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

Percentage Accurate: 99.8% → 99.8%

Time: 22.6s

Alternatives: 15

Speedup: 1.0×

Specification

Math

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

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 1/2) (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 - 1/2), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 1/2) (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 - 1/2), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]

Alternative 1: 95.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{min}\left(\mathsf{min}\left(z, t\right), a\right)\\ t_2 := x \cdot \log y\\ t_3 := \mathsf{max}\left(\mathsf{min}\left(z, t\right), a\right)\\ t_4 := \mathsf{max}\left(\mathsf{max}\left(z, t\right), t\_3\right)\\ \mathbf{if}\;t\_4 \leq 879999999999999958507063942391341293078620439980425991327011484655074736196101580184131712581632:\\ \;\;\;\;\left(\mathsf{min}\left(\mathsf{max}\left(z, t\right), t\_3\right) + \left(t\_1 + \left(t\_2 + \log c \cdot \left(b - \frac{1}{2}\right)\right)\right)\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;\left(\left(t\_4 + \left(t\_1 + t\_2\right)\right) + \frac{-1}{2} \cdot \log c\right) + y \cdot i\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  (let* ((t_1 (fmin (fmin z t) a))
       (t_2 (* x (log y)))
       (t_3 (fmax (fmin z t) a))
       (t_4 (fmax (fmax z t) t_3)))
  (if (<=
       t_4
       879999999999999958507063942391341293078620439980425991327011484655074736196101580184131712581632)
    (+
     (+ (fmin (fmax z t) t_3) (+ t_1 (+ t_2 (* (log c) (- b 1/2)))))
     (* y i))
    (+ (+ (+ t_4 (+ t_1 t_2)) (* -1/2 (log c))) (* 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 = x * log(y);
	double t_3 = fmax(fmin(z, t), a);
	double t_4 = fmax(fmax(z, t), t_3);
	double tmp;
	if (t_4 <= 8.8e+95) {
		tmp = (fmin(fmax(z, t), t_3) + (t_1 + (t_2 + (log(c) * (b - 0.5))))) + (y * i);
	} else {
		tmp = ((t_4 + (t_1 + t_2)) + (-0.5 * log(c))) + (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) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = fmin(fmin(z, t), a)
    t_2 = x * log(y)
    t_3 = fmax(fmin(z, t), a)
    t_4 = fmax(fmax(z, t), t_3)
    if (t_4 <= 8.8d+95) then
        tmp = (fmin(fmax(z, t), t_3) + (t_1 + (t_2 + (log(c) * (b - 0.5d0))))) + (y * i)
    else
        tmp = ((t_4 + (t_1 + t_2)) + ((-0.5d0) * log(c))) + (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 = fmin(fmin(z, t), a);
	double t_2 = x * Math.log(y);
	double t_3 = fmax(fmin(z, t), a);
	double t_4 = fmax(fmax(z, t), t_3);
	double tmp;
	if (t_4 <= 8.8e+95) {
		tmp = (fmin(fmax(z, t), t_3) + (t_1 + (t_2 + (Math.log(c) * (b - 0.5))))) + (y * i);
	} else {
		tmp = ((t_4 + (t_1 + t_2)) + (-0.5 * Math.log(c))) + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = fmin(fmin(z, t), a)
	t_2 = x * math.log(y)
	t_3 = fmax(fmin(z, t), a)
	t_4 = fmax(fmax(z, t), t_3)
	tmp = 0
	if t_4 <= 8.8e+95:
		tmp = (fmin(fmax(z, t), t_3) + (t_1 + (t_2 + (math.log(c) * (b - 0.5))))) + (y * i)
	else:
		tmp = ((t_4 + (t_1 + t_2)) + (-0.5 * math.log(c))) + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fmin(fmin(z, t), a)
	t_2 = Float64(x * log(y))
	t_3 = fmax(fmin(z, t), a)
	t_4 = fmax(fmax(z, t), t_3)
	tmp = 0.0
	if (t_4 <= 8.8e+95)
		tmp = Float64(Float64(fmin(fmax(z, t), t_3) + Float64(t_1 + Float64(t_2 + Float64(log(c) * Float64(b - 0.5))))) + Float64(y * i));
	else
		tmp = Float64(Float64(Float64(t_4 + Float64(t_1 + t_2)) + Float64(-0.5 * log(c))) + 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 = x * log(y);
	t_3 = max(min(z, t), a);
	t_4 = max(max(z, t), t_3);
	tmp = 0.0;
	if (t_4 <= 8.8e+95)
		tmp = (min(max(z, t), t_3) + (t_1 + (t_2 + (log(c) * (b - 0.5))))) + (y * i);
	else
		tmp = ((t_4 + (t_1 + t_2)) + (-0.5 * log(c))) + (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[(x * N[Log[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]}, If[LessEqual[t$95$4, 879999999999999958507063942391341293078620439980425991327011484655074736196101580184131712581632], N[(N[(N[Min[N[Max[z, t], $MachinePrecision], t$95$3], $MachinePrecision] + N[(t$95$1 + N[(t$95$2 + N[(N[Log[c], $MachinePrecision] * N[(b - 1/2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t$95$4 + N[(t$95$1 + t$95$2), $MachinePrecision]), $MachinePrecision] + N[(-1/2 * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 2 regimes

