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

Percentage Accurate: 99.8% → 99.8%

Time: 12.7s

Alternatives: 15

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.8% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* b (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 * 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 * 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 * 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 * 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(b * 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 * 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[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in b around inf

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

   1. lower-*.f64 N/A

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

   2. lower-log.f64 97.8%

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

4. Applied rewrites 97.8%

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

Alternative 2: 97.2% accurate, 0.3× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return ((fmax(fmax(z, t), fmax(fmin(z, t), a)) + (fmin(fmin(z, t), a) + (x * log(y)))) + (b * 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 = ((fmax(fmax(z, t), fmax(fmin(z, t), a)) + (fmin(fmin(z, t), a) + (x * log(y)))) + (b * 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 ((fmax(fmax(z, t), fmax(fmin(z, t), a)) + (fmin(fmin(z, t), a) + (x * Math.log(y)))) + (b * Math.log(c))) + (y * i);
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in b around inf

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

   1. lower-*.f64 N/A

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

   2. lower-log.f64 97.8%

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

4. Applied rewrites 97.8%

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

5. Taylor expanded in t around 0

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

   1. lower-+.f64 N/A

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

   2. lower-+.f64 N/A

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

   3. lower-*.f64 N/A

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

   4. lower-log.f64 82.6%

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

7. Applied rewrites 82.6%

   \[\leadsto \left(\color{blue}{\left(a + \left(z + x \cdot \log y\right)\right)} + b \cdot \log c\right) + y \cdot i \]
8. Add Preprocessing

Alternative 3: 93.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{max}\left(t, \mathsf{max}\left(z, a\right)\right)\\ t_2 := \left(\left(t\_1 + x \cdot \log y\right) + b \cdot \log c\right) + y \cdot i\\ \mathbf{if}\;x \leq -2.25 \cdot 10^{+138}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+216}:\\ \;\;\;\;\left(\left(\left(\mathsf{min}\left(z, a\right) + \mathsf{min}\left(t, \mathsf{max}\left(z, a\right)\right)\right) + t\_1\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  (let* ((t_1 (fmax t (fmax z a)))
       (t_2 (+ (+ (+ t_1 (* x (log y))) (* b (log c))) (* y i))))
  (if (<= x -2.25e+138)
    t_2
    (if (<= x 1.05e+216)
      (+
       (+
        (+ (+ (fmin z a) (fmin t (fmax z a))) t_1)
        (* (- b 0.5) (log c)))
       (* y i))
      t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fmax(t, fmax(z, a));
	double t_2 = ((t_1 + (x * log(y))) + (b * log(c))) + (y * i);
	double tmp;
	if (x <= -2.25e+138) {
		tmp = t_2;
	} else if (x <= 1.05e+216) {
		tmp = (((fmin(z, a) + fmin(t, fmax(z, a))) + t_1) + ((b - 0.5) * log(c))) + (y * i);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = fmax(t, fmax(z, a))
    t_2 = ((t_1 + (x * log(y))) + (b * log(c))) + (y * i)
    if (x <= (-2.25d+138)) then
        tmp = t_2
    else if (x <= 1.05d+216) then
        tmp = (((fmin(z, a) + fmin(t, fmax(z, a))) + t_1) + ((b - 0.5d0) * log(c))) + (y * i)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fmax(t, fmax(z, a));
	double t_2 = ((t_1 + (x * Math.log(y))) + (b * Math.log(c))) + (y * i);
	double tmp;
	if (x <= -2.25e+138) {
		tmp = t_2;
	} else if (x <= 1.05e+216) {
		tmp = (((fmin(z, a) + fmin(t, fmax(z, a))) + t_1) + ((b - 0.5) * Math.log(c))) + (y * i);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = fmax(t, fmax(z, a))
	t_2 = ((t_1 + (x * math.log(y))) + (b * math.log(c))) + (y * i)
	tmp = 0
	if x <= -2.25e+138:
		tmp = t_2
	elif x <= 1.05e+216:
		tmp = (((fmin(z, a) + fmin(t, fmax(z, a))) + t_1) + ((b - 0.5) * math.log(c))) + (y * i)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fmax(t, fmax(z, a))
	t_2 = Float64(Float64(Float64(t_1 + Float64(x * log(y))) + Float64(b * log(c))) + Float64(y * i))
	tmp = 0.0
	if (x <= -2.25e+138)
		tmp = t_2;
	elseif (x <= 1.05e+216)
		tmp = Float64(Float64(Float64(Float64(fmin(z, a) + fmin(t, fmax(z, a))) + t_1) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = max(t, max(z, a));
	t_2 = ((t_1 + (x * log(y))) + (b * log(c))) + (y * i);
	tmp = 0.0;
	if (x <= -2.25e+138)
		tmp = t_2;
	elseif (x <= 1.05e+216)
		tmp = (((min(z, a) + min(t, max(z, a))) + t_1) + ((b - 0.5) * log(c))) + (y * i);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[Max[t, N[Max[z, a], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$1 + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.25e+138], t$95$2, If[LessEqual[x, 1.05e+216], N[(N[(N[(N[(N[Min[z, a], $MachinePrecision] + N[Min[t, N[Max[z, a], $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.2499999999999999e138 or 1.05e216 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower-log.f64 97.8%

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

   4. Applied rewrites 97.8%

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

   5. Taylor expanded in t around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-log.f64 82.6%

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

   7. Applied rewrites 82.6%

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

   8. Taylor expanded in z around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-log.f64 68.1%

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

   10. Applied rewrites 68.1%

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

   if -2.2499999999999999e138 < x < 1.05e216

   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

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

   4. Applied rewrites 84.9%

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

Alternative 4: 88.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} t_1 := --1 \cdot \left(x \cdot \log y\right)\\ \mathbf{if}\;x \leq -6 \cdot 10^{+253}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+216}:\\ \;\;\;\;\left(\left(\left(z + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  (let* ((t_1 (- (* -1.0 (* x (log y))))))
  (if (<= x -6e+253)
    t_1
    (if (<= x 1.05e+216)
      (+ (+ (+ (+ z t) a) (* (- b 0.5) (log c))) (* y i))
      t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -(-1.0 * (x * log(y)));
	double tmp;
	if (x <= -6e+253) {
		tmp = t_1;
	} else if (x <= 1.05e+216) {
		tmp = (((z + t) + a) + ((b - 0.5) * log(c))) + (y * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -((-1.0d0) * (x * log(y)))
    if (x <= (-6d+253)) then
        tmp = t_1
    else if (x <= 1.05d+216) then
        tmp = (((z + t) + a) + ((b - 0.5d0) * log(c))) + (y * i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -(-1.0 * (x * Math.log(y)));
	double tmp;
	if (x <= -6e+253) {
		tmp = t_1;
	} else if (x <= 1.05e+216) {
		tmp = (((z + t) + a) + ((b - 0.5) * Math.log(c))) + (y * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = -(-1.0 * (x * math.log(y)))
	tmp = 0
	if x <= -6e+253:
		tmp = t_1
	elif x <= 1.05e+216:
		tmp = (((z + t) + a) + ((b - 0.5) * math.log(c))) + (y * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(-Float64(-1.0 * Float64(x * log(y))))
	tmp = 0.0
	if (x <= -6e+253)
		tmp = t_1;
	elseif (x <= 1.05e+216)
		tmp = Float64(Float64(Float64(Float64(z + t) + a) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = -(-1.0 * (x * log(y)));
	tmp = 0.0;
	if (x <= -6e+253)
		tmp = t_1;
	elseif (x <= 1.05e+216)
		tmp = (((z + t) + a) + ((b - 0.5) * log(c))) + (y * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = (-N[(-1.0 * N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision])}, If[LessEqual[x, -6e+253], t$95$1, If[LessEqual[x, 1.05e+216], N[(N[(N[(N[(z + t), $MachinePrecision] + 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 < -5.9999999999999996e253 or 1.05e216 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in i around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

