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

Percentage Accurate: 99.8% → 99.8%

Time: 7.6s

Alternatives: 18

Speedup: 1.1×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.1× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (fma (- b 0.5) (log c) (+ (fma i y (+ a (fma (log y) x z))) t)))

C

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

Julia

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

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision] + N[(N[(i * y + N[(a + N[(N[Log[y], $MachinePrecision] * x + z), $MachinePrecision]), $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. lift-+.f64 N/A

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

   3. +-commutative N/A

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

   4. associate-+l+ N/A

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

   5. lift-*.f64 N/A

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

   6. +-commutative N/A

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

   7. lower-fma.f64 N/A

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

   8. lift-+.f64 N/A

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

   9. +-commutative N/A

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

   10. lift-+.f64 N/A

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

   11. associate-+r+ N/A

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

   12. associate-+r+ N/A

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

   13. lower-+.f64 N/A

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

3. Applied rewrites 99.8%

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

Alternative 2: 99.8% accurate, 1.1× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (+ (fma i y (+ (fma (log c) (- b 0.5) (fma (log y) x t)) z)) a))

C

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

Julia

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

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(i * y + N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + N[(N[Log[y], $MachinePrecision] * x + t), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]

Derivation

1. Initial program 99.8%

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

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

   4. +-commutative N/A

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

   5. lift-+.f64 N/A

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

   6. associate-+r+ N/A

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

   7. associate-+r+ N/A

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

   8. lower-+.f64 N/A

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

3. Applied rewrites 99.8%

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

Alternative 3: 98.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \leq -1 \cdot 10^{+21}:\\ \;\;\;\;t + \left(z + \mathsf{fma}\left(i, y, \mathsf{fma}\left(x, \log y, \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, \mathsf{fma}\left(x, \log y, \mathsf{fma}\left(\log c, b - 0.5, t\right)\right)\right) + a\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<=
      (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i))
      -1e+21)
   (+ t (+ z (fma i y (fma x (log y) (* (log c) (- b 0.5))))))
   (+ (fma y i (fma x (log y) (fma (log c) (- b 0.5) t))) a)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i)) <= -1e+21) {
		tmp = t + (z + fma(i, y, fma(x, log(y), (log(c) * (b - 0.5)))));
	} else {
		tmp = fma(y, i, fma(x, log(y), fma(log(c), (b - 0.5), t))) + a;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + z) + t) + a) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i)) <= -1e+21)
		tmp = Float64(t + Float64(z + fma(i, y, fma(x, log(y), Float64(log(c) * Float64(b - 0.5))))));
	else
		tmp = Float64(fma(y, i, fma(x, log(y), fma(log(c), Float64(b - 0.5), t))) + a);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], -1e+21], N[(t + N[(z + N[(i * y + N[(x * N[Log[y], $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i + N[(x * N[Log[y], $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < -1e21

   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 77.6

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

   4. Applied rewrites 77.6%

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

   if -1e21 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i))

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-log.f64 N/A

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

      8. lower--.f64 77.1

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

   4. Applied rewrites 77.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 77.1

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

   6. Applied rewrites 77.1%

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

Alternative 4: 93.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\log c, b - 0.5, t\right)\\ \mathbf{if}\;z \leq -3.9 \cdot 10^{+96}:\\ \;\;\;\;\mathsf{fma}\left(i, y, t\_1 + z\right) + a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, \mathsf{fma}\left(x, \log y, t\_1\right)\right) + a\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fma (log c) (- b 0.5) t)))
   (if (<= z -3.9e+96)
     (+ (fma i y (+ t_1 z)) a)
     (+ (fma y i (fma x (log y) t_1)) a))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fma(log(c), (b - 0.5), t);
	double tmp;
	if (z <= -3.9e+96) {
		tmp = fma(i, y, (t_1 + z)) + a;
	} else {
		tmp = fma(y, i, fma(x, log(y), t_1)) + a;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	t_1 = fma(log(c), Float64(b - 0.5), t)
	tmp = 0.0
	if (z <= -3.9e+96)
		tmp = Float64(fma(i, y, Float64(t_1 + z)) + a);
	else
		tmp = Float64(fma(y, i, fma(x, log(y), t_1)) + a);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + t), $MachinePrecision]}, If[LessEqual[z, -3.9e+96], N[(N[(i * y + N[(t$95$1 + z), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision], N[(N[(y * i + N[(x * N[Log[y], $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.9e96

   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

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

      4. +-commutative N/A

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

      5. lift-+.f64 N/A

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

      6. associate-+r+ N/A

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

      7. associate-+r+ N/A

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

      8. lower-+.f64 N/A

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 84.2%

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

   if -3.9e96 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-log.f64 N/A

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

      8. lower--.f64 77.1

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

   4. Applied rewrites 77.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 77.1

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

   6. Applied rewrites 77.1%

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

Alternative 5: 93.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+90}:\\ \;\;\;\;\mathsf{fma}\left(i, y, \mathsf{fma}\left(\log c, b - 0.5, t\right) + z\right) + a\\ \mathbf{else}:\\ \;\;\;\;a + \mathsf{fma}\left(i, y, \mathsf{fma}\left(x, \log y, \log c \cdot \left(b - 0.5\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -6e+90)
   (+ (fma i y (+ (fma (log c) (- b 0.5) t) z)) a)
   (+ a (fma i y (fma x (log y) (* (log c) (- b 0.5)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -6e+90) {
		tmp = fma(i, y, (fma(log(c), (b - 0.5), t) + z)) + a;
	} else {
		tmp = a + fma(i, y, fma(x, log(y), (log(c) * (b - 0.5))));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -6e+90)
		tmp = Float64(fma(i, y, Float64(fma(log(c), Float64(b - 0.5), t) + z)) + a);
	else
		tmp = Float64(a + fma(i, y, fma(x, log(y), Float64(log(c) * Float64(b - 0.5)))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -6e+90], N[(N[(i * y + N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + t), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision], N[(a + N[(i * y + N[(x * N[Log[y], $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.99999999999999957e90

