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

Percentage Accurate: 99.8% → 99.8%

Time: 12.6s

Alternatives: 14

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-+.f64 N/A

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

   4. lift-+.f64 N/A

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

   5. associate-+l+ N/A

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

   6. associate-+r+ N/A

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

   7. lower-+.f64 N/A

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

   8. lift-*.f64 N/A

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

   9. *-commutative N/A

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

   10. lower-fma.f64 N/A

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

   11. lift-+.f64 N/A

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

   12. lift-*.f64 N/A

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

   13. *-commutative N/A

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

   14. lower-fma.f64 N/A

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

   15. +-commutative N/A

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

   16. lower-+.f64 99.8

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

3. Applied rewrites 99.8%

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

Alternative 2: 84.6% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in t around 0

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

   1. lower-+.f64 N/A

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

   2. lower-+.f64 N/A

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

   3. lower-fma.f64 N/A

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

   4. lower-fma.f64 N/A

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

   5. lower-log.f64 N/A

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

   6. lower-*.f64 N/A

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

   7. lower-log.f64 N/A

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

   8. lower--.f64 84.6

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

4. Applied rewrites 84.6%

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

Alternative 3: 79.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log c \cdot \left(b - 0.5\right)\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+225}:\\ \;\;\;\;a + \mathsf{fma}\left(1, x \cdot \log y, \mathsf{fma}\left(i, y, z\right)\right)\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+78}:\\ \;\;\;\;a + \left(z + \mathsf{fma}\left(i, y, t\_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \mathsf{fma}\left(i, y, \mathsf{fma}\left(x, \log y, t\_1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (log c) (- b 0.5))))
   (if (<= z -4.2e+225)
     (+ a (fma 1.0 (* x (log y)) (fma i y z)))
     (if (<= z -3.8e+78)
       (+ a (+ z (fma i y t_1)))
       (+ a (fma i y (fma x (log y) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = log(c) * (b - 0.5);
	double tmp;
	if (z <= -4.2e+225) {
		tmp = a + fma(1.0, (x * log(y)), fma(i, y, z));
	} else if (z <= -3.8e+78) {
		tmp = a + (z + fma(i, y, t_1));
	} else {
		tmp = a + fma(i, y, fma(x, log(y), t_1));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(log(c) * Float64(b - 0.5))
	tmp = 0.0
	if (z <= -4.2e+225)
		tmp = Float64(a + fma(1.0, Float64(x * log(y)), fma(i, y, z)));
	elseif (z <= -3.8e+78)
		tmp = Float64(a + Float64(z + fma(i, y, t_1)));
	else
		tmp = Float64(a + fma(i, y, fma(x, log(y), t_1)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.2e+225], N[(a + N[(1.0 * N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(i * y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.8e+78], N[(a + N[(z + N[(i * y + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(i * y + N[(x * N[Log[y], $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.2e225

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-log.f64 N/A

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

      8. lower--.f64 84.6

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

   4. Applied rewrites 84.6%

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

      1. lift-+.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-+r+ N/A

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

      5. +-commutative N/A

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

      6. lift-fma.f64 N/A

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

      7. sum-to-mult N/A

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

      8. lower-fma.f64 N/A

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

   6. Applied rewrites 75.1%

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

   7. Taylor expanded in x around inf

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

   9. Applied rewrites 68.2%

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

   if -4.2e225 < z < -3.7999999999999999e78

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-log.f64 N/A

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

      8. lower--.f64 84.6

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

   4. Applied rewrites 84.6%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-log.f64 N/A

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

      3. lower--.f64 69.6

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

   7. Applied rewrites 69.6%

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

   if -3.7999999999999999e78 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-log.f64 N/A

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

      8. lower--.f64 84.6

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

   4. Applied rewrites 84.6%

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

   5. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-log.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-log.f64 N/A

