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

Percentage Accurate: 99.8% → 99.8%

Time: 7.5s

Alternatives: 18

Speedup: 1.1×

Specification

Math

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

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

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

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, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

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

   3. lift-*.f64 N/A

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

   4. lower-fma.f64 99.8%

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

   5. lift-+.f64 N/A

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

   6. lift-+.f64 N/A

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

   7. associate-+l+ N/A

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

   8. lift-+.f64 N/A

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

   9. +-commutative N/A

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

   10. associate-+l+ N/A

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

   11. +-commutative N/A

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

   12. lower-+.f64 N/A

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

3. Applied rewrites 99.8%

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

Alternative 2: 94.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := \log c \cdot \left(b - 0.5\right)\\ t_2 := \mathsf{max}\left(t, \mathsf{max}\left(z, a\right)\right)\\ t_3 := t\_2 + \mathsf{fma}\left(i, y, \mathsf{fma}\left(x, \log y, t\_1\right)\right)\\ \mathbf{if}\;x \leq -4.4 \cdot 10^{+197}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{+110}:\\ \;\;\;\;t\_2 + \left(\mathsf{min}\left(t, \mathsf{max}\left(z, a\right)\right) + \left(\mathsf{min}\left(z, a\right) + \mathsf{fma}\left(i, y, t\_1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (log c) (- b 0.5)))
        (t_2 (fmax t (fmax z a)))
        (t_3 (+ t_2 (fma i y (fma x (log y) t_1)))))
   (if (<= x -4.4e+197)
     t_3
     (if (<= x 5.4e+110)
       (+ t_2 (+ (fmin t (fmax z a)) (+ (fmin z a) (fma i y t_1))))
       t_3))))

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 = fmax(t, fmax(z, a));
	double t_3 = t_2 + fma(i, y, fma(x, log(y), t_1));
	double tmp;
	if (x <= -4.4e+197) {
		tmp = t_3;
	} else if (x <= 5.4e+110) {
		tmp = t_2 + (fmin(t, fmax(z, a)) + (fmin(z, a) + fma(i, y, t_1)));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(log(c) * Float64(b - 0.5))
	t_2 = fmax(t, fmax(z, a))
	t_3 = Float64(t_2 + fma(i, y, fma(x, log(y), t_1)))
	tmp = 0.0
	if (x <= -4.4e+197)
		tmp = t_3;
	elseif (x <= 5.4e+110)
		tmp = Float64(t_2 + Float64(fmin(t, fmax(z, a)) + Float64(fmin(z, a) + fma(i, y, t_1))));
	else
		tmp = t_3;
	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[Max[t, N[Max[z, a], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(i * y + N[(x * N[Log[y], $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.4e+197], t$95$3, If[LessEqual[x, 5.4e+110], N[(t$95$2 + N[(N[Min[t, N[Max[z, a], $MachinePrecision]], $MachinePrecision] + N[(N[Min[z, a], $MachinePrecision] + N[(i * y + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.39999999999999979e197 or 5.40000000000000019e110 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-log.f64 N/A

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

      8. lower--.f64 84.1%

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

   4. Applied rewrites 84.1%

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

   5. Taylor expanded in t 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 69.2%

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

   7. Applied rewrites 69.2%

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

   if -4.39999999999999979e197 < x < 5.40000000000000019e110

   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%

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

Alternative 3: 93.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_1 := \log c \cdot \left(b - 0.5\right)\\ t_2 := \mathsf{max}\left(t, \mathsf{max}\left(z, a\right)\right)\\ t_3 := \mathsf{fma}\left(i, y, \mathsf{fma}\left(x, \log y, t\_1\right)\right)\\ t_4 := \mathsf{min}\left(t, \mathsf{max}\left(z, a\right)\right)\\ \mathbf{if}\;x \leq -4.4 \cdot 10^{+197}:\\ \;\;\;\;t\_2 + t\_3\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{+110}:\\ \;\;\;\;t\_2 + \left(t\_4 + \left(\mathsf{min}\left(z, a\right) + \mathsf{fma}\left(i, y, t\_1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2 + \left(t\_4 + t\_3\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (log c) (- b 0.5)))
        (t_2 (fmax t (fmax z a)))
        (t_3 (fma i y (fma x (log y) t_1)))
        (t_4 (fmin t (fmax z a))))
   (if (<= x -4.4e+197)
     (+ t_2 t_3)
     (if (<= x 5.4e+110)
       (+ t_2 (+ t_4 (+ (fmin z a) (fma i y t_1))))
       (+ t_2 (+ t_4 t_3))))))

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 = fmax(t, fmax(z, a));
	double t_3 = fma(i, y, fma(x, log(y), t_1));
	double t_4 = fmin(t, fmax(z, a));
	double tmp;
	if (x <= -4.4e+197) {
		tmp = t_2 + t_3;
	} else if (x <= 5.4e+110) {
		tmp = t_2 + (t_4 + (fmin(z, a) + fma(i, y, t_1)));
	} else {
		tmp = t_2 + (t_4 + t_3);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(log(c) * Float64(b - 0.5))
	t_2 = fmax(t, fmax(z, a))
	t_3 = fma(i, y, fma(x, log(y), t_1))
	t_4 = fmin(t, fmax(z, a))
	tmp = 0.0
	if (x <= -4.4e+197)
		tmp = Float64(t_2 + t_3);
	elseif (x <= 5.4e+110)
		tmp = Float64(t_2 + Float64(t_4 + Float64(fmin(z, a) + fma(i, y, t_1))));
	else
		tmp = Float64(t_2 + Float64(t_4 + t_3));
	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[Max[t, N[Max[z, a], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$3 = N[(i * y + N[(x * N[Log[y], $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[Min[t, N[Max[z, a], $MachinePrecision]], $MachinePrecision]}, If[LessEqual[x, -4.4e+197], N[(t$95$2 + t$95$3), $MachinePrecision], If[LessEqual[x, 5.4e+110], N[(t$95$2 + N[(t$95$4 + N[(N[Min[z, a], $MachinePrecision] + N[(i * y + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$2 + N[(t$95$4 + t$95$3), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.39999999999999979e197

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-log.f64 N/A

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

      8. lower--.f64 84.1%

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

   4. Applied rewrites 84.1%

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

   5. Taylor expanded in t 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 69.2%

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

   7. Applied rewrites 69.2%

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

   if -4.39999999999999979e197 < x < 5.40000000000000019e110

   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%

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

   if 5.40000000000000019e110 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-log.f64 N/A

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

      8. lower--.f64 84.1%

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

   4. Applied rewrites 84.1%

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

Alternative 4: 87.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq -2.45 \cdot 10^{+210}:\\ \;\;\;\;\mathsf{fma}\left(\log y, x, \mathsf{fma}\left(b - 0.5, \log c, t\right)\right) + a\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + \mathsf{fma}\left(i, y, \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -2.45e+210)
   (+ (fma (log y) x (fma (- b 0.5) (log c) t)) a)
   (+ a (+ t (+ z (fma i 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 (x <= -2.45e+210) {
		tmp = fma(log(y), x, fma((b - 0.5), log(c), t)) + a;
	} else {
		tmp = a + (t + (z + fma(i, y, (log(c) * (b - 0.5)))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -2.45e+210)
		tmp = Float64(fma(log(y), x, fma(Float64(b - 0.5), log(c), t)) + a);
	else
		tmp = Float64(a + Float64(t + Float64(z + fma(i, y, Float64(log(c) * Float64(b - 0.5))))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -2.45e+210], N[(N[(N[Log[y], $MachinePrecision] * x + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision], N[(a + N[(t + N[(z + N[(i * y + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.45000000000000003e210

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-log.f64 N/A

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

      8. lower--.f64 84.1%

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

   4. Applied rewrites 84.1%

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

   5. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-log.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower--.f64 61.2%

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

   7. Applied rewrites 61.2%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 61.2%

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

   9. Applied rewrites 61.2%

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

   if -2.45000000000000003e210 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0

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

      1. 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%

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

Alternative 5: 87.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq -2.45 \cdot 10^{+210}:\\ \;\;\;\;a + \left(t + \mathsf{fma}\left(x, \log y, \log c \cdot -0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + \mathsf{fma}\left(i, y, \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -2.45e+210)
   (+ a (+ t (fma x (log y) (* (log c) -0.5))))
   (+ a (+ t (+ z (fma i 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 (x <= -2.45e+210) {
		tmp = a + (t + fma(x, log(y), (log(c) * -0.5)));
	} else {
		tmp = a + (t + (z + fma(i, y, (log(c) * (b - 0.5)))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -2.45e+210)
		tmp = Float64(a + Float64(t + fma(x, log(y), Float64(log(c) * -0.5))));
	else
		tmp = Float64(a + Float64(t + Float64(z + fma(i, y, Float64(log(c) * Float64(b - 0.5))))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -2.45e+210], N[(a + N[(t + N[(x * N[Log[y], $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(t + N[(z + N[(i * y + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.45000000000000003e210