   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

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

      4. +-commutative N/A

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

      5. lift-+.f64 N/A

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

      6. associate-+r+ N/A

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

      7. associate-+r+ N/A

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

      8. lower-+.f64 N/A

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 84.2%

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

   if -5.99999999999999957e90 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-log.f64 N/A

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

      8. lower--.f64 77.1

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

   4. Applied rewrites 77.1%

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

   5. Taylor expanded in t around 0

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

      1. lower-+.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-log.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-log.f64 N/A

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

      7. lower--.f64 76.6

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

   7. Applied rewrites 76.6%

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

Alternative 6: 90.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := \left(\mathsf{fma}\left(\log c, b - 0.5, \log y \cdot x\right) + t\right) + a\\ \mathbf{if}\;x \leq -2.5 \cdot 10^{+172}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+171}:\\ \;\;\;\;\mathsf{fma}\left(i, y, \mathsf{fma}\left(\log c, b - 0.5, t\right) + z\right) + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (+ (fma (log c) (- b 0.5) (* (log y) x)) t) a)))
   (if (<= x -2.5e+172)
     t_1
     (if (<= x 3.3e+171)
       (+ (fma i y (+ (fma (log c) (- b 0.5) t) z)) a)
       t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (fma(log(c), (b - 0.5), (log(y) * x)) + t) + a;
	double tmp;
	if (x <= -2.5e+172) {
		tmp = t_1;
	} else if (x <= 3.3e+171) {
		tmp = fma(i, y, (fma(log(c), (b - 0.5), t) + z)) + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(fma(log(c), Float64(b - 0.5), Float64(log(y) * x)) + t) + a)
	tmp = 0.0
	if (x <= -2.5e+172)
		tmp = t_1;
	elseif (x <= 3.3e+171)
		tmp = Float64(fma(i, y, Float64(fma(log(c), Float64(b - 0.5), t) + z)) + a);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision]}, If[LessEqual[x, -2.5e+172], t$95$1, If[LessEqual[x, 3.3e+171], N[(N[(i * y + N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + t), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.5e172 or 3.29999999999999991e171 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-log.f64 N/A

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

      8. lower--.f64 77.1

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

   4. Applied rewrites 77.1%

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

   5. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-log.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-log.f64 N/A

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

      10. lower--.f64 60.8

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

   7. Applied rewrites 60.8%

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

   8. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-log.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-log.f64 N/A

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

      5. lower--.f64 55.0

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

   10. Applied rewrites 55.0%

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

       1. lift-+.f64 N/A

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

       2. +-commutative N/A

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

       3. lower-+.f64 55.0

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

   12. Applied rewrites 55.0%

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

   if -2.5e172 < x < 3.29999999999999991e171

   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

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

      4. +-commutative N/A

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

      5. lift-+.f64 N/A

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

      6. associate-+r+ N/A

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

      7. associate-+r+ N/A

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

      8. lower-+.f64 N/A

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 84.2%

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

Alternative 7: 88.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := a + \left(t + \mathsf{fma}\left(x, \log y, -0.5 \cdot \log c\right)\right)\\ \mathbf{if}\;x \leq -2.5 \cdot 10^{+172}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+225}:\\ \;\;\;\;\mathsf{fma}\left(i, y, \mathsf{fma}\left(\log c, b - 0.5, t\right) + z\right) + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (+ t (fma x (log y) (* -0.5 (log c)))))))
   (if (<= x -2.5e+172)
     t_1
     (if (<= x 2.1e+225)
       (+ (fma i y (+ (fma (log c) (- b 0.5) t) z)) a)
       t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (t + fma(x, log(y), (-0.5 * log(c))));
	double tmp;
	if (x <= -2.5e+172) {
		tmp = t_1;
	} else if (x <= 2.1e+225) {
		tmp = fma(i, y, (fma(log(c), (b - 0.5), t) + z)) + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(t + fma(x, log(y), Float64(-0.5 * log(c)))))
	tmp = 0.0
	if (x <= -2.5e+172)
		tmp = t_1;
	elseif (x <= 2.1e+225)
		tmp = Float64(fma(i, y, Float64(fma(log(c), Float64(b - 0.5), t) + z)) + a);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(t + N[(x * N[Log[y], $MachinePrecision] + N[(-0.5 * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.5e+172], t$95$1, If[LessEqual[x, 2.1e+225], N[(N[(i * y + N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + t), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.5e172 or 2.1e225 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-log.f64 N/A

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

      8. lower--.f64 77.1

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

   4. Applied rewrites 77.1%

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

   5. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-log.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-log.f64 N/A

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

      10. lower--.f64 60.8

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

   7. Applied rewrites 60.8%

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

   8. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-log.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-log.f64 N/A