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

      7. lower--.f64 69.6

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

   7. Applied rewrites 69.6%

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

Alternative 4: 78.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{+61}:\\ \;\;\;\;a + \left(t + \left(\mathsf{fma}\left(\log c, b - 0.5, i \cdot y\right) + z\right)\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+183}:\\ \;\;\;\;a + \mathsf{fma}\left(1, x \cdot \log y, \mathsf{fma}\left(i, y, z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(z + \mathsf{fma}\left(x, \log y, \log c \cdot \left(b - 0.5\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= b -2e+61)
   (+ a (+ t (+ (fma (log c) (- b 0.5) (* i y)) z)))
   (if (<= b 4e+183)
     (+ a (fma 1.0 (* x (log y)) (fma i y z)))
     (+ a (+ z (fma x (log y) (* (log c) (- b 0.5))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (b <= -2e+61) {
		tmp = a + (t + (fma(log(c), (b - 0.5), (i * y)) + z));
	} else if (b <= 4e+183) {
		tmp = a + fma(1.0, (x * log(y)), fma(i, y, z));
	} else {
		tmp = a + (z + fma(x, log(y), (log(c) * (b - 0.5))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (b <= -2e+61)
		tmp = Float64(a + Float64(t + Float64(fma(log(c), Float64(b - 0.5), Float64(i * y)) + z)));
	elseif (b <= 4e+183)
		tmp = Float64(a + fma(1.0, Float64(x * log(y)), fma(i, y, z)));
	else
		tmp = Float64(a + Float64(z + fma(x, log(y), Float64(log(c) * Float64(b - 0.5)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[b, -2e+61], N[(a + N[(t + N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + N[(i * y), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4e+183], N[(a + N[(1.0 * N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(i * y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(z + N[(x * N[Log[y], $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.9999999999999999e61

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-log.f64 N/A

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

      7. lower--.f64 84.5

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

   4. Applied rewrites 84.5%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 84.5

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

      4. lift-fma.f64 N/A

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

      5. +-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 84.5

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

   6. Applied rewrites 84.5%

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

   if -1.9999999999999999e61 < b < 3.99999999999999979e183

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-log.f64 N/A

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

      8. lower--.f64 84.6

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

   4. Applied rewrites 84.6%

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

      1. lift-+.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-+r+ N/A

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

      5. +-commutative N/A

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

      6. lift-fma.f64 N/A

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

      7. sum-to-mult N/A

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

      8. lower-fma.f64 N/A

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

   6. Applied rewrites 75.1%

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

   7. Taylor expanded in x around inf

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

   9. Applied rewrites 68.2%

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

   if 3.99999999999999979e183 < b

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-log.f64 N/A

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

      8. lower--.f64 84.6

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

   4. Applied rewrites 84.6%

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

   5. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-log.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-log.f64 N/A

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

      7. lower--.f64 62.4

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

   7. Applied rewrites 62.4%

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

Alternative 5: 77.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{+61}:\\ \;\;\;\;a + \left(t + \left(\mathsf{fma}\left(\log c, b - 0.5, i \cdot y\right) + z\right)\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+194}:\\ \;\;\;\;a + \mathsf{fma}\left(1, x \cdot \log y, \mathsf{fma}\left(i, y, z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(\log c, b - 0.5, z\right) + a\right) + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= b -2e+61)
   (+ a (+ t (+ (fma (log c) (- b 0.5) (* i y)) z)))
   (if (<= b 9.5e+194)
     (+ a (fma 1.0 (* x (log y)) (fma i y z)))
     (+ (+ (fma (log c) (- b 0.5) z) a) (* y i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (b <= -2e+61) {
		tmp = a + (t + (fma(log(c), (b - 0.5), (i * y)) + z));
	} else if (b <= 9.5e+194) {
		tmp = a + fma(1.0, (x * log(y)), fma(i, y, z));
	} else {
		tmp = (fma(log(c), (b - 0.5), z) + a) + (y * i);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (b <= -2e+61)
		tmp = Float64(a + Float64(t + Float64(fma(log(c), Float64(b - 0.5), Float64(i * y)) + z)));
	elseif (b <= 9.5e+194)
		tmp = Float64(a + fma(1.0, Float64(x * log(y)), fma(i, y, z)));
	else
		tmp = Float64(Float64(fma(log(c), Float64(b - 0.5), z) + a) + Float64(y * i));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[b, -2e+61], N[(a + N[(t + N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + N[(i * y), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.5e+194], N[(a + N[(1.0 * N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(i * y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + z), $MachinePrecision] + a), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.9999999999999999e61

