\\ \;\;\;\;\left(\mathsf{fma}\left(\log y, x, z\right) - 0.5 \cdot \log c\right) + t\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+233}:\\ \;\;\;\;\left(\mathsf{fma}\left(\log c, b - 0.5, t + z\right) + a\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;t + \left(z + \mathsf{fma}\left(x, \log y, \log c \cdot -0.5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -3e+151)
   (+ (- (fma (log y) x z) (* 0.5 (log c))) t)
   (if (<= x 7.5e+233)
     (+ (+ (fma (log c) (- b 0.5) (+ t z)) a) (* y i))
     (+ t (+ z (fma x (log y) (* (log c) -0.5)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -3e+151) {
		tmp = (fma(log(y), x, z) - (0.5 * log(c))) + t;
	} else if (x <= 7.5e+233) {
		tmp = (fma(log(c), (b - 0.5), (t + z)) + a) + (y * i);
	} else {
		tmp = t + (z + fma(x, log(y), (log(c) * -0.5)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -3e+151)
		tmp = Float64(Float64(fma(log(y), x, z) - Float64(0.5 * log(c))) + t);
	elseif (x <= 7.5e+233)
		tmp = Float64(Float64(fma(log(c), Float64(b - 0.5), Float64(t + z)) + a) + Float64(y * i));
	else
		tmp = Float64(t + Float64(z + fma(x, log(y), Float64(log(c) * -0.5))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -3e+151], N[(N[(N[(N[Log[y], $MachinePrecision] * x + z), $MachinePrecision] - N[(0.5 * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision], If[LessEqual[x, 7.5e+233], N[(N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + N[(t + z), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.9999999999999999e151

   1. Initial program 99.8%

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

   2. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-log.f64 N/A

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

      8. lower--.f64 84.8

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

   4. Applied rewrites 84.8%

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

   5. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-log.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower--.f64 63.1

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

   7. Applied rewrites 63.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 63.1

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

   9. Applied rewrites 63.1%

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

   10. Taylor expanded in b around 0

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

   12. Applied rewrites 47.9%

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

   if -2.9999999999999999e151 < x < 7.4999999999999997e233

   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. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-+.f64 N/A

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

      4. associate-+r+ N/A

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

      5. lower-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 99.8

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

      9. lift-+.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 99.8

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

      12. lift-+.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-fma.f64 99.8

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 84.0%

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

   if 7.4999999999999997e233 < 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 a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-log.f64 N/A

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

      8. lower--.f64 84.8

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

   4. Applied rewrites 84.8%

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

   5. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-log.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower--.f64 63.1

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

   7. Applied rewrites 63.1%

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

   8. Taylor expanded in b around 0

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

   10. Applied rewrites 47.9%

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

Alternative 9: 87.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+151}:\\ \;\;\;\;\left(\mathsf{fma}\left(\log y, x, z\right) - 0.5 \cdot \log c\right) + t\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+233}:\\ \;\;\;\;\left(\mathsf{fma}\left(\log c, b - 0.5, t + z\right) + a\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \left(x \cdot \mathsf{fma}\left(-1, \log y, -1 \cdot \frac{z}{x}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -3e+151)
   (+ (- (fma (log y) x z) (* 0.5 (log c))) t)
   (if (<= x 7.5e+233)
     (+ (+ (fma (log c) (- b 0.5) (+ t z)) a) (* y i))
     (* -1.0 (* x (fma -1.0 (log y) (* -1.0 (/ z x))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -3e+151) {
		tmp = (fma(log(y), x, z) - (0.5 * log(c))) + t;
	} else if (x <= 7.5e+233) {
		tmp = (fma(log(c), (b - 0.5), (t + z)) + a) + (y * i);
	} else {
		tmp = -1.0 * (x * fma(-1.0, log(y), (-1.0 * (z / x))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -3e+151)
		tmp = Float64(Float64(fma(log(y), x, z) - Float64(0.5 * log(c))) + t);
	elseif (x <= 7.5e+233)
		tmp = Float64(Float64(fma(log(c), Float64(b - 0.5), Float64(t + z)) + a) + Float64(y * i));
	else
		tmp = Float64(-1.0 * Float64(x * fma(-1.0, log(y), Float64(-1.0 * Float64(z / x)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -3e+151], N[(N[(N[(N[Log[y], $MachinePrecision] * x + z), $MachinePrecision] - N[(0.5 * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision], If[LessEqual[x, 7.5e+233], N[(N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + N[(t + z), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(-1.0 * N[(x * N[(-1.0 * N[Log[y], $MachinePrecision] + N[(-1.0 * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.9999999999999999e151