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

      5. lower--.f64 55.0

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

   10. Applied rewrites 55.0%

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

   11. Taylor expanded in b around 0

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

       1. lower-*.f64 N/A

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

       2. lower-log.f64 39.4

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

   13. Applied rewrites 39.4%

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

   if -2.5e172 < x < 2.1e225

   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

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

      4. +-commutative N/A

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

      5. lift-+.f64 N/A

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

      6. associate-+r+ N/A

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

      7. associate-+r+ N/A

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

      8. lower-+.f64 N/A

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 84.2%

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

Alternative 8: 87.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -1.05 \cdot 10^{+281}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+225}:\\ \;\;\;\;\mathsf{fma}\left(i, y, \mathsf{fma}\left(\log c, b - 0.5, t\right) + z\right) + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -1.05e+281)
     t_1
     (if (<= x 2.6e+225)
       (+ (fma i y (+ (fma (log c) (- b 0.5) t) z)) a)
       t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * log(y);
	double tmp;
	if (x <= -1.05e+281) {
		tmp = t_1;
	} else if (x <= 2.6e+225) {
		tmp = fma(i, y, (fma(log(c), (b - 0.5), t) + z)) + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -1.05e+281)
		tmp = t_1;
	elseif (x <= 2.6e+225)
		tmp = Float64(fma(i, y, Float64(fma(log(c), Float64(b - 0.5), t) + z)) + a);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.05e+281], t$95$1, If[LessEqual[x, 2.6e+225], N[(N[(i * y + N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + t), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.05000000000000003e281 or 2.60000000000000004e225 < x

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. lift-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lift-+.f64 N/A

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

      9. +-commutative N/A

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

      10. lift-+.f64 N/A

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

      11. associate-+r+ N/A

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

      12. associate-+r+ N/A

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

      13. lower-+.f64 N/A

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-log.f64 16.9

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

   6. Applied rewrites 16.9%

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

   if -1.05000000000000003e281 < x < 2.60000000000000004e225

   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

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

      4. +-commutative N/A

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

      5. lift-+.f64 N/A

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

      6. associate-+r+ N/A

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

      7. associate-+r+ N/A

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

      8. lower-+.f64 N/A

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 84.2%

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

Alternative 9: 77.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+87}:\\ \;\;\;\;\mathsf{fma}\left(-0.5, \log c, \mathsf{fma}\left(i, y, a + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \mathsf{fma}\left(i, y, \log c \cdot \left(b - 0.5\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -3.5e+87)
   (fma -0.5 (log c) (+ (fma i y (+ a z)) t))
   (+ a (+ t (fma i y (* (log c) (- b 0.5)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -3.5e+87) {
		tmp = fma(-0.5, log(c), (fma(i, y, (a + z)) + t));
	} else {
		tmp = a + (t + fma(i, y, (log(c) * (b - 0.5))));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -3.5e+87)
		tmp = fma(-0.5, log(c), Float64(fma(i, y, Float64(a + z)) + t));
	else
		tmp = Float64(a + Float64(t + fma(i, y, Float64(log(c) * Float64(b - 0.5)))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -3.5e+87], N[(-0.5 * N[Log[c], $MachinePrecision] + N[(N[(i * y + N[(a + z), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision], N[(a + N[(t + N[(i * y + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.49999999999999986e87

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. lift-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lift-+.f64 N/A

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

      9. +-commutative N/A

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

      10. lift-+.f64 N/A

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

      11. associate-+r+ N/A

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

      12. associate-+r+ N/A

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

      13. lower-+.f64 N/A

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 84.2%

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

   7. Taylor expanded in b around 0

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

   9. Applied rewrites 68.2%

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

   if -3.49999999999999986e87 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-log.f64 N/A

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

      8. lower--.f64 77.1

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

   4. Applied rewrites 77.1%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower-log.f64 N/A

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

      3. lower--.f64 61.8

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

   7. Applied rewrites 61.8%

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

Alternative 10: 74.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := a + \left(t + \log c \cdot \left(b - 0.5\right)\right)\\ t_2 := \left(b - 0.5\right) \cdot \log c\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+214}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+185}:\\ \;\;\;\;\mathsf{fma}\left(-0.5, \log c, \mathsf{fma}\left(i, y, a + z\right) + t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (+ t (* (log c) (- b 0.5))))) (t_2 (* (- b 0.5) (log c))))
   (if (<= t_2 -5e+214)
     t_1
     (if (<= t_2 2e+185) (fma -0.5 (log c) (+ (fma i y (+ a z)) t)) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (t + (log(c) * (b - 0.5)));
	double t_2 = (b - 0.5) * log(c);
	double tmp;
	if (t_2 <= -5e+214) {
		tmp = t_1;
	} else if (t_2 <= 2e+185) {
		tmp = fma(-0.5, log(c), (fma(i, y, (a + z)) + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(t + Float64(log(c) * Float64(b - 0.5))))
	t_2 = Float64(Float64(b - 0.5) * log(c))
	tmp = 0.0
	if (t_2 <= -5e+214)
		tmp = t_1;
	elseif (t_2 <= 2e+185)
		tmp = fma(-0.5, log(c), Float64(fma(i, y, Float64(a + z)) + t));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(t + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+214], t$95$1, If[LessEqual[t$95$2, 2e+185], N[(-0.5 * N[Log[c], $MachinePrecision] + N[(N[(i * y + N[(a + z), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c)) < -4.99999999999999953e214 or 2e185 < (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-log.f64 N/A

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

      8. lower--.f64 77.1

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

   4. Applied rewrites 77.1%

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

   5. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-log.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-log.f64 N/A

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

      10. lower--.f64 60.8

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

   7. Applied rewrites 60.8%

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

   8. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-log.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-log.f64 N/A

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

      5. lower--.f64 55.0

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

   10. Applied rewrites 55.0%

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

   11. Taylor expanded in x around 0

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

       1. lower-*.f64 N/A

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

       2. lower-log.f64 N/A

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

       3. lower--.f64 39.8

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

   13. Applied rewrites 39.8%

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

   if -4.99999999999999953e214 < (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c)) < 2e185

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. lift-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lift-+.f64 N/A

