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

Percentage Accurate: 99.8% → 99.8%

Time: 15.5s

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: 76.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log c \cdot \left(b - 0.5\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+200}:\\ \;\;\;\;y \cdot i + \left(z + b \cdot \log c\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+104}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (log c) (- b 0.5))))
   (if (<= t_1 -1e+200)
     (+ (* y i) (+ z (* b (log c))))
     (if (<= t_1 2e+104)
       (+ (* y i) (+ a (+ z (* x (log y)))))
       (+ (* 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 = log(c) * (b - 0.5);
	double tmp;
	if (t_1 <= -1e+200) {
		tmp = (y * i) + (z + (b * log(c)));
	} else if (t_1 <= 2e+104) {
		tmp = (y * i) + (a + (z + (x * log(y))));
	} 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 = log(c) * (b - 0.5d0)
    if (t_1 <= (-1d+200)) then
        tmp = (y * i) + (z + (b * log(c)))
    else if (t_1 <= 2d+104) then
        tmp = (y * i) + (a + (z + (x * log(y))))
    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 = Math.log(c) * (b - 0.5);
	double tmp;
	if (t_1 <= -1e+200) {
		tmp = (y * i) + (z + (b * Math.log(c)));
	} else if (t_1 <= 2e+104) {
		tmp = (y * i) + (a + (z + (x * Math.log(y))));
	} else {
		tmp = (y * i) + (a + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = math.log(c) * (b - 0.5)
	tmp = 0
	if t_1 <= -1e+200:
		tmp = (y * i) + (z + (b * math.log(c)))
	elif t_1 <= 2e+104:
		tmp = (y * i) + (a + (z + (x * math.log(y))))
	else:
		tmp = (y * i) + (a + t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(log(c) * Float64(b - 0.5))
	tmp = 0.0
	if (t_1 <= -1e+200)
		tmp = Float64(Float64(y * i) + Float64(z + Float64(b * log(c))));
	elseif (t_1 <= 2e+104)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + Float64(x * log(y)))));
	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 = log(c) * (b - 0.5);
	tmp = 0.0;
	if (t_1 <= -1e+200)
		tmp = (y * i) + (z + (b * log(c)));
	elseif (t_1 <= 2e+104)
		tmp = (y * i) + (a + (z + (x * log(y))));
	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[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+200], N[(N[(y * i), $MachinePrecision] + N[(z + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+104], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + N[(x * N[Log[y], $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 (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c)) < -9.9999999999999997e199

   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 0 91.4%

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

   4. Taylor expanded in z around inf 68.6%

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

      1. associate-+r+ 68.6%

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

      2. sub-neg 68.6%

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

      3. metadata-eval 68.6%

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

      4. associate-/l* 68.6%

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

   6. Simplified 68.6%

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

   7. Taylor expanded in b around inf 68.6%

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

      1. associate-/l* 68.6%

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

   9. Simplified 68.6%

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

   10. Taylor expanded in z around 0 90.6%

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

   if -9.9999999999999997e199 < (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c)) < 2e104

   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. Step-by-step derivation

      1. add-cbrt-cube 99.8%

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

      2. pow3 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in b around inf 96.7%

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

      1. *-commutative 96.7%

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

   7. Simplified 96.7%

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

   8. Taylor expanded in t around 0 81.1%

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

   9. Taylor expanded in b around 0 78.1%

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

   if 2e104 < (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))

   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 a around inf 77.7%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\log c \cdot \left(b - 0.5\right) \leq -1 \cdot 10^{+200}:\\ \;\;\;\;y \cdot i + \left(z + b \cdot \log c\right)\\ \mathbf{elif}\;\log c \cdot \left(b - 0.5\right) \leq 2 \cdot 10^{+104}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \log c \cdot \left(b - 0.5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 92.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+161} \lor \neg \left(x \leq 1.6 \cdot 10^{+158}\right):\\ \;\;\;\;y \cdot i + \left(a + \left(z + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -1.15e+161) (not (<= x 1.6e+158)))
   (+ (* y i) (+ a (+ z (* x (log y)))))
   (fma y i (+ a (+ t (+ z (* (log c) (- b 0.5))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1.15e+161) || !(x <= 1.6e+158)) {
		tmp = (y * i) + (a + (z + (x * log(y))));
	} else {
		tmp = fma(y, i, (a + (t + (z + (log(c) * (b - 0.5))))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -1.15e+161) || !(x <= 1.6e+158))
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + Float64(x * log(y)))));
	else
		tmp = fma(y, i, Float64(a + Float64(t + Float64(z + Float64(log(c) * Float64(b - 0.5))))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -1.15e+161], N[Not[LessEqual[x, 1.6e+158]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * i + 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 < -1.15e161 or 1.59999999999999997e158 < 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. Step-by-step derivation