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-log.f64 N/A

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

      8. lower--.f64 84.1%

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

   4. Applied rewrites 84.1%

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

   5. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-log.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower--.f64 61.2%

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

   7. Applied rewrites 61.2%

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

   8. Taylor expanded in b around 0

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

   10. Applied rewrites 46.3%

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

   if -2.45000000000000003e210 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0

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

      1. 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%

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

Alternative 6: 86.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+253}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + \mathsf{fma}\left(i, y, \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -6e+253)
   (* x (log y))
   (+ a (+ t (+ z (fma i 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 (x <= -6e+253) {
		tmp = x * log(y);
	} else {
		tmp = a + (t + (z + fma(i, y, (log(c) * (b - 0.5)))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -6e+253)
		tmp = Float64(x * log(y));
	else
		tmp = Float64(a + Float64(t + Float64(z + fma(i, y, Float64(log(c) * Float64(b - 0.5))))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -6e+253], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(a + N[(t + N[(z + N[(i * y + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.9999999999999996e253

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 99.8%

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

      5. lift-+.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. associate-+l+ N/A

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

      8. lift-+.f64 N/A

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

      9. +-commutative N/A

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

      10. associate-+l+ N/A

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

      11. +-commutative N/A

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

      12. lower-+.f64 N/A

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-log.f64 16.5%

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

   6. Applied rewrites 16.5%

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

   if -5.9999999999999996e253 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0

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

      1. 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%

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

Alternative 7: 86.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+253}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, \left(\mathsf{fma}\left(\log c, b - 0.5, z\right) + a\right) + t\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -6e+253)
   (* x (log y))
   (fma y i (+ (+ (fma (log c) (- b 0.5) z) a) t))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -6e+253) {
		tmp = x * log(y);
	} else {
		tmp = fma(y, i, ((fma(log(c), (b - 0.5), z) + a) + t));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -6e+253)
		tmp = Float64(x * log(y));
	else
		tmp = fma(y, i, Float64(Float64(fma(log(c), Float64(b - 0.5), z) + a) + t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -6e+253], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(y * i + N[(N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + z), $MachinePrecision] + a), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.9999999999999996e253

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 99.8%

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

      5. lift-+.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. associate-+l+ N/A

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

      8. lift-+.f64 N/A

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

      9. +-commutative N/A

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

      10. associate-+l+ N/A

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

      11. +-commutative N/A

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

      12. lower-+.f64 N/A

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-log.f64 16.5%

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

   6. Applied rewrites 16.5%

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

   if -5.9999999999999996e253 < x

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 99.8%

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

      5. lift-+.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. associate-+l+ N/A

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

      8. lift-+.f64 N/A

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

      9. +-commutative N/A

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

      10. associate-+l+ N/A

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

      11. +-commutative N/A

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

      12. lower-+.f64 N/A

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 84.5%

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

Alternative 8: 80.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{max}\left(z, a\right) + \left(t + \mathsf{fma}\left(i, y, \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{if}\;b \leq -5.9 \cdot 10^{+165}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{+96}:\\ \;\;\;\;\mathsf{fma}\left(y, i, \left(\mathsf{fma}\left(\log c, -0.5, \mathsf{min}\left(z, a\right)\right) + \mathsf{max}\left(z, a\right)\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (fmax z a) (+ t (fma i y (* (log c) (- b 0.5)))))))
   (if (<= b -5.9e+165)
     t_1
     (if (<= b 2.8e+96)
       (fma y i (+ (+ (fma (log c) -0.5 (fmin z a)) (fmax z a)) t))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fmax(z, a) + (t + fma(i, y, (log(c) * (b - 0.5))));
	double tmp;
	if (b <= -5.9e+165) {
		tmp = t_1;
	} else if (b <= 2.8e+96) {
		tmp = fma(y, i, ((fma(log(c), -0.5, fmin(z, a)) + fmax(z, a)) + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(fmax(z, a) + Float64(t + fma(i, y, Float64(log(c) * Float64(b - 0.5)))))
	tmp = 0.0
	if (b <= -5.9e+165)
		tmp = t_1;
	elseif (b <= 2.8e+96)
		tmp = fma(y, i, Float64(Float64(fma(log(c), -0.5, fmin(z, a)) + fmax(z, a)) + t));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[Max[z, a], $MachinePrecision] + N[(t + N[(i * y + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.9e+165], t$95$1, If[LessEqual[b, 2.8e+96], N[(y * i + N[(N[(N[(N[Log[c], $MachinePrecision] * -0.5 + N[Min[z, a], $MachinePrecision]), $MachinePrecision] + N[Max[z, a], $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -5.89999999999999996e165 or 2.8e96 < 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 z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-log.f64 N/A

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

      8. lower--.f64 84.1%

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

   4. Applied rewrites 84.1%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-log.f64 N/A

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

      3. lower--.f64 69.0%

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

   7. Applied rewrites 69.0%

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

   if -5.89999999999999996e165 < b < 2.8e96

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 99.8%

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

      5. lift-+.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. associate-+l+ N/A

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

      8. lift-+.f64 N/A

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

      9. +-commutative N/A

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

      10. associate-+l+ N/A

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

      11. +-commutative N/A

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

      12. lower-+.f64 N/A

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 84.5%

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

   7. Taylor expanded in b around 0

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

   9. Applied rewrites 69.5%

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

Alternative 9: 73.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \mathbf{if}\;b \leq -8.8 \cdot 10^{+195}:\\ \;\;\;\;a + \left(\mathsf{max}\left(z, t\right) + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{+120}:\\ \;\;\;\;\mathsf{fma}\left(y, i, \left(\mathsf{fma}\left(\log c, -0.5, \mathsf{min}\left(z, t\right)\right) + a\right) + \mathsf{max}\left(z, t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, \frac{b \cdot \left(\mathsf{max}\left(z, t\right) \cdot \log c\right)}{\mathsf{max}\left(z, t\right)}\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= b -8.8e+195)
   (+ a (+ (fmax z t) (* (log c) (- b 0.5))))
   (if (<= b 4.2e+120)
     (fma y i (+ (+ (fma (log c) -0.5 (fmin z t)) a) (fmax z t)))
     (fma y i (/ (* b (* (fmax z t) (log c))) (fmax z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (b <= -8.8e+195) {
		tmp = a + (fmax(z, t) + (log(c) * (b - 0.5)));
	} else if (b <= 4.2e+120) {
		tmp = fma(y, i, ((fma(log(c), -0.5, fmin(z, t)) + a) + fmax(z, t)));
	} else {
		tmp = fma(y, i, ((b * (fmax(z, t) * log(c))) / fmax(z, t)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (b <= -8.8e+195)
		tmp = Float64(a + Float64(fmax(z, t) + Float64(log(c) * Float64(b - 0.5))));
	elseif (b <= 4.2e+120)
		tmp = fma(y, i, Float64(Float64(fma(log(c), -0.5, fmin(z, t)) + a) + fmax(z, t)));
	else
		tmp = fma(y, i, Float64(Float64(b * Float64(fmax(z, t) * log(c))) / fmax(z, t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[b, -8.8e+195], N[(a + N[(N[Max[z, t], $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.2e+120], N[(y * i + N[(N[(N[(N[Log[c], $MachinePrecision] * -0.5 + N[Min[z, t], $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision] + N[Max[z, t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * i + N[(N[(b * N[(N[Max[z, t], $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[Max[z, t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.7999999999999999e195

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-log.f64 N/A

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

      8. lower--.f64 84.1%

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

   4. Applied rewrites 84.1%

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

   5. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-log.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower--.f64 61.2%

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

   7. Applied rewrites 61.2%

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

   8. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-log.f64 N/A

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

      3. lower--.f64 46.1%

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

   10. Applied rewrites 46.1%

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

   if -8.7999999999999999e195 < b < 4.2000000000000001e120

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 99.8%

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

      5. lift-+.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. associate-+l+ N/A

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

      8. lift-+.f64 N/A

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

      9. +-commutative N/A

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

      10. associate-+l+ N/A

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

      11. +-commutative N/A

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

      12. lower-+.f64 N/A

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 84.5%

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

   7. Taylor expanded in b around 0

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

   9. Applied rewrites 69.5%

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

   if 4.2000000000000001e120 < 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

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 99.8%

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

      5. lift-+.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. associate-+l+ N/A