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

      9. +-commutative N/A

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

      10. lift-+.f64 N/A

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

      11. associate-+r+ N/A

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

      12. associate-+r+ N/A

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

      13. lower-+.f64 N/A

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 84.2%

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

   7. Taylor expanded in b around 0

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

   9. Applied rewrites 68.2%

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

Alternative 11: 65.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+307}:\\ \;\;\;\;i \cdot y\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{+21}:\\ \;\;\;\;-1 \cdot \left(-1 \cdot z\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+305}:\\ \;\;\;\;a + \left(t + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(1 + \frac{y \cdot i}{a}\right) \cdot a\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (+
          (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c)))
          (* y i))))
   (if (<= t_1 -5e+307)
     (* i y)
     (if (<= t_1 -1e+21)
       (* -1.0 (* -1.0 z))
       (if (<= t_1 5e+305)
         (+ a (+ t (* (log c) (- b 0.5))))
         (* (+ 1.0 (/ (* y i) a)) a))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
	double tmp;
	if (t_1 <= -5e+307) {
		tmp = i * y;
	} else if (t_1 <= -1e+21) {
		tmp = -1.0 * (-1.0 * z);
	} else if (t_1 <= 5e+305) {
		tmp = a + (t + (log(c) * (b - 0.5)));
	} else {
		tmp = (1.0 + ((y * i) / a)) * a;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (((((x * log(y)) + z) + t) + a) + ((b - 0.5d0) * log(c))) + (y * i)
    if (t_1 <= (-5d+307)) then
        tmp = i * y
    else if (t_1 <= (-1d+21)) then
        tmp = (-1.0d0) * ((-1.0d0) * z)
    else if (t_1 <= 5d+305) then
        tmp = a + (t + (log(c) * (b - 0.5d0)))
    else
        tmp = (1.0d0 + ((y * i) / a)) * a
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (((((x * Math.log(y)) + z) + t) + a) + ((b - 0.5) * Math.log(c))) + (y * i);
	double tmp;
	if (t_1 <= -5e+307) {
		tmp = i * y;
	} else if (t_1 <= -1e+21) {
		tmp = -1.0 * (-1.0 * z);
	} else if (t_1 <= 5e+305) {
		tmp = a + (t + (Math.log(c) * (b - 0.5)));
	} else {
		tmp = (1.0 + ((y * i) / a)) * a;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	t_1 = (((((x * math.log(y)) + z) + t) + a) + ((b - 0.5) * math.log(c))) + (y * i)
	tmp = 0
	if t_1 <= -5e+307:
		tmp = i * y
	elif t_1 <= -1e+21:
		tmp = -1.0 * (-1.0 * z)
	elif t_1 <= 5e+305:
		tmp = a + (t + (math.log(c) * (b - 0.5)))
	else:
		tmp = (1.0 + ((y * i) / a)) * a
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + z) + t) + a) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i))
	tmp = 0.0
	if (t_1 <= -5e+307)
		tmp = Float64(i * y);
	elseif (t_1 <= -1e+21)
		tmp = Float64(-1.0 * Float64(-1.0 * z));
	elseif (t_1 <= 5e+305)
		tmp = Float64(a + Float64(t + Float64(log(c) * Float64(b - 0.5))));
	else
		tmp = Float64(Float64(1.0 + Float64(Float64(y * i) / a)) * a);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
	tmp = 0.0;
	if (t_1 <= -5e+307)
		tmp = i * y;
	elseif (t_1 <= -1e+21)
		tmp = -1.0 * (-1.0 * z);
	elseif (t_1 <= 5e+305)
		tmp = a + (t + (log(c) * (b - 0.5)));
	else
		tmp = (1.0 + ((y * i) / a)) * a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+307], N[(i * y), $MachinePrecision], If[LessEqual[t$95$1, -1e+21], N[(-1.0 * N[(-1.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+305], N[(a + N[(t + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 + N[(N[(y * i), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] * a), $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)) < -5e307

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. lift-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lift-+.f64 N/A

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

      9. +-commutative N/A

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

      10. lift-+.f64 N/A

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

      11. associate-+r+ N/A

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

      12. associate-+r+ N/A

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

      13. lower-+.f64 N/A

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in y around inf

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

      1. lower-*.f64 23.9

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

   6. Applied rewrites 23.9%

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

   if -5e307 < (+.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)) < -1e21

   1. Initial program 99.8%

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

   2. Taylor expanded in a around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

   4. Applied rewrites 78.9%

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

   5. Taylor expanded in z around inf

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

      1. lower-*.f64 23.1

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

   7. Applied rewrites 23.1%

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

   if -1e21 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < 5.00000000000000009e305

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-log.f64 N/A

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

      8. lower--.f64 77.1

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

   4. Applied rewrites 77.1%

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

   5. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-log.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-log.f64 N/A

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

      10. lower--.f64 60.8

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

   7. Applied rewrites 60.8%

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

   8. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-log.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-log.f64 N/A

