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

Percentage Accurate: 99.8% → 99.8%

Time: 7.9s

Alternatives: 14

Speedup: 0.9×

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, 0.9× speedup

Math

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

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 (fmin z a))) (fmax 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, fmin(z, a))) + fmax(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, fmin(z, a))) + fmax(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 + N[Min[z, a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[Max[z, a], $MachinePrecision]), $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: 95.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(y, i, \mathsf{fma}\left(\log y, x, \left(\mathsf{fma}\left(-0.5, \log c, a\right) + t\right) + z\right)\right)\\ \mathbf{if}\;x \leq -1.95 \cdot 10^{+139}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{+124}:\\ \;\;\;\;\mathsf{fma}\left(y, i, z + \mathsf{fma}\left(b - 0.5, \log c, t + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fma y i (fma (log y) x (+ (+ (fma -0.5 (log c) a) t) z)))))
   (if (<= x -1.95e+139)
     t_1
     (if (<= x 1.22e+124)
       (fma y i (+ z (fma (- b 0.5) (log c) (+ t a))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fma(y, i, fma(log(y), x, ((fma(-0.5, log(c), a) + t) + z)));
	double tmp;
	if (x <= -1.95e+139) {
		tmp = t_1;
	} else if (x <= 1.22e+124) {
		tmp = fma(y, i, (z + fma((b - 0.5), log(c), (t + a))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fma(y, i, fma(log(y), x, Float64(Float64(fma(-0.5, log(c), a) + t) + z)))
	tmp = 0.0
	if (x <= -1.95e+139)
		tmp = t_1;
	elseif (x <= 1.22e+124)
		tmp = fma(y, i, Float64(z + fma(Float64(b - 0.5), log(c), Float64(t + a))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(y * i + N[(N[Log[y], $MachinePrecision] * x + N[(N[(N[(-0.5 * N[Log[c], $MachinePrecision] + a), $MachinePrecision] + t), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.95e+139], t$95$1, If[LessEqual[x, 1.22e+124], N[(y * i + N[(z + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision] + N[(t + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.95000000000000003e139 or 1.22e124 < 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. 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. lift-+.f64 N/A

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

      3. associate-+l+ N/A

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

      4. lift-fma.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. +-commutative N/A

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

      7. associate-+l+ N/A

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

      8. lift-fma.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-+l+ N/A

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

      11. lift-*.f64 N/A

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

      12. lift-fma.f64 N/A

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

      13. lift-+.f64 N/A

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

      14. associate-+r+ N/A

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

      15. lift-*.f64 N/A

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

      16. lift-+.f64 N/A

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

      17. lower-fma.f64 99.8%

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

   5. Applied rewrites 99.8%

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

   6. Taylor expanded in b around 0

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

   8. Applied rewrites 84.0%

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

   if -1.95000000000000003e139 < x < 1.22e124

   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 84.1%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate-+l+ N/A

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

      4. lift-fma.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. lower-+.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 84.1%

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

   8. Applied rewrites 84.1%

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

Alternative 3: 91.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq -7.1 \cdot 10^{+221}:\\ \;\;\;\;t + \mathsf{fma}\left(i, y, \mathsf{fma}\left(x, \log y, \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+209}:\\ \;\;\;\;\mathsf{fma}\left(y, i, z + \mathsf{fma}\left(b - 0.5, \log c, t + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(\log y \cdot x\right) + y \cdot i\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -7.1e+221)
   (+ t (fma i y (fma x (log y) (* (log c) (- b 0.5)))))
   (if (<= x 2.8e+209)
     (fma y i (+ z (fma (- b 0.5) (log c) (+ t a))))
     (+ (* 1.0 (* (log y) x)) (* y i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -7.1e+221) {
		tmp = t + fma(i, y, fma(x, log(y), (log(c) * (b - 0.5))));
	} else if (x <= 2.8e+209) {
		tmp = fma(y, i, (z + fma((b - 0.5), log(c), (t + a))));
	} else {
		tmp = (1.0 * (log(y) * x)) + (y * i);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -7.1e+221)
		tmp = Float64(t + fma(i, y, fma(x, log(y), Float64(log(c) * Float64(b - 0.5)))));
	elseif (x <= 2.8e+209)
		tmp = fma(y, i, Float64(z + fma(Float64(b - 0.5), log(c), Float64(t + a))));
	else
		tmp = Float64(Float64(1.0 * Float64(log(y) * x)) + Float64(y * i));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -7.1e+221], N[(t + N[(i * y + N[(x * N[Log[y], $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.8e+209], N[(y * i + N[(z + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision] + N[(t + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 * N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.09999999999999985e221

   1. Initial program 99.8%

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

   2. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-log.f64 N/A

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

      8. lower--.f64 84.5%

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

   4. Applied rewrites 84.5%

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

   5. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-log.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-log.f64 N/A

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

      7. lower--.f64 69.8%

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

   7. Applied rewrites 69.8%

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

   if -7.09999999999999985e221 < x < 2.80000000000000013e209

   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 84.1%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate-+l+ N/A

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

      4. lift-fma.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. lower-+.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 84.1%

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

   8. Applied rewrites 84.1%

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

   if 2.80000000000000013e209 < x

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      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. lift-+.f64 N/A

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

      6. associate-+l+ N/A

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

      7. associate-+l+ N/A

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

      8. sum-to-mult N/A

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

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

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

   3. Applied rewrites 73.6%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 38.7%

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

Alternative 4: 90.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} t_1 := 1 \cdot \left(\log y \cdot x\right) + y \cdot i\\ \mathbf{if}\;x \leq -7.1 \cdot 10^{+221}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+209}:\\ \;\;\;\;\mathsf{fma}\left(y, i, z + \mathsf{fma}\left(b - 0.5, \log c, t + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* 1.0 (* (log y) x)) (* y i))))
   (if (<= x -7.1e+221)
     t_1
     (if (<= x 2.8e+209)
       (fma y i (+ z (fma (- b 0.5) (log c) (+ t a))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (1.0 * (log(y) * x)) + (y * i);
	double tmp;
	if (x <= -7.1e+221) {
		tmp = t_1;
	} else if (x <= 2.8e+209) {
		tmp = fma(y, i, (z + fma((b - 0.5), log(c), (t + a))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(1.0 * Float64(log(y) * x)) + Float64(y * i))
	tmp = 0.0
	if (x <= -7.1e+221)
		tmp = t_1;
	elseif (x <= 2.8e+209)
		tmp = fma(y, i, Float64(z + fma(Float64(b - 0.5), log(c), Float64(t + a))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(1.0 * N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7.1e+221], t$95$1, If[LessEqual[x, 2.8e+209], N[(y * i + N[(z + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision] + N[(t + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -7.09999999999999985e221 or 2.80000000000000013e209 < x