   4. Applied rewrites 68.9%

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

   5. Taylor expanded in a around inf

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

      1. lower-*.f64 16.6%

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

   7. Applied rewrites 16.6%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 16.6%

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

      4. lift-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 16.6%

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

   9. Applied rewrites 16.6%

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

   10. Taylor expanded in x around inf

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

       1. lower-*.f64 N/A

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

       2. lower-*.f64 N/A

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

       3. lower-log.f64 16.2%

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

   12. Applied rewrites 16.2%

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

   if -5.9999999999999996e253 < x < 1.05e216

   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

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

   4. Applied rewrites 84.9%

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

Alternative 5: 86.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} t_1 := --1 \cdot \left(x \cdot \log y\right)\\ \mathbf{if}\;x \leq -6 \cdot 10^{+253}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+216}:\\ \;\;\;\;\left(\left(\left(t + z\right) + a\right) + b \cdot \log c\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  (let* ((t_1 (- (* -1.0 (* x (log y))))))
  (if (<= x -6e+253)
    t_1
    (if (<= x 1.05e+216)
      (+ (+ (+ (+ t z) a) (* b (log c))) (* y i))
      t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -(-1.0 * (x * log(y)));
	double tmp;
	if (x <= -6e+253) {
		tmp = t_1;
	} else if (x <= 1.05e+216) {
		tmp = (((t + z) + a) + (b * log(c))) + (y * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -((-1.0d0) * (x * log(y)))
    if (x <= (-6d+253)) then
        tmp = t_1
    else if (x <= 1.05d+216) then
        tmp = (((t + z) + a) + (b * log(c))) + (y * i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -(-1.0 * (x * Math.log(y)));
	double tmp;
	if (x <= -6e+253) {
		tmp = t_1;
	} else if (x <= 1.05e+216) {
		tmp = (((t + z) + a) + (b * Math.log(c))) + (y * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = -(-1.0 * (x * math.log(y)))
	tmp = 0
	if x <= -6e+253:
		tmp = t_1
	elif x <= 1.05e+216:
		tmp = (((t + z) + a) + (b * math.log(c))) + (y * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(-Float64(-1.0 * Float64(x * log(y))))
	tmp = 0.0
	if (x <= -6e+253)
		tmp = t_1;
	elseif (x <= 1.05e+216)
		tmp = Float64(Float64(Float64(Float64(t + z) + a) + Float64(b * log(c))) + Float64(y * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = -(-1.0 * (x * log(y)));
	tmp = 0.0;
	if (x <= -6e+253)
		tmp = t_1;
	elseif (x <= 1.05e+216)
		tmp = (((t + z) + a) + (b * log(c))) + (y * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = (-N[(-1.0 * N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision])}, If[LessEqual[x, -6e+253], t$95$1, If[LessEqual[x, 1.05e+216], N[(N[(N[(N[(t + z), $MachinePrecision] + a), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.9999999999999996e253 or 1.05e216 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in i around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

   4. Applied rewrites 68.9%

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

   5. Taylor expanded in a around inf

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

      1. lower-*.f64 16.6%

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

   7. Applied rewrites 16.6%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 16.6%

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

      4. lift-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 16.6%

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

   9. Applied rewrites 16.6%

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

   10. Taylor expanded in x around inf

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

       1. lower-*.f64 N/A

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

       2. lower-*.f64 N/A

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

       3. lower-log.f64 16.2%

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

   12. Applied rewrites 16.2%

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

   if -5.9999999999999996e253 < x < 1.05e216

   1. Initial program 99.8%

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

   2. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower-log.f64 97.8%

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

   4. Applied rewrites 97.8%

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

   5. Taylor expanded in x around 0

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

      1. lower-+.f64 83.0%

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

   7. Applied rewrites 83.0%

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

Alternative 6: 85.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := --1 \cdot \left(x \cdot \log y\right)\\ \mathbf{if}\;x \leq -6 \cdot 10^{+253}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+216}:\\ \;\;\;\;\left(\left(\mathsf{max}\left(\mathsf{max}\left(z, t\right), \mathsf{max}\left(\mathsf{min}\left(z, t\right), a\right)\right) + \mathsf{min}\left(\mathsf{min}\left(z, t\right), a\right)\right) + b \cdot \log c\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  (let* ((t_1 (- (* -1.0 (* x (log y))))))
  (if (<= x -6e+253)
    t_1
    (if (<= x 1.05e+216)
      (+
       (+
        (+ (fmax (fmax z t) (fmax (fmin z t) a)) (fmin (fmin z t) a))
        (* b (log c)))
       (* y i))
      t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -(-1.0 * (x * log(y)));
	double tmp;
	if (x <= -6e+253) {
		tmp = t_1;
	} else if (x <= 1.05e+216) {
		tmp = ((fmax(fmax(z, t), fmax(fmin(z, t), a)) + fmin(fmin(z, t), a)) + (b * log(c))) + (y * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -((-1.0d0) * (x * log(y)))
    if (x <= (-6d+253)) then
        tmp = t_1
    else if (x <= 1.05d+216) then
        tmp = ((fmax(fmax(z, t), fmax(fmin(z, t), a)) + fmin(fmin(z, t), a)) + (b * log(c))) + (y * i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -(-1.0 * (x * Math.log(y)));
	double tmp;
	if (x <= -6e+253) {
		tmp = t_1;
	} else if (x <= 1.05e+216) {
		tmp = ((fmax(fmax(z, t), fmax(fmin(z, t), a)) + fmin(fmin(z, t), a)) + (b * Math.log(c))) + (y * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = -(-1.0 * (x * math.log(y)))
	tmp = 0
	if x <= -6e+253:
		tmp = t_1
	elif x <= 1.05e+216:
		tmp = ((fmax(fmax(z, t), fmax(fmin(z, t), a)) + fmin(fmin(z, t), a)) + (b * math.log(c))) + (y * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(-Float64(-1.0 * Float64(x * log(y))))
	tmp = 0.0
	if (x <= -6e+253)
		tmp = t_1;
	elseif (x <= 1.05e+216)
		tmp = Float64(Float64(Float64(fmax(fmax(z, t), fmax(fmin(z, t), a)) + fmin(fmin(z, t), a)) + Float64(b * log(c))) + Float64(y * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = -(-1.0 * (x * log(y)));
	tmp = 0.0;
	if (x <= -6e+253)
		tmp = t_1;
	elseif (x <= 1.05e+216)
		tmp = ((max(max(z, t), max(min(z, t), a)) + min(min(z, t), a)) + (b * log(c))) + (y * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = (-N[(-1.0 * N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision])}, If[LessEqual[x, -6e+253], t$95$1, If[LessEqual[x, 1.05e+216], N[(N[(N[(N[Max[N[Max[z, t], $MachinePrecision], N[Max[N[Min[z, t], $MachinePrecision], a], $MachinePrecision]], $MachinePrecision] + N[Min[N[Min[z, t], $MachinePrecision], a], $MachinePrecision]), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.9999999999999996e253 or 1.05e216 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in i around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

