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

Percentage Accurate: 99.8% → 99.8%

Time: 20.9s

Alternatives: 15

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

Alternative 2: 90.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log c \cdot \left(b - 0.5\right)\\ \mathbf{if}\;\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \leq -5 \cdot 10^{+18}:\\ \;\;\;\;t + \left(z + \mathsf{fma}\left(i, y, \mathsf{fma}\left(x, \log y, t\_1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + \mathsf{fma}\left(i, y, t\_1\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (log c) (- b 0.5))))
   (if (<=
        (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i))
        -5e+18)
     (+ t (+ z (fma i y (fma x (log y) t_1))))
     (+ a (+ t (+ z (fma i y t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = log(c) * (b - 0.5);
	double tmp;
	if (((((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i)) <= -5e+18) {
		tmp = t + (z + fma(i, y, fma(x, log(y), t_1)));
	} else {
		tmp = a + (t + (z + fma(i, y, t_1)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(log(c) * Float64(b - 0.5))
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + z) + t) + a) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i)) <= -5e+18)
		tmp = Float64(t + Float64(z + fma(i, y, fma(x, log(y), t_1))));
	else
		tmp = Float64(a + Float64(t + Float64(z + fma(i, y, t_1))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], -5e+18], N[(t + N[(z + N[(i * y + N[(x * N[Log[y], $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(t + N[(z + N[(i * y + t$95$1), $MachinePrecision]), $MachinePrecision]), $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)) < -5e18

   1. Initial program 99.8%

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

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 85.1%

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

   if -5e18 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i))

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 83.8%

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

Alternative 3: 89.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+206}:\\ \;\;\;\;t + \mathsf{fma}\left(i, y, \mathsf{fma}\left(x, \log y, \log c \cdot -0.5\right)\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+241}:\\ \;\;\;\;a + \left(t + \left(z + \mathsf{fma}\left(i, y, \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t + \mathsf{fma}\left(\log y, x, \mathsf{fma}\left(b - 0.5, \log c, z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -9.5e+206)
   (+ t (fma i y (fma x (log y) (* (log c) -0.5))))
   (if (<= x 3.2e+241)
     (+ a (+ t (+ z (fma i y (* (log c) (- b 0.5))))))
     (+ t (fma (log y) x (fma (- b 0.5) (log c) z))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -9.5e+206) {
		tmp = t + fma(i, y, fma(x, log(y), (log(c) * -0.5)));
	} else if (x <= 3.2e+241) {
		tmp = a + (t + (z + fma(i, y, (log(c) * (b - 0.5)))));
	} else {
		tmp = t + fma(log(y), x, fma((b - 0.5), log(c), z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -9.5e+206)
		tmp = Float64(t + fma(i, y, fma(x, log(y), Float64(log(c) * -0.5))));
	elseif (x <= 3.2e+241)
		tmp = Float64(a + Float64(t + Float64(z + fma(i, y, Float64(log(c) * Float64(b - 0.5))))));
	else
		tmp = Float64(t + fma(log(y), x, fma(Float64(b - 0.5), log(c), z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -9.5e+206], N[(t + N[(i * y + N[(x * N[Log[y], $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.2e+241], N[(a + N[(t + N[(z + N[(i * y + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[Log[y], $MachinePrecision] * x + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.49999999999999966e206

   1. Initial program 99.8%

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

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 85.1%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 62.1%

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

   8. Taylor expanded in z around 0

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

   10. Applied rewrites 70.6%

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

   11. Taylor expanded in b around 0

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

   13. Applied rewrites 55.2%

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

   if -9.49999999999999966e206 < x < 3.20000000000000004e241

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 83.8%

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

   if 3.20000000000000004e241 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 85.1%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 62.1%