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      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. lift-+.f64 N/A

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

      6. associate-+l+ N/A

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

      7. associate-+l+ N/A

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

      8. sum-to-mult N/A

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

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

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

   3. Applied rewrites 73.6%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 38.7%

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

   if -7.09999999999999985e221 < x < 2.80000000000000013e209

   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 84.1%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate-+l+ N/A

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

      4. lift-fma.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. lower-+.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 84.1%

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

   8. Applied rewrites 84.1%

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

Alternative 5: 78.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_1 := \left(\mathsf{fma}\left(i, y, \log c \cdot \left(b - 0.5\right)\right) + z\right) + \mathsf{min}\left(t, a\right)\\ \mathbf{if}\;b \leq -1.15 \cdot 10^{+212}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{+143}:\\ \;\;\;\;\mathsf{fma}\left(y, i, \left(\mathsf{fma}\left(\log c, -0.5, z\right) + \mathsf{max}\left(t, a\right)\right) + \mathsf{min}\left(t, a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (+ (fma i y (* (log c) (- b 0.5))) z) (fmin t a))))
   (if (<= b -1.15e+212)
     t_1
     (if (<= b 2.8e+143)
       (fma y i (+ (+ (fma (log c) -0.5 z) (fmax t a)) (fmin t a)))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (fma(i, y, (log(c) * (b - 0.5))) + z) + fmin(t, a);
	double tmp;
	if (b <= -1.15e+212) {
		tmp = t_1;
	} else if (b <= 2.8e+143) {
		tmp = fma(y, i, ((fma(log(c), -0.5, z) + fmax(t, a)) + fmin(t, a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(fma(i, y, Float64(log(c) * Float64(b - 0.5))) + z) + fmin(t, a))
	tmp = 0.0
	if (b <= -1.15e+212)
		tmp = t_1;
	elseif (b <= 2.8e+143)
		tmp = fma(y, i, Float64(Float64(fma(log(c), -0.5, z) + fmax(t, a)) + fmin(t, a)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(i * y + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + N[Min[t, a], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.15e+212], t$95$1, If[LessEqual[b, 2.8e+143], N[(y * i + N[(N[(N[(N[Log[c], $MachinePrecision] * -0.5 + z), $MachinePrecision] + N[Max[t, a], $MachinePrecision]), $MachinePrecision] + N[Min[t, a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.1499999999999999e212 or 2.79999999999999998e143 < 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 a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-log.f64 N/A

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

      8. lower--.f64 84.5%

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

   4. Applied rewrites 84.5%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-log.f64 N/A

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

      3. lower--.f64 69.1%

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

   7. Applied rewrites 69.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 69.1%

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

      4. lift-+.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 69.1%

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

   9. Applied rewrites 69.1%

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

   if -1.1499999999999999e212 < b < 2.79999999999999998e143

   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 84.1%

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

   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 68.7%

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

Alternative 6: 73.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} t_1 := b \cdot \log c\\ \mathbf{if}\;b \leq -1.15 \cdot 10^{+212}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{+240}:\\ \;\;\;\;\mathsf{fma}\left(y, i, \left(\mathsf{fma}\left(\log c, -0.5, z\right) + a\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* b (log c))))
   (if (<= b -1.15e+212)
     t_1
     (if (<= b 3.5e+240) (fma y i (+ (+ (fma (log c) -0.5 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 = b * log(c);
	double tmp;
	if (b <= -1.15e+212) {
		tmp = t_1;
	} else if (b <= 3.5e+240) {
		tmp = fma(y, i, ((fma(log(c), -0.5, z) + a) + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(b * log(c))
	tmp = 0.0
	if (b <= -1.15e+212)
		tmp = t_1;
	elseif (b <= 3.5e+240)
		tmp = fma(y, i, Float64(Float64(fma(log(c), -0.5, 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[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.15e+212], t$95$1, If[LessEqual[b, 3.5e+240], N[(y * i + N[(N[(N[(N[Log[c], $MachinePrecision] * -0.5 + z), $MachinePrecision] + a), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.1499999999999999e212 or 3.50000000000000033e240 < 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 b around inf

      \[\leadsto \color{blue}{b \cdot \log c} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\log c} \]

      2. lower-log.f64 16.8%

         \[\leadsto b \cdot \log c \]

   4. Applied rewrites 16.8%

      \[\leadsto \color{blue}{b \cdot \log c} \]