   4. Applied rewrites 68.9%

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

   5. Taylor expanded in a around inf

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

      1. lower-*.f64 16.6%

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

   7. Applied rewrites 16.6%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 16.6%

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

      4. lift-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 16.6%

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

   9. Applied rewrites 16.6%

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

   10. Taylor expanded in x around inf

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

       1. lower-*.f64 N/A

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

       2. lower-*.f64 N/A

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

       3. lower-log.f64 16.2%

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

   12. Applied rewrites 16.2%

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

   if -5.9999999999999996e253 < x < 1.05e216

   1. Initial program 99.8%

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

   2. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower-log.f64 97.8%

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

   4. Applied rewrites 97.8%

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

   5. Taylor expanded in t around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-log.f64 82.6%

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

   7. Applied rewrites 82.6%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 68.0%

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

Alternative 7: 62.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_1 := --1 \cdot \left(x \cdot \log y\right)\\ t_2 := \mathsf{max}\left(\mathsf{max}\left(z, t\right), \mathsf{max}\left(\mathsf{min}\left(z, t\right), a\right)\right)\\ \mathbf{if}\;x \leq -6 \cdot 10^{+253}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+210}:\\ \;\;\;\;\left(1 + \frac{\mathsf{min}\left(\mathsf{min}\left(z, t\right), a\right)}{t\_2}\right) \cdot t\_2 + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  (let* ((t_1 (- (* -1.0 (* x (log y)))))
       (t_2 (fmax (fmax z t) (fmax (fmin z t) a))))
  (if (<= x -6e+253)
    t_1
    (if (<= x 5.6e+210)
      (+ (* (+ 1.0 (/ (fmin (fmin z t) a) t_2)) t_2) (* y i))
      t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -(-1.0 * (x * log(y)));
	double t_2 = fmax(fmax(z, t), fmax(fmin(z, t), a));
	double tmp;
	if (x <= -6e+253) {
		tmp = t_1;
	} else if (x <= 5.6e+210) {
		tmp = ((1.0 + (fmin(fmin(z, t), a) / t_2)) * t_2) + (y * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = -((-1.0d0) * (x * log(y)))
    t_2 = fmax(fmax(z, t), fmax(fmin(z, t), a))
    if (x <= (-6d+253)) then
        tmp = t_1
    else if (x <= 5.6d+210) then
        tmp = ((1.0d0 + (fmin(fmin(z, t), a) / t_2)) * t_2) + (y * i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -(-1.0 * (x * Math.log(y)));
	double t_2 = fmax(fmax(z, t), fmax(fmin(z, t), a));
	double tmp;
	if (x <= -6e+253) {
		tmp = t_1;
	} else if (x <= 5.6e+210) {
		tmp = ((1.0 + (fmin(fmin(z, t), a) / t_2)) * t_2) + (y * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = -(-1.0 * (x * math.log(y)))
	t_2 = fmax(fmax(z, t), fmax(fmin(z, t), a))
	tmp = 0
	if x <= -6e+253:
		tmp = t_1
	elif x <= 5.6e+210:
		tmp = ((1.0 + (fmin(fmin(z, t), a) / t_2)) * t_2) + (y * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(-Float64(-1.0 * Float64(x * log(y))))
	t_2 = fmax(fmax(z, t), fmax(fmin(z, t), a))
	tmp = 0.0
	if (x <= -6e+253)
		tmp = t_1;
	elseif (x <= 5.6e+210)
		tmp = Float64(Float64(Float64(1.0 + Float64(fmin(fmin(z, t), a) / t_2)) * t_2) + Float64(y * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = -(-1.0 * (x * log(y)));
	t_2 = max(max(z, t), max(min(z, t), a));
	tmp = 0.0;
	if (x <= -6e+253)
		tmp = t_1;
	elseif (x <= 5.6e+210)
		tmp = ((1.0 + (min(min(z, t), a) / t_2)) * t_2) + (y * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = (-N[(-1.0 * N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision])}, Block[{t$95$2 = N[Max[N[Max[z, t], $MachinePrecision], N[Max[N[Min[z, t], $MachinePrecision], a], $MachinePrecision]], $MachinePrecision]}, If[LessEqual[x, -6e+253], t$95$1, If[LessEqual[x, 5.6e+210], N[(N[(N[(1.0 + N[(N[Min[N[Min[z, t], $MachinePrecision], a], $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.9999999999999996e253 or 5.6000000000000004e210 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in i around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

