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

Percentage Accurate: 99.9% → 99.9%

Time: 23.4s

Alternatives: 17

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

real(8) function code(x, y, z, t, a, b, c, i)
    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: 99.9% 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

real(8) function code(x, y, z, t, a, b, c, i)
    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: 99.9% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. +-commutative 99.8%

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

   2. fma-def 99.8%

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

   3. +-commutative 99.8%

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

   4. fma-def 99.9%

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

   5. sub-neg 99.9%

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

   6. metadata-eval 99.9%

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

   7. +-commutative 99.9%

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

   8. associate-+l+ 99.9%

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

   9. associate-+r+ 99.9%

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

   10. +-commutative 99.9%

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

   11. fma-def 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = ((a + (t + (z + (x * log(y))))) + (log(c) * (b - 0.5d0))) + (y * i)
end function

Java

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

Python

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

Julia

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

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp = code(x, y, z, t, a, b, c, i)
	tmp = ((a + (t + (z + (x * log(y))))) + (log(c) * (b - 0.5))) + (y * i);
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(N[(a + N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $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. Final simplification 99.8%

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

Alternative 3: 89.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} t_1 := \log c \cdot \left(b - 0.5\right)\\ \mathbf{if}\;x \leq -6 \cdot 10^{+193} \lor \neg \left(x \leq 4 \cdot 10^{+234}\right):\\ \;\;\;\;t + \left(z + \left(x \cdot \log y + t_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + t_1\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (log c) (- b 0.5))))
   (if (or (<= x -6e+193) (not (<= x 4e+234)))
     (+ t (+ z (+ (* x (log y)) t_1)))
     (+ (* y i) (+ a (+ t (+ z t_1)))))))

C

assert(z < t && t < a);
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 <= -6e+193) || !(x <= 4e+234)) {
		tmp = t + (z + ((x * log(y)) + t_1));
	} else {
		tmp = (y * i) + (a + (t + (z + t_1)));
	}
	return tmp;
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    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 = log(c) * (b - 0.5d0)
    if ((x <= (-6d+193)) .or. (.not. (x <= 4d+234))) then
        tmp = t + (z + ((x * log(y)) + t_1))
    else
        tmp = (y * i) + (a + (t + (z + t_1)))
    end if
    code = tmp
end function

Java

assert z < t && t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = Math.log(c) * (b - 0.5);
	double tmp;
	if ((x <= -6e+193) || !(x <= 4e+234)) {
		tmp = t + (z + ((x * Math.log(y)) + t_1));
	} else {
		tmp = (y * i) + (a + (t + (z + t_1)));
	}
	return tmp;
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	t_1 = math.log(c) * (b - 0.5)
	tmp = 0
	if (x <= -6e+193) or not (x <= 4e+234):
		tmp = t + (z + ((x * math.log(y)) + t_1))
	else:
		tmp = (y * i) + (a + (t + (z + t_1)))
	return tmp

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(log(c) * Float64(b - 0.5))
	tmp = 0.0
	if ((x <= -6e+193) || !(x <= 4e+234))
		tmp = Float64(t + Float64(z + Float64(Float64(x * log(y)) + t_1)));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(t + Float64(z + t_1))));
	end
	return tmp
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = log(c) * (b - 0.5);
	tmp = 0.0;
	if ((x <= -6e+193) || ~((x <= 4e+234)))
		tmp = t + (z + ((x * log(y)) + t_1));
	else
		tmp = (y * i) + (a + (t + (z + t_1)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -6e+193], N[Not[LessEqual[x, 4e+234]], $MachinePrecision]], N[(t + N[(z + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(t + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -6e193 or 4.00000000000000007e234 < x

   1. Initial program 99.6%

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

      1. add-cube-cbrt 98.7%

         \[\leadsto \left(\left(\left(\left(\color{blue}{\left(\sqrt[3]{x \cdot \log y} \cdot \sqrt[3]{x \cdot \log y}\right) \cdot \sqrt[3]{x \cdot \log y}} + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      2. pow3 98.5%

         \[\leadsto \left(\left(\left(\left(\color{blue}{{\left(\sqrt[3]{x \cdot \log y}\right)}^{3}} + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   3. Applied egg-rr 98.5%

      \[\leadsto \left(\left(\left(\left(\color{blue}{{\left(\sqrt[3]{x \cdot \log y}\right)}^{3}} + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Taylor expanded in a around 0 89.4%

      \[\leadsto \color{blue}{\left(t + \left(z + \left(\log c \cdot \left(b - 0.5\right) + {1}^{0.3333333333333333} \cdot \left(x \cdot \log y\right)\right)\right)\right)} + y \cdot i \]
   5. Step-by-step derivation

      1. associate-+r+ 89.4%

         \[\leadsto \color{blue}{\left(\left(t + z\right) + \left(\log c \cdot \left(b - 0.5\right) + {1}^{0.3333333333333333} \cdot \left(x \cdot \log y\right)\right)\right)} + y \cdot i \]

      2. sub-neg 89.4%

         \[\leadsto \left(\left(t + z\right) + \left(\log c \cdot \color{blue}{\left(b + \left(-0.5\right)\right)} + {1}^{0.3333333333333333} \cdot \left(x \cdot \log y\right)\right)\right) + y \cdot i \]

      3. metadata-eval 89.4%

         \[\leadsto \left(\left(t + z\right) + \left(\log c \cdot \left(b + \color{blue}{-0.5}\right) + {1}^{0.3333333333333333} \cdot \left(x \cdot \log y\right)\right)\right) + y \cdot i \]

      4. fma-def 89.4%

         \[\leadsto \left(\left(t + z\right) + \color{blue}{\mathsf{fma}\left(\log c, b + -0.5, {1}^{0.3333333333333333} \cdot \left(x \cdot \log y\right)\right)}\right) + y \cdot i \]

