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

Percentage Accurate: 99.8% → 99.9%

Time: 6.1s

Alternatives: 19

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: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

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

   3. lift-+.f64 N/A

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

   4. lift-+.f64 N/A

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

   5. lift-+.f64 N/A

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

   6. lift-*.f64 N/A

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

   7. lift-log.f64 N/A

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

   8. lift--.f64 N/A

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

   9. lift-*.f64 N/A

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

   10. lift-log.f64 N/A

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

   11. +-commutative N/A

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

   12. lift-*.f64 N/A

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

   13. lower-fma.f64 N/A

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

3. Applied rewrites 99.9%

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

Alternative 2: 48.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{if}\;t\_1 \leq -5:\\ \;\;\;\;\mathsf{fma}\left(y, i, z\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+306}:\\ \;\;\;\;\left(\log y \cdot x + t\right) + a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, \log c \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (+
          (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c)))
          (* y i))))
   (if (<= t_1 -5.0)
     (fma y i z)
     (if (<= t_1 5e+306) (+ (+ (* (log y) x) t) a) (fma y i (* (log c) b))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
	double tmp;
	if (t_1 <= -5.0) {
		tmp = fma(y, i, z);
	} else if (t_1 <= 5e+306) {
		tmp = ((log(y) * x) + t) + a;
	} else {
		tmp = fma(y, i, (log(c) * b));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + z) + t) + a) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i))
	tmp = 0.0
	if (t_1 <= -5.0)
		tmp = fma(y, i, z);
	elseif (t_1 <= 5e+306)
		tmp = Float64(Float64(Float64(log(y) * x) + t) + a);
	else
		tmp = fma(y, i, Float64(log(c) * b));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5.0], N[(y * i + z), $MachinePrecision], If[LessEqual[t$95$1, 5e+306], N[(N[(N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision], N[(y * i + N[(N[Log[c], $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 38.5%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 38.5

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

   6. Applied rewrites 38.5%

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

   if -5 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < 4.99999999999999993e306

   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 b around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

   4. Applied rewrites 83.1%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-log.f64 53.3

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

   7. Applied rewrites 53.3%

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

   if 4.99999999999999993e306 < (+.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. lift-+.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-log.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. lift-log.f64 N/A

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

      11. +-commutative N/A

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

      12. lift-*.f64 N/A

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

      13. lower-fma.f64 N/A

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lift-log.f64 91.2

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

   6. Applied rewrites 91.2%

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

Alternative 3: 48.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{if}\;t\_1 \leq -5:\\ \;\;\;\;\mathsf{fma}\left(y, i, z\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+306}:\\ \;\;\;\;\left(\log y \cdot x + t\right) + a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (+
          (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c)))
          (* y i))))
   (if (<= t_1 -5.0)
     (fma y i z)
     (if (<= t_1 5e+306) (+ (+ (* (log y) x) t) a) (fma y i a)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
	double tmp;
	if (t_1 <= -5.0) {
		tmp = fma(y, i, z);
	} else if (t_1 <= 5e+306) {
		tmp = ((log(y) * x) + t) + a;
	} else {
		tmp = fma(y, i, a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + z) + t) + a) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i))
	tmp = 0.0
	if (t_1 <= -5.0)
		tmp = fma(y, i, z);
	elseif (t_1 <= 5e+306)
		tmp = Float64(Float64(Float64(log(y) * x) + t) + a);
	else
		tmp = fma(y, i, a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5.0], N[(y * i + z), $MachinePrecision], If[LessEqual[t$95$1, 5e+306], N[(N[(N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision], N[(y * i + a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 38.5%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 38.5

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

   6. Applied rewrites 38.5%

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

   if -5 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < 4.99999999999999993e306

   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 b around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

   4. Applied rewrites 83.1%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-log.f64 53.3

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

   7. Applied rewrites 53.3%

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

   if 4.99999999999999993e306 < (+.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. lift-+.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-log.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. lift-log.f64 N/A

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

      11. +-commutative N/A

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

      12. lift-*.f64 N/A

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

      13. lower-fma.f64 N/A

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in a around inf

      \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{a}\right) \]
   5. Step-by-step derivation