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-log.f64 N/A

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

      7. lower--.f64 84.5

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

   4. Applied rewrites 84.5%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 84.5

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

      4. lift-fma.f64 N/A

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

      5. +-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 84.5

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

   6. Applied rewrites 84.5%

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

   if -1.9999999999999999e61 < b < 9.5e194

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-log.f64 N/A

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

      8. lower--.f64 84.6

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

   4. Applied rewrites 84.6%

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

      1. lift-+.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-+r+ N/A

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

      5. +-commutative N/A

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

      6. lift-fma.f64 N/A

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

      7. sum-to-mult N/A

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

      8. lower-fma.f64 N/A

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

   6. Applied rewrites 75.1%

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

   7. Taylor expanded in x around inf

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

   9. Applied rewrites 68.2%

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

   if 9.5e194 < b

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-+.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. associate-+l+ N/A

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

      6. associate-+r+ N/A

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

      7. lower-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lift-+.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. +-commutative N/A

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

      16. lower-+.f64 99.8

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 84.5%

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

   7. Taylor expanded in t around 0

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

   9. Applied rewrites 69.6%

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

Alternative 6: 77.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{+61}:\\ \;\;\;\;a + \left(z + \mathsf{fma}\left(i, y, \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+194}:\\ \;\;\;\;a + \mathsf{fma}\left(1, x \cdot \log y, \mathsf{fma}\left(i, y, z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(\log c, b - 0.5, z\right) + a\right) + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= b -2e+61)
   (+ a (+ z (fma i y (* (log c) (- b 0.5)))))
   (if (<= b 9.5e+194)
     (+ a (fma 1.0 (* x (log y)) (fma i y z)))
     (+ (+ (fma (log c) (- b 0.5) z) a) (* y i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (b <= -2e+61) {
		tmp = a + (z + fma(i, y, (log(c) * (b - 0.5))));
	} else if (b <= 9.5e+194) {
		tmp = a + fma(1.0, (x * log(y)), fma(i, y, z));
	} else {
		tmp = (fma(log(c), (b - 0.5), z) + a) + (y * i);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (b <= -2e+61)
		tmp = Float64(a + Float64(z + fma(i, y, Float64(log(c) * Float64(b - 0.5)))));
	elseif (b <= 9.5e+194)
		tmp = Float64(a + fma(1.0, Float64(x * log(y)), fma(i, y, z)));
	else
		tmp = Float64(Float64(fma(log(c), Float64(b - 0.5), z) + a) + Float64(y * i));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[b, -2e+61], N[(a + N[(z + N[(i * y + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.5e+194], N[(a + N[(1.0 * N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(i * y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + z), $MachinePrecision] + a), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.9999999999999999e61

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-log.f64 N/A

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

      8. lower--.f64 84.6

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

   4. Applied rewrites 84.6%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-log.f64 N/A

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

      3. lower--.f64 69.6

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

   7. Applied rewrites 69.6%

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

   if -1.9999999999999999e61 < b < 9.5e194

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-log.f64 N/A

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

      8. lower--.f64 84.6

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

   4. Applied rewrites 84.6%

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

      1. lift-+.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-+r+ N/A

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

      5. +-commutative N/A

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

      6. lift-fma.f64 N/A

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

      7. sum-to-mult N/A

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

      8. lower-fma.f64 N/A

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

   6. Applied rewrites 75.1%

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

   7. Taylor expanded in x around inf

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

   9. Applied rewrites 68.2%

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

   if 9.5e194 < b

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-+.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. associate-+l+ N/A

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

      6. associate-+r+ N/A

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

      7. lower-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lift-+.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. +-commutative N/A

