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

Percentage Accurate: 99.8% → 99.8%

Time: 16.9s

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: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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: 99.8% accurate, 0.4× speedup

Math

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

FPCore

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

C

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), (z + fma(x, log(y), (t + a)))));
}

Julia

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

Wolfram

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

Derivation

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. associate-+l+ 99.9%

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

   2. +-commutative 99.9%

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

   3. associate-+l+ 99.9%

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

   4. associate-+r+ 99.9%

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

   5. +-commutative 99.9%

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

   6. +-commutative 99.9%

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

   7. associate-+l+ 99.9%

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

   8. associate-+l+ 99.9%

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

   9. +-commutative 99.9%

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

   10. fma-define 99.9%

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

   11. +-commutative 99.9%

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

   12. fma-define 99.9%

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

   13. sub-neg 99.9%

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

   14. metadata-eval 99.9%

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

   15. +-commutative 99.9%

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

3. Simplified 99.9%

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

Alternative 2: 91.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -1.7 \cdot 10^{+158}:\\ \;\;\;\;y \cdot i + \left(z + t\_1\right)\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+63}:\\ \;\;\;\;a + \left(\left(z + t\right) + \mathsf{fma}\left(\log c, b + -0.5, y \cdot i\right)\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+184}:\\ \;\;\;\;a + \left(t + \left(z + \left(t\_1 + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -1.7e+158)
     (+ (* y i) (+ z t_1))
     (if (<= x 1.6e+63)
       (+ a (+ (+ z t) (fma (log c) (+ b -0.5) (* y i))))
       (if (<= x 1.7e+184)
         (+ a (+ t (+ z (+ t_1 (* (log c) (- b 0.5))))))
         (+ (* y i) (+ a t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * log(y);
	double tmp;
	if (x <= -1.7e+158) {
		tmp = (y * i) + (z + t_1);
	} else if (x <= 1.6e+63) {
		tmp = a + ((z + t) + fma(log(c), (b + -0.5), (y * i)));
	} else if (x <= 1.7e+184) {
		tmp = a + (t + (z + (t_1 + (log(c) * (b - 0.5)))));
	} else {
		tmp = (y * i) + (a + t_1);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -1.7e+158)
		tmp = Float64(Float64(y * i) + Float64(z + t_1));
	elseif (x <= 1.6e+63)
		tmp = Float64(a + Float64(Float64(z + t) + fma(log(c), Float64(b + -0.5), Float64(y * i))));
	elseif (x <= 1.7e+184)
		tmp = Float64(a + Float64(t + Float64(z + Float64(t_1 + Float64(log(c) * Float64(b - 0.5))))));
	else
		tmp = Float64(Float64(y * i) + Float64(a + t_1));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.7e+158], N[(N[(y * i), $MachinePrecision] + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.6e+63], N[(a + N[(N[(z + t), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.7e+184], N[(a + N[(t + N[(z + N[(t$95$1 + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.7e158

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 99.8%

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

   4. Taylor expanded in z around inf 90.6%

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

   5. Taylor expanded in x around 0 90.6%

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

   if -1.7e158 < x < 1.60000000000000006e63

   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. Add Preprocessing

   3. Taylor expanded in x around 0 98.2%

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

      1. associate-+r+ 98.2%

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

      2. +-commutative 98.2%

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

      3. sub-neg 98.2%

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

      4. metadata-eval 98.2%

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

      5. *-commutative 98.2%

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

      6. fma-undefine 98.2%

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

      7. +-commutative 98.2%

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

   5. Simplified 98.2%

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

   if 1.60000000000000006e63 < x < 1.7000000000000001e184

   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. Add Preprocessing

   3. Taylor expanded in y around 0 94.2%

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

   if 1.7000000000000001e184 < 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. Add Preprocessing

   3. Taylor expanded in x around inf 99.7%

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

   4. Taylor expanded in a around inf 91.6%

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

   5. Taylor expanded in x around 0 91.6%

      \[\leadsto \color{blue}{\left(a + x \cdot \log y\right)} + y \cdot i \]
3. Recombined 4 regimes into one program.

