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

Percentage Accurate: 99.8% → 99.8%

Time: 18.0s

Alternatives: 18

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

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

FPCore

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

Julia

function code(x, y, z, t, a, b, c, i)
	return fma(y, i, fma(Float64(b - 0.5), log(c), Float64(t + fma(x, log(y), Float64(z + 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[(t + N[(x * N[Log[y], $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

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

   1. associate-+l+ 99.8%

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

   2. +-commutative 99.8%

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

   3. associate-+r+ 99.8%

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

   4. +-commutative 99.8%

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

   5. associate-+l+ 99.8%

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

   6. +-commutative 99.8%

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

   7. fma-def 99.8%

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

   8. +-commutative 99.8%

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

   9. fma-def 99.8%

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

   10. +-commutative 99.8%

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

   11. associate-+l+ 99.8%

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

   12. fma-def 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Final simplification 99.8%

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

Alternative 3: 97.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in b around inf 97.2%

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

3. Final simplification 97.2%

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

Alternative 4: 94.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \left(t + z\right)\\ \mathbf{if}\;x \leq -1.22 \cdot 10^{+176}:\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + t_1\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+99}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + t_1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \mathsf{fma}\left(\log y, x, z + \left(t + a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (+ t z))))
   (if (<= x -1.22e+176)
     (+ (* y i) (+ (* x (log y)) t_1))
     (if (<= x 6.2e+99)
       (+ (* y i) (+ (* (- b 0.5) (log c)) t_1))
       (+ (* y i) (fma (log y) x (+ z (+ t a))))))))

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);
	double tmp;
	if (x <= -1.22e+176) {
		tmp = (y * i) + ((x * log(y)) + t_1);
	} else if (x <= 6.2e+99) {
		tmp = (y * i) + (((b - 0.5) * log(c)) + t_1);
	} else {
		tmp = (y * i) + fma(log(y), x, (z + (t + a)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(t + z))
	tmp = 0.0
	if (x <= -1.22e+176)
		tmp = Float64(Float64(y * i) + Float64(Float64(x * log(y)) + t_1));
	elseif (x <= 6.2e+99)
		tmp = Float64(Float64(y * i) + Float64(Float64(Float64(b - 0.5) * log(c)) + t_1));
	else
		tmp = Float64(Float64(y * i) + fma(log(y), x, Float64(z + Float64(t + a))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(t + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.22e+176], N[(N[(y * i), $MachinePrecision] + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.2e+99], N[(N[(y * i), $MachinePrecision] + N[(N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[Log[y], $MachinePrecision] * x + N[(z + N[(t + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.2199999999999999e176

   1. Initial program 99.7%

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

   2. Taylor expanded in b around inf 99.7%

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

   3. Taylor expanded in b around 0 97.1%

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

   if -1.2199999999999999e176 < x < 6.2000000000000001e99

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 99.4%

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

   if 6.2000000000000001e99 < x

   1. Initial program 99.7%

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

   2. Taylor expanded in b around inf 99.7%

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

   3. Taylor expanded in b around 0 96.4%

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

      1. fma-def 96.5%

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

      2. +-commutative 96.5%

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

      3. +-commutative 96.5%

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

      4. associate-+l+ 96.5%

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

      5. +-commutative 96.5%

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

   5. Simplified 96.5%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.22 \cdot 10^{+176}:\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + \left(a + \left(t + z\right)\right)\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+99}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(a + \left(t + z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \mathsf{fma}\left(\log y, x, z + \left(t + a\right)\right)\\ \end{array} \]

Alternative 5: 87.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -2 \cdot 10^{+176} \lor \neg \left(b - 0.5 \leq 5 \cdot 10^{+82}\right):\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + \left(a + \left(t + z\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (- b 0.5) -2e+176) (not (<= (- b 0.5) 5e+82)))
   (+ (* y i) (+ a (* b (log c))))
   (+ (* y i) (+ (* x (log y)) (+ a (+ t z))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((b - 0.5) <= -2e+176) || !((b - 0.5) <= 5e+82)) {
		tmp = (y * i) + (a + (b * log(c)));
	} else {
		tmp = (y * i) + ((x * log(y)) + (a + (t + z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((b - 0.5d0) <= (-2d+176)) .or. (.not. ((b - 0.5d0) <= 5d+82))) then
        tmp = (y * i) + (a + (b * log(c)))
    else
        tmp = (y * i) + ((x * log(y)) + (a + (t + z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((b - 0.5) <= -2e+176) || !((b - 0.5) <= 5e+82)) {
		tmp = (y * i) + (a + (b * Math.log(c)));
	} else {
		tmp = (y * i) + ((x * Math.log(y)) + (a + (t + z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((b - 0.5) <= -2e+176) or not ((b - 0.5) <= 5e+82):
		tmp = (y * i) + (a + (b * math.log(c)))
	else:
		tmp = (y * i) + ((x * math.log(y)) + (a + (t + z)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(b - 0.5) <= -2e+176) || !(Float64(b - 0.5) <= 5e+82))
		tmp = Float64(Float64(y * i) + Float64(a + Float64(b * log(c))));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(x * log(y)) + Float64(a + Float64(t + z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((b - 0.5) <= -2e+176) || ~(((b - 0.5) <= 5e+82)))
		tmp = (y * i) + (a + (b * log(c)));
	else
		tmp = (y * i) + ((x * log(y)) + (a + (t + z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(b - 0.5), $MachinePrecision], -2e+176], N[Not[LessEqual[N[(b - 0.5), $MachinePrecision], 5e+82]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(a + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(a + N[(t + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 b 1/2) < -2e176 or 5.00000000000000015e82 < (-.f64 b 1/2)