   if -1.1499999999999999e212 < b < 3.50000000000000033e240

   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 84.1%

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

   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 68.7%

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

Alternative 7: 62.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{min}\left(t, \mathsf{max}\left(z, a\right)\right)\\ t_2 := \mathsf{max}\left(t, \mathsf{max}\left(z, a\right)\right)\\ t_3 := \left(\left(\left(\left(x \cdot \log y + \mathsf{min}\left(z, a\right)\right) + t\_1\right) + t\_2\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{if}\;t\_3 \leq 100:\\ \;\;\;\;\left(\mathsf{fma}\left(i, y, \log c \cdot -0.5\right) + \mathsf{min}\left(z, a\right)\right) + t\_1\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+180}:\\ \;\;\;\;\left(\left(-i\right) - \frac{t\_2}{y}\right) \cdot \left(-y\right)\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+305}:\\ \;\;\;\;-\left(-t\_2\right)\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(\log y \cdot x\right) + y \cdot i\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fmin t (fmax z a)))
        (t_2 (fmax t (fmax z a)))
        (t_3
         (+
          (+
           (+ (+ (+ (* x (log y)) (fmin z a)) t_1) t_2)
           (* (- b 0.5) (log c)))
          (* y i))))
   (if (<= t_3 100.0)
     (+ (+ (fma i y (* (log c) -0.5)) (fmin z a)) t_1)
     (if (<= t_3 2e+180)
       (* (- (- i) (/ t_2 y)) (- y))
       (if (<= t_3 2e+305) (- (- t_2)) (+ (* 1.0 (* (log y) x)) (* 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(t, fmax(z, a));
	double t_2 = fmax(t, fmax(z, a));
	double t_3 = (((((x * log(y)) + fmin(z, a)) + t_1) + t_2) + ((b - 0.5) * log(c))) + (y * i);
	double tmp;
	if (t_3 <= 100.0) {
		tmp = (fma(i, y, (log(c) * -0.5)) + fmin(z, a)) + t_1;
	} else if (t_3 <= 2e+180) {
		tmp = (-i - (t_2 / y)) * -y;
	} else if (t_3 <= 2e+305) {
		tmp = -(-t_2);
	} else {
		tmp = (1.0 * (log(y) * x)) + (y * i);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fmin(t, fmax(z, a))
	t_2 = fmax(t, fmax(z, a))
	t_3 = Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + fmin(z, a)) + t_1) + t_2) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i))
	tmp = 0.0
	if (t_3 <= 100.0)
		tmp = Float64(Float64(fma(i, y, Float64(log(c) * -0.5)) + fmin(z, a)) + t_1);
	elseif (t_3 <= 2e+180)
		tmp = Float64(Float64(Float64(-i) - Float64(t_2 / y)) * Float64(-y));
	elseif (t_3 <= 2e+305)
		tmp = Float64(-Float64(-t_2));
	else
		tmp = Float64(Float64(1.0 * Float64(log(y) * x)) + Float64(y * i));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[Min[t, N[Max[z, a], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[Max[t, N[Max[z, a], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[Min[z, a], $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] + t$95$2), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, 100.0], N[(N[(N[(i * y + N[(N[Log[c], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision] + N[Min[z, a], $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[t$95$3, 2e+180], N[(N[((-i) - N[(t$95$2 / y), $MachinePrecision]), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[t$95$3, 2e+305], (-(-t$95$2)), N[(N[(1.0 * N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]), $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)) < 100

   1. Initial program 99.8%

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

   2. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-log.f64 N/A

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

      8. lower--.f64 84.5%

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

   4. Applied rewrites 84.5%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-log.f64 N/A

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

      3. lower--.f64 69.1%

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

   7. Applied rewrites 69.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 69.1%

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

      4. lift-+.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 69.1%

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

   9. Applied rewrites 69.1%

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

   10. Taylor expanded in b around 0

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

   12. Applied rewrites 54.0%

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

   if 100 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < 2e180

   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 68.9%

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

   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 32.3%

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

   7. Applied rewrites 32.3%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

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

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

      6. lower-*.f64 N/A

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

   9. Applied rewrites 32.3%

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

   if 2e180 < (+.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)) < 1.9999999999999999e305

   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 68.9%

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

   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 16.4%

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

   7. Applied rewrites 16.4%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 16.4%

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

      4. lift-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lift-neg.f64 16.4%

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

   9. Applied rewrites 16.4%

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

   if 1.9999999999999999e305 < (+.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. lift-+.f64 N/A

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

      6. associate-+l+ N/A

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

      7. associate-+l+ N/A

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

      8. sum-to-mult N/A

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

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

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

   3. Applied rewrites 73.6%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 38.7%

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

Alternative 8: 55.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{min}\left(\mathsf{min}\left(z, t\right), a\right)\\ t_2 := 1 \cdot \left(\log y \cdot x\right) + y \cdot i\\ t_3 := \mathsf{max}\left(\mathsf{min}\left(z, t\right), a\right)\\ t_4 := \mathsf{max}\left(\mathsf{max}\left(z, t\right), t\_3\right)\\ t_5 := \left(\left(\left(\left(x \cdot \log y + t\_1\right) + \mathsf{min}\left(\mathsf{max}\left(z, t\right), t\_3\right)\right) + t\_4\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{if}\;t\_5 \leq -4 \cdot 10^{+299}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_5 \leq -0.5:\\ \;\;\;\;--1 \cdot t\_1\\ \mathbf{elif}\;t\_5 \leq 2 \cdot 10^{+180}:\\ \;\;\;\;\left(\left(-i\right) - \frac{t\_4}{y}\right) \cdot \left(-y\right)\\ \mathbf{elif}\;t\_5 \leq 2 \cdot 10^{+305}:\\ \;\;\;\;-\left(-t\_4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fmin (fmin z t) a))
        (t_2 (+ (* 1.0 (* (log y) x)) (* y i)))
        (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 -4e+299)
     t_2
     (if (<= t_5 -0.5)
       (- (* -1.0 t_1))
       (if (<= t_5 2e+180)
         (* (- (- i) (/ t_4 y)) (- y))
         (if (<= t_5 2e+305) (- (- 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 * (log(y) * x)) + (y * i);
	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 <= -4e+299) {
		tmp = t_2;
	} else if (t_5 <= -0.5) {
		tmp = -(-1.0 * t_1);
	} else if (t_5 <= 2e+180) {
		tmp = (-i - (t_4 / y)) * -y;
	} else if (t_5 <= 2e+305) {
		tmp = -(-t_4);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = fmin(fmin(z, t), a)
    t_2 = (1.0d0 * (log(y) * x)) + (y * i)
    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 - 0.5d0) * log(c))) + (y * i)
    if (t_5 <= (-4d+299)) then
        tmp = t_2
    else if (t_5 <= (-0.5d0)) then
        tmp = -((-1.0d0) * t_1)
    else if (t_5 <= 2d+180) then
        tmp = (-i - (t_4 / y)) * -y
    else if (t_5 <= 2d+305) then
        tmp = -(-t_4)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fmin(fmin(z, t), a);
	double t_2 = (1.0 * (Math.log(y) * x)) + (y * i);
	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 <= -4e+299) {
		tmp = t_2;
	} else if (t_5 <= -0.5) {
		tmp = -(-1.0 * t_1);
	} else if (t_5 <= 2e+180) {
		tmp = (-i - (t_4 / y)) * -y;
	} else if (t_5 <= 2e+305) {
		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 * (math.log(y) * x)) + (y * i)
	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 <= -4e+299:
		tmp = t_2
	elif t_5 <= -0.5:
		tmp = -(-1.0 * t_1)
	elif t_5 <= 2e+180:
		tmp = (-i - (t_4 / y)) * -y
	elif t_5 <= 2e+305:
		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(log(y) * x)) + Float64(y * i))
	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 <= -4e+299)
		tmp = t_2;
	elseif (t_5 <= -0.5)
		tmp = Float64(-Float64(-1.0 * t_1));
	elseif (t_5 <= 2e+180)
		tmp = Float64(Float64(Float64(-i) - Float64(t_4 / y)) * Float64(-y));
	elseif (t_5 <= 2e+305)
		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 * (log(y) * x)) + (y * i);
	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 <= -4e+299)
		tmp = t_2;
	elseif (t_5 <= -0.5)
		tmp = -(-1.0 * t_1);
	elseif (t_5 <= 2e+180)
		tmp = (-i - (t_4 / y)) * -y;
	elseif (t_5 <= 2e+305)
		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[(N[(1.0 * N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] + N[(y * i), $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, -4e+299], t$95$2, If[LessEqual[t$95$5, -0.5], (-N[(-1.0 * t$95$1), $MachinePrecision]), If[LessEqual[t$95$5, 2e+180], N[(N[((-i) - N[(t$95$4 / y), $MachinePrecision]), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[t$95$5, 2e+305], (-(-t$95$4)), t$95$2]]]]]]]]]