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

      8. lift-+.f64 N/A

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

      9. +-commutative N/A

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

      10. associate-+l+ N/A

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

      11. +-commutative N/A

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

      12. lower-+.f64 N/A

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

   3. Applied rewrites 99.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. sum-to-mult-rev N/A

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

      4. add-to-fraction N/A

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

      5. associate-*l/ N/A

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

      6. lower-/.f64 N/A

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

   5. Applied rewrites 69.3%

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

   6. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-log.f64 34.5%

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

   8. Applied rewrites 34.5%

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

Alternative 10: 65.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{min}\left(\mathsf{min}\left(z, t\right), a\right)\\ t_2 := \mathsf{max}\left(\mathsf{min}\left(z, t\right), a\right)\\ t_3 := \mathsf{min}\left(\mathsf{max}\left(z, t\right), t\_2\right)\\ t_4 := \mathsf{fma}\left(y, i, \frac{b \cdot \left(t\_3 \cdot \log c\right)}{t\_3}\right)\\ t_5 := \mathsf{max}\left(\mathsf{max}\left(z, t\right), t\_2\right)\\ t_6 := \left(\left(\left(\left(x \cdot \log y + t\_1\right) + t\_3\right) + t\_5\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{if}\;t\_6 \leq -5 \cdot 10^{+278}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_6 \leq -2 \cdot 10^{+62}:\\ \;\;\;\;--1 \cdot t\_1\\ \mathbf{elif}\;t\_6 \leq 10^{+308}:\\ \;\;\;\;t\_5 + \left(t\_3 + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fmin (fmin z t) a))
        (t_2 (fmax (fmin z t) a))
        (t_3 (fmin (fmax z t) t_2))
        (t_4 (fma y i (/ (* b (* t_3 (log c))) t_3)))
        (t_5 (fmax (fmax z t) t_2))
        (t_6
         (+
          (+ (+ (+ (+ (* x (log y)) t_1) t_3) t_5) (* (- b 0.5) (log c)))
          (* y i))))
   (if (<= t_6 -5e+278)
     t_4
     (if (<= t_6 -2e+62)
       (- (* -1.0 t_1))
       (if (<= t_6 1e+308) (+ t_5 (+ t_3 (* (log c) (- b 0.5)))) t_4)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fmin(fmin(z, t), a);
	double t_2 = fmax(fmin(z, t), a);
	double t_3 = fmin(fmax(z, t), t_2);
	double t_4 = fma(y, i, ((b * (t_3 * log(c))) / t_3));
	double t_5 = fmax(fmax(z, t), t_2);
	double t_6 = (((((x * log(y)) + t_1) + t_3) + t_5) + ((b - 0.5) * log(c))) + (y * i);
	double tmp;
	if (t_6 <= -5e+278) {
		tmp = t_4;
	} else if (t_6 <= -2e+62) {
		tmp = -(-1.0 * t_1);
	} else if (t_6 <= 1e+308) {
		tmp = t_5 + (t_3 + (log(c) * (b - 0.5)));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fmin(fmin(z, t), a)
	t_2 = fmax(fmin(z, t), a)
	t_3 = fmin(fmax(z, t), t_2)
	t_4 = fma(y, i, Float64(Float64(b * Float64(t_3 * log(c))) / t_3))
	t_5 = fmax(fmax(z, t), t_2)
	t_6 = Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + t_1) + t_3) + t_5) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i))
	tmp = 0.0
	if (t_6 <= -5e+278)
		tmp = t_4;
	elseif (t_6 <= -2e+62)
		tmp = Float64(-Float64(-1.0 * t_1));
	elseif (t_6 <= 1e+308)
		tmp = Float64(t_5 + Float64(t_3 + Float64(log(c) * Float64(b - 0.5))));
	else
		tmp = t_4;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[Min[N[Min[z, t], $MachinePrecision], a], $MachinePrecision]}, Block[{t$95$2 = N[Max[N[Min[z, t], $MachinePrecision], a], $MachinePrecision]}, Block[{t$95$3 = N[Min[N[Max[z, t], $MachinePrecision], t$95$2], $MachinePrecision]}, Block[{t$95$4 = N[(y * i + N[(N[(b * N[(t$95$3 * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[Max[N[Max[z, t], $MachinePrecision], t$95$2], $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] + t$95$3), $MachinePrecision] + t$95$5), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$6, -5e+278], t$95$4, If[LessEqual[t$95$6, -2e+62], (-N[(-1.0 * t$95$1), $MachinePrecision]), If[LessEqual[t$95$6, 1e+308], N[(t$95$5 + N[(t$95$3 + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < -5.00000000000000029e278 or 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. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 99.8%

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

      5. lift-+.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. associate-+l+ N/A

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

      8. lift-+.f64 N/A

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

      9. +-commutative N/A

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

      10. associate-+l+ N/A

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

      11. +-commutative N/A

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

      12. lower-+.f64 N/A

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

   3. Applied rewrites 99.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. sum-to-mult-rev N/A

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

      4. add-to-fraction N/A

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

      5. associate-*l/ N/A

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

      6. lower-/.f64 N/A

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

   5. Applied rewrites 69.3%

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

   6. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-log.f64 34.5%

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

   8. Applied rewrites 34.5%

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

   if -5.00000000000000029e278 < (+.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)) < -2.00000000000000007e62

   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 y around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

   4. Applied rewrites 68.8%

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

   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 15.6%

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

   7. Applied rewrites 15.6%

      \[\leadsto -1 \cdot \left(-1 \cdot \color{blue}{a}\right) \]
   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 15.6%

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

      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 15.6%

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

   9. Applied rewrites 15.6%

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

   10. Taylor expanded in z around inf

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

       1. lower-*.f64 16.7%

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

   12. Applied rewrites 16.7%

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

   if -2.00000000000000007e62 < (+.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 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-log.f64 N/A

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

      8. lower--.f64 84.1%

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

   4. Applied rewrites 84.1%

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

   5. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-log.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower--.f64 61.2%

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

   7. Applied rewrites 61.2%

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

   8. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-log.f64 N/A

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

      3. lower--.f64 46.1%

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

   10. Applied rewrites 46.1%

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

Alternative 11: 65.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{min}\left(\mathsf{min}\left(z, t\right), a\right)\\ t_2 := \mathsf{max}\left(\mathsf{min}\left(z, t\right), a\right)\\ t_3 := \mathsf{min}\left(\mathsf{max}\left(z, t\right), t\_2\right)\\ t_4 := \mathsf{max}\left(\mathsf{max}\left(z, t\right), t\_2\right)\\ t_5 := \left(\left(\left(\left(x \cdot \log y + t\_1\right) + t\_3\right) + t\_4\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{if}\;t\_5 \leq -\infty:\\ \;\;\;\;1 \cdot t\_3 + y \cdot i\\ \mathbf{elif}\;t\_5 \leq -2 \cdot 10^{+62}:\\ \;\;\;\;--1 \cdot t\_1\\ \mathbf{elif}\;t\_5 \leq 10^{+308}:\\ \;\;\;\;t\_4 + \left(t\_3 + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \left(y \cdot \mathsf{fma}\left(-1, i, -1 \cdot \frac{t\_4}{y}\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fmin (fmin z t) a))
        (t_2 (fmax (fmin z t) a))
        (t_3 (fmin (fmax z t) t_2))
        (t_4 (fmax (fmax z t) t_2))
        (t_5
         (+
          (+ (+ (+ (+ (* x (log y)) t_1) t_3) t_4) (* (- b 0.5) (log c)))
          (* y i))))
   (if (<= t_5 (- INFINITY))
     (+ (* 1.0 t_3) (* y i))
     (if (<= t_5 -2e+62)
       (- (* -1.0 t_1))
       (if (<= t_5 1e+308)
         (+ t_4 (+ t_3 (* (log c) (- b 0.5))))
         (* -1.0 (* y (fma -1.0 i (* -1.0 (/ t_4 y))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fmin(fmin(z, t), a);
	double t_2 = fmax(fmin(z, t), a);
	double t_3 = fmin(fmax(z, t), t_2);
	double t_4 = fmax(fmax(z, t), t_2);
	double t_5 = (((((x * log(y)) + t_1) + t_3) + t_4) + ((b - 0.5) * log(c))) + (y * i);
	double tmp;
	if (t_5 <= -((double) INFINITY)) {
		tmp = (1.0 * t_3) + (y * i);
	} else if (t_5 <= -2e+62) {
		tmp = -(-1.0 * t_1);
	} else if (t_5 <= 1e+308) {
		tmp = t_4 + (t_3 + (log(c) * (b - 0.5)));
	} else {
		tmp = -1.0 * (y * fma(-1.0, i, (-1.0 * (t_4 / y))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fmin(fmin(z, t), a)
	t_2 = fmax(fmin(z, t), a)
	t_3 = fmin(fmax(z, t), t_2)
	t_4 = fmax(fmax(z, t), t_2)
	t_5 = Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + t_1) + t_3) + t_4) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i))
	tmp = 0.0
	if (t_5 <= Float64(-Inf))
		tmp = Float64(Float64(1.0 * t_3) + Float64(y * i));
	elseif (t_5 <= -2e+62)
		tmp = Float64(-Float64(-1.0 * t_1));
	elseif (t_5 <= 1e+308)
		tmp = Float64(t_4 + Float64(t_3 + Float64(log(c) * Float64(b - 0.5))));
	else
		tmp = Float64(-1.0 * Float64(y * fma(-1.0, i, Float64(-1.0 * Float64(t_4 / y)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[Min[N[Min[z, t], $MachinePrecision], a], $MachinePrecision]}, Block[{t$95$2 = N[Max[N[Min[z, t], $MachinePrecision], a], $MachinePrecision]}, Block[{t$95$3 = N[Min[N[Max[z, t], $MachinePrecision], t$95$2], $MachinePrecision]}, Block[{t$95$4 = N[Max[N[Max[z, t], $MachinePrecision], t$95$2], $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] + t$95$3), $MachinePrecision] + t$95$4), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$5, (-Infinity)], N[(N[(1.0 * t$95$3), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$5, -2e+62], (-N[(-1.0 * t$95$1), $MachinePrecision]), If[LessEqual[t$95$5, 1e+308], N[(t$95$4 + N[(t$95$3 + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-1.0 * N[(y * N[(-1.0 * i + N[(-1.0 * N[(t$95$4 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate-+l+ N/A