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

      5. lower--.f64 55.0

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

   10. Applied rewrites 55.0%

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

   11. Taylor expanded in x around 0

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

       1. lower-*.f64 N/A

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

       2. lower-log.f64 N/A

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

       3. lower--.f64 39.8

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

   13. Applied rewrites 39.8%

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

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

   1. Initial program 99.8%

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

   2. Taylor expanded in a around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

   4. Applied rewrites 78.9%

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

   5. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 41.6

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

   7. Applied rewrites 41.6%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

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

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

   9. Applied rewrites 41.6%

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

Alternative 12: 65.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+307}:\\ \;\;\;\;i \cdot y\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{+21}:\\ \;\;\;\;-1 \cdot \left(-1 \cdot z\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+305}:\\ \;\;\;\;a + \left(t + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \left(a \cdot \left(-1 \cdot \left(y \cdot \frac{i}{a}\right) - 1\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (+
          (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c)))
          (* y i))))
   (if (<= t_1 -5e+307)
     (* i y)
     (if (<= t_1 -1e+21)
       (* -1.0 (* -1.0 z))
       (if (<= t_1 5e+305)
         (+ a (+ t (* (log c) (- b 0.5))))
         (* -1.0 (* a (- (* -1.0 (* y (/ i a))) 1.0))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
	double tmp;
	if (t_1 <= -5e+307) {
		tmp = i * y;
	} else if (t_1 <= -1e+21) {
		tmp = -1.0 * (-1.0 * z);
	} else if (t_1 <= 5e+305) {
		tmp = a + (t + (log(c) * (b - 0.5)));
	} else {
		tmp = -1.0 * (a * ((-1.0 * (y * (i / a))) - 1.0));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (((((x * log(y)) + z) + t) + a) + ((b - 0.5d0) * log(c))) + (y * i)
    if (t_1 <= (-5d+307)) then
        tmp = i * y
    else if (t_1 <= (-1d+21)) then
        tmp = (-1.0d0) * ((-1.0d0) * z)
    else if (t_1 <= 5d+305) then
        tmp = a + (t + (log(c) * (b - 0.5d0)))
    else
        tmp = (-1.0d0) * (a * (((-1.0d0) * (y * (i / a))) - 1.0d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (((((x * Math.log(y)) + z) + t) + a) + ((b - 0.5) * Math.log(c))) + (y * i);
	double tmp;
	if (t_1 <= -5e+307) {
		tmp = i * y;
	} else if (t_1 <= -1e+21) {
		tmp = -1.0 * (-1.0 * z);
	} else if (t_1 <= 5e+305) {
		tmp = a + (t + (Math.log(c) * (b - 0.5)));
	} else {
		tmp = -1.0 * (a * ((-1.0 * (y * (i / a))) - 1.0));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	t_1 = (((((x * math.log(y)) + z) + t) + a) + ((b - 0.5) * math.log(c))) + (y * i)
	tmp = 0
	if t_1 <= -5e+307:
		tmp = i * y
	elif t_1 <= -1e+21:
		tmp = -1.0 * (-1.0 * z)
	elif t_1 <= 5e+305:
		tmp = a + (t + (math.log(c) * (b - 0.5)))
	else:
		tmp = -1.0 * (a * ((-1.0 * (y * (i / a))) - 1.0))
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + z) + t) + a) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i))
	tmp = 0.0
	if (t_1 <= -5e+307)
		tmp = Float64(i * y);
	elseif (t_1 <= -1e+21)
		tmp = Float64(-1.0 * Float64(-1.0 * z));
	elseif (t_1 <= 5e+305)
		tmp = Float64(a + Float64(t + Float64(log(c) * Float64(b - 0.5))));
	else
		tmp = Float64(-1.0 * Float64(a * Float64(Float64(-1.0 * Float64(y * Float64(i / a))) - 1.0)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
	tmp = 0.0;
	if (t_1 <= -5e+307)
		tmp = i * y;
	elseif (t_1 <= -1e+21)
		tmp = -1.0 * (-1.0 * z);
	elseif (t_1 <= 5e+305)
		tmp = a + (t + (log(c) * (b - 0.5)));
	else
		tmp = -1.0 * (a * ((-1.0 * (y * (i / a))) - 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+307], N[(i * y), $MachinePrecision], If[LessEqual[t$95$1, -1e+21], N[(-1.0 * N[(-1.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+305], N[(a + N[(t + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-1.0 * N[(a * N[(N[(-1.0 * N[(y * N[(i / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < -5e307

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. lift-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lift-+.f64 N/A

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

      9. +-commutative N/A

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

      10. lift-+.f64 N/A

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

      11. associate-+r+ N/A

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

      12. associate-+r+ N/A

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

      13. lower-+.f64 N/A

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in y around inf

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

      1. lower-*.f64 23.9

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

   6. Applied rewrites 23.9%

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

   if -5e307 < (+.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)) < -1e21

   1. Initial program 99.8%

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

   2. Taylor expanded in a around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

   4. Applied rewrites 78.9%

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

   5. Taylor expanded in z around inf

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

      1. lower-*.f64 23.1

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

   7. Applied rewrites 23.1%

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

   if -1e21 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < 5.00000000000000009e305

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-log.f64 N/A

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

      8. lower--.f64 77.1

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

   4. Applied rewrites 77.1%

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

   5. Taylor expanded in i around inf

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

      1. lower-*.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-log.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-log.f64 N/A

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

      10. lower--.f64 60.8

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

   7. Applied rewrites 60.8%

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

   8. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-log.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-log.f64 N/A

