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

Percentage Accurate: 99.8% → 99.8%

Time: 22.7s

Alternatives: 24

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

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

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 (log y) x z) a) (fma i y 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(log(y), x, z) + a) + fma(i, y, 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(Float64(fma(log(y), x, z) + a) + fma(i, y, 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[(N[(N[Log[y], $MachinePrecision] * x + z), $MachinePrecision] + a), $MachinePrecision] + N[(i * y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

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

3. Applied rewrites 99.8%

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

Alternative 2: 93.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(i, y, \mathsf{fma}\left(\log c, b - 0.5, \mathsf{fma}\left(\log y, x, t\right)\right)\right) + a\\ \mathbf{if}\;x \leq -1.7 \cdot 10^{+160}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{+164}:\\ \;\;\;\;\left(\mathsf{fma}\left(i, y, z\right) + \mathsf{fma}\left(\log c, b - 0.5, t\right)\right) + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 i y (fma (log c) (- b 0.5) (fma (log y) x t))) a)))
   (if (<= x -1.7e+160)
     t_1
     (if (<= x 8.6e+164)
       (+ (+ (fma i y z) (fma (log c) (- b 0.5) t)) 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(i, y, fma(log(c), (b - 0.5), fma(log(y), x, t))) + a;
	double tmp;
	if (x <= -1.7e+160) {
		tmp = t_1;
	} else if (x <= 8.6e+164) {
		tmp = (fma(i, y, z) + fma(log(c), (b - 0.5), t)) + 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(fma(i, y, fma(log(c), Float64(b - 0.5), fma(log(y), x, t))) + a)
	tmp = 0.0
	if (x <= -1.7e+160)
		tmp = t_1;
	elseif (x <= 8.6e+164)
		tmp = Float64(Float64(fma(i, y, z) + fma(log(c), Float64(b - 0.5), t)) + 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[(i * y + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + N[(N[Log[y], $MachinePrecision] * x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]}, If[LessEqual[x, -1.7e+160], t$95$1, If[LessEqual[x, 8.6e+164], N[(N[(N[(i * y + z), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.70000000000000015e160 or 8.6e164 < x

   1. Initial program 99.5%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 86.4%

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

   if -1.70000000000000015e160 < x < 8.6e164

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. associate-+r+ N/A

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

      5. associate-+l+ N/A

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

      6. lower-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-log.f64 N/A

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

      11. lift--.f64 95.7

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

   4. Applied rewrites 95.7%

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

Alternative 3: 91.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;i \leq -2.8 \cdot 10^{-44}:\\ \;\;\;\;\left(\left(z + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{elif}\;i \leq 2200000000000:\\ \;\;\;\;\left(\mathsf{fma}\left(\log y, x, \mathsf{fma}\left(\log c, b - 0.5, z\right)\right) + a\right) + t\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(i, y, z\right) + \mathsf{fma}\left(\log c, b - 0.5, t\right)\right) + a\\ \end{array} \end{array} \]

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 (<= i -2.8e-44)
   (+ (+ (+ z a) (* (- b 0.5) (log c))) (* y i))
   (if (<= i 2200000000000.0)
     (+ (+ (fma (log y) x (fma (log c) (- b 0.5) z)) a) t)
     (+ (+ (fma i y z) (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 (i <= -2.8e-44) {
		tmp = ((z + a) + ((b - 0.5) * log(c))) + (y * i);
	} else if (i <= 2200000000000.0) {
		tmp = (fma(log(y), x, fma(log(c), (b - 0.5), z)) + a) + t;
	} else {
		tmp = (fma(i, y, z) + 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 (i <= -2.8e-44)
		tmp = Float64(Float64(Float64(z + a) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i));
	elseif (i <= 2200000000000.0)
		tmp = Float64(Float64(fma(log(y), x, fma(log(c), Float64(b - 0.5), z)) + a) + t);
	else
		tmp = Float64(Float64(fma(i, y, z) + 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[i, -2.8e-44], N[(N[(N[(z + a), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2200000000000.0], N[(N[(N[(N[Log[y], $MachinePrecision] * x + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision] + t), $MachinePrecision], N[(N[(N[(i * y + z), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if i < -2.8e-44

   1. Initial program 99.7%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 86.5%

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

   if -2.8e-44 < i < 2.2e12

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 95.5%

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

   if 2.2e12 < 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 x around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. associate-+r+ N/A

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

      5. associate-+l+ N/A

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

      6. lower-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-log.f64 N/A

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

      11. lift--.f64 88.3

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

   4. Applied rewrites 88.3%

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

Alternative 4: 91.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := \log y \cdot x\\ \mathbf{if}\;x \leq -2.35 \cdot 10^{+160}:\\ \;\;\;\;\mathsf{fma}\left(i, y, t\_1\right) + a\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+207}:\\ \;\;\;\;\left(\mathsf{fma}\left(i, y, z\right) + \mathsf{fma}\left(\log c, b - 0.5, t\right)\right) + a\\ \mathbf{else}:\\ \;\;\;\;\left(t\_1 + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \end{array} \end{array} \]

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 (* (log y) x)))
   (if (<= x -2.35e+160)
     (+ (fma i y t_1) a)
     (if (<= x 7.5e+207)
       (+ (+ (fma i y z) (fma (log c) (- b 0.5) t)) a)
       (+ (+ t_1 (* (- b 0.5) (log c))) (* y i))))))

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 = log(y) * x;
	double tmp;
	if (x <= -2.35e+160) {
		tmp = fma(i, y, t_1) + a;
	} else if (x <= 7.5e+207) {
		tmp = (fma(i, y, z) + fma(log(c), (b - 0.5), t)) + a;
	} else {
		tmp = (t_1 + ((b - 0.5) * log(c))) + (y * i);
	}
	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(log(y) * x)
	tmp = 0.0
	if (x <= -2.35e+160)
		tmp = Float64(fma(i, y, t_1) + a);
	elseif (x <= 7.5e+207)
		tmp = Float64(Float64(fma(i, y, z) + fma(log(c), Float64(b - 0.5), t)) + a);
	else
		tmp = Float64(Float64(t_1 + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i));
	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[y], $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -2.35e+160], N[(N[(i * y + t$95$1), $MachinePrecision] + a), $MachinePrecision], If[LessEqual[x, 7.5e+207], N[(N[(N[(i * y + z), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision], N[(N[(t$95$1 + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.34999999999999985e160