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

      16. lower-+.f64 99.8

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 84.5%

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

   7. Taylor expanded in t around 0

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

   9. Applied rewrites 69.6%

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

Alternative 7: 75.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \left(z + \mathsf{fma}\left(i, y, \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{if}\;b \leq -2 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+194}:\\ \;\;\;\;a + \mathsf{fma}\left(1, x \cdot \log y, \mathsf{fma}\left(i, y, z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (+ z (fma i y (* (log c) (- b 0.5)))))))
   (if (<= b -2e+61)
     t_1
     (if (<= b 9.5e+194) (+ a (fma 1.0 (* x (log y)) (fma i y z))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (z + fma(i, y, (log(c) * (b - 0.5))));
	double tmp;
	if (b <= -2e+61) {
		tmp = t_1;
	} else if (b <= 9.5e+194) {
		tmp = a + fma(1.0, (x * log(y)), fma(i, y, z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(z + fma(i, y, Float64(log(c) * Float64(b - 0.5)))))
	tmp = 0.0
	if (b <= -2e+61)
		tmp = t_1;
	elseif (b <= 9.5e+194)
		tmp = Float64(a + fma(1.0, Float64(x * log(y)), fma(i, y, z)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(z + N[(i * y + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2e+61], t$95$1, If[LessEqual[b, 9.5e+194], N[(a + N[(1.0 * N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(i * y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.9999999999999999e61 or 9.5e194 < b

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-log.f64 N/A

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

      8. lower--.f64 84.6

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

   4. Applied rewrites 84.6%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-log.f64 N/A

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

      3. lower--.f64 69.6

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

   7. Applied rewrites 69.6%

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

   if -1.9999999999999999e61 < b < 9.5e194

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-log.f64 N/A

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

      8. lower--.f64 84.6

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

   4. Applied rewrites 84.6%

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

      1. lift-+.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-+r+ N/A

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

      5. +-commutative N/A

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

      6. lift-fma.f64 N/A

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

      7. sum-to-mult N/A

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

      8. lower-fma.f64 N/A

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

   6. Applied rewrites 75.1%

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

   7. Taylor expanded in x around inf

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

   9. Applied rewrites 68.2%

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

Alternative 8: 74.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log c \cdot \left(b - 0.5\right)\\ t_2 := \left(b - 0.5\right) \cdot \log c\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+225}:\\ \;\;\;\;a + \left(t + \left(z + t\_1\right)\right)\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+173}:\\ \;\;\;\;a + \mathsf{fma}\left(1, x \cdot \log y, \mathsf{fma}\left(i, y, z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \mathsf{fma}\left(i, y, t\_1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (log c) (- b 0.5))) (t_2 (* (- b 0.5) (log c))))
   (if (<= t_2 -1e+225)
     (+ a (+ t (+ z t_1)))
     (if (<= t_2 5e+173)
       (+ a (fma 1.0 (* x (log y)) (fma i y z)))
       (+ a (+ t (fma i y t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = log(c) * (b - 0.5);
	double t_2 = (b - 0.5) * log(c);
	double tmp;
	if (t_2 <= -1e+225) {
		tmp = a + (t + (z + t_1));
	} else if (t_2 <= 5e+173) {
		tmp = a + fma(1.0, (x * log(y)), fma(i, y, z));
	} else {
		tmp = a + (t + fma(i, y, t_1));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(log(c) * Float64(b - 0.5))
	t_2 = Float64(Float64(b - 0.5) * log(c))
	tmp = 0.0
	if (t_2 <= -1e+225)
		tmp = Float64(a + Float64(t + Float64(z + t_1)));
	elseif (t_2 <= 5e+173)
		tmp = Float64(a + fma(1.0, Float64(x * log(y)), fma(i, y, z)));
	else
		tmp = Float64(a + Float64(t + fma(i, y, t_1)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+225], N[(a + N[(t + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+173], N[(a + N[(1.0 * N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(i * y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(t + N[(i * y + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c)) < -9.99999999999999928e224

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-log.f64 N/A

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

      7. lower--.f64 84.5

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

   4. Applied rewrites 84.5%

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

   5. Taylor expanded in y around 0

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

      1. lower-*.f64 N/A

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

      2. lower-log.f64 N/A

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

      3. lower--.f64 62.2

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

   7. Applied rewrites 62.2%

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

   if -9.99999999999999928e224 < (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c)) < 5.00000000000000034e173