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

   9. Applied rewrites 62.1%

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

Alternative 4: 89.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+207}:\\ \;\;\;\;t + \left(z + \mathsf{fma}\left(x, \log y, \log c \cdot -0.5\right)\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+241}:\\ \;\;\;\;a + \left(t + \left(z + \mathsf{fma}\left(i, y, \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t + \mathsf{fma}\left(\log y, x, \mathsf{fma}\left(b - 0.5, \log c, z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -1.8e+207)
   (+ t (+ z (fma x (log y) (* (log c) -0.5))))
   (if (<= x 3.2e+241)
     (+ a (+ t (+ z (fma i y (* (log c) (- b 0.5))))))
     (+ t (fma (log y) x (fma (- b 0.5) (log c) z))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -1.8e+207) {
		tmp = t + (z + fma(x, log(y), (log(c) * -0.5)));
	} else if (x <= 3.2e+241) {
		tmp = a + (t + (z + fma(i, y, (log(c) * (b - 0.5)))));
	} else {
		tmp = t + fma(log(y), x, fma((b - 0.5), log(c), z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -1.8e+207)
		tmp = Float64(t + Float64(z + fma(x, log(y), Float64(log(c) * -0.5))));
	elseif (x <= 3.2e+241)
		tmp = Float64(a + Float64(t + Float64(z + fma(i, y, Float64(log(c) * Float64(b - 0.5))))));
	else
		tmp = Float64(t + fma(log(y), x, fma(Float64(b - 0.5), log(c), z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -1.8e+207], N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.2e+241], N[(a + N[(t + N[(z + N[(i * y + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[Log[y], $MachinePrecision] * x + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.80000000000000007e207

   1. Initial program 99.8%

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

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 85.1%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 62.1%

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

   8. Taylor expanded in b around 0

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

   10. Applied rewrites 46.6%

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

   if -1.80000000000000007e207 < x < 3.20000000000000004e241

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 83.8%

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

   if 3.20000000000000004e241 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 85.1%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 62.1%

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

   9. Applied rewrites 62.1%

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

Alternative 5: 88.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(z + \mathsf{fma}\left(x, \log y, \log c \cdot -0.5\right)\right)\\ \mathbf{if}\;x \leq -1.8 \cdot 10^{+207}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+244}:\\ \;\;\;\;a + \left(t + \left(z + \mathsf{fma}\left(i, y, \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ t (+ z (fma x (log y) (* (log c) -0.5))))))
   (if (<= x -1.8e+207)
     t_1
     (if (<= x 1.9e+244)
       (+ a (+ t (+ z (fma i y (* (log c) (- b 0.5))))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = t + (z + fma(x, log(y), (log(c) * -0.5)));
	double tmp;
	if (x <= -1.8e+207) {
		tmp = t_1;
	} else if (x <= 1.9e+244) {
		tmp = a + (t + (z + fma(i, y, (log(c) * (b - 0.5)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(t + Float64(z + fma(x, log(y), Float64(log(c) * -0.5))))
	tmp = 0.0
	if (x <= -1.8e+207)
		tmp = t_1;
	elseif (x <= 1.9e+244)
		tmp = Float64(a + Float64(t + Float64(z + fma(i, y, Float64(log(c) * Float64(b - 0.5))))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.8e+207], t$95$1, If[LessEqual[x, 1.9e+244], N[(a + N[(t + N[(z + N[(i * y + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.80000000000000007e207 or 1.89999999999999991e244 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 85.1%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 62.1%

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

   8. Taylor expanded in b around 0

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

   10. Applied rewrites 46.6%

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

   if -1.80000000000000007e207 < x < 1.89999999999999991e244

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 83.8%

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

Alternative 6: 84.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -1.8 \cdot 10^{+207}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+248}:\\ \;\;\;\;a + \left(t + \left(z + \mathsf{fma}\left(i, y, \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -1.8e+207)
     t_1
     (if (<= x 1.1e+248)
       (+ a (+ t (+ z (fma i y (* (log c) (- b 0.5))))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * log(y);
	double tmp;
	if (x <= -1.8e+207) {
		tmp = t_1;
	} else if (x <= 1.1e+248) {
		tmp = a + (t + (z + fma(i, y, (log(c) * (b - 0.5)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -1.8e+207)
		tmp = t_1;
	elseif (x <= 1.1e+248)
		tmp = Float64(a + Float64(t + Float64(z + fma(i, y, Float64(log(c) * Float64(b - 0.5))))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.8e+207], t$95$1, If[LessEqual[x, 1.1e+248], N[(a + N[(t + N[(z + N[(i * y + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.80000000000000007e207 or 1.1e248 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in a around -inf