2. if a < 8.7999999999999996e95

   1. Initial program 99.8%

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

   2. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-log.f64 N/A

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

      8. lower--.f64 83.8%

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

   4. Applied rewrites 83.8%

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

   if 8.7999999999999996e95 < a

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 84.5%

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

   5. Taylor expanded in b around 0

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

   7. Applied rewrites 69.8%

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

   8. Taylor expanded in t around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-log.f64 69.0%

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

   10. Applied rewrites 69.0%

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

Alternative 2: 92.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{max}\left(\mathsf{min}\left(z, t\right), a\right)\\ t_2 := \mathsf{min}\left(\mathsf{min}\left(z, t\right), a\right)\\ t_3 := \mathsf{max}\left(\mathsf{max}\left(z, t\right), t\_1\right)\\ t_4 := \left(\left(t\_3 + \left(t\_2 + x \cdot \log y\right)\right) + \frac{-1}{2} \cdot \log c\right) + y \cdot i\\ \mathbf{if}\;x \leq -3550000000000000150029738640376626954316728168075833588523823906463939223777785428892323454743652302061568:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x \leq 1049999999999999974685639735482438568778688196460848270285520923497646456255682135894950006688309094612255899648:\\ \;\;\;\;\left(\left(\left(t\_2 + \mathsf{min}\left(\mathsf{max}\left(z, t\right), t\_1\right)\right) + t\_3\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  (let* ((t_1 (fmax (fmin z t) a))
       (t_2 (fmin (fmin z t) a))
       (t_3 (fmax (fmax z t) t_1))
       (t_4
        (+
         (+ (+ t_3 (+ t_2 (* x (log y)))) (* -1/2 (log c)))
         (* y i))))
  (if (<=
       x
       -3550000000000000150029738640376626954316728168075833588523823906463939223777785428892323454743652302061568)
    t_4
    (if (<=
         x
         1049999999999999974685639735482438568778688196460848270285520923497646456255682135894950006688309094612255899648)
      (+
       (+ (+ (+ t_2 (fmin (fmax z t) t_1)) t_3) (* (- b 1/2) (log c)))
       (* y i))
      t_4))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fmax(fmin(z, t), a);
	double t_2 = fmin(fmin(z, t), a);
	double t_3 = fmax(fmax(z, t), t_1);
	double t_4 = ((t_3 + (t_2 + (x * log(y)))) + (-0.5 * log(c))) + (y * i);
	double tmp;
	if (x <= -3.55e+105) {
		tmp = t_4;
	} else if (x <= 1.05e+111) {
		tmp = (((t_2 + fmin(fmax(z, t), t_1)) + t_3) + ((b - 0.5) * log(c))) + (y * i);
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = fmax(fmin(z, t), a)
    t_2 = fmin(fmin(z, t), a)
    t_3 = fmax(fmax(z, t), t_1)
    t_4 = ((t_3 + (t_2 + (x * log(y)))) + ((-0.5d0) * log(c))) + (y * i)
    if (x <= (-3.55d+105)) then
        tmp = t_4
    else if (x <= 1.05d+111) then
        tmp = (((t_2 + fmin(fmax(z, t), t_1)) + t_3) + ((b - 0.5d0) * log(c))) + (y * i)
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fmax(fmin(z, t), a);
	double t_2 = fmin(fmin(z, t), a);
	double t_3 = fmax(fmax(z, t), t_1);
	double t_4 = ((t_3 + (t_2 + (x * Math.log(y)))) + (-0.5 * Math.log(c))) + (y * i);
	double tmp;
	if (x <= -3.55e+105) {
		tmp = t_4;
	} else if (x <= 1.05e+111) {
		tmp = (((t_2 + fmin(fmax(z, t), t_1)) + t_3) + ((b - 0.5) * Math.log(c))) + (y * i);
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = fmax(fmin(z, t), a)
	t_2 = fmin(fmin(z, t), a)
	t_3 = fmax(fmax(z, t), t_1)
	t_4 = ((t_3 + (t_2 + (x * math.log(y)))) + (-0.5 * math.log(c))) + (y * i)
	tmp = 0
	if x <= -3.55e+105:
		tmp = t_4
	elif x <= 1.05e+111:
		tmp = (((t_2 + fmin(fmax(z, t), t_1)) + t_3) + ((b - 0.5) * math.log(c))) + (y * i)
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fmax(fmin(z, t), a)
	t_2 = fmin(fmin(z, t), a)
	t_3 = fmax(fmax(z, t), t_1)
	t_4 = Float64(Float64(Float64(t_3 + Float64(t_2 + Float64(x * log(y)))) + Float64(-0.5 * log(c))) + Float64(y * i))
	tmp = 0.0
	if (x <= -3.55e+105)
		tmp = t_4;
	elseif (x <= 1.05e+111)
		tmp = Float64(Float64(Float64(Float64(t_2 + fmin(fmax(z, t), t_1)) + t_3) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i));
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = max(min(z, t), a);
	t_2 = min(min(z, t), a);
	t_3 = max(max(z, t), t_1);
	t_4 = ((t_3 + (t_2 + (x * log(y)))) + (-0.5 * log(c))) + (y * i);
	tmp = 0.0;
	if (x <= -3.55e+105)
		tmp = t_4;
	elseif (x <= 1.05e+111)
		tmp = (((t_2 + min(max(z, t), t_1)) + t_3) + ((b - 0.5) * log(c))) + (y * i);
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[Max[N[Min[z, t], $MachinePrecision], a], $MachinePrecision]}, Block[{t$95$2 = N[Min[N[Min[z, t], $MachinePrecision], a], $MachinePrecision]}, Block[{t$95$3 = N[Max[N[Max[z, t], $MachinePrecision], t$95$1], $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$3 + N[(t$95$2 + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-1/2 * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3550000000000000150029738640376626954316728168075833588523823906463939223777785428892323454743652302061568], t$95$4, If[LessEqual[x, 1049999999999999974685639735482438568778688196460848270285520923497646456255682135894950006688309094612255899648], N[(N[(N[(N[(t$95$2 + N[Min[N[Max[z, t], $MachinePrecision], t$95$1], $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision] + N[(N[(b - 1/2), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.5500000000000002e105 or 1.05e111 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 84.5%

