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

Percentage Accurate: 99.8% → 99.8%

Time: 23.9s

Alternatives: 26

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. associate-+l+ 99.9%

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

   3. +-commutative 99.9%

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

   4. associate-+l+ 99.9%

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

   5. +-commutative 99.9%

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

   6. associate-+l+ 99.9%

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

   7. +-commutative 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%

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

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. Final simplification 99.9%

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

Alternative 2: 99.8% accurate, 0.7× speedup

Math

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

FPCore

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(N[(t + a), $MachinePrecision] + N[(x * N[Log[y], $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(b + -0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision] + 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. 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. associate-+l+ 99.9%

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

   3. fma-define 99.9%

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

   4. sub-neg 99.9%

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

   5. metadata-eval 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 3: 94.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+104}:\\ \;\;\;\;a + \left(t + \left(z + \mathsf{fma}\left(i, y, x \cdot \log y\right)\right)\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+123}:\\ \;\;\;\;a + \left(t + \left(z + \left(y \cdot i + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \left(\log y + b \cdot \frac{\log c}{x}\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -2.5e+104)
   (+ a (+ t (+ z (fma i y (* x (log y))))))
   (if (<= x 4.6e+123)
     (+ a (+ t (+ z (+ (* y i) (* (log c) (- b 0.5))))))
     (+ a (+ t (+ z (* x (+ (log y) (* b (/ (log c) x))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -2.5e+104) {
		tmp = a + (t + (z + fma(i, y, (x * log(y)))));
	} else if (x <= 4.6e+123) {
		tmp = a + (t + (z + ((y * i) + (log(c) * (b - 0.5)))));
	} else {
		tmp = a + (t + (z + (x * (log(y) + (b * (log(c) / x))))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -2.5e+104)
		tmp = Float64(a + Float64(t + Float64(z + fma(i, y, Float64(x * log(y))))));
	elseif (x <= 4.6e+123)
		tmp = Float64(a + Float64(t + Float64(z + Float64(Float64(y * i) + Float64(log(c) * Float64(b - 0.5))))));
	else
		tmp = Float64(a + Float64(t + Float64(z + Float64(x * Float64(log(y) + Float64(b * Float64(log(c) / x)))))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -2.5e+104], N[(a + N[(t + N[(z + N[(i * y + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.6e+123], N[(a + N[(t + N[(z + N[(N[(y * i), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(t + N[(z + N[(x * N[(N[Log[y], $MachinePrecision] + N[(b * N[(N[Log[c], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.4999999999999998e104

   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 b around inf 99.8%

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

      1. *-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in b around 0 92.8%

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

      1. fma-define 92.9%

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

   8. Simplified 92.9%

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

   if -2.4999999999999998e104 < x < 4.59999999999999981e123

   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 97.9%

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

   if 4.59999999999999981e123 < x

   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 b around inf 99.9%

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

      1. *-commutative 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in y around 0 94.7%

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

   7. Taylor expanded in x around inf 94.7%

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

      1. associate-/l* 94.7%

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

   9. Simplified 94.7%

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

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+104}:\\ \;\;\;\;a + \left(t + \left(z + \mathsf{fma}\left(i, y, x \cdot \log y\right)\right)\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+123}:\\ \;\;\;\;a + \left(t + \left(z + \left(y \cdot i + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \left(\log y + b \cdot \frac{\log c}{x}\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 94.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -1.6 \cdot 10^{+104}:\\ \;\;\;\;a + \left(t + \left(z + \mathsf{fma}\left(i, y, t\_1\right)\right)\right)\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+125}:\\ \;\;\;\;a + \left(t + \left(z + \left(y \cdot i + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + \left(t\_1 + b \cdot \log c\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -1.6e+104)
     (+ a (+ t (+ z (fma i y t_1))))
     (if (<= x 2e+125)
       (+ a (+ t (+ z (+ (* y i) (* (log c) (- b 0.5))))))
       (+ a (+ t (+ z (+ t_1 (* b (log c))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * log(y);
	double tmp;
	if (x <= -1.6e+104) {
		tmp = a + (t + (z + fma(i, y, t_1)));
	} else if (x <= 2e+125) {
		tmp = a + (t + (z + ((y * i) + (log(c) * (b - 0.5)))));
	} else {
		tmp = a + (t + (z + (t_1 + (b * log(c)))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -1.6e+104)
		tmp = Float64(a + Float64(t + Float64(z + fma(i, y, t_1))));
	elseif (x <= 2e+125)
		tmp = Float64(a + Float64(t + Float64(z + Float64(Float64(y * i) + Float64(log(c) * Float64(b - 0.5))))));
	else
		tmp = Float64(a + Float64(t + Float64(z + Float64(t_1 + Float64(b * log(c))))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.6e+104], N[(a + N[(t + N[(z + N[(i * y + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2e+125], N[(a + N[(t + N[(z + N[(N[(y * i), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(t + N[(z + N[(t$95$1 + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.6e104

   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 b around inf 99.8%

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

      1. *-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in b around 0 92.8%

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

      1. fma-define 92.9%

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

   8. Simplified 92.9%

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

   if -1.6e104 < x < 1.9999999999999998e125

   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 97.9%

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

   if 1.9999999999999998e125 < x

   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 b around inf 99.9%

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

      1. *-commutative 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in y around 0 94.7%

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

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+104}:\\ \;\;\;\;a + \left(t + \left(z + \mathsf{fma}\left(i, y, x \cdot \log y\right)\right)\right)\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+125}:\\ \;\;\;\;a + \left(t + \left(z + \left(y \cdot i + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + \left(x \cdot \log y + b \cdot \log c\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) + ((log(c) * (b - 0.5d0)) + (a + (t + (z + (x * log(y))))))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

3. Final simplification 99.9%

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

Alternative 6: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

3. Taylor expanded in b around inf 98.0%

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

   1. *-commutative 98.0%

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

5. Simplified 98.0%

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

6. Final simplification 98.0%

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

Alternative 7: 95.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -2.15 \cdot 10^{+104}:\\ \;\;\;\;a + \left(t + \left(z + \mathsf{fma}\left(i, y, t\_1\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+114}:\\ \;\;\;\;a + \left(t + \left(z + \left(y \cdot i + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + t\_1\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -2.15e+104)
     (+ a (+ t (+ z (fma i y t_1))))
     (if (<= x 1.9e+114)
       (+ a (+ t (+ z (+ (* y i) (* (log c) (- b 0.5))))))
       (+ (* y i) (+ a (+ t (+ z t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * log(y);
	double tmp;
	if (x <= -2.15e+104) {
		tmp = a + (t + (z + fma(i, y, t_1)));
	} else if (x <= 1.9e+114) {
		tmp = a + (t + (z + ((y * i) + (log(c) * (b - 0.5)))));
	} else {
		tmp = (y * i) + (a + (t + (z + t_1)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -2.15e+104)
		tmp = Float64(a + Float64(t + Float64(z + fma(i, y, t_1))));
	elseif (x <= 1.9e+114)
		tmp = Float64(a + Float64(t + Float64(z + Float64(Float64(y * i) + Float64(log(c) * Float64(b - 0.5))))));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(t + Float64(z + t_1))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.15e+104], N[(a + N[(t + N[(z + N[(i * y + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.9e+114], N[(a + N[(t + N[(z + N[(N[(y * i), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(t + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.1500000000000001e104

   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 b around inf 99.8%

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

      1. *-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in b around 0 92.8%

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

      1. fma-define 92.9%

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

   8. Simplified 92.9%

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

   if -2.1500000000000001e104 < x < 1.9e114

   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 97.8%

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

   if 1.9e114 < x

   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 b around inf 99.9%

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

      1. *-commutative 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in b around 0 88.5%