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

   4. Applied rewrites 73.2%

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

   6. Applied rewrites 73.1%

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

   7. Taylor expanded in x around inf

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

   9. Applied rewrites 17.1%

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

   if -1.80000000000000007e207 < x < 1.1e248

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 83.8%

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

Alternative 7: 71.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 1.3 \cdot 10^{+178}:\\ \;\;\;\;t + \left(z + \mathsf{fma}\left(i, y, \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \left(a \cdot \left(-1 \cdot \frac{z}{a} - 1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 1.3e+178)
   (+ t (+ z (fma i y (* (log c) (- b 0.5)))))
   (* -1.0 (* a (- (* -1.0 (/ z a)) 1.0)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 1.3e+178) {
		tmp = t + (z + fma(i, y, (log(c) * (b - 0.5))));
	} else {
		tmp = -1.0 * (a * ((-1.0 * (z / a)) - 1.0));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 1.3e+178)
		tmp = Float64(t + Float64(z + fma(i, y, Float64(log(c) * Float64(b - 0.5)))));
	else
		tmp = Float64(-1.0 * Float64(a * Float64(Float64(-1.0 * Float64(z / a)) - 1.0)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 1.3e+178], N[(t + N[(z + N[(i * y + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-1.0 * N[(a * N[(N[(-1.0 * N[(z / a), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 1.3e178

   1. Initial program 99.8%

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

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 85.1%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 69.4%

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

   if 1.3e178 < a

   1. Initial program 99.8%

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

   2. Taylor expanded in a around -inf

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

   4. Applied rewrites 73.2%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 25.5%

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

Alternative 8: 48.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(i, y, \log c \cdot \left(b - 0.5\right)\right)\\ t_2 := \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{if}\;t\_2 \leq 200000000:\\ \;\;\;\;t + \left(z + t\_1\right)\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;-1 \cdot \left(a \cdot \left(-1 \cdot \frac{b \cdot \log c}{a} - 1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fma i y (* (log c) (- b 0.5))))
        (t_2
         (+
          (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c)))
          (* y i))))
   (if (<= t_2 200000000.0)
     (+ t (+ z t_1))
     (if (<= t_2 INFINITY)
       (* -1.0 (* a (- (* -1.0 (/ (* b (log c)) a)) 1.0)))
       (+ t t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fma(i, y, (log(c) * (b - 0.5)));
	double t_2 = (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
	double tmp;
	if (t_2 <= 200000000.0) {
		tmp = t + (z + t_1);
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = -1.0 * (a * ((-1.0 * ((b * log(c)) / a)) - 1.0));
	} else {
		tmp = t + t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fma(i, y, Float64(log(c) * Float64(b - 0.5)))
	t_2 = Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + z) + t) + a) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i))
	tmp = 0.0
	if (t_2 <= 200000000.0)
		tmp = Float64(t + Float64(z + t_1));
	elseif (t_2 <= Inf)
		tmp = Float64(-1.0 * Float64(a * Float64(Float64(-1.0 * Float64(Float64(b * log(c)) / a)) - 1.0)));
	else
		tmp = Float64(t + t_1);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(i * y + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, 200000000.0], N[(t + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, Infinity], N[(-1.0 * N[(a * N[(N[(-1.0 * N[(N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < 2e8

   1. Initial program 99.8%

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

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 85.1%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 69.4%