   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. Taylor expanded in a around inf 70.8%

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

   3. Taylor expanded in b around inf 70.8%

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

   if -2e176 < (-.f64 b 1/2) < 5.00000000000000015e82

   1. Initial program 99.9%

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

   2. Taylor expanded in b around inf 96.0%

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

   3. Taylor expanded in b around 0 95.3%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -2 \cdot 10^{+176} \lor \neg \left(b - 0.5 \leq 5 \cdot 10^{+82}\right):\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + \left(a + \left(t + z\right)\right)\right)\\ \end{array} \]

Alternative 6: 60.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - 0.5\right) \cdot \log c\\ t_2 := y \cdot i + \left(x \cdot \log y + \left(t + z\right)\right)\\ \mathbf{if}\;a \leq 2.6 \cdot 10^{-69}:\\ \;\;\;\;y \cdot i + \left(z + t_1\right)\\ \mathbf{elif}\;a \leq 0.0037:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+71}:\\ \;\;\;\;y \cdot i + \left(a + t_1\right)\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+105}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (- b 0.5) (log c)))
        (t_2 (+ (* y i) (+ (* x (log y)) (+ t z)))))
   (if (<= a 2.6e-69)
     (+ (* y i) (+ z t_1))
     (if (<= a 0.0037)
       t_2
       (if (<= a 1.4e+71)
         (+ (* y i) (+ a t_1))
         (if (<= a 1.3e+105) t_2 (+ (* y i) (+ a (* 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 = (b - 0.5) * log(c);
	double t_2 = (y * i) + ((x * log(y)) + (t + z));
	double tmp;
	if (a <= 2.6e-69) {
		tmp = (y * i) + (z + t_1);
	} else if (a <= 0.0037) {
		tmp = t_2;
	} else if (a <= 1.4e+71) {
		tmp = (y * i) + (a + t_1);
	} else if (a <= 1.3e+105) {
		tmp = t_2;
	} else {
		tmp = (y * i) + (a + (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b - 0.5d0) * log(c)
    t_2 = (y * i) + ((x * log(y)) + (t + z))
    if (a <= 2.6d-69) then
        tmp = (y * i) + (z + t_1)
    else if (a <= 0.0037d0) then
        tmp = t_2
    else if (a <= 1.4d+71) then
        tmp = (y * i) + (a + t_1)
    else if (a <= 1.3d+105) then
        tmp = t_2
    else
        tmp = (y * i) + (a + (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 t_1 = (b - 0.5) * Math.log(c);
	double t_2 = (y * i) + ((x * Math.log(y)) + (t + z));
	double tmp;
	if (a <= 2.6e-69) {
		tmp = (y * i) + (z + t_1);
	} else if (a <= 0.0037) {
		tmp = t_2;
	} else if (a <= 1.4e+71) {
		tmp = (y * i) + (a + t_1);
	} else if (a <= 1.3e+105) {
		tmp = t_2;
	} else {
		tmp = (y * i) + (a + (b * Math.log(c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (b - 0.5) * math.log(c)
	t_2 = (y * i) + ((x * math.log(y)) + (t + z))
	tmp = 0
	if a <= 2.6e-69:
		tmp = (y * i) + (z + t_1)
	elif a <= 0.0037:
		tmp = t_2
	elif a <= 1.4e+71:
		tmp = (y * i) + (a + t_1)
	elif a <= 1.3e+105:
		tmp = t_2
	else:
		tmp = (y * i) + (a + (b * math.log(c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(b - 0.5) * log(c))
	t_2 = Float64(Float64(y * i) + Float64(Float64(x * log(y)) + Float64(t + z)))
	tmp = 0.0
	if (a <= 2.6e-69)
		tmp = Float64(Float64(y * i) + Float64(z + t_1));
	elseif (a <= 0.0037)
		tmp = t_2;
	elseif (a <= 1.4e+71)
		tmp = Float64(Float64(y * i) + Float64(a + t_1));
	elseif (a <= 1.3e+105)
		tmp = t_2;
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(b * log(c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (b - 0.5) * log(c);
	t_2 = (y * i) + ((x * log(y)) + (t + z));
	tmp = 0.0;
	if (a <= 2.6e-69)
		tmp = (y * i) + (z + t_1);
	elseif (a <= 0.0037)
		tmp = t_2;
	elseif (a <= 1.4e+71)
		tmp = (y * i) + (a + t_1);
	elseif (a <= 1.3e+105)
		tmp = t_2;
	else
		tmp = (y * i) + (a + (b * log(c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * i), $MachinePrecision] + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(t + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, 2.6e-69], N[(N[(y * i), $MachinePrecision] + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 0.0037], t$95$2, If[LessEqual[a, 1.4e+71], N[(N[(y * i), $MachinePrecision] + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.3e+105], t$95$2, N[(N[(y * i), $MachinePrecision] + N[(a + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < 2.6000000000000002e-69