      1. *-commutative 88.4

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

      2. +-commutative 88.4

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

      3. *-commutative 88.4

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

      4. +-commutative 88.4

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

      5. associate-+l+ 88.4

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

      6. +-commutative 88.4

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

   6. Applied rewrites 88.4%

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

Alternative 4: 41.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{if}\;t\_1 \leq -5:\\ \;\;\;\;\mathsf{fma}\left(y, i, z\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+306}:\\ \;\;\;\;\log y \cdot x + a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (+
          (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c)))
          (* y i))))
   (if (<= t_1 -5.0)
     (fma y i z)
     (if (<= t_1 5e+306) (+ (* (log y) x) a) (fma y i a)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
	double tmp;
	if (t_1 <= -5.0) {
		tmp = fma(y, i, z);
	} else if (t_1 <= 5e+306) {
		tmp = (log(y) * x) + a;
	} else {
		tmp = fma(y, i, a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + z) + t) + a) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i))
	tmp = 0.0
	if (t_1 <= -5.0)
		tmp = fma(y, i, z);
	elseif (t_1 <= 5e+306)
		tmp = Float64(Float64(log(y) * x) + a);
	else
		tmp = fma(y, i, a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5.0], N[(y * i + z), $MachinePrecision], If[LessEqual[t$95$1, 5e+306], N[(N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision] + a), $MachinePrecision], N[(y * i + a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 38.5%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 38.5

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

   6. Applied rewrites 38.5%

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

   if -5 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < 4.99999999999999993e306

   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 b around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

   4. Applied rewrites 83.1%

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

   5. Taylor expanded in x around inf

      \[\leadsto x \cdot \log y + a \]
   6. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-log.f64 36.1

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

   7. Applied rewrites 36.1%

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

   if 4.99999999999999993e306 < (+.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. lift-+.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-log.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. lift-log.f64 N/A

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

      11. +-commutative N/A

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

      12. lift-*.f64 N/A

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

      13. lower-fma.f64 N/A

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in a around inf

      \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{a}\right) \]
   5. Step-by-step derivation

      1. *-commutative 88.4

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

      2. +-commutative 88.4

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

      3. *-commutative 88.4

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

      4. +-commutative 88.4

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

      5. associate-+l+ 88.4

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

      6. +-commutative 88.4

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

   6. Applied rewrites 88.4%

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

Alternative 5: 48.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;i \cdot y\\ \mathbf{elif}\;t\_1 \leq -100:\\ \;\;\;\;\left(z + t\right) + a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (+
          (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c)))
          (* y i))))
   (if (<= t_1 (- INFINITY))
     (* i y)
     (if (<= t_1 -100.0) (+ (+ z t) a) (fma y i a)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = i * y;
	} else if (t_1 <= -100.0) {
		tmp = (z + t) + a;
	} else {
		tmp = fma(y, i, a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + z) + t) + a) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(i * y);
	elseif (t_1 <= -100.0)
		tmp = Float64(Float64(z + t) + a);
	else
		tmp = fma(y, i, a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(i * y), $MachinePrecision], If[LessEqual[t$95$1, -100.0], N[(N[(z + t), $MachinePrecision] + a), $MachinePrecision], N[(y * i + a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 96.4

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

   4. Applied rewrites 96.4%

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

   if -inf.0 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < -100

   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 b around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

   4. Applied rewrites 81.4%

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

   5. Taylor expanded in z around inf

      \[\leadsto \left(z + t\right) + a \]
   6. Step-by-step derivation

   7. Applied rewrites 52.7%

      \[\leadsto \left(z + t\right) + a \]

   if -100 < (+.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. lift-+.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-log.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. lift-log.f64 N/A

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

      11. +-commutative N/A

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

      12. lift-*.f64 N/A

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

      13. lower-fma.f64 N/A

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in a around inf

      \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{a}\right) \]
   5. Step-by-step derivation