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

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{+104}:\\ \;\;\;\;a + \left(t + \left(z + \mathsf{fma}\left(i, y, x \cdot \log y\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+114}:\\ \;\;\;\;a + \left(t + \left(z + \left(y \cdot i + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 49.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \left(t + b \cdot \log c\right)\\ t_2 := y \cdot i + x \cdot \log y\\ t_3 := a + \left(z + t\right)\\ \mathbf{if}\;z \leq -1.28 \cdot 10^{+222}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{+207}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{+176}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -0.016:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-125}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-266}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-296}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-138}:\\ \;\;\;\;a + \left(t + y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (+ t (* b (log c)))))
        (t_2 (+ (* y i) (* x (log y))))
        (t_3 (+ a (+ z t))))
   (if (<= z -1.28e+222)
     t_3
     (if (<= z -9.2e+207)
       t_2
       (if (<= z -1.02e+176)
         t_3
         (if (<= z -0.016)
           t_1
           (if (<= z -9e-125)
             t_2
             (if (<= z -2.4e-266)
               t_1
               (if (<= z -9.2e-296)
                 t_2
                 (if (<= z 6e-138) (+ a (+ t (* y i))) t_1))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (t + (b * log(c)));
	double t_2 = (y * i) + (x * log(y));
	double t_3 = a + (z + t);
	double tmp;
	if (z <= -1.28e+222) {
		tmp = t_3;
	} else if (z <= -9.2e+207) {
		tmp = t_2;
	} else if (z <= -1.02e+176) {
		tmp = t_3;
	} else if (z <= -0.016) {
		tmp = t_1;
	} else if (z <= -9e-125) {
		tmp = t_2;
	} else if (z <= -2.4e-266) {
		tmp = t_1;
	} else if (z <= -9.2e-296) {
		tmp = t_2;
	} else if (z <= 6e-138) {
		tmp = a + (t + (y * i));
	} else {
		tmp = 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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a + (t + (b * log(c)))
    t_2 = (y * i) + (x * log(y))
    t_3 = a + (z + t)
    if (z <= (-1.28d+222)) then
        tmp = t_3
    else if (z <= (-9.2d+207)) then
        tmp = t_2
    else if (z <= (-1.02d+176)) then
        tmp = t_3
    else if (z <= (-0.016d0)) then
        tmp = t_1
    else if (z <= (-9d-125)) then
        tmp = t_2
    else if (z <= (-2.4d-266)) then
        tmp = t_1
    else if (z <= (-9.2d-296)) then
        tmp = t_2
    else if (z <= 6d-138) then
        tmp = a + (t + (y * i))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (t + (b * Math.log(c)));
	double t_2 = (y * i) + (x * Math.log(y));
	double t_3 = a + (z + t);
	double tmp;
	if (z <= -1.28e+222) {
		tmp = t_3;
	} else if (z <= -9.2e+207) {
		tmp = t_2;
	} else if (z <= -1.02e+176) {
		tmp = t_3;
	} else if (z <= -0.016) {
		tmp = t_1;
	} else if (z <= -9e-125) {
		tmp = t_2;
	} else if (z <= -2.4e-266) {
		tmp = t_1;
	} else if (z <= -9.2e-296) {
		tmp = t_2;
	} else if (z <= 6e-138) {
		tmp = a + (t + (y * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (t + (b * math.log(c)))
	t_2 = (y * i) + (x * math.log(y))
	t_3 = a + (z + t)
	tmp = 0
	if z <= -1.28e+222:
		tmp = t_3
	elif z <= -9.2e+207:
		tmp = t_2
	elif z <= -1.02e+176:
		tmp = t_3
	elif z <= -0.016:
		tmp = t_1
	elif z <= -9e-125:
		tmp = t_2
	elif z <= -2.4e-266:
		tmp = t_1
	elif z <= -9.2e-296:
		tmp = t_2
	elif z <= 6e-138:
		tmp = a + (t + (y * i))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(t + Float64(b * log(c))))
	t_2 = Float64(Float64(y * i) + Float64(x * log(y)))
	t_3 = Float64(a + Float64(z + t))
	tmp = 0.0
	if (z <= -1.28e+222)
		tmp = t_3;
	elseif (z <= -9.2e+207)
		tmp = t_2;
	elseif (z <= -1.02e+176)
		tmp = t_3;
	elseif (z <= -0.016)
		tmp = t_1;
	elseif (z <= -9e-125)
		tmp = t_2;
	elseif (z <= -2.4e-266)
		tmp = t_1;
	elseif (z <= -9.2e-296)
		tmp = t_2;
	elseif (z <= 6e-138)
		tmp = Float64(a + Float64(t + Float64(y * i)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (t + (b * log(c)));
	t_2 = (y * i) + (x * log(y));
	t_3 = a + (z + t);
	tmp = 0.0;
	if (z <= -1.28e+222)
		tmp = t_3;
	elseif (z <= -9.2e+207)
		tmp = t_2;
	elseif (z <= -1.02e+176)
		tmp = t_3;
	elseif (z <= -0.016)
		tmp = t_1;
	elseif (z <= -9e-125)
		tmp = t_2;
	elseif (z <= -2.4e-266)
		tmp = t_1;
	elseif (z <= -9.2e-296)
		tmp = t_2;
	elseif (z <= 6e-138)
		tmp = a + (t + (y * i));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(t + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * i), $MachinePrecision] + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.28e+222], t$95$3, If[LessEqual[z, -9.2e+207], t$95$2, If[LessEqual[z, -1.02e+176], t$95$3, If[LessEqual[z, -0.016], t$95$1, If[LessEqual[z, -9e-125], t$95$2, If[LessEqual[z, -2.4e-266], t$95$1, If[LessEqual[z, -9.2e-296], t$95$2, If[LessEqual[z, 6e-138], N[(a + N[(t + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.28e222 or -9.19999999999999979e207 < z < -1.02000000000000001e176

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 98.8%

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

   4. Taylor expanded in z around inf 84.6%

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

   if -1.28e222 < z < -9.19999999999999979e207 or -0.016 < z < -9.00000000000000024e-125 or -2.4e-266 < z < -9.20000000000000016e-296

   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 b around inf 99.9%

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

      1. *-commutative 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in x around -inf 64.5%

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

      1. mul-1-neg 64.5%

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

      2. distribute-lft-out 64.5%

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

      3. +-commutative 64.5%

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

   8. Simplified 64.5%

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

   9. Taylor expanded in x around inf 36.5%

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

       1. associate-*r* 36.5%

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

       2. neg-mul-1 36.5%

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

   11. Simplified 36.5%

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

   12. Taylor expanded in x around 0 36.5%

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

   if -1.02000000000000001e176 < z < -0.016 or -9.00000000000000024e-125 < z < -2.4e-266 or 6.0000000000000001e-138 < 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 x around 0 81.8%