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-+l+ 99.8%

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

      3. associate-+r+ 99.8%

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

      4. fma-udef 99.8%

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

      5. add-cube-cbrt 98.7%

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

      6. pow2 98.7%

         \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{t + \mathsf{fma}\left(x, \log y, z + a\right)}\right)}^{2}} \cdot \sqrt[3]{t + \mathsf{fma}\left(x, \log y, z + a\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      7. fma-udef 98.7%

         \[\leadsto \left({\left(\sqrt[3]{t + \color{blue}{\left(x \cdot \log y + \left(z + a\right)\right)}}\right)}^{2} \cdot \sqrt[3]{t + \mathsf{fma}\left(x, \log y, z + a\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      8. associate-+r+ 98.7%

         \[\leadsto \left({\left(\sqrt[3]{t + \color{blue}{\left(\left(x \cdot \log y + z\right) + a\right)}}\right)}^{2} \cdot \sqrt[3]{t + \mathsf{fma}\left(x, \log y, z + a\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      9. associate-+l+ 98.7%

         \[\leadsto \left({\left(\sqrt[3]{\color{blue}{\left(t + \left(x \cdot \log y + z\right)\right) + a}}\right)}^{2} \cdot \sqrt[3]{t + \mathsf{fma}\left(x, \log y, z + a\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      10. +-commutative 98.7%

          \[\leadsto \left({\left(\sqrt[3]{\color{blue}{\left(\left(x \cdot \log y + z\right) + t\right)} + a}\right)}^{2} \cdot \sqrt[3]{t + \mathsf{fma}\left(x, \log y, z + a\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      11. associate-+l+ 98.7%

          \[\leadsto \left({\left(\sqrt[3]{\color{blue}{\left(x \cdot \log y + z\right) + \left(t + a\right)}}\right)}^{2} \cdot \sqrt[3]{t + \mathsf{fma}\left(x, \log y, z + a\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      12. fma-def 98.7%

          \[\leadsto \left({\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(x, \log y, z\right)} + \left(t + a\right)}\right)}^{2} \cdot \sqrt[3]{t + \mathsf{fma}\left(x, \log y, z + a\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

      13. fma-udef 98.7%

          \[\leadsto \left({\left(\sqrt[3]{\mathsf{fma}\left(x, \log y, z\right) + \left(t + a\right)}\right)}^{2} \cdot \sqrt[3]{t + \color{blue}{\left(x \cdot \log y + \left(z + a\right)\right)}} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   3. Applied egg-rr 98.7%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(x, \log y, z\right) + \left(t + a\right)}\right)}^{2} \cdot \sqrt[3]{\mathsf{fma}\left(x, \log y, z\right) + \left(t + a\right)}} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]

   4. Taylor expanded in z around inf 62.7%

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

   if 2.6000000000000002e-69 < a < 0.0037000000000000002 or 1.40000000000000001e71 < a < 1.3000000000000001e105

   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. Taylor expanded in b around inf 99.6%

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

   3. Taylor expanded in b around 0 84.2%

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

   4. Taylor expanded in a around 0 84.1%

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

   if 0.0037000000000000002 < a < 1.40000000000000001e71

   1. Initial program 100.0%

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

   2. Taylor expanded in a around inf 49.0%

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

   if 1.3000000000000001e105 < a

   1. Initial program 99.9%

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

   2. Taylor expanded in a around inf 74.5%

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

   3. Taylor expanded in b around inf 74.5%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 2.6 \cdot 10^{-69}:\\ \;\;\;\;y \cdot i + \left(z + \left(b - 0.5\right) \cdot \log c\right)\\ \mathbf{elif}\;a \leq 0.0037:\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + \left(t + z\right)\right)\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+71}:\\ \;\;\;\;y \cdot i + \left(a + \left(b - 0.5\right) \cdot \log c\right)\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+105}:\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + \left(t + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \end{array} \]