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+158}:\\ \;\;\;\;y \cdot i + \left(z + x \cdot \log y\right)\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+63}:\\ \;\;\;\;a + \left(\left(z + t\right) + \mathsf{fma}\left(\log c, b + -0.5, y \cdot i\right)\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+184}:\\ \;\;\;\;a + \left(t + \left(z + \left(x \cdot \log y + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + x \cdot \log y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 91.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -1.65 \cdot 10^{+158}:\\ \;\;\;\;y \cdot i + \left(z + t\_1\right)\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+174}:\\ \;\;\;\;a + \left(\left(z + t\right) + \mathsf{fma}\left(\log c, b + -0.5, y \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -1.65e+158)
     (+ (* y i) (+ z t_1))
     (if (<= x 3.4e+174)
       (+ a (+ (+ z t) (fma (log c) (+ b -0.5) (* y i))))
       (+ (* y i) (+ a t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * log(y);
	double tmp;
	if (x <= -1.65e+158) {
		tmp = (y * i) + (z + t_1);
	} else if (x <= 3.4e+174) {
		tmp = a + ((z + t) + fma(log(c), (b + -0.5), (y * i)));
	} else {
		tmp = (y * i) + (a + t_1);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -1.65e+158)
		tmp = Float64(Float64(y * i) + Float64(z + t_1));
	elseif (x <= 3.4e+174)
		tmp = Float64(a + Float64(Float64(z + t) + fma(log(c), Float64(b + -0.5), Float64(y * i))));
	else
		tmp = Float64(Float64(y * i) + Float64(a + t_1));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.65e+158], N[(N[(y * i), $MachinePrecision] + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.4e+174], N[(a + N[(N[(z + t), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.65000000000000009e158

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 99.8%

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

   4. Taylor expanded in z around inf 90.6%

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

   5. Taylor expanded in x around 0 90.6%

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

   if -1.65000000000000009e158 < x < 3.4000000000000001e174

   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. Add Preprocessing

   3. Taylor expanded in x around 0 95.2%

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

      1. associate-+r+ 95.2%

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

      2. +-commutative 95.2%

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

      3. sub-neg 95.2%

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

      4. metadata-eval 95.2%

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

      5. *-commutative 95.2%

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

      6. fma-undefine 95.2%

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

      7. +-commutative 95.2%

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

   5. Simplified 95.2%

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

   if 3.4000000000000001e174 < 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. Add Preprocessing

   3. Taylor expanded in x around inf 99.8%

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

   4. Taylor expanded in a around inf 89.7%

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

   5. Taylor expanded in x around 0 89.7%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+158}:\\ \;\;\;\;y \cdot i + \left(z + x \cdot \log y\right)\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+174}:\\ \;\;\;\;a + \left(\left(z + t\right) + \mathsf{fma}\left(\log c, b + -0.5, y \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + x \cdot \log y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.8% accurate, 1.0× speedup

Math

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

FPCore

(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

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

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

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

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

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

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

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 99.9%

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

3. Final simplification 99.9%

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

Alternative 5: 91.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -1.65 \cdot 10^{+158}:\\ \;\;\;\;y \cdot i + \left(z + t\_1\right)\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+173}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -1.65e+158)
     (+ (* y i) (+ z t_1))
     (if (<= x 3.5e+173)
       (+ (* y i) (+ a (+ t (+ z (* (log c) (- b 0.5))))))
       (+ (* y i) (+ a t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * log(y);
	double tmp;
	if (x <= -1.65e+158) {
		tmp = (y * i) + (z + t_1);
	} else if (x <= 3.5e+173) {
		tmp = (y * i) + (a + (t + (z + (log(c) * (b - 0.5)))));
	} else {
		tmp = (y * i) + (a + t_1);
	}
	return tmp;
}