      1. add-cbrt-cube 99.5%

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

      2. pow3 99.5%

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

   4. Applied egg-rr 99.5%

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

   5. Taylor expanded in b around inf 99.5%

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

      1. *-commutative 99.5%

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

   7. Simplified 99.5%

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

   8. Taylor expanded in t around 0 91.6%

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

   9. Taylor expanded in b around 0 83.5%

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

   if -1.15e161 < x < 1.59999999999999997e158

   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. Taylor expanded in x around 0 97.5%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+161} \lor \neg \left(x \leq 1.6 \cdot 10^{+158}\right):\\ \;\;\;\;y \cdot i + \left(a + \left(z + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \end{array} \]
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: 83.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 = (y * i) + ((a + (z + (x * log(y)))) + (b * log(c)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(y * i), $MachinePrecision] + N[(N[(a + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[Log[c], $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. Add Preprocessing
3. Step-by-step derivation

   1. add-cbrt-cube 99.8%

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

   2. pow3 99.8%

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

4. Applied egg-rr 99.8%

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

5. Taylor expanded in b around inf 97.4%

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

   1. *-commutative 97.4%

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

7. Simplified 97.4%

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

8. Taylor expanded in t around 0 84.3%

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

9. Final simplification 84.3%

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

Alternative 6: 92.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+160} \lor \neg \left(x \leq 1.45 \cdot 10^{+155}\right):\\ \;\;\;\;y \cdot i + \left(a + \left(z + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -2.3e+160) (not (<= x 1.45e+155)))
   (+ (* y i) (+ a (+ z (* x (log y)))))
   (+ (* y i) (+ (* (log c) (- b 0.5)) (+ a (+ 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 <= -2.3e+160) || !(x <= 1.45e+155)) {
		tmp = (y * i) + (a + (z + (x * log(y))));
	} else {
		tmp = (y * i) + ((log(c) * (b - 0.5)) + (a + (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 <= (-2.3d+160)) .or. (.not. (x <= 1.45d+155))) then
        tmp = (y * i) + (a + (z + (x * log(y))))
    else
        tmp = (y * i) + ((log(c) * (b - 0.5d0)) + (a + (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 <= -2.3e+160) || !(x <= 1.45e+155)) {
		tmp = (y * i) + (a + (z + (x * Math.log(y))));
	} else {
		tmp = (y * i) + ((Math.log(c) * (b - 0.5)) + (a + (z + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -2.3e+160) or not (x <= 1.45e+155):
		tmp = (y * i) + (a + (z + (x * math.log(y))))
	else:
		tmp = (y * i) + ((math.log(c) * (b - 0.5)) + (a + (z + t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -2.3e+160) || !(x <= 1.45e+155))
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + Float64(x * log(y)))));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(log(c) * Float64(b - 0.5)) + Float64(a + 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 <= -2.3e+160) || ~((x <= 1.45e+155)))
		tmp = (y * i) + (a + (z + (x * log(y))));
	else
		tmp = (y * i) + ((log(c) * (b - 0.5)) + (a + (z + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -2.3e+160], N[Not[LessEqual[x, 1.45e+155]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.29999999999999987e160 or 1.45e155 < 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. Step-by-step derivation