Alternative 7: 94.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \left(t + z\right)\\ \mathbf{if}\;x \leq -6 \cdot 10^{+176} \lor \neg \left(x \leq 1.7 \cdot 10^{+98}\right):\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + t_1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (+ t z))))
   (if (or (<= x -6e+176) (not (<= x 1.7e+98)))
     (+ (* y i) (+ (* x (log y)) t_1))
     (+ (* y i) (+ (* (- 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);
	double tmp;
	if ((x <= -6e+176) || !(x <= 1.7e+98)) {
		tmp = (y * i) + ((x * log(y)) + t_1);
	} else {
		tmp = (y * i) + (((b - 0.5) * log(c)) + 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)
    if ((x <= (-6d+176)) .or. (.not. (x <= 1.7d+98))) then
        tmp = (y * i) + ((x * log(y)) + t_1)
    else
        tmp = (y * i) + (((b - 0.5d0) * log(c)) + 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);
	double tmp;
	if ((x <= -6e+176) || !(x <= 1.7e+98)) {
		tmp = (y * i) + ((x * Math.log(y)) + t_1);
	} else {
		tmp = (y * i) + (((b - 0.5) * Math.log(c)) + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (t + z)
	tmp = 0
	if (x <= -6e+176) or not (x <= 1.7e+98):
		tmp = (y * i) + ((x * math.log(y)) + t_1)
	else:
		tmp = (y * i) + (((b - 0.5) * math.log(c)) + t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(t + z))
	tmp = 0.0
	if ((x <= -6e+176) || !(x <= 1.7e+98))
		tmp = Float64(Float64(y * i) + Float64(Float64(x * log(y)) + t_1));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(Float64(b - 0.5) * log(c)) + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (t + z);
	tmp = 0.0;
	if ((x <= -6e+176) || ~((x <= 1.7e+98)))
		tmp = (y * i) + ((x * log(y)) + t_1);
	else
		tmp = (y * i) + (((b - 0.5) * log(c)) + 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 + z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -6e+176], N[Not[LessEqual[x, 1.7e+98]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -6e176 or 1.69999999999999986e98 < x

   1. Initial program 99.7%

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

   2. Taylor expanded in b around inf 99.7%

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

   3. Taylor expanded in b around 0 96.7%

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

   if -6e176 < x < 1.69999999999999986e98

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 99.4%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+176} \lor \neg \left(x \leq 1.7 \cdot 10^{+98}\right):\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + \left(a + \left(t + z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(a + \left(t + z\right)\right)\right)\\ \end{array} \]

Alternative 8: 61.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \left(t + z\right)\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+110}:\\ \;\;\;\;y \cdot i + t_1\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{+58} \lor \neg \left(z \leq -2.4 \cdot 10^{+14}\right):\\ \;\;\;\;y \cdot i + \left(a + \left(b - 0.5\right) \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (+ t z))))
   (if (<= z -3.2e+110)
     (+ (* y i) t_1)
     (if (or (<= z -7.4e+58) (not (<= z -2.4e+14)))
       (+ (* y i) (+ a (* (- b 0.5) (log c))))
       (+ (* x (log y)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (t + z);
	double tmp;
	if (z <= -3.2e+110) {
		tmp = (y * i) + t_1;
	} else if ((z <= -7.4e+58) || !(z <= -2.4e+14)) {
		tmp = (y * i) + (a + ((b - 0.5) * log(c)));
	} else {
		tmp = (x * log(y)) + 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)
    if (z <= (-3.2d+110)) then
        tmp = (y * i) + t_1
    else if ((z <= (-7.4d+58)) .or. (.not. (z <= (-2.4d+14)))) then
        tmp = (y * i) + (a + ((b - 0.5d0) * log(c)))
    else
        tmp = (x * log(y)) + 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);
	double tmp;
	if (z <= -3.2e+110) {
		tmp = (y * i) + t_1;
	} else if ((z <= -7.4e+58) || !(z <= -2.4e+14)) {
		tmp = (y * i) + (a + ((b - 0.5) * Math.log(c)));
	} else {
		tmp = (x * Math.log(y)) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (t + z)
	tmp = 0
	if z <= -3.2e+110:
		tmp = (y * i) + t_1
	elif (z <= -7.4e+58) or not (z <= -2.4e+14):
		tmp = (y * i) + (a + ((b - 0.5) * math.log(c)))
	else:
		tmp = (x * math.log(y)) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(t + z))
	tmp = 0.0
	if (z <= -3.2e+110)
		tmp = Float64(Float64(y * i) + t_1);
	elseif ((z <= -7.4e+58) || !(z <= -2.4e+14))
		tmp = Float64(Float64(y * i) + Float64(a + Float64(Float64(b - 0.5) * log(c))));
	else
		tmp = Float64(Float64(x * log(y)) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (t + z);
	tmp = 0.0;
	if (z <= -3.2e+110)
		tmp = (y * i) + t_1;
	elseif ((z <= -7.4e+58) || ~((z <= -2.4e+14)))
		tmp = (y * i) + (a + ((b - 0.5) * log(c)));
	else
		tmp = (x * log(y)) + 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 + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.2e+110], N[(N[(y * i), $MachinePrecision] + t$95$1), $MachinePrecision], If[Or[LessEqual[z, -7.4e+58], N[Not[LessEqual[z, -2.4e+14]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(a + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.19999999999999994e110