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)) < -4.0000000000000002e299 or 1.9999999999999999e305 < (+.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. lift-+.f64 N/A

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

      6. associate-+l+ N/A

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

      7. associate-+l+ N/A

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

      8. sum-to-mult N/A

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

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

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

   3. Applied rewrites 73.6%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 38.7%

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

   if -4.0000000000000002e299 < (+.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)) < -0.5

   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 68.9%

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

   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 16.4%

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

   7. Applied rewrites 16.4%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 16.4%

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

      4. lift-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lift-neg.f64 16.4%

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

   9. Applied rewrites 16.4%

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

   10. Taylor expanded in z around inf

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

       1. lower-*.f64 16.0%

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

   12. Applied rewrites 16.0%

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

   if -0.5 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < 2e180

   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 68.9%

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

   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 32.3%

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

   7. Applied rewrites 32.3%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

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

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

      6. lower-*.f64 N/A

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

   9. Applied rewrites 32.3%

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

   if 2e180 < (+.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)) < 1.9999999999999999e305

   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 68.9%

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

   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 16.4%

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

   7. Applied rewrites 16.4%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 16.4%

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

      4. lift-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lift-neg.f64 16.4%

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

   9. Applied rewrites 16.4%

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

Alternative 9: 55.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{min}\left(\mathsf{min}\left(z, t\right), a\right)\\ t_2 := \mathsf{max}\left(\mathsf{min}\left(z, t\right), a\right)\\ t_3 := \mathsf{max}\left(\mathsf{max}\left(z, t\right), t\_2\right)\\ t_4 := \left(\left(-i\right) - \frac{t\_3}{y}\right) \cdot \left(-y\right)\\ t_5 := \left(\left(\left(\left(x \cdot \log y + t\_1\right) + \mathsf{min}\left(\mathsf{max}\left(z, t\right), t\_2\right)\right) + t\_3\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{if}\;t\_5 \leq -1 \cdot 10^{+292}:\\ \;\;\;\;-1 \cdot \left(y \cdot \mathsf{fma}\left(-1, i, -1 \cdot \frac{t\_1}{y}\right)\right)\\ \mathbf{elif}\;t\_5 \leq -0.5:\\ \;\;\;\;--1 \cdot t\_1\\ \mathbf{elif}\;t\_5 \leq 2 \cdot 10^{+180}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_5 \leq 2 \cdot 10^{+305}:\\ \;\;\;\;-\left(-t\_3\right)\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \]

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 (fmax (fmax z t) t_2))
        (t_4 (* (- (- i) (/ t_3 y)) (- y)))
        (t_5
         (+
          (+
           (+ (+ (+ (* x (log y)) t_1) (fmin (fmax z t) t_2)) t_3)
           (* (- b 0.5) (log c)))
          (* y i))))
   (if (<= t_5 -1e+292)
     (* -1.0 (* y (fma -1.0 i (* -1.0 (/ t_1 y)))))
     (if (<= t_5 -0.5)
       (- (* -1.0 t_1))
       (if (<= t_5 2e+180) t_4 (if (<= t_5 2e+305) (- (- t_3)) 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 = fmax(fmax(z, t), t_2);
	double t_4 = (-i - (t_3 / y)) * -y;
	double t_5 = (((((x * log(y)) + t_1) + fmin(fmax(z, t), t_2)) + t_3) + ((b - 0.5) * log(c))) + (y * i);
	double tmp;
	if (t_5 <= -1e+292) {
		tmp = -1.0 * (y * fma(-1.0, i, (-1.0 * (t_1 / y))));
	} else if (t_5 <= -0.5) {
		tmp = -(-1.0 * t_1);
	} else if (t_5 <= 2e+180) {
		tmp = t_4;
	} else if (t_5 <= 2e+305) {
		tmp = -(-t_3);
	} 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 = fmax(fmax(z, t), t_2)
	t_4 = Float64(Float64(Float64(-i) - Float64(t_3 / y)) * Float64(-y))
	t_5 = 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))
	tmp = 0.0
	if (t_5 <= -1e+292)
		tmp = Float64(-1.0 * Float64(y * fma(-1.0, i, Float64(-1.0 * Float64(t_1 / y)))));
	elseif (t_5 <= -0.5)
		tmp = Float64(-Float64(-1.0 * t_1));
	elseif (t_5 <= 2e+180)
		tmp = t_4;
	elseif (t_5 <= 2e+305)
		tmp = Float64(-Float64(-t_3));
	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[Max[N[Max[z, t], $MachinePrecision], t$95$2], $MachinePrecision]}, Block[{t$95$4 = N[(N[((-i) - N[(t$95$3 / y), $MachinePrecision]), $MachinePrecision] * (-y)), $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$2], $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$5, -1e+292], N[(-1.0 * N[(y * N[(-1.0 * i + N[(-1.0 * N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$5, -0.5], (-N[(-1.0 * t$95$1), $MachinePrecision]), If[LessEqual[t$95$5, 2e+180], t$95$4, If[LessEqual[t$95$5, 2e+305], (-(-t$95$3)), t$95$4]]]]]]]]]