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

   5. Taylor expanded in b around 0

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

   7. Applied rewrites 69.8%

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

   8. Taylor expanded in t around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-log.f64 69.0%

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

   10. Applied rewrites 69.0%

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

   if -3.5500000000000002e105 < x < 1.05e111

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 84.5%

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

Alternative 3: 90.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{min}\left(t, \mathsf{max}\left(z, a\right)\right)\\ t_2 := x \cdot \log y\\ t_3 := \mathsf{max}\left(t, \mathsf{max}\left(z, a\right)\right)\\ \mathbf{if}\;x \leq -3599999999999999879581681787739427058599582932568556174433318048436749902375581436811618887180905028255744:\\ \;\;\;\;\left(t\_1 + \left(\mathsf{min}\left(z, a\right) + \left(t\_2 + \log c \cdot \frac{-1}{2}\right)\right)\right) + y \cdot i\\ \mathbf{elif}\;x \leq 1049999999999999974685639735482438568778688196460848270285520923497646456255682135894950006688309094612255899648:\\ \;\;\;\;\left(\left(\left(\mathsf{min}\left(z, a\right) + t\_1\right) + t\_3\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;\left(\left(t\_3 + t\_2\right) + \frac{-1}{2} \cdot \log c\right) + y \cdot i\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  (let* ((t_1 (fmin t (fmax z a)))
       (t_2 (* x (log y)))
       (t_3 (fmax t (fmax z a))))
  (if (<=
       x
       -3599999999999999879581681787739427058599582932568556174433318048436749902375581436811618887180905028255744)
    (+ (+ t_1 (+ (fmin z a) (+ t_2 (* (log c) -1/2)))) (* y i))
    (if (<=
         x
         1049999999999999974685639735482438568778688196460848270285520923497646456255682135894950006688309094612255899648)
      (+ (+ (+ (+ (fmin z a) t_1) t_3) (* (- b 1/2) (log c))) (* y i))
      (+ (+ (+ t_3 t_2) (* -1/2 (log c))) (* y i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fmin(t, fmax(z, a));
	double t_2 = x * log(y);
	double t_3 = fmax(t, fmax(z, a));
	double tmp;
	if (x <= -3.6e+105) {
		tmp = (t_1 + (fmin(z, a) + (t_2 + (log(c) * -0.5)))) + (y * i);
	} else if (x <= 1.05e+111) {
		tmp = (((fmin(z, a) + t_1) + t_3) + ((b - 0.5) * log(c))) + (y * i);
	} else {
		tmp = ((t_3 + t_2) + (-0.5 * log(c))) + (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) :: t_3
    real(8) :: tmp
    t_1 = fmin(t, fmax(z, a))
    t_2 = x * log(y)
    t_3 = fmax(t, fmax(z, a))
    if (x <= (-3.6d+105)) then
        tmp = (t_1 + (fmin(z, a) + (t_2 + (log(c) * (-0.5d0))))) + (y * i)
    else if (x <= 1.05d+111) then
        tmp = (((fmin(z, a) + t_1) + t_3) + ((b - 0.5d0) * log(c))) + (y * i)
    else
        tmp = ((t_3 + t_2) + ((-0.5d0) * log(c))) + (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 = fmin(t, fmax(z, a));
	double t_2 = x * Math.log(y);
	double t_3 = fmax(t, fmax(z, a));
	double tmp;
	if (x <= -3.6e+105) {
		tmp = (t_1 + (fmin(z, a) + (t_2 + (Math.log(c) * -0.5)))) + (y * i);
	} else if (x <= 1.05e+111) {
		tmp = (((fmin(z, a) + t_1) + t_3) + ((b - 0.5) * Math.log(c))) + (y * i);
	} else {
		tmp = ((t_3 + t_2) + (-0.5 * Math.log(c))) + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = fmin(t, fmax(z, a))
	t_2 = x * math.log(y)
	t_3 = fmax(t, fmax(z, a))
	tmp = 0
	if x <= -3.6e+105:
		tmp = (t_1 + (fmin(z, a) + (t_2 + (math.log(c) * -0.5)))) + (y * i)
	elif x <= 1.05e+111:
		tmp = (((fmin(z, a) + t_1) + t_3) + ((b - 0.5) * math.log(c))) + (y * i)
	else:
		tmp = ((t_3 + t_2) + (-0.5 * math.log(c))) + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fmin(t, fmax(z, a))
	t_2 = Float64(x * log(y))
	t_3 = fmax(t, fmax(z, a))
	tmp = 0.0
	if (x <= -3.6e+105)
		tmp = Float64(Float64(t_1 + Float64(fmin(z, a) + Float64(t_2 + Float64(log(c) * -0.5)))) + Float64(y * i));
	elseif (x <= 1.05e+111)
		tmp = Float64(Float64(Float64(Float64(fmin(z, a) + t_1) + t_3) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i));
	else
		tmp = Float64(Float64(Float64(t_3 + t_2) + Float64(-0.5 * log(c))) + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = min(t, max(z, a));
	t_2 = x * log(y);
	t_3 = max(t, max(z, a));
	tmp = 0.0;
	if (x <= -3.6e+105)
		tmp = (t_1 + (min(z, a) + (t_2 + (log(c) * -0.5)))) + (y * i);
	elseif (x <= 1.05e+111)
		tmp = (((min(z, a) + t_1) + t_3) + ((b - 0.5) * log(c))) + (y * i);
	else
		tmp = ((t_3 + t_2) + (-0.5 * log(c))) + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[Min[t, N[Max[z, a], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[Max[t, N[Max[z, a], $MachinePrecision]], $MachinePrecision]}, If[LessEqual[x, -3599999999999999879581681787739427058599582932568556174433318048436749902375581436811618887180905028255744], N[(N[(t$95$1 + N[(N[Min[z, a], $MachinePrecision] + N[(t$95$2 + N[(N[Log[c], $MachinePrecision] * -1/2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1049999999999999974685639735482438568778688196460848270285520923497646456255682135894950006688309094612255899648], N[(N[(N[(N[(N[Min[z, a], $MachinePrecision] + t$95$1), $MachinePrecision] + t$95$3), $MachinePrecision] + N[(N[(b - 1/2), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t$95$3 + t$95$2), $MachinePrecision] + N[(-1/2 * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.5999999999999999e105

   1. Initial program 99.8%

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

   2. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-+.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. lower-log.f64 N/A