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-log.f64 N/A

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

      8. lower--.f64 84.6

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

   4. Applied rewrites 84.6%

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

      1. lift-+.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-+r+ N/A

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

      5. +-commutative N/A

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

      6. lift-fma.f64 N/A

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

      7. sum-to-mult N/A

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

      8. lower-fma.f64 N/A

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

   6. Applied rewrites 75.1%

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

   7. Taylor expanded in x around inf

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

   9. Applied rewrites 68.2%

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

   if 5.00000000000000034e173 < (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-log.f64 N/A

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

      7. lower--.f64 84.5

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

   4. Applied rewrites 84.5%

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

   5. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-log.f64 N/A

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

      5. lower--.f64 69.4

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

   7. Applied rewrites 69.4%

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

Alternative 9: 74.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{if}\;b - 0.5 \leq -1 \cdot 10^{+215}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b - 0.5 \leq 10^{+195}:\\ \;\;\;\;a + \mathsf{fma}\left(1, x \cdot \log y, \mathsf{fma}\left(i, y, z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (+ t (+ z (* (log c) (- b 0.5)))))))
   (if (<= (- b 0.5) -1e+215)
     t_1
     (if (<= (- b 0.5) 1e+195)
       (+ a (fma 1.0 (* x (log y)) (fma i y z)))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (t + (z + (log(c) * (b - 0.5))));
	double tmp;
	if ((b - 0.5) <= -1e+215) {
		tmp = t_1;
	} else if ((b - 0.5) <= 1e+195) {
		tmp = a + fma(1.0, (x * log(y)), fma(i, y, z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(t + Float64(z + Float64(log(c) * Float64(b - 0.5)))))
	tmp = 0.0
	if (Float64(b - 0.5) <= -1e+215)
		tmp = t_1;
	elseif (Float64(b - 0.5) <= 1e+195)
		tmp = Float64(a + fma(1.0, Float64(x * log(y)), fma(i, y, z)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(t + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b - 0.5), $MachinePrecision], -1e+215], t$95$1, If[LessEqual[N[(b - 0.5), $MachinePrecision], 1e+195], N[(a + N[(1.0 * N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(i * y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 b #s(literal 1/2 binary64)) < -9.99999999999999907e214 or 9.99999999999999977e194 < (-.f64 b #s(literal 1/2 binary64))

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-log.f64 N/A

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

      7. lower--.f64 84.5

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

   4. Applied rewrites 84.5%

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

   5. Taylor expanded in y around 0

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

      1. lower-*.f64 N/A

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

      2. lower-log.f64 N/A

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

      3. lower--.f64 62.2

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

   7. Applied rewrites 62.2%

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

   if -9.99999999999999907e214 < (-.f64 b #s(literal 1/2 binary64)) < 9.99999999999999977e194

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-log.f64 N/A

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

      8. lower--.f64 84.6

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

   4. Applied rewrites 84.6%

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

      1. lift-+.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-+r+ N/A

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

      5. +-commutative N/A

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

      6. lift-fma.f64 N/A

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

      7. sum-to-mult N/A

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

      8. lower-fma.f64 N/A

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

   6. Applied rewrites 75.1%

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

   7. Taylor expanded in x around inf

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

   9. Applied rewrites 68.2%

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

Alternative 10: 74.0% accurate, 0.4× speedup

Math

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

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 1e+308)
       (+ a (+ t (+ z (* (log c) (- b 0.5)))))
       (* (- (* (- i) (/ y z))) z)))))

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 <= 1e+308) {
		tmp = a + (t + (z + (log(c) * (b - 0.5))));
	} else {
		tmp = -(-i * (y / z)) * z;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (((((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 <= 1e+308) {
		tmp = a + (t + (z + (Math.log(c) * (b - 0.5))));
	} else {
		tmp = -(-i * (y / z)) * z;
	}
	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 <= 1e+308:
		tmp = a + (t + (z + (math.log(c) * (b - 0.5))))
	else:
		tmp = -(-i * (y / z)) * z
	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 <= 1e+308)
		tmp = Float64(a + Float64(t + Float64(z + Float64(log(c) * Float64(b - 0.5)))));
	else
		tmp = Float64(Float64(-Float64(Float64(-i) * Float64(y / z))) * z);
	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 <= 1e+308)
		tmp = a + (t + (z + (log(c) * (b - 0.5))));
	else
		tmp = -(-i * (y / z)) * z;
	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, 1e+308], N[(a + N[(t + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-N[((-i) * N[(y / z), $MachinePrecision]), $MachinePrecision]) * z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-log.f64 N/A