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)) < -1e292

   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 68.9%

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

   5. Taylor expanded in z around inf

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

      1. lower-/.f64 32.2%

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

   7. Applied rewrites 32.2%

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

   if -1e292 < (+.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)) < -0.5

   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 68.9%

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

   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 16.4%

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

   7. Applied rewrites 16.4%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 16.4%

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

      4. lift-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lift-neg.f64 16.4%

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

   9. Applied rewrites 16.4%

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

   10. Taylor expanded in z around inf

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

       1. lower-*.f64 16.0%

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

   12. Applied rewrites 16.0%

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

   if -0.5 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < 2e180 or 1.9999999999999999e305 < (+.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 68.9%

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

   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 32.3%

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

   7. Applied rewrites 32.3%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

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

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

      6. lower-*.f64 N/A

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

   9. Applied rewrites 32.3%

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

   if 2e180 < (+.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)) < 1.9999999999999999e305

   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 68.9%

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

   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 16.4%

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

   7. Applied rewrites 16.4%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 16.4%

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

      4. lift-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lift-neg.f64 16.4%

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

   9. Applied rewrites 16.4%

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

Alternative 10: 55.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{min}\left(\mathsf{min}\left(z, t\right), a\right)\\ t_2 := \mathsf{max}\left(\mathsf{min}\left(z, t\right), a\right)\\ t_3 := \mathsf{min}\left(\mathsf{max}\left(z, t\right), t\_2\right)\\ t_4 := \mathsf{max}\left(\mathsf{max}\left(z, t\right), t\_2\right)\\ t_5 := \left(\left(-i\right) - \frac{t\_4}{y}\right) \cdot \left(-y\right)\\ t_6 := \left(\left(\left(\left(x \cdot \log y + t\_1\right) + t\_3\right) + t\_4\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{if}\;t\_6 \leq -2 \cdot 10^{+300}:\\ \;\;\;\;\left(\left(-i\right) - \frac{t\_3}{y}\right) \cdot \left(-y\right)\\ \mathbf{elif}\;t\_6 \leq -0.5:\\ \;\;\;\;--1 \cdot t\_1\\ \mathbf{elif}\;t\_6 \leq 2 \cdot 10^{+180}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;t\_6 \leq 2 \cdot 10^{+305}:\\ \;\;\;\;-\left(-t\_4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_5\\ \end{array} \]

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 (* (- (- i) (/ t_4 y)) (- y)))
        (t_6
         (+
          (+ (+ (+ (+ (* x (log y)) t_1) t_3) t_4) (* (- b 0.5) (log c)))
          (* y i))))
   (if (<= t_6 -2e+300)
     (* (- (- i) (/ t_3 y)) (- y))
     (if (<= t_6 -0.5)
       (- (* -1.0 t_1))
       (if (<= t_6 2e+180) t_5 (if (<= t_6 2e+305) (- (- 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 = (-i - (t_4 / y)) * -y;
	double t_6 = (((((x * log(y)) + t_1) + t_3) + t_4) + ((b - 0.5) * log(c))) + (y * i);
	double tmp;
	if (t_6 <= -2e+300) {
		tmp = (-i - (t_3 / y)) * -y;
	} else if (t_6 <= -0.5) {
		tmp = -(-1.0 * t_1);
	} else if (t_6 <= 2e+180) {
		tmp = t_5;
	} else if (t_6 <= 2e+305) {
		tmp = -(-t_4);
	} else {
		tmp = t_5;
	}
	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) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    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 = (-i - (t_4 / y)) * -y
    t_6 = (((((x * log(y)) + t_1) + t_3) + t_4) + ((b - 0.5d0) * log(c))) + (y * i)
    if (t_6 <= (-2d+300)) then
        tmp = (-i - (t_3 / y)) * -y
    else if (t_6 <= (-0.5d0)) then
        tmp = -((-1.0d0) * t_1)
    else if (t_6 <= 2d+180) then
        tmp = t_5
    else if (t_6 <= 2d+305) then
        tmp = -(-t_4)
    else
        tmp = t_5
    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 = fmin(fmax(z, t), t_2);
	double t_4 = fmax(fmax(z, t), t_2);
	double t_5 = (-i - (t_4 / y)) * -y;
	double t_6 = (((((x * Math.log(y)) + t_1) + t_3) + t_4) + ((b - 0.5) * Math.log(c))) + (y * i);
	double tmp;
	if (t_6 <= -2e+300) {
		tmp = (-i - (t_3 / y)) * -y;
	} else if (t_6 <= -0.5) {
		tmp = -(-1.0 * t_1);
	} else if (t_6 <= 2e+180) {
		tmp = t_5;
	} else if (t_6 <= 2e+305) {
		tmp = -(-t_4);
	} else {
		tmp = t_5;
	}
	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 = (-i - (t_4 / y)) * -y
	t_6 = (((((x * math.log(y)) + t_1) + t_3) + t_4) + ((b - 0.5) * math.log(c))) + (y * i)
	tmp = 0
	if t_6 <= -2e+300:
		tmp = (-i - (t_3 / y)) * -y
	elif t_6 <= -0.5:
		tmp = -(-1.0 * t_1)
	elif t_6 <= 2e+180:
		tmp = t_5
	elif t_6 <= 2e+305:
		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 = Float64(Float64(Float64(-i) - Float64(t_4 / y)) * Float64(-y))
	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 <= -2e+300)
		tmp = Float64(Float64(Float64(-i) - Float64(t_3 / y)) * Float64(-y));
	elseif (t_6 <= -0.5)
		tmp = Float64(-Float64(-1.0 * t_1));
	elseif (t_6 <= 2e+180)
		tmp = t_5;
	elseif (t_6 <= 2e+305)
		tmp = Float64(-Float64(-t_4));
	else
		tmp = t_5;
	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 = (-i - (t_4 / y)) * -y;
	t_6 = (((((x * log(y)) + t_1) + t_3) + t_4) + ((b - 0.5) * log(c))) + (y * i);
	tmp = 0.0;
	if (t_6 <= -2e+300)
		tmp = (-i - (t_3 / y)) * -y;
	elseif (t_6 <= -0.5)
		tmp = -(-1.0 * t_1);
	elseif (t_6 <= 2e+180)
		tmp = t_5;
	elseif (t_6 <= 2e+305)
		tmp = -(-t_4);
	else
		tmp = t_5;
	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[((-i) - N[(t$95$4 / y), $MachinePrecision]), $MachinePrecision] * (-y)), $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, -2e+300], N[(N[((-i) - N[(t$95$3 / y), $MachinePrecision]), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[t$95$6, -0.5], (-N[(-1.0 * t$95$1), $MachinePrecision]), If[LessEqual[t$95$6, 2e+180], t$95$5, If[LessEqual[t$95$6, 2e+305], (-(-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)) < -2.0000000000000001e300