   1. Initial program 99.6%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 87.0%

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

   5. Taylor expanded in x around inf

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

      1. remove-double-neg N/A

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

      2. *-commutative N/A

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

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

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

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

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

      5. mul-1-neg N/A

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

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

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

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

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

      8. distribute-rgt-neg-out N/A

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

      9. log-rec N/A

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

      10. lower-*.f64 N/A

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

      11. log-rec N/A

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

      12. distribute-rgt-neg-out N/A

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

      13. *-commutative N/A

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

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

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

      15. metadata-eval N/A

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

      16. *-rgt-identity N/A

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

      17. lift-log.f64 77.6

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

   7. Applied rewrites 77.6%

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

   if -2.34999999999999985e160 < x < 7.49999999999999986e207

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. associate-+r+ N/A

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

      5. associate-+l+ N/A

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

      6. lower-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-log.f64 N/A

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

      11. lift--.f64 94.3

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

   4. Applied rewrites 94.3%

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

   if 7.49999999999999986e207 < x

   1. Initial program 99.2%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-log.f64 80.9

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

   4. Applied rewrites 80.9%

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

Alternative 5: 91.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(i, y, \log y \cdot x\right) + a\\ \mathbf{if}\;x \leq -2.35 \cdot 10^{+160}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+216}:\\ \;\;\;\;\left(\mathsf{fma}\left(i, y, z\right) + \mathsf{fma}\left(\log c, b - 0.5, t\right)\right) + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 i y (* (log y) x)) a)))
   (if (<= x -2.35e+160)
     t_1
     (if (<= x 2.1e+216)
       (+ (+ (fma i y z) (fma (log c) (- b 0.5) t)) 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(i, y, (log(y) * x)) + a;
	double tmp;
	if (x <= -2.35e+160) {
		tmp = t_1;
	} else if (x <= 2.1e+216) {
		tmp = (fma(i, y, z) + fma(log(c), (b - 0.5), t)) + 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(fma(i, y, Float64(log(y) * x)) + a)
	tmp = 0.0
	if (x <= -2.35e+160)
		tmp = t_1;
	elseif (x <= 2.1e+216)
		tmp = Float64(Float64(fma(i, y, z) + fma(log(c), Float64(b - 0.5), t)) + 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[(i * y + N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]}, If[LessEqual[x, -2.35e+160], t$95$1, If[LessEqual[x, 2.1e+216], N[(N[(N[(i * y + z), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.34999999999999985e160 or 2.10000000000000001e216 < x

   1. Initial program 99.5%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 88.2%

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

   5. Taylor expanded in x around inf

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

      1. remove-double-neg N/A

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

      2. *-commutative N/A

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

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

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

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

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

      5. mul-1-neg N/A

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

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

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

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

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

      8. distribute-rgt-neg-out N/A

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

      9. log-rec N/A

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

      10. lower-*.f64 N/A

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

      11. log-rec N/A

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

      12. distribute-rgt-neg-out N/A

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

      13. *-commutative N/A

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

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

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

      15. metadata-eval N/A

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

      16. *-rgt-identity N/A

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

      17. lift-log.f64 79.9

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

   7. Applied rewrites 79.9%

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

   if -2.34999999999999985e160 < x < 2.10000000000000001e216

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. +-commutative N/A

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

      4. associate-+r+ N/A

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

      5. associate-+l+ N/A

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

      6. lower-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-fma.f64 N/A

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

      10. lift-log.f64 N/A

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

      11. lift--.f64 94.0

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

   4. Applied rewrites 94.0%

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

Alternative 6: 90.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(i, y, \log y \cdot x\right) + a\\ \mathbf{if}\;x \leq -2.35 \cdot 10^{+160}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+216}:\\ \;\;\;\;\left(\left(z + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 i y (* (log y) x)) a)))
   (if (<= x -2.35e+160)
     t_1
     (if (<= x 2.1e+216) (+ (+ (+ z a) (* (- b 0.5) (log c))) (* y i)) 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(i, y, (log(y) * x)) + a;
	double tmp;
	if (x <= -2.35e+160) {
		tmp = t_1;
	} else if (x <= 2.1e+216) {
		tmp = ((z + a) + ((b - 0.5) * log(c))) + (y * i);
	} 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(fma(i, y, Float64(log(y) * x)) + a)
	tmp = 0.0
	if (x <= -2.35e+160)
		tmp = t_1;
	elseif (x <= 2.1e+216)
		tmp = Float64(Float64(Float64(z + a) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i));
	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[(i * y + N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]}, If[LessEqual[x, -2.35e+160], t$95$1, If[LessEqual[x, 2.1e+216], N[(N[(N[(z + a), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.34999999999999985e160 or 2.10000000000000001e216 < x

   1. Initial program 99.5%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 88.2%

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

   5. Taylor expanded in x around inf

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

      1. remove-double-neg N/A

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

      2. *-commutative N/A

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

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

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

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

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

      5. mul-1-neg N/A

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

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

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

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

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

      8. distribute-rgt-neg-out N/A

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

      9. log-rec N/A

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

      10. lower-*.f64 N/A

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

      11. log-rec N/A

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

      12. distribute-rgt-neg-out N/A

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

      13. *-commutative N/A

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

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

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

      15. metadata-eval N/A

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

      16. *-rgt-identity N/A

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

      17. lift-log.f64 79.9

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

   7. Applied rewrites 79.9%

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

   if -2.34999999999999985e160 < x < 2.10000000000000001e216

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 93.2%

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

Alternative 7: 83.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := \left(b - 0.5\right) \cdot \log c\\ \mathbf{if}\;\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + t\_1\right) + y \cdot i \leq -1000000:\\ \;\;\;\;\left(z + t\_1\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;\left(\left(t + a\right) + t\_1\right) + y \cdot i\\ \end{array} \end{array} \]