   4. Applied rewrites 68.9%

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

   5. Taylor expanded in a around inf

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

      1. lower-*.f64 16.6%

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

   7. Applied rewrites 16.6%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 16.6%

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

      4. lift-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 16.6%

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

   9. Applied rewrites 16.6%

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

   10. Taylor expanded in x around inf

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

       1. lower-*.f64 N/A

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

       2. lower-*.f64 N/A

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

       3. lower-log.f64 16.2%

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

   12. Applied rewrites 16.2%

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

   if -5.9999999999999996e253 < x < 5.6000000000000004e210

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. sum-to-mult N/A

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

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

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

   3. Applied rewrites 73.7%

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

   4. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-log.f64 46.5%

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

   6. Applied rewrites 46.5%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 46.5%

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

   8. Applied rewrites 46.5%

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

   9. Taylor expanded in z around inf

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

       1. lower-/.f64 46.7%

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

   11. Applied rewrites 46.7%

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

Alternative 8: 61.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_1 := --1 \cdot \left(b \cdot \log c\right)\\ t_2 := \mathsf{max}\left(\mathsf{max}\left(z, t\right), \mathsf{max}\left(\mathsf{min}\left(z, t\right), a\right)\right)\\ \mathbf{if}\;b \leq -7.2 \cdot 10^{+172}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{+246}:\\ \;\;\;\;\left(1 + \frac{\mathsf{min}\left(\mathsf{min}\left(z, t\right), a\right)}{t\_2}\right) \cdot t\_2 + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  (let* ((t_1 (- (* -1.0 (* b (log c)))))
       (t_2 (fmax (fmax z t) (fmax (fmin z t) a))))
  (if (<= b -7.2e+172)
    t_1
    (if (<= b 6.2e+246)
      (+ (* (+ 1.0 (/ (fmin (fmin z t) a) t_2)) t_2) (* y i))
      t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -(-1.0 * (b * log(c)));
	double t_2 = fmax(fmax(z, t), fmax(fmin(z, t), a));
	double tmp;
	if (b <= -7.2e+172) {
		tmp = t_1;
	} else if (b <= 6.2e+246) {
		tmp = ((1.0 + (fmin(fmin(z, t), a) / t_2)) * t_2) + (y * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = -((-1.0d0) * (b * log(c)))
    t_2 = fmax(fmax(z, t), fmax(fmin(z, t), a))
    if (b <= (-7.2d+172)) then
        tmp = t_1
    else if (b <= 6.2d+246) then
        tmp = ((1.0d0 + (fmin(fmin(z, t), a) / t_2)) * t_2) + (y * i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -(-1.0 * (b * Math.log(c)));
	double t_2 = fmax(fmax(z, t), fmax(fmin(z, t), a));
	double tmp;
	if (b <= -7.2e+172) {
		tmp = t_1;
	} else if (b <= 6.2e+246) {
		tmp = ((1.0 + (fmin(fmin(z, t), a) / t_2)) * t_2) + (y * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = -(-1.0 * (b * math.log(c)))
	t_2 = fmax(fmax(z, t), fmax(fmin(z, t), a))
	tmp = 0
	if b <= -7.2e+172:
		tmp = t_1
	elif b <= 6.2e+246:
		tmp = ((1.0 + (fmin(fmin(z, t), a) / t_2)) * t_2) + (y * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(-Float64(-1.0 * Float64(b * log(c))))
	t_2 = fmax(fmax(z, t), fmax(fmin(z, t), a))
	tmp = 0.0
	if (b <= -7.2e+172)
		tmp = t_1;
	elseif (b <= 6.2e+246)
		tmp = Float64(Float64(Float64(1.0 + Float64(fmin(fmin(z, t), a) / t_2)) * t_2) + Float64(y * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = -(-1.0 * (b * log(c)));
	t_2 = max(max(z, t), max(min(z, t), a));
	tmp = 0.0;
	if (b <= -7.2e+172)
		tmp = t_1;
	elseif (b <= 6.2e+246)
		tmp = ((1.0 + (min(min(z, t), a) / t_2)) * t_2) + (y * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = (-N[(-1.0 * N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision])}, Block[{t$95$2 = N[Max[N[Max[z, t], $MachinePrecision], N[Max[N[Min[z, t], $MachinePrecision], a], $MachinePrecision]], $MachinePrecision]}, If[LessEqual[b, -7.2e+172], t$95$1, If[LessEqual[b, 6.2e+246], N[(N[(N[(1.0 + N[(N[Min[N[Min[z, t], $MachinePrecision], a], $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if b < -7.1999999999999995e172 or 6.1999999999999998e246 < b

   1. Initial program 99.8%

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

   2. Taylor expanded in i around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

   4. Applied rewrites 68.9%

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

   5. Taylor expanded in a around inf

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

      1. lower-*.f64 16.6%

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

   7. Applied rewrites 16.6%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 16.6%

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

      4. lift-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 16.6%

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

   9. Applied rewrites 16.6%

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

   10. Taylor expanded in b around inf

       \[\leadsto --1 \cdot \left(b \cdot \log c\right) \]
   11. Step-by-step derivation

       1. lower-*.f64 N/A

          \[\leadsto --1 \cdot \left(b \cdot \log c\right) \]

       2. lower-*.f64 N/A

          \[\leadsto --1 \cdot \left(b \cdot \log c\right) \]

       3. lower-log.f64 16.4%

          \[\leadsto --1 \cdot \left(b \cdot \log c\right) \]

   12. Applied rewrites 16.4%

       \[\leadsto --1 \cdot \left(b \cdot \log c\right) \]

   if -7.1999999999999995e172 < b < 6.1999999999999998e246

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. sum-to-mult N/A

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

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

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

   3. Applied rewrites 73.7%

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

   4. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-log.f64 46.5%

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

   6. Applied rewrites 46.5%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 46.5%

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

   8. Applied rewrites 46.5%

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

   9. Taylor expanded in z around inf

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

       1. lower-/.f64 46.7%

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

   11. Applied rewrites 46.7%

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

Alternative 9: 61.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{max}\left(\mathsf{max}\left(z, t\right), \mathsf{max}\left(\mathsf{min}\left(z, t\right), a\right)\right)\\ t_2 := \mathsf{min}\left(\mathsf{min}\left(z, t\right), a\right)\\ \mathbf{if}\;t\_2 \leq -1.75 \cdot 10^{+280}:\\ \;\;\;\;--1 \cdot t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(1 + \frac{t\_2}{t\_1}\right) \cdot t\_1 + y \cdot i\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  (let* ((t_1 (fmax (fmax z t) (fmax (fmin z t) a)))
       (t_2 (fmin (fmin z t) a)))
  (if (<= t_2 -1.75e+280)
    (- (* -1.0 t_2))
    (+ (* (+ 1.0 (/ t_2 t_1)) t_1) (* y i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fmax(fmax(z, t), fmax(fmin(z, t), a));
	double t_2 = fmin(fmin(z, t), a);
	double tmp;
	if (t_2 <= -1.75e+280) {
		tmp = -(-1.0 * t_2);
	} else {
		tmp = ((1.0 + (t_2 / t_1)) * t_1) + (y * i);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = fmax(fmax(z, t), fmax(fmin(z, t), a))
    t_2 = fmin(fmin(z, t), a)
    if (t_2 <= (-1.75d+280)) then
        tmp = -((-1.0d0) * t_2)
    else
        tmp = ((1.0d0 + (t_2 / t_1)) * t_1) + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fmax(fmax(z, t), fmax(fmin(z, t), a));
	double t_2 = fmin(fmin(z, t), a);
	double tmp;
	if (t_2 <= -1.75e+280) {
		tmp = -(-1.0 * t_2);
	} else {
		tmp = ((1.0 + (t_2 / t_1)) * t_1) + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = fmax(fmax(z, t), fmax(fmin(z, t), a))
	t_2 = fmin(fmin(z, t), a)
	tmp = 0
	if t_2 <= -1.75e+280:
		tmp = -(-1.0 * t_2)
	else:
		tmp = ((1.0 + (t_2 / t_1)) * t_1) + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fmax(fmax(z, t), fmax(fmin(z, t), a))
	t_2 = fmin(fmin(z, t), a)
	tmp = 0.0
	if (t_2 <= -1.75e+280)
		tmp = Float64(-Float64(-1.0 * t_2));
	else
		tmp = Float64(Float64(Float64(1.0 + Float64(t_2 / t_1)) * t_1) + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = max(max(z, t), max(min(z, t), a));
	t_2 = min(min(z, t), a);
	tmp = 0.0;
	if (t_2 <= -1.75e+280)
		tmp = -(-1.0 * t_2);
	else
		tmp = ((1.0 + (t_2 / t_1)) * t_1) + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[Max[N[Max[z, t], $MachinePrecision], N[Max[N[Min[z, t], $MachinePrecision], a], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[Min[N[Min[z, t], $MachinePrecision], a], $MachinePrecision]}, If[LessEqual[t$95$2, -1.75e+280], (-N[(-1.0 * t$95$2), $MachinePrecision]), N[(N[(N[(1.0 + N[(t$95$2 / t$95$1), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7500000000000001e280