      1. add-cbrt-cube 99.5%

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

      2. pow3 99.5%

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

   4. Applied egg-rr 99.5%

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

   5. Taylor expanded in b around inf 99.5%

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

      1. *-commutative 99.5%

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

   7. Simplified 99.5%

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

   8. Taylor expanded in t around 0 91.6%

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

   9. Taylor expanded in b around 0 83.5%

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

   if -2.29999999999999987e160 < x < 1.45e155

   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 97.4%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+160} \lor \neg \left(x \leq 1.45 \cdot 10^{+155}\right):\\ \;\;\;\;y \cdot i + \left(a + \left(z + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 80.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+160} \lor \neg \left(x \leq 10^{+157}\right):\\ \;\;\;\;y \cdot i + \left(a + \left(z + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(z + a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -1.45e+160) (not (<= x 1e+157)))
   (+ (* y i) (+ a (+ z (* x (log y)))))
   (+ (* y i) (+ (* (log c) (- b 0.5)) (+ z a)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1.45e+160) || !(x <= 1e+157)) {
		tmp = (y * i) + (a + (z + (x * log(y))));
	} else {
		tmp = (y * i) + ((log(c) * (b - 0.5)) + (z + 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 ((x <= (-1.45d+160)) .or. (.not. (x <= 1d+157))) then
        tmp = (y * i) + (a + (z + (x * log(y))))
    else
        tmp = (y * i) + ((log(c) * (b - 0.5d0)) + (z + 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 ((x <= -1.45e+160) || !(x <= 1e+157)) {
		tmp = (y * i) + (a + (z + (x * Math.log(y))));
	} else {
		tmp = (y * i) + ((Math.log(c) * (b - 0.5)) + (z + a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -1.45e+160) or not (x <= 1e+157):
		tmp = (y * i) + (a + (z + (x * math.log(y))))
	else:
		tmp = (y * i) + ((math.log(c) * (b - 0.5)) + (z + a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -1.45e+160) || !(x <= 1e+157))
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + Float64(x * log(y)))));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(log(c) * Float64(b - 0.5)) + Float64(z + a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -1.45e+160) || ~((x <= 1e+157)))
		tmp = (y * i) + (a + (z + (x * log(y))));
	else
		tmp = (y * i) + ((log(c) * (b - 0.5)) + (z + a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -1.45e+160], N[Not[LessEqual[x, 1e+157]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.45e160 or 9.99999999999999983e156 < 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. Step-by-step derivation

      1. add-cbrt-cube 99.5%

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

      2. pow3 99.5%

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

   4. Applied egg-rr 99.5%

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

   5. Taylor expanded in b around inf 99.5%

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

      1. *-commutative 99.5%

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

   7. Simplified 99.5%

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

   8. Taylor expanded in t around 0 91.6%

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

   9. Taylor expanded in b around 0 83.5%

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

   if -1.45e160 < x < 9.99999999999999983e156

   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 82.6%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+160} \lor \neg \left(x \leq 10^{+157}\right):\\ \;\;\;\;y \cdot i + \left(a + \left(z + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(z + a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.25 \cdot 10^{+179} \lor \neg \left(b \leq 1.4 \cdot 10^{+199}\right):\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;a + \left(z + y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= b -2.25e+179) (not (<= b 1.4e+199)))
   (+ (* y i) (* b (log c)))
   (+ a (+ 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 ((b <= -2.25e+179) || !(b <= 1.4e+199)) {
		tmp = (y * i) + (b * log(c));
	} else {
		tmp = a + (z + (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 ((b <= (-2.25d+179)) .or. (.not. (b <= 1.4d+199))) then
        tmp = (y * i) + (b * log(c))
    else
        tmp = a + (z + (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 ((b <= -2.25e+179) || !(b <= 1.4e+199)) {
		tmp = (y * i) + (b * Math.log(c));
	} else {
		tmp = a + (z + (y * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (b <= -2.25e+179) or not (b <= 1.4e+199):
		tmp = (y * i) + (b * math.log(c))
	else:
		tmp = a + (z + (y * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((b <= -2.25e+179) || !(b <= 1.4e+199))
		tmp = Float64(Float64(y * i) + Float64(b * log(c)));
	else
		tmp = Float64(a + Float64(z + Float64(y * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((b <= -2.25e+179) || ~((b <= 1.4e+199)))
		tmp = (y * i) + (b * log(c));
	else
		tmp = a + (z + (y * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[b, -2.25e+179], N[Not[LessEqual[b, 1.4e+199]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.2500000000000001e179 or 1.40000000000000005e199 < b