   1. Initial program 99.8%

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

   2. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-log.f64 N/A

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

      8. lower--.f64 84.8

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

   4. Applied rewrites 84.8%

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

   5. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-log.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower--.f64 63.1

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

   7. Applied rewrites 63.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 63.1

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

   9. Applied rewrites 63.1%

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

   10. Taylor expanded in b around 0

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

   12. Applied rewrites 47.9%

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

   if -2.9999999999999999e151 < x < 7.4999999999999997e233

   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. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-+.f64 N/A

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

      4. associate-+r+ N/A

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

      5. lower-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 99.8

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

      9. lift-+.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 99.8

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

      12. lift-+.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-fma.f64 99.8

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 84.0%

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

   if 7.4999999999999997e233 < 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 -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-log.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

   4. Applied rewrites 73.0%

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

   5. Taylor expanded in z around inf

      \[\leadsto -1 \cdot \left(x \cdot \mathsf{fma}\left(-1, \log y, -1 \cdot \frac{z}{x}\right)\right) \]
   6. Step-by-step derivation

      1. lower-/.f64 26.6

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

   7. Applied rewrites 26.6%

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

Alternative 10: 84.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -1 \cdot \left(x \cdot \mathsf{fma}\left(-1, \log y, -1 \cdot \frac{z}{x}\right)\right)\\ \mathbf{if}\;x \leq -3 \cdot 10^{+151}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+233}:\\ \;\;\;\;\left(\mathsf{fma}\left(\log c, b - 0.5, t + z\right) + a\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* -1.0 (* x (fma -1.0 (log y) (* -1.0 (/ z x)))))))
   (if (<= x -3e+151)
     t_1
     (if (<= x 7.5e+233)
       (+ (+ (fma (log c) (- b 0.5) (+ t z)) a) (* y i))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -1.0 * (x * fma(-1.0, log(y), (-1.0 * (z / x))));
	double tmp;
	if (x <= -3e+151) {
		tmp = t_1;
	} else if (x <= 7.5e+233) {
		tmp = (fma(log(c), (b - 0.5), (t + z)) + a) + (y * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(-1.0 * Float64(x * fma(-1.0, log(y), Float64(-1.0 * Float64(z / x)))))
	tmp = 0.0
	if (x <= -3e+151)
		tmp = t_1;
	elseif (x <= 7.5e+233)
		tmp = Float64(Float64(fma(log(c), Float64(b - 0.5), Float64(t + z)) + a) + Float64(y * i));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(-1.0 * N[(x * N[(-1.0 * N[Log[y], $MachinePrecision] + N[(-1.0 * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3e+151], t$95$1, If[LessEqual[x, 7.5e+233], N[(N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + N[(t + z), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.9999999999999999e151 or 7.4999999999999997e233 < 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 -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-log.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

   4. Applied rewrites 73.0%

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

   5. Taylor expanded in z around inf

      \[\leadsto -1 \cdot \left(x \cdot \mathsf{fma}\left(-1, \log y, -1 \cdot \frac{z}{x}\right)\right) \]
   6. Step-by-step derivation

      1. lower-/.f64 26.6

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

   7. Applied rewrites 26.6%

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

   if -2.9999999999999999e151 < x < 7.4999999999999997e233

   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. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-+.f64 N/A