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

      4. lift-+.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. sum-to-mult N/A

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

      8. lower-unsound-*.f64 N/A

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

   3. Applied rewrites 73.9%

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

   4. Taylor expanded in t around inf

      \[\leadsto \color{blue}{1} \cdot t + y \cdot i \]
   5. Step-by-step derivation

   6. Applied rewrites 38.9%

      \[\leadsto \color{blue}{1} \cdot t + y \cdot i \]

   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)) < -2.00000000000000007e62

   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 y around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

   4. Applied rewrites 68.8%

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

   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 15.6%

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

   7. Applied rewrites 15.6%

      \[\leadsto -1 \cdot \left(-1 \cdot \color{blue}{a}\right) \]
   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 15.6%

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

      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 15.6%

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

   9. Applied rewrites 15.6%

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

   10. Taylor expanded in z around inf

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

       1. lower-*.f64 16.7%

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

   12. Applied rewrites 16.7%

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

   if -2.00000000000000007e62 < (+.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 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-log.f64 N/A

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

      8. lower--.f64 84.1%

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

   4. Applied rewrites 84.1%

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

   5. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-log.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower--.f64 61.2%

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

   7. Applied rewrites 61.2%

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

   8. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-log.f64 N/A

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

      3. lower--.f64 46.1%

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

   10. Applied rewrites 46.1%

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

   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 y around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

   4. Applied rewrites 68.8%

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

   5. Taylor expanded in a around inf

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

      1. lower-/.f64 32.5%

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

   7. Applied rewrites 32.5%

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

Alternative 12: 62.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{min}\left(\mathsf{min}\left(z, t\right), a\right)\\ t_2 := \mathsf{max}\left(\mathsf{min}\left(z, t\right), a\right)\\ t_3 := \mathsf{min}\left(\mathsf{max}\left(z, t\right), t\_2\right)\\ t_4 := \mathsf{max}\left(\mathsf{max}\left(z, t\right), t\_2\right)\\ t_5 := \left(\left(\left(\left(x \cdot \log y + t\_1\right) + t\_3\right) + t\_4\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{if}\;t\_5 \leq -\infty:\\ \;\;\;\;1 \cdot t\_3 + y \cdot i\\ \mathbf{elif}\;t\_5 \leq -2 \cdot 10^{+62}:\\ \;\;\;\;--1 \cdot t\_1\\ \mathbf{elif}\;t\_5 \leq 4 \cdot 10^{+307}:\\ \;\;\;\;t\_4 + \left(t\_3 + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_4}{t\_3} \cdot t\_3 + y \cdot i\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fmin (fmin z t) a))
        (t_2 (fmax (fmin z t) a))
        (t_3 (fmin (fmax z t) t_2))
        (t_4 (fmax (fmax z t) t_2))
        (t_5
         (+
          (+ (+ (+ (+ (* x (log y)) t_1) t_3) t_4) (* (- b 0.5) (log c)))
          (* y i))))
   (if (<= t_5 (- INFINITY))
     (+ (* 1.0 t_3) (* y i))
     (if (<= t_5 -2e+62)
       (- (* -1.0 t_1))
       (if (<= t_5 4e+307)
         (+ t_4 (+ t_3 (* (log c) (- b 0.5))))
         (+ (* (/ t_4 t_3) t_3) (* y i)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fmin(fmin(z, t), a);
	double t_2 = fmax(fmin(z, t), a);
	double t_3 = fmin(fmax(z, t), t_2);
	double t_4 = fmax(fmax(z, t), t_2);
	double t_5 = (((((x * log(y)) + t_1) + t_3) + t_4) + ((b - 0.5) * log(c))) + (y * i);
	double tmp;
	if (t_5 <= -((double) INFINITY)) {
		tmp = (1.0 * t_3) + (y * i);
	} else if (t_5 <= -2e+62) {
		tmp = -(-1.0 * t_1);
	} else if (t_5 <= 4e+307) {
		tmp = t_4 + (t_3 + (log(c) * (b - 0.5)));
	} else {
		tmp = ((t_4 / t_3) * t_3) + (y * i);
	}
	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 = fmin(fmin(z, t), a);
	double t_2 = fmax(fmin(z, t), a);
	double t_3 = fmin(fmax(z, t), t_2);
	double t_4 = fmax(fmax(z, t), t_2);
	double t_5 = (((((x * Math.log(y)) + t_1) + t_3) + t_4) + ((b - 0.5) * Math.log(c))) + (y * i);
	double tmp;
	if (t_5 <= -Double.POSITIVE_INFINITY) {
		tmp = (1.0 * t_3) + (y * i);
	} else if (t_5 <= -2e+62) {
		tmp = -(-1.0 * t_1);
	} else if (t_5 <= 4e+307) {
		tmp = t_4 + (t_3 + (Math.log(c) * (b - 0.5)));
	} else {
		tmp = ((t_4 / t_3) * t_3) + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = fmin(fmin(z, t), a)
	t_2 = fmax(fmin(z, t), a)
	t_3 = fmin(fmax(z, t), t_2)
	t_4 = fmax(fmax(z, t), t_2)
	t_5 = (((((x * math.log(y)) + t_1) + t_3) + t_4) + ((b - 0.5) * math.log(c))) + (y * i)
	tmp = 0
	if t_5 <= -math.inf:
		tmp = (1.0 * t_3) + (y * i)
	elif t_5 <= -2e+62:
		tmp = -(-1.0 * t_1)
	elif t_5 <= 4e+307:
		tmp = t_4 + (t_3 + (math.log(c) * (b - 0.5)))
	else:
		tmp = ((t_4 / t_3) * t_3) + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fmin(fmin(z, t), a)
	t_2 = fmax(fmin(z, t), a)
	t_3 = fmin(fmax(z, t), t_2)
	t_4 = fmax(fmax(z, t), t_2)
	t_5 = Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + t_1) + t_3) + t_4) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i))
	tmp = 0.0
	if (t_5 <= Float64(-Inf))
		tmp = Float64(Float64(1.0 * t_3) + Float64(y * i));
	elseif (t_5 <= -2e+62)
		tmp = Float64(-Float64(-1.0 * t_1));
	elseif (t_5 <= 4e+307)
		tmp = Float64(t_4 + Float64(t_3 + Float64(log(c) * Float64(b - 0.5))));
	else
		tmp = Float64(Float64(Float64(t_4 / t_3) * t_3) + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = min(min(z, t), a);
	t_2 = max(min(z, t), a);
	t_3 = min(max(z, t), t_2);
	t_4 = max(max(z, t), t_2);
	t_5 = (((((x * log(y)) + t_1) + t_3) + t_4) + ((b - 0.5) * log(c))) + (y * i);
	tmp = 0.0;
	if (t_5 <= -Inf)
		tmp = (1.0 * t_3) + (y * i);
	elseif (t_5 <= -2e+62)
		tmp = -(-1.0 * t_1);
	elseif (t_5 <= 4e+307)
		tmp = t_4 + (t_3 + (log(c) * (b - 0.5)));
	else
		tmp = ((t_4 / t_3) * t_3) + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[Min[N[Min[z, t], $MachinePrecision], a], $MachinePrecision]}, Block[{t$95$2 = N[Max[N[Min[z, t], $MachinePrecision], a], $MachinePrecision]}, Block[{t$95$3 = N[Min[N[Max[z, t], $MachinePrecision], t$95$2], $MachinePrecision]}, Block[{t$95$4 = N[Max[N[Max[z, t], $MachinePrecision], t$95$2], $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] + t$95$3), $MachinePrecision] + t$95$4), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$5, (-Infinity)], N[(N[(1.0 * t$95$3), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$5, -2e+62], (-N[(-1.0 * t$95$1), $MachinePrecision]), If[LessEqual[t$95$5, 4e+307], N[(t$95$4 + N[(t$95$3 + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t$95$4 / t$95$3), $MachinePrecision] * t$95$3), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate-+l+ N/A