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

      8. lower--.f64 83.8%

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

   4. Applied rewrites 83.8%

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

   5. Taylor expanded in b around 0

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

   7. Applied rewrites 69.2%

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

   if -3.5999999999999999e105 < x < 1.05e111

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 84.5%

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

   if 1.05e111 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 84.5%

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

   5. Taylor expanded in b around 0

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

   7. Applied rewrites 69.8%

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

   8. Taylor expanded in t around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-log.f64 69.0%

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

   10. Applied rewrites 69.0%

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

   11. Taylor expanded in z around 0

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

       1. lower-+.f64 N/A

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

       2. lower-*.f64 N/A

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

       3. lower-log.f64 54.7%

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

   13. Applied rewrites 54.7%

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

Alternative 4: 90.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{min}\left(t, \mathsf{max}\left(z, a\right)\right)\\ t_2 := \mathsf{max}\left(t, \mathsf{max}\left(z, a\right)\right)\\ \mathbf{if}\;x \leq -3599999999999999879581681787739427058599582932568556174433318048436749902375581436811618887180905028255744:\\ \;\;\;\;\mathsf{134\_z0z1z2z3z4}\left(\left(-i\right), \left(-1 \cdot t\_1 - \left(\log y \cdot x + \mathsf{min}\left(z, a\right)\right)\right), \left(\frac{1}{i}\right), 1, y\right)\\ \mathbf{elif}\;x \leq 1049999999999999974685639735482438568778688196460848270285520923497646456255682135894950006688309094612255899648:\\ \;\;\;\;\left(\left(\left(\mathsf{min}\left(z, a\right) + t\_1\right) + t\_2\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;\left(\left(t\_2 + x \cdot \log y\right) + \frac{-1}{2} \cdot \log c\right) + y \cdot i\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  (let* ((t_1 (fmin t (fmax z a))) (t_2 (fmax t (fmax z a))))
  (if (<=
       x
       -3599999999999999879581681787739427058599582932568556174433318048436749902375581436811618887180905028255744)
    (134-z0z1z2z3z4
     (- i)
     (- (* -1 t_1) (+ (* (log y) x) (fmin z a)))
     (/ 1 i)
     1
     y)
    (if (<=
         x
         1049999999999999974685639735482438568778688196460848270285520923497646456255682135894950006688309094612255899648)
      (+ (+ (+ (+ (fmin z a) t_1) t_2) (* (- b 1/2) (log c))) (* y i))
      (+ (+ (+ t_2 (* x (log y))) (* -1/2 (log c))) (* y i))))))

Derivation

1. Split input into 3 regimes

2. if x < -3.5999999999999999e105

   1. Initial program 99.8%

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

   2. 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 70.1%

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

   6. Applied rewrites 98.8%

      \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(-i\right), \color{blue}{\left(\left(\left(\frac{1}{2} - b\right) \cdot \log c - \left(a + t\right)\right) - \left(\log y \cdot x + z\right)\right)}, \left(\frac{1}{i}\right), 1, y\right) \]

   7. Taylor expanded in t around inf

      \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(-i\right), \left(-1 \cdot t - \left(\color{blue}{\log y \cdot x} + z\right)\right), \left(\frac{1}{i}\right), 1, y\right) \]
   8. Step-by-step derivation

      1. lower-*.f64 67.1%

         \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(-i\right), \left(-1 \cdot t - \left(\log y \cdot \color{blue}{x} + z\right)\right), \left(\frac{1}{i}\right), 1, y\right) \]

   9. Applied rewrites 67.1%

      \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(-i\right), \left(-1 \cdot t - \left(\color{blue}{\log y \cdot x} + z\right)\right), \left(\frac{1}{i}\right), 1, y\right) \]

   if -3.5999999999999999e105 < x < 1.05e111

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 84.5%

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

   if 1.05e111 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 84.5%

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

   5. Taylor expanded in b around 0

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

   7. Applied rewrites 69.8%

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

   8. Taylor expanded in t around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-log.f64 69.0%

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

   10. Applied rewrites 69.0%

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

   11. Taylor expanded in z around 0

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

       1. lower-+.f64 N/A

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

       2. lower-*.f64 N/A

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

       3. lower-log.f64 54.7%

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

   13. Applied rewrites 54.7%

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

Alternative 5: 89.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq -3599999999999999879581681787739427058599582932568556174433318048436749902375581436811618887180905028255744:\\ \;\;\;\;\mathsf{134\_z0z1z2z3z4}\left(\left(-i\right), \left(-1 \cdot \mathsf{min}\left(t, a\right) - \left(\log y \cdot x + z\right)\right), \left(\frac{1}{i}\right), 1, y\right)\\ \mathbf{elif}\;x \leq 4999999999999999681793534688837958868212853663785036782419720361679078139026353774446693497293473788990517591304702846227575332082657167871886131204710002780090859851360619284064431218701999138176915986960331575388717979146899858120583984847024514138112:\\ \;\;\;\;\left(\left(\left(z + \mathsf{min}\left(t, a\right)\right) + \mathsf{max}\left(t, a\right)\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;\mathsf{134\_z0z1z2z3z4}\left(\left(-i\right), \left(\left(-\log y\right) \cdot x\right), \left(\frac{1}{i}\right), 1, y\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  (if (<=
     x
     -3599999999999999879581681787739427058599582932568556174433318048436749902375581436811618887180905028255744)
  (134-z0z1z2z3z4
   (- i)
   (- (* -1 (fmin t a)) (+ (* (log y) x) z))
   (/ 1 i)
   1
   y)
  (if (<=
       x
       4999999999999999681793534688837958868212853663785036782419720361679078139026353774446693497293473788990517591304702846227575332082657167871886131204710002780090859851360619284064431218701999138176915986960331575388717979146899858120583984847024514138112)
    (+
     (+ (+ (+ z (fmin t a)) (fmax t a)) (* (- b 1/2) (log c)))
     (* y i))
    (134-z0z1z2z3z4 (- i) (* (- (log y)) x) (/ 1 i) 1 y))))

Derivation

1. Split input into 3 regimes

2. if x < -3.5999999999999999e105

   1. Initial program 99.8%

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

   2. 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 70.1%

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

   6. Applied rewrites 98.8%

      \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(-i\right), \color{blue}{\left(\left(\left(\frac{1}{2} - b\right) \cdot \log c - \left(a + t\right)\right) - \left(\log y \cdot x + z\right)\right)}, \left(\frac{1}{i}\right), 1, y\right) \]