   1. Initial program 99.9%

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

   2. Taylor expanded in b around inf 99.9%

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

   3. Taylor expanded in b around 0 94.4%

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

   4. Taylor expanded in x around 0 84.4%

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

   if -3.19999999999999994e110 < z < -7.4000000000000004e58 or -2.4e14 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in a around inf 59.0%

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

   if -7.4000000000000004e58 < z < -2.4e14

   1. Initial program 100.0%

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

   2. Taylor expanded in b around inf 100.0%

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

   3. Taylor expanded in b around 0 100.0%

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

   4. Taylor expanded in y around 0 90.0%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+110}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + z\right)\right)\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{+58} \lor \neg \left(z \leq -2.4 \cdot 10^{+14}\right):\\ \;\;\;\;y \cdot i + \left(a + \left(b - 0.5\right) \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y + \left(a + \left(t + z\right)\right)\\ \end{array} \]

Alternative 9: 93.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \left(t + z\right)\\ \mathbf{if}\;x \leq -6 \cdot 10^{+176} \lor \neg \left(x \leq 3 \cdot 10^{+95}\right):\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + t_1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(b \cdot \log c + t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (+ t z))))
   (if (or (<= x -6e+176) (not (<= x 3e+95)))
     (+ (* y i) (+ (* x (log y)) t_1))
     (+ (* y i) (+ (* b (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);
	double tmp;
	if ((x <= -6e+176) || !(x <= 3e+95)) {
		tmp = (y * i) + ((x * log(y)) + t_1);
	} else {
		tmp = (y * i) + ((b * log(c)) + 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)
    if ((x <= (-6d+176)) .or. (.not. (x <= 3d+95))) then
        tmp = (y * i) + ((x * log(y)) + t_1)
    else
        tmp = (y * i) + ((b * log(c)) + 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);
	double tmp;
	if ((x <= -6e+176) || !(x <= 3e+95)) {
		tmp = (y * i) + ((x * Math.log(y)) + t_1);
	} else {
		tmp = (y * i) + ((b * Math.log(c)) + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (t + z)
	tmp = 0
	if (x <= -6e+176) or not (x <= 3e+95):
		tmp = (y * i) + ((x * math.log(y)) + t_1)
	else:
		tmp = (y * i) + ((b * math.log(c)) + t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(t + z))
	tmp = 0.0
	if ((x <= -6e+176) || !(x <= 3e+95))
		tmp = Float64(Float64(y * i) + Float64(Float64(x * log(y)) + t_1));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(b * log(c)) + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (t + z);
	tmp = 0.0;
	if ((x <= -6e+176) || ~((x <= 3e+95)))
		tmp = (y * i) + ((x * log(y)) + t_1);
	else
		tmp = (y * i) + ((b * log(c)) + 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 + z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -6e+176], N[Not[LessEqual[x, 3e+95]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -6e176 or 2.99999999999999991e95 < x

   1. Initial program 99.7%

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

   2. Taylor expanded in b around inf 99.7%

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

   3. Taylor expanded in b around 0 96.7%

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

   if -6e176 < x < 2.99999999999999991e95

   1. Initial program 99.9%

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

   2. Taylor expanded in b around inf 96.1%

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

   3. Taylor expanded in x around 0 95.7%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+176} \lor \neg \left(x \leq 3 \cdot 10^{+95}\right):\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + \left(a + \left(t + z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(b \cdot \log c + \left(a + \left(t + z\right)\right)\right)\\ \end{array} \]