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

   4. Taylor expanded in b around inf 54.5%

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

      1. *-commutative 54.5%

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

   6. Simplified 54.5%

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

   if -9.20000000000000016e-296 < z < 6.0000000000000001e-138

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 85.0%

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

   4. Taylor expanded in i around inf 56.2%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.28 \cdot 10^{+222}:\\ \;\;\;\;a + \left(z + t\right)\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{+207}:\\ \;\;\;\;y \cdot i + x \cdot \log y\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{+176}:\\ \;\;\;\;a + \left(z + t\right)\\ \mathbf{elif}\;z \leq -0.016:\\ \;\;\;\;a + \left(t + b \cdot \log c\right)\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-125}:\\ \;\;\;\;y \cdot i + x \cdot \log y\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-266}:\\ \;\;\;\;a + \left(t + b \cdot \log c\right)\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-296}:\\ \;\;\;\;y \cdot i + x \cdot \log y\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-138}:\\ \;\;\;\;a + \left(t + y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + b \cdot \log c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 47.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \log c\\ t_2 := a + \left(z + t\right)\\ t_3 := a + \left(t + y \cdot i\right)\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+227}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{+209}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.18 \cdot 10^{+176}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{+96}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-49} \lor \neg \left(z \leq 2.65 \cdot 10^{-287}\right):\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log y + \frac{a}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* b (log c))) (t_2 (+ a (+ z t))) (t_3 (+ a (+ t (* y i)))))
   (if (<= z -5.2e+227)
     t_2
     (if (<= z -4.9e+209)
       t_1
       (if (<= z -1.18e+176)
         t_2
         (if (<= z -6.8e+96)
           t_3
           (if (<= z -3.9e+50)
             t_1
             (if (or (<= z -5.5e-49) (not (<= z 2.65e-287)))
               t_3
               (* x (+ (log y) (/ a x)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = b * log(c);
	double t_2 = a + (z + t);
	double t_3 = a + (t + (y * i));
	double tmp;
	if (z <= -5.2e+227) {
		tmp = t_2;
	} else if (z <= -4.9e+209) {
		tmp = t_1;
	} else if (z <= -1.18e+176) {
		tmp = t_2;
	} else if (z <= -6.8e+96) {
		tmp = t_3;
	} else if (z <= -3.9e+50) {
		tmp = t_1;
	} else if ((z <= -5.5e-49) || !(z <= 2.65e-287)) {
		tmp = t_3;
	} else {
		tmp = x * (log(y) + (a / x));
	}
	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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = b * log(c)
    t_2 = a + (z + t)
    t_3 = a + (t + (y * i))
    if (z <= (-5.2d+227)) then
        tmp = t_2
    else if (z <= (-4.9d+209)) then
        tmp = t_1
    else if (z <= (-1.18d+176)) then
        tmp = t_2
    else if (z <= (-6.8d+96)) then
        tmp = t_3
    else if (z <= (-3.9d+50)) then
        tmp = t_1
    else if ((z <= (-5.5d-49)) .or. (.not. (z <= 2.65d-287))) then
        tmp = t_3
    else
        tmp = x * (log(y) + (a / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = b * Math.log(c);
	double t_2 = a + (z + t);
	double t_3 = a + (t + (y * i));
	double tmp;
	if (z <= -5.2e+227) {
		tmp = t_2;
	} else if (z <= -4.9e+209) {
		tmp = t_1;
	} else if (z <= -1.18e+176) {
		tmp = t_2;
	} else if (z <= -6.8e+96) {
		tmp = t_3;
	} else if (z <= -3.9e+50) {
		tmp = t_1;
	} else if ((z <= -5.5e-49) || !(z <= 2.65e-287)) {
		tmp = t_3;
	} else {
		tmp = x * (Math.log(y) + (a / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = b * math.log(c)
	t_2 = a + (z + t)
	t_3 = a + (t + (y * i))
	tmp = 0
	if z <= -5.2e+227:
		tmp = t_2
	elif z <= -4.9e+209:
		tmp = t_1
	elif z <= -1.18e+176:
		tmp = t_2
	elif z <= -6.8e+96:
		tmp = t_3
	elif z <= -3.9e+50:
		tmp = t_1
	elif (z <= -5.5e-49) or not (z <= 2.65e-287):
		tmp = t_3
	else:
		tmp = x * (math.log(y) + (a / x))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(b * log(c))
	t_2 = Float64(a + Float64(z + t))
	t_3 = Float64(a + Float64(t + Float64(y * i)))
	tmp = 0.0
	if (z <= -5.2e+227)
		tmp = t_2;
	elseif (z <= -4.9e+209)
		tmp = t_1;
	elseif (z <= -1.18e+176)
		tmp = t_2;
	elseif (z <= -6.8e+96)
		tmp = t_3;
	elseif (z <= -3.9e+50)
		tmp = t_1;
	elseif ((z <= -5.5e-49) || !(z <= 2.65e-287))
		tmp = t_3;
	else
		tmp = Float64(x * Float64(log(y) + Float64(a / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = b * log(c);
	t_2 = a + (z + t);
	t_3 = a + (t + (y * i));
	tmp = 0.0;
	if (z <= -5.2e+227)
		tmp = t_2;
	elseif (z <= -4.9e+209)
		tmp = t_1;
	elseif (z <= -1.18e+176)
		tmp = t_2;
	elseif (z <= -6.8e+96)
		tmp = t_3;
	elseif (z <= -3.9e+50)
		tmp = t_1;
	elseif ((z <= -5.5e-49) || ~((z <= 2.65e-287)))
		tmp = t_3;
	else
		tmp = x * (log(y) + (a / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a + N[(t + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.2e+227], t$95$2, If[LessEqual[z, -4.9e+209], t$95$1, If[LessEqual[z, -1.18e+176], t$95$2, If[LessEqual[z, -6.8e+96], t$95$3, If[LessEqual[z, -3.9e+50], t$95$1, If[Or[LessEqual[z, -5.5e-49], N[Not[LessEqual[z, 2.65e-287]], $MachinePrecision]], t$95$3, N[(x * N[(N[Log[y], $MachinePrecision] + N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.19999999999999964e227 or -4.8999999999999998e209 < z < -1.18000000000000006e176

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 98.8%

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

   4. Taylor expanded in z around inf 84.6%

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

   if -5.19999999999999964e227 < z < -4.8999999999999998e209 or -6.8000000000000002e96 < z < -3.89999999999999967e50

   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. Add Preprocessing

   3. Taylor expanded in a around -inf 82.7%

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

   4. Taylor expanded in b around inf 46.8%

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

      1. mul-1-neg 46.8%

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

      2. distribute-rgt-neg-in 46.8%

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

   6. Simplified 46.8%

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

   if -1.18000000000000006e176 < z < -6.8000000000000002e96 or -3.89999999999999967e50 < z < -5.50000000000000031e-49 or 2.64999999999999974e-287 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 84.6%

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

   4. Taylor expanded in i around inf 54.0%

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

   if -5.50000000000000031e-49 < z < 2.64999999999999974e-287

   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 b around inf 96.6%

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

      1. *-commutative 96.6%

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

   5. Simplified 96.6%

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

   6. Taylor expanded in x around -inf 72.8%

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

      1. mul-1-neg 72.8%

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

      2. distribute-lft-out 72.8%

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

      3. +-commutative 72.8%

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

   8. Simplified 72.8%

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

   9. Taylor expanded in a around inf 48.0%

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

   10. Taylor expanded in y around 0 34.8%

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

4. Final simplification 52.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+227}:\\ \;\;\;\;a + \left(z + t\right)\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{+209}:\\ \;\;\;\;b \cdot \log c\\ \mathbf{elif}\;z \leq -1.18 \cdot 10^{+176}:\\ \;\;\;\;a + \left(z + t\right)\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{+96}:\\ \;\;\;\;a + \left(t + y \cdot i\right)\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{+50}:\\ \;\;\;\;b \cdot \log c\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-49} \lor \neg \left(z \leq 2.65 \cdot 10^{-287}\right):\\ \;\;\;\;a + \left(t + y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log y + \frac{a}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 43.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \log c\\ t_2 := a + \left(z + t\right)\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+227}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{+209}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.18 \cdot 10^{+176}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -0.016 \lor \neg \left(z \leq 2.65 \cdot 10^{-287}\right):\\ \;\;\;\;a + \left(t + t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log y + \frac{a}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* b (log c))) (t_2 (+ a (+ z t))))
   (if (<= z -5.2e+227)
     t_2
     (if (<= z -4.9e+209)
       t_1
       (if (<= z -1.18e+176)
         t_2
         (if (or (<= z -0.016) (not (<= z 2.65e-287)))
           (+ a (+ t t_1))
           (* x (+ (log y) (/ a x)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = b * log(c);
	double t_2 = a + (z + t);
	double tmp;
	if (z <= -5.2e+227) {
		tmp = t_2;
	} else if (z <= -4.9e+209) {
		tmp = t_1;
	} else if (z <= -1.18e+176) {
		tmp = t_2;
	} else if ((z <= -0.016) || !(z <= 2.65e-287)) {
		tmp = a + (t + t_1);
	} else {
		tmp = x * (log(y) + (a / x));
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = b * log(c)
    t_2 = a + (z + t)
    if (z <= (-5.2d+227)) then
        tmp = t_2
    else if (z <= (-4.9d+209)) then
        tmp = t_1
    else if (z <= (-1.18d+176)) then
        tmp = t_2
    else if ((z <= (-0.016d0)) .or. (.not. (z <= 2.65d-287))) then
        tmp = a + (t + t_1)
    else
        tmp = x * (log(y) + (a / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = b * Math.log(c);
	double t_2 = a + (z + t);
	double tmp;
	if (z <= -5.2e+227) {
		tmp = t_2;
	} else if (z <= -4.9e+209) {
		tmp = t_1;
	} else if (z <= -1.18e+176) {
		tmp = t_2;
	} else if ((z <= -0.016) || !(z <= 2.65e-287)) {
		tmp = a + (t + t_1);
	} else {
		tmp = x * (Math.log(y) + (a / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = b * math.log(c)
	t_2 = a + (z + t)
	tmp = 0
	if z <= -5.2e+227:
		tmp = t_2
	elif z <= -4.9e+209:
		tmp = t_1
	elif z <= -1.18e+176:
		tmp = t_2
	elif (z <= -0.016) or not (z <= 2.65e-287):
		tmp = a + (t + t_1)
	else:
		tmp = x * (math.log(y) + (a / x))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(b * log(c))
	t_2 = Float64(a + Float64(z + t))
	tmp = 0.0
	if (z <= -5.2e+227)
		tmp = t_2;
	elseif (z <= -4.9e+209)
		tmp = t_1;
	elseif (z <= -1.18e+176)
		tmp = t_2;
	elseif ((z <= -0.016) || !(z <= 2.65e-287))
		tmp = Float64(a + Float64(t + t_1));
	else
		tmp = Float64(x * Float64(log(y) + Float64(a / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = b * log(c);
	t_2 = a + (z + t);
	tmp = 0.0;
	if (z <= -5.2e+227)
		tmp = t_2;
	elseif (z <= -4.9e+209)
		tmp = t_1;
	elseif (z <= -1.18e+176)
		tmp = t_2;
	elseif ((z <= -0.016) || ~((z <= 2.65e-287)))
		tmp = a + (t + t_1);
	else
		tmp = x * (log(y) + (a / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.2e+227], t$95$2, If[LessEqual[z, -4.9e+209], t$95$1, If[LessEqual[z, -1.18e+176], t$95$2, If[Or[LessEqual[z, -0.016], N[Not[LessEqual[z, 2.65e-287]], $MachinePrecision]], N[(a + N[(t + t$95$1), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[Log[y], $MachinePrecision] + N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.19999999999999964e227 or -4.8999999999999998e209 < z < -1.18000000000000006e176