      5. pow-base-1 89.4%

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

      6. *-lft-identity 89.4%

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

   6. Simplified 89.4%

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

   7. Taylor expanded in y around 0 83.4%

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

   if -6e193 < x < 4.00000000000000007e234

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 95.5%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+193} \lor \neg \left(x \leq 4 \cdot 10^{+234}\right):\\ \;\;\;\;t + \left(z + \left(x \cdot \log y + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \end{array} \]

Alternative 4: 89.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{+195} \lor \neg \left(x \leq 6 \cdot 10^{+234}\right):\\ \;\;\;\;t + \left(z + \left(x \cdot \log y + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \mathsf{fma}\left(\log c, b + -0.5, a + \left(z + t\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -1.95e+195) (not (<= x 6e+234)))
   (+ t (+ z (+ (* x (log y)) (* (log c) (- b 0.5)))))
   (+ (* y i) (fma (log c) (+ b -0.5) (+ a (+ z t))))))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1.95e+195) || !(x <= 6e+234)) {
		tmp = t + (z + ((x * log(y)) + (log(c) * (b - 0.5))));
	} else {
		tmp = (y * i) + fma(log(c), (b + -0.5), (a + (z + t)));
	}
	return tmp;
}

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -1.95e+195) || !(x <= 6e+234))
		tmp = Float64(t + Float64(z + Float64(Float64(x * log(y)) + Float64(log(c) * Float64(b - 0.5)))));
	else
		tmp = Float64(Float64(y * i) + fma(log(c), Float64(b + -0.5), Float64(a + Float64(z + t))));
	end
	return tmp
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -1.95e+195], N[Not[LessEqual[x, 6e+234]], $MachinePrecision]], N[(t + N[(z + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.9499999999999999e195 or 5.9999999999999998e234 < x

   1. Initial program 99.6%

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

      1. add-cube-cbrt 98.7%

         \[\leadsto \left(\left(\left(\left(\color{blue}{\left(\sqrt[3]{x \cdot \log y} \cdot \sqrt[3]{x \cdot \log y}\right) \cdot \sqrt[3]{x \cdot \log y}} + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      2. pow3 98.5%

         \[\leadsto \left(\left(\left(\left(\color{blue}{{\left(\sqrt[3]{x \cdot \log y}\right)}^{3}} + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   3. Applied egg-rr 98.5%

      \[\leadsto \left(\left(\left(\left(\color{blue}{{\left(\sqrt[3]{x \cdot \log y}\right)}^{3}} + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Taylor expanded in a around 0 89.4%

      \[\leadsto \color{blue}{\left(t + \left(z + \left(\log c \cdot \left(b - 0.5\right) + {1}^{0.3333333333333333} \cdot \left(x \cdot \log y\right)\right)\right)\right)} + y \cdot i \]
   5. Step-by-step derivation

      1. associate-+r+ 89.4%

         \[\leadsto \color{blue}{\left(\left(t + z\right) + \left(\log c \cdot \left(b - 0.5\right) + {1}^{0.3333333333333333} \cdot \left(x \cdot \log y\right)\right)\right)} + y \cdot i \]

      2. sub-neg 89.4%

         \[\leadsto \left(\left(t + z\right) + \left(\log c \cdot \color{blue}{\left(b + \left(-0.5\right)\right)} + {1}^{0.3333333333333333} \cdot \left(x \cdot \log y\right)\right)\right) + y \cdot i \]

      3. metadata-eval 89.4%

         \[\leadsto \left(\left(t + z\right) + \left(\log c \cdot \left(b + \color{blue}{-0.5}\right) + {1}^{0.3333333333333333} \cdot \left(x \cdot \log y\right)\right)\right) + y \cdot i \]

      4. fma-def 89.4%

         \[\leadsto \left(\left(t + z\right) + \color{blue}{\mathsf{fma}\left(\log c, b + -0.5, {1}^{0.3333333333333333} \cdot \left(x \cdot \log y\right)\right)}\right) + y \cdot i \]

      5. pow-base-1 89.4%

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

      6. *-lft-identity 89.4%

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

   6. Simplified 89.4%

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

   7. Taylor expanded in y around 0 83.4%

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

   if -1.9499999999999999e195 < x < 5.9999999999999998e234

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 95.5%

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

      1. associate-+r+ 95.5%

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

      2. +-commutative 95.5%

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

      3. *-commutative 95.5%

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

      4. sub-neg 95.5%

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

      5. metadata-eval 95.5%

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

      6. associate-+r+ 95.5%

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

      7. +-commutative 95.5%

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

      8. +-commutative 95.5%

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

      9. associate-+r+ 95.5%

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

      10. +-commutative 95.5%

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

      11. *-commutative 95.5%

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

      12. fma-def 95.5%

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

      13. +-commutative 95.5%

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

      14. associate-+r+ 95.5%

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

      15. +-commutative 95.5%

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

      16. +-commutative 95.5%

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

      17. +-commutative 95.5%

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

   4. Simplified 95.5%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{+195} \lor \neg \left(x \leq 6 \cdot 10^{+234}\right):\\ \;\;\;\;t + \left(z + \left(x \cdot \log y + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \mathsf{fma}\left(\log c, b + -0.5, a + \left(z + t\right)\right)\\ \end{array} \]

Alternative 5: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    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) + ((a + (t + (z + (x * log(y))))) + (b * log(c)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in b around inf 97.0%