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
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * log(y)
    if (x <= (-1.65d+158)) then
        tmp = (y * i) + (z + t_1)
    else if (x <= 3.5d+173) then
        tmp = (y * i) + (a + (t + (z + (log(c) * (b - 0.5d0)))))
    else
        tmp = (y * i) + (a + t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * Math.log(y);
	double tmp;
	if (x <= -1.65e+158) {
		tmp = (y * i) + (z + t_1);
	} else if (x <= 3.5e+173) {
		tmp = (y * i) + (a + (t + (z + (Math.log(c) * (b - 0.5)))));
	} else {
		tmp = (y * i) + (a + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x * math.log(y)
	tmp = 0
	if x <= -1.65e+158:
		tmp = (y * i) + (z + t_1)
	elif x <= 3.5e+173:
		tmp = (y * i) + (a + (t + (z + (math.log(c) * (b - 0.5)))))
	else:
		tmp = (y * i) + (a + t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -1.65e+158)
		tmp = Float64(Float64(y * i) + Float64(z + t_1));
	elseif (x <= 3.5e+173)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(t + Float64(z + Float64(log(c) * Float64(b - 0.5))))));
	else
		tmp = Float64(Float64(y * i) + Float64(a + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x * log(y);
	tmp = 0.0;
	if (x <= -1.65e+158)
		tmp = (y * i) + (z + t_1);
	elseif (x <= 3.5e+173)
		tmp = (y * i) + (a + (t + (z + (log(c) * (b - 0.5)))));
	else
		tmp = (y * i) + (a + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.65e+158], N[(N[(y * i), $MachinePrecision] + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.5e+173], 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], N[(N[(y * i), $MachinePrecision] + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.65000000000000009e158

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 99.8%

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

   4. Taylor expanded in z around inf 90.6%

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

   5. Taylor expanded in x around 0 90.6%

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

   if -1.65000000000000009e158 < x < 3.4999999999999999e173

   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. Add Preprocessing

   3. Taylor expanded in x around 0 95.2%

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

   if 3.4999999999999999e173 < 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. Add Preprocessing

   3. Taylor expanded in x around inf 99.8%

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

   4. Taylor expanded in a around inf 89.7%

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

   5. Taylor expanded in x around 0 89.7%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+158}:\\ \;\;\;\;y \cdot i + \left(z + x \cdot \log y\right)\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+173}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + x \cdot \log y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 80.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.8 \cdot 10^{-101}:\\ \;\;\;\;a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-63}:\\ \;\;\;\;y \cdot i + \left(z + x \cdot \log y\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(\left(z + t\right) + y \cdot \left(i + b \cdot \frac{\log c}{y}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 1.8e-101)
   (+ a (+ t (+ z (* (log c) (- b 0.5)))))
   (if (<= y 4.5e-63)
     (+ (* y i) (+ z (* x (log y))))
     (+ a (+ (+ z t) (* y (+ i (* b (/ (log c) y)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 1.8e-101) {
		tmp = a + (t + (z + (log(c) * (b - 0.5))));
	} else if (y <= 4.5e-63) {
		tmp = (y * i) + (z + (x * log(y)));
	} else {
		tmp = a + ((z + t) + (y * (i + (b * (log(c) / y)))));
	}
	return tmp;
}

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
    real(8) :: tmp
    if (y <= 1.8d-101) then
        tmp = a + (t + (z + (log(c) * (b - 0.5d0))))
    else if (y <= 4.5d-63) then
        tmp = (y * i) + (z + (x * log(y)))
    else
        tmp = a + ((z + t) + (y * (i + (b * (log(c) / y)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 1.8e-101) {
		tmp = a + (t + (z + (Math.log(c) * (b - 0.5))));
	} else if (y <= 4.5e-63) {
		tmp = (y * i) + (z + (x * Math.log(y)));
	} else {
		tmp = a + ((z + t) + (y * (i + (b * (Math.log(c) / y)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 1.8e-101:
		tmp = a + (t + (z + (math.log(c) * (b - 0.5))))
	elif y <= 4.5e-63:
		tmp = (y * i) + (z + (x * math.log(y)))
	else:
		tmp = a + ((z + t) + (y * (i + (b * (math.log(c) / y)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 1.8e-101)
		tmp = Float64(a + Float64(t + Float64(z + Float64(log(c) * Float64(b - 0.5)))));
	elseif (y <= 4.5e-63)
		tmp = Float64(Float64(y * i) + Float64(z + Float64(x * log(y))));
	else
		tmp = Float64(a + Float64(Float64(z + t) + Float64(y * Float64(i + Float64(b * Float64(log(c) / y))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= 1.8e-101)
		tmp = a + (t + (z + (log(c) * (b - 0.5))));
	elseif (y <= 4.5e-63)
		tmp = (y * i) + (z + (x * log(y)));
	else
		tmp = a + ((z + t) + (y * (i + (b * (log(c) / y)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 1.8e-101], N[(a + N[(t + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.5e-63], N[(N[(y * i), $MachinePrecision] + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(N[(z + t), $MachinePrecision] + N[(y * N[(i + N[(b * N[(N[Log[c], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 1.8e-101