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

      4. lift-+.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. sum-to-mult N/A

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

      8. lower-unsound-*.f64 N/A

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

   3. Applied rewrites 73.9%

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

   4. Taylor expanded in t around inf

      \[\leadsto \color{blue}{1} \cdot t + y \cdot i \]
   5. Step-by-step derivation

   6. Applied rewrites 38.9%

      \[\leadsto \color{blue}{1} \cdot t + y \cdot i \]

   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)) < -2.00000000000000007e62

   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 y around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

   4. Applied rewrites 68.8%

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

   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 15.6%

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

   7. Applied rewrites 15.6%

      \[\leadsto -1 \cdot \left(-1 \cdot \color{blue}{a}\right) \]
   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 15.6%

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

      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 15.6%

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

   9. Applied rewrites 15.6%

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

   10. Taylor expanded in z around inf

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

       1. lower-*.f64 16.7%

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

   12. Applied rewrites 16.7%

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

   if -2.00000000000000007e62 < (+.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)) < 3.99999999999999994e307

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-log.f64 N/A

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

      8. lower--.f64 84.1%

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

   4. Applied rewrites 84.1%

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

   5. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-log.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower--.f64 61.2%

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

   7. Applied rewrites 61.2%

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

   8. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-log.f64 N/A

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

      3. lower--.f64 46.1%

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

   10. Applied rewrites 46.1%

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

   if 3.99999999999999994e307 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i))

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate-+l+ N/A

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

      4. lift-+.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. sum-to-mult N/A

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

      8. lower-unsound-*.f64 N/A

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

   3. Applied rewrites 73.9%

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

   4. Taylor expanded in a around inf

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

      1. lower-/.f64 31.9%

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

   6. Applied rewrites 31.9%

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

Alternative 13: 57.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{min}\left(\mathsf{min}\left(z, t\right), a\right)\\ t_2 := \mathsf{max}\left(\mathsf{min}\left(z, t\right), a\right)\\ t_3 := \mathsf{min}\left(\mathsf{max}\left(z, t\right), t\_2\right)\\ t_4 := \mathsf{max}\left(\mathsf{max}\left(z, t\right), t\_2\right)\\ t_5 := \mathsf{fma}\left(y, i, \frac{t\_4 \cdot t\_3}{t\_3}\right)\\ t_6 := \left(\left(\left(\left(x \cdot \log y + t\_1\right) + t\_3\right) + t\_4\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{if}\;t\_6 \leq -\infty:\\ \;\;\;\;1 \cdot t\_3 + y \cdot i\\ \mathbf{elif}\;t\_6 \leq -1 \cdot 10^{+103}:\\ \;\;\;\;--1 \cdot t\_1\\ \mathbf{elif}\;t\_6 \leq 2 \cdot 10^{+237}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;t\_6 \leq 4 \cdot 10^{+303}:\\ \;\;\;\;-\left(-t\_4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_5\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fmin (fmin z t) a))
        (t_2 (fmax (fmin z t) a))
        (t_3 (fmin (fmax z t) t_2))
        (t_4 (fmax (fmax z t) t_2))
        (t_5 (fma y i (/ (* t_4 t_3) t_3)))
        (t_6
         (+
          (+ (+ (+ (+ (* x (log y)) t_1) t_3) t_4) (* (- b 0.5) (log c)))
          (* y i))))
   (if (<= t_6 (- INFINITY))
     (+ (* 1.0 t_3) (* y i))
     (if (<= t_6 -1e+103)
       (- (* -1.0 t_1))
       (if (<= t_6 2e+237) t_5 (if (<= t_6 4e+303) (- (- t_4)) t_5))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fmin(fmin(z, t), a);
	double t_2 = fmax(fmin(z, t), a);
	double t_3 = fmin(fmax(z, t), t_2);
	double t_4 = fmax(fmax(z, t), t_2);
	double t_5 = fma(y, i, ((t_4 * t_3) / t_3));
	double t_6 = (((((x * log(y)) + t_1) + t_3) + t_4) + ((b - 0.5) * log(c))) + (y * i);
	double tmp;
	if (t_6 <= -((double) INFINITY)) {
		tmp = (1.0 * t_3) + (y * i);
	} else if (t_6 <= -1e+103) {
		tmp = -(-1.0 * t_1);
	} else if (t_6 <= 2e+237) {
		tmp = t_5;
	} else if (t_6 <= 4e+303) {
		tmp = -(-t_4);
	} else {
		tmp = t_5;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fmin(fmin(z, t), a)
	t_2 = fmax(fmin(z, t), a)
	t_3 = fmin(fmax(z, t), t_2)
	t_4 = fmax(fmax(z, t), t_2)
	t_5 = fma(y, i, Float64(Float64(t_4 * t_3) / t_3))
	t_6 = Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + t_1) + t_3) + t_4) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i))
	tmp = 0.0
	if (t_6 <= Float64(-Inf))
		tmp = Float64(Float64(1.0 * t_3) + Float64(y * i));
	elseif (t_6 <= -1e+103)
		tmp = Float64(-Float64(-1.0 * t_1));
	elseif (t_6 <= 2e+237)
		tmp = t_5;
	elseif (t_6 <= 4e+303)
		tmp = Float64(-Float64(-t_4));
	else
		tmp = t_5;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[Min[N[Min[z, t], $MachinePrecision], a], $MachinePrecision]}, Block[{t$95$2 = N[Max[N[Min[z, t], $MachinePrecision], a], $MachinePrecision]}, Block[{t$95$3 = N[Min[N[Max[z, t], $MachinePrecision], t$95$2], $MachinePrecision]}, Block[{t$95$4 = N[Max[N[Max[z, t], $MachinePrecision], t$95$2], $MachinePrecision]}, Block[{t$95$5 = N[(y * i + N[(N[(t$95$4 * t$95$3), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] + t$95$3), $MachinePrecision] + t$95$4), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$6, (-Infinity)], N[(N[(1.0 * t$95$3), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$6, -1e+103], (-N[(-1.0 * t$95$1), $MachinePrecision]), If[LessEqual[t$95$6, 2e+237], t$95$5, If[LessEqual[t$95$6, 4e+303], (-(-t$95$4)), t$95$5]]]]]]]]]]

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. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate-+l+ N/A

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

      4. lift-+.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. sum-to-mult N/A

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

      8. lower-unsound-*.f64 N/A

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

   3. Applied rewrites 73.9%

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

   4. Taylor expanded in t around inf

      \[\leadsto \color{blue}{1} \cdot t + y \cdot i \]
   5. Step-by-step derivation

   6. Applied rewrites 38.9%

      \[\leadsto \color{blue}{1} \cdot t + y \cdot i \]

   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)) < -1e103

   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 y around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

   4. Applied rewrites 68.8%

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

   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 15.6%

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

   7. Applied rewrites 15.6%

      \[\leadsto -1 \cdot \left(-1 \cdot \color{blue}{a}\right) \]
   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 15.6%

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

      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 15.6%

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

   9. Applied rewrites 15.6%

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

   10. Taylor expanded in z around inf

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

       1. lower-*.f64 16.7%

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

   12. Applied rewrites 16.7%

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

   if -1e103 < (+.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)) < 1.99999999999999988e237 or 4e303 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i))

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 99.8%

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

      5. lift-+.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. associate-+l+ N/A

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

      8. lift-+.f64 N/A

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

      9. +-commutative N/A

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

      10. associate-+l+ N/A

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

      11. +-commutative N/A

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

      12. lower-+.f64 N/A

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

   3. Applied rewrites 99.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. sum-to-mult-rev N/A

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

      4. add-to-fraction N/A

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

      5. associate-*l/ N/A

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

      6. lower-/.f64 N/A

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

   5. Applied rewrites 69.3%

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

   6. Taylor expanded in a around inf

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

      1. lower-*.f64 33.7%

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

   8. Applied rewrites 33.7%

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

   if 1.99999999999999988e237 < (+.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)) < 4e303