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

      5. lower--.f64 55.0

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

   10. Applied rewrites 55.0%

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

   11. Taylor expanded in x around 0

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

       1. lower-*.f64 N/A

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

       2. lower-log.f64 N/A

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

       3. lower--.f64 39.8

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

   13. Applied rewrites 39.8%

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

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

   1. Initial program 99.8%

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

   2. Taylor expanded in a around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

   4. Applied rewrites 78.9%

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

   5. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 41.6

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

   7. Applied rewrites 41.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 41.3

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

   9. Applied rewrites 41.3%

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

Alternative 13: 59.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+307}:\\ \;\;\;\;i \cdot y\\ \mathbf{elif}\;t\_1 \leq 200:\\ \;\;\;\;-1 \cdot \left(-1 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(1 + \frac{y \cdot i}{a}\right) \cdot a\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (+
          (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c)))
          (* y i))))
   (if (<= t_1 -5e+307)
     (* i y)
     (if (<= t_1 200.0) (* -1.0 (* -1.0 z)) (* (+ 1.0 (/ (* y i) a)) a)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
	double tmp;
	if (t_1 <= -5e+307) {
		tmp = i * y;
	} else if (t_1 <= 200.0) {
		tmp = -1.0 * (-1.0 * z);
	} else {
		tmp = (1.0 + ((y * i) / a)) * a;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (((((x * log(y)) + z) + t) + a) + ((b - 0.5d0) * log(c))) + (y * i)
    if (t_1 <= (-5d+307)) then
        tmp = i * y
    else if (t_1 <= 200.0d0) then
        tmp = (-1.0d0) * ((-1.0d0) * z)
    else
        tmp = (1.0d0 + ((y * i) / a)) * a
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (((((x * Math.log(y)) + z) + t) + a) + ((b - 0.5) * Math.log(c))) + (y * i);
	double tmp;
	if (t_1 <= -5e+307) {
		tmp = i * y;
	} else if (t_1 <= 200.0) {
		tmp = -1.0 * (-1.0 * z);
	} else {
		tmp = (1.0 + ((y * i) / a)) * a;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	t_1 = (((((x * math.log(y)) + z) + t) + a) + ((b - 0.5) * math.log(c))) + (y * i)
	tmp = 0
	if t_1 <= -5e+307:
		tmp = i * y
	elif t_1 <= 200.0:
		tmp = -1.0 * (-1.0 * z)
	else:
		tmp = (1.0 + ((y * i) / a)) * a
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + z) + t) + a) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i))
	tmp = 0.0
	if (t_1 <= -5e+307)
		tmp = Float64(i * y);
	elseif (t_1 <= 200.0)
		tmp = Float64(-1.0 * Float64(-1.0 * z));
	else
		tmp = Float64(Float64(1.0 + Float64(Float64(y * i) / a)) * a);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
	tmp = 0.0;
	if (t_1 <= -5e+307)
		tmp = i * y;
	elseif (t_1 <= 200.0)
		tmp = -1.0 * (-1.0 * z);
	else
		tmp = (1.0 + ((y * i) / a)) * a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+307], N[(i * y), $MachinePrecision], If[LessEqual[t$95$1, 200.0], N[(-1.0 * N[(-1.0 * z), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 + N[(N[(y * i), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < -5e307

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. lift-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lift-+.f64 N/A

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

      9. +-commutative N/A

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

      10. lift-+.f64 N/A

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

      11. associate-+r+ N/A

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

      12. associate-+r+ N/A

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

      13. lower-+.f64 N/A

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in y around inf

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

      1. lower-*.f64 23.9

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

   6. Applied rewrites 23.9%

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

   if -5e307 < (+.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)) < 200

   1. Initial program 99.8%

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

   2. Taylor expanded in a around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

   4. Applied rewrites 78.9%

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

   5. Taylor expanded in z around inf

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

      1. lower-*.f64 23.1

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

   7. Applied rewrites 23.1%

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

   if 200 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i))

   1. Initial program 99.8%

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

   2. Taylor expanded in a around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

   4. Applied rewrites 78.9%

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

   5. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 41.6

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

   7. Applied rewrites 41.6%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

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

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

   9. Applied rewrites 41.6%

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

Alternative 14: 55.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+307}:\\ \;\;\;\;i \cdot y\\ \mathbf{elif}\;t\_1 \leq -100:\\ \;\;\;\;-1 \cdot \left(-1 \cdot z\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+305}:\\ \;\;\;\;\left(1 + \frac{z}{a}\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;i \cdot y\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (+
          (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c)))
          (* y i))))
   (if (<= t_1 -5e+307)
     (* i y)
     (if (<= t_1 -100.0)
       (* -1.0 (* -1.0 z))
       (if (<= t_1 5e+305) (* (+ 1.0 (/ z a)) a) (* i y))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
	double tmp;
	if (t_1 <= -5e+307) {
		tmp = i * y;
	} else if (t_1 <= -100.0) {
		tmp = -1.0 * (-1.0 * z);
	} else if (t_1 <= 5e+305) {
		tmp = (1.0 + (z / a)) * a;
	} else {
		tmp = i * y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (((((x * log(y)) + z) + t) + a) + ((b - 0.5d0) * log(c))) + (y * i)
    if (t_1 <= (-5d+307)) then
        tmp = i * y
    else if (t_1 <= (-100.0d0)) then
        tmp = (-1.0d0) * ((-1.0d0) * z)
    else if (t_1 <= 5d+305) then
        tmp = (1.0d0 + (z / a)) * a
    else
        tmp = i * y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (((((x * Math.log(y)) + z) + t) + a) + ((b - 0.5) * Math.log(c))) + (y * i);
	double tmp;
	if (t_1 <= -5e+307) {
		tmp = i * y;
	} else if (t_1 <= -100.0) {
		tmp = -1.0 * (-1.0 * z);
	} else if (t_1 <= 5e+305) {
		tmp = (1.0 + (z / a)) * a;
	} else {
		tmp = i * y;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	t_1 = (((((x * math.log(y)) + z) + t) + a) + ((b - 0.5) * math.log(c))) + (y * i)
	tmp = 0
	if t_1 <= -5e+307:
		tmp = i * y
	elif t_1 <= -100.0:
		tmp = -1.0 * (-1.0 * z)
	elif t_1 <= 5e+305:
		tmp = (1.0 + (z / a)) * a
	else:
		tmp = i * y
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + z) + t) + a) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i))
	tmp = 0.0
	if (t_1 <= -5e+307)
		tmp = Float64(i * y);
	elseif (t_1 <= -100.0)
		tmp = Float64(-1.0 * Float64(-1.0 * z));
	elseif (t_1 <= 5e+305)
		tmp = Float64(Float64(1.0 + Float64(z / a)) * a);
	else
		tmp = Float64(i * y);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
	tmp = 0.0;
	if (t_1 <= -5e+307)
		tmp = i * y;
	elseif (t_1 <= -100.0)
		tmp = -1.0 * (-1.0 * z);
	elseif (t_1 <= 5e+305)
		tmp = (1.0 + (z / a)) * a;
	else
		tmp = i * y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+307], N[(i * y), $MachinePrecision], If[LessEqual[t$95$1, -100.0], N[(-1.0 * N[(-1.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+305], N[(N[(1.0 + N[(z / a), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision], 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)) < -5e307 or 5.00000000000000009e305 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i))