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 (* (- b 0.5) (log c))))
   (if (<= (+ (+ (+ (+ (+ (* x (log y)) z) t) a) t_1) (* y i)) -1000000.0)
     (+ (+ z t_1) (* y i))
     (+ (+ (+ t a) t_1) (* y i)))))

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 = (b - 0.5) * log(c);
	double tmp;
	if (((((((x * log(y)) + z) + t) + a) + t_1) + (y * i)) <= -1000000.0) {
		tmp = (z + t_1) + (y * i);
	} else {
		tmp = ((t + a) + t_1) + (y * i);
	}
	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 = (b - 0.5d0) * log(c)
    if (((((((x * log(y)) + z) + t) + a) + t_1) + (y * i)) <= (-1000000.0d0)) then
        tmp = (z + t_1) + (y * i)
    else
        tmp = ((t + a) + t_1) + (y * i)
    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 = (b - 0.5) * Math.log(c);
	double tmp;
	if (((((((x * Math.log(y)) + z) + t) + a) + t_1) + (y * i)) <= -1000000.0) {
		tmp = (z + t_1) + (y * i);
	} else {
		tmp = ((t + a) + t_1) + (y * i);
	}
	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 = (b - 0.5) * math.log(c)
	tmp = 0
	if ((((((x * math.log(y)) + z) + t) + a) + t_1) + (y * i)) <= -1000000.0:
		tmp = (z + t_1) + (y * i)
	else:
		tmp = ((t + a) + t_1) + (y * i)
	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(b - 0.5) * log(c))
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + z) + t) + a) + t_1) + Float64(y * i)) <= -1000000.0)
		tmp = Float64(Float64(z + t_1) + Float64(y * i));
	else
		tmp = Float64(Float64(Float64(t + a) + t_1) + Float64(y * i));
	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 = (b - 0.5) * log(c);
	tmp = 0.0;
	if (((((((x * log(y)) + z) + t) + a) + t_1) + (y * i)) <= -1000000.0)
		tmp = (z + t_1) + (y * i);
	else
		tmp = ((t + a) + t_1) + (y * i);
	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[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + t$95$1), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], -1000000.0], N[(N[(z + t$95$1), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t + a), $MachinePrecision] + t$95$1), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < -1e6

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 82.5%

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

   if -1e6 < (+.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 99.7%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 83.8%

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

Alternative 8: 82.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := \left(b - 0.5\right) \cdot \log c\\ \mathbf{if}\;\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + t\_1\right) + y \cdot i \leq -1000000:\\ \;\;\;\;\left(z + t\_1\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;\left(a + t\_1\right) + y \cdot i\\ \end{array} \end{array} \]

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 (* (- b 0.5) (log c))))
   (if (<= (+ (+ (+ (+ (+ (* x (log y)) z) t) a) t_1) (* y i)) -1000000.0)
     (+ (+ z t_1) (* y i))
     (+ (+ a t_1) (* y i)))))

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 = (b - 0.5) * log(c);
	double tmp;
	if (((((((x * log(y)) + z) + t) + a) + t_1) + (y * i)) <= -1000000.0) {
		tmp = (z + t_1) + (y * i);
	} else {
		tmp = (a + t_1) + (y * i);
	}
	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 = (b - 0.5d0) * log(c)
    if (((((((x * log(y)) + z) + t) + a) + t_1) + (y * i)) <= (-1000000.0d0)) then
        tmp = (z + t_1) + (y * i)
    else
        tmp = (a + t_1) + (y * i)
    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 = (b - 0.5) * Math.log(c);
	double tmp;
	if (((((((x * Math.log(y)) + z) + t) + a) + t_1) + (y * i)) <= -1000000.0) {
		tmp = (z + t_1) + (y * i);
	} else {
		tmp = (a + t_1) + (y * i);
	}
	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 = (b - 0.5) * math.log(c)
	tmp = 0
	if ((((((x * math.log(y)) + z) + t) + a) + t_1) + (y * i)) <= -1000000.0:
		tmp = (z + t_1) + (y * i)
	else:
		tmp = (a + t_1) + (y * i)
	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(b - 0.5) * log(c))
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + z) + t) + a) + t_1) + Float64(y * i)) <= -1000000.0)
		tmp = Float64(Float64(z + t_1) + Float64(y * i));
	else
		tmp = Float64(Float64(a + t_1) + Float64(y * i));
	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 = (b - 0.5) * log(c);
	tmp = 0.0;
	if (((((((x * log(y)) + z) + t) + a) + t_1) + (y * i)) <= -1000000.0)
		tmp = (z + t_1) + (y * i);
	else
		tmp = (a + t_1) + (y * i);
	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[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + t$95$1), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], -1000000.0], N[(N[(z + t$95$1), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(N[(a + t$95$1), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < -1e6

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 82.5%

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

   if -1e6 < (+.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 99.7%

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

   2. Taylor expanded in a around inf

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

   4. Applied rewrites 83.1%

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

Alternative 9: 76.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := \left(b - 0.5\right) \cdot \log c\\ t_2 := \left(a + t\_1\right) + y \cdot i\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+217}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+201}:\\ \;\;\;\;\left(\left(z + a\right) + \left(-\log \left(\sqrt{c}\right)\right)\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 (* (- b 0.5) (log c))) (t_2 (+ (+ a t_1) (* y i))))
   (if (<= t_1 -2e+217)
     t_2
     (if (<= t_1 5e+201) (+ (+ (+ z a) (- (log (sqrt c)))) (* y i)) t_2))))