   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 0 95.7%

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

   4. Taylor expanded in b around inf 83.0%

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

      1. *-commutative 83.0%

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

   6. Simplified 83.0%

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

   if -2.2500000000000001e179 < b < 1.40000000000000005e199

   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 83.0%

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

   4. Taylor expanded in z around inf 63.0%

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

      1. associate-+r+ 63.0%

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

      2. sub-neg 63.0%

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

      3. metadata-eval 63.0%

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

      4. associate-/l* 63.0%

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

   6. Simplified 63.0%

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

   7. Taylor expanded in a around inf 49.5%

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

   8. Taylor expanded in z around 0 59.5%

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

      1. *-commutative 59.5%

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

   10. Simplified 59.5%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.25 \cdot 10^{+179} \lor \neg \left(b \leq 1.4 \cdot 10^{+199}\right):\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;a + \left(z + y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.7 \cdot 10^{+162} \lor \neg \left(x \leq 9 \cdot 10^{+214}\right):\\ \;\;\;\;a + \left(t + x \cdot \log y\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(z + y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -5.7e+162) (not (<= x 9e+214)))
   (+ a (+ t (* x (log y))))
   (+ a (+ 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 ((x <= -5.7e+162) || !(x <= 9e+214)) {
		tmp = a + (t + (x * log(y)));
	} else {
		tmp = a + (z + (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 ((x <= (-5.7d+162)) .or. (.not. (x <= 9d+214))) then
        tmp = a + (t + (x * log(y)))
    else
        tmp = a + (z + (y * i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -5.7e+162) || !(x <= 9e+214)) {
		tmp = a + (t + (x * Math.log(y)));
	} else {
		tmp = a + (z + (y * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -5.7e+162) or not (x <= 9e+214):
		tmp = a + (t + (x * math.log(y)))
	else:
		tmp = a + (z + (y * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -5.7e+162) || !(x <= 9e+214))
		tmp = Float64(a + Float64(t + Float64(x * log(y))));
	else
		tmp = Float64(a + Float64(z + Float64(y * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -5.7e+162) || ~((x <= 9e+214)))
		tmp = a + (t + (x * log(y)));
	else
		tmp = a + (z + (y * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -5.7e+162], N[Not[LessEqual[x, 9e+214]], $MachinePrecision]], N[(a + N[(t + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.69999999999999997e162 or 8.99999999999999935e214 < 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. associate-+l+ 99.6%

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

      2. +-commutative 99.6%

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

      3. associate-+l+ 99.6%

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

      4. associate-+r+ 99.6%

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

      5. +-commutative 99.6%

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

      6. +-commutative 99.6%

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

      7. associate-+l+ 99.6%

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

      8. associate-+l+ 99.6%

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

      9. +-commutative 99.6%

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

      10. fma-define 99.6%

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

      11. +-commutative 99.6%

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

      12. fma-define 99.6%

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

      13. sub-neg 99.6%

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

      14. metadata-eval 99.6%

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

      15. +-commutative 99.6%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around inf 58.0%

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

      1. +-commutative 58.0%

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

      2. associate-/l* 58.0%

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

      3. sub-neg 58.0%

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

      4. metadata-eval 58.0%

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

      5. associate-/l* 58.0%

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

      6. +-commutative 58.0%

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

      7. associate-/l* 57.7%

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

   7. Simplified 57.7%

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

   8. Taylor expanded in x around inf 48.6%

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

   9. Taylor expanded in a around 0 79.7%

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

   if -5.69999999999999997e162 < x < 8.99999999999999935e214

   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 96.1%

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

   4. Taylor expanded in z around inf 70.6%

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

      1. associate-+r+ 70.6%

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

      2. sub-neg 70.6%

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

      3. metadata-eval 70.6%

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

      4. associate-/l* 70.6%

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

   6. Simplified 70.6%

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

   7. Taylor expanded in a around inf 51.0%

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

   8. Taylor expanded in z around 0 60.0%

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

      1. *-commutative 60.0%

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

   10. Simplified 60.0%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.7 \cdot 10^{+162} \lor \neg \left(x \leq 9 \cdot 10^{+214}\right):\\ \;\;\;\;a + \left(t + x \cdot \log y\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(z + y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+83}:\\ \;\;\;\;a + \left(z + y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \log c \cdot \left(b - 0.5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -8.8e+83)
   (+ a (+ z (* y i)))
   (+ (* y i) (+ a (* (log c) (- b 0.5))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -8.8e+83) {
		tmp = a + (z + (y * i));
	} else {
		tmp = (y * i) + (a + (log(c) * (b - 0.5)));
	}
	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 <= (-8.8d+83)) then
        tmp = a + (z + (y * i))
    else
        tmp = (y * i) + (a + (log(c) * (b - 0.5d0)))
    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 <= -8.8e+83) {
		tmp = a + (z + (y * i));
	} else {
		tmp = (y * i) + (a + (Math.log(c) * (b - 0.5)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -8.8e+83:
		tmp = a + (z + (y * i))
	else:
		tmp = (y * i) + (a + (math.log(c) * (b - 0.5)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -8.8e+83)
		tmp = Float64(a + Float64(z + Float64(y * i)));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(log(c) * Float64(b - 0.5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -8.8e+83)
		tmp = a + (z + (y * i));
	else
		tmp = (y * i) + (a + (log(c) * (b - 0.5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -8.8e+83], N[(a + N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.79999999999999995e83