   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. Add Preprocessing

   3. Taylor expanded in y around 0 97.8%

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

   4. Taylor expanded in x around 0 71.9%

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

   if 1.8e-101 < y < 4.5e-63

   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. Add Preprocessing

   3. Taylor expanded in x around inf 80.8%

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

   4. Taylor expanded in z around inf 63.9%

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

   5. Taylor expanded in x around 0 76.5%

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

   if 4.5e-63 < 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. Add Preprocessing

   3. Taylor expanded in x around 0 89.7%

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

      1. associate-+r+ 89.7%

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

      2. +-commutative 89.7%

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

      3. sub-neg 89.7%

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

      4. metadata-eval 89.7%

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

      5. *-commutative 89.7%

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

      6. fma-undefine 89.7%

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

      7. +-commutative 89.7%

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

   5. Simplified 89.7%

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

   6. Taylor expanded in y around inf 88.6%

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

   7. Taylor expanded in b around inf 87.5%

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

      1. associate-/l* 87.4%

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

   9. Simplified 87.4%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.8 \cdot 10^{-101}:\\ \;\;\;\;a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-63}:\\ \;\;\;\;y \cdot i + \left(z + x \cdot \log y\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(\left(z + t\right) + y \cdot \left(i + b \cdot \frac{\log c}{y}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{+210} \lor \neg \left(b \leq 3.9 \cdot 10^{+133}\right):\\ \;\;\;\;a + \left(\left(z + t\right) + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(y \cdot i + \left(z + t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= b -1.6e+210) (not (<= b 3.9e+133)))
   (+ a (+ (+ z t) (* b (log c))))
   (+ a (+ (* y i) (+ z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((b <= -1.6e+210) || !(b <= 3.9e+133)) {
		tmp = a + ((z + t) + (b * log(c)));
	} else {
		tmp = a + ((y * i) + (z + t));
	}
	return tmp;
}

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
    real(8) :: tmp
    if ((b <= (-1.6d+210)) .or. (.not. (b <= 3.9d+133))) then
        tmp = a + ((z + t) + (b * log(c)))
    else
        tmp = a + ((y * i) + (z + t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((b <= -1.6e+210) || !(b <= 3.9e+133)) {
		tmp = a + ((z + t) + (b * Math.log(c)));
	} else {
		tmp = a + ((y * i) + (z + t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (b <= -1.6e+210) or not (b <= 3.9e+133):
		tmp = a + ((z + t) + (b * math.log(c)))
	else:
		tmp = a + ((y * i) + (z + t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((b <= -1.6e+210) || !(b <= 3.9e+133))
		tmp = Float64(a + Float64(Float64(z + t) + Float64(b * log(c))));
	else
		tmp = Float64(a + Float64(Float64(y * i) + Float64(z + t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((b <= -1.6e+210) || ~((b <= 3.9e+133)))
		tmp = a + ((z + t) + (b * log(c)));
	else
		tmp = a + ((y * i) + (z + t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[b, -1.6e+210], N[Not[LessEqual[b, 3.9e+133]], $MachinePrecision]], N[(a + N[(N[(z + t), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(N[(y * i), $MachinePrecision] + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.6000000000000001e210 or 3.90000000000000014e133 < b