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

   if 2e8 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < +inf.0

   1. Initial program 99.8%

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

   2. Taylor expanded in a around -inf

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

   4. Applied rewrites 73.2%

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

   5. Taylor expanded in b around inf

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

   7. Applied rewrites 25.8%

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

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

   1. Initial program 99.8%

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

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 85.1%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 62.1%

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

   8. Taylor expanded in z around 0

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

   10. Applied rewrites 70.6%

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

   11. Taylor expanded in x around 0

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

   13. Applied rewrites 55.2%

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

Alternative 9: 42.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot 1 + y \cdot i\\ t_2 := \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 200000000:\\ \;\;\;\;t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;-1 \cdot \left(a \cdot \left(-1 \cdot \frac{z}{a} - 1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* t 1.0) (* y i)))
        (t_2
         (+
          (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c)))
          (* y i))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 200000000.0)
       (+ t (+ z (* (log c) (- b 0.5))))
       (if (<= t_2 INFINITY) (* -1.0 (* a (- (* -1.0 (/ z a)) 1.0))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (t * 1.0) + (y * i);
	double t_2 = (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= 200000000.0) {
		tmp = t + (z + (log(c) * (b - 0.5)));
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = -1.0 * (a * ((-1.0 * (z / a)) - 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (t * 1.0) + (y * i);
	double t_2 = (((((x * Math.log(y)) + z) + t) + a) + ((b - 0.5) * Math.log(c))) + (y * i);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= 200000000.0) {
		tmp = t + (z + (Math.log(c) * (b - 0.5)));
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = -1.0 * (a * ((-1.0 * (z / a)) - 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (t * 1.0) + (y * i)
	t_2 = (((((x * math.log(y)) + z) + t) + a) + ((b - 0.5) * math.log(c))) + (y * i)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= 200000000.0:
		tmp = t + (z + (math.log(c) * (b - 0.5)))
	elif t_2 <= math.inf:
		tmp = -1.0 * (a * ((-1.0 * (z / a)) - 1.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(t * 1.0) + Float64(y * i))
	t_2 = Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + z) + t) + a) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= 200000000.0)
		tmp = Float64(t + Float64(z + Float64(log(c) * Float64(b - 0.5))));
	elseif (t_2 <= Inf)
		tmp = Float64(-1.0 * Float64(a * Float64(Float64(-1.0 * Float64(z / a)) - 1.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (t * 1.0) + (y * i);
	t_2 = (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= 200000000.0)
		tmp = t + (z + (log(c) * (b - 0.5)));
	elseif (t_2 <= Inf)
		tmp = -1.0 * (a * ((-1.0 * (z / a)) - 1.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(t * 1.0), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, 200000000.0], N[(t + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, Infinity], N[(-1.0 * N[(a * N[(N[(-1.0 * N[(z / a), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 99.8%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 71.3%

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

   5. Taylor expanded in b around inf

      \[\leadsto t \cdot \frac{b \cdot \log c}{\color{blue}{t}} + y \cdot i \]

   7. Applied rewrites 32.3%

      \[\leadsto t \cdot \frac{b \cdot \log c}{\color{blue}{t}} + y \cdot i \]

   8. Taylor expanded in t around inf

      \[\leadsto t \cdot 1 + y \cdot i \]

   10. Applied rewrites 38.5%

       \[\leadsto t \cdot 1 + y \cdot i \]

   if -inf.0 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < 2e8

   1. Initial program 99.8%

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

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 85.1%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 62.1%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 46.5%