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 = (b - 0.5) * log(c);
	double t_2 = (a + t_1) + (y * i);
	double tmp;
	if (t_1 <= -2e+217) {
		tmp = t_2;
	} else if (t_1 <= 5e+201) {
		tmp = ((z + a) + -log(sqrt(c))) + (y * i);
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = (b - 0.5d0) * log(c)
    t_2 = (a + t_1) + (y * i)
    if (t_1 <= (-2d+217)) then
        tmp = t_2
    else if (t_1 <= 5d+201) then
        tmp = ((z + a) + -log(sqrt(c))) + (y * i)
    else
        tmp = t_2
    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 = (b - 0.5) * Math.log(c);
	double t_2 = (a + t_1) + (y * i);
	double tmp;
	if (t_1 <= -2e+217) {
		tmp = t_2;
	} else if (t_1 <= 5e+201) {
		tmp = ((z + a) + -Math.log(Math.sqrt(c))) + (y * i);
	} else {
		tmp = t_2;
	}
	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 = (b - 0.5) * math.log(c)
	t_2 = (a + t_1) + (y * i)
	tmp = 0
	if t_1 <= -2e+217:
		tmp = t_2
	elif t_1 <= 5e+201:
		tmp = ((z + a) + -math.log(math.sqrt(c))) + (y * i)
	else:
		tmp = t_2
	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(b - 0.5) * log(c))
	t_2 = Float64(Float64(a + t_1) + Float64(y * i))
	tmp = 0.0
	if (t_1 <= -2e+217)
		tmp = t_2;
	elseif (t_1 <= 5e+201)
		tmp = Float64(Float64(Float64(z + a) + Float64(-log(sqrt(c)))) + Float64(y * i));
	else
		tmp = t_2;
	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 = (b - 0.5) * log(c);
	t_2 = (a + t_1) + (y * i);
	tmp = 0.0;
	if (t_1 <= -2e+217)
		tmp = t_2;
	elseif (t_1 <= 5e+201)
		tmp = ((z + a) + -log(sqrt(c))) + (y * i);
	else
		tmp = t_2;
	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[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a + t$95$1), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+217], t$95$2, If[LessEqual[t$95$1, 5e+201], N[(N[(N[(z + a), $MachinePrecision] + (-N[Log[N[Sqrt[c], $MachinePrecision]], $MachinePrecision])), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c)) < -1.99999999999999992e217 or 4.9999999999999995e201 < (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))

   1. Initial program 99.4%

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

   2. Taylor expanded in a around inf

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

   4. Applied rewrites 85.0%

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

   if -1.99999999999999992e217 < (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c)) < 4.9999999999999995e201

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 81.8%

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

   5. Taylor expanded in b around 0

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

      1. metadata-eval N/A

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

      2. distribute-lft-neg-out N/A

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

      3. lower-neg.f64 N/A

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

      4. log-pow-rev N/A

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

      5. lower-log.f64 N/A

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

      6. unpow1/2 N/A

         \[\leadsto \left(\left(z + a\right) + \left(-\log \left(\sqrt{c}\right)\right)\right) + y \cdot i \]

      7. lower-sqrt.f64 75.2

         \[\leadsto \left(\left(z + a\right) + \left(-\log \left(\sqrt{c}\right)\right)\right) + y \cdot i \]

   7. Applied rewrites 75.2%

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

Alternative 10: 75.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(i, y, \log y \cdot x\right) + a\\ t_2 := \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{if}\;t\_2 \leq -1.1 \cdot 10^{+306}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;t\_2 \leq 200:\\ \;\;\;\;\mathsf{fma}\left(b - 0.5, \log c, z\right)\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+256}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+296}:\\ \;\;\;\;\left(\log c \cdot b + t\right) + a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 i y (* (log y) x)) a))
        (t_2
         (+
          (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c)))
          (* y i))))
   (if (<= t_2 -1.1e+306)
     (+ z (* y i))
     (if (<= t_2 200.0)
       (fma (- b 0.5) (log c) z)
       (if (<= t_2 5e+256)
         t_1
         (if (<= t_2 2e+296) (+ (+ (* (log c) b) t) 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(i, y, (log(y) * x)) + a;
	double t_2 = (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
	double tmp;
	if (t_2 <= -1.1e+306) {
		tmp = z + (y * i);
	} else if (t_2 <= 200.0) {
		tmp = fma((b - 0.5), log(c), z);
	} else if (t_2 <= 5e+256) {
		tmp = t_1;
	} else if (t_2 <= 2e+296) {
		tmp = ((log(c) * b) + t) + 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(fma(i, y, Float64(log(y) * x)) + a)
	t_2 = 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_2 <= -1.1e+306)
		tmp = Float64(z + Float64(y * i));
	elseif (t_2 <= 200.0)
		tmp = fma(Float64(b - 0.5), log(c), z);
	elseif (t_2 <= 5e+256)
		tmp = t_1;
	elseif (t_2 <= 2e+296)
		tmp = Float64(Float64(Float64(log(c) * b) + t) + 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[(i * y + N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]}, Block[{t$95$2 = 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$2, -1.1e+306], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 200.0], N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision] + z), $MachinePrecision], If[LessEqual[t$95$2, 5e+256], t$95$1, If[LessEqual[t$95$2, 2e+296], N[(N[(N[(N[Log[c], $MachinePrecision] * b), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision], t$95$1]]]]]]

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)) < -1.1e306

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 91.0%

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

   if -1.1e306 < (+.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%

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in z around inf

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

   6. Applied rewrites 68.9%

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

   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)) < 5.00000000000000015e256 or 1.99999999999999996e296 < (+.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 99.6%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 98.4%

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

   5. Taylor expanded in x around inf

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

      1. remove-double-neg N/A

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

      2. *-commutative N/A

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

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

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

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

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

      5. mul-1-neg N/A

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

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

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

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

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

      8. distribute-rgt-neg-out N/A

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

      9. log-rec N/A

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

      10. lower-*.f64 N/A

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

      11. log-rec N/A

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

      12. distribute-rgt-neg-out N/A

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

      13. *-commutative N/A

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

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

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

      15. metadata-eval N/A

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

      16. *-rgt-identity N/A

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

      17. lift-log.f64 81.8

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

   7. Applied rewrites 81.8%

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

   if 5.00000000000000015e256 < (+.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)) < 1.99999999999999996e296

   1. Initial program 99.8%

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

   2. Taylor expanded in a around inf

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

   4. Applied rewrites 51.4%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

   7. Applied rewrites 82.1%

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

   8. Taylor expanded in b around inf

      \[\leadsto \left(b \cdot \log c + t\right) + a \]
   9. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-log.f64 70.1