   7. Taylor expanded in t around inf

      \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(-i\right), \left(-1 \cdot t - \left(\color{blue}{\log y \cdot x} + z\right)\right), \left(\frac{1}{i}\right), 1, y\right) \]
   8. Step-by-step derivation

      1. lower-*.f64 67.1%

         \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(-i\right), \left(-1 \cdot t - \left(\log y \cdot \color{blue}{x} + z\right)\right), \left(\frac{1}{i}\right), 1, y\right) \]

   9. Applied rewrites 67.1%

      \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(-i\right), \left(-1 \cdot t - \left(\color{blue}{\log y \cdot x} + z\right)\right), \left(\frac{1}{i}\right), 1, y\right) \]

   if -3.5999999999999999e105 < x < 4.9999999999999997e252

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 84.5%

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

   if 4.9999999999999997e252 < x

   1. Initial program 99.8%

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

   2. 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 70.1%

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

   6. Applied rewrites 98.8%

      \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(-i\right), \color{blue}{\left(\left(\left(\frac{1}{2} - b\right) \cdot \log c - \left(a + t\right)\right) - \left(\log y \cdot x + z\right)\right)}, \left(\frac{1}{i}\right), 1, y\right) \]

   7. Taylor expanded in x around inf

      \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(-i\right), \left(-1 \cdot \color{blue}{\left(x \cdot \log y\right)}\right), \left(\frac{1}{i}\right), 1, y\right) \]
   8. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(-i\right), \left(-1 \cdot \left(x \cdot \color{blue}{\log y}\right)\right), \left(\frac{1}{i}\right), 1, y\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(-i\right), \left(-1 \cdot \left(x \cdot \log y\right)\right), \left(\frac{1}{i}\right), 1, y\right) \]

      3. lower-log.f64 37.9%

         \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(-i\right), \left(-1 \cdot \left(x \cdot \log y\right)\right), \left(\frac{1}{i}\right), 1, y\right) \]

   9. Applied rewrites 37.9%

      \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(-i\right), \left(-1 \cdot \color{blue}{\left(x \cdot \log y\right)}\right), \left(\frac{1}{i}\right), 1, y\right) \]
   10. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(-i\right), \left(-1 \cdot \left(x \cdot \color{blue}{\log y}\right)\right), \left(\frac{1}{i}\right), 1, y\right) \]

       2. mul-1-neg N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(-i\right), \left(\mathsf{neg}\left(x \cdot \log y\right)\right), \left(\frac{1}{i}\right), 1, y\right) \]

       3. lift-log.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(-i\right), \left(\mathsf{neg}\left(x \cdot \log y\right)\right), \left(\frac{1}{i}\right), 1, y\right) \]

       4. lift-*.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(-i\right), \left(\mathsf{neg}\left(x \cdot \log y\right)\right), \left(\frac{1}{i}\right), 1, y\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(-i\right), \left(\mathsf{neg}\left(\log y \cdot x\right)\right), \left(\frac{1}{i}\right), 1, y\right) \]

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

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(-i\right), \left(\left(\mathsf{neg}\left(\log y\right)\right) \cdot x\right), \left(\frac{1}{i}\right), 1, y\right) \]

       7. lower-*.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(-i\right), \left(\left(\mathsf{neg}\left(\log y\right)\right) \cdot x\right), \left(\frac{1}{i}\right), 1, y\right) \]

       8. lower-neg.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(-i\right), \left(\left(-\log y\right) \cdot x\right), \left(\frac{1}{i}\right), 1, y\right) \]

       9. lift-log.f64 37.9%

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(-i\right), \left(\left(-\log y\right) \cdot x\right), \left(\frac{1}{i}\right), 1, y\right) \]

   11. Applied rewrites 37.9%

       \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(-i\right), \left(\left(-\log y\right) \cdot x\right), \left(\frac{1}{i}\right), 1, y\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 86.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{134\_z0z1z2z3z4}\left(\left(-i\right), \left(\left(-\log y\right) \cdot x\right), \left(\frac{1}{i}\right), 1, y\right)\\ \mathbf{if}\;x \leq -3599999999999999879581681787739427058599582932568556174433318048436749902375581436811618887180905028255744:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4999999999999999681793534688837958868212853663785036782419720361679078139026353774446693497293473788990517591304702846227575332082657167871886131204710002780090859851360619284064431218701999138176915986960331575388717979146899858120583984847024514138112:\\ \;\;\;\;\left(\left(\left(z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  (let* ((t_1 (134-z0z1z2z3z4 (- i) (* (- (log y)) x) (/ 1 i) 1 y)))
  (if (<=
       x
       -3599999999999999879581681787739427058599582932568556174433318048436749902375581436811618887180905028255744)
    t_1
    (if (<=
         x
         4999999999999999681793534688837958868212853663785036782419720361679078139026353774446693497293473788990517591304702846227575332082657167871886131204710002780090859851360619284064431218701999138176915986960331575388717979146899858120583984847024514138112)
      (+ (+ (+ (+ z t) a) (* (- b 1/2) (log c))) (* y i))
      t_1))))

Derivation

1. Split input into 2 regimes

2. if x < -3.5999999999999999e105 or 4.9999999999999997e252 < x

   1. Initial program 99.8%

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

   2. 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 70.1%

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

   6. Applied rewrites 98.8%

      \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(-i\right), \color{blue}{\left(\left(\left(\frac{1}{2} - b\right) \cdot \log c - \left(a + t\right)\right) - \left(\log y \cdot x + z\right)\right)}, \left(\frac{1}{i}\right), 1, y\right) \]

   7. Taylor expanded in x around inf

      \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(-i\right), \left(-1 \cdot \color{blue}{\left(x \cdot \log y\right)}\right), \left(\frac{1}{i}\right), 1, y\right) \]
   8. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(-i\right), \left(-1 \cdot \left(x \cdot \color{blue}{\log y}\right)\right), \left(\frac{1}{i}\right), 1, y\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(-i\right), \left(-1 \cdot \left(x \cdot \log y\right)\right), \left(\frac{1}{i}\right), 1, y\right) \]