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 98.8%

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

   4. Taylor expanded in z around inf 84.6%

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

   if -5.19999999999999964e227 < z < -4.8999999999999998e209

   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 81.2%

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

   4. Taylor expanded in b around inf 41.8%

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

      1. mul-1-neg 41.8%

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

      2. distribute-rgt-neg-in 41.8%

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

   6. Simplified 41.8%

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

   if -1.18000000000000006e176 < z < -0.016 or 2.64999999999999974e-287 < 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 x around 0 84.6%

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

   4. Taylor expanded in b around inf 52.5%

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

      1. *-commutative 52.5%

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

   6. Simplified 52.5%

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

   if -0.016 < z < 2.64999999999999974e-287

   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 b around inf 97.0%

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

      1. *-commutative 97.0%

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

   5. Simplified 97.0%

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

   6. Taylor expanded in x around -inf 70.5%

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

      1. mul-1-neg 70.5%

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

      2. distribute-lft-out 70.5%

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

      3. +-commutative 70.5%

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

   8. Simplified 70.5%

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

   9. Taylor expanded in a around inf 45.6%

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

   10. Taylor expanded in y around 0 31.0%

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

4. Final simplification 49.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+227}:\\ \;\;\;\;a + \left(z + t\right)\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{+209}:\\ \;\;\;\;b \cdot \log c\\ \mathbf{elif}\;z \leq -1.18 \cdot 10^{+176}:\\ \;\;\;\;a + \left(z + t\right)\\ \mathbf{elif}\;z \leq -0.016 \lor \neg \left(z \leq 2.65 \cdot 10^{-287}\right):\\ \;\;\;\;a + \left(t + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log y + \frac{a}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 70.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \left(t + \left(z + \left(b + -0.5\right) \cdot \log c\right)\right)\\ t_2 := a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{if}\;x \leq -2.5 \cdot 10^{+104}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-242}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-102}:\\ \;\;\;\;y \cdot i + b \cdot \left(\log c + \frac{a}{b}\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+112}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (+ t (+ z (* (+ b -0.5) (log c))))))
        (t_2 (+ a (+ t (+ z (* x (log y)))))))
   (if (<= x -2.5e+104)
     t_2
     (if (<= x 5.5e-242)
       t_1
       (if (<= x 9.2e-102)
         (+ (* y i) (* b (+ (log c) (/ a b))))
         (if (<= x 5.8e+112) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (t + (z + ((b + -0.5) * log(c))));
	double t_2 = a + (t + (z + (x * log(y))));
	double tmp;
	if (x <= -2.5e+104) {
		tmp = t_2;
	} else if (x <= 5.5e-242) {
		tmp = t_1;
	} else if (x <= 9.2e-102) {
		tmp = (y * i) + (b * (log(c) + (a / b)));
	} else if (x <= 5.8e+112) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = a + (t + (z + ((b + (-0.5d0)) * log(c))))
    t_2 = a + (t + (z + (x * log(y))))
    if (x <= (-2.5d+104)) then
        tmp = t_2
    else if (x <= 5.5d-242) then
        tmp = t_1
    else if (x <= 9.2d-102) then
        tmp = (y * i) + (b * (log(c) + (a / b)))
    else if (x <= 5.8d+112) then
        tmp = t_1
    else
        tmp = t_2
    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 = a + (t + (z + ((b + -0.5) * Math.log(c))));
	double t_2 = a + (t + (z + (x * Math.log(y))));
	double tmp;
	if (x <= -2.5e+104) {
		tmp = t_2;
	} else if (x <= 5.5e-242) {
		tmp = t_1;
	} else if (x <= 9.2e-102) {
		tmp = (y * i) + (b * (Math.log(c) + (a / b)));
	} else if (x <= 5.8e+112) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (t + (z + ((b + -0.5) * math.log(c))))
	t_2 = a + (t + (z + (x * math.log(y))))
	tmp = 0
	if x <= -2.5e+104:
		tmp = t_2
	elif x <= 5.5e-242:
		tmp = t_1
	elif x <= 9.2e-102:
		tmp = (y * i) + (b * (math.log(c) + (a / b)))
	elif x <= 5.8e+112:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(t + Float64(z + Float64(Float64(b + -0.5) * log(c)))))
	t_2 = Float64(a + Float64(t + Float64(z + Float64(x * log(y)))))
	tmp = 0.0
	if (x <= -2.5e+104)
		tmp = t_2;
	elseif (x <= 5.5e-242)
		tmp = t_1;
	elseif (x <= 9.2e-102)
		tmp = Float64(Float64(y * i) + Float64(b * Float64(log(c) + Float64(a / b))));
	elseif (x <= 5.8e+112)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (t + (z + ((b + -0.5) * log(c))));
	t_2 = a + (t + (z + (x * log(y))));
	tmp = 0.0;
	if (x <= -2.5e+104)
		tmp = t_2;
	elseif (x <= 5.5e-242)
		tmp = t_1;
	elseif (x <= 9.2e-102)
		tmp = (y * i) + (b * (log(c) + (a / b)));
	elseif (x <= 5.8e+112)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(t + N[(z + N[(N[(b + -0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a + N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.5e+104], t$95$2, If[LessEqual[x, 5.5e-242], t$95$1, If[LessEqual[x, 9.2e-102], N[(N[(y * i), $MachinePrecision] + N[(b * N[(N[Log[c], $MachinePrecision] + N[(a / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.8e+112], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.4999999999999998e104 or 5.8000000000000004e112 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf 99.8%

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

      1. *-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in y around 0 89.2%

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

   7. Taylor expanded in b around 0 80.1%

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

      1. +-commutative 80.1%

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

   9. Simplified 80.1%

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

   if -2.4999999999999998e104 < x < 5.4999999999999998e-242 or 9.19999999999999946e-102 < x < 5.8000000000000004e112