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

      4. associate-+r+ N/A

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

      5. lower-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 99.8

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

      9. lift-+.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 99.8

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

      12. lift-+.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-fma.f64 99.8

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 84.0%

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

Alternative 11: 75.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+151}:\\ \;\;\;\;-1 \cdot \left(x \cdot \mathsf{fma}\left(-1, \log y, -1 \cdot \frac{z}{x}\right)\right)\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+161}:\\ \;\;\;\;t + \left(z + \mathsf{fma}\left(i, y, \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \left(x \cdot \mathsf{fma}\left(-1, \log y, -1 \cdot \frac{a}{x}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -2.7e+151)
   (* -1.0 (* x (fma -1.0 (log y) (* -1.0 (/ z x)))))
   (if (<= x 1.6e+161)
     (+ t (+ z (fma i y (* (log c) (- b 0.5)))))
     (* -1.0 (* x (fma -1.0 (log y) (* -1.0 (/ a x))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -2.7e+151) {
		tmp = -1.0 * (x * fma(-1.0, log(y), (-1.0 * (z / x))));
	} else if (x <= 1.6e+161) {
		tmp = t + (z + fma(i, y, (log(c) * (b - 0.5))));
	} else {
		tmp = -1.0 * (x * fma(-1.0, log(y), (-1.0 * (a / x))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -2.7e+151)
		tmp = Float64(-1.0 * Float64(x * fma(-1.0, log(y), Float64(-1.0 * Float64(z / x)))));
	elseif (x <= 1.6e+161)
		tmp = Float64(t + Float64(z + fma(i, y, Float64(log(c) * Float64(b - 0.5)))));
	else
		tmp = Float64(-1.0 * Float64(x * fma(-1.0, log(y), Float64(-1.0 * Float64(a / x)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -2.7e+151], N[(-1.0 * N[(x * N[(-1.0 * N[Log[y], $MachinePrecision] + N[(-1.0 * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.6e+161], N[(t + N[(z + N[(i * y + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-1.0 * N[(x * N[(-1.0 * N[Log[y], $MachinePrecision] + N[(-1.0 * N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.7000000000000001e151

   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 -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-log.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

   4. Applied rewrites 73.0%

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

   5. Taylor expanded in z around inf

      \[\leadsto -1 \cdot \left(x \cdot \mathsf{fma}\left(-1, \log y, -1 \cdot \frac{z}{x}\right)\right) \]
   6. Step-by-step derivation

      1. lower-/.f64 26.6

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

   7. Applied rewrites 26.6%

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

   if -2.7000000000000001e151 < x < 1.60000000000000001e161

   1. Initial program 99.8%

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

   2. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-log.f64 N/A

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

      8. lower--.f64 84.8

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

   4. Applied rewrites 84.8%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-log.f64 N/A

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

      3. lower--.f64 69.3

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

   7. Applied rewrites 69.3%

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

   if 1.60000000000000001e161 < 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 -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-log.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

   4. Applied rewrites 73.0%

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

   5. Taylor expanded in a around inf

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

      1. lower-/.f64 26.2

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

   7. Applied rewrites 26.2%

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

Alternative 12: 74.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -1 \cdot \left(x \cdot \mathsf{fma}\left(-1, \log y, -1 \cdot \frac{a}{x}\right)\right)\\ \mathbf{if}\;x \leq -1 \cdot 10^{+200}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+161}:\\ \;\;\;\;t + \left(z + \mathsf{fma}\left(i, y, \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* -1.0 (* x (fma -1.0 (log y) (* -1.0 (/ a x)))))))
   (if (<= x -1e+200)
     t_1
     (if (<= x 1.6e+161) (+ t (+ z (fma i y (* (log c) (- b 0.5))))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -1.0 * (x * fma(-1.0, log(y), (-1.0 * (a / x))));
	double tmp;
	if (x <= -1e+200) {
		tmp = t_1;
	} else if (x <= 1.6e+161) {
		tmp = t + (z + fma(i, y, (log(c) * (b - 0.5))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(-1.0 * Float64(x * fma(-1.0, log(y), Float64(-1.0 * Float64(a / x)))))
	tmp = 0.0
	if (x <= -1e+200)
		tmp = t_1;
	elseif (x <= 1.6e+161)
		tmp = Float64(t + Float64(z + fma(i, y, Float64(log(c) * Float64(b - 0.5)))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(-1.0 * N[(x * N[(-1.0 * N[Log[y], $MachinePrecision] + N[(-1.0 * N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1e+200], t$95$1, If[LessEqual[x, 1.6e+161], N[(t + N[(z + N[(i * y + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -9.9999999999999997e199 or 1.60000000000000001e161 < 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 -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-log.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