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

   1. *-commutative 97.0%

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

4. Simplified 97.0%

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

5. Final simplification 97.0%

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

Alternative 6: 66.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot \log y + y \cdot i\\ t_2 := a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{if}\;y \leq 6.55 \cdot 10^{+47}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+76}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+93}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+128}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+139}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+189}:\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+242}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x (log y)) (* y i)))
        (t_2 (+ a (+ z (* (log c) (- b 0.5))))))
   (if (<= y 6.55e+47)
     t_2
     (if (<= y 7.2e+76)
       t_1
       (if (<= y 3e+93)
         t_2
         (if (<= y 3.8e+128)
           t_1
           (if (<= y 5.2e+139)
             t_2
             (if (<= y 8.2e+189)
               (+ (* y i) (* b (log c)))
               (if (<= y 3.6e+242) (+ z (* y i)) t_1)))))))))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * log(y)) + (y * i);
	double t_2 = a + (z + (log(c) * (b - 0.5)));
	double tmp;
	if (y <= 6.55e+47) {
		tmp = t_2;
	} else if (y <= 7.2e+76) {
		tmp = t_1;
	} else if (y <= 3e+93) {
		tmp = t_2;
	} else if (y <= 3.8e+128) {
		tmp = t_1;
	} else if (y <= 5.2e+139) {
		tmp = t_2;
	} else if (y <= 8.2e+189) {
		tmp = (y * i) + (b * log(c));
	} else if (y <= 3.6e+242) {
		tmp = z + (y * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * log(y)) + (y * i)
    t_2 = a + (z + (log(c) * (b - 0.5d0)))
    if (y <= 6.55d+47) then
        tmp = t_2
    else if (y <= 7.2d+76) then
        tmp = t_1
    else if (y <= 3d+93) then
        tmp = t_2
    else if (y <= 3.8d+128) then
        tmp = t_1
    else if (y <= 5.2d+139) then
        tmp = t_2
    else if (y <= 8.2d+189) then
        tmp = (y * i) + (b * log(c))
    else if (y <= 3.6d+242) then
        tmp = z + (y * i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert z < t && t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * Math.log(y)) + (y * i);
	double t_2 = a + (z + (Math.log(c) * (b - 0.5)));
	double tmp;
	if (y <= 6.55e+47) {
		tmp = t_2;
	} else if (y <= 7.2e+76) {
		tmp = t_1;
	} else if (y <= 3e+93) {
		tmp = t_2;
	} else if (y <= 3.8e+128) {
		tmp = t_1;
	} else if (y <= 5.2e+139) {
		tmp = t_2;
	} else if (y <= 8.2e+189) {
		tmp = (y * i) + (b * Math.log(c));
	} else if (y <= 3.6e+242) {
		tmp = z + (y * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	t_1 = (x * math.log(y)) + (y * i)
	t_2 = a + (z + (math.log(c) * (b - 0.5)))
	tmp = 0
	if y <= 6.55e+47:
		tmp = t_2
	elif y <= 7.2e+76:
		tmp = t_1
	elif y <= 3e+93:
		tmp = t_2
	elif y <= 3.8e+128:
		tmp = t_1
	elif y <= 5.2e+139:
		tmp = t_2
	elif y <= 8.2e+189:
		tmp = (y * i) + (b * math.log(c))
	elif y <= 3.6e+242:
		tmp = z + (y * i)
	else:
		tmp = t_1
	return tmp

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * log(y)) + Float64(y * i))
	t_2 = Float64(a + Float64(z + Float64(log(c) * Float64(b - 0.5))))
	tmp = 0.0
	if (y <= 6.55e+47)
		tmp = t_2;
	elseif (y <= 7.2e+76)
		tmp = t_1;
	elseif (y <= 3e+93)
		tmp = t_2;
	elseif (y <= 3.8e+128)
		tmp = t_1;
	elseif (y <= 5.2e+139)
		tmp = t_2;
	elseif (y <= 8.2e+189)
		tmp = Float64(Float64(y * i) + Float64(b * log(c)));
	elseif (y <= 3.6e+242)
		tmp = Float64(z + Float64(y * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * log(y)) + (y * i);
	t_2 = a + (z + (log(c) * (b - 0.5)));
	tmp = 0.0;
	if (y <= 6.55e+47)
		tmp = t_2;
	elseif (y <= 7.2e+76)
		tmp = t_1;
	elseif (y <= 3e+93)
		tmp = t_2;
	elseif (y <= 3.8e+128)
		tmp = t_1;
	elseif (y <= 5.2e+139)
		tmp = t_2;
	elseif (y <= 8.2e+189)
		tmp = (y * i) + (b * log(c));
	elseif (y <= 3.6e+242)
		tmp = z + (y * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, 6.55e+47], t$95$2, If[LessEqual[y, 7.2e+76], t$95$1, If[LessEqual[y, 3e+93], t$95$2, If[LessEqual[y, 3.8e+128], t$95$1, If[LessEqual[y, 5.2e+139], t$95$2, If[LessEqual[y, 8.2e+189], N[(N[(y * i), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6e+242], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < 6.55000000000000025e47 or 7.2000000000000006e76 < y < 2.99999999999999978e93 or 3.7999999999999999e128 < y < 5.20000000000000044e139

   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 86.3%

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

      1. associate-+r+ 86.3%

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

      2. +-commutative 86.3%

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

      3. *-commutative 86.3%

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

      4. sub-neg 86.3%

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

      5. metadata-eval 86.3%

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

      6. associate-+r+ 86.3%

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

      7. +-commutative 86.3%

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

      8. +-commutative 86.3%

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

      9. associate-+r+ 86.3%

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

      10. +-commutative 86.3%

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

      11. *-commutative 86.3%

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

      12. fma-def 86.3%

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

      13. +-commutative 86.3%

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

      14. associate-+r+ 86.3%

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

      15. +-commutative 86.3%

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

      16. +-commutative 86.3%

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

      17. +-commutative 86.3%

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

   4. Simplified 86.3%

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

   5. Taylor expanded in t around 0 69.2%

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

   6. Taylor expanded in y around 0 65.8%

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

   if 6.55000000000000025e47 < y < 7.2000000000000006e76 or 2.99999999999999978e93 < y < 3.7999999999999999e128 or 3.59999999999999995e242 < y