   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 68.9%

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

   5. Taylor expanded in t around inf

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

      1. lower-/.f64 32.7%

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

   7. Applied rewrites 32.7%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

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

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

      6. lower-*.f64 N/A

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

   9. Applied rewrites 32.7%

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

   if -2.0000000000000001e300 < (+.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)) < -0.5

   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 68.9%

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

   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 16.4%

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

   7. Applied rewrites 16.4%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 16.4%

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

      4. lift-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lift-neg.f64 16.4%

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

   9. Applied rewrites 16.4%

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

   10. Taylor expanded in z around inf

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

       1. lower-*.f64 16.0%

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

   12. Applied rewrites 16.0%

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

   if -0.5 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < 2e180 or 1.9999999999999999e305 < (+.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 68.9%

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

   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 32.3%

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

   7. Applied rewrites 32.3%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

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

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

      6. lower-*.f64 N/A

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

   9. Applied rewrites 32.3%

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

   if 2e180 < (+.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)) < 1.9999999999999999e305

   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 68.9%

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

   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 16.4%

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

   7. Applied rewrites 16.4%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 16.4%

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

      4. lift-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lift-neg.f64 16.4%

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

   9. Applied rewrites 16.4%

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

Alternative 11: 55.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{min}\left(\mathsf{min}\left(z, t\right), a\right)\\ t_2 := \mathsf{max}\left(\mathsf{min}\left(z, t\right), a\right)\\ t_3 := \mathsf{max}\left(\mathsf{max}\left(z, t\right), t\_2\right)\\ t_4 := \left(\left(-i\right) - \frac{t\_3}{y}\right) \cdot \left(-y\right)\\ t_5 := \left(\left(\left(\left(x \cdot \log y + t\_1\right) + \mathsf{min}\left(\mathsf{max}\left(z, t\right), t\_2\right)\right) + t\_3\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{if}\;t\_5 \leq -2 \cdot 10^{+300}:\\ \;\;\;\;i \cdot y\\ \mathbf{elif}\;t\_5 \leq -0.5:\\ \;\;\;\;--1 \cdot t\_1\\ \mathbf{elif}\;t\_5 \leq 2 \cdot 10^{+180}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_5 \leq 2 \cdot 10^{+305}:\\ \;\;\;\;-\left(-t\_3\right)\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \]

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 (fmax (fmax z t) t_2))
        (t_4 (* (- (- i) (/ t_3 y)) (- y)))
        (t_5
         (+
          (+
           (+ (+ (+ (* x (log y)) t_1) (fmin (fmax z t) t_2)) t_3)
           (* (- b 0.5) (log c)))
          (* y i))))
   (if (<= t_5 -2e+300)
     (* i y)
     (if (<= t_5 -0.5)
       (- (* -1.0 t_1))
       (if (<= t_5 2e+180) t_4 (if (<= t_5 2e+305) (- (- t_3)) 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 = fmax(fmax(z, t), t_2);
	double t_4 = (-i - (t_3 / y)) * -y;
	double t_5 = (((((x * log(y)) + t_1) + fmin(fmax(z, t), t_2)) + t_3) + ((b - 0.5) * log(c))) + (y * i);
	double tmp;
	if (t_5 <= -2e+300) {
		tmp = i * y;
	} else if (t_5 <= -0.5) {
		tmp = -(-1.0 * t_1);
	} else if (t_5 <= 2e+180) {
		tmp = t_4;
	} else if (t_5 <= 2e+305) {
		tmp = -(-t_3);
	} else {
		tmp = t_4;
	}
	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) :: t_4
    real(8) :: t_5
    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)
    t_4 = (-i - (t_3 / y)) * -y
    t_5 = (((((x * log(y)) + t_1) + fmin(fmax(z, t), t_2)) + t_3) + ((b - 0.5d0) * log(c))) + (y * i)
    if (t_5 <= (-2d+300)) then
        tmp = i * y
    else if (t_5 <= (-0.5d0)) then
        tmp = -((-1.0d0) * t_1)
    else if (t_5 <= 2d+180) then
        tmp = t_4
    else if (t_5 <= 2d+305) then
        tmp = -(-t_3)
    else
        tmp = t_4
    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 t_4 = (-i - (t_3 / y)) * -y;
	double t_5 = (((((x * Math.log(y)) + t_1) + fmin(fmax(z, t), t_2)) + t_3) + ((b - 0.5) * Math.log(c))) + (y * i);
	double tmp;
	if (t_5 <= -2e+300) {
		tmp = i * y;
	} else if (t_5 <= -0.5) {
		tmp = -(-1.0 * t_1);
	} else if (t_5 <= 2e+180) {
		tmp = t_4;
	} else if (t_5 <= 2e+305) {
		tmp = -(-t_3);
	} 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 = fmax(fmax(z, t), t_2)
	t_4 = (-i - (t_3 / y)) * -y
	t_5 = (((((x * math.log(y)) + t_1) + fmin(fmax(z, t), t_2)) + t_3) + ((b - 0.5) * math.log(c))) + (y * i)
	tmp = 0
	if t_5 <= -2e+300:
		tmp = i * y
	elif t_5 <= -0.5:
		tmp = -(-1.0 * t_1)
	elif t_5 <= 2e+180:
		tmp = t_4
	elif t_5 <= 2e+305:
		tmp = -(-t_3)
	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 = fmax(fmax(z, t), t_2)
	t_4 = Float64(Float64(Float64(-i) - Float64(t_3 / y)) * Float64(-y))
	t_5 = 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))
	tmp = 0.0
	if (t_5 <= -2e+300)
		tmp = Float64(i * y);
	elseif (t_5 <= -0.5)
		tmp = Float64(-Float64(-1.0 * t_1));
	elseif (t_5 <= 2e+180)
		tmp = t_4;
	elseif (t_5 <= 2e+305)
		tmp = Float64(-Float64(-t_3));
	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 = max(max(z, t), t_2);
	t_4 = (-i - (t_3 / y)) * -y;
	t_5 = (((((x * log(y)) + t_1) + min(max(z, t), t_2)) + t_3) + ((b - 0.5) * log(c))) + (y * i);
	tmp = 0.0;
	if (t_5 <= -2e+300)
		tmp = i * y;
	elseif (t_5 <= -0.5)
		tmp = -(-1.0 * t_1);
	elseif (t_5 <= 2e+180)
		tmp = t_4;
	elseif (t_5 <= 2e+305)
		tmp = -(-t_3);
	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[Max[N[Max[z, t], $MachinePrecision], t$95$2], $MachinePrecision]}, Block[{t$95$4 = N[(N[((-i) - N[(t$95$3 / y), $MachinePrecision]), $MachinePrecision] * (-y)), $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$2], $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$5, -2e+300], N[(i * y), $MachinePrecision], If[LessEqual[t$95$5, -0.5], (-N[(-1.0 * t$95$1), $MachinePrecision]), If[LessEqual[t$95$5, 2e+180], t$95$4, If[LessEqual[t$95$5, 2e+305], (-(-t$95$3)), t$95$4]]]]]]]]]