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

      8. lower--.f64 84.6

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

   4. Applied rewrites 84.6%

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

      1. lift-+.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-+r+ N/A

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

      5. +-commutative N/A

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

      6. lift-fma.f64 N/A

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

      7. sum-to-mult N/A

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

      8. lower-fma.f64 N/A

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

   6. Applied rewrites 75.1%

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

   7. Taylor expanded in y around inf

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

      1. lower-*.f64 24.0

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

   9. Applied rewrites 24.0%

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

   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)) < 1e308

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-log.f64 N/A

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

      7. lower--.f64 84.5

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

   4. Applied rewrites 84.5%

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

   5. Taylor expanded in y around 0

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

      1. lower-*.f64 N/A

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

      2. lower-log.f64 N/A

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

      3. lower--.f64 62.2

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

   7. Applied rewrites 62.2%

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

   if 1e308 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i))

   1. Initial program 99.8%

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

   2. Taylor expanded in z around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

   4. Applied rewrites 72.9%

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

   5. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 20.4

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

   7. Applied rewrites 20.4%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. distribute-lft-neg-in N/A

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

      6. lower-*.f64 N/A

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

   9. Applied rewrites 20.2%

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

Alternative 11: 29.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;i \cdot y\\ \mathbf{elif}\;t\_1 \leq -50:\\ \;\;\;\;--1 \cdot z\\ \mathbf{elif}\;t\_1 \leq 10^{+308}:\\ \;\;\;\;-\left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-\left(-i\right) \cdot \frac{y}{z}\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (+
          (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c)))
          (* y i))))
   (if (<= t_1 (- INFINITY))
     (* i y)
     (if (<= t_1 -50.0)
       (- (* -1.0 z))
       (if (<= t_1 1e+308) (- (- a)) (* (- (* (- i) (/ y z))) z))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = i * y;
	} else if (t_1 <= -50.0) {
		tmp = -(-1.0 * z);
	} else if (t_1 <= 1e+308) {
		tmp = -(-a);
	} else {
		tmp = -(-i * (y / z)) * z;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (((((x * Math.log(y)) + z) + t) + a) + ((b - 0.5) * Math.log(c))) + (y * i);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = i * y;
	} else if (t_1 <= -50.0) {
		tmp = -(-1.0 * z);
	} else if (t_1 <= 1e+308) {
		tmp = -(-a);
	} else {
		tmp = -(-i * (y / z)) * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (((((x * math.log(y)) + z) + t) + a) + ((b - 0.5) * math.log(c))) + (y * i)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = i * y
	elif t_1 <= -50.0:
		tmp = -(-1.0 * z)
	elif t_1 <= 1e+308:
		tmp = -(-a)
	else:
		tmp = -(-i * (y / z)) * z
	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 <= -50.0)
		tmp = Float64(-Float64(-1.0 * z));
	elseif (t_1 <= 1e+308)
		tmp = Float64(-Float64(-a));
	else
		tmp = Float64(Float64(-Float64(Float64(-i) * Float64(y / z))) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = i * y;
	elseif (t_1 <= -50.0)
		tmp = -(-1.0 * z);
	elseif (t_1 <= 1e+308)
		tmp = -(-a);
	else
		tmp = -(-i * (y / z)) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(i * y), $MachinePrecision], If[LessEqual[t$95$1, -50.0], (-N[(-1.0 * z), $MachinePrecision]), If[LessEqual[t$95$1, 1e+308], (-(-a)), N[((-N[((-i) * N[(y / z), $MachinePrecision]), $MachinePrecision]) * z), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-log.f64 N/A