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

   if 2e8 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < +inf.0

   1. Initial program 99.8%

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

   2. Taylor expanded in a around -inf

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

   4. Applied rewrites 73.2%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 25.5%

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

Alternative 10: 42.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log c \cdot \left(b - 0.5\right)\\ t_2 := \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t \cdot 1 + y \cdot i\\ \mathbf{elif}\;t\_2 \leq 200000000:\\ \;\;\;\;t + \left(z + t\_1\right)\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;-1 \cdot \left(a \cdot \left(-1 \cdot \frac{z}{a} - 1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t + \mathsf{fma}\left(i, y, t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (log c) (- b 0.5)))
        (t_2
         (+
          (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c)))
          (* y i))))
   (if (<= t_2 (- INFINITY))
     (+ (* t 1.0) (* y i))
     (if (<= t_2 200000000.0)
       (+ t (+ z t_1))
       (if (<= t_2 INFINITY)
         (* -1.0 (* a (- (* -1.0 (/ z a)) 1.0)))
         (+ t (fma i y t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = log(c) * (b - 0.5);
	double t_2 = (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = (t * 1.0) + (y * i);
	} else if (t_2 <= 200000000.0) {
		tmp = t + (z + t_1);
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = -1.0 * (a * ((-1.0 * (z / a)) - 1.0));
	} else {
		tmp = t + fma(i, y, t_1);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(log(c) * Float64(b - 0.5))
	t_2 = Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + z) + t) + a) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(t * 1.0) + Float64(y * i));
	elseif (t_2 <= 200000000.0)
		tmp = Float64(t + Float64(z + t_1));
	elseif (t_2 <= Inf)
		tmp = Float64(-1.0 * Float64(a * Float64(Float64(-1.0 * Float64(z / a)) - 1.0)));
	else
		tmp = Float64(t + fma(i, y, t_1));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(t * 1.0), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 200000000.0], N[(t + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, Infinity], N[(-1.0 * N[(a * N[(N[(-1.0 * N[(z / a), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(i * y + t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 99.8%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 71.3%

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

   5. Taylor expanded in b around inf

      \[\leadsto t \cdot \frac{b \cdot \log c}{\color{blue}{t}} + y \cdot i \]

   7. Applied rewrites 32.3%

      \[\leadsto t \cdot \frac{b \cdot \log c}{\color{blue}{t}} + y \cdot i \]

   8. Taylor expanded in t around inf

      \[\leadsto t \cdot 1 + y \cdot i \]

   10. Applied rewrites 38.5%

       \[\leadsto t \cdot 1 + y \cdot i \]

   if -inf.0 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < 2e8

   1. Initial program 99.8%

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

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 85.1%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 62.1%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 46.5%

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

   if 2e8 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < +inf.0

   1. Initial program 99.8%

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

   2. Taylor expanded in a around -inf

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

   4. Applied rewrites 73.2%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 25.5%

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

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

   1. Initial program 99.8%

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

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 85.1%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 62.1%

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

   8. Taylor expanded in z around 0

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

   10. Applied rewrites 70.6%

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

   11. Taylor expanded in x around 0

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

   13. Applied rewrites 55.2%

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

Alternative 11: 26.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot 1 + y \cdot i\\ t_2 := \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -40:\\ \;\;\;\;-1 \cdot \left(-1 \cdot z\right)\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;-1 \cdot \left(a \cdot -1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* t 1.0) (* y i)))
        (t_2
         (+
          (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c)))
          (* y i))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -40.0)
       (* -1.0 (* -1.0 z))
       (if (<= t_2 INFINITY) (* -1.0 (* a -1.0)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (t * 1.0) + (y * i);
	double t_2 = (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -40.0) {
		tmp = -1.0 * (-1.0 * z);
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = -1.0 * (a * -1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (t * 1.0) + (y * i);
	double t_2 = (((((x * Math.log(y)) + z) + t) + a) + ((b - 0.5) * Math.log(c))) + (y * i);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -40.0) {
		tmp = -1.0 * (-1.0 * z);
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = -1.0 * (a * -1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (t * 1.0) + (y * i)
	t_2 = (((((x * math.log(y)) + z) + t) + a) + ((b - 0.5) * math.log(c))) + (y * i)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -40.0:
		tmp = -1.0 * (-1.0 * z)
	elif t_2 <= math.inf:
		tmp = -1.0 * (a * -1.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(t * 1.0) + Float64(y * i))
	t_2 = Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + z) + t) + a) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -40.0)
		tmp = Float64(-1.0 * Float64(-1.0 * z));
	elseif (t_2 <= Inf)
		tmp = Float64(-1.0 * Float64(a * -1.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (t * 1.0) + (y * i);
	t_2 = (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -40.0)
		tmp = -1.0 * (-1.0 * z);
	elseif (t_2 <= Inf)
		tmp = -1.0 * (a * -1.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(t * 1.0), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -40.0], N[(-1.0 * N[(-1.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, Infinity], N[(-1.0 * N[(a * -1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 99.8%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 71.3%