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 94.1%

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

      1. associate-+r+ 94.1%

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

      2. +-commutative 94.1%

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

      3. sub-neg 94.1%

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

      4. metadata-eval 94.1%

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

      5. *-commutative 94.1%

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

      6. fma-undefine 94.1%

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

      7. +-commutative 94.1%

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

   5. Simplified 94.1%

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

   6. Taylor expanded in b around inf 81.0%

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

      1. *-commutative 81.0%

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

   8. Simplified 81.0%

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

   if -1.6000000000000001e210 < b < 3.90000000000000014e133

   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. Add Preprocessing

   3. Taylor expanded in x around 0 78.1%

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

      1. associate-+r+ 78.1%

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

      2. +-commutative 78.1%

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

      3. sub-neg 78.1%

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

      4. metadata-eval 78.1%

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

      5. *-commutative 78.1%

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

      6. fma-undefine 78.1%

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

      7. +-commutative 78.1%

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

   5. Simplified 78.1%

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

   6. Taylor expanded in y around inf 72.2%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{+210} \lor \neg \left(b \leq 3.9 \cdot 10^{+133}\right):\\ \;\;\;\;a + \left(\left(z + t\right) + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(y \cdot i + \left(z + t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;z \leq -5 \cdot 10^{+144}:\\ \;\;\;\;y \cdot i + \left(z + t\_1\right)\\ \mathbf{elif}\;z \leq -3.65 \cdot 10^{+18}:\\ \;\;\;\;a + \left(\left(z + t\right) + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= z -5e+144)
     (+ (* y i) (+ z t_1))
     (if (<= z -3.65e+18)
       (+ a (+ (+ z t) (* b (log c))))
       (+ (* y i) (+ a t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * log(y);
	double tmp;
	if (z <= -5e+144) {
		tmp = (y * i) + (z + t_1);
	} else if (z <= -3.65e+18) {
		tmp = a + ((z + t) + (b * log(c)));
	} else {
		tmp = (y * i) + (a + t_1);
	}
	return tmp;
}

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
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * log(y)
    if (z <= (-5d+144)) then
        tmp = (y * i) + (z + t_1)
    else if (z <= (-3.65d+18)) then
        tmp = a + ((z + t) + (b * log(c)))
    else
        tmp = (y * i) + (a + t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * Math.log(y);
	double tmp;
	if (z <= -5e+144) {
		tmp = (y * i) + (z + t_1);
	} else if (z <= -3.65e+18) {
		tmp = a + ((z + t) + (b * Math.log(c)));
	} else {
		tmp = (y * i) + (a + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x * math.log(y)
	tmp = 0
	if z <= -5e+144:
		tmp = (y * i) + (z + t_1)
	elif z <= -3.65e+18:
		tmp = a + ((z + t) + (b * math.log(c)))
	else:
		tmp = (y * i) + (a + t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (z <= -5e+144)
		tmp = Float64(Float64(y * i) + Float64(z + t_1));
	elseif (z <= -3.65e+18)
		tmp = Float64(a + Float64(Float64(z + t) + Float64(b * log(c))));
	else
		tmp = Float64(Float64(y * i) + Float64(a + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x * log(y);
	tmp = 0.0;
	if (z <= -5e+144)
		tmp = (y * i) + (z + t_1);
	elseif (z <= -3.65e+18)
		tmp = a + ((z + t) + (b * log(c)));
	else
		tmp = (y * i) + (a + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5e+144], N[(N[(y * i), $MachinePrecision] + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.65e+18], N[(a + N[(N[(z + t), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.9999999999999999e144

   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. Add Preprocessing

   3. Taylor expanded in x around inf 70.4%

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

   4. Taylor expanded in z around inf 59.0%

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

   5. Taylor expanded in x around 0 73.6%

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

   if -4.9999999999999999e144 < z < -3.65e18

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 85.2%

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

      1. associate-+r+ 85.2%

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

      2. +-commutative 85.2%

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

      3. sub-neg 85.2%

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

      4. metadata-eval 85.2%

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

      5. *-commutative 85.2%

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

      6. fma-undefine 85.2%

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

      7. +-commutative 85.2%

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

   5. Simplified 85.2%

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

   6. Taylor expanded in b around inf 56.9%

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

      1. *-commutative 56.9%

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

   8. Simplified 56.9%

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

   if -3.65e18 < z

   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. Add Preprocessing

   3. Taylor expanded in x around inf 75.5%

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

   4. Taylor expanded in a around inf 52.8%

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

   5. Taylor expanded in x around 0 59.9%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+144}:\\ \;\;\;\;y \cdot i + \left(z + x \cdot \log y\right)\\ \mathbf{elif}\;z \leq -3.65 \cdot 10^{+18}:\\ \;\;\;\;a + \left(\left(z + t\right) + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + x \cdot \log y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+143}:\\ \;\;\;\;a + \left(y \cdot i + \left(z + t\right)\right)\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+18}:\\ \;\;\;\;a + \left(\left(z + t\right) + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + x \cdot \log y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -3.1e+143)
   (+ a (+ (* y i) (+ z t)))
   (if (<= z -3.6e+18)
     (+ a (+ (+ z t) (* b (log c))))
     (+ (* y i) (+ a (* x (log y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -3.1e+143) {
		tmp = a + ((y * i) + (z + t));
	} else if (z <= -3.6e+18) {
		tmp = a + ((z + t) + (b * log(c)));
	} else {
		tmp = (y * i) + (a + (x * log(y)));
	}
	return tmp;
}