   4. Applied rewrites 73.0%

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

   5. Taylor expanded in a around inf

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

      1. lower-/.f64 26.2

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

   7. Applied rewrites 26.2%

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

   if -9.9999999999999997e199 < x < 1.60000000000000001e161

   1. Initial program 99.8%

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

   2. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-log.f64 N/A

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

      8. lower--.f64 84.8

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

   4. Applied rewrites 84.8%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-log.f64 N/A

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

      3. lower--.f64 69.3

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

   7. Applied rewrites 69.3%

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

Alternative 13: 74.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -2.4 \cdot 10^{+200}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+233}:\\ \;\;\;\;t + \left(z + \mathsf{fma}\left(i, y, \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -2.4e+200)
     t_1
     (if (<= x 7.5e+233) (+ t (+ z (fma i y (* (log c) (- b 0.5))))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * log(y);
	double tmp;
	if (x <= -2.4e+200) {
		tmp = t_1;
	} else if (x <= 7.5e+233) {
		tmp = t + (z + fma(i, y, (log(c) * (b - 0.5))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -2.4e+200)
		tmp = t_1;
	elseif (x <= 7.5e+233)
		tmp = Float64(t + Float64(z + fma(i, y, Float64(log(c) * Float64(b - 0.5)))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.4e+200], t$95$1, If[LessEqual[x, 7.5e+233], N[(t + N[(z + N[(i * y + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.4000000000000001e200 or 7.4999999999999997e233 < 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. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-+.f64 N/A

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

      4. associate-+r+ N/A

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

      5. lower-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 99.8

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

      9. lift-+.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 99.8

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

      12. lift-+.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. *-commutative N/A

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

      15. lower-fma.f64 99.8

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-log.f64 17.0

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

   6. Applied rewrites 17.0%

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

   if -2.4000000000000001e200 < x < 7.4999999999999997e233

   1. Initial program 99.8%

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

   2. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-log.f64 N/A

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

      8. lower--.f64 84.8

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

   4. Applied rewrites 84.8%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-log.f64 N/A

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

      3. lower--.f64 69.3

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

   7. Applied rewrites 69.3%

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

Alternative 14: 42.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ t_2 := 1 \cdot \left(i \cdot y\right)\\ \mathbf{if}\;t\_1 \leq -6 \cdot 10^{+296}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+16}:\\ \;\;\;\;\left(z - \log c \cdot \left(0.5 - b\right)\right) + t\\ \mathbf{elif}\;t\_1 \leq 10^{+307}:\\ \;\;\;\;-\left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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)))
        (t_2 (* 1.0 (* i y))))
   (if (<= t_1 -6e+296)
     t_2
     (if (<= t_1 1e+16)
       (+ (- z (* (log c) (- 0.5 b))) t)
       (if (<= t_1 1e+307) (- (- 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 = (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
	double t_2 = 1.0 * (i * y);
	double tmp;
	if (t_1 <= -6e+296) {
		tmp = t_2;
	} else if (t_1 <= 1e+16) {
		tmp = (z - (log(c) * (0.5 - b))) + t;
	} else if (t_1 <= 1e+307) {
		tmp = -(-a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (((((x * log(y)) + z) + t) + a) + ((b - 0.5d0) * log(c))) + (y * i)
    t_2 = 1.0d0 * (i * y)
    if (t_1 <= (-6d+296)) then
        tmp = t_2
    else if (t_1 <= 1d+16) then
        tmp = (z - (log(c) * (0.5d0 - b))) + t
    else if (t_1 <= 1d+307) then
        tmp = -(-a)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (((((x * Math.log(y)) + z) + t) + a) + ((b - 0.5) * Math.log(c))) + (y * i);
	double t_2 = 1.0 * (i * y);
	double tmp;
	if (t_1 <= -6e+296) {
		tmp = t_2;
	} else if (t_1 <= 1e+16) {
		tmp = (z - (Math.log(c) * (0.5 - b))) + t;
	} else if (t_1 <= 1e+307) {
		tmp = -(-a);
	} else {
		tmp = t_2;
	}
	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)
	t_2 = 1.0 * (i * y)
	tmp = 0
	if t_1 <= -6e+296:
		tmp = t_2
	elif t_1 <= 1e+16:
		tmp = (z - (math.log(c) * (0.5 - b))) + t
	elif t_1 <= 1e+307:
		tmp = -(-a)
	else:
		tmp = t_2
	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))
	t_2 = Float64(1.0 * Float64(i * y))
	tmp = 0.0
	if (t_1 <= -6e+296)
		tmp = t_2;
	elseif (t_1 <= 1e+16)
		tmp = Float64(Float64(z - Float64(log(c) * Float64(0.5 - b))) + t);
	elseif (t_1 <= 1e+307)
		tmp = Float64(-Float64(-a));
	else
		tmp = t_2;
	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);
	t_2 = 1.0 * (i * y);
	tmp = 0.0;
	if (t_1 <= -6e+296)
		tmp = t_2;
	elseif (t_1 <= 1e+16)
		tmp = (z - (log(c) * (0.5 - b))) + t;
	elseif (t_1 <= 1e+307)
		tmp = -(-a);
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(1.0 * N[(i * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -6e+296], t$95$2, If[LessEqual[t$95$1, 1e+16], N[(N[(z - N[(N[Log[c], $MachinePrecision] * N[(0.5 - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision], If[LessEqual[t$95$1, 1e+307], (-(-a)), t$95$2]]]]]