   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 i around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

   4. Applied rewrites 68.9%

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

   5. Taylor expanded in a around inf

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

      1. lower-*.f64 16.6%

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

   7. Applied rewrites 16.6%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 16.6%

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

      4. lift-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 16.6%

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

   9. Applied rewrites 16.6%

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

   10. Taylor expanded in z around inf

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

       1. lower-*.f64 16.0%

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

   12. Applied rewrites 16.0%

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

   if -1.7500000000000001e280 < z

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. sum-to-mult N/A

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

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

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

   3. Applied rewrites 73.7%

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

   4. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-log.f64 46.5%

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

   6. Applied rewrites 46.5%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 46.5%

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

   8. Applied rewrites 46.5%

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

   9. Taylor expanded in z around inf

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

       1. lower-/.f64 46.7%

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

   11. Applied rewrites 46.7%

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

Alternative 10: 61.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{min}\left(\mathsf{min}\left(z, t\right), a\right)\\ t_2 := \mathsf{max}\left(\mathsf{min}\left(z, t\right), a\right)\\ t_3 := \mathsf{min}\left(\mathsf{max}\left(z, t\right), t\_2\right)\\ t_4 := \mathsf{max}\left(\mathsf{max}\left(z, t\right), t\_2\right)\\ t_5 := \left(1 + \frac{t\_3}{t\_4}\right) \cdot t\_4 + y \cdot i\\ t_6 := \left(\left(\left(\left(x \cdot \log y + t\_1\right) + t\_3\right) + t\_4\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{if}\;t\_6 \leq -4 \cdot 10^{+306}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;t\_6 \leq -2 \cdot 10^{+33}:\\ \;\;\;\;--1 \cdot t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_5\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  (let* ((t_1 (fmin (fmin z t) a))
       (t_2 (fmax (fmin z t) a))
       (t_3 (fmin (fmax z t) t_2))
       (t_4 (fmax (fmax z t) t_2))
       (t_5 (+ (* (+ 1.0 (/ t_3 t_4)) t_4) (* y i)))
       (t_6
        (+
         (+
          (+ (+ (+ (* x (log y)) t_1) t_3) t_4)
          (* (- b 0.5) (log c)))
         (* y i))))
  (if (<= t_6 -4e+306) t_5 (if (<= t_6 -2e+33) (- (* -1.0 t_1)) t_5))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fmin(fmin(z, t), a);
	double t_2 = fmax(fmin(z, t), a);
	double t_3 = fmin(fmax(z, t), t_2);
	double t_4 = fmax(fmax(z, t), t_2);
	double t_5 = ((1.0 + (t_3 / t_4)) * t_4) + (y * i);
	double t_6 = (((((x * log(y)) + t_1) + t_3) + t_4) + ((b - 0.5) * log(c))) + (y * i);
	double tmp;
	if (t_6 <= -4e+306) {
		tmp = t_5;
	} else if (t_6 <= -2e+33) {
		tmp = -(-1.0 * t_1);
	} else {
		tmp = t_5;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = fmin(fmin(z, t), a)
    t_2 = fmax(fmin(z, t), a)
    t_3 = fmin(fmax(z, t), t_2)
    t_4 = fmax(fmax(z, t), t_2)
    t_5 = ((1.0d0 + (t_3 / t_4)) * t_4) + (y * i)
    t_6 = (((((x * log(y)) + t_1) + t_3) + t_4) + ((b - 0.5d0) * log(c))) + (y * i)
    if (t_6 <= (-4d+306)) then
        tmp = t_5
    else if (t_6 <= (-2d+33)) then
        tmp = -((-1.0d0) * t_1)
    else
        tmp = t_5
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fmin(fmin(z, t), a);
	double t_2 = fmax(fmin(z, t), a);
	double t_3 = fmin(fmax(z, t), t_2);
	double t_4 = fmax(fmax(z, t), t_2);
	double t_5 = ((1.0 + (t_3 / t_4)) * t_4) + (y * i);
	double t_6 = (((((x * Math.log(y)) + t_1) + t_3) + t_4) + ((b - 0.5) * Math.log(c))) + (y * i);
	double tmp;
	if (t_6 <= -4e+306) {
		tmp = t_5;
	} else if (t_6 <= -2e+33) {
		tmp = -(-1.0 * t_1);
	} else {
		tmp = t_5;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = fmin(fmin(z, t), a)
	t_2 = fmax(fmin(z, t), a)
	t_3 = fmin(fmax(z, t), t_2)
	t_4 = fmax(fmax(z, t), t_2)
	t_5 = ((1.0 + (t_3 / t_4)) * t_4) + (y * i)
	t_6 = (((((x * math.log(y)) + t_1) + t_3) + t_4) + ((b - 0.5) * math.log(c))) + (y * i)
	tmp = 0
	if t_6 <= -4e+306:
		tmp = t_5
	elif t_6 <= -2e+33:
		tmp = -(-1.0 * t_1)
	else:
		tmp = t_5
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fmin(fmin(z, t), a)
	t_2 = fmax(fmin(z, t), a)
	t_3 = fmin(fmax(z, t), t_2)
	t_4 = fmax(fmax(z, t), t_2)
	t_5 = Float64(Float64(Float64(1.0 + Float64(t_3 / t_4)) * t_4) + Float64(y * i))
	t_6 = Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + t_1) + t_3) + t_4) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i))
	tmp = 0.0
	if (t_6 <= -4e+306)
		tmp = t_5;
	elseif (t_6 <= -2e+33)
		tmp = Float64(-Float64(-1.0 * t_1));
	else
		tmp = t_5;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = min(min(z, t), a);
	t_2 = max(min(z, t), a);
	t_3 = min(max(z, t), t_2);
	t_4 = max(max(z, t), t_2);
	t_5 = ((1.0 + (t_3 / t_4)) * t_4) + (y * i);
	t_6 = (((((x * log(y)) + t_1) + t_3) + t_4) + ((b - 0.5) * log(c))) + (y * i);
	tmp = 0.0;
	if (t_6 <= -4e+306)
		tmp = t_5;
	elseif (t_6 <= -2e+33)
		tmp = -(-1.0 * t_1);
	else
		tmp = t_5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[Min[N[Min[z, t], $MachinePrecision], a], $MachinePrecision]}, Block[{t$95$2 = N[Max[N[Min[z, t], $MachinePrecision], a], $MachinePrecision]}, Block[{t$95$3 = N[Min[N[Max[z, t], $MachinePrecision], t$95$2], $MachinePrecision]}, Block[{t$95$4 = N[Max[N[Max[z, t], $MachinePrecision], t$95$2], $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(1.0 + N[(t$95$3 / t$95$4), $MachinePrecision]), $MachinePrecision] * t$95$4), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] + t$95$3), $MachinePrecision] + t$95$4), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$6, -4e+306], t$95$5, If[LessEqual[t$95$6, -2e+33], (-N[(-1.0 * t$95$1), $MachinePrecision]), t$95$5]]]]]]]]