   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 97.5%

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

   4. Taylor expanded in i around 0 78.7%

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

      1. +-commutative 78.7%

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

      2. +-commutative 78.7%

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

      3. sub-neg 78.7%

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

      4. metadata-eval 78.7%

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

   6. Simplified 78.7%

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

   if 5.4999999999999998e-242 < x < 9.19999999999999946e-102

   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 b around inf 95.7%

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

      1. *-commutative 95.7%

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

   5. Simplified 95.7%

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

   6. Taylor expanded in b around inf 79.1%

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

      1. associate-+r+ 79.1%

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

      2. associate-/l* 79.1%

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

   8. Simplified 79.1%

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

   9. Taylor expanded in a around inf 74.2%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+104}:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-242}:\\ \;\;\;\;a + \left(t + \left(z + \left(b + -0.5\right) \cdot \log c\right)\right)\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-102}:\\ \;\;\;\;y \cdot i + b \cdot \left(\log c + \frac{a}{b}\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+112}:\\ \;\;\;\;a + \left(t + \left(z + \left(b + -0.5\right) \cdot \log c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 70.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{if}\;x \leq -2.45 \cdot 10^{+104}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-61}:\\ \;\;\;\;a + \left(t + \left(z + b \cdot \log c\right)\right)\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-189}:\\ \;\;\;\;y \cdot i + b \cdot \left(\log c + \frac{z}{b}\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+113}:\\ \;\;\;\;a + \left(t + \left(z + \left(b + -0.5\right) \cdot \log c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (+ t (+ z (* x (log y)))))))
   (if (<= x -2.45e+104)
     t_1
     (if (<= x -1.45e-61)
       (+ a (+ t (+ z (* b (log c)))))
       (if (<= x -1.9e-189)
         (+ (* y i) (* b (+ (log c) (/ z b))))
         (if (<= x 3.1e+113) (+ a (+ t (+ z (* (+ b -0.5) (log c))))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (t + (z + (x * log(y))));
	double tmp;
	if (x <= -2.45e+104) {
		tmp = t_1;
	} else if (x <= -1.45e-61) {
		tmp = a + (t + (z + (b * log(c))));
	} else if (x <= -1.9e-189) {
		tmp = (y * i) + (b * (log(c) + (z / b)));
	} else if (x <= 3.1e+113) {
		tmp = a + (t + (z + ((b + -0.5) * log(c))));
	} else {
		tmp = 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 = a + (t + (z + (x * log(y))))
    if (x <= (-2.45d+104)) then
        tmp = t_1
    else if (x <= (-1.45d-61)) then
        tmp = a + (t + (z + (b * log(c))))
    else if (x <= (-1.9d-189)) then
        tmp = (y * i) + (b * (log(c) + (z / b)))
    else if (x <= 3.1d+113) then
        tmp = a + (t + (z + ((b + (-0.5d0)) * log(c))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (t + (z + (x * Math.log(y))));
	double tmp;
	if (x <= -2.45e+104) {
		tmp = t_1;
	} else if (x <= -1.45e-61) {
		tmp = a + (t + (z + (b * Math.log(c))));
	} else if (x <= -1.9e-189) {
		tmp = (y * i) + (b * (Math.log(c) + (z / b)));
	} else if (x <= 3.1e+113) {
		tmp = a + (t + (z + ((b + -0.5) * Math.log(c))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (t + (z + (x * math.log(y))))
	tmp = 0
	if x <= -2.45e+104:
		tmp = t_1
	elif x <= -1.45e-61:
		tmp = a + (t + (z + (b * math.log(c))))
	elif x <= -1.9e-189:
		tmp = (y * i) + (b * (math.log(c) + (z / b)))
	elif x <= 3.1e+113:
		tmp = a + (t + (z + ((b + -0.5) * math.log(c))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(t + Float64(z + Float64(x * log(y)))))
	tmp = 0.0
	if (x <= -2.45e+104)
		tmp = t_1;
	elseif (x <= -1.45e-61)
		tmp = Float64(a + Float64(t + Float64(z + Float64(b * log(c)))));
	elseif (x <= -1.9e-189)
		tmp = Float64(Float64(y * i) + Float64(b * Float64(log(c) + Float64(z / b))));
	elseif (x <= 3.1e+113)
		tmp = Float64(a + Float64(t + Float64(z + Float64(Float64(b + -0.5) * log(c)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (t + (z + (x * log(y))));
	tmp = 0.0;
	if (x <= -2.45e+104)
		tmp = t_1;
	elseif (x <= -1.45e-61)
		tmp = a + (t + (z + (b * log(c))));
	elseif (x <= -1.9e-189)
		tmp = (y * i) + (b * (log(c) + (z / b)));
	elseif (x <= 3.1e+113)
		tmp = a + (t + (z + ((b + -0.5) * log(c))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.45e+104], t$95$1, If[LessEqual[x, -1.45e-61], N[(a + N[(t + N[(z + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.9e-189], N[(N[(y * i), $MachinePrecision] + N[(b * N[(N[Log[c], $MachinePrecision] + N[(z / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.1e+113], N[(a + N[(t + N[(z + N[(N[(b + -0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.44999999999999993e104 or 3.09999999999999991e113 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf 99.8%

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

      1. *-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in y around 0 89.2%

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

   7. Taylor expanded in b around 0 80.1%

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

      1. +-commutative 80.1%

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

   9. Simplified 80.1%

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

   if -2.44999999999999993e104 < x < -1.45e-61

   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 b around inf 99.9%

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

      1. *-commutative 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in y around 0 89.0%

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

   7. Taylor expanded in x around 0 86.1%

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

      1. +-commutative 86.1%

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

   9. Simplified 86.1%

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

   if -1.45e-61 < x < -1.90000000000000011e-189

   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 b around inf 95.9%

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

      1. *-commutative 95.9%

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

   5. Simplified 95.9%

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

   6. Taylor expanded in b around inf 88.7%

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

      1. associate-+r+ 88.7%

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

      2. associate-/l* 88.7%

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

   8. Simplified 88.7%

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

   9. Taylor expanded in z around inf 84.9%

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

   if -1.90000000000000011e-189 < x < 3.09999999999999991e113

   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 97.6%

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

   4. Taylor expanded in i around 0 75.6%

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

      1. +-commutative 75.6%

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

      2. +-commutative 75.6%

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

      3. sub-neg 75.6%

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

      4. metadata-eval 75.6%

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

   6. Simplified 75.6%

      \[\leadsto \color{blue}{a + \left(\left(\log c \cdot \left(b + -0.5\right) + z\right) + t\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.45 \cdot 10^{+104}:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-61}:\\ \;\;\;\;a + \left(t + \left(z + b \cdot \log c\right)\right)\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-189}:\\ \;\;\;\;y \cdot i + b \cdot \left(\log c + \frac{z}{b}\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+113}:\\ \;\;\;\;a + \left(t + \left(z + \left(b + -0.5\right) \cdot \log c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 71.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \left(t + \left(z + b \cdot \log c\right)\right)\\ t_2 := a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{if}\;x \leq -1.8 \cdot 10^{+104}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-242}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-193}:\\ \;\;\;\;a + \left(t + y \cdot i\right)\\ \mathbf{elif}\;x \leq 1.32 \cdot 10^{+113}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (+ t (+ z (* b (log c))))))
        (t_2 (+ a (+ t (+ z (* x (log y)))))))
   (if (<= x -1.8e+104)
     t_2
     (if (<= x 5.5e-242)
       t_1
       (if (<= x 2e-193) (+ a (+ t (* y i))) (if (<= x 1.32e+113) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (t + (z + (b * log(c))));
	double t_2 = a + (t + (z + (x * log(y))));
	double tmp;
	if (x <= -1.8e+104) {
		tmp = t_2;
	} else if (x <= 5.5e-242) {
		tmp = t_1;
	} else if (x <= 2e-193) {
		tmp = a + (t + (y * i));
	} else if (x <= 1.32e+113) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = a + (t + (z + (b * log(c))))
    t_2 = a + (t + (z + (x * log(y))))
    if (x <= (-1.8d+104)) then
        tmp = t_2
    else if (x <= 5.5d-242) then
        tmp = t_1
    else if (x <= 2d-193) then
        tmp = a + (t + (y * i))
    else if (x <= 1.32d+113) then
        tmp = t_1
    else
        tmp = t_2
    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 = a + (t + (z + (b * Math.log(c))));
	double t_2 = a + (t + (z + (x * Math.log(y))));
	double tmp;
	if (x <= -1.8e+104) {
		tmp = t_2;
	} else if (x <= 5.5e-242) {
		tmp = t_1;
	} else if (x <= 2e-193) {
		tmp = a + (t + (y * i));
	} else if (x <= 1.32e+113) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (t + (z + (b * math.log(c))))
	t_2 = a + (t + (z + (x * math.log(y))))
	tmp = 0
	if x <= -1.8e+104:
		tmp = t_2
	elif x <= 5.5e-242:
		tmp = t_1
	elif x <= 2e-193:
		tmp = a + (t + (y * i))
	elif x <= 1.32e+113:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(t + Float64(z + Float64(b * log(c)))))
	t_2 = Float64(a + Float64(t + Float64(z + Float64(x * log(y)))))
	tmp = 0.0
	if (x <= -1.8e+104)
		tmp = t_2;
	elseif (x <= 5.5e-242)
		tmp = t_1;
	elseif (x <= 2e-193)
		tmp = Float64(a + Float64(t + Float64(y * i)));
	elseif (x <= 1.32e+113)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (t + (z + (b * log(c))));
	t_2 = a + (t + (z + (x * log(y))));
	tmp = 0.0;
	if (x <= -1.8e+104)
		tmp = t_2;
	elseif (x <= 5.5e-242)
		tmp = t_1;
	elseif (x <= 2e-193)
		tmp = a + (t + (y * i));
	elseif (x <= 1.32e+113)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(t + N[(z + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a + N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.8e+104], t$95$2, If[LessEqual[x, 5.5e-242], t$95$1, If[LessEqual[x, 2e-193], N[(a + N[(t + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.32e+113], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.8e104 or 1.31999999999999996e113 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf 99.8%

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

      1. *-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in y around 0 89.2%

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

   7. Taylor expanded in b around 0 80.1%

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

      1. +-commutative 80.1%

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

   9. Simplified 80.1%

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

   if -1.8e104 < x < 5.4999999999999998e-242 or 2.0000000000000001e-193 < x < 1.31999999999999996e113