      3. lower-log.f64 37.9%

         \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(-i\right), \left(-1 \cdot \left(x \cdot \log y\right)\right), \left(\frac{1}{i}\right), 1, y\right) \]

   9. Applied rewrites 37.9%

      \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(-i\right), \left(-1 \cdot \color{blue}{\left(x \cdot \log y\right)}\right), \left(\frac{1}{i}\right), 1, y\right) \]
   10. Step-by-step derivation

       1. lift-*.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(-i\right), \left(-1 \cdot \left(x \cdot \color{blue}{\log y}\right)\right), \left(\frac{1}{i}\right), 1, y\right) \]

       2. mul-1-neg N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(-i\right), \left(\mathsf{neg}\left(x \cdot \log y\right)\right), \left(\frac{1}{i}\right), 1, y\right) \]

       3. lift-log.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(-i\right), \left(\mathsf{neg}\left(x \cdot \log y\right)\right), \left(\frac{1}{i}\right), 1, y\right) \]

       4. lift-*.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(-i\right), \left(\mathsf{neg}\left(x \cdot \log y\right)\right), \left(\frac{1}{i}\right), 1, y\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(-i\right), \left(\mathsf{neg}\left(\log y \cdot x\right)\right), \left(\frac{1}{i}\right), 1, y\right) \]

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

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(-i\right), \left(\left(\mathsf{neg}\left(\log y\right)\right) \cdot x\right), \left(\frac{1}{i}\right), 1, y\right) \]

       7. lower-*.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(-i\right), \left(\left(\mathsf{neg}\left(\log y\right)\right) \cdot x\right), \left(\frac{1}{i}\right), 1, y\right) \]

       8. lower-neg.f64 N/A

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(-i\right), \left(\left(-\log y\right) \cdot x\right), \left(\frac{1}{i}\right), 1, y\right) \]

       9. lift-log.f64 37.9%

          \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(-i\right), \left(\left(-\log y\right) \cdot x\right), \left(\frac{1}{i}\right), 1, y\right) \]

   11. Applied rewrites 37.9%

       \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(-i\right), \left(\left(-\log y\right) \cdot x\right), \left(\frac{1}{i}\right), 1, y\right) \]

   if -3.5999999999999999e105 < x < 4.9999999999999997e252

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 84.5%

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

Alternative 7: 84.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq -2900000000000000069204150533318179972423531164014983082171454639135575083669141427456118715053209327656255939076123855554686929346306229350604672279211178777041260228043399439241445376:\\ \;\;\;\;i \cdot \left(y - \frac{\left(-x\right) \cdot \log y}{i}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(z + t\right) + a\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  (if (<=
     x
     -2900000000000000069204150533318179972423531164014983082171454639135575083669141427456118715053209327656255939076123855554686929346306229350604672279211178777041260228043399439241445376)
  (* i (- y (/ (* (- x) (log y)) i)))
  (+ (+ (+ (+ z t) a) (* (- b 1/2) (log c))) (* y i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -2.9e+183) {
		tmp = i * (y - ((-x * log(y)) / i));
	} else {
		tmp = (((z + t) + a) + ((b - 0.5) * log(c))) + (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) :: tmp
    if (x <= (-2.9d+183)) then
        tmp = i * (y - ((-x * log(y)) / i))
    else
        tmp = (((z + t) + a) + ((b - 0.5d0) * log(c))) + (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 tmp;
	if (x <= -2.9e+183) {
		tmp = i * (y - ((-x * Math.log(y)) / i));
	} else {
		tmp = (((z + t) + a) + ((b - 0.5) * Math.log(c))) + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if x <= -2.9e+183:
		tmp = i * (y - ((-x * math.log(y)) / i))
	else:
		tmp = (((z + t) + a) + ((b - 0.5) * math.log(c))) + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -2.9e+183)
		tmp = Float64(i * Float64(y - Float64(Float64(Float64(-x) * log(y)) / i)));
	else
		tmp = Float64(Float64(Float64(Float64(z + t) + a) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (x <= -2.9e+183)
		tmp = i * (y - ((-x * log(y)) / i));
	else
		tmp = (((z + t) + a) + ((b - 0.5) * log(c))) + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -2900000000000000069204150533318179972423531164014983082171454639135575083669141427456118715053209327656255939076123855554686929346306229350604672279211178777041260228043399439241445376], N[(i * N[(y - N[(N[((-x) * N[Log[y], $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(z + t), $MachinePrecision] + a), $MachinePrecision] + N[(N[(b - 1/2), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.9000000000000001e183

   1. Initial program 99.8%

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

   2. 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 70.1%

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

   6. Applied rewrites 98.8%

      \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(-i\right), \color{blue}{\left(\left(\left(\frac{1}{2} - b\right) \cdot \log c - \left(a + t\right)\right) - \left(\log y \cdot x + z\right)\right)}, \left(\frac{1}{i}\right), 1, y\right) \]

   7. Taylor expanded in x around inf

      \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(-i\right), \left(-1 \cdot \color{blue}{\left(x \cdot \log y\right)}\right), \left(\frac{1}{i}\right), 1, y\right) \]
   8. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(-i\right), \left(-1 \cdot \left(x \cdot \color{blue}{\log y}\right)\right), \left(\frac{1}{i}\right), 1, y\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(-i\right), \left(-1 \cdot \left(x \cdot \log y\right)\right), \left(\frac{1}{i}\right), 1, y\right) \]

      3. lower-log.f64 37.9%

         \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(-i\right), \left(-1 \cdot \left(x \cdot \log y\right)\right), \left(\frac{1}{i}\right), 1, y\right) \]

   9. Applied rewrites 37.9%

      \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(-i\right), \left(-1 \cdot \color{blue}{\left(x \cdot \log y\right)}\right), \left(\frac{1}{i}\right), 1, y\right) \]
   10. Step-by-step derivation