   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 y around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

   4. Applied rewrites 68.8%

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

   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 15.6%

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

   7. Applied rewrites 15.6%

      \[\leadsto -1 \cdot \left(-1 \cdot \color{blue}{a}\right) \]
   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 15.6%

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

      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 15.6%

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

   9. Applied rewrites 15.6%

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

Alternative 14: 56.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{min}\left(\mathsf{min}\left(z, t\right), a\right)\\ t_2 := \mathsf{max}\left(\mathsf{min}\left(z, t\right), a\right)\\ t_3 := \mathsf{min}\left(\mathsf{max}\left(z, t\right), t\_2\right)\\ t_4 := \mathsf{max}\left(\mathsf{max}\left(z, t\right), t\_2\right)\\ t_5 := \left(\left(\left(\left(x \cdot \log y + t\_1\right) + t\_3\right) + t\_4\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{if}\;t\_5 \leq -\infty:\\ \;\;\;\;1 \cdot t\_3 + y \cdot i\\ \mathbf{elif}\;t\_5 \leq -1 \cdot 10^{+103}:\\ \;\;\;\;--1 \cdot t\_1\\ \mathbf{elif}\;t\_5 \leq 4 \cdot 10^{+295}:\\ \;\;\;\;\mathsf{fma}\left(y, i, \frac{t\_4 \cdot t\_3}{t\_3}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_4}{t\_3} \cdot t\_3 + y \cdot i\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fmin (fmin z t) a))
        (t_2 (fmax (fmin z t) a))
        (t_3 (fmin (fmax z t) t_2))
        (t_4 (fmax (fmax z t) t_2))
        (t_5
         (+
          (+ (+ (+ (+ (* x (log y)) t_1) t_3) t_4) (* (- b 0.5) (log c)))
          (* y i))))
   (if (<= t_5 (- INFINITY))
     (+ (* 1.0 t_3) (* y i))
     (if (<= t_5 -1e+103)
       (- (* -1.0 t_1))
       (if (<= t_5 4e+295)
         (fma y i (/ (* t_4 t_3) t_3))
         (+ (* (/ t_4 t_3) t_3) (* y i)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fmin(fmin(z, t), a);
	double t_2 = fmax(fmin(z, t), a);
	double t_3 = fmin(fmax(z, t), t_2);
	double t_4 = fmax(fmax(z, t), t_2);
	double t_5 = (((((x * log(y)) + t_1) + t_3) + t_4) + ((b - 0.5) * log(c))) + (y * i);
	double tmp;
	if (t_5 <= -((double) INFINITY)) {
		tmp = (1.0 * t_3) + (y * i);
	} else if (t_5 <= -1e+103) {
		tmp = -(-1.0 * t_1);
	} else if (t_5 <= 4e+295) {
		tmp = fma(y, i, ((t_4 * t_3) / t_3));
	} else {
		tmp = ((t_4 / t_3) * t_3) + (y * i);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fmin(fmin(z, t), a)
	t_2 = fmax(fmin(z, t), a)
	t_3 = fmin(fmax(z, t), t_2)
	t_4 = fmax(fmax(z, t), t_2)
	t_5 = Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + t_1) + t_3) + t_4) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i))
	tmp = 0.0
	if (t_5 <= Float64(-Inf))
		tmp = Float64(Float64(1.0 * t_3) + Float64(y * i));
	elseif (t_5 <= -1e+103)
		tmp = Float64(-Float64(-1.0 * t_1));
	elseif (t_5 <= 4e+295)
		tmp = fma(y, i, Float64(Float64(t_4 * t_3) / t_3));
	else
		tmp = Float64(Float64(Float64(t_4 / t_3) * t_3) + Float64(y * i));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[Min[N[Min[z, t], $MachinePrecision], a], $MachinePrecision]}, Block[{t$95$2 = N[Max[N[Min[z, t], $MachinePrecision], a], $MachinePrecision]}, Block[{t$95$3 = N[Min[N[Max[z, t], $MachinePrecision], t$95$2], $MachinePrecision]}, Block[{t$95$4 = N[Max[N[Max[z, t], $MachinePrecision], t$95$2], $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] + t$95$3), $MachinePrecision] + t$95$4), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$5, (-Infinity)], N[(N[(1.0 * t$95$3), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$5, -1e+103], (-N[(-1.0 * t$95$1), $MachinePrecision]), If[LessEqual[t$95$5, 4e+295], N[(y * i + N[(N[(t$95$4 * t$95$3), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t$95$4 / t$95$3), $MachinePrecision] * t$95$3), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate-+l+ N/A

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

      4. lift-+.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. sum-to-mult N/A

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

      8. lower-unsound-*.f64 N/A

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

   3. Applied rewrites 73.9%

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

   4. Taylor expanded in t around inf

      \[\leadsto \color{blue}{1} \cdot t + y \cdot i \]
   5. Step-by-step derivation

   6. Applied rewrites 38.9%

      \[\leadsto \color{blue}{1} \cdot t + y \cdot i \]

   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)) < -1e103

   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 y around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

   4. Applied rewrites 68.8%

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

   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 15.6%

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

   7. Applied rewrites 15.6%

      \[\leadsto -1 \cdot \left(-1 \cdot \color{blue}{a}\right) \]
   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 15.6%

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

      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 15.6%

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

   9. Applied rewrites 15.6%

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

   10. Taylor expanded in z around inf

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

       1. lower-*.f64 16.7%

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

   12. Applied rewrites 16.7%

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

   if -1e103 < (+.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)) < 3.9999999999999999e295

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 99.8%

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

      5. lift-+.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. associate-+l+ N/A

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

      8. lift-+.f64 N/A

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

      9. +-commutative N/A

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

      10. associate-+l+ N/A

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

      11. +-commutative N/A

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

      12. lower-+.f64 N/A

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

   3. Applied rewrites 99.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. sum-to-mult-rev N/A

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

      4. add-to-fraction N/A

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

      5. associate-*l/ N/A

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

      6. lower-/.f64 N/A

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

   5. Applied rewrites 69.3%

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

   6. Taylor expanded in a around inf

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

      1. lower-*.f64 33.7%

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

   8. Applied rewrites 33.7%

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

   if 3.9999999999999999e295 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i))