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)) < -4.0000000000000001e306 or -1.9999999999999999e33 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i))

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. sum-to-mult N/A

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

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

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

   3. Applied rewrites 73.7%

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

   4. Taylor expanded in t around inf

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

      1. lower-/.f64 46.8%

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

   6. Applied rewrites 46.8%

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

   if -4.0000000000000001e306 < (+.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)) < -1.9999999999999999e33

   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 i around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

   4. Applied rewrites 68.9%

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

   5. Taylor expanded in a around inf

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

      1. lower-*.f64 16.6%

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

   7. Applied rewrites 16.6%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 16.6%

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

      4. lift-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 16.6%

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

   9. Applied rewrites 16.6%

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

   10. Taylor expanded in z around inf

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

       1. lower-*.f64 16.0%

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

   12. Applied rewrites 16.0%

       \[\leadsto --1 \cdot z \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 58.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{min}\left(\mathsf{min}\left(z, t\right), a\right)\\ t_2 := \mathsf{max}\left(\mathsf{min}\left(z, t\right), a\right)\\ t_3 := \mathsf{max}\left(\mathsf{max}\left(z, t\right), t\_2\right)\\ t_4 := \left(\left(\left(\left(x \cdot \log y + t\_1\right) + \mathsf{min}\left(\mathsf{max}\left(z, t\right), t\_2\right)\right) + t\_3\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{if}\;t\_4 \leq -\infty:\\ \;\;\;\;--1 \cdot \left(i \cdot y\right)\\ \mathbf{elif}\;t\_4 \leq -2 \cdot 10^{+33}:\\ \;\;\;\;--1 \cdot t\_1\\ \mathbf{else}:\\ \;\;\;\;1 \cdot t\_3 + y \cdot i\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  (let* ((t_1 (fmin (fmin z t) a))
       (t_2 (fmax (fmin z t) a))
       (t_3 (fmax (fmax z t) t_2))
       (t_4
        (+
         (+
          (+ (+ (+ (* x (log y)) t_1) (fmin (fmax z t) t_2)) t_3)
          (* (- b 0.5) (log c)))
         (* y i))))
  (if (<= t_4 (- INFINITY))
    (- (* -1.0 (* i y)))
    (if (<= t_4 -2e+33) (- (* -1.0 t_1)) (+ (* 1.0 t_3) (* y i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fmin(fmin(z, t), a);
	double t_2 = fmax(fmin(z, t), a);
	double t_3 = fmax(fmax(z, t), t_2);
	double t_4 = (((((x * log(y)) + t_1) + fmin(fmax(z, t), t_2)) + t_3) + ((b - 0.5) * log(c))) + (y * i);
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = -(-1.0 * (i * y));
	} else if (t_4 <= -2e+33) {
		tmp = -(-1.0 * t_1);
	} else {
		tmp = (1.0 * t_3) + (y * i);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fmin(fmin(z, t), a);
	double t_2 = fmax(fmin(z, t), a);
	double t_3 = fmax(fmax(z, t), t_2);
	double t_4 = (((((x * Math.log(y)) + t_1) + fmin(fmax(z, t), t_2)) + t_3) + ((b - 0.5) * Math.log(c))) + (y * i);
	double tmp;
	if (t_4 <= -Double.POSITIVE_INFINITY) {
		tmp = -(-1.0 * (i * y));
	} else if (t_4 <= -2e+33) {
		tmp = -(-1.0 * t_1);
	} else {
		tmp = (1.0 * t_3) + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = fmin(fmin(z, t), a)
	t_2 = fmax(fmin(z, t), a)
	t_3 = fmax(fmax(z, t), t_2)
	t_4 = (((((x * math.log(y)) + t_1) + fmin(fmax(z, t), t_2)) + t_3) + ((b - 0.5) * math.log(c))) + (y * i)
	tmp = 0
	if t_4 <= -math.inf:
		tmp = -(-1.0 * (i * y))
	elif t_4 <= -2e+33:
		tmp = -(-1.0 * t_1)
	else:
		tmp = (1.0 * t_3) + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fmin(fmin(z, t), a)
	t_2 = fmax(fmin(z, t), a)
	t_3 = fmax(fmax(z, t), t_2)
	t_4 = Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + t_1) + fmin(fmax(z, t), t_2)) + t_3) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i))
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = Float64(-Float64(-1.0 * Float64(i * y)));
	elseif (t_4 <= -2e+33)
		tmp = Float64(-Float64(-1.0 * t_1));
	else
		tmp = Float64(Float64(1.0 * t_3) + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = min(min(z, t), a);
	t_2 = max(min(z, t), a);
	t_3 = max(max(z, t), t_2);
	t_4 = (((((x * log(y)) + t_1) + min(max(z, t), t_2)) + t_3) + ((b - 0.5) * log(c))) + (y * i);
	tmp = 0.0;
	if (t_4 <= -Inf)
		tmp = -(-1.0 * (i * y));
	elseif (t_4 <= -2e+33)
		tmp = -(-1.0 * t_1);
	else
		tmp = (1.0 * t_3) + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[Min[N[Min[z, t], $MachinePrecision], a], $MachinePrecision]}, Block[{t$95$2 = N[Max[N[Min[z, t], $MachinePrecision], a], $MachinePrecision]}, Block[{t$95$3 = N[Max[N[Max[z, t], $MachinePrecision], t$95$2], $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] + N[Min[N[Max[z, t], $MachinePrecision], t$95$2], $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], (-N[(-1.0 * N[(i * y), $MachinePrecision]), $MachinePrecision]), If[LessEqual[t$95$4, -2e+33], (-N[(-1.0 * t$95$1), $MachinePrecision]), N[(N[(1.0 * t$95$3), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 99.8%