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)) < -2.0000000000000001e300

   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. lift-+.f64 N/A

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

      3. associate-+l+ N/A

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

      4. lift-fma.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. +-commutative N/A

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

      7. associate-+l+ N/A

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

      8. lift-fma.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-+l+ N/A

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

      11. lift-*.f64 N/A

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

      12. lift-fma.f64 N/A

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

      13. lift-+.f64 N/A

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

      14. associate-+r+ N/A

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

      15. lift-*.f64 N/A

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

      16. lift-+.f64 N/A

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

      17. lower-fma.f64 99.8%

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

   5. Applied rewrites 99.8%

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

   6. Taylor expanded in y around inf

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

      1. lower-*.f64 24.1%

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

   8. Applied rewrites 24.1%

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

   if -2.0000000000000001e300 < (+.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)) < -0.5

   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 68.9%

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

   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 16.4%

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

   7. Applied rewrites 16.4%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 16.4%

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

      4. lift-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lift-neg.f64 16.4%

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

   9. Applied rewrites 16.4%

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

   10. Taylor expanded in z around inf

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

       1. lower-*.f64 16.0%

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

   12. Applied rewrites 16.0%

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

   if -0.5 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < 2e180 or 1.9999999999999999e305 < (+.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 68.9%

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

   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 32.3%

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

   7. Applied rewrites 32.3%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

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

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

      6. lower-*.f64 N/A

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

   9. Applied rewrites 32.3%

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

   if 2e180 < (+.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)) < 1.9999999999999999e305

   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 68.9%

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

   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 16.4%

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

   7. Applied rewrites 16.4%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 16.4%

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

      4. lift-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lift-neg.f64 16.4%

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

   9. Applied rewrites 16.4%

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

Alternative 12: 54.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{min}\left(\mathsf{min}\left(z, t\right), a\right)\\ t_2 := \mathsf{max}\left(\mathsf{min}\left(z, t\right), a\right)\\ t_3 := \mathsf{max}\left(\mathsf{max}\left(z, t\right), t\_2\right)\\ t_4 := \left(\left(\left(\left(x \cdot \log y + t\_1\right) + \mathsf{min}\left(\mathsf{max}\left(z, t\right), t\_2\right)\right) + t\_3\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{if}\;t\_4 \leq -2 \cdot 10^{+300}:\\ \;\;\;\;i \cdot y\\ \mathbf{elif}\;t\_4 \leq -0.5:\\ \;\;\;\;--1 \cdot t\_1\\ \mathbf{elif}\;t\_4 \leq 2 \cdot 10^{+305}:\\ \;\;\;\;-\left(-t\_3\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot y\\ \end{array} \]

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))
        (t_4
         (+
          (+
           (+ (+ (+ (* x (log y)) t_1) (fmin (fmax z t) t_2)) t_3)
           (* (- b 0.5) (log c)))
          (* y i))))
   (if (<= t_4 -2e+300)
     (* i y)
     (if (<= t_4 -0.5)
       (- (* -1.0 t_1))
       (if (<= t_4 2e+305) (- (- t_3)) (* i 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 = fmax(fmax(z, t), t_2);
	double t_4 = (((((x * log(y)) + t_1) + fmin(fmax(z, t), t_2)) + t_3) + ((b - 0.5) * log(c))) + (y * i);
	double tmp;
	if (t_4 <= -2e+300) {
		tmp = i * y;
	} else if (t_4 <= -0.5) {
		tmp = -(-1.0 * t_1);
	} else if (t_4 <= 2e+305) {
		tmp = -(-t_3);
	} else {
		tmp = i * y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    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)
    t_4 = (((((x * log(y)) + t_1) + fmin(fmax(z, t), t_2)) + t_3) + ((b - 0.5d0) * log(c))) + (y * i)
    if (t_4 <= (-2d+300)) then
        tmp = i * y
    else if (t_4 <= (-0.5d0)) then
        tmp = -((-1.0d0) * t_1)
    else if (t_4 <= 2d+305) then
        tmp = -(-t_3)
    else
        tmp = i * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fmin(fmin(z, t), a);
	double t_2 = fmax(fmin(z, t), a);
	double t_3 = fmax(fmax(z, t), t_2);
	double t_4 = (((((x * Math.log(y)) + t_1) + fmin(fmax(z, t), t_2)) + t_3) + ((b - 0.5) * Math.log(c))) + (y * i);
	double tmp;
	if (t_4 <= -2e+300) {
		tmp = i * y;
	} else if (t_4 <= -0.5) {
		tmp = -(-1.0 * t_1);
	} else if (t_4 <= 2e+305) {
		tmp = -(-t_3);
	} else {
		tmp = i * y;
	}
	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)
	t_4 = (((((x * math.log(y)) + t_1) + fmin(fmax(z, t), t_2)) + t_3) + ((b - 0.5) * math.log(c))) + (y * i)
	tmp = 0
	if t_4 <= -2e+300:
		tmp = i * y
	elif t_4 <= -0.5:
		tmp = -(-1.0 * t_1)
	elif t_4 <= 2e+305:
		tmp = -(-t_3)
	else:
		tmp = i * 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 = fmax(fmax(z, t), t_2)
	t_4 = 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))
	tmp = 0.0
	if (t_4 <= -2e+300)
		tmp = Float64(i * y);
	elseif (t_4 <= -0.5)
		tmp = Float64(-Float64(-1.0 * t_1));
	elseif (t_4 <= 2e+305)
		tmp = Float64(-Float64(-t_3));
	else
		tmp = Float64(i * y);
	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);
	t_4 = (((((x * log(y)) + t_1) + min(max(z, t), t_2)) + t_3) + ((b - 0.5) * log(c))) + (y * i);
	tmp = 0.0;
	if (t_4 <= -2e+300)
		tmp = i * y;
	elseif (t_4 <= -0.5)
		tmp = -(-1.0 * t_1);
	elseif (t_4 <= 2e+305)
		tmp = -(-t_3);
	else
		tmp = i * y;
	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]}, Block[{t$95$4 = 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]}, If[LessEqual[t$95$4, -2e+300], N[(i * y), $MachinePrecision], If[LessEqual[t$95$4, -0.5], (-N[(-1.0 * t$95$1), $MachinePrecision]), If[LessEqual[t$95$4, 2e+305], (-(-t$95$3)), N[(i * y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < -2.0000000000000001e300 or 1.9999999999999999e305 < (+.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. lift-+.f64 N/A