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate-+l+ N/A

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

      4. lift-+.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. sum-to-mult N/A

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

      8. lower-unsound-*.f64 N/A

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

   3. Applied rewrites 73.9%

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

   4. Taylor expanded in a around inf

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

      1. lower-/.f64 31.9%

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

   6. Applied rewrites 31.9%

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

Alternative 15: 56.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{min}\left(\mathsf{min}\left(z, t\right), a\right)\\ t_2 := \mathsf{max}\left(\mathsf{min}\left(z, t\right), a\right)\\ t_3 := \mathsf{min}\left(\mathsf{max}\left(z, t\right), t\_2\right)\\ t_4 := 1 \cdot t\_3 + y \cdot i\\ t_5 := \mathsf{max}\left(\mathsf{max}\left(z, t\right), t\_2\right)\\ t_6 := \left(\left(\left(\left(x \cdot \log y + t\_1\right) + t\_3\right) + t\_5\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{if}\;t\_6 \leq -\infty:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_6 \leq -2 \cdot 10^{+17}:\\ \;\;\;\;--1 \cdot t\_1\\ \mathbf{elif}\;t\_6 \leq 10^{+308}:\\ \;\;\;\;-\left(-t\_5\right)\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fmin (fmin z t) a))
        (t_2 (fmax (fmin z t) a))
        (t_3 (fmin (fmax z t) t_2))
        (t_4 (+ (* 1.0 t_3) (* y i)))
        (t_5 (fmax (fmax z t) t_2))
        (t_6
         (+
          (+ (+ (+ (+ (* x (log y)) t_1) t_3) t_5) (* (- b 0.5) (log c)))
          (* y i))))
   (if (<= t_6 (- INFINITY))
     t_4
     (if (<= t_6 -2e+17)
       (- (* -1.0 t_1))
       (if (<= t_6 1e+308) (- (- t_5)) t_4)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fmin(fmin(z, t), a);
	double t_2 = fmax(fmin(z, t), a);
	double t_3 = fmin(fmax(z, t), t_2);
	double t_4 = (1.0 * t_3) + (y * i);
	double t_5 = fmax(fmax(z, t), t_2);
	double t_6 = (((((x * log(y)) + t_1) + t_3) + t_5) + ((b - 0.5) * log(c))) + (y * i);
	double tmp;
	if (t_6 <= -((double) INFINITY)) {
		tmp = t_4;
	} else if (t_6 <= -2e+17) {
		tmp = -(-1.0 * t_1);
	} else if (t_6 <= 1e+308) {
		tmp = -(-t_5);
	} else {
		tmp = t_4;
	}
	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 = fmin(fmin(z, t), a);
	double t_2 = fmax(fmin(z, t), a);
	double t_3 = fmin(fmax(z, t), t_2);
	double t_4 = (1.0 * t_3) + (y * i);
	double t_5 = fmax(fmax(z, t), t_2);
	double t_6 = (((((x * Math.log(y)) + t_1) + t_3) + t_5) + ((b - 0.5) * Math.log(c))) + (y * i);
	double tmp;
	if (t_6 <= -Double.POSITIVE_INFINITY) {
		tmp = t_4;
	} else if (t_6 <= -2e+17) {
		tmp = -(-1.0 * t_1);
	} else if (t_6 <= 1e+308) {
		tmp = -(-t_5);
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = fmin(fmin(z, t), a)
	t_2 = fmax(fmin(z, t), a)
	t_3 = fmin(fmax(z, t), t_2)
	t_4 = (1.0 * t_3) + (y * i)
	t_5 = fmax(fmax(z, t), t_2)
	t_6 = (((((x * math.log(y)) + t_1) + t_3) + t_5) + ((b - 0.5) * math.log(c))) + (y * i)
	tmp = 0
	if t_6 <= -math.inf:
		tmp = t_4
	elif t_6 <= -2e+17:
		tmp = -(-1.0 * t_1)
	elif t_6 <= 1e+308:
		tmp = -(-t_5)
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fmin(fmin(z, t), a)
	t_2 = fmax(fmin(z, t), a)
	t_3 = fmin(fmax(z, t), t_2)
	t_4 = Float64(Float64(1.0 * t_3) + Float64(y * i))
	t_5 = fmax(fmax(z, t), t_2)
	t_6 = Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + t_1) + t_3) + t_5) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i))
	tmp = 0.0
	if (t_6 <= Float64(-Inf))
		tmp = t_4;
	elseif (t_6 <= -2e+17)
		tmp = Float64(-Float64(-1.0 * t_1));
	elseif (t_6 <= 1e+308)
		tmp = Float64(-Float64(-t_5));
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = min(min(z, t), a);
	t_2 = max(min(z, t), a);
	t_3 = min(max(z, t), t_2);
	t_4 = (1.0 * t_3) + (y * i);
	t_5 = max(max(z, t), t_2);
	t_6 = (((((x * log(y)) + t_1) + t_3) + t_5) + ((b - 0.5) * log(c))) + (y * i);
	tmp = 0.0;
	if (t_6 <= -Inf)
		tmp = t_4;
	elseif (t_6 <= -2e+17)
		tmp = -(-1.0 * t_1);
	elseif (t_6 <= 1e+308)
		tmp = -(-t_5);
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[Min[N[Min[z, t], $MachinePrecision], a], $MachinePrecision]}, Block[{t$95$2 = N[Max[N[Min[z, t], $MachinePrecision], a], $MachinePrecision]}, Block[{t$95$3 = N[Min[N[Max[z, t], $MachinePrecision], t$95$2], $MachinePrecision]}, Block[{t$95$4 = N[(N[(1.0 * t$95$3), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[Max[N[Max[z, t], $MachinePrecision], t$95$2], $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] + t$95$3), $MachinePrecision] + t$95$5), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$6, (-Infinity)], t$95$4, If[LessEqual[t$95$6, -2e+17], (-N[(-1.0 * t$95$1), $MachinePrecision]), If[LessEqual[t$95$6, 1e+308], (-(-t$95$5)), t$95$4]]]]]]]]]

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 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. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate-+l+ N/A

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

      4. lift-+.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. sum-to-mult N/A

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

      8. lower-unsound-*.f64 N/A

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

   3. Applied rewrites 73.9%

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

   4. Taylor expanded in t around inf

      \[\leadsto \color{blue}{1} \cdot t + y \cdot i \]
   5. Step-by-step derivation

   6. Applied rewrites 38.9%

      \[\leadsto \color{blue}{1} \cdot t + y \cdot i \]

   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)) < -2e17

   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 y around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

   4. Applied rewrites 68.8%

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

   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 15.6%

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

   7. Applied rewrites 15.6%

      \[\leadsto -1 \cdot \left(-1 \cdot \color{blue}{a}\right) \]
   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 15.6%

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

      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 15.6%

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

   9. Applied rewrites 15.6%

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

   10. Taylor expanded in z around inf

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

       1. lower-*.f64 16.7%

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

   12. Applied rewrites 16.7%

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

   if -2e17 < (+.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 y around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

   4. Applied rewrites 68.8%

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

   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 15.6%

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

   7. Applied rewrites 15.6%

      \[\leadsto -1 \cdot \left(-1 \cdot \color{blue}{a}\right) \]
   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 15.6%

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

      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 15.6%

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

   9. Applied rewrites 15.6%

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

Alternative 16: 55.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{min}\left(\mathsf{min}\left(z, t\right), a\right)\\ t_2 := --1 \cdot \left(i \cdot y\right)\\ t_3 := \mathsf{max}\left(\mathsf{min}\left(z, t\right), a\right)\\ t_4 := \mathsf{max}\left(\mathsf{max}\left(z, t\right), t\_3\right)\\ t_5 := \left(\left(\left(\left(x \cdot \log y + t\_1\right) + \mathsf{min}\left(\mathsf{max}\left(z, t\right), t\_3\right)\right) + t\_4\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{if}\;t\_5 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_5 \leq -2 \cdot 10^{+17}:\\ \;\;\;\;--1 \cdot t\_1\\ \mathbf{elif}\;t\_5 \leq 10^{+308}:\\ \;\;\;\;-\left(-t\_4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fmin (fmin z t) a))
        (t_2 (- (* -1.0 (* i y))))
        (t_3 (fmax (fmin z t) a))
        (t_4 (fmax (fmax z t) t_3))
        (t_5
         (+
          (+
           (+ (+ (+ (* x (log y)) t_1) (fmin (fmax z t) t_3)) t_4)
           (* (- b 0.5) (log c)))
          (* y i))))
   (if (<= t_5 (- INFINITY))
     t_2
     (if (<= t_5 -2e+17)
       (- (* -1.0 t_1))
       (if (<= t_5 1e+308) (- (- t_4)) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fmin(fmin(z, t), a);
	double t_2 = -(-1.0 * (i * y));
	double t_3 = fmax(fmin(z, t), a);
	double t_4 = fmax(fmax(z, t), t_3);
	double t_5 = (((((x * log(y)) + t_1) + fmin(fmax(z, t), t_3)) + t_4) + ((b - 0.5) * log(c))) + (y * i);
	double tmp;
	if (t_5 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_5 <= -2e+17) {
		tmp = -(-1.0 * t_1);
	} else if (t_5 <= 1e+308) {
		tmp = -(-t_4);
	} else {
		tmp = t_2;
	}
	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 = fmin(fmin(z, t), a);
	double t_2 = -(-1.0 * (i * y));
	double t_3 = fmax(fmin(z, t), a);
	double t_4 = fmax(fmax(z, t), t_3);
	double t_5 = (((((x * Math.log(y)) + t_1) + fmin(fmax(z, t), t_3)) + t_4) + ((b - 0.5) * Math.log(c))) + (y * i);
	double tmp;
	if (t_5 <= -Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else if (t_5 <= -2e+17) {
		tmp = -(-1.0 * t_1);
	} else if (t_5 <= 1e+308) {
		tmp = -(-t_4);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = fmin(fmin(z, t), a)
	t_2 = -(-1.0 * (i * y))
	t_3 = fmax(fmin(z, t), a)
	t_4 = fmax(fmax(z, t), t_3)
	t_5 = (((((x * math.log(y)) + t_1) + fmin(fmax(z, t), t_3)) + t_4) + ((b - 0.5) * math.log(c))) + (y * i)
	tmp = 0
	if t_5 <= -math.inf:
		tmp = t_2
	elif t_5 <= -2e+17:
		tmp = -(-1.0 * t_1)
	elif t_5 <= 1e+308:
		tmp = -(-t_4)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fmin(fmin(z, t), a)
	t_2 = Float64(-Float64(-1.0 * Float64(i * y)))
	t_3 = fmax(fmin(z, t), a)
	t_4 = fmax(fmax(z, t), t_3)
	t_5 = Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + t_1) + fmin(fmax(z, t), t_3)) + t_4) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i))
	tmp = 0.0
	if (t_5 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_5 <= -2e+17)
		tmp = Float64(-Float64(-1.0 * t_1));
	elseif (t_5 <= 1e+308)
		tmp = Float64(-Float64(-t_4));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = min(min(z, t), a);
	t_2 = -(-1.0 * (i * y));
	t_3 = max(min(z, t), a);
	t_4 = max(max(z, t), t_3);
	t_5 = (((((x * log(y)) + t_1) + min(max(z, t), t_3)) + t_4) + ((b - 0.5) * log(c))) + (y * i);
	tmp = 0.0;
	if (t_5 <= -Inf)
		tmp = t_2;
	elseif (t_5 <= -2e+17)
		tmp = -(-1.0 * t_1);
	elseif (t_5 <= 1e+308)
		tmp = -(-t_4);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[Min[N[Min[z, t], $MachinePrecision], a], $MachinePrecision]}, Block[{t$95$2 = (-N[(-1.0 * N[(i * y), $MachinePrecision]), $MachinePrecision])}, Block[{t$95$3 = N[Max[N[Min[z, t], $MachinePrecision], a], $MachinePrecision]}, Block[{t$95$4 = N[Max[N[Max[z, t], $MachinePrecision], t$95$3], $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] + N[Min[N[Max[z, t], $MachinePrecision], t$95$3], $MachinePrecision]), $MachinePrecision] + t$95$4), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$5, (-Infinity)], t$95$2, If[LessEqual[t$95$5, -2e+17], (-N[(-1.0 * t$95$1), $MachinePrecision]), If[LessEqual[t$95$5, 1e+308], (-(-t$95$4)), t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