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

   10. Applied rewrites 70.1%

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

Alternative 11: 75.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b, \log c, y \cdot i\right)\\ t_2 := \left(b - 0.5\right) \cdot \log c\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+217}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+201}:\\ \;\;\;\;\left(\left(z + a\right) + \left(-\log \left(\sqrt{c}\right)\right)\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 b (log c) (* y i))) (t_2 (* (- b 0.5) (log c))))
   (if (<= t_2 -2e+217)
     t_1
     (if (<= t_2 5e+201) (+ (+ (+ z a) (- (log (sqrt c)))) (* y i)) 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(b, log(c), (y * i));
	double t_2 = (b - 0.5) * log(c);
	double tmp;
	if (t_2 <= -2e+217) {
		tmp = t_1;
	} else if (t_2 <= 5e+201) {
		tmp = ((z + a) + -log(sqrt(c))) + (y * i);
	} 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 = fma(b, log(c), Float64(y * i))
	t_2 = Float64(Float64(b - 0.5) * log(c))
	tmp = 0.0
	if (t_2 <= -2e+217)
		tmp = t_1;
	elseif (t_2 <= 5e+201)
		tmp = Float64(Float64(Float64(z + a) + Float64(-log(sqrt(c)))) + Float64(y * i));
	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[(b * N[Log[c], $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+217], t$95$1, If[LessEqual[t$95$2, 5e+201], N[(N[(N[(z + a), $MachinePrecision] + (-N[Log[N[Sqrt[c], $MachinePrecision]], $MachinePrecision])), $MachinePrecision] + N[(y * i), $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)) < -1.99999999999999992e217 or 4.9999999999999995e201 < (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))

   1. Initial program 99.4%

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

   3. Applied rewrites 99.7%

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

   4. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lift-*.f64 77.9

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

   6. Applied rewrites 77.9%

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

   7. Taylor expanded in b around inf

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

   9. Applied rewrites 77.9%

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

   if -1.99999999999999992e217 < (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c)) < 4.9999999999999995e201

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 81.8%

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

   5. Taylor expanded in b around 0

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

      1. metadata-eval N/A

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

      2. distribute-lft-neg-out N/A

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

      3. lower-neg.f64 N/A

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

      4. log-pow-rev N/A

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

      5. lower-log.f64 N/A

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

      6. unpow1/2 N/A

         \[\leadsto \left(\left(z + a\right) + \left(-\log \left(\sqrt{c}\right)\right)\right) + y \cdot i \]

      7. lower-sqrt.f64 75.2

         \[\leadsto \left(\left(z + a\right) + \left(-\log \left(\sqrt{c}\right)\right)\right) + y \cdot i \]

   7. Applied rewrites 75.2%

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

Alternative 12: 72.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{if}\;t\_1 \leq -1.1 \cdot 10^{+306}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;t\_1 \leq 200:\\ \;\;\;\;\mathsf{fma}\left(b - 0.5, \log c, z\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+308}:\\ \;\;\;\;\left(\log c \cdot b + t\right) + a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, \log c, y \cdot i\right)\\ \end{array} \end{array} \]

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 -1.1e+306)
     (+ z (* y i))
     (if (<= t_1 200.0)
       (fma (- b 0.5) (log c) z)
       (if (<= t_1 1e+308)
         (+ (+ (* (log c) b) t) a)
         (fma b (log c) (* y i)))))))

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 <= -1.1e+306) {
		tmp = z + (y * i);
	} else if (t_1 <= 200.0) {
		tmp = fma((b - 0.5), log(c), z);
	} else if (t_1 <= 1e+308) {
		tmp = ((log(c) * b) + t) + a;
	} else {
		tmp = fma(b, log(c), (y * i));
	}
	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 <= -1.1e+306)
		tmp = Float64(z + Float64(y * i));
	elseif (t_1 <= 200.0)
		tmp = fma(Float64(b - 0.5), log(c), z);
	elseif (t_1 <= 1e+308)
		tmp = Float64(Float64(Float64(log(c) * b) + t) + a);
	else
		tmp = fma(b, log(c), Float64(y * i));
	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[(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, -1.1e+306], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 200.0], N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision] + z), $MachinePrecision], If[LessEqual[t$95$1, 1e+308], N[(N[(N[(N[Log[c], $MachinePrecision] * b), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision], N[(b * N[Log[c], $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < -1.1e306

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 91.0%

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

   if -1.1e306 < (+.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%

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in z around inf

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

   6. Applied rewrites 68.9%

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

   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)) < 1e308

   1. Initial program 99.8%

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

   2. Taylor expanded in a around inf

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

   4. Applied rewrites 51.0%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

   7. Applied rewrites 82.6%

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

   8. Taylor expanded in b around inf

      \[\leadsto \left(b \cdot \log c + t\right) + a \]
   9. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-log.f64 69.0

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

   10. Applied rewrites 69.0%

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

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

   1. Initial program 98.7%

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

   3. Applied rewrites 99.5%

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

   4. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lift-*.f64 96.0

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

   6. Applied rewrites 96.0%

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

   7. Taylor expanded in b around inf

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

   9. Applied rewrites 96.0%

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

Alternative 13: 72.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{if}\;t\_1 \leq -1.1 \cdot 10^{+306}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;t\_1 \leq 200:\\ \;\;\;\;\mathsf{fma}\left(b - 0.5, \log c, z\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+308}:\\ \;\;\;\;\log c \cdot b + a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, \log c, y \cdot i\right)\\ \end{array} \end{array} \]

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 -1.1e+306)
     (+ z (* y i))
     (if (<= t_1 200.0)
       (fma (- b 0.5) (log c) z)
       (if (<= t_1 1e+308) (+ (* (log c) b) a) (fma b (log c) (* y i)))))))