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

   2. Taylor expanded in i around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

   4. Applied rewrites 68.9%

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

   5. Taylor expanded in a around inf

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

      1. lower-*.f64 16.6%

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

   7. Applied rewrites 16.6%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 16.6%

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

      4. lift-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 16.6%

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

   9. Applied rewrites 16.6%

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

   10. Taylor expanded in y around inf

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

       1. lower-*.f64 N/A

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

       2. lower-*.f64 24.8%

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

   12. Applied rewrites 24.8%

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

   if -inf.0 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < -1.9999999999999999e33

   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 i around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

   4. Applied rewrites 68.9%

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

   5. Taylor expanded in a around inf

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

      1. lower-*.f64 16.6%

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

   7. Applied rewrites 16.6%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 16.6%

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

      4. lift-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 16.6%

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

   9. Applied rewrites 16.6%

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

   10. Taylor expanded in z around inf

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

       1. lower-*.f64 16.0%

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

   12. Applied rewrites 16.0%

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

   if -1.9999999999999999e33 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i))

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. sum-to-mult N/A

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

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

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

   3. Applied rewrites 73.7%

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

   4. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-log.f64 46.5%

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

   6. Applied rewrites 46.5%

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

   7. Taylor expanded in a around inf

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

   9. Applied rewrites 39.3%

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

Alternative 12: 57.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{min}\left(\mathsf{min}\left(z, t\right), a\right)\\ t_2 := --1 \cdot \left(i \cdot y\right)\\ t_3 := \mathsf{max}\left(\mathsf{min}\left(z, t\right), a\right)\\ t_4 := \mathsf{max}\left(\mathsf{max}\left(z, t\right), t\_3\right)\\ t_5 := \left(\left(\left(\left(x \cdot \log y + t\_1\right) + \mathsf{min}\left(\mathsf{max}\left(z, t\right), t\_3\right)\right) + t\_4\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{if}\;t\_5 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_5 \leq -50:\\ \;\;\;\;--1 \cdot t\_1\\ \mathbf{elif}\;t\_5 \leq 10^{+308}:\\ \;\;\;\;-\left(-t\_4\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  (let* ((t_1 (fmin (fmin z t) a))
       (t_2 (- (* -1.0 (* i y))))
       (t_3 (fmax (fmin z t) a))
       (t_4 (fmax (fmax z t) t_3))
       (t_5
        (+
         (+
          (+ (+ (+ (* x (log y)) t_1) (fmin (fmax z t) t_3)) t_4)
          (* (- b 0.5) (log c)))
         (* y i))))
  (if (<= t_5 (- INFINITY))
    t_2
    (if (<= t_5 -50.0)
      (- (* -1.0 t_1))
      (if (<= t_5 1e+308) (- (- t_4)) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fmin(fmin(z, t), a);
	double t_2 = -(-1.0 * (i * y));
	double t_3 = fmax(fmin(z, t), a);
	double t_4 = fmax(fmax(z, t), t_3);
	double t_5 = (((((x * log(y)) + t_1) + fmin(fmax(z, t), t_3)) + t_4) + ((b - 0.5) * log(c))) + (y * i);
	double tmp;
	if (t_5 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_5 <= -50.0) {
		tmp = -(-1.0 * t_1);
	} else if (t_5 <= 1e+308) {
		tmp = -(-t_4);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fmin(fmin(z, t), a);
	double t_2 = -(-1.0 * (i * y));
	double t_3 = fmax(fmin(z, t), a);
	double t_4 = fmax(fmax(z, t), t_3);
	double t_5 = (((((x * Math.log(y)) + t_1) + fmin(fmax(z, t), t_3)) + t_4) + ((b - 0.5) * Math.log(c))) + (y * i);
	double tmp;
	if (t_5 <= -Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else if (t_5 <= -50.0) {
		tmp = -(-1.0 * t_1);
	} else if (t_5 <= 1e+308) {
		tmp = -(-t_4);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = fmin(fmin(z, t), a)
	t_2 = -(-1.0 * (i * y))
	t_3 = fmax(fmin(z, t), a)
	t_4 = fmax(fmax(z, t), t_3)
	t_5 = (((((x * math.log(y)) + t_1) + fmin(fmax(z, t), t_3)) + t_4) + ((b - 0.5) * math.log(c))) + (y * i)
	tmp = 0
	if t_5 <= -math.inf:
		tmp = t_2
	elif t_5 <= -50.0:
		tmp = -(-1.0 * t_1)
	elif t_5 <= 1e+308:
		tmp = -(-t_4)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fmin(fmin(z, t), a)
	t_2 = Float64(-Float64(-1.0 * Float64(i * y)))
	t_3 = fmax(fmin(z, t), a)
	t_4 = fmax(fmax(z, t), t_3)
	t_5 = Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + t_1) + fmin(fmax(z, t), t_3)) + t_4) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i))
	tmp = 0.0
	if (t_5 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_5 <= -50.0)
		tmp = Float64(-Float64(-1.0 * t_1));
	elseif (t_5 <= 1e+308)
		tmp = Float64(-Float64(-t_4));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = min(min(z, t), a);
	t_2 = -(-1.0 * (i * y));
	t_3 = max(min(z, t), a);
	t_4 = max(max(z, t), t_3);
	t_5 = (((((x * log(y)) + t_1) + min(max(z, t), t_3)) + t_4) + ((b - 0.5) * log(c))) + (y * i);
	tmp = 0.0;
	if (t_5 <= -Inf)
		tmp = t_2;
	elseif (t_5 <= -50.0)
		tmp = -(-1.0 * t_1);
	elseif (t_5 <= 1e+308)
		tmp = -(-t_4);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[Min[N[Min[z, t], $MachinePrecision], a], $MachinePrecision]}, Block[{t$95$2 = (-N[(-1.0 * N[(i * y), $MachinePrecision]), $MachinePrecision])}, Block[{t$95$3 = N[Max[N[Min[z, t], $MachinePrecision], a], $MachinePrecision]}, Block[{t$95$4 = N[Max[N[Max[z, t], $MachinePrecision], t$95$3], $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] + N[Min[N[Max[z, t], $MachinePrecision], t$95$3], $MachinePrecision]), $MachinePrecision] + t$95$4), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$5, (-Infinity)], t$95$2, If[LessEqual[t$95$5, -50.0], (-N[(-1.0 * t$95$1), $MachinePrecision]), If[LessEqual[t$95$5, 1e+308], (-(-t$95$4)), t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < -inf.0 or 1e308 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i))