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

      8. lower--.f64 84.6

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

   4. Applied rewrites 84.6%

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

      1. lift-+.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-+r+ N/A

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

      5. +-commutative N/A

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

      6. lift-fma.f64 N/A

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

      7. sum-to-mult N/A

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

      8. lower-fma.f64 N/A

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

   6. Applied rewrites 75.1%

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

   7. Taylor expanded in y around inf

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

      1. lower-*.f64 24.0

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

   9. Applied rewrites 24.0%

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

   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)) < -50

   1. Initial program 99.8%

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

   2. Taylor expanded in z around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

   4. Applied rewrites 72.9%

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

   5. Taylor expanded in a around inf

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

      1. lower-*.f64 17.1

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

   7. Applied rewrites 17.1%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 17.1

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

      4. lift-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 17.1

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

   9. Applied rewrites 17.1%

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

   10. Taylor expanded in z around inf

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

       1. lower-*.f64 16.4

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

   12. Applied rewrites 16.4%

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

   if -50 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < 1e308

   1. Initial program 99.8%

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

   2. Taylor expanded in z around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

   4. Applied rewrites 72.9%

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

   5. Taylor expanded in a around inf

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

      1. lower-*.f64 17.1

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

   7. Applied rewrites 17.1%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 17.1

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

      4. lift-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 17.1

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

   9. Applied rewrites 17.1%

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

   if 1e308 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i))

   1. Initial program 99.8%

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

   2. Taylor expanded in z around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

   4. Applied rewrites 72.9%

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

   5. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 20.4

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

   7. Applied rewrites 20.4%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. distribute-lft-neg-in N/A

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

      6. lower-*.f64 N/A

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

   9. Applied rewrites 20.2%

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

Alternative 12: 28.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;i \cdot y\\ \mathbf{elif}\;t\_1 \leq -50:\\ \;\;\;\;--1 \cdot z\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+305}:\\ \;\;\;\;-\left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot y\\ \end{array} \end{array} \]

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 -50.0)
       (- (* -1.0 z))
       (if (<= t_1 5e+305) (- (- 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 <= -50.0) {
		tmp = -(-1.0 * z);
	} else if (t_1 <= 5e+305) {
		tmp = -(-a);
	} else {
		tmp = i * y;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (((((x * Math.log(y)) + z) + t) + a) + ((b - 0.5) * Math.log(c))) + (y * i);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = i * y;
	} else if (t_1 <= -50.0) {
		tmp = -(-1.0 * z);
	} else if (t_1 <= 5e+305) {
		tmp = -(-a);
	} else {
		tmp = i * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (((((x * math.log(y)) + z) + t) + a) + ((b - 0.5) * math.log(c))) + (y * i)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = i * y
	elif t_1 <= -50.0:
		tmp = -(-1.0 * z)
	elif t_1 <= 5e+305:
		tmp = -(-a)
	else:
		tmp = i * y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + z) + t) + a) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(i * y);
	elseif (t_1 <= -50.0)
		tmp = Float64(-Float64(-1.0 * z));
	elseif (t_1 <= 5e+305)
		tmp = Float64(-Float64(-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 <= -50.0)
		tmp = -(-1.0 * z);
	elseif (t_1 <= 5e+305)
		tmp = -(-a);
	else
		tmp = i * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(i * y), $MachinePrecision], If[LessEqual[t$95$1, -50.0], (-N[(-1.0 * z), $MachinePrecision]), If[LessEqual[t$95$1, 5e+305], (-(-a)), N[(i * y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < -inf.0 or 5.00000000000000009e305 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i))

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-log.f64 N/A

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

      8. lower--.f64 84.6

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

   4. Applied rewrites 84.6%

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

      1. lift-+.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-+r+ N/A

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

      5. +-commutative N/A

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

      6. lift-fma.f64 N/A

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

      7. sum-to-mult N/A

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

      8. lower-fma.f64 N/A

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

   6. Applied rewrites 75.1%

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

   7. Taylor expanded in y around inf

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

      1. lower-*.f64 24.0

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

   9. Applied rewrites 24.0%

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

   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)) < -50

   1. Initial program 99.8%

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

   2. Taylor expanded in z around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

   4. Applied rewrites 72.9%

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

   5. Taylor expanded in a around inf

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

      1. lower-*.f64 17.1

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

   7. Applied rewrites 17.1%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 17.1

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

      4. lift-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 17.1

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

   9. Applied rewrites 17.1%

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

   10. Taylor expanded in z around inf

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

       1. lower-*.f64 16.4

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

   12. Applied rewrites 16.4%

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

   if -50 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < 5.00000000000000009e305