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 <= -1.1e+306) {
		tmp = z + (y * i);
	} else if (t_1 <= 200.0) {
		tmp = fma((b - 0.5), log(c), z);
	} else if (t_1 <= 1e+308) {
		tmp = (log(c) * b) + a;
	} else {
		tmp = fma(b, log(c), (y * i));
	}
	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 <= -1.1e+306)
		tmp = Float64(z + Float64(y * i));
	elseif (t_1 <= 200.0)
		tmp = fma(Float64(b - 0.5), log(c), z);
	elseif (t_1 <= 1e+308)
		tmp = Float64(Float64(log(c) * b) + a);
	else
		tmp = fma(b, log(c), Float64(y * i));
	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[(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, -1.1e+306], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 200.0], N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision] + z), $MachinePrecision], If[LessEqual[t$95$1, 1e+308], N[(N[(N[Log[c], $MachinePrecision] * b), $MachinePrecision] + a), $MachinePrecision], N[(b * N[Log[c], $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < -1.1e306

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 91.0%

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

   if -1.1e306 < (+.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%

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in z around inf

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

   6. Applied rewrites 68.9%

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

   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)) < 1e308

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 98.3%

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

   5. Taylor expanded in b around inf

      \[\leadsto b \cdot \log c + a \]
   6. Step-by-step derivation

      1. *-commutative N/A

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

      2. lift-log.f64 N/A

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

      3. lift-*.f64 68.3

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

   7. Applied rewrites 68.3%

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

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

   1. Initial program 98.7%

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

   3. Applied rewrites 99.5%

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

   4. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lift-*.f64 96.0

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

   6. Applied rewrites 96.0%

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

   7. Taylor expanded in b around inf

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

   9. Applied rewrites 96.0%

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

Alternative 14: 72.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := \left(\left(\left(\left(t\_1 + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{if}\;t\_2 \leq -1.1 \cdot 10^{+306}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;t\_2 \leq 200:\\ \;\;\;\;\mathsf{fma}\left(b - 0.5, \log c, z\right)\\ \mathbf{elif}\;t\_2 \leq 10^{+308}:\\ \;\;\;\;\log c \cdot b + a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, t\_1\right)\\ \end{array} \end{array} \]

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)))
        (t_2 (+ (+ (+ (+ (+ t_1 z) t) a) (* (- b 0.5) (log c))) (* y i))))
   (if (<= t_2 -1.1e+306)
     (+ z (* y i))
     (if (<= t_2 200.0)
       (fma (- b 0.5) (log c) z)
       (if (<= t_2 1e+308) (+ (* (log c) b) a) (fma y i 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 t_2 = ((((t_1 + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
	double tmp;
	if (t_2 <= -1.1e+306) {
		tmp = z + (y * i);
	} else if (t_2 <= 200.0) {
		tmp = fma((b - 0.5), log(c), z);
	} else if (t_2 <= 1e+308) {
		tmp = (log(c) * b) + a;
	} else {
		tmp = fma(y, i, 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))
	t_2 = Float64(Float64(Float64(Float64(Float64(t_1 + z) + t) + a) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i))
	tmp = 0.0
	if (t_2 <= -1.1e+306)
		tmp = Float64(z + Float64(y * i));
	elseif (t_2 <= 200.0)
		tmp = fma(Float64(b - 0.5), log(c), z);
	elseif (t_2 <= 1e+308)
		tmp = Float64(Float64(log(c) * b) + a);
	else
		tmp = fma(y, i, 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]}, Block[{t$95$2 = N[(N[(N[(N[(N[(t$95$1 + 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$2, -1.1e+306], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 200.0], N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision] + z), $MachinePrecision], If[LessEqual[t$95$2, 1e+308], N[(N[(N[Log[c], $MachinePrecision] * b), $MachinePrecision] + a), $MachinePrecision], N[(y * i + t$95$1), $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)) < -1.1e306

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 91.0%

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

   if -1.1e306 < (+.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%

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in z around inf

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

   6. Applied rewrites 68.9%

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

   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)) < 1e308

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 98.3%

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

   5. Taylor expanded in b around inf

      \[\leadsto b \cdot \log c + a \]
   6. Step-by-step derivation

      1. *-commutative N/A

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

      2. lift-log.f64 N/A

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

      3. lift-*.f64 68.3

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

   7. Applied rewrites 68.3%

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

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

   1. Initial program 98.7%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-log.f64 95.7

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

   4. Applied rewrites 95.7%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 95.7

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

      7. lift-*.f64 N/A

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

      8. lift-log.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lift-log.f64 95.7

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

   6. Applied rewrites 95.7%

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

Alternative 15: 72.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{if}\;t\_1 \leq -1.1 \cdot 10^{+306}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;t\_1 \leq 200:\\ \;\;\;\;\mathsf{fma}\left(b - 0.5, \log c, z\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+308}:\\ \;\;\;\;\log c \cdot b + a\\ \mathbf{else}:\\ \;\;\;\;i \cdot y\\ \end{array} \end{array} \]

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 -1.1e+306)
     (+ z (* y i))
     (if (<= t_1 200.0)
       (fma (- b 0.5) (log c) z)
       (if (<= t_1 1e+308) (+ (* (log c) b) 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 <= -1.1e+306) {
		tmp = z + (y * i);
	} else if (t_1 <= 200.0) {
		tmp = fma((b - 0.5), log(c), z);
	} else if (t_1 <= 1e+308) {
		tmp = (log(c) * b) + 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 <= -1.1e+306)
		tmp = Float64(z + Float64(y * i));
	elseif (t_1 <= 200.0)
		tmp = fma(Float64(b - 0.5), log(c), z);
	elseif (t_1 <= 1e+308)
		tmp = Float64(Float64(log(c) * b) + a);
	else
		tmp = Float64(i * y);
	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[(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, -1.1e+306], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 200.0], N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision] + z), $MachinePrecision], If[LessEqual[t$95$1, 1e+308], N[(N[(N[Log[c], $MachinePrecision] * b), $MachinePrecision] + a), $MachinePrecision], N[(i * y), $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)) < -1.1e306