   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 b around inf 97.5%

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

      1. *-commutative 97.5%

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

   5. Simplified 97.5%

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

   6. Taylor expanded in y around 0 77.3%

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

   7. Taylor expanded in x around 0 75.1%

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

      1. +-commutative 75.1%

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

   9. Simplified 75.1%

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

   if 5.4999999999999998e-242 < x < 2.0000000000000001e-193

   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 99.8%

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

   4. Taylor expanded in i around inf 90.2%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+104}:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-242}:\\ \;\;\;\;a + \left(t + \left(z + b \cdot \log c\right)\right)\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-193}:\\ \;\;\;\;a + \left(t + y \cdot i\right)\\ \mathbf{elif}\;x \leq 1.32 \cdot 10^{+113}:\\ \;\;\;\;a + \left(t + \left(z + b \cdot \log c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 95.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+104} \lor \neg \left(x \leq 2.35 \cdot 10^{+114}\right):\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + \left(y \cdot i + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -2.3e+104) (not (<= x 2.35e+114)))
   (+ (* y i) (+ a (+ t (+ z (* x (log y))))))
   (+ a (+ t (+ z (+ (* y i) (* (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 <= -2.3e+104) || !(x <= 2.35e+114)) {
		tmp = (y * i) + (a + (t + (z + (x * log(y)))));
	} else {
		tmp = a + (t + (z + ((y * i) + (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 ((x <= (-2.3d+104)) .or. (.not. (x <= 2.35d+114))) then
        tmp = (y * i) + (a + (t + (z + (x * log(y)))))
    else
        tmp = a + (t + (z + ((y * i) + (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 ((x <= -2.3e+104) || !(x <= 2.35e+114)) {
		tmp = (y * i) + (a + (t + (z + (x * Math.log(y)))));
	} else {
		tmp = a + (t + (z + ((y * i) + (Math.log(c) * (b - 0.5)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -2.3e+104) or not (x <= 2.35e+114):
		tmp = (y * i) + (a + (t + (z + (x * math.log(y)))))
	else:
		tmp = a + (t + (z + ((y * i) + (math.log(c) * (b - 0.5)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -2.3e+104) || !(x <= 2.35e+114))
		tmp = Float64(Float64(y * i) + Float64(a + Float64(t + Float64(z + Float64(x * log(y))))));
	else
		tmp = Float64(a + Float64(t + Float64(z + Float64(Float64(y * i) + 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 ((x <= -2.3e+104) || ~((x <= 2.35e+114)))
		tmp = (y * i) + (a + (t + (z + (x * log(y)))));
	else
		tmp = a + (t + (z + ((y * i) + (log(c) * (b - 0.5)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -2.3e+104], N[Not[LessEqual[x, 2.35e+114]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(a + N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(t + N[(z + N[(N[(y * i), $MachinePrecision] + 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 < -2.29999999999999985e104 or 2.35e114 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf 99.8%

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

      1. *-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in b around 0 90.7%

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

   if -2.29999999999999985e104 < x < 2.35e114

   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 97.8%

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

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+104} \lor \neg \left(x \leq 2.35 \cdot 10^{+114}\right):\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + \left(y \cdot i + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 88.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+139} \lor \neg \left(x \leq 3.9 \cdot 10^{+155}\right):\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + \left(y \cdot i + b \cdot \log c\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -2.1e+139) (not (<= x 3.9e+155)))
   (+ a (+ t (+ z (* x (log y)))))
   (+ a (+ t (+ z (+ (* y i) (* b (log c))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -2.1e+139) || !(x <= 3.9e+155)) {
		tmp = a + (t + (z + (x * log(y))));
	} else {
		tmp = a + (t + (z + ((y * i) + (b * log(c)))));
	}
	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 <= (-2.1d+139)) .or. (.not. (x <= 3.9d+155))) then
        tmp = a + (t + (z + (x * log(y))))
    else
        tmp = a + (t + (z + ((y * i) + (b * log(c)))))
    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 <= -2.1e+139) || !(x <= 3.9e+155)) {
		tmp = a + (t + (z + (x * Math.log(y))));
	} else {
		tmp = a + (t + (z + ((y * i) + (b * Math.log(c)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -2.1e+139) or not (x <= 3.9e+155):
		tmp = a + (t + (z + (x * math.log(y))))
	else:
		tmp = a + (t + (z + ((y * i) + (b * math.log(c)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -2.1e+139) || !(x <= 3.9e+155))
		tmp = Float64(a + Float64(t + Float64(z + Float64(x * log(y)))));
	else
		tmp = Float64(a + Float64(t + Float64(z + Float64(Float64(y * i) + Float64(b * log(c))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -2.1e+139) || ~((x <= 3.9e+155)))
		tmp = a + (t + (z + (x * log(y))));
	else
		tmp = a + (t + (z + ((y * i) + (b * log(c)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -2.1e+139], N[Not[LessEqual[x, 3.9e+155]], $MachinePrecision]], N[(a + N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(t + N[(z + N[(N[(y * i), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.0999999999999999e139 or 3.8999999999999998e155 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf 99.8%

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

      1. *-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in y around 0 92.6%

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

   7. Taylor expanded in b around 0 82.9%

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

      1. +-commutative 82.9%

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

   9. Simplified 82.9%

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

   if -2.0999999999999999e139 < x < 3.8999999999999998e155

   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 b around inf 97.3%

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

      1. *-commutative 97.3%

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

   5. Simplified 97.3%

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

   6. Taylor expanded in x around 0 93.9%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+139} \lor \neg \left(x \leq 3.9 \cdot 10^{+155}\right):\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + \left(y \cdot i + b \cdot \log c\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 93.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+104} \lor \neg \left(x \leq 5.7 \cdot 10^{+113}\right):\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + \left(y \cdot i + b \cdot \log c\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -2.5e+104) (not (<= x 5.7e+113)))
   (+ (* y i) (+ a (+ t (+ z (* x (log y))))))
   (+ a (+ t (+ z (+ (* y i) (* b (log c))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -2.5e+104) || !(x <= 5.7e+113)) {
		tmp = (y * i) + (a + (t + (z + (x * log(y)))));
	} else {
		tmp = a + (t + (z + ((y * i) + (b * log(c)))));
	}
	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 <= (-2.5d+104)) .or. (.not. (x <= 5.7d+113))) then
        tmp = (y * i) + (a + (t + (z + (x * log(y)))))
    else
        tmp = a + (t + (z + ((y * i) + (b * log(c)))))
    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 <= -2.5e+104) || !(x <= 5.7e+113)) {
		tmp = (y * i) + (a + (t + (z + (x * Math.log(y)))));
	} else {
		tmp = a + (t + (z + ((y * i) + (b * Math.log(c)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -2.5e+104) or not (x <= 5.7e+113):
		tmp = (y * i) + (a + (t + (z + (x * math.log(y)))))
	else:
		tmp = a + (t + (z + ((y * i) + (b * math.log(c)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -2.5e+104) || !(x <= 5.7e+113))
		tmp = Float64(Float64(y * i) + Float64(a + Float64(t + Float64(z + Float64(x * log(y))))));
	else
		tmp = Float64(a + Float64(t + Float64(z + Float64(Float64(y * i) + Float64(b * log(c))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -2.5e+104) || ~((x <= 5.7e+113)))
		tmp = (y * i) + (a + (t + (z + (x * log(y)))));
	else
		tmp = a + (t + (z + ((y * i) + (b * log(c)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -2.5e+104], N[Not[LessEqual[x, 5.7e+113]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(a + N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(t + N[(z + N[(N[(y * i), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.4999999999999998e104 or 5.6999999999999998e113 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf 99.8%