   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 inf 82.6%

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

   if 5.20000000000000044e139 < y < 8.2000000000000004e189

   1. Initial program 99.9%

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

      1. add-cube-cbrt 99.9%

         \[\leadsto \left(\left(\left(\left(\color{blue}{\left(\sqrt[3]{x \cdot \log y} \cdot \sqrt[3]{x \cdot \log y}\right) \cdot \sqrt[3]{x \cdot \log y}} + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      2. pow3 99.9%

         \[\leadsto \left(\left(\left(\left(\color{blue}{{\left(\sqrt[3]{x \cdot \log y}\right)}^{3}} + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   3. Applied egg-rr 99.9%

      \[\leadsto \left(\left(\left(\left(\color{blue}{{\left(\sqrt[3]{x \cdot \log y}\right)}^{3}} + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Taylor expanded in b around inf 77.7%

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

      1. *-commutative 77.7%

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

   6. Simplified 77.7%

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

   if 8.2000000000000004e189 < y < 3.59999999999999995e242

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 57.6%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 6.55 \cdot 10^{+47}:\\ \;\;\;\;a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+76}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+93}:\\ \;\;\;\;a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+128}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+139}:\\ \;\;\;\;a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+189}:\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+242}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \end{array} \]

Alternative 7: 89.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+192} \lor \neg \left(x \leq 4.1 \cdot 10^{+207}\right):\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -1.05e+192) (not (<= x 4.1e+207)))
   (+ (* x (log y)) (* y i))
   (+ (* y i) (+ a (+ t (+ z (* (log c) (- b 0.5))))))))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1.05e+192) || !(x <= 4.1e+207)) {
		tmp = (x * log(y)) + (y * i);
	} else {
		tmp = (y * i) + (a + (t + (z + (log(c) * (b - 0.5)))));
	}
	return tmp;
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    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 <= (-1.05d+192)) .or. (.not. (x <= 4.1d+207))) then
        tmp = (x * log(y)) + (y * i)
    else
        tmp = (y * i) + (a + (t + (z + (log(c) * (b - 0.5d0)))))
    end if
    code = tmp
end function

Java

assert z < t && t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1.05e+192) || !(x <= 4.1e+207)) {
		tmp = (x * Math.log(y)) + (y * i);
	} else {
		tmp = (y * i) + (a + (t + (z + (Math.log(c) * (b - 0.5)))));
	}
	return tmp;
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -1.05e+192) or not (x <= 4.1e+207):
		tmp = (x * math.log(y)) + (y * i)
	else:
		tmp = (y * i) + (a + (t + (z + (math.log(c) * (b - 0.5)))))
	return tmp

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -1.05e+192) || !(x <= 4.1e+207))
		tmp = Float64(Float64(x * log(y)) + Float64(y * i));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(t + Float64(z + Float64(log(c) * Float64(b - 0.5))))));
	end
	return tmp
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -1.05e+192) || ~((x <= 4.1e+207)))
		tmp = (x * log(y)) + (y * i);
	else
		tmp = (y * i) + (a + (t + (z + (log(c) * (b - 0.5)))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -1.05e+192], N[Not[LessEqual[x, 4.1e+207]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(t + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.04999999999999997e192 or 4.1e207 < x

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 74.6%

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

   if -1.04999999999999997e192 < x < 4.1e207

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 97.1%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+192} \lor \neg \left(x \leq 4.1 \cdot 10^{+207}\right):\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \end{array} \]

Alternative 8: 89.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+193} \lor \neg \left(x \leq 1.5 \cdot 10^{+206}\right):\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -9.5e+193) (not (<= x 1.5e+206)))
   (+ (* x (log y)) (* y i))
   (+ (* y i) (+ a (+ z (* (log c) (- b 0.5)))))))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -9.5e+193) || !(x <= 1.5e+206)) {
		tmp = (x * log(y)) + (y * i);
	} else {
		tmp = (y * i) + (a + (z + (log(c) * (b - 0.5))));
	}
	return tmp;
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    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 <= (-9.5d+193)) .or. (.not. (x <= 1.5d+206))) then
        tmp = (x * log(y)) + (y * i)
    else
        tmp = (y * i) + (a + (z + (log(c) * (b - 0.5d0))))
    end if
    code = tmp
end function

Java

assert z < t && t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -9.5e+193) || !(x <= 1.5e+206)) {
		tmp = (x * Math.log(y)) + (y * i);
	} else {
		tmp = (y * i) + (a + (z + (Math.log(c) * (b - 0.5))));
	}
	return tmp;
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -9.5e+193) or not (x <= 1.5e+206):
		tmp = (x * math.log(y)) + (y * i)
	else:
		tmp = (y * i) + (a + (z + (math.log(c) * (b - 0.5))))
	return tmp

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -9.5e+193) || !(x <= 1.5e+206))
		tmp = Float64(Float64(x * log(y)) + Float64(y * i));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + Float64(log(c) * Float64(b - 0.5)))));
	end
	return tmp
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -9.5e+193) || ~((x <= 1.5e+206)))
		tmp = (x * log(y)) + (y * i);
	else
		tmp = (y * i) + (a + (z + (log(c) * (b - 0.5))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -9.5e+193], N[Not[LessEqual[x, 1.5e+206]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.4999999999999997e193 or 1.5000000000000001e206 < x