      1. *-commutative 38.4

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

      2. +-commutative 38.4

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

      3. *-commutative 38.4

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

      4. +-commutative 38.4

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

      5. associate-+l+ 38.4

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

      6. +-commutative 38.4

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

   6. Applied rewrites 38.4%

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

Alternative 6: 57.1% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 83.2

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

   4. Applied rewrites 83.2%

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

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

   1. Initial program 99.8%

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

   2. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

   4. Applied rewrites 82.4%

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

   5. Taylor expanded in z around inf

      \[\leadsto \left(z + t\right) + a \]
   6. Step-by-step derivation

   7. Applied rewrites 52.3%

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

Alternative 7: 42.8% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 83.2

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

   4. Applied rewrites 83.2%

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

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

   1. Initial program 99.8%

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

   2. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

   4. Applied rewrites 82.4%

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

   5. Taylor expanded in z around inf

      \[\leadsto z + a \]
   6. Step-by-step derivation

   7. Applied rewrites 35.4%

      \[\leadsto z + a \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 54.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \leq -5000000000:\\ \;\;\;\;\mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - 0.5, z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - 0.5, a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<=
      (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i))
      -5000000000.0)
   (fma y i (fma (log c) (- b 0.5) z))
   (fma y i (fma (log c) (- b 0.5) a))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i)) <= -5000000000.0) {
		tmp = fma(y, i, fma(log(c), (b - 0.5), z));
	} else {
		tmp = fma(y, i, fma(log(c), (b - 0.5), a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + z) + t) + a) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i)) <= -5000000000.0)
		tmp = fma(y, i, fma(log(c), Float64(b - 0.5), z));
	else
		tmp = fma(y, i, fma(log(c), Float64(b - 0.5), a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], -5000000000.0], N[(y * i + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision], N[(y * i + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < -5e9

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. 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. lift-+.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-log.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. lift-log.f64 N/A

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

      11. +-commutative N/A

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

      12. lift-*.f64 N/A

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

      13. lower-fma.f64 N/A

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

   3. Applied rewrites 99.9%

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

   4. Taylor expanded in z around inf

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

      1. +-commutative 54.6

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

      2. *-commutative 54.6

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

      3. +-commutative 54.6

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

      4. associate-+l+ 54.6

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

   6. Applied rewrites 54.6%

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

   if -5e9 < (+.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. lift-+.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-log.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. lift-log.f64 N/A

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

      11. +-commutative N/A

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

      12. lift-*.f64 N/A

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

      13. lower-fma.f64 N/A

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in a around inf

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

      1. +-commutative 54.5

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

      2. *-commutative 54.5

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

      3. +-commutative 54.5

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

      4. associate-+l+ 54.5

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

   6. Applied rewrites 54.5%

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

Alternative 9: 47.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \leq -5000000000:\\ \;\;\;\;\mathsf{fma}\left(y, i, z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - 0.5, a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<=
      (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i))
      -5000000000.0)
   (fma y i z)
   (fma y i (fma (log c) (- b 0.5) a))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i)) <= -5000000000.0) {
		tmp = fma(y, i, z);
	} else {
		tmp = fma(y, i, fma(log(c), (b - 0.5), a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + z) + t) + a) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i)) <= -5000000000.0)
		tmp = fma(y, i, z);
	else
		tmp = fma(y, i, fma(log(c), Float64(b - 0.5), a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], -5000000000.0], N[(y * i + z), $MachinePrecision], N[(y * i + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < -5e9

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 39.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 39.1

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

   6. Applied rewrites 39.1%

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

   if -5e9 < (+.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. lift-+.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-log.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. lift-log.f64 N/A

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

      11. +-commutative N/A

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

      12. lift-*.f64 N/A

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

      13. lower-fma.f64 N/A

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in a around inf

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

      1. +-commutative 54.5

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

      2. *-commutative 54.5

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

      3. +-commutative 54.5

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

      4. associate-+l+ 54.5

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

   6. Applied rewrites 54.5%

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

Alternative 10: 38.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \leq -5:\\ \;\;\;\;\mathsf{fma}\left(y, i, z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<=
      (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i))
      -5.0)
   (fma y i z)
   (fma y i a)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i)) <= -5.0) {
		tmp = fma(y, i, z);
	} else {
		tmp = fma(y, i, 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)) <= -5.0)
		tmp = fma(y, i, z);
	else
		tmp = fma(y, i, a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], -5.0], N[(y * i + z), $MachinePrecision], N[(y * i + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 38.5%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 38.5