Alternative 10: 73.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \left(t + z\right)\\ t_2 := x \cdot \log y + t_1\\ \mathbf{if}\;x \leq -3.9 \cdot 10^{+175}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-32}:\\ \;\;\;\;y \cdot i + t_1\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{+60}:\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (+ t z))) (t_2 (+ (* x (log y)) t_1)))
   (if (<= x -3.9e+175)
     t_2
     (if (<= x 2.1e-32)
       (+ (* y i) t_1)
       (if (<= x 5.4e+60) (+ (* y i) (+ a (* b (log c)))) 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);
	double t_2 = (x * log(y)) + t_1;
	double tmp;
	if (x <= -3.9e+175) {
		tmp = t_2;
	} else if (x <= 2.1e-32) {
		tmp = (y * i) + t_1;
	} else if (x <= 5.4e+60) {
		tmp = (y * i) + (a + (b * log(c)));
	} 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)
    t_2 = (x * log(y)) + t_1
    if (x <= (-3.9d+175)) then
        tmp = t_2
    else if (x <= 2.1d-32) then
        tmp = (y * i) + t_1
    else if (x <= 5.4d+60) then
        tmp = (y * i) + (a + (b * log(c)))
    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);
	double t_2 = (x * Math.log(y)) + t_1;
	double tmp;
	if (x <= -3.9e+175) {
		tmp = t_2;
	} else if (x <= 2.1e-32) {
		tmp = (y * i) + t_1;
	} else if (x <= 5.4e+60) {
		tmp = (y * i) + (a + (b * Math.log(c)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (t + z)
	t_2 = (x * math.log(y)) + t_1
	tmp = 0
	if x <= -3.9e+175:
		tmp = t_2
	elif x <= 2.1e-32:
		tmp = (y * i) + t_1
	elif x <= 5.4e+60:
		tmp = (y * i) + (a + (b * math.log(c)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(t + z))
	t_2 = Float64(Float64(x * log(y)) + t_1)
	tmp = 0.0
	if (x <= -3.9e+175)
		tmp = t_2;
	elseif (x <= 2.1e-32)
		tmp = Float64(Float64(y * i) + t_1);
	elseif (x <= 5.4e+60)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(b * log(c))));
	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);
	t_2 = (x * log(y)) + t_1;
	tmp = 0.0;
	if (x <= -3.9e+175)
		tmp = t_2;
	elseif (x <= 2.1e-32)
		tmp = (y * i) + t_1;
	elseif (x <= 5.4e+60)
		tmp = (y * i) + (a + (b * log(c)));
	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 + z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[x, -3.9e+175], t$95$2, If[LessEqual[x, 2.1e-32], N[(N[(y * i), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[x, 5.4e+60], N[(N[(y * i), $MachinePrecision] + N[(a + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.89999999999999972e175 or 5.3999999999999999e60 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in b around inf 99.8%

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

   3. Taylor expanded in b around 0 93.1%

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

   4. Taylor expanded in y around 0 80.8%

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

   if -3.89999999999999972e175 < x < 2.0999999999999999e-32

   1. Initial program 99.9%

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

   2. Taylor expanded in b around inf 96.2%

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

   3. Taylor expanded in b around 0 79.4%

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

   4. Taylor expanded in x around 0 78.9%

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

   if 2.0999999999999999e-32 < x < 5.3999999999999999e60

   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. Taylor expanded in a around inf 78.8%

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

   3. Taylor expanded in b around inf 74.0%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{+175}:\\ \;\;\;\;x \cdot \log y + \left(a + \left(t + z\right)\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-32}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + z\right)\right)\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{+60}:\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y + \left(a + \left(t + z\right)\right)\\ \end{array} \]

Alternative 11: 75.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \left(t + z\right)\\ \mathbf{if}\;x \leq -2.55 \cdot 10^{+175} \lor \neg \left(x \leq 9.5 \cdot 10^{+188}\right):\\ \;\;\;\;x \cdot \log y + t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (+ t z))))
   (if (or (<= x -2.55e+175) (not (<= x 9.5e+188)))
     (+ (* x (log y)) t_1)
     (+ (* 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 + z);
	double tmp;
	if ((x <= -2.55e+175) || !(x <= 9.5e+188)) {
		tmp = (x * log(y)) + t_1;
	} else {
		tmp = (y * i) + 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)
    if ((x <= (-2.55d+175)) .or. (.not. (x <= 9.5d+188))) then
        tmp = (x * log(y)) + t_1
    else
        tmp = (y * i) + 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);
	double tmp;
	if ((x <= -2.55e+175) || !(x <= 9.5e+188)) {
		tmp = (x * Math.log(y)) + t_1;
	} else {
		tmp = (y * i) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (t + z)
	tmp = 0
	if (x <= -2.55e+175) or not (x <= 9.5e+188):
		tmp = (x * math.log(y)) + t_1
	else:
		tmp = (y * i) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(t + z))
	tmp = 0.0
	if ((x <= -2.55e+175) || !(x <= 9.5e+188))
		tmp = Float64(Float64(x * log(y)) + t_1);
	else
		tmp = Float64(Float64(y * i) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (t + z);
	tmp = 0.0;
	if ((x <= -2.55e+175) || ~((x <= 9.5e+188)))
		tmp = (x * log(y)) + t_1;
	else
		tmp = (y * i) + 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 + z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -2.55e+175], N[Not[LessEqual[x, 9.5e+188]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.55000000000000003e175 or 9.4999999999999996e188 < x

   1. Initial program 99.7%

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

   2. Taylor expanded in b around inf 99.7%

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

   3. Taylor expanded in b around 0 95.7%

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

   4. Taylor expanded in y around 0 86.9%

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

   if -2.55000000000000003e175 < x < 9.4999999999999996e188

   1. Initial program 99.9%

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

   2. Taylor expanded in b around inf 96.5%

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

   3. Taylor expanded in b around 0 78.0%

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

   4. Taylor expanded in x around 0 75.7%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.55 \cdot 10^{+175} \lor \neg \left(x \leq 9.5 \cdot 10^{+188}\right):\\ \;\;\;\;x \cdot \log y + \left(a + \left(t + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + z\right)\right)\\ \end{array} \]