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 74.6%

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

   if -9.4999999999999997e193 < x < 1.5000000000000001e206

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 97.1%

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

      1. associate-+r+ 97.1%

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

      2. +-commutative 97.1%

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

      3. *-commutative 97.1%

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

      4. sub-neg 97.1%

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

      5. metadata-eval 97.1%

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

      6. associate-+r+ 97.1%

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

      7. +-commutative 97.1%

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

      8. +-commutative 97.1%

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

      9. associate-+r+ 97.1%

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

      10. +-commutative 97.1%

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

      11. *-commutative 97.1%

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

      12. fma-def 97.1%

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

      13. +-commutative 97.1%

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

      14. associate-+r+ 97.1%

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

      15. +-commutative 97.1%

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

      16. +-commutative 97.1%

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

      17. +-commutative 97.1%

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

   4. Simplified 97.1%

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

   5. Taylor expanded in t around 0 82.5%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+193} \lor \neg \left(x \leq 1.5 \cdot 10^{+206}\right):\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \end{array} \]

Alternative 9: 71.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 6.55 \cdot 10^{+47}:\\ \;\;\;\;a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+59}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(b \cdot \log c + \left(z + t\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 6.55e+47)
   (+ a (+ z (* (log c) (- b 0.5))))
   (if (<= y 5e+59)
     (+ (* x (log y)) (* y i))
     (+ (* y i) (+ (* b (log c)) (+ z t))))))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 6.55e+47) {
		tmp = a + (z + (log(c) * (b - 0.5)));
	} else if (y <= 5e+59) {
		tmp = (x * log(y)) + (y * i);
	} else {
		tmp = (y * i) + ((b * log(c)) + (z + t));
	}
	return tmp;
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    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 (y <= 6.55d+47) then
        tmp = a + (z + (log(c) * (b - 0.5d0)))
    else if (y <= 5d+59) then
        tmp = (x * log(y)) + (y * i)
    else
        tmp = (y * i) + ((b * log(c)) + (z + t))
    end if
    code = tmp
end function

Java

assert z < t && t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 6.55e+47) {
		tmp = a + (z + (Math.log(c) * (b - 0.5)));
	} else if (y <= 5e+59) {
		tmp = (x * Math.log(y)) + (y * i);
	} else {
		tmp = (y * i) + ((b * Math.log(c)) + (z + t));
	}
	return tmp;
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 6.55e+47:
		tmp = a + (z + (math.log(c) * (b - 0.5)))
	elif y <= 5e+59:
		tmp = (x * math.log(y)) + (y * i)
	else:
		tmp = (y * i) + ((b * math.log(c)) + (z + t))
	return tmp

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 6.55e+47)
		tmp = Float64(a + Float64(z + Float64(log(c) * Float64(b - 0.5))));
	elseif (y <= 5e+59)
		tmp = Float64(Float64(x * log(y)) + Float64(y * i));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(b * log(c)) + Float64(z + t)));
	end
	return tmp
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= 6.55e+47)
		tmp = a + (z + (log(c) * (b - 0.5)));
	elseif (y <= 5e+59)
		tmp = (x * log(y)) + (y * i);
	else
		tmp = (y * i) + ((b * log(c)) + (z + t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 6.55e+47], N[(a + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5e+59], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision] + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 6.55000000000000025e47

   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 84.8%

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

      1. associate-+r+ 84.8%

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

      2. +-commutative 84.8%

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

      3. *-commutative 84.8%

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

      4. sub-neg 84.8%

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

      5. metadata-eval 84.8%

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

      6. associate-+r+ 84.8%

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

      7. +-commutative 84.8%

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

      8. +-commutative 84.8%

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

      9. associate-+r+ 84.8%

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

      10. +-commutative 84.8%

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

      11. *-commutative 84.8%

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

      12. fma-def 84.8%

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

      13. +-commutative 84.8%

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

      14. associate-+r+ 84.8%

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

      15. +-commutative 84.8%

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

      16. +-commutative 84.8%

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

      17. +-commutative 84.8%

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

   4. Simplified 84.8%

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

   5. Taylor expanded in t around 0 68.1%

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

   6. Taylor expanded in y around 0 65.8%

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

   if 6.55000000000000025e47 < y < 4.9999999999999997e59

   1. Initial program 99.3%

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

   2. Taylor expanded in x around inf 85.9%

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

   if 4.9999999999999997e59 < y

   1. Initial program 99.9%

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

      1. add-cube-cbrt 99.8%

         \[\leadsto \left(\left(\left(\left(\color{blue}{\left(\sqrt[3]{x \cdot \log y} \cdot \sqrt[3]{x \cdot \log y}\right) \cdot \sqrt[3]{x \cdot \log y}} + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      2. pow3 99.8%

         \[\leadsto \left(\left(\left(\left(\color{blue}{{\left(\sqrt[3]{x \cdot \log y}\right)}^{3}} + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   3. Applied egg-rr 99.8%

      \[\leadsto \left(\left(\left(\left(\color{blue}{{\left(\sqrt[3]{x \cdot \log y}\right)}^{3}} + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Taylor expanded in a around 0 90.8%

      \[\leadsto \color{blue}{\left(t + \left(z + \left(\log c \cdot \left(b - 0.5\right) + {1}^{0.3333333333333333} \cdot \left(x \cdot \log y\right)\right)\right)\right)} + y \cdot i \]
   5. Step-by-step derivation

      1. associate-+r+ 90.8%

         \[\leadsto \color{blue}{\left(\left(t + z\right) + \left(\log c \cdot \left(b - 0.5\right) + {1}^{0.3333333333333333} \cdot \left(x \cdot \log y\right)\right)\right)} + y \cdot i \]