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 91.0%

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

   if -1.1e306 < (+.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%

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in z around inf

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

   6. Applied rewrites 68.9%

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

   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)) < 1e308

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 98.3%

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

   5. Taylor expanded in b around inf

      \[\leadsto b \cdot \log c + a \]
   6. Step-by-step derivation

      1. *-commutative N/A

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

      2. lift-log.f64 N/A

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

      3. lift-*.f64 68.3

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

   7. Applied rewrites 68.3%

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

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

   1. Initial program 98.7%

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

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 93.5

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

   4. Applied rewrites 93.5%

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

Alternative 16: 68.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{if}\;t\_1 \leq -200:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;t\_1 \leq 10^{+308}:\\ \;\;\;\;\log c \cdot b + a\\ \mathbf{else}:\\ \;\;\;\;i \cdot y\\ \end{array} \end{array} \]

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 -200.0)
     (+ z (* y i))
     (if (<= t_1 1e+308) (+ (* (log c) b) 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 <= -200.0) {
		tmp = z + (y * i);
	} else if (t_1 <= 1e+308) {
		tmp = (log(c) * b) + 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 <= (-200.0d0)) then
        tmp = z + (y * i)
    else if (t_1 <= 1d+308) then
        tmp = (log(c) * b) + 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 <= -200.0) {
		tmp = z + (y * i);
	} else if (t_1 <= 1e+308) {
		tmp = (Math.log(c) * b) + 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 <= -200.0:
		tmp = z + (y * i)
	elif t_1 <= 1e+308:
		tmp = (math.log(c) * b) + 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 <= -200.0)
		tmp = Float64(z + Float64(y * i));
	elseif (t_1 <= 1e+308)
		tmp = Float64(Float64(log(c) * b) + 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 <= -200.0)
		tmp = z + (y * i);
	elseif (t_1 <= 1e+308)
		tmp = (log(c) * b) + 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, -200.0], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+308], N[(N[(N[Log[c], $MachinePrecision] * b), $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)) < -200

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 66.2%

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

   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)) < 1e308

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 98.3%

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

   5. Taylor expanded in b around inf

      \[\leadsto b \cdot \log c + a \]
   6. Step-by-step derivation

      1. *-commutative N/A

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

      2. lift-log.f64 N/A

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

      3. lift-*.f64 66.9

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

   7. Applied rewrites 66.9%

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

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

   1. Initial program 98.7%

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

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 93.5

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

   4. Applied rewrites 93.5%

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

Alternative 17: 56.6% accurate, 3.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 3.4 \cdot 10^{+164}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;\left(z + t\right) + a\\ \end{array} \end{array} \]

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 (<= a 3.4e+164) (+ z (* y i)) (+ (+ z 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 (a <= 3.4e+164) {
		tmp = z + (y * i);
	} else {
		tmp = (z + t) + 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) :: tmp
    if (a <= 3.4d+164) then
        tmp = z + (y * i)
    else
        tmp = (z + t) + 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 tmp;
	if (a <= 3.4e+164) {
		tmp = z + (y * i);
	} else {
		tmp = (z + t) + 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):
	tmp = 0
	if a <= 3.4e+164:
		tmp = z + (y * i)
	else:
		tmp = (z + 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 (a <= 3.4e+164)
		tmp = Float64(z + Float64(y * i));
	else
		tmp = Float64(Float64(z + t) + 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)
	tmp = 0.0;
	if (a <= 3.4e+164)
		tmp = z + (y * i);
	else
		tmp = (z + t) + 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_] := If[LessEqual[a, 3.4e+164], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(N[(z + t), $MachinePrecision] + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 3.4000000000000001e164

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 52.7%

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

   if 3.4000000000000001e164 < a

   1. Initial program 99.7%

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

   2. Taylor expanded in a around inf

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

   4. Applied rewrites 55.8%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

   7. Applied rewrites 91.6%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 65.2%

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

Alternative 18: 56.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{if}\;t\_1 \leq -1.1 \cdot 10^{+306}:\\ \;\;\;\;t + y \cdot i\\ \mathbf{elif}\;t\_1 \leq 10^{+308}:\\ \;\;\;\;\left(z + t\right) + a\\ \mathbf{else}:\\ \;\;\;\;i \cdot y\\ \end{array} \end{array} \]

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 -1.1e+306)
     (+ t (* y i))
     (if (<= t_1 1e+308) (+ (+ z t) 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 <= -1.1e+306) {
		tmp = t + (y * i);
	} else if (t_1 <= 1e+308) {
		tmp = (z + t) + 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 <= (-1.1d+306)) then
        tmp = t + (y * i)
    else if (t_1 <= 1d+308) then
        tmp = (z + t) + 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 <= -1.1e+306) {
		tmp = t + (y * i);
	} else if (t_1 <= 1e+308) {
		tmp = (z + t) + 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 <= -1.1e+306:
		tmp = t + (y * i)
	elif t_1 <= 1e+308:
		tmp = (z + t) + 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 <= -1.1e+306)
		tmp = Float64(t + Float64(y * i));
	elseif (t_1 <= 1e+308)
		tmp = Float64(Float64(z + t) + 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 <= -1.1e+306)
		tmp = t + (y * i);
	elseif (t_1 <= 1e+308)
		tmp = (z + t) + 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, -1.1e+306], N[(t + N[(y * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+308], N[(N[(z + t), $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)) < -1.1e306

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 81.6%

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

   if -1.1e306 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < 1e308

   1. Initial program 99.8%

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

   2. Taylor expanded in a around inf

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

   4. Applied rewrites 26.3%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

   7. Applied rewrites 82.5%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 50.7%

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

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

   1. Initial program 98.7%

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

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 93.5

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

   4. Applied rewrites 93.5%

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

Alternative 19: 56.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{if}\;t\_1 \leq -1.1 \cdot 10^{+306}:\\ \;\;\;\;i \cdot y\\ \mathbf{elif}\;t\_1 \leq 10^{+308}:\\ \;\;\;\;\left(z + t\right) + a\\ \mathbf{else}:\\ \;\;\;\;i \cdot y\\ \end{array} \end{array} \]