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

   6. Applied rewrites 38.5%

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

   if -5 < (+.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. lift-+.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-log.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. lift-log.f64 N/A

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

      11. +-commutative N/A

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

      12. lift-*.f64 N/A

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

      13. lower-fma.f64 N/A

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in a around inf

      \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{a}\right) \]
   5. Step-by-step derivation

      1. *-commutative 38.5

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

      2. +-commutative 38.5

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

      3. *-commutative 38.5

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

      4. +-commutative 38.5

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

      5. associate-+l+ 38.5

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

      6. +-commutative 38.5

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

   6. Applied rewrites 38.5%

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

Alternative 11: 16.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \leq -5:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<=
      (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i))
      -5.0)
   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)) <= -5.0) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((((((x * log(y)) + z) + t) + a) + ((b - 0.5d0) * log(c))) + (y * i)) <= (-5.0d0)) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((((((x * Math.log(y)) + z) + t) + a) + ((b - 0.5) * Math.log(c))) + (y * i)) <= -5.0) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((((((x * math.log(y)) + z) + t) + a) + ((b - 0.5) * math.log(c))) + (y * i)) <= -5.0:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + z) + t) + a) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i)) <= -5.0)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i)) <= -5.0)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], -5.0], z, a]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 17.3%

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

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

   1. Initial program 99.8%

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

   2. Taylor expanded in a around inf

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

   4. Applied rewrites 16.3%

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

Alternative 12: 92.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\log c, -0.5, \mathsf{fma}\left(x, \log y, \mathsf{fma}\left(i, y, z\right)\right)\right) + a\\ \mathbf{if}\;x \leq -2.3 \cdot 10^{+201}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+169}:\\ \;\;\;\;\left(\left(\mathsf{fma}\left(\log c, b - 0.5, z\right) + t\right) + a\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (fma (log c) -0.5 (fma x (log y) (fma i y z))) a)))
   (if (<= x -2.3e+201)
     t_1
     (if (<= x 6.2e+169)
       (+ (+ (+ (fma (log c) (- b 0.5) z) t) 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 = fma(log(c), -0.5, fma(x, log(y), fma(i, y, z))) + a;
	double tmp;
	if (x <= -2.3e+201) {
		tmp = t_1;
	} else if (x <= 6.2e+169) {
		tmp = ((fma(log(c), (b - 0.5), z) + t) + a) + (y * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(fma(log(c), -0.5, fma(x, log(y), fma(i, y, z))) + a)
	tmp = 0.0
	if (x <= -2.3e+201)
		tmp = t_1;
	elseif (x <= 6.2e+169)
		tmp = Float64(Float64(Float64(fma(log(c), Float64(b - 0.5), z) + t) + 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[(N[(N[Log[c], $MachinePrecision] * -0.5 + N[(x * N[Log[y], $MachinePrecision] + N[(i * y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]}, If[LessEqual[x, -2.3e+201], t$95$1, If[LessEqual[x, 6.2e+169], N[(N[(N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.3000000000000001e201 or 6.2e169 < x