      2. sub-neg 90.8%

         \[\leadsto \left(\left(t + z\right) + \left(\log c \cdot \color{blue}{\left(b + \left(-0.5\right)\right)} + {1}^{0.3333333333333333} \cdot \left(x \cdot \log y\right)\right)\right) + y \cdot i \]

      3. metadata-eval 90.8%

         \[\leadsto \left(\left(t + z\right) + \left(\log c \cdot \left(b + \color{blue}{-0.5}\right) + {1}^{0.3333333333333333} \cdot \left(x \cdot \log y\right)\right)\right) + y \cdot i \]

      4. fma-def 90.8%

         \[\leadsto \left(\left(t + z\right) + \color{blue}{\mathsf{fma}\left(\log c, b + -0.5, {1}^{0.3333333333333333} \cdot \left(x \cdot \log y\right)\right)}\right) + y \cdot i \]

      5. pow-base-1 90.8%

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

      6. *-lft-identity 90.8%

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

   6. Simplified 90.8%

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

   7. Taylor expanded in b around inf 84.0%

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

      1. *-commutative 84.0%

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

   9. Simplified 84.0%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 6.55 \cdot 10^{+47}:\\ \;\;\;\;a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+59}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(b \cdot \log c + \left(z + t\right)\right)\\ \end{array} \]

Alternative 10: 59.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 3.15 \cdot 10^{-21}:\\ \;\;\;\;\mathsf{fma}\left(y, i, z\right)\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{+19}:\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{elif}\;a \leq 1.66 \cdot 10^{+128}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 3.15e-21)
   (fma y i z)
   (if (<= a 1.95e+19)
     (+ (* y i) (* b (log c)))
     (if (<= a 1.66e+128) (+ z (* y i)) (fma y i a)))))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 3.15e-21) {
		tmp = fma(y, i, z);
	} else if (a <= 1.95e+19) {
		tmp = (y * i) + (b * log(c));
	} else if (a <= 1.66e+128) {
		tmp = z + (y * i);
	} else {
		tmp = fma(y, i, a);
	}
	return tmp;
}

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 3.15e-21)
		tmp = fma(y, i, z);
	elseif (a <= 1.95e+19)
		tmp = Float64(Float64(y * i) + Float64(b * log(c)));
	elseif (a <= 1.66e+128)
		tmp = Float64(z + Float64(y * i));
	else
		tmp = fma(y, i, a);
	end
	return tmp
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 3.15e-21], N[(y * i + z), $MachinePrecision], If[LessEqual[a, 1.95e+19], N[(N[(y * i), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.66e+128], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(y * i + a), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < 3.15e-21

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 45.1%

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

   3. Taylor expanded in z around 0 45.1%

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

      1. +-commutative 45.1%

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

      2. *-commutative 45.1%

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

      3. fma-udef 45.1%

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

   5. Simplified 45.1%

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

   if 3.15e-21 < a < 1.95e19

   1. Initial program 99.7%

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

      1. add-cube-cbrt 99.5%

         \[\leadsto \left(\left(\left(\left(\color{blue}{\left(\sqrt[3]{x \cdot \log y} \cdot \sqrt[3]{x \cdot \log y}\right) \cdot \sqrt[3]{x \cdot \log y}} + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      2. pow3 99.5%

         \[\leadsto \left(\left(\left(\left(\color{blue}{{\left(\sqrt[3]{x \cdot \log y}\right)}^{3}} + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   3. Applied egg-rr 99.5%

      \[\leadsto \left(\left(\left(\left(\color{blue}{{\left(\sqrt[3]{x \cdot \log y}\right)}^{3}} + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Taylor expanded in b around inf 67.4%

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

      1. *-commutative 67.4%

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

   6. Simplified 67.4%

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

   if 1.95e19 < a < 1.6599999999999999e128

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 51.0%

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

   if 1.6599999999999999e128 < a

   1. Initial program 99.9%

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

   2. Taylor expanded in a around inf 56.0%

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

   3. Taylor expanded in a around 0 56.0%

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

      1. +-commutative 56.0%

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

      2. *-commutative 56.0%

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

      3. fma-def 56.0%

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

   5. Simplified 56.0%

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

4. Final simplification 48.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 3.15 \cdot 10^{-21}:\\ \;\;\;\;\mathsf{fma}\left(y, i, z\right)\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{+19}:\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{elif}\;a \leq 1.66 \cdot 10^{+128}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, a\right)\\ \end{array} \]

Alternative 11: 59.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 4.2 \cdot 10^{+128}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 4.2e+128) (+ z (* y i)) (fma y i a)))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 4.2e+128) {
		tmp = z + (y * i);
	} else {
		tmp = fma(y, i, a);
	}
	return tmp;
}

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 4.2e+128)
		tmp = Float64(z + Float64(y * i));
	else
		tmp = fma(y, i, a);
	end
	return tmp
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 4.2e+128], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(y * i + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 4.1999999999999999e128

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 45.2%

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

   if 4.1999999999999999e128 < a

   1. Initial program 99.9%

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

   2. Taylor expanded in a around inf 56.0%

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

   3. Taylor expanded in a around 0 56.0%

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

      1. +-commutative 56.0%

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

      2. *-commutative 56.0%

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

      3. fma-def 56.0%

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

   5. Simplified 56.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, a\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 46.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 4.2 \cdot 10^{+128}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, a\right)\\ \end{array} \]

Alternative 12: 59.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 5.8 \cdot 10^{+128}:\\ \;\;\;\;\mathsf{fma}\left(y, i, z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 5.8e+128) (fma y i z) (fma y i a)))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 5.8e+128) {
		tmp = fma(y, i, z);
	} else {
		tmp = fma(y, i, a);
	}
	return tmp;
}