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

      1. *-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in b around 0 90.7%

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

   if -2.4999999999999998e104 < x < 5.6999999999999998e113

   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 b around inf 97.1%

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

      1. *-commutative 97.1%

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

   5. Simplified 97.1%

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

   6. Taylor expanded in x around 0 95.1%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+104} \lor \neg \left(x \leq 5.7 \cdot 10^{+113}\right):\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + \left(y \cdot i + b \cdot \log c\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 72.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+104} \lor \neg \left(x \leq 1.55 \cdot 10^{+114}\right):\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + \left(b + -0.5\right) \cdot \log c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -2.5e+104) (not (<= x 1.55e+114)))
   (+ a (+ t (+ z (* x (log y)))))
   (+ a (+ t (+ z (* (+ b -0.5) (log c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -2.5e+104) || !(x <= 1.55e+114)) {
		tmp = a + (t + (z + (x * log(y))));
	} else {
		tmp = a + (t + (z + ((b + -0.5) * log(c))));
	}
	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 <= (-2.5d+104)) .or. (.not. (x <= 1.55d+114))) then
        tmp = a + (t + (z + (x * log(y))))
    else
        tmp = a + (t + (z + ((b + (-0.5d0)) * log(c))))
    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 <= -2.5e+104) || !(x <= 1.55e+114)) {
		tmp = a + (t + (z + (x * Math.log(y))));
	} else {
		tmp = a + (t + (z + ((b + -0.5) * Math.log(c))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -2.5e+104) or not (x <= 1.55e+114):
		tmp = a + (t + (z + (x * math.log(y))))
	else:
		tmp = a + (t + (z + ((b + -0.5) * math.log(c))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -2.5e+104) || !(x <= 1.55e+114))
		tmp = Float64(a + Float64(t + Float64(z + Float64(x * log(y)))));
	else
		tmp = Float64(a + Float64(t + Float64(z + Float64(Float64(b + -0.5) * log(c)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -2.5e+104) || ~((x <= 1.55e+114)))
		tmp = a + (t + (z + (x * log(y))));
	else
		tmp = a + (t + (z + ((b + -0.5) * log(c))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -2.5e+104], N[Not[LessEqual[x, 1.55e+114]], $MachinePrecision]], N[(a + N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(t + N[(z + N[(N[(b + -0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.4999999999999998e104 or 1.55e114 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf 99.8%

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

      1. *-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in y around 0 89.2%

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

   7. Taylor expanded in b around 0 80.1%

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

      1. +-commutative 80.1%

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

   9. Simplified 80.1%

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

   if -2.4999999999999998e104 < x < 1.55e114

   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 97.8%

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

   4. Taylor expanded in i around 0 75.5%

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

      1. +-commutative 75.5%

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

      2. +-commutative 75.5%

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

      3. sub-neg 75.5%

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

      4. metadata-eval 75.5%

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

   6. Simplified 75.5%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+104} \lor \neg \left(x \leq 1.55 \cdot 10^{+114}\right):\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + \left(b + -0.5\right) \cdot \log c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 66.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1.55 \cdot 10^{+79}:\\ \;\;\;\;y \cdot i + x \cdot \log y\\ \mathbf{elif}\;i \leq 2.2 \cdot 10^{+219}:\\ \;\;\;\;a + \left(t + \left(z + b \cdot \log c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= i -1.55e+79)
   (+ (* y i) (* x (log y)))
   (if (<= i 2.2e+219) (+ a (+ t (+ z (* b (log c))))) (+ a (+ t (* y i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (i <= -1.55e+79) {
		tmp = (y * i) + (x * log(y));
	} else if (i <= 2.2e+219) {
		tmp = a + (t + (z + (b * log(c))));
	} else {
		tmp = a + (t + (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 (i <= (-1.55d+79)) then
        tmp = (y * i) + (x * log(y))
    else if (i <= 2.2d+219) then
        tmp = a + (t + (z + (b * log(c))))
    else
        tmp = a + (t + (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 (i <= -1.55e+79) {
		tmp = (y * i) + (x * Math.log(y));
	} else if (i <= 2.2e+219) {
		tmp = a + (t + (z + (b * Math.log(c))));
	} else {
		tmp = a + (t + (y * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if i <= -1.55e+79:
		tmp = (y * i) + (x * math.log(y))
	elif i <= 2.2e+219:
		tmp = a + (t + (z + (b * math.log(c))))
	else:
		tmp = a + (t + (y * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (i <= -1.55e+79)
		tmp = Float64(Float64(y * i) + Float64(x * log(y)));
	elseif (i <= 2.2e+219)
		tmp = Float64(a + Float64(t + Float64(z + Float64(b * log(c)))));
	else
		tmp = Float64(a + Float64(t + Float64(y * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (i <= -1.55e+79)
		tmp = (y * i) + (x * log(y));
	elseif (i <= 2.2e+219)
		tmp = a + (t + (z + (b * log(c))));
	else
		tmp = a + (t + (y * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[i, -1.55e+79], N[(N[(y * i), $MachinePrecision] + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.2e+219], N[(a + N[(t + N[(z + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(t + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if i < -1.5499999999999999e79

   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 b around inf 99.9%

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

      1. *-commutative 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in x around -inf 81.4%

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

      1. mul-1-neg 81.4%

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

      2. distribute-lft-out 81.4%

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

      3. +-commutative 81.4%

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

   8. Simplified 81.4%

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

   9. Taylor expanded in x around inf 68.6%

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

       1. associate-*r* 68.6%

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

       2. neg-mul-1 68.6%

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

   11. Simplified 68.6%

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

   12. Taylor expanded in x around 0 68.6%

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

   if -1.5499999999999999e79 < i < 2.2000000000000001e219

   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 b around inf 97.4%

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

      1. *-commutative 97.4%

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

   5. Simplified 97.4%

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

   6. Taylor expanded in y around 0 89.7%

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

   7. Taylor expanded in x around 0 72.6%

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

      1. +-commutative 72.6%

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

   9. Simplified 72.6%

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

   if 2.2000000000000001e219 < i

   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 88.3%

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

   4. Taylor expanded in i around inf 82.3%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.55 \cdot 10^{+79}:\\ \;\;\;\;y \cdot i + x \cdot \log y\\ \mathbf{elif}\;i \leq 2.2 \cdot 10^{+219}:\\ \;\;\;\;a + \left(t + \left(z + b \cdot \log c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 57.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \left(z + t\right)\\ \mathbf{if}\;y \leq 1.75 \cdot 10^{-269}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-250}:\\ \;\;\;\;b \cdot \log c\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (+ z t))))
   (if (<= y 1.75e-269)
     t_1
     (if (<= y 3e-250)
       (* b (log c))
       (if (<= y 3.7e+52) t_1 (+ a (+ t (* y i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (z + t);
	double tmp;
	if (y <= 1.75e-269) {
		tmp = t_1;
	} else if (y <= 3e-250) {
		tmp = b * log(c);
	} else if (y <= 3.7e+52) {
		tmp = t_1;
	} else {
		tmp = a + (t + (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) :: t_1
    real(8) :: tmp
    t_1 = a + (z + t)
    if (y <= 1.75d-269) then
        tmp = t_1
    else if (y <= 3d-250) then
        tmp = b * log(c)
    else if (y <= 3.7d+52) then
        tmp = t_1
    else
        tmp = a + (t + (y * i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (z + t);
	double tmp;
	if (y <= 1.75e-269) {
		tmp = t_1;
	} else if (y <= 3e-250) {
		tmp = b * Math.log(c);
	} else if (y <= 3.7e+52) {
		tmp = t_1;
	} else {
		tmp = a + (t + (y * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (z + t)
	tmp = 0
	if y <= 1.75e-269:
		tmp = t_1
	elif y <= 3e-250:
		tmp = b * math.log(c)
	elif y <= 3.7e+52:
		tmp = t_1
	else:
		tmp = a + (t + (y * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(z + t))
	tmp = 0.0
	if (y <= 1.75e-269)
		tmp = t_1;
	elseif (y <= 3e-250)
		tmp = Float64(b * log(c));
	elseif (y <= 3.7e+52)
		tmp = t_1;
	else
		tmp = Float64(a + Float64(t + Float64(y * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (z + t);
	tmp = 0.0;
	if (y <= 1.75e-269)
		tmp = t_1;
	elseif (y <= 3e-250)
		tmp = b * log(c);
	elseif (y <= 3.7e+52)
		tmp = t_1;
	else
		tmp = a + (t + (y * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, 1.75e-269], t$95$1, If[LessEqual[y, 3e-250], N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.7e+52], t$95$1, N[(a + N[(t + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < 1.75000000000000009e-269 or 3.00000000000000016e-250 < y < 3.7e52