   1. Initial program 99.8%

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

   2. Taylor expanded in z around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

   4. Applied rewrites 72.9%

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

   5. Taylor expanded in a around inf

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

      1. lower-*.f64 17.1

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

   7. Applied rewrites 17.1%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 17.1

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

      4. lift-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 17.1

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

   9. Applied rewrites 17.1%

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

Alternative 13: 26.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{if}\;t\_1 \leq 500:\\ \;\;\;\;i \cdot y\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+305}:\\ \;\;\;\;-\left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot y\\ \end{array} \end{array} \]

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_1 500.0) (* i y) (if (<= t_1 5e+305) (- (- 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 <= 500.0) {
		tmp = i * y;
	} else if (t_1 <= 5e+305) {
		tmp = -(-a);
	} else {
		tmp = i * y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (((((x * log(y)) + z) + t) + a) + ((b - 0.5d0) * log(c))) + (y * i)
    if (t_1 <= 500.0d0) then
        tmp = i * y
    else if (t_1 <= 5d+305) then
        tmp = -(-a)
    else
        tmp = i * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (((((x * Math.log(y)) + z) + t) + a) + ((b - 0.5) * Math.log(c))) + (y * i);
	double tmp;
	if (t_1 <= 500.0) {
		tmp = i * y;
	} else if (t_1 <= 5e+305) {
		tmp = -(-a);
	} else {
		tmp = i * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (((((x * math.log(y)) + z) + t) + a) + ((b - 0.5) * math.log(c))) + (y * i)
	tmp = 0
	if t_1 <= 500.0:
		tmp = i * y
	elif t_1 <= 5e+305:
		tmp = -(-a)
	else:
		tmp = i * y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + z) + t) + a) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i))
	tmp = 0.0
	if (t_1 <= 500.0)
		tmp = Float64(i * y);
	elseif (t_1 <= 5e+305)
		tmp = Float64(-Float64(-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 <= 500.0)
		tmp = i * y;
	elseif (t_1 <= 5e+305)
		tmp = -(-a);
	else
		tmp = i * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 500.0], N[(i * y), $MachinePrecision], If[LessEqual[t$95$1, 5e+305], (-(-a)), 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)) < 500 or 5.00000000000000009e305 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i))

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-log.f64 N/A

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

      8. lower--.f64 84.6

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

   4. Applied rewrites 84.6%

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

      1. lift-+.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-+r+ N/A

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

      5. +-commutative N/A

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

      6. lift-fma.f64 N/A

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

      7. sum-to-mult N/A

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

      8. lower-fma.f64 N/A

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

   6. Applied rewrites 75.1%

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

   7. Taylor expanded in y around inf

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

      1. lower-*.f64 24.0

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

   9. Applied rewrites 24.0%

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

   if 500 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < 5.00000000000000009e305

   1. Initial program 99.8%

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

   2. Taylor expanded in z around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

   4. Applied rewrites 72.9%

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

   5. Taylor expanded in a around inf

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

      1. lower-*.f64 17.1

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

   7. Applied rewrites 17.1%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 17.1

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

      4. lift-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 17.1

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

   9. Applied rewrites 17.1%

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

Alternative 14: 17.1% accurate, 12.8× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in z around -inf

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

   1. lower-*.f64 N/A

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

   2. lower-*.f64 N/A

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

   3. lower--.f64 N/A

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

4. Applied rewrites 72.9%

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

5. Taylor expanded in a around inf

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

   1. lower-*.f64 17.1

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

7. Applied rewrites 17.1%

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

   1. lift-*.f64 N/A

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

   2. mul-1-neg N/A

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

   3. lower-neg.f64 17.1

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

   4. lift-*.f64 N/A

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

   5. mul-1-neg N/A

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

   6. lower-neg.f64 17.1

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

9. Applied rewrites 17.1%

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

Reproduce

herbie shell --seed 2025142 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, B"
  :precision binary64
  (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i)))