       1. lift-134-z0z1z2z3z4 N/A

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

       2. lift-neg.f64 N/A

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

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

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

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

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

       5. sub-negate-rev N/A

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

       6. lower-*.f64 N/A

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

       7. lower--.f64 N/A

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

   11. Applied rewrites 32.9%

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

   if -2.9000000000000001e183 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 84.5%

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

Alternative 8: 84.5% accurate, 1.9× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  (+ (+ (+ (+ z t) a) (* (- b 1/2) (log c))) (* y i)))

C

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

Python

def code(x, y, z, t, a, b, c, i):
	return (((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(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 = (((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[(z + t), $MachinePrecision] + a), $MachinePrecision] + N[(N[(b - 1/2), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in x around 0

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

4. Applied rewrites 84.5%

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

Alternative 9: 82.9% accurate, 1.9× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  (+ (+ (+ (+ 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 (((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 = (((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 (((z + t) + a) + (b * Math.log(c))) + (y * i);
}

Python

def code(x, y, z, t, a, b, c, i):
	return (((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(z + t) + a) + Float64(b * log(c))) + Float64(y * i))
end

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in x around 0

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

4. Applied rewrites 84.5%

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

5. Taylor expanded in b around inf

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

   1. lower-*.f64 N/A

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

   2. lower-log.f64 82.9%

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

7. Applied rewrites 82.9%

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

Alternative 10: 71.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} t_1 := b \cdot \log c\\ \mathbf{if}\;b \leq -220000000000000007326340945888506653530663275816339520787551061483281194676992796675380578830910283831394710160078130540983823370103972914382310371986209239684302748330385406265864769173821619794310214916639484596526893062295164526571011132358656:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 159999999999999989944552393973900225604372920958349972403300010855230793642961654112601228541105453547752781156718400530593792829447325901273825939842848991414158271414760636416:\\ \;\;\;\;1 \cdot \left(a + \left(t + z\right)\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  (let* ((t_1 (* b (log c))))
  (if (<=
       b
       -220000000000000007326340945888506653530663275816339520787551061483281194676992796675380578830910283831394710160078130540983823370103972914382310371986209239684302748330385406265864769173821619794310214916639484596526893062295164526571011132358656)
    t_1
    (if (<=
         b
         159999999999999989944552393973900225604372920958349972403300010855230793642961654112601228541105453547752781156718400530593792829447325901273825939842848991414158271414760636416)
      (+ (* 1 (+ a (+ t z))) (* 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 = b * log(c);
	double tmp;
	if (b <= -2.2e+245) {
		tmp = t_1;
	} else if (b <= 1.6e+176) {
		tmp = (1.0 * (a + (t + z))) + (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 = b * log(c)
    if (b <= (-2.2d+245)) then
        tmp = t_1
    else if (b <= 1.6d+176) then
        tmp = (1.0d0 * (a + (t + z))) + (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 = b * Math.log(c);
	double tmp;
	if (b <= -2.2e+245) {
		tmp = t_1;
	} else if (b <= 1.6e+176) {
		tmp = (1.0 * (a + (t + z))) + (y * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = b * math.log(c)
	tmp = 0
	if b <= -2.2e+245:
		tmp = t_1
	elif b <= 1.6e+176:
		tmp = (1.0 * (a + (t + z))) + (y * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(b * log(c))
	tmp = 0.0
	if (b <= -2.2e+245)
		tmp = t_1;
	elseif (b <= 1.6e+176)
		tmp = Float64(Float64(1.0 * Float64(a + Float64(t + z))) + 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 = b * log(c);
	tmp = 0.0;
	if (b <= -2.2e+245)
		tmp = t_1;
	elseif (b <= 1.6e+176)
		tmp = (1.0 * (a + (t + z))) + (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[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -220000000000000007326340945888506653530663275816339520787551061483281194676992796675380578830910283831394710160078130540983823370103972914382310371986209239684302748330385406265864769173821619794310214916639484596526893062295164526571011132358656], t$95$1, If[LessEqual[b, 159999999999999989944552393973900225604372920958349972403300010855230793642961654112601228541105453547752781156718400530593792829447325901273825939842848991414158271414760636416], N[(N[(1 * N[(a + N[(t + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.2000000000000001e245 or 1.5999999999999999e176 < b

   1. Initial program 99.8%

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

   2. 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 70.1%

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

   6. Applied rewrites 98.8%

      \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(-i\right), \color{blue}{\left(\left(\left(\frac{1}{2} - b\right) \cdot \log c - \left(a + t\right)\right) - \left(\log y \cdot x + z\right)\right)}, \left(\frac{1}{i}\right), 1, y\right) \]

   7. Taylor expanded in b around inf

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

      1. lower-*.f64 N/A

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

      2. lower-log.f64 16.1%

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

   9. Applied rewrites 16.1%

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

   if -2.2000000000000001e245 < b < 1.5999999999999999e176

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 84.5%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. fp-cancel-sign-sub-inv N/A

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

      4. lift--.f64 N/A

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

      5. sub-negate-rev N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. sub-to-mult N/A

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

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

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

   6. Applied rewrites 83.3%

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

   7. Taylor expanded in x around inf

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

   9. Applied rewrites 68.1%

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

Alternative 11: 68.1% accurate, 11.7× speedup

Math

\[1 \cdot \left(a + \left(t + z\right)\right) + y \cdot i \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  (+ (* 1 (+ a (+ t z))) (* y i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (1.0 * (a + (t + z))) + (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 = (1.0d0 * (a + (t + z))) + (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 (1.0 * (a + (t + z))) + (y * i);
}

Python

def code(x, y, z, t, a, b, c, i):
	return (1.0 * (a + (t + z))) + (y * i)

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(1.0 * Float64(a + Float64(t + z))) + Float64(y * i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = (1.0 * (a + (t + z))) + (y * i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(1 * N[(a + N[(t + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in x around 0

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

4. Applied rewrites 84.5%

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

   1. lift-+.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. fp-cancel-sign-sub-inv N/A