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
    real(8) :: tmp
    if (z <= (-3.1d+143)) then
        tmp = a + ((y * i) + (z + t))
    else if (z <= (-3.6d+18)) then
        tmp = a + ((z + t) + (b * log(c)))
    else
        tmp = (y * i) + (a + (x * log(y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -3.1e+143) {
		tmp = a + ((y * i) + (z + t));
	} else if (z <= -3.6e+18) {
		tmp = a + ((z + t) + (b * Math.log(c)));
	} else {
		tmp = (y * i) + (a + (x * Math.log(y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -3.1e+143:
		tmp = a + ((y * i) + (z + t))
	elif z <= -3.6e+18:
		tmp = a + ((z + t) + (b * math.log(c)))
	else:
		tmp = (y * i) + (a + (x * math.log(y)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -3.1e+143)
		tmp = Float64(a + Float64(Float64(y * i) + Float64(z + t)));
	elseif (z <= -3.6e+18)
		tmp = Float64(a + Float64(Float64(z + t) + Float64(b * log(c))));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(x * log(y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -3.1e+143)
		tmp = a + ((y * i) + (z + t));
	elseif (z <= -3.6e+18)
		tmp = a + ((z + t) + (b * log(c)));
	else
		tmp = (y * i) + (a + (x * log(y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -3.1e+143], N[(a + N[(N[(y * i), $MachinePrecision] + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.6e+18], N[(a + N[(N[(z + t), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.0999999999999999e143

   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. Add Preprocessing

   3. Taylor expanded in x around 0 89.1%

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

      1. associate-+r+ 89.1%

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

      2. +-commutative 89.1%

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

      3. sub-neg 89.1%

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

      4. metadata-eval 89.1%

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

      5. *-commutative 89.1%

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

      6. fma-undefine 89.1%

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

      7. +-commutative 89.1%

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

   5. Simplified 89.1%

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

   6. Taylor expanded in y around inf 86.1%

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

   if -3.0999999999999999e143 < z < -3.6e18

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 85.2%

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

      1. associate-+r+ 85.2%

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

      2. +-commutative 85.2%

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

      3. sub-neg 85.2%

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

      4. metadata-eval 85.2%

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

      5. *-commutative 85.2%

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

      6. fma-undefine 85.2%

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

      7. +-commutative 85.2%

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

   5. Simplified 85.2%

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

   6. Taylor expanded in b around inf 56.9%

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

      1. *-commutative 56.9%

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

   8. Simplified 56.9%

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

   if -3.6e18 < z

   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. Add Preprocessing

   3. Taylor expanded in x around inf 75.5%

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

   4. Taylor expanded in a around inf 52.8%

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

   5. Taylor expanded in x around 0 59.9%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+143}:\\ \;\;\;\;a + \left(y \cdot i + \left(z + t\right)\right)\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+18}:\\ \;\;\;\;a + \left(\left(z + t\right) + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + x \cdot \log y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 71.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 3.9 \cdot 10^{+36}:\\ \;\;\;\;t + \left(z + \left(y \cdot i + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + x \cdot \log y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 3.9e+36)
   (+ t (+ z (+ (* y i) (* (log c) (- b 0.5)))))
   (+ (* y i) (+ a (* x (log y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 3.9e+36) {
		tmp = t + (z + ((y * i) + (log(c) * (b - 0.5))));
	} else {
		tmp = (y * i) + (a + (x * log(y)));
	}
	return tmp;
}