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

   5. Taylor expanded in b around inf

      \[\leadsto t \cdot \frac{b \cdot \log c}{\color{blue}{t}} + y \cdot i \]

   7. Applied rewrites 32.3%

      \[\leadsto t \cdot \frac{b \cdot \log c}{\color{blue}{t}} + y \cdot i \]

   8. Taylor expanded in t around inf

      \[\leadsto t \cdot 1 + y \cdot i \]

   10. Applied rewrites 38.5%

       \[\leadsto t \cdot 1 + y \cdot i \]

   if -inf.0 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < -40

   1. Initial program 99.8%

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

   2. Taylor expanded in a around -inf

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

   4. Applied rewrites 73.2%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 15.8%

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

   if -40 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < +inf.0

   1. Initial program 99.8%

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

   2. Taylor expanded in a around -inf

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

   4. Applied rewrites 73.2%

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

   5. Taylor expanded in a around inf

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

   7. Applied rewrites 15.7%

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

Alternative 12: 21.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot 1 + y \cdot i\\ t_2 := \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -40:\\ \;\;\;\;-1 \cdot \left(-1 \cdot z\right)\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;-1 \cdot \left(a \cdot \left(-1 \cdot \frac{z}{a} - 1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* t 1.0) (* y i)))
        (t_2
         (+
          (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c)))
          (* y i))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -40.0)
       (* -1.0 (* -1.0 z))
       (if (<= t_2 INFINITY) (* -1.0 (* a (- (* -1.0 (/ z a)) 1.0))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (t * 1.0) + (y * i);
	double t_2 = (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -40.0) {
		tmp = -1.0 * (-1.0 * z);
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = -1.0 * (a * ((-1.0 * (z / a)) - 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (t * 1.0) + (y * i);
	double t_2 = (((((x * Math.log(y)) + z) + t) + a) + ((b - 0.5) * Math.log(c))) + (y * i);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -40.0) {
		tmp = -1.0 * (-1.0 * z);
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = -1.0 * (a * ((-1.0 * (z / a)) - 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (t * 1.0) + (y * i)
	t_2 = (((((x * math.log(y)) + z) + t) + a) + ((b - 0.5) * math.log(c))) + (y * i)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -40.0:
		tmp = -1.0 * (-1.0 * z)
	elif t_2 <= math.inf:
		tmp = -1.0 * (a * ((-1.0 * (z / a)) - 1.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(t * 1.0) + Float64(y * i))
	t_2 = Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + z) + t) + a) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -40.0)
		tmp = Float64(-1.0 * Float64(-1.0 * z));
	elseif (t_2 <= Inf)
		tmp = Float64(-1.0 * Float64(a * Float64(Float64(-1.0 * Float64(z / a)) - 1.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (t * 1.0) + (y * i);
	t_2 = (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -40.0)
		tmp = -1.0 * (-1.0 * z);
	elseif (t_2 <= Inf)
		tmp = -1.0 * (a * ((-1.0 * (z / a)) - 1.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(t * 1.0), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -40.0], N[(-1.0 * N[(-1.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, Infinity], N[(-1.0 * N[(a * N[(N[(-1.0 * N[(z / a), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 99.8%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 71.3%

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

   5. Taylor expanded in b around inf

      \[\leadsto t \cdot \frac{b \cdot \log c}{\color{blue}{t}} + y \cdot i \]

   7. Applied rewrites 32.3%

      \[\leadsto t \cdot \frac{b \cdot \log c}{\color{blue}{t}} + y \cdot i \]