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 5.8e+128)
		tmp = fma(y, i, z);
	else
		tmp = fma(y, i, a);
	end
	return tmp
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 5.8e+128], N[(y * i + z), $MachinePrecision], N[(y * i + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 5.8000000000000001e128

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 45.2%

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

   3. Taylor expanded in z around 0 45.2%

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

      1. +-commutative 45.2%

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

      2. *-commutative 45.2%

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

      3. fma-udef 45.2%

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

   5. Simplified 45.2%

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

   if 5.8000000000000001e128 < a

   1. Initial program 99.9%

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

   2. Taylor expanded in a around inf 56.0%

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

   3. Taylor expanded in a around 0 56.0%

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

      1. +-commutative 56.0%

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

      2. *-commutative 56.0%

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

      3. fma-def 56.0%

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

   5. Simplified 56.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, a\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 46.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 5.8 \cdot 10^{+128}:\\ \;\;\;\;\mathsf{fma}\left(y, i, z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, a\right)\\ \end{array} \]

Alternative 13: 34.1% accurate, 30.7× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 1.1 \cdot 10^{-126}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+57}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 1.1e-126) z (if (<= y 1.2e+57) a (* y i))))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 1.1e-126) {
		tmp = z;
	} else if (y <= 1.2e+57) {
		tmp = a;
	} else {
		tmp = y * i;
	}
	return tmp;
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    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 (y <= 1.1d-126) then
        tmp = z
    else if (y <= 1.2d+57) then
        tmp = a
    else
        tmp = y * i
    end if
    code = tmp
end function

Java

assert z < t && t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 1.1e-126) {
		tmp = z;
	} else if (y <= 1.2e+57) {
		tmp = a;
	} else {
		tmp = y * i;
	}
	return tmp;
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 1.1e-126:
		tmp = z
	elif y <= 1.2e+57:
		tmp = a
	else:
		tmp = y * i
	return tmp

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 1.1e-126)
		tmp = z;
	elseif (y <= 1.2e+57)
		tmp = a;
	else
		tmp = Float64(y * i);
	end
	return tmp
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= 1.1e-126)
		tmp = z;
	elseif (y <= 1.2e+57)
		tmp = a;
	else
		tmp = y * i;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 1.1e-126], z, If[LessEqual[y, 1.2e+57], a, N[(y * i), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 1.10000000000000007e-126

   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 82.6%

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

      1. associate-+r+ 82.6%

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

      2. +-commutative 82.6%

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

      3. *-commutative 82.6%

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

      4. sub-neg 82.6%

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

      5. metadata-eval 82.6%

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

      6. associate-+r+ 82.6%

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

      7. +-commutative 82.6%

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

      8. +-commutative 82.6%

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

      9. associate-+r+ 82.6%

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

      10. +-commutative 82.6%

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

      11. *-commutative 82.6%

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

      12. fma-def 82.6%

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

      13. +-commutative 82.6%

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

      14. associate-+r+ 82.6%

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

      15. +-commutative 82.6%

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

      16. +-commutative 82.6%

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

      17. +-commutative 82.6%

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

   4. Simplified 82.6%

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

   5. Taylor expanded in b around 0 56.5%

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

      1. associate-+r+ 56.5%

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

      2. *-commutative 56.5%

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

   7. Simplified 56.5%

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

   8. Taylor expanded in z around inf 21.2%

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

   if 1.10000000000000007e-126 < y < 1.20000000000000002e57

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 83.8%

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

      1. associate-+r+ 83.8%

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

      2. +-commutative 83.8%

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

      3. *-commutative 83.8%

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

      4. sub-neg 83.8%

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

      5. metadata-eval 83.8%

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

      6. associate-+r+ 83.8%

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

      7. +-commutative 83.8%

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

      8. +-commutative 83.8%

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

      9. associate-+r+ 83.8%

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

      10. +-commutative 83.8%

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

      11. *-commutative 83.8%

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

      12. fma-def 83.8%

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

      13. +-commutative 83.8%

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

      14. associate-+r+ 83.8%

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

      15. +-commutative 83.8%

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

      16. +-commutative 83.8%

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

      17. +-commutative 83.8%

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

   4. Simplified 83.8%

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

   5. Taylor expanded in b around 0 67.8%

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

      1. associate-+r+ 67.8%

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

      2. *-commutative 67.8%

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

   7. Simplified 67.8%

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

   8. Taylor expanded in a around inf 18.1%

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

   if 1.20000000000000002e57 < y

   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 60.9%

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

   3. Taylor expanded in a around 0 52.6%

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

      1. *-commutative 52.6%

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

   5. Simplified 52.6%

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

4. Final simplification 33.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.1 \cdot 10^{-126}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+57}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \]

Alternative 14: 53.8% accurate, 31.0× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+216}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -1.65e+216) z (+ a (* y i))))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -1.65e+216) {
		tmp = z;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    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 (z <= (-1.65d+216)) then
        tmp = z
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

assert z < t && t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -1.65e+216) {
		tmp = z;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -1.65e+216:
		tmp = z
	else:
		tmp = a + (y * i)
	return tmp

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -1.65e+216)
		tmp = z;
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -1.65e+216)
		tmp = z;
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -1.65e+216], z, N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.65e216

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 95.1%

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

      1. associate-+r+ 95.1%

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

      2. +-commutative 95.1%

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

      3. *-commutative 95.1%

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

      4. sub-neg 95.1%

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

      5. metadata-eval 95.1%

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

      6. associate-+r+ 95.1%

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

      7. +-commutative 95.1%

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

      8. +-commutative 95.1%

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

      9. associate-+r+ 95.1%

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

      10. +-commutative 95.1%

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

      11. *-commutative 95.1%

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

      12. fma-def 95.1%

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

      13. +-commutative 95.1%

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

      14. associate-+r+ 95.1%

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

      15. +-commutative 95.1%

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

      16. +-commutative 95.1%

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

      17. +-commutative 95.1%

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

   4. Simplified 95.1%

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

   5. Taylor expanded in b around 0 95.1%

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

      1. associate-+r+ 95.1%

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

      2. *-commutative 95.1%

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

   7. Simplified 95.1%

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

   8. Taylor expanded in z around inf 68.5%

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

   if -1.65e216 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in a around inf 39.9%

      \[\leadsto \color{blue}{a} + y \cdot i \]
3. Recombined 2 regimes into one program.