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
    real(8) :: tmp
    if (a <= 3.9d+36) then
        tmp = t + (z + ((y * i) + (log(c) * (b - 0.5d0))))
    else
        tmp = (y * i) + (a + (x * log(y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 3.9e+36) {
		tmp = t + (z + ((y * i) + (Math.log(c) * (b - 0.5))));
	} else {
		tmp = (y * i) + (a + (x * Math.log(y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 3.9e+36:
		tmp = t + (z + ((y * i) + (math.log(c) * (b - 0.5))))
	else:
		tmp = (y * i) + (a + (x * math.log(y)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 3.9e+36)
		tmp = Float64(t + Float64(z + Float64(Float64(y * i) + Float64(log(c) * Float64(b - 0.5)))));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(x * log(y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 3.9e+36)
		tmp = t + (z + ((y * i) + (log(c) * (b - 0.5))));
	else
		tmp = (y * i) + (a + (x * log(y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 3.9e+36], N[(t + N[(z + N[(N[(y * i), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 3.90000000000000021e36

   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. Add Preprocessing

   3. Taylor expanded in x around 0 81.6%

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

      1. associate-+r+ 81.6%

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

      2. +-commutative 81.6%

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

      3. sub-neg 81.6%

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

      4. metadata-eval 81.6%

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

      5. *-commutative 81.6%

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

      6. fma-undefine 81.6%

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

      7. +-commutative 81.6%

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

   5. Simplified 81.6%

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

   6. Taylor expanded in a around 0 70.6%

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

   if 3.90000000000000021e36 < 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. Add Preprocessing

   3. Taylor expanded in x around inf 84.3%

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

   4. Taylor expanded in a around inf 58.8%

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

   5. Taylor expanded in x around 0 66.8%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 3.9 \cdot 10^{+36}:\\ \;\;\;\;t + \left(z + \left(y \cdot i + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + x \cdot \log y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 72.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+224} \lor \neg \left(x \leq 1.56 \cdot 10^{+218}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;a + \left(y \cdot i + \left(z + t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -4.4e+224) (not (<= x 1.56e+218)))
   (* x (log y))
   (+ a (+ (* y i) (+ z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -4.4e+224) || !(x <= 1.56e+218)) {
		tmp = x * log(y);
	} else {
		tmp = a + ((y * i) + (z + t));
	}
	return tmp;
}

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
    real(8) :: tmp
    if ((x <= (-4.4d+224)) .or. (.not. (x <= 1.56d+218))) then
        tmp = x * log(y)
    else
        tmp = a + ((y * i) + (z + t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -4.4e+224) || !(x <= 1.56e+218)) {
		tmp = x * Math.log(y);
	} else {
		tmp = a + ((y * i) + (z + t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -4.4e+224) or not (x <= 1.56e+218):
		tmp = x * math.log(y)
	else:
		tmp = a + ((y * i) + (z + t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -4.4e+224) || !(x <= 1.56e+218))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(a + Float64(Float64(y * i) + Float64(z + t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -4.4e+224) || ~((x <= 1.56e+218)))
		tmp = x * log(y);
	else
		tmp = a + ((y * i) + (z + t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -4.4e+224], N[Not[LessEqual[x, 1.56e+218]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(a + N[(N[(y * i), $MachinePrecision] + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.3999999999999999e224 or 1.55999999999999997e218 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 76.2%

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

   if -4.3999999999999999e224 < x < 1.55999999999999997e218

   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. Add Preprocessing

   3. Taylor expanded in x around 0 92.5%

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

      1. associate-+r+ 92.5%

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

      2. +-commutative 92.5%

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

      3. sub-neg 92.5%

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

      4. metadata-eval 92.5%

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

      5. *-commutative 92.5%

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

      6. fma-undefine 92.5%

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

      7. +-commutative 92.5%

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

   5. Simplified 92.5%

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

   6. Taylor expanded in y around inf 72.3%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+224} \lor \neg \left(x \leq 1.56 \cdot 10^{+218}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;a + \left(y \cdot i + \left(z + t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 43.7% accurate, 21.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+83}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -1.15e+83) (+ z (* y i)) (+ a (* y i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -1.15e+83) {
		tmp = z + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

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
    real(8) :: tmp
    if (z <= (-1.15d+83)) then
        tmp = z + (y * i)
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -1.15e+83) {
		tmp = z + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -1.15e+83:
		tmp = z + (y * i)
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -1.15e+83)
		tmp = Float64(z + Float64(y * i));
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -1.15e+83)
		tmp = z + (y * i);
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -1.15e+83], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.14999999999999997e83