   1. Initial program 99.7%

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

   2. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

   4. Applied rewrites 92.2%

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

   5. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. lower-fma.f64 N/A

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

      6. lift-log.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-+.f64 N/A

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

      10. *-commutative N/A

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

      11. +-commutative N/A

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

      12. lift-fma.f64 N/A

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

      13. lift-log.f64 N/A

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

      14. lift-*.f64 86.0

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

   7. Applied rewrites 86.0%

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

      1. lift-log.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lift-+.f64 N/A

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

      5. lift-log.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-fma.f64 N/A

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

      8. lower-fma.f64 N/A

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

      9. lift-log.f64 N/A

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

      10. associate-+l+ N/A

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

      11. *-commutative N/A

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

      12. +-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lift-log.f64 N/A

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

      15. +-commutative N/A

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

      16. lower-fma.f64 86.0

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

   9. Applied rewrites 86.0%

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

   if -2.3000000000000001e201 < x < 6.2e169

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lift-log.f64 N/A

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

      8. lift--.f64 94.2

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

   4. Applied rewrites 94.2%

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

Alternative 13: 91.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{+204}:\\ \;\;\;\;\mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b, \log y \cdot x\right)\right)\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+169}:\\ \;\;\;\;\left(\left(\mathsf{fma}\left(\log c, b - 0.5, z\right) + t\right) + a\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-0.5, \log c, \mathsf{fma}\left(x, \log y, i \cdot y\right)\right) + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -2.25e+204)
   (fma y i (fma (log c) b (* (log y) x)))
   (if (<= x 7e+169)
     (+ (+ (+ (fma (log c) (- b 0.5) z) t) a) (* y i))
     (+ (fma -0.5 (log c) (fma x (log y) (* i y))) a))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -2.25e+204) {
		tmp = fma(y, i, fma(log(c), b, (log(y) * x)));
	} else if (x <= 7e+169) {
		tmp = ((fma(log(c), (b - 0.5), z) + t) + a) + (y * i);
	} else {
		tmp = fma(-0.5, log(c), fma(x, log(y), (i * y))) + a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -2.25e+204)
		tmp = fma(y, i, fma(log(c), b, Float64(log(y) * x)));
	elseif (x <= 7e+169)
		tmp = Float64(Float64(Float64(fma(log(c), Float64(b - 0.5), z) + t) + a) + Float64(y * i));
	else
		tmp = Float64(fma(-0.5, log(c), fma(x, log(y), Float64(i * y))) + a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -2.25e+204], N[(y * i + N[(N[Log[c], $MachinePrecision] * b + N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7e+169], N[(N[(N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(N[(-0.5 * N[Log[c], $MachinePrecision] + N[(x * N[Log[y], $MachinePrecision] + N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.25000000000000001e204

   1. Initial program 99.7%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   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. lift-+.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-log.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. lift-log.f64 N/A

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

      11. +-commutative N/A

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

      12. lift-*.f64 N/A

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

      13. lower-fma.f64 N/A

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

   3. Applied rewrites 99.7%

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

   4. Taylor expanded in x around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lift-log.f64 83.0

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

   6. Applied rewrites 83.0%

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

   7. Taylor expanded in b around inf

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

   9. Applied rewrites 83.0%

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

   if -2.25000000000000001e204 < x < 7.00000000000000038e169

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lift-log.f64 N/A

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

      8. lift--.f64 94.1

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

   4. Applied rewrites 94.1%

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

   if 7.00000000000000038e169 < x

   1. Initial program 99.7%

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

   2. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

   4. Applied rewrites 91.5%

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

   5. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. lower-fma.f64 N/A

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

      6. lift-log.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. lower-+.f64 N/A

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

      10. *-commutative N/A

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

      11. +-commutative N/A

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

      12. lift-fma.f64 N/A

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

      13. lift-log.f64 N/A

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

      14. lift-*.f64 84.6

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

   7. Applied rewrites 84.6%

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

   8. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lift-log.f64 N/A

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

      4. lift-*.f64 77.5

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

   10. Applied rewrites 77.5%

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

Alternative 14: 90.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b, \log y \cdot x\right)\right)\\ \mathbf{if}\;x \leq -2.25 \cdot 10^{+204}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+125}:\\ \;\;\;\;\left(\left(\mathsf{fma}\left(\log c, b - 0.5, z\right) + t\right) + a\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fma y i (fma (log c) b (* (log y) x)))))
   (if (<= x -2.25e+204)
     t_1
     (if (<= x 9.5e+125)
       (+ (+ (+ (fma (log c) (- b 0.5) z) t) 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 = fma(y, i, fma(log(c), b, (log(y) * x)));
	double tmp;
	if (x <= -2.25e+204) {
		tmp = t_1;
	} else if (x <= 9.5e+125) {
		tmp = ((fma(log(c), (b - 0.5), z) + t) + a) + (y * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fma(y, i, fma(log(c), b, Float64(log(y) * x)))
	tmp = 0.0
	if (x <= -2.25e+204)
		tmp = t_1;
	elseif (x <= 9.5e+125)
		tmp = Float64(Float64(Float64(fma(log(c), Float64(b - 0.5), z) + t) + 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[(y * i + N[(N[Log[c], $MachinePrecision] * b + N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.25e+204], t$95$1, If[LessEqual[x, 9.5e+125], N[(N[(N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.25000000000000001e204 or 9.50000000000000041e125 < 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. lift-+.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-log.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. lift-log.f64 N/A