Alternative 12: 74.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+197} \lor \neg \left(x \leq 6.8 \cdot 10^{+201}\right):\\ \;\;\;\;y \cdot i + x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -7.5e+197) (not (<= x 6.8e+201)))
   (+ (* y i) (* x (log y)))
   (+ (* y i) (+ a (+ t z)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -7.5e+197) || !(x <= 6.8e+201)) {
		tmp = (y * i) + (x * log(y));
	} else {
		tmp = (y * i) + (a + (t + z));
	}
	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 <= (-7.5d+197)) .or. (.not. (x <= 6.8d+201))) then
        tmp = (y * i) + (x * log(y))
    else
        tmp = (y * i) + (a + (t + z))
    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 <= -7.5e+197) || !(x <= 6.8e+201)) {
		tmp = (y * i) + (x * Math.log(y));
	} else {
		tmp = (y * i) + (a + (t + z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -7.5e+197) or not (x <= 6.8e+201):
		tmp = (y * i) + (x * math.log(y))
	else:
		tmp = (y * i) + (a + (t + z))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -7.5e+197) || !(x <= 6.8e+201))
		tmp = Float64(Float64(y * i) + Float64(x * log(y)));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(t + z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -7.5e+197) || ~((x <= 6.8e+201)))
		tmp = (y * i) + (x * log(y));
	else
		tmp = (y * i) + (a + (t + z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -7.5e+197], N[Not[LessEqual[x, 6.8e+201]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(t + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.50000000000000046e197 or 6.8e201 < x

   1. Initial program 99.7%

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

   2. Taylor expanded in b around inf 99.7%

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

   3. Taylor expanded in x around inf 74.7%

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

   if -7.50000000000000046e197 < x < 6.8e201

   1. Initial program 99.9%

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

   2. Taylor expanded in b around inf 96.6%

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

   3. Taylor expanded in b around 0 78.4%

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

   4. Taylor expanded in x around 0 75.7%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+197} \lor \neg \left(x \leq 6.8 \cdot 10^{+201}\right):\\ \;\;\;\;y \cdot i + x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + z\right)\right)\\ \end{array} \]

Alternative 13: 71.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.8 \cdot 10^{+256} \lor \neg \left(b \leq 1.02 \cdot 10^{+229}\right):\\ \;\;\;\;b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= b -4.8e+256) (not (<= b 1.02e+229)))
   (* b (log c))
   (+ (* y i) (+ a (+ t z)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((b <= -4.8e+256) || !(b <= 1.02e+229)) {
		tmp = b * log(c);
	} else {
		tmp = (y * i) + (a + (t + z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((b <= (-4.8d+256)) .or. (.not. (b <= 1.02d+229))) then
        tmp = b * log(c)
    else
        tmp = (y * i) + (a + (t + z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((b <= -4.8e+256) || !(b <= 1.02e+229)) {
		tmp = b * Math.log(c);
	} else {
		tmp = (y * i) + (a + (t + z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (b <= -4.8e+256) or not (b <= 1.02e+229):
		tmp = b * math.log(c)
	else:
		tmp = (y * i) + (a + (t + z))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((b <= -4.8e+256) || !(b <= 1.02e+229))
		tmp = Float64(b * log(c));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(t + z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((b <= -4.8e+256) || ~((b <= 1.02e+229)))
		tmp = b * log(c);
	else
		tmp = (y * i) + (a + (t + z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[b, -4.8e+256], N[Not[LessEqual[b, 1.02e+229]], $MachinePrecision]], N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(t + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.80000000000000028e256 or 1.01999999999999994e229 < b

   1. Initial program 99.5%

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

      1. associate-+l+ 99.5%

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

      2. +-commutative 99.5%

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

      3. associate-+r+ 99.5%

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

      4. +-commutative 99.5%

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

      5. associate-+l+ 99.5%

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

      6. +-commutative 99.5%

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

      7. fma-def 99.5%

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

      8. +-commutative 99.5%

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

      9. fma-def 99.6%

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

      10. +-commutative 99.6%

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

      11. associate-+l+ 99.6%

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

      12. fma-def 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in a around 0 99.2%

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

   5. Taylor expanded in y around inf 99.2%

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

   6. Taylor expanded in b around inf 86.1%

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

   if -4.80000000000000028e256 < b < 1.01999999999999994e229

   1. Initial program 99.9%

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

   2. Taylor expanded in b around inf 96.9%

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

   3. Taylor expanded in b around 0 88.5%

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

   4. Taylor expanded in x around 0 72.9%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.8 \cdot 10^{+256} \lor \neg \left(b \leq 1.02 \cdot 10^{+229}\right):\\ \;\;\;\;b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + z\right)\right)\\ \end{array} \]