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 -1.1e+306) (* i y) (if (<= t_1 1e+308) (+ (+ z t) 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 <= -1.1e+306) {
		tmp = i * y;
	} else if (t_1 <= 1e+308) {
		tmp = (z + t) + 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 <= (-1.1d+306)) then
        tmp = i * y
    else if (t_1 <= 1d+308) then
        tmp = (z + t) + 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 <= -1.1e+306) {
		tmp = i * y;
	} else if (t_1 <= 1e+308) {
		tmp = (z + t) + 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 <= -1.1e+306:
		tmp = i * y
	elif t_1 <= 1e+308:
		tmp = (z + t) + 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 <= -1.1e+306)
		tmp = Float64(i * y);
	elseif (t_1 <= 1e+308)
		tmp = Float64(Float64(z + t) + 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 <= -1.1e+306)
		tmp = i * y;
	elseif (t_1 <= 1e+308)
		tmp = (z + t) + 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, -1.1e+306], N[(i * y), $MachinePrecision], If[LessEqual[t$95$1, 1e+308], N[(N[(z + t), $MachinePrecision] + a), $MachinePrecision], N[(i * y), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < -1.1e306 or 1e308 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i))

   1. Initial program 99.4%

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

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 87.2

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

   4. Applied rewrites 87.2%

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

   if -1.1e306 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < 1e308

   1. Initial program 99.8%

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

   2. Taylor expanded in a around inf

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

   4. Applied rewrites 26.3%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

   7. Applied rewrites 82.5%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 50.7%

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

Alternative 20: 55.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{if}\;t\_1 \leq -1.1 \cdot 10^{+306}:\\ \;\;\;\;i \cdot y\\ \mathbf{elif}\;t\_1 \leq 10^{+308}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;i \cdot y\\ \end{array} \end{array} \]

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 -1.1e+306) (* i y) (if (<= t_1 1e+308) (+ z 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 <= -1.1e+306) {
		tmp = i * y;
	} else if (t_1 <= 1e+308) {
		tmp = z + 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 <= (-1.1d+306)) then
        tmp = i * y
    else if (t_1 <= 1d+308) then
        tmp = z + 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 <= -1.1e+306) {
		tmp = i * y;
	} else if (t_1 <= 1e+308) {
		tmp = z + 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 <= -1.1e+306:
		tmp = i * y
	elif t_1 <= 1e+308:
		tmp = z + 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 <= -1.1e+306)
		tmp = Float64(i * y);
	elseif (t_1 <= 1e+308)
		tmp = Float64(z + 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 <= -1.1e+306)
		tmp = i * y;
	elseif (t_1 <= 1e+308)
		tmp = z + 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, -1.1e+306], N[(i * y), $MachinePrecision], If[LessEqual[t$95$1, 1e+308], N[(z + a), $MachinePrecision], N[(i * y), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < -1.1e306 or 1e308 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i))

   1. Initial program 99.4%

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

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 87.2

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

   4. Applied rewrites 87.2%

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

   if -1.1e306 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < 1e308

   1. Initial program 99.8%

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

   2. Taylor expanded in a around inf

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

   4. Applied rewrites 26.3%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

   7. Applied rewrites 82.5%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 50.0%

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

Alternative 21: 44.4% accurate, 0.9× speedup

Math

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

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))
      -200.0)
   z
   (+ 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)) <= -200.0) {
		tmp = z;
	} else {
		tmp = t + 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) :: tmp
    if (((((((x * log(y)) + z) + t) + a) + ((b - 0.5d0) * log(c))) + (y * i)) <= (-200.0d0)) then
        tmp = z
    else
        tmp = t + 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 tmp;
	if (((((((x * Math.log(y)) + z) + t) + a) + ((b - 0.5) * Math.log(c))) + (y * i)) <= -200.0) {
		tmp = z;
	} else {
		tmp = t + 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):
	tmp = 0
	if ((((((x * math.log(y)) + z) + t) + a) + ((b - 0.5) * math.log(c))) + (y * i)) <= -200.0:
		tmp = z
	else:
		tmp = 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)) <= -200.0)
		tmp = z;
	else
		tmp = Float64(t + 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)
	tmp = 0.0;
	if (((((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i)) <= -200.0)
		tmp = z;
	else
		tmp = t + 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_] := 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], -200.0], z, N[(t + 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)) < -200

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 44.3%

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

   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 99.7%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 98.3%

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

   5. Taylor expanded in t around inf

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

   7. Applied rewrites 44.4%

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

Alternative 22: 44.1% accurate, 10.1× speedup

Math

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

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 (+ 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 z + a;
}

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 = z + a
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 z + a;
}

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 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(z + a)
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 = 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[(z + a), $MachinePrecision]

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in a around inf

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

4. Applied rewrites 22.9%

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

5. Taylor expanded in x around 0

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

   1. +-commutative N/A

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

   2. lower-+.f64 N/A

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

7. Applied rewrites 84.4%

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

8. Taylor expanded in z around inf

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

10. Applied rewrites 44.0%

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

Alternative 23: 44.0% accurate, 0.9× speedup

Math

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

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))
      -200.0)
   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) {
	double tmp;
	if (((((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i)) <= -200.0) {
		tmp = z;
	} else {
		tmp = 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) :: tmp
    if (((((((x * log(y)) + z) + t) + a) + ((b - 0.5d0) * log(c))) + (y * i)) <= (-200.0d0)) then
        tmp = z
    else
        tmp = 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 tmp;
	if (((((((x * Math.log(y)) + z) + t) + a) + ((b - 0.5) * Math.log(c))) + (y * i)) <= -200.0) {
		tmp = z;
	} else {
		tmp = 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):
	tmp = 0
	if ((((((x * math.log(y)) + z) + t) + a) + ((b - 0.5) * math.log(c))) + (y * i)) <= -200.0:
		tmp = z
	else:
		tmp = 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)) <= -200.0)
		tmp = z;
	else
		tmp = 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)
	tmp = 0.0;
	if (((((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i)) <= -200.0)
		tmp = z;
	else
		tmp = 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_] := 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], -200.0], z, a]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 44.3%

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

   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 99.7%

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

   2. Taylor expanded in a around inf

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

   4. Applied rewrites 43.9%

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

Alternative 24: 22.9% accurate, 37.6× speedup

Math

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

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 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 a;
}

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 = a
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 a;
}

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 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 a
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 = 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_] := a

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in a around inf

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

4. Applied rewrites 22.9%

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

Reproduce

herbie shell --seed 2025130 
(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)))