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

      11. +-commutative N/A

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

      12. lift-*.f64 N/A

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

      13. lower-fma.f64 N/A

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in x around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lift-log.f64 76.6

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

   6. Applied rewrites 76.6%

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

   7. Taylor expanded in b around inf

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

   9. Applied rewrites 76.6%

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

   if -2.25000000000000001e204 < x < 9.50000000000000041e125

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lift-log.f64 N/A

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

      8. lift--.f64 95.0

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

   4. Applied rewrites 95.0%

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

Alternative 15: 90.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log y \cdot x\\ \mathbf{if}\;x \leq -2.6 \cdot 10^{+204}:\\ \;\;\;\;\mathsf{fma}\left(y, i, t\_1\right)\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+169}:\\ \;\;\;\;\left(\left(\mathsf{fma}\left(\log c, b - 0.5, z\right) + t\right) + a\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;t\_1 + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (log y) x)))
   (if (<= x -2.6e+204)
     (fma y i t_1)
     (if (<= x 9.5e+169)
       (+ (+ (+ (fma (log c) (- b 0.5) z) t) a) (* y i))
       (+ t_1 (* y i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = log(y) * x;
	double tmp;
	if (x <= -2.6e+204) {
		tmp = fma(y, i, t_1);
	} else if (x <= 9.5e+169) {
		tmp = ((fma(log(c), (b - 0.5), z) + t) + a) + (y * i);
	} else {
		tmp = t_1 + (y * i);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(log(y) * x)
	tmp = 0.0
	if (x <= -2.6e+204)
		tmp = fma(y, i, t_1);
	elseif (x <= 9.5e+169)
		tmp = Float64(Float64(Float64(fma(log(c), Float64(b - 0.5), z) + t) + a) + Float64(y * i));
	else
		tmp = Float64(t_1 + Float64(y * i));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -2.6e+204], N[(y * i + t$95$1), $MachinePrecision], If[LessEqual[x, 9.5e+169], N[(N[(N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(y * i), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.6000000000000001e204

   1. Initial program 99.7%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   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. lift-+.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-log.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. lift-log.f64 N/A

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

      11. +-commutative N/A

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

      12. lift-*.f64 N/A

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

      13. lower-fma.f64 N/A

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

   3. Applied rewrites 99.7%

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

   4. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lift-log.f64 77.4

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

   6. Applied rewrites 77.4%

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

   if -2.6000000000000001e204 < x < 9.4999999999999995e169

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lift-log.f64 N/A

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

      8. lift--.f64 94.1

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

   4. Applied rewrites 94.1%

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

   if 9.4999999999999995e169 < x

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-log.f64 70.5

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

   4. Applied rewrites 70.5%

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

Alternative 16: 90.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log y \cdot x\\ \mathbf{if}\;x \leq -2.6 \cdot 10^{+204}:\\ \;\;\;\;\mathsf{fma}\left(y, i, t\_1\right)\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+169}:\\ \;\;\;\;\mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b - 0.5, \left(a + t\right) + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (log y) x)))
   (if (<= x -2.6e+204)
     (fma y i t_1)
     (if (<= x 9.5e+169)
       (fma y i (fma (log c) (- b 0.5) (+ (+ a t) z)))
       (+ t_1 (* y i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = log(y) * x;
	double tmp;
	if (x <= -2.6e+204) {
		tmp = fma(y, i, t_1);
	} else if (x <= 9.5e+169) {
		tmp = fma(y, i, fma(log(c), (b - 0.5), ((a + t) + z)));
	} else {
		tmp = t_1 + (y * i);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(log(y) * x)
	tmp = 0.0
	if (x <= -2.6e+204)
		tmp = fma(y, i, t_1);
	elseif (x <= 9.5e+169)
		tmp = fma(y, i, fma(log(c), Float64(b - 0.5), Float64(Float64(a + t) + z)));
	else
		tmp = Float64(t_1 + Float64(y * i));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -2.6e+204], N[(y * i + t$95$1), $MachinePrecision], If[LessEqual[x, 9.5e+169], N[(y * i + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + N[(N[(a + t), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(y * i), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.6000000000000001e204