   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 88.6%

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

   4. Taylor expanded in z around inf 88.4%

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

      1. associate-+r+ 88.4%

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

      2. sub-neg 88.4%

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

      3. metadata-eval 88.4%

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

      4. associate-/l* 88.5%

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

   6. Simplified 88.5%

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

   7. Taylor expanded in a around inf 65.6%

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

   8. Taylor expanded in z around 0 65.7%

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

      1. *-commutative 65.7%

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

   10. Simplified 65.7%

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

   if -8.79999999999999995e83 < 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. Add Preprocessing

   3. Taylor expanded in a around inf 62.6%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+83}:\\ \;\;\;\;a + \left(z + y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \log c \cdot \left(b - 0.5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 9 \cdot 10^{+155}:\\ \;\;\;\;y \cdot i + \left(z + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(z + y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 9e+155) (+ (* y i) (+ z (* b (log c)))) (+ a (+ 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 (a <= 9e+155) {
		tmp = (y * i) + (z + (b * log(c)));
	} else {
		tmp = a + (z + (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 (a <= 9d+155) then
        tmp = (y * i) + (z + (b * log(c)))
    else
        tmp = a + (z + (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 (a <= 9e+155) {
		tmp = (y * i) + (z + (b * Math.log(c)));
	} else {
		tmp = a + (z + (y * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 9e+155:
		tmp = (y * i) + (z + (b * math.log(c)))
	else:
		tmp = a + (z + (y * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 9e+155)
		tmp = Float64(Float64(y * i) + Float64(z + Float64(b * log(c))));
	else
		tmp = Float64(a + Float64(z + Float64(y * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 9e+155)
		tmp = (y * i) + (z + (b * log(c)));
	else
		tmp = a + (z + (y * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 9e+155], N[(N[(y * i), $MachinePrecision] + N[(z + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 8.99999999999999947e155

   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 84.6%

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

   4. Taylor expanded in z around inf 62.3%

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

      1. associate-+r+ 62.3%

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

      2. sub-neg 62.3%

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

      3. metadata-eval 62.3%

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

      4. associate-/l* 62.3%

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

   6. Simplified 62.3%

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

   7. Taylor expanded in b around inf 49.1%

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

      1. associate-/l* 49.1%

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

   9. Simplified 49.1%

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

   10. Taylor expanded in z around 0 57.4%

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

   if 8.99999999999999947e155 < 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 0 91.3%

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

   4. Taylor expanded in z around inf 63.6%

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

      1. associate-+r+ 63.6%

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

      2. sub-neg 63.6%

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

      3. metadata-eval 63.6%

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

      4. associate-/l* 63.6%

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

   6. Simplified 63.6%

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

   7. Taylor expanded in a around inf 56.8%

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

   8. Taylor expanded in z around 0 81.6%

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

      1. *-commutative 81.6%

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

   10. Simplified 81.6%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 9 \cdot 10^{+155}:\\ \;\;\;\;y \cdot i + \left(z + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(z + y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 58.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{+225} \lor \neg \left(x \leq 5.2 \cdot 10^{+221}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;a + \left(z + y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -2.25e+225) (not (<= x 5.2e+221)))
   (* x (log y))
   (+ a (+ 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 ((x <= -2.25e+225) || !(x <= 5.2e+221)) {
		tmp = x * log(y);
	} else {
		tmp = a + (z + (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 ((x <= (-2.25d+225)) .or. (.not. (x <= 5.2d+221))) then
        tmp = x * log(y)
    else
        tmp = a + (z + (y * i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -2.25e+225) || !(x <= 5.2e+221)) {
		tmp = x * Math.log(y);
	} else {
		tmp = a + (z + (y * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -2.25e+225) or not (x <= 5.2e+221):
		tmp = x * math.log(y)
	else:
		tmp = a + (z + (y * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -2.25e+225) || !(x <= 5.2e+221))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(a + Float64(z + Float64(y * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -2.25e+225) || ~((x <= 5.2e+221)))
		tmp = x * log(y);
	else
		tmp = a + (z + (y * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -2.25e+225], N[Not[LessEqual[x, 5.2e+221]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(a + N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.24999999999999988e225 or 5.20000000000000008e221 < 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. associate-+l+ 99.6%