   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. Add Preprocessing

   3. Taylor expanded in x around inf 70.0%

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

   4. Taylor expanded in z around inf 60.9%

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

   5. Taylor expanded in x around 0 60.7%

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

      1. +-commutative 60.7%

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

   7. Simplified 60.7%

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

   if -1.14999999999999997e83 < z

   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. Add Preprocessing

   3. Taylor expanded in x around inf 76.7%

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

   4. Taylor expanded in a around inf 52.7%

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

   5. Taylor expanded in x around 0 41.0%

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

4. Final simplification 43.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+83}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 41.6% accurate, 21.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+170}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -1.75e+170) z (+ a (* y i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -1.75e+170) {
		tmp = z;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

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
    real(8) :: tmp
    if (z <= (-1.75d+170)) then
        tmp = z
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -1.75e+170) {
		tmp = z;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -1.75e+170:
		tmp = z
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -1.75e+170)
		tmp = z;
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -1.75e+170)
		tmp = z;
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -1.75e+170], z, N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.75000000000000003e170

   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. Add Preprocessing

   3. Taylor expanded in z around inf 56.3%

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

   if -1.75000000000000003e170 < z

   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. Add Preprocessing

   3. Taylor expanded in x around inf 75.8%

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

   4. Taylor expanded in a around inf 52.3%

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

   5. Taylor expanded in x around 0 40.7%

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

4. Final simplification 41.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+170}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 68.0% accurate, 24.3× speedup

Math

\[\begin{array}{l} \\ a + \left(y \cdot i + \left(z + t\right)\right) \end{array} \]

FPCore

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

C

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

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 = a + ((y * i) + (z + t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. Add Preprocessing

3. Taylor expanded in x around 0 81.2%

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

   1. associate-+r+ 81.2%

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

   2. +-commutative 81.2%

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

   3. sub-neg 81.2%

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

   4. metadata-eval 81.2%

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

   5. *-commutative 81.2%

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

   6. fma-undefine 81.3%

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

   7. +-commutative 81.3%

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

5. Simplified 81.3%

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

6. Taylor expanded in y around inf 64.3%

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

7. Final simplification 64.3%

   \[\leadsto a + \left(y \cdot i + \left(z + t\right)\right) \]
8. Add Preprocessing

Alternative 15: 30.1% accurate, 27.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 8.8 \cdot 10^{+71}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (if (<= y 8.8e+71) z (* y i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 8.8e+71) {
		tmp = z;
	} else {
		tmp = y * i;
	}
	return tmp;
}

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
    real(8) :: tmp
    if (y <= 8.8d+71) then
        tmp = z
    else
        tmp = y * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 8.8e+71) {
		tmp = z;
	} else {
		tmp = y * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 8.8e+71:
		tmp = z
	else:
		tmp = y * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 8.8e+71)
		tmp = z;
	else
		tmp = Float64(y * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= 8.8e+71)
		tmp = z;
	else
		tmp = y * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 8.8e+71], z, N[(y * i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 8.79999999999999978e71

   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. Add Preprocessing

   3. Taylor expanded in z around inf 14.0%

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

   if 8.79999999999999978e71 < 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. Add Preprocessing

   3. Taylor expanded in y around inf 52.4%

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

      1. *-commutative 52.4%

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

   5. Simplified 52.4%

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

Alternative 16: 21.1% accurate, 36.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+94}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (if (<= z -8.5e+94) z a))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -8.5e+94) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

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
    real(8) :: tmp
    if (z <= (-8.5d+94)) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -8.5e+94) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -8.5e+94:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -8.5e+94)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -8.5e+94)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -8.5e+94], z, a]

Derivation

1. Split input into 2 regimes

2. if z < -8.50000000000000054e94

   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. Add Preprocessing

   3. Taylor expanded in z around inf 43.8%

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

   if -8.50000000000000054e94 < z

   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. Add Preprocessing

   3. Taylor expanded in a around inf 16.2%

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

Alternative 17: 16.3% accurate, 219.0× speedup

Math

\[\begin{array}{l} \\ a \end{array} \]

FPCore

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

C

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

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 = a
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := a

Derivation

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. Add Preprocessing

3. Taylor expanded in a around inf 15.7%

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

Reproduce

herbie shell --seed 2024087 
(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)))