   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 83.7%

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

   4. Taylor expanded in z around inf 53.6%

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

   if 1.75000000000000009e-269 < y < 3.00000000000000016e-250

   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 34.3%

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

   4. Taylor expanded in b around inf 60.7%

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

      1. mul-1-neg 60.7%

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

      2. distribute-rgt-neg-in 60.7%

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

   6. Simplified 60.7%

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

   if 3.7e52 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 84.8%

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

   4. Taylor expanded in i around inf 64.0%

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

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.75 \cdot 10^{-269}:\\ \;\;\;\;a + \left(z + t\right)\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-250}:\\ \;\;\;\;b \cdot \log c\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+52}:\\ \;\;\;\;a + \left(z + t\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 49.8% accurate, 14.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -7.5 \cdot 10^{+106} \lor \neg \left(i \leq 2.7 \cdot 10^{+257}\right):\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + \left(z + t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= i -7.5e+106) (not (<= i 2.7e+257))) (* y i) (+ 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 ((i <= -7.5e+106) || !(i <= 2.7e+257)) {
		tmp = y * i;
	} else {
		tmp = 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 ((i <= (-7.5d+106)) .or. (.not. (i <= 2.7d+257))) then
        tmp = y * i
    else
        tmp = 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 ((i <= -7.5e+106) || !(i <= 2.7e+257)) {
		tmp = y * i;
	} else {
		tmp = a + (z + t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (i <= -7.5e+106) or not (i <= 2.7e+257):
		tmp = y * i
	else:
		tmp = a + (z + t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((i <= -7.5e+106) || !(i <= 2.7e+257))
		tmp = Float64(y * i);
	else
		tmp = 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 ((i <= -7.5e+106) || ~((i <= 2.7e+257)))
		tmp = y * i;
	else
		tmp = a + (z + t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[i, -7.5e+106], N[Not[LessEqual[i, 2.7e+257]], $MachinePrecision]], N[(y * i), $MachinePrecision], N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -7.50000000000000058e106 or 2.6999999999999997e257 < i

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 62.8%

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

      1. *-commutative 62.8%

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

   5. Simplified 62.8%

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

   if -7.50000000000000058e106 < i < 2.6999999999999997e257

   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 82.3%

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

   4. Taylor expanded in z around inf 48.8%

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

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -7.5 \cdot 10^{+106} \lor \neg \left(i \leq 2.7 \cdot 10^{+257}\right):\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + \left(z + t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 51.4% accurate, 14.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -8.5 \cdot 10^{+104}:\\ \;\;\;\;t + y \cdot i\\ \mathbf{elif}\;i \leq 6.4 \cdot 10^{+259}:\\ \;\;\;\;a + \left(z + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= i -8.5e+104)
   (+ t (* y i))
   (if (<= i 6.4e+259) (+ a (+ z t)) (* y i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (i <= -8.5e+104) {
		tmp = t + (y * i);
	} else if (i <= 6.4e+259) {
		tmp = a + (z + t);
	} else {
		tmp = y * i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (i <= (-8.5d+104)) then
        tmp = t + (y * i)
    else if (i <= 6.4d+259) then
        tmp = a + (z + t)
    else
        tmp = y * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (i <= -8.5e+104) {
		tmp = t + (y * i);
	} else if (i <= 6.4e+259) {
		tmp = a + (z + t);
	} else {
		tmp = y * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if i <= -8.5e+104:
		tmp = t + (y * i)
	elif i <= 6.4e+259:
		tmp = a + (z + t)
	else:
		tmp = y * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (i <= -8.5e+104)
		tmp = Float64(t + Float64(y * i));
	elseif (i <= 6.4e+259)
		tmp = Float64(a + Float64(z + t));
	else
		tmp = Float64(y * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (i <= -8.5e+104)
		tmp = t + (y * i);
	elseif (i <= 6.4e+259)
		tmp = a + (z + t);
	else
		tmp = y * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[i, -8.5e+104], N[(t + N[(y * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 6.4e+259], N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision], N[(y * i), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if i < -8.4999999999999999e104

   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 b around inf 99.9%

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

      1. *-commutative 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in b around inf 79.9%

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

      1. associate-+r+ 79.9%

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

      2. associate-/l* 79.9%

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

   8. Simplified 79.9%

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

   9. Taylor expanded in t around inf 69.5%

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

   if -8.4999999999999999e104 < i < 6.40000000000000036e259

   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 82.3%

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

   4. Taylor expanded in z around inf 48.8%

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

   if 6.40000000000000036e259 < i

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 86.2%

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

      1. *-commutative 86.2%

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

   5. Simplified 86.2%

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

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -8.5 \cdot 10^{+104}:\\ \;\;\;\;t + y \cdot i\\ \mathbf{elif}\;i \leq 6.4 \cdot 10^{+259}:\\ \;\;\;\;a + \left(z + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 22.0% accurate, 16.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.18 \cdot 10^{+176}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{+29}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -1.18e+176) z (if (<= z -6.4e+29) (* 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 (z <= -1.18e+176) {
		tmp = z;
	} else if (z <= -6.4e+29) {
		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 (z <= (-1.18d+176)) then
        tmp = z
    else if (z <= (-6.4d+29)) 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 (z <= -1.18e+176) {
		tmp = z;
	} else if (z <= -6.4e+29) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -1.18e+176:
		tmp = z
	elif z <= -6.4e+29:
		tmp = y * i
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -1.18e+176)
		tmp = z;
	elseif (z <= -6.4e+29)
		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 (z <= -1.18e+176)
		tmp = z;
	elseif (z <= -6.4e+29)
		tmp = y * i;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -1.18e+176], z, If[LessEqual[z, -6.4e+29], N[(y * i), $MachinePrecision], a]]

Derivation

1. Split input into 3 regimes

2. if z < -1.18000000000000006e176

   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 z around inf 64.6%

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

   if -1.18000000000000006e176 < z < -6.39999999999999973e29

   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 y around inf 22.3%

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

      1. *-commutative 22.3%

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

   5. Simplified 22.3%

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

   if -6.39999999999999973e29 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf 15.8%

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

4. Final simplification 22.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.18 \cdot 10^{+176}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{+29}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 59.0% accurate, 18.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 10^{+54}:\\ \;\;\;\;a + \left(z + t\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 1e+54) (+ a (+ z t)) (+ a (+ t (* y i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 1e+54) {
		tmp = a + (z + t);
	} else {
		tmp = a + (t + (y * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= 1d+54) then
        tmp = a + (z + t)
    else
        tmp = a + (t + (y * i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 1e+54) {
		tmp = a + (z + t);
	} else {
		tmp = a + (t + (y * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 1e+54:
		tmp = a + (z + t)
	else:
		tmp = a + (t + (y * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 1e+54)
		tmp = Float64(a + Float64(z + t));
	else
		tmp = Float64(a + Float64(t + Float64(y * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= 1e+54)
		tmp = a + (z + t);
	else
		tmp = a + (t + (y * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 1e+54], N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision], N[(a + N[(t + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.0000000000000001e54

   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 83.5%

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

   4. Taylor expanded in z around inf 51.0%

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

   if 1.0000000000000001e54 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 84.8%

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

   4. Taylor expanded in i around inf 64.0%

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

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 10^{+54}:\\ \;\;\;\;a + \left(z + t\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 54.2% accurate, 21.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.45 \cdot 10^{+55}:\\ \;\;\;\;a + \left(z + t\right)\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 1.45e+55) (+ a (+ z t)) (+ 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 (y <= 1.45e+55) {
		tmp = a + (z + t);
	} 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 (y <= 1.45d+55) then
        tmp = a + (z + t)
    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 (y <= 1.45e+55) {
		tmp = a + (z + t);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 1.45e+55:
		tmp = a + (z + t)
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 1.45e+55)
		tmp = Float64(a + Float64(z + t));
	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 (y <= 1.45e+55)
		tmp = a + (z + t);
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 1.45e+55], N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.4499999999999999e55

   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 83.5%

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

   4. Taylor expanded in z around inf 51.0%

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

   if 1.4499999999999999e55 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf 99.8%

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

      1. *-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in x around -inf 75.5%

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

      1. mul-1-neg 75.5%

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

      2. distribute-lft-out 75.5%

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

      3. +-commutative 75.5%

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

   8. Simplified 75.5%

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

   9. Taylor expanded in a around inf 57.7%

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

   10. Taylor expanded in x around 0 52.3%

       \[\leadsto \color{blue}{i \cdot y - -1 \cdot a} \]
   11. Step-by-step derivation

       1. *-commutative 52.3%

          \[\leadsto \color{blue}{y \cdot i} - -1 \cdot a \]

       2. mul-1-neg 52.3%

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

   12. Simplified 52.3%

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

4. Final simplification 51.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.45 \cdot 10^{+55}:\\ \;\;\;\;a + \left(z + t\right)\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 21.1% accurate, 36.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+161}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (if (<= z -2.5e+161) z a))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -2.5e+161) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-2.5d+161)) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -2.5e+161) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -2.5e+161:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -2.5e+161)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -2.5e+161)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -2.5e+161], z, a]

Derivation

1. Split input into 2 regimes

2. if z < -2.4999999999999998e161

   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 58.7%

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

   if -2.4999999999999998e161 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf 16.2%

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

4. Final simplification 21.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+161}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 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 a around inf 15.2%

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

4. Final simplification 15.2%

   \[\leadsto a \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024066 
(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)))