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. lift-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lift-+.f64 N/A

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

      9. +-commutative N/A

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

      10. lift-+.f64 N/A

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

      11. associate-+r+ N/A

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

      12. associate-+r+ N/A

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

      13. lower-+.f64 N/A

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in y around inf

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

      1. lower-*.f64 23.9

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

   6. Applied rewrites 23.9%

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

   if -5e307 < (+.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 -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

   4. Applied rewrites 78.9%

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

   5. Taylor expanded in z around inf

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

      1. lower-*.f64 23.1

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

   7. Applied rewrites 23.1%

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

   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)) < 5.00000000000000009e305

   1. Initial program 99.8%

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

   2. Taylor expanded in a around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

   4. Applied rewrites 78.9%

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

   5. Taylor expanded in z around inf

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

      1. lower-/.f64 37.2

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

   7. Applied rewrites 37.2%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

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

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

   9. Applied rewrites 37.2%

      \[\leadsto \color{blue}{\left(1 + \frac{z}{a}\right) \cdot a} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 15: 55.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+307}:\\ \;\;\;\;i \cdot y\\ \mathbf{elif}\;t\_1 \leq -100:\\ \;\;\;\;-1 \cdot \left(-1 \cdot z\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+305}:\\ \;\;\;\;-1 \cdot \left(a \cdot -1\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot y\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (+
          (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c)))
          (* y i))))
   (if (<= t_1 -5e+307)
     (* i y)
     (if (<= t_1 -100.0)
       (* -1.0 (* -1.0 z))
       (if (<= t_1 5e+305) (* -1.0 (* a -1.0)) (* i y))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
	double tmp;
	if (t_1 <= -5e+307) {
		tmp = i * y;
	} else if (t_1 <= -100.0) {
		tmp = -1.0 * (-1.0 * z);
	} else if (t_1 <= 5e+305) {
		tmp = -1.0 * (a * -1.0);
	} else {
		tmp = i * y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (((((x * log(y)) + z) + t) + a) + ((b - 0.5d0) * log(c))) + (y * i)
    if (t_1 <= (-5d+307)) then
        tmp = i * y
    else if (t_1 <= (-100.0d0)) then
        tmp = (-1.0d0) * ((-1.0d0) * z)
    else if (t_1 <= 5d+305) then
        tmp = (-1.0d0) * (a * (-1.0d0))
    else
        tmp = i * y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (((((x * Math.log(y)) + z) + t) + a) + ((b - 0.5) * Math.log(c))) + (y * i);
	double tmp;
	if (t_1 <= -5e+307) {
		tmp = i * y;
	} else if (t_1 <= -100.0) {
		tmp = -1.0 * (-1.0 * z);
	} else if (t_1 <= 5e+305) {
		tmp = -1.0 * (a * -1.0);
	} else {
		tmp = i * y;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	t_1 = (((((x * math.log(y)) + z) + t) + a) + ((b - 0.5) * math.log(c))) + (y * i)
	tmp = 0
	if t_1 <= -5e+307:
		tmp = i * y
	elif t_1 <= -100.0:
		tmp = -1.0 * (-1.0 * z)
	elif t_1 <= 5e+305:
		tmp = -1.0 * (a * -1.0)
	else:
		tmp = i * y
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + z) + t) + a) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i))
	tmp = 0.0
	if (t_1 <= -5e+307)
		tmp = Float64(i * y);
	elseif (t_1 <= -100.0)
		tmp = Float64(-1.0 * Float64(-1.0 * z));
	elseif (t_1 <= 5e+305)
		tmp = Float64(-1.0 * Float64(a * -1.0));
	else
		tmp = Float64(i * y);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
	tmp = 0.0;
	if (t_1 <= -5e+307)
		tmp = i * y;
	elseif (t_1 <= -100.0)
		tmp = -1.0 * (-1.0 * z);
	elseif (t_1 <= 5e+305)
		tmp = -1.0 * (a * -1.0);
	else
		tmp = i * y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+307], N[(i * y), $MachinePrecision], If[LessEqual[t$95$1, -100.0], N[(-1.0 * N[(-1.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+305], N[(-1.0 * N[(a * -1.0), $MachinePrecision]), $MachinePrecision], 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)) < -5e307 or 5.00000000000000009e305 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i))

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. lift-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lift-+.f64 N/A

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

      9. +-commutative N/A

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

      10. lift-+.f64 N/A

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

      11. associate-+r+ N/A

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

      12. associate-+r+ N/A

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

      13. lower-+.f64 N/A

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in y around inf

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

      1. lower-*.f64 23.9

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

   6. Applied rewrites 23.9%

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

   if -5e307 < (+.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 -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

   4. Applied rewrites 78.9%

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

   5. Taylor expanded in z around inf

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

      1. lower-*.f64 23.1

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

   7. Applied rewrites 23.1%

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

   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)) < 5.00000000000000009e305