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)) < -6.00000000000000025e296 or 9.99999999999999986e306 < (+.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. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. sum-to-mult N/A

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

      4. lower-*.f64 N/A

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

   3. Applied rewrites 65.5%

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

   4. Taylor expanded in y around inf

      \[\leadsto \color{blue}{1} \cdot \left(i \cdot y\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 23.4%

      \[\leadsto \color{blue}{1} \cdot \left(i \cdot y\right) \]

   if -6.00000000000000025e296 < (+.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)) < 1e16

   1. Initial program 99.8%

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

   2. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-log.f64 N/A

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

      8. lower--.f64 84.8

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

   4. Applied rewrites 84.8%

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

   5. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-log.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower--.f64 63.1

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

   7. Applied rewrites 63.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 63.1

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

   9. Applied rewrites 63.1%

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

   10. Taylor expanded in x around 0

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

       1. lower--.f64 N/A

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

       2. lower-*.f64 N/A

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

       3. lower-log.f64 N/A

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

       4. lower--.f64 47.7

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

   12. Applied rewrites 47.7%

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

   if 1e16 < (+.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)) < 9.99999999999999986e306

   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 -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-log.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

   4. Applied rewrites 73.0%

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

   5. Taylor expanded in a around inf

      \[\leadsto -1 \cdot \left(-1 \cdot \color{blue}{a}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 16.0

         \[\leadsto -1 \cdot \left(-1 \cdot a\right) \]

   7. Applied rewrites 16.0%

      \[\leadsto -1 \cdot \left(-1 \cdot \color{blue}{a}\right) \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(-1 \cdot a\right) \]

      3. lower-neg.f64 16.0

         \[\leadsto --1 \cdot a \]

      4. lift-*.f64 N/A

         \[\leadsto --1 \cdot a \]