   8. Taylor expanded in t around inf

      \[\leadsto t \cdot 1 + y \cdot i \]

   10. Applied rewrites 38.5%

       \[\leadsto t \cdot 1 + y \cdot i \]

   if -inf.0 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < -40

   1. Initial program 99.8%

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

   2. Taylor expanded in a around -inf

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

   4. Applied rewrites 73.2%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 15.8%

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

   if -40 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i)) < +inf.0

   1. Initial program 99.8%

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

   2. Taylor expanded in a around -inf

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

   4. Applied rewrites 73.2%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 25.5%

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

Alternative 13: 15.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \leq -40:\\ \;\;\;\;-1 \cdot \left(-1 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \left(a \cdot -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<=
      (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i))
      -40.0)
   (* -1.0 (* -1.0 z))
   (* -1.0 (* a -1.0))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i)) <= -40.0) {
		tmp = -1.0 * (-1.0 * z);
	} else {
		tmp = -1.0 * (a * -1.0);
	}
	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 * log(y)) + z) + t) + a) + ((b - 0.5d0) * log(c))) + (y * i)) <= (-40.0d0)) then
        tmp = (-1.0d0) * ((-1.0d0) * z)
    else
        tmp = (-1.0d0) * (a * (-1.0d0))
    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 * Math.log(y)) + z) + t) + a) + ((b - 0.5) * Math.log(c))) + (y * i)) <= -40.0) {
		tmp = -1.0 * (-1.0 * z);
	} else {
		tmp = -1.0 * (a * -1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((((((x * math.log(y)) + z) + t) + a) + ((b - 0.5) * math.log(c))) + (y * i)) <= -40.0:
		tmp = -1.0 * (-1.0 * z)
	else:
		tmp = -1.0 * (a * -1.0)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + z) + t) + a) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i)) <= -40.0)
		tmp = Float64(-1.0 * Float64(-1.0 * z));
	else
		tmp = Float64(-1.0 * Float64(a * -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i)) <= -40.0)
		tmp = -1.0 * (-1.0 * z);
	else
		tmp = -1.0 * (a * -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], -40.0], N[(-1.0 * N[(-1.0 * z), $MachinePrecision]), $MachinePrecision], N[(-1.0 * N[(a * -1.0), $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)) < -40

   1. Initial program 99.8%

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

   2. Taylor expanded in a around -inf

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

   4. Applied rewrites 73.2%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 15.8%

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

   if -40 < (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 x (log.f64 y)) z) t) a) (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))) (*.f64 y i))

   1. Initial program 99.8%

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

   2. Taylor expanded in a around -inf

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

   4. Applied rewrites 73.2%

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

   5. Taylor expanded in a around inf

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

   7. Applied rewrites 15.7%

      \[\leadsto -1 \cdot \left(a \cdot -1\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 15.8% accurate, 5.4× speedup

Math

\[\begin{array}{l} \\ -1 \cdot \left(-1 \cdot z\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (* -1.0 (* -1.0 z)))

C

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

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) * ((-1.0d0) * z)
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 * (-1.0 * z);
}

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(-1.0 * N[(-1.0 * z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in a around -inf

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

4. Applied rewrites 73.2%

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

5. Taylor expanded in z around inf

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

7. Applied rewrites 15.8%

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

Alternative 15: 15.5% accurate, 7.6× speedup

Math

\[\begin{array}{l} \\ -1 \cdot \left(-t\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (* -1.0 (- t)))

C

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

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) * -t
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 * -t;
}

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(-1.0 * (-t)), $MachinePrecision]

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in a around -inf

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

4. Applied rewrites 73.2%

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

5. Taylor expanded in t around inf

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

7. Applied rewrites 15.9%

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

9. Applied rewrites 15.9%

   \[\leadsto -1 \cdot \color{blue}{\left(-t\right)} \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2025153 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, B"
  :precision binary64
  (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i)))