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

   4. lift--.f64 N/A

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

   5. sub-negate-rev N/A

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

   6. lift--.f64 N/A

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

   7. lift-*.f64 N/A

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

   8. sub-to-mult N/A

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

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

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

6. Applied rewrites 83.3%

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

7. Taylor expanded in x around inf

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

9. Applied rewrites 68.1%

   \[\leadsto \color{blue}{1} \cdot \left(a + \left(t + z\right)\right) + y \cdot i \]
10. Add Preprocessing

Alternative 12: 67.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{min}\left(\mathsf{min}\left(z, t\right), a\right)\\ t_2 := \mathsf{max}\left(\mathsf{min}\left(z, t\right), a\right)\\ t_3 := \mathsf{max}\left(\mathsf{max}\left(z, t\right), t\_2\right)\\ \mathbf{if}\;\left(\left(\left(\left(x \cdot \log y + t\_1\right) + \mathsf{min}\left(\mathsf{max}\left(z, t\right), t\_2\right)\right) + t\_3\right) + \left(b - \frac{1}{2}\right) \cdot \log c\right) + y \cdot i \leq -2000000000:\\ \;\;\;\;y \cdot i + \left(-t\_1\right) \cdot -1\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \left(-1 \cdot t\_3\right) + y \cdot i\\ \end{array} \]

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)))
  (if (<=
       (+
        (+
         (+ (+ (+ (* x (log y)) t_1) (fmin (fmax z t) t_2)) t_3)
         (* (- b 1/2) (log c)))
        (* y i))
       -2000000000)
    (+ (* y i) (* (- t_1) -1))
    (+ (* -1 (* -1 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 tmp;
	if (((((((x * log(y)) + t_1) + fmin(fmax(z, t), t_2)) + t_3) + ((b - 0.5) * log(c))) + (y * i)) <= -2000000000.0) {
		tmp = (y * i) + (-t_1 * -1.0);
	} else {
		tmp = (-1.0 * (-1.0 * t_3)) + (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) :: 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)) <= (-2000000000.0d0)) then
        tmp = (y * i) + (-t_1 * (-1.0d0))
    else
        tmp = ((-1.0d0) * ((-1.0d0) * t_3)) + (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 = 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)) <= -2000000000.0) {
		tmp = (y * i) + (-t_1 * -1.0);
	} else {
		tmp = (-1.0 * (-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)
	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)) <= -2000000000.0:
		tmp = (y * i) + (-t_1 * -1.0)
	else:
		tmp = (-1.0 * (-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)
	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)) <= -2000000000.0)
		tmp = Float64(Float64(y * i) + Float64(Float64(-t_1) * -1.0));
	else
		tmp = Float64(Float64(-1.0 * 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);
	tmp = 0.0;
	if (((((((x * log(y)) + t_1) + min(max(z, t), t_2)) + t_3) + ((b - 0.5) * log(c))) + (y * i)) <= -2000000000.0)
		tmp = (y * i) + (-t_1 * -1.0);
	else
		tmp = (-1.0 * (-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]}, 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 - 1/2), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], -2000000000], N[(N[(y * i), $MachinePrecision] + N[((-t$95$1) * -1), $MachinePrecision]), $MachinePrecision], N[(N[(-1 * N[(-1 * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < -2e9

   1. Initial program 99.8%

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

   2. Taylor expanded in z around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

   4. Applied rewrites 72.9%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 37.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 37.9%

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

      4. lift-*.f64 N/A

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

      5. mul-1-neg N/A

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

   9. Applied rewrites 37.9%

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

   if -2e9 < (+.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%

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

   2. Taylor expanded in z around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

   4. Applied rewrites 72.9%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 37.9%

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

   8. Taylor expanded in a around inf

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

      1. lower-*.f64 38.7%

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

   10. Applied rewrites 38.7%

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

Alternative 13: 45.1% accurate, 1.1× speedup

Math

\[y \cdot i + \left(-\mathsf{min}\left(\mathsf{min}\left(z, t\right), a\right)\right) \cdot -1 \]

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  (+ (* y i) (* (- (fmin (fmin z t) a)) -1)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (y * i) + (-fmin(fmin(z, t), a) * -1.0);
}

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 = (y * i) + (-fmin(fmin(z, t), a) * (-1.0d0))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (y * i) + (-fmin(fmin(z, t), a) * -1.0);
}

Python

def code(x, y, z, t, a, b, c, i):
	return (y * i) + (-fmin(fmin(z, t), a) * -1.0)

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(y * i) + Float64(Float64(-fmin(fmin(z, t), a)) * -1.0))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = (y * i) + (-min(min(z, t), a) * -1.0);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(y * i), $MachinePrecision] + N[((-N[Min[N[Min[z, t], $MachinePrecision], a], $MachinePrecision]) * -1), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in z around -inf

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

   1. lower-*.f64 N/A

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

   2. lower-*.f64 N/A

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

   3. lower--.f64 N/A

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

4. Applied rewrites 72.9%

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

5. Taylor expanded in z around inf

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

7. Applied rewrites 37.9%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lower-+.f64 37.9%

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

   4. lift-*.f64 N/A

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

   5. mul-1-neg N/A

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

9. Applied rewrites 37.9%

   \[\leadsto \color{blue}{y \cdot i + \left(-z\right) \cdot -1} \]
10. Add Preprocessing

Alternative 14: 24.0% accurate, 21.3× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
  :precision binary64
  (* 1 (* i y)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return 1.0 * (i * y);
}

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 = 1.0d0 * (i * y)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return 1.0 * (i * y);
}

Python

def code(x, y, z, t, a, b, c, i):
	return 1.0 * (i * y)

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(1.0 * Float64(i * y))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = 1.0 * (i * y);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(1 * N[(i * y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. add-flip N/A

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

   4. sub-to-mult N/A

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

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

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

3. Applied rewrites 66.0%

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

4. Taylor expanded in y around inf

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

6. Applied rewrites 24.0%

   \[\leadsto \color{blue}{1} \cdot \left(i \cdot y\right) \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2025271 -o generate:evaluate
(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 1/2) (log c))) (* y i)))