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

      3. associate-+l+ N/A

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

      4. lift-fma.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. +-commutative N/A

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

      7. associate-+l+ N/A

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

      8. lift-fma.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-+l+ N/A

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

      11. lift-*.f64 N/A

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

      12. lift-fma.f64 N/A

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

      13. lift-+.f64 N/A

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

      14. associate-+r+ N/A

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

      15. lift-*.f64 N/A

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

      16. lift-+.f64 N/A

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

      17. lower-fma.f64 99.8%

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

   5. Applied rewrites 99.8%

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

   6. Taylor expanded in y around inf

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

      1. lower-*.f64 24.1%

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

   8. Applied rewrites 24.1%

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

   if -2.0000000000000001e300 < (+.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)) < -0.5

   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 68.9%

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

   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 16.4%

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

   7. Applied rewrites 16.4%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 16.4%

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

      4. lift-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lift-neg.f64 16.4%

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

   9. Applied rewrites 16.4%

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

   10. Taylor expanded in z around inf

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

       1. lower-*.f64 16.0%

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

   12. Applied rewrites 16.0%

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

   if -0.5 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < 1.9999999999999999e305

   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 68.9%

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

   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 16.4%

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

   7. Applied rewrites 16.4%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 16.4%

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

      4. lift-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lift-neg.f64 16.4%

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

   9. Applied rewrites 16.4%

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

Alternative 13: 35.9% accurate, 2.0× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{max}\left(t, \mathsf{max}\left(z, a\right)\right)\\ \mathbf{if}\;t\_1 \leq 1.5 \cdot 10^{+130}:\\ \;\;\;\;i \cdot y\\ \mathbf{else}:\\ \;\;\;\;-\left(-t\_1\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fmax t (fmax z a)))) (if (<= t_1 1.5e+130) (* i y) (- (- t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fmax(t, fmax(z, a));
	double tmp;
	if (t_1 <= 1.5e+130) {
		tmp = i * y;
	} else {
		tmp = -(-t_1);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = fmax(t, fmax(z, a))
    if (t_1 <= 1.5d+130) then
        tmp = i * y
    else
        tmp = -(-t_1)
    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 = fmax(t, fmax(z, a));
	double tmp;
	if (t_1 <= 1.5e+130) {
		tmp = i * y;
	} else {
		tmp = -(-t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = fmax(t, fmax(z, a))
	tmp = 0
	if t_1 <= 1.5e+130:
		tmp = i * y
	else:
		tmp = -(-t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fmax(t, fmax(z, a))
	tmp = 0.0
	if (t_1 <= 1.5e+130)
		tmp = Float64(i * y);
	else
		tmp = Float64(-Float64(-t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = max(t, max(z, a));
	tmp = 0.0;
	if (t_1 <= 1.5e+130)
		tmp = i * y;
	else
		tmp = -(-t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[Max[t, N[Max[z, a], $MachinePrecision]], $MachinePrecision]}, If[LessEqual[t$95$1, 1.5e+130], N[(i * y), $MachinePrecision], (-(-t$95$1))]]

Derivation

1. Split input into 2 regimes

2. if a < 1.5e130

   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. lift-+.f64 N/A

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

      3. associate-+l+ N/A

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

      4. lift-fma.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. +-commutative N/A

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

      7. associate-+l+ N/A

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

      8. lift-fma.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-+l+ N/A

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

      11. lift-*.f64 N/A

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

      12. lift-fma.f64 N/A

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

      13. lift-+.f64 N/A

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

      14. associate-+r+ N/A

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

      15. lift-*.f64 N/A

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

      16. lift-+.f64 N/A

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

      17. lower-fma.f64 99.8%

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

   5. Applied rewrites 99.8%

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

   6. Taylor expanded in y around inf

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

      1. lower-*.f64 24.1%

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

   8. Applied rewrites 24.1%

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

   if 1.5e130 < a

   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 68.9%

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

   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 16.4%

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

   7. Applied rewrites 16.4%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 16.4%

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

      4. lift-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lift-neg.f64 16.4%

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

   9. Applied rewrites 16.4%

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

Alternative 14: 22.9% 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 68.9%

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

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 16.4%

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

7. Applied rewrites 16.4%

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

   1. lift-*.f64 N/A

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

   2. mul-1-neg N/A

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

   3. lower-neg.f64 16.4%

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

   4. lift-*.f64 N/A

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

   5. mul-1-neg N/A

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

   6. lift-neg.f64 16.4%

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

9. Applied rewrites 16.4%

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

Reproduce

herbie shell --seed 2025187 
(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)))