      5. mul-1-neg N/A

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

      6. lower-neg.f64 16.0

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

   9. Applied rewrites 16.0%

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

Alternative 15: 27.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ t_2 := 1 \cdot \left(i \cdot y\right)\\ \mathbf{if}\;t\_1 \leq -6 \cdot 10^{+296}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{+15}:\\ \;\;\;\;--1 \cdot z\\ \mathbf{elif}\;t\_1 \leq 10^{+307}:\\ \;\;\;\;-\left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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)))
        (t_2 (* 1.0 (* i y))))
   (if (<= t_1 -6e+296)
     t_2
     (if (<= t_1 -2e+15) (- (* -1.0 z)) (if (<= t_1 1e+307) (- (- 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 = (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
	double t_2 = 1.0 * (i * y);
	double tmp;
	if (t_1 <= -6e+296) {
		tmp = t_2;
	} else if (t_1 <= -2e+15) {
		tmp = -(-1.0 * z);
	} else if (t_1 <= 1e+307) {
		tmp = -(-a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (((((x * log(y)) + z) + t) + a) + ((b - 0.5d0) * log(c))) + (y * i)
    t_2 = 1.0d0 * (i * y)
    if (t_1 <= (-6d+296)) then
        tmp = t_2
    else if (t_1 <= (-2d+15)) then
        tmp = -((-1.0d0) * z)
    else if (t_1 <= 1d+307) then
        tmp = -(-a)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (((((x * Math.log(y)) + z) + t) + a) + ((b - 0.5) * Math.log(c))) + (y * i);
	double t_2 = 1.0 * (i * y);
	double tmp;
	if (t_1 <= -6e+296) {
		tmp = t_2;
	} else if (t_1 <= -2e+15) {
		tmp = -(-1.0 * z);
	} else if (t_1 <= 1e+307) {
		tmp = -(-a);
	} else {
		tmp = t_2;
	}
	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)
	t_2 = 1.0 * (i * y)
	tmp = 0
	if t_1 <= -6e+296:
		tmp = t_2
	elif t_1 <= -2e+15:
		tmp = -(-1.0 * z)
	elif t_1 <= 1e+307:
		tmp = -(-a)
	else:
		tmp = t_2
	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))
	t_2 = Float64(1.0 * Float64(i * y))
	tmp = 0.0
	if (t_1 <= -6e+296)
		tmp = t_2;
	elseif (t_1 <= -2e+15)
		tmp = Float64(-Float64(-1.0 * z));
	elseif (t_1 <= 1e+307)
		tmp = Float64(-Float64(-a));
	else
		tmp = t_2;
	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);
	t_2 = 1.0 * (i * y);
	tmp = 0.0;
	if (t_1 <= -6e+296)
		tmp = t_2;
	elseif (t_1 <= -2e+15)
		tmp = -(-1.0 * z);
	elseif (t_1 <= 1e+307)
		tmp = -(-a);
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(1.0 * N[(i * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -6e+296], t$95$2, If[LessEqual[t$95$1, -2e+15], (-N[(-1.0 * z), $MachinePrecision]), If[LessEqual[t$95$1, 1e+307], (-(-a)), t$95$2]]]]]

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)) < -6.00000000000000025e296 or 9.99999999999999986e306 < (+.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. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. sum-to-mult N/A

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

      4. lower-*.f64 N/A

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

   3. Applied rewrites 65.5%

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

   4. Taylor expanded in y around inf

      \[\leadsto \color{blue}{1} \cdot \left(i \cdot y\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 23.4%

      \[\leadsto \color{blue}{1} \cdot \left(i \cdot y\right) \]

   if -6.00000000000000025e296 < (+.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)) < -2e15

   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 -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-log.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

   4. Applied rewrites 73.0%

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

   5. Taylor expanded in a around inf

      \[\leadsto -1 \cdot \left(-1 \cdot \color{blue}{a}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 16.0

         \[\leadsto -1 \cdot \left(-1 \cdot a\right) \]

   7. Applied rewrites 16.0%

      \[\leadsto -1 \cdot \left(-1 \cdot \color{blue}{a}\right) \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(-1 \cdot a\right) \]

      3. lower-neg.f64 16.0

         \[\leadsto --1 \cdot a \]

      4. lift-*.f64 N/A

         \[\leadsto --1 \cdot a \]

      5. mul-1-neg N/A

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

      6. lower-neg.f64 16.0

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

   9. Applied rewrites 16.0%

      \[\leadsto \color{blue}{-\left(-a\right)} \]

   10. Taylor expanded in z around inf

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

       1. lower-*.f64 16.6

          \[\leadsto --1 \cdot z \]

   12. Applied rewrites 16.6%

       \[\leadsto --1 \cdot z \]

   if -2e15 < (+.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)) < 9.99999999999999986e306

   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 -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-log.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

   4. Applied rewrites 73.0%

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

   5. Taylor expanded in a around inf

      \[\leadsto -1 \cdot \left(-1 \cdot \color{blue}{a}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 16.0

         \[\leadsto -1 \cdot \left(-1 \cdot a\right) \]

   7. Applied rewrites 16.0%

      \[\leadsto -1 \cdot \left(-1 \cdot \color{blue}{a}\right) \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(-1 \cdot a\right) \]

      3. lower-neg.f64 16.0

         \[\leadsto --1 \cdot a \]

      4. lift-*.f64 N/A

         \[\leadsto --1 \cdot a \]