4. Final simplification 41.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+216}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]

Alternative 15: 59.9% accurate, 31.0× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 3.1 \cdot 10^{+128}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 3.1e+128) (+ z (* y i)) (+ a (* y i))))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 3.1e+128) {
		tmp = z + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 3.1d+128) then
        tmp = z + (y * i)
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

assert z < t && t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 3.1e+128) {
		tmp = z + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 3.1e+128:
		tmp = z + (y * i)
	else:
		tmp = a + (y * i)
	return tmp

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 3.1e+128)
		tmp = Float64(z + Float64(y * i));
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 3.1e+128)
		tmp = z + (y * i);
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 3.1e+128], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 3.10000000000000004e128

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 45.2%

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

   if 3.10000000000000004e128 < a

   1. Initial program 99.9%

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

   2. Taylor expanded in a around inf 56.0%

      \[\leadsto \color{blue}{a} + y \cdot i \]
3. Recombined 2 regimes into one program.

4. Final simplification 46.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 3.1 \cdot 10^{+128}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]

Alternative 16: 38.3% accurate, 71.5× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 4.4 \cdot 10^{+128}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

NOTE: z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i) :precision binary64 (if (<= a 4.4e+128) z a))

C

assert(z < t && t < a);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 4.4e+128) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 4.4d+128) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

assert z < t && t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 4.4e+128) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

[z, t, a] = sort([z, t, a])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 4.4e+128:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

z, t, a = sort([z, t, a])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 4.4e+128)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

z, t, a = num2cell(sort([z, t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 4.4e+128)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 4.4e+128], z, a]

Derivation

1. Split input into 2 regimes

2. if a < 4.40000000000000033e128

   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 85.0%

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

      1. associate-+r+ 85.0%

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

      2. +-commutative 85.0%

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

      3. *-commutative 85.0%

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

      4. sub-neg 85.0%

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

      5. metadata-eval 85.0%

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

      6. associate-+r+ 85.0%

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

      7. +-commutative 85.0%

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

      8. +-commutative 85.0%

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

      9. associate-+r+ 85.0%

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

      10. +-commutative 85.0%

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

      11. *-commutative 85.0%

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

      12. fma-def 85.0%

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

      13. +-commutative 85.0%

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

      14. associate-+r+ 85.0%

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

      15. +-commutative 85.0%

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

      16. +-commutative 85.0%

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

      17. +-commutative 85.0%

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

   4. Simplified 85.0%

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

   5. Taylor expanded in b around 0 68.0%

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

      1. associate-+r+ 68.0%

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

      2. *-commutative 68.0%

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

   7. Simplified 68.0%

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

   8. Taylor expanded in z around inf 19.8%

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

   if 4.40000000000000033e128 < a

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 94.3%

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

      1. associate-+r+ 94.3%

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

      2. +-commutative 94.3%

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

      3. *-commutative 94.3%

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

      4. sub-neg 94.3%

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

      5. metadata-eval 94.3%

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

      6. associate-+r+ 94.3%

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

      7. +-commutative 94.3%

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

      8. +-commutative 94.3%

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

      9. associate-+r+ 94.3%

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

      10. +-commutative 94.3%

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

      11. *-commutative 94.3%

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

      12. fma-def 94.3%

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

      13. +-commutative 94.3%

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

      14. associate-+r+ 94.3%

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

      15. +-commutative 94.3%

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

      16. +-commutative 94.3%

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

      17. +-commutative 94.3%

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

   4. Simplified 94.3%

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

   5. Taylor expanded in b around 0 77.1%

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

      1. associate-+r+ 77.1%

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

      2. *-commutative 77.1%

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

   7. Simplified 77.1%

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

   8. Taylor expanded in a around inf 45.7%

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

4. Final simplification 23.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 4.4 \cdot 10^{+128}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 17: 23.4% accurate, 219.0× speedup

Math

\[\begin{array}{l} [z, t, a] = \mathsf{sort}([z, t, a])\\ \\ a \end{array} \]

FPCore

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

C

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

Fortran

NOTE: z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = a
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := a

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in x around 0 86.4%

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

   1. associate-+r+ 86.4%

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

   2. +-commutative 86.4%

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

   3. *-commutative 86.4%

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

   4. sub-neg 86.4%

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

   5. metadata-eval 86.4%

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

   6. associate-+r+ 86.4%

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

   7. +-commutative 86.4%

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

   8. +-commutative 86.4%

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

   9. associate-+r+ 86.4%

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

   10. +-commutative 86.4%

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

   11. *-commutative 86.4%

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

   12. fma-def 86.4%

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

   13. +-commutative 86.4%

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

   14. associate-+r+ 86.4%

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

   15. +-commutative 86.4%

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

   16. +-commutative 86.4%

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

   17. +-commutative 86.4%

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

4. Simplified 86.4%

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

5. Taylor expanded in b around 0 69.4%

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

   1. associate-+r+ 69.4%

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

   2. *-commutative 69.4%

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

7. Simplified 69.4%

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

8. Taylor expanded in a around inf 15.6%

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

9. Final simplification 15.6%

   \[\leadsto a \]

Reproduce

herbie shell --seed 2023301 
(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)))