   1. Initial program 99.8%

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

   2. Taylor expanded in a around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

   4. Applied rewrites 78.9%

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

   5. Taylor expanded in a around inf

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

   7. Applied rewrites 22.5%

      \[\leadsto -1 \cdot \left(a \cdot -1\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 16: 40.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+307}:\\ \;\;\;\;i \cdot y\\ \mathbf{elif}\;t\_1 \leq 200:\\ \;\;\;\;-1 \cdot \left(-1 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot y\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (+
          (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c)))
          (* y i))))
   (if (<= t_1 -5e+307)
     (* i y)
     (if (<= t_1 200.0) (* -1.0 (* -1.0 z)) (* i y)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
	double tmp;
	if (t_1 <= -5e+307) {
		tmp = i * y;
	} else if (t_1 <= 200.0) {
		tmp = -1.0 * (-1.0 * z);
	} else {
		tmp = i * y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (((((x * log(y)) + z) + t) + a) + ((b - 0.5d0) * log(c))) + (y * i)
    if (t_1 <= (-5d+307)) then
        tmp = i * y
    else if (t_1 <= 200.0d0) then
        tmp = (-1.0d0) * ((-1.0d0) * z)
    else
        tmp = i * y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (((((x * Math.log(y)) + z) + t) + a) + ((b - 0.5) * Math.log(c))) + (y * i);
	double tmp;
	if (t_1 <= -5e+307) {
		tmp = i * y;
	} else if (t_1 <= 200.0) {
		tmp = -1.0 * (-1.0 * z);
	} else {
		tmp = i * y;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	t_1 = (((((x * math.log(y)) + z) + t) + a) + ((b - 0.5) * math.log(c))) + (y * i)
	tmp = 0
	if t_1 <= -5e+307:
		tmp = i * y
	elif t_1 <= 200.0:
		tmp = -1.0 * (-1.0 * z)
	else:
		tmp = i * y
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + z) + t) + a) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i))
	tmp = 0.0
	if (t_1 <= -5e+307)
		tmp = Float64(i * y);
	elseif (t_1 <= 200.0)
		tmp = Float64(-1.0 * Float64(-1.0 * z));
	else
		tmp = Float64(i * y);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
	tmp = 0.0;
	if (t_1 <= -5e+307)
		tmp = i * y;
	elseif (t_1 <= 200.0)
		tmp = -1.0 * (-1.0 * z);
	else
		tmp = i * y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+307], N[(i * y), $MachinePrecision], If[LessEqual[t$95$1, 200.0], N[(-1.0 * N[(-1.0 * z), $MachinePrecision]), $MachinePrecision], N[(i * y), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < -5e307 or 200 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i))

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. lift-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lift-+.f64 N/A

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

      9. +-commutative N/A

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

      10. lift-+.f64 N/A

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

      11. associate-+r+ N/A

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

      12. associate-+r+ N/A

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

      13. lower-+.f64 N/A

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in y around inf

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

      1. lower-*.f64 23.9

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

   6. Applied rewrites 23.9%

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

   if -5e307 < (+.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)) < 200

   1. Initial program 99.8%

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

   2. Taylor expanded in a around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

   4. Applied rewrites 78.9%

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

   5. Taylor expanded in z around inf

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

      1. lower-*.f64 23.1

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

   7. Applied rewrites 23.1%

      \[\leadsto -1 \cdot \left(-1 \cdot \color{blue}{z}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 17: 23.9% accurate, 9.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ i \cdot y \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i) :precision binary64 (* i y))

C

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

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
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 = i * y
end function

Java

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

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	return i * y

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	return Float64(i * y)
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp = code(x, y, z, t, a, b, c, i)
	tmp = i * y;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(i * y), $MachinePrecision]

Derivation

1. Initial program 99.8%

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

   1. lift-+.f64 N/A

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

   2. lift-+.f64 N/A

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

   3. +-commutative N/A

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

   4. associate-+l+ N/A

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

   5. lift-*.f64 N/A

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

   6. +-commutative N/A

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

   7. lower-fma.f64 N/A

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

   8. lift-+.f64 N/A

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

   9. +-commutative N/A

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

   10. lift-+.f64 N/A

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

   11. associate-+r+ N/A

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

   12. associate-+r+ N/A

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

   13. lower-+.f64 N/A

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

3. Applied rewrites 99.8%

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

4. Taylor expanded in y around inf

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

   1. lower-*.f64 23.9

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

6. Applied rewrites 23.9%

   \[\leadsto \color{blue}{i \cdot y} \]
7. Add Preprocessing

Alternative 18: 2.9% accurate, 12.8× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i) :precision binary64 (- (- t)))

C

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

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
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 = -(-t)
end function

Java

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

Python

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

Julia

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

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp = code(x, y, z, t, a, b, c, i)
	tmp = -(-t);
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := (-(-t))

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in a around -inf

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

   1. lower-*.f64 N/A

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

   2. lower-*.f64 N/A

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

   3. lower--.f64 N/A

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

4. Applied rewrites 78.9%

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

5. Taylor expanded in t around inf

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

   1. lower-*.f64 2.9

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

7. Applied rewrites 2.9%

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

   1. lift-*.f64 N/A

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

   2. mul-1-neg N/A

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

   3. lower-neg.f64 2.9

      \[\leadsto --1 \cdot t \]

   4. lift-*.f64 N/A

      \[\leadsto --1 \cdot t \]

   5. mul-1-neg N/A

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

   6. lower-neg.f64 2.9

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

9. Applied rewrites 2.9%

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

Reproduce

herbie shell --seed 2025143 
(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)))