Alternative 14: 42.7% accurate, 19.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 0.52 \lor \neg \left(a \leq 9 \cdot 10^{+70}\right) \land a \leq 2.8 \cdot 10^{+108}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= a 0.52) (and (not (<= a 9e+70)) (<= a 2.8e+108)))
   (+ z (* y i))
   (+ a (* y i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a <= 0.52) || (!(a <= 9e+70) && (a <= 2.8e+108))) {
		tmp = z + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((a <= 0.52d0) .or. (.not. (a <= 9d+70)) .and. (a <= 2.8d+108)) then
        tmp = z + (y * i)
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((a <= 0.52) || (!(a <= 9e+70) && (a <= 2.8e+108))) {
		tmp = z + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (a <= 0.52) or (not (a <= 9e+70) and (a <= 2.8e+108)):
		tmp = z + (y * i)
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((a <= 0.52) || (!(a <= 9e+70) && (a <= 2.8e+108)))
		tmp = Float64(z + Float64(y * i));
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((a <= 0.52) || (~((a <= 9e+70)) && (a <= 2.8e+108)))
		tmp = z + (y * i);
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[a, 0.52], And[N[Not[LessEqual[a, 9e+70]], $MachinePrecision], LessEqual[a, 2.8e+108]]], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 0.52000000000000002 or 8.9999999999999999e70 < a < 2.7999999999999998e108

   1. Initial program 99.8%

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

   2. Taylor expanded in b around inf 96.6%

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

   3. Taylor expanded in z around inf 43.6%

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

   if 0.52000000000000002 < a < 8.9999999999999999e70 or 2.7999999999999998e108 < a

   1. Initial program 99.9%

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

   2. Taylor expanded in b around inf 99.1%

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

   3. Taylor expanded in a around inf 56.8%

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

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 0.52 \lor \neg \left(a \leq 9 \cdot 10^{+70}\right) \land a \leq 2.8 \cdot 10^{+108}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]

Alternative 15: 67.1% accurate, 24.3× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = (y * i) + (a + (t + z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in b around inf 97.2%

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

3. Taylor expanded in b around 0 81.8%

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

4. Taylor expanded in x around 0 67.2%

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

5. Final simplification 67.2%

   \[\leadsto y \cdot i + \left(a + \left(t + z\right)\right) \]

Alternative 16: 28.9% accurate, 30.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -4.6 \cdot 10^{+51}:\\ \;\;\;\;y \cdot i\\ \mathbf{elif}\;i \leq 7.2 \cdot 10^{+127}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= i -4.6e+51) (* y i) (if (<= i 7.2e+127) 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 (i <= -4.6e+51) {
		tmp = y * i;
	} else if (i <= 7.2e+127) {
		tmp = a;
	} 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 <= (-4.6d+51)) then
        tmp = y * i
    else if (i <= 7.2d+127) then
        tmp = a
    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 <= -4.6e+51) {
		tmp = y * i;
	} else if (i <= 7.2e+127) {
		tmp = a;
	} else {
		tmp = y * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if i <= -4.6e+51:
		tmp = y * i
	elif i <= 7.2e+127:
		tmp = a
	else:
		tmp = y * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (i <= -4.6e+51)
		tmp = Float64(y * i);
	elseif (i <= 7.2e+127)
		tmp = a;
	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 <= -4.6e+51)
		tmp = y * i;
	elseif (i <= 7.2e+127)
		tmp = a;
	else
		tmp = y * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[i, -4.6e+51], N[(y * i), $MachinePrecision], If[LessEqual[i, 7.2e+127], a, N[(y * i), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if i < -4.6000000000000001e51 or 7.19999999999999958e127 < 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. Step-by-step derivation

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+l+ 99.9%

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

      6. +-commutative 99.9%

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

      7. fma-def 99.9%

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

      8. +-commutative 99.9%

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

      9. fma-def 99.9%

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

      10. +-commutative 99.9%

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

      11. associate-+l+ 99.9%

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

      12. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around 0 88.9%

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

   5. Taylor expanded in y around inf 49.8%

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

      1. *-commutative 49.8%

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

   7. Simplified 49.8%

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

   if -4.6000000000000001e51 < i < 7.19999999999999958e127

   1. Initial program 99.8%

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

   2. Taylor expanded in b around inf 96.1%

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

   3. Taylor expanded in a around inf 20.4%

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

   4. Taylor expanded in a around inf 18.2%

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

4. Final simplification 30.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4.6 \cdot 10^{+51}:\\ \;\;\;\;y \cdot i\\ \mathbf{elif}\;i \leq 7.2 \cdot 10^{+127}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \]

Alternative 17: 37.5% accurate, 43.8× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = a + (y * i)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in b around inf 97.2%

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

3. Taylor expanded in a around inf 35.4%

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

4. Final simplification 35.4%

   \[\leadsto a + y \cdot i \]

Alternative 18: 16.1% 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 99.8%

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

2. Taylor expanded in b around inf 97.2%

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

3. Taylor expanded in a around inf 35.4%

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

4. Taylor expanded in a around inf 16.1%

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

5. Final simplification 16.1%

   \[\leadsto a \]

Reproduce

herbie shell --seed 2023268 
(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)))