   1. Initial program 99.8%

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

   2. Taylor expanded in i around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

   4. Applied rewrites 68.9%

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

   5. Taylor expanded in a around inf

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

      1. lower-*.f64 16.6%

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

   7. Applied rewrites 16.6%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 16.6%

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

      4. lift-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 16.6%

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

   9. Applied rewrites 16.6%

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

   10. Taylor expanded in y around inf

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

       1. lower-*.f64 N/A

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

       2. lower-*.f64 24.8%

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

   12. Applied rewrites 24.8%

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

   if -inf.0 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < -50

   1. Initial program 99.8%

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

   2. Taylor expanded in i around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

   4. Applied rewrites 68.9%

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

   5. Taylor expanded in a around inf

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

      1. lower-*.f64 16.6%

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

   7. Applied rewrites 16.6%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 16.6%

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

      4. lift-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 16.6%

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

   9. Applied rewrites 16.6%

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

   10. Taylor expanded in z around inf

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

       1. lower-*.f64 16.0%

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

   12. Applied rewrites 16.0%

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

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

   1. Initial program 99.8%

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

   2. Taylor expanded in i around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

   4. Applied rewrites 68.9%

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

   5. Taylor expanded in a around inf

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

      1. lower-*.f64 16.6%

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

   7. Applied rewrites 16.6%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 16.6%

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

      4. lift-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 16.6%

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

   9. Applied rewrites 16.6%

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

Alternative 13: 44.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{min}\left(\mathsf{min}\left(z, t\right), a\right)\\ t_2 := \mathsf{max}\left(\mathsf{min}\left(z, t\right), a\right)\\ t_3 := \mathsf{max}\left(\mathsf{max}\left(z, t\right), t\_2\right)\\ \mathbf{if}\;\left(\left(\left(\left(x \cdot \log y + t\_1\right) + \mathsf{min}\left(\mathsf{max}\left(z, t\right), t\_2\right)\right) + t\_3\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \leq -50:\\ \;\;\;\;--1 \cdot t\_1\\ \mathbf{else}:\\ \;\;\;\;-\left(-t\_3\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  (let* ((t_1 (fmin (fmin z t) a))
       (t_2 (fmax (fmin z t) a))
       (t_3 (fmax (fmax z t) t_2)))
  (if (<=
       (+
        (+
         (+ (+ (+ (* x (log y)) t_1) (fmin (fmax z t) t_2)) t_3)
         (* (- b 0.5) (log c)))
        (* y i))
       -50.0)
    (- (* -1.0 t_1))
    (- (- t_3)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fmin(fmin(z, t), a);
	double t_2 = fmax(fmin(z, t), a);
	double t_3 = fmax(fmax(z, t), t_2);
	double tmp;
	if (((((((x * log(y)) + t_1) + fmin(fmax(z, t), t_2)) + t_3) + ((b - 0.5) * log(c))) + (y * i)) <= -50.0) {
		tmp = -(-1.0 * t_1);
	} else {
		tmp = -(-t_3);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = fmin(fmin(z, t), a)
    t_2 = fmax(fmin(z, t), a)
    t_3 = fmax(fmax(z, t), t_2)
    if (((((((x * log(y)) + t_1) + fmin(fmax(z, t), t_2)) + t_3) + ((b - 0.5d0) * log(c))) + (y * i)) <= (-50.0d0)) then
        tmp = -((-1.0d0) * t_1)
    else
        tmp = -(-t_3)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fmin(fmin(z, t), a);
	double t_2 = fmax(fmin(z, t), a);
	double t_3 = fmax(fmax(z, t), t_2);
	double tmp;
	if (((((((x * Math.log(y)) + t_1) + fmin(fmax(z, t), t_2)) + t_3) + ((b - 0.5) * Math.log(c))) + (y * i)) <= -50.0) {
		tmp = -(-1.0 * t_1);
	} else {
		tmp = -(-t_3);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = fmin(fmin(z, t), a)
	t_2 = fmax(fmin(z, t), a)
	t_3 = fmax(fmax(z, t), t_2)
	tmp = 0
	if ((((((x * math.log(y)) + t_1) + fmin(fmax(z, t), t_2)) + t_3) + ((b - 0.5) * math.log(c))) + (y * i)) <= -50.0:
		tmp = -(-1.0 * t_1)
	else:
		tmp = -(-t_3)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fmin(fmin(z, t), a)
	t_2 = fmax(fmin(z, t), a)
	t_3 = fmax(fmax(z, t), t_2)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + t_1) + fmin(fmax(z, t), t_2)) + t_3) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i)) <= -50.0)
		tmp = Float64(-Float64(-1.0 * t_1));
	else
		tmp = Float64(-Float64(-t_3));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = min(min(z, t), a);
	t_2 = max(min(z, t), a);
	t_3 = max(max(z, t), t_2);
	tmp = 0.0;
	if (((((((x * log(y)) + t_1) + min(max(z, t), t_2)) + t_3) + ((b - 0.5) * log(c))) + (y * i)) <= -50.0)
		tmp = -(-1.0 * t_1);
	else
		tmp = -(-t_3);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[Min[N[Min[z, t], $MachinePrecision], a], $MachinePrecision]}, Block[{t$95$2 = N[Max[N[Min[z, t], $MachinePrecision], a], $MachinePrecision]}, Block[{t$95$3 = N[Max[N[Max[z, t], $MachinePrecision], t$95$2], $MachinePrecision]}, If[LessEqual[N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] + N[Min[N[Max[z, t], $MachinePrecision], t$95$2], $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], -50.0], (-N[(-1.0 * t$95$1), $MachinePrecision]), (-(-t$95$3))]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.8%

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

   2. Taylor expanded in i around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

   4. Applied rewrites 68.9%

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

   5. Taylor expanded in a around inf

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

      1. lower-*.f64 16.6%

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

   7. Applied rewrites 16.6%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 16.6%

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

      4. lift-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 16.6%

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

   9. Applied rewrites 16.6%

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

   10. Taylor expanded in z around inf

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

       1. lower-*.f64 16.0%

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

   12. Applied rewrites 16.0%

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

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

   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 i around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

   4. Applied rewrites 68.9%

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

   5. Taylor expanded in a around inf

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

      1. lower-*.f64 16.6%

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

   7. Applied rewrites 16.6%

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

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 16.6%

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

      4. lift-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 16.6%

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

   9. Applied rewrites 16.6%

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

Alternative 14: 22.6% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := (-(-N[Max[t, N[Max[z, a], $MachinePrecision]], $MachinePrecision]))

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in i around -inf

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

   1. lower-*.f64 N/A

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

   2. lower-*.f64 N/A

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

   3. lower-+.f64 N/A

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

   4. lower-*.f64 N/A

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

   5. lower-*.f64 N/A

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

   6. lower-/.f64 N/A

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

4. Applied rewrites 68.9%

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

5. Taylor expanded in a around inf

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

   1. lower-*.f64 16.6%

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

7. Applied rewrites 16.6%

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

   1. lift-*.f64 N/A

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

   2. mul-1-neg N/A

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

   3. lower-neg.f64 16.6%

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

   4. lift-*.f64 N/A

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

   5. mul-1-neg N/A

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

   6. lower-neg.f64 16.6%

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

9. Applied rewrites 16.6%

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

Reproduce

herbie shell --seed 2025258 
(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)))