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

      2. +-commutative 99.6%

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

      3. associate-+l+ 99.6%

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

      4. associate-+r+ 99.6%

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

      5. +-commutative 99.6%

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

      6. +-commutative 99.6%

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

      7. associate-+l+ 99.6%

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

      8. associate-+l+ 99.6%

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

      9. +-commutative 99.6%

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

      10. fma-define 99.6%

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

      11. +-commutative 99.6%

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

      12. fma-define 99.6%

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

      13. sub-neg 99.6%

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

      14. metadata-eval 99.6%

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

      15. +-commutative 99.6%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around inf 55.0%

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

      1. +-commutative 55.0%

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

      2. associate-/l* 55.0%

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

      3. sub-neg 55.0%

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

      4. metadata-eval 55.0%

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

      5. associate-/l* 55.0%

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

      6. +-commutative 55.0%

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

      7. associate-/l* 54.7%

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

   7. Simplified 54.7%

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

   8. Taylor expanded in x around inf 48.0%

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

   9. Taylor expanded in x around inf 73.7%

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

   if -2.24999999999999988e225 < x < 5.20000000000000008e221

   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 94.5%

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

   4. Taylor expanded in z around inf 69.2%

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

      1. associate-+r+ 69.2%

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

      2. sub-neg 69.2%

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

      3. metadata-eval 69.2%

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

      4. associate-/l* 69.2%

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

   6. Simplified 69.2%

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

   7. Taylor expanded in a around inf 49.3%

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

   8. Taylor expanded in z around 0 57.7%

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

      1. *-commutative 57.7%

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

   10. Simplified 57.7%

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

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{+225} \lor \neg \left(x \leq 5.2 \cdot 10^{+221}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;a + \left(z + y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 43.6% accurate, 21.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 8.5 \cdot 10^{+145}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 8.5e+145) (+ 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 (a <= 8.5e+145) {
		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 (a <= 8.5d+145) 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 (a <= 8.5e+145) {
		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 a <= 8.5e+145:
		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 (a <= 8.5e+145)
		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 (a <= 8.5e+145)
		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[a, 8.5e+145], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 8.49999999999999977e145

   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 84.9%

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

   4. Taylor expanded in z around inf 39.2%

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

   if 8.49999999999999977e145 < 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 0 89.2%

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

   4. Taylor expanded in a around inf 72.6%

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

Alternative 14: 27.5% accurate, 27.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 6.2 \cdot 10^{+104}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (if (<= a 6.2e+104) (* y i) a))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 6.2e+104) {
		tmp = y * i;
	} 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 (a <= 6.2d+104) then
        tmp = y * i
    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 (a <= 6.2e+104) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 6.2e+104:
		tmp = y * i
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 6.2e+104)
		tmp = Float64(y * i);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 6.2e+104)
		tmp = y * i;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 6.2e+104], N[(y * i), $MachinePrecision], a]

Derivation

1. Split input into 2 regimes

2. if a < 6.20000000000000033e104

   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. Taylor expanded in y around inf 25.2%

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

      1. *-commutative 25.2%

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

   7. Simplified 25.2%

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

   if 6.20000000000000033e104 < a

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 82.5%

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

   4. Taylor expanded in a around inf 58.5%

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

   5. Taylor expanded in a around inf 45.0%

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

Alternative 15: 52.7% accurate, 31.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(a + N[(z + N[(y * i), $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 85.5%

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

4. Taylor expanded in z around inf 62.5%

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

   1. associate-+r+ 62.5%

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

   2. sub-neg 62.5%

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

   3. metadata-eval 62.5%

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

   4. associate-/l* 62.5%

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

6. Simplified 62.5%

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

7. Taylor expanded in a around inf 44.3%

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

8. Taylor expanded in z around 0 52.3%

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

   1. *-commutative 52.3%

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

10. Simplified 52.3%

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

Alternative 16: 37.9% accurate, 43.8× speedup

Math

\[\begin{array}{l} \\ a + y \cdot i \end{array} \]

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(a + 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. Taylor expanded in x around 0 85.5%

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

4. Taylor expanded in a around inf 39.0%

   \[\leadsto \color{blue}{a} + y \cdot i \]
5. Add Preprocessing

Alternative 17: 16.2% 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 x around 0 85.5%

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

4. Taylor expanded in a around inf 39.0%

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

5. Taylor expanded in a around inf 17.1%

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

Reproduce

herbie shell --seed 2024137 
(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)))