      5. mul-1-neg N/A

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

      6. lower-neg.f64 16.0

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

   9. Applied rewrites 16.0%

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

Alternative 16: 16.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \leq -2 \cdot 10^{+15}:\\ \;\;\;\;--1 \cdot z\\ \mathbf{else}:\\ \;\;\;\;-\left(-a\right)\\ \end{array} \end{array} \]

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))
      -2e+15)
   (- (* -1.0 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)) <= -2e+15) {
		tmp = -(-1.0 * 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)) <= (-2d+15)) then
        tmp = -((-1.0d0) * 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)) <= -2e+15) {
		tmp = -(-1.0 * 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)) <= -2e+15:
		tmp = -(-1.0 * 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)) <= -2e+15)
		tmp = Float64(-Float64(-1.0 * 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)) <= -2e+15)
		tmp = -(-1.0 * 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], -2e+15], (-N[(-1.0 * z), $MachinePrecision]), (-(-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)) < -2e15

   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 -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-log.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

   4. Applied rewrites 73.0%

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

   5. Taylor expanded in a around inf

      \[\leadsto -1 \cdot \left(-1 \cdot \color{blue}{a}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 16.0

         \[\leadsto -1 \cdot \left(-1 \cdot a\right) \]

   7. Applied rewrites 16.0%

      \[\leadsto -1 \cdot \left(-1 \cdot \color{blue}{a}\right) \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(-1 \cdot a\right) \]

      3. lower-neg.f64 16.0

         \[\leadsto --1 \cdot a \]

      4. lift-*.f64 N/A

         \[\leadsto --1 \cdot a \]

      5. mul-1-neg N/A

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

      6. lower-neg.f64 16.0

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

   9. Applied rewrites 16.0%

      \[\leadsto \color{blue}{-\left(-a\right)} \]

   10. Taylor expanded in z around inf

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

       1. lower-*.f64 16.6

          \[\leadsto --1 \cdot z \]

   12. Applied rewrites 16.6%

       \[\leadsto --1 \cdot z \]

   if -2e15 < (+.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 x around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-log.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

   4. Applied rewrites 73.0%

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

   5. Taylor expanded in a around inf

      \[\leadsto -1 \cdot \left(-1 \cdot \color{blue}{a}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 16.0

         \[\leadsto -1 \cdot \left(-1 \cdot a\right) \]

   7. Applied rewrites 16.0%

      \[\leadsto -1 \cdot \left(-1 \cdot \color{blue}{a}\right) \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(-1 \cdot a\right) \]

      3. lower-neg.f64 16.0

         \[\leadsto --1 \cdot a \]

      4. lift-*.f64 N/A

         \[\leadsto --1 \cdot a \]

      5. mul-1-neg N/A

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

      6. lower-neg.f64 16.0

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

   9. Applied rewrites 16.0%

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

Alternative 17: 16.0% 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 x around -inf

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

   1. lower-*.f64 N/A

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

   2. lower-*.f64 N/A

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

   3. lower-fma.f64 N/A

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

   4. lower-log.f64 N/A

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

   5. lower-*.f64 N/A

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

   6. lower-/.f64 N/A

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

4. Applied rewrites 73.0%

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

5. Taylor expanded in a around inf

   \[\leadsto -1 \cdot \left(-1 \cdot \color{blue}{a}\right) \]
6. Step-by-step derivation

   1. lower-*.f64 16.0

      \[\leadsto -1 \cdot \left(-1 \cdot a\right) \]

7. Applied rewrites 16.0%

   \[\leadsto -1 \cdot \left(-1 \cdot \color{blue}{a}\right) \]
8. Step-by-step derivation

   1. lift-*.f64 N/A

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

   2. mul-1-neg N/A

      \[\leadsto \mathsf{neg}\left(-1 \cdot a\right) \]

   3. lower-neg.f64 16.0

      \[\leadsto --1 \cdot a \]

   4. lift-*.f64 N/A

      \[\leadsto --1 \cdot a \]

   5. mul-1-neg N/A

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

   6. lower-neg.f64 16.0

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

9. Applied rewrites 16.0%

   \[\leadsto \color{blue}{-\left(-a\right)} \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2025156 
(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)))