   1. Initial program 99.7%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   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. lift-+.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-log.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. lift-log.f64 N/A

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

      11. +-commutative N/A

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

      12. lift-*.f64 N/A

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

      13. lower-fma.f64 N/A

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

   3. Applied rewrites 99.7%

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

   4. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lift-log.f64 77.4

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

   6. Applied rewrites 77.4%

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

   if -2.6000000000000001e204 < x < 9.4999999999999995e169

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. 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. lift-+.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-log.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. lift-log.f64 N/A

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

      11. +-commutative N/A

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

      12. lift-*.f64 N/A

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

      13. lower-fma.f64 N/A

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

   3. Applied rewrites 99.9%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 94.1%

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

   if 9.4999999999999995e169 < x

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-log.f64 70.5

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

   4. Applied rewrites 70.5%

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

Alternative 17: 88.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log y \cdot x\\ \mathbf{if}\;x \leq -2.6 \cdot 10^{+204}:\\ \;\;\;\;\mathsf{fma}\left(y, i, t\_1\right)\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+169}:\\ \;\;\;\;\mathsf{fma}\left(y, i, \mathsf{fma}\left(\log c, b, \left(a + t\right) + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (log y) x)))
   (if (<= x -2.6e+204)
     (fma y i t_1)
     (if (<= x 9.5e+169)
       (fma y i (fma (log c) b (+ (+ a t) z)))
       (+ t_1 (* y i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = log(y) * x;
	double tmp;
	if (x <= -2.6e+204) {
		tmp = fma(y, i, t_1);
	} else if (x <= 9.5e+169) {
		tmp = fma(y, i, fma(log(c), b, ((a + t) + z)));
	} else {
		tmp = t_1 + (y * i);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(log(y) * x)
	tmp = 0.0
	if (x <= -2.6e+204)
		tmp = fma(y, i, t_1);
	elseif (x <= 9.5e+169)
		tmp = fma(y, i, fma(log(c), b, Float64(Float64(a + t) + z)));
	else
		tmp = Float64(t_1 + Float64(y * i));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -2.6e+204], N[(y * i + t$95$1), $MachinePrecision], If[LessEqual[x, 9.5e+169], N[(y * i + N[(N[Log[c], $MachinePrecision] * b + N[(N[(a + t), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(y * i), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.6000000000000001e204

   1. Initial program 99.7%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   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. lift-+.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-log.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. lift-log.f64 N/A

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

      11. +-commutative N/A

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

      12. lift-*.f64 N/A

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

      13. lower-fma.f64 N/A

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

   3. Applied rewrites 99.7%

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

   4. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lift-log.f64 77.4

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

   6. Applied rewrites 77.4%

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

   if -2.6000000000000001e204 < x < 9.4999999999999995e169

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. 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. lift-+.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-log.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. lift-log.f64 N/A

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

      11. +-commutative N/A

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

      12. lift-*.f64 N/A

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

      13. lower-fma.f64 N/A

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

   3. Applied rewrites 99.9%

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

   4. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift-log.f64 94.2

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

   6. Applied rewrites 94.2%

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

   7. Taylor expanded in x around 0

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

   9. Applied rewrites 94.1%

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

   10. Taylor expanded in b around inf

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

   12. Applied rewrites 92.2%

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

   if 9.4999999999999995e169 < x

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-log.f64 70.5

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

   4. Applied rewrites 70.5%

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

Alternative 18: 31.0% accurate, 58.5× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(z + a), $MachinePrecision]

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in b around 0

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

   1. +-commutative N/A

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

   2. lower-+.f64 N/A

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

4. Applied rewrites 84.2%

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

5. Taylor expanded in z around inf

   \[\leadsto z + a \]
6. Step-by-step derivation

7. Applied rewrites 31.0%

   \[\leadsto z + a \]
8. Add Preprocessing

Alternative 19: 16.4% accurate, 234.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = a
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in a around inf

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

4. Applied rewrites 16.4%

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

Reproduce

herbie shell --seed 2025105 
(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)))