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

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

   4. Applied rewrites 68.8%

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

   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 15.6%

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

   7. Applied rewrites 15.6%

      \[\leadsto -1 \cdot \left(-1 \cdot \color{blue}{a}\right) \]
   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 15.6%

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

      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 15.6%

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

   9. Applied rewrites 15.6%

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

   10. Taylor expanded in y around inf

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

       1. lower-*.f64 N/A

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

       2. lower-*.f64 24.7%

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

   12. Applied rewrites 24.7%

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

   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)) < -2e17

   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 y around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

   4. Applied rewrites 68.8%

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

   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 15.6%

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

   7. Applied rewrites 15.6%

      \[\leadsto -1 \cdot \left(-1 \cdot \color{blue}{a}\right) \]
   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 15.6%

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

      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 15.6%

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

   9. Applied rewrites 15.6%

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

   10. Taylor expanded in z around inf

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

       1. lower-*.f64 16.7%

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

   12. Applied rewrites 16.7%

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

   if -2e17 < (+.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 y around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

   4. Applied rewrites 68.8%

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

   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 15.6%

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

   7. Applied rewrites 15.6%

      \[\leadsto -1 \cdot \left(-1 \cdot \color{blue}{a}\right) \]
   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 15.6%

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

      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 15.6%

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

   9. Applied rewrites 15.6%

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

Alternative 17: 44.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{min}\left(\mathsf{min}\left(z, t\right), a\right)\\ t_2 := \mathsf{max}\left(\mathsf{min}\left(z, t\right), a\right)\\ t_3 := \mathsf{max}\left(\mathsf{max}\left(z, t\right), t\_2\right)\\ \mathbf{if}\;\left(\left(\left(\left(x \cdot \log y + t\_1\right) + \mathsf{min}\left(\mathsf{max}\left(z, t\right), t\_2\right)\right) + t\_3\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \leq -2 \cdot 10^{+17}:\\ \;\;\;\;--1 \cdot t\_1\\ \mathbf{else}:\\ \;\;\;\;-\left(-t\_3\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fmin (fmin z t) a))
        (t_2 (fmax (fmin z t) a))
        (t_3 (fmax (fmax z t) t_2)))
   (if (<=
        (+
         (+
          (+ (+ (+ (* x (log y)) t_1) (fmin (fmax z t) t_2)) t_3)
          (* (- b 0.5) (log c)))
         (* y i))
        -2e+17)
     (- (* -1.0 t_1))
     (- (- t_3)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fmin(fmin(z, t), a);
	double t_2 = fmax(fmin(z, t), a);
	double t_3 = fmax(fmax(z, t), t_2);
	double tmp;
	if (((((((x * log(y)) + t_1) + fmin(fmax(z, t), t_2)) + t_3) + ((b - 0.5) * log(c))) + (y * i)) <= -2e+17) {
		tmp = -(-1.0 * t_1);
	} else {
		tmp = -(-t_3);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = fmin(fmin(z, t), a)
    t_2 = fmax(fmin(z, t), a)
    t_3 = fmax(fmax(z, t), t_2)
    if (((((((x * log(y)) + t_1) + fmin(fmax(z, t), t_2)) + t_3) + ((b - 0.5d0) * log(c))) + (y * i)) <= (-2d+17)) then
        tmp = -((-1.0d0) * t_1)
    else
        tmp = -(-t_3)
    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 = fmin(fmin(z, t), a);
	double t_2 = fmax(fmin(z, t), a);
	double t_3 = fmax(fmax(z, t), t_2);
	double tmp;
	if (((((((x * Math.log(y)) + t_1) + fmin(fmax(z, t), t_2)) + t_3) + ((b - 0.5) * Math.log(c))) + (y * i)) <= -2e+17) {
		tmp = -(-1.0 * t_1);
	} else {
		tmp = -(-t_3);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = fmin(fmin(z, t), a)
	t_2 = fmax(fmin(z, t), a)
	t_3 = fmax(fmax(z, t), t_2)
	tmp = 0
	if ((((((x * math.log(y)) + t_1) + fmin(fmax(z, t), t_2)) + t_3) + ((b - 0.5) * math.log(c))) + (y * i)) <= -2e+17:
		tmp = -(-1.0 * t_1)
	else:
		tmp = -(-t_3)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fmin(fmin(z, t), a)
	t_2 = fmax(fmin(z, t), a)
	t_3 = fmax(fmax(z, t), t_2)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + t_1) + fmin(fmax(z, t), t_2)) + t_3) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i)) <= -2e+17)
		tmp = Float64(-Float64(-1.0 * t_1));
	else
		tmp = Float64(-Float64(-t_3));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = min(min(z, t), a);
	t_2 = max(min(z, t), a);
	t_3 = max(max(z, t), t_2);
	tmp = 0.0;
	if (((((((x * log(y)) + t_1) + min(max(z, t), t_2)) + t_3) + ((b - 0.5) * log(c))) + (y * i)) <= -2e+17)
		tmp = -(-1.0 * t_1);
	else
		tmp = -(-t_3);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[Min[N[Min[z, t], $MachinePrecision], a], $MachinePrecision]}, Block[{t$95$2 = N[Max[N[Min[z, t], $MachinePrecision], a], $MachinePrecision]}, Block[{t$95$3 = N[Max[N[Max[z, t], $MachinePrecision], t$95$2], $MachinePrecision]}, If[LessEqual[N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] + N[Min[N[Max[z, t], $MachinePrecision], t$95$2], $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], -2e+17], (-N[(-1.0 * t$95$1), $MachinePrecision]), (-(-t$95$3))]]]]

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)) < -2e17

   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 y around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

   4. Applied rewrites 68.8%

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

   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 15.6%

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

   7. Applied rewrites 15.6%

      \[\leadsto -1 \cdot \left(-1 \cdot \color{blue}{a}\right) \]
   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 15.6%

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

      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 15.6%

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

   9. Applied rewrites 15.6%

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

   10. Taylor expanded in z around inf

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

       1. lower-*.f64 16.7%

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

   12. Applied rewrites 16.7%

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

   if -2e17 < (+.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 y around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

   4. Applied rewrites 68.8%

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

   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 15.6%

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

   7. Applied rewrites 15.6%

      \[\leadsto -1 \cdot \left(-1 \cdot \color{blue}{a}\right) \]
   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 15.6%

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

      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 15.6%

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

   9. Applied rewrites 15.6%

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

Alternative 18: 22.5% accurate, 4.2× speedup

Math

\[-\left(-\mathsf{max}\left(t, \mathsf{max}\left(z, a\right)\right)\right) \]

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := (-(-N[Max[t, N[Max[z, a], $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 y around -inf

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

   1. lower-*.f64 N/A

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

   2. lower-*.f64 N/A

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

   3. lower-fma.f64 N/A

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

   4. lower-*.f64 N/A

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

   5. lower-/.f64 N/A

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

4. Applied rewrites 68.8%

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

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 15.6%

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

7. Applied rewrites 15.6%

   \[\leadsto -1 \cdot \left(-1 \cdot \color{blue}{a}\right) \]
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 15.6%

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

   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 15.6%

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

9. Applied rewrites 15.6%

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

Reproduce

herbie shell --seed 2025181 
(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)))