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

Percentage Accurate: 99.8% → 99.8%

Time: 18.9s

Alternatives: 13

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, 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]

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. Final simplification 99.9%

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

Alternative 2: 89.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+211} \lor \neg \left(x \leq 3.8 \cdot 10^{+180}\right):\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + \mathsf{fma}\left(\log c, b + -0.5, a\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -1.9e+211) (not (<= x 3.8e+180)))
   (+ (* x (log y)) (* y i))
   (+ (* y i) (+ t (+ z (fma (log c) (+ b -0.5) a))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1.9e+211) || !(x <= 3.8e+180)) {
		tmp = (x * log(y)) + (y * i);
	} else {
		tmp = (y * i) + (t + (z + fma(log(c), (b + -0.5), a)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -1.9e+211) || !(x <= 3.8e+180))
		tmp = Float64(Float64(x * log(y)) + Float64(y * i));
	else
		tmp = Float64(Float64(y * i) + Float64(t + Float64(z + fma(log(c), Float64(b + -0.5), a))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -1.9e+211], N[Not[LessEqual[x, 3.8e+180]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(t + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.90000000000000008e211 or 3.8e180 < x

   1. Initial program 99.6%

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

   2. Taylor expanded in x around inf 80.5%

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

   if -1.90000000000000008e211 < x < 3.8e180

   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 96.5%

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

      1. +-commutative 96.5%

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

      2. associate-+r+ 96.5%

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

      3. +-commutative 96.5%

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

      4. sub-neg 96.5%

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

      5. metadata-eval 96.5%

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

      6. *-commutative 96.5%

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

      7. associate-+r+ 96.5%

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

      8. +-commutative 96.5%

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

      9. +-commutative 96.5%

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

      10. associate-+l+ 96.5%

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

      11. +-commutative 96.5%

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

      12. *-commutative 96.5%

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

      13. fma-def 96.5%

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

      14. +-commutative 96.5%

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

   4. Simplified 96.5%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+211} \lor \neg \left(x \leq 3.8 \cdot 10^{+180}\right):\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + \mathsf{fma}\left(\log c, b + -0.5, a\right)\right)\right)\\ \end{array} \]

Alternative 3: 98.0% accurate, 1.0× speedup

Math

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

FPCore

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in b around inf 98.8%

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

   1. *-commutative 98.8%

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

4. Simplified 98.8%

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

5. Final simplification 98.8%

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

Alternative 4: 82.5% accurate, 1.0× speedup

Math

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

FPCore

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

Python

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

Julia

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

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = (y * i) + ((b * log(c)) + (((x * log(y)) + z) + a));
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[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + a), $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. Taylor expanded in b around inf 98.8%

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

   1. *-commutative 98.8%

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

4. Simplified 98.8%

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

5. Taylor expanded in t around 0 83.5%

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

6. Final simplification 83.5%

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

Alternative 5: 89.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+211} \lor \neg \left(x \leq 8 \cdot 10^{+180}\right):\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(t + a\right) + \left(z + \log c \cdot \left(b + -0.5\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -1.8e+211) (not (<= x 8e+180)))
   (+ (* x (log y)) (* y i))
   (+ (* y i) (+ (+ t a) (+ z (* (log c) (+ b -0.5)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1.8e+211) || !(x <= 8e+180)) {
		tmp = (x * log(y)) + (y * i);
	} else {
		tmp = (y * i) + ((t + a) + (z + (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 <= (-1.8d+211)) .or. (.not. (x <= 8d+180))) then
        tmp = (x * log(y)) + (y * i)
    else
        tmp = (y * i) + ((t + a) + (z + (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 <= -1.8e+211) || !(x <= 8e+180)) {
		tmp = (x * Math.log(y)) + (y * i);
	} else {
		tmp = (y * i) + ((t + a) + (z + (Math.log(c) * (b + -0.5))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -1.8e+211) or not (x <= 8e+180):
		tmp = (x * math.log(y)) + (y * i)
	else:
		tmp = (y * i) + ((t + a) + (z + (math.log(c) * (b + -0.5))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -1.8e+211) || !(x <= 8e+180))
		tmp = Float64(Float64(x * log(y)) + Float64(y * i));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(t + a) + Float64(z + 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 <= -1.8e+211) || ~((x <= 8e+180)))
		tmp = (x * log(y)) + (y * i);
	else
		tmp = (y * i) + ((t + a) + (z + (log(c) * (b + -0.5))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -1.8e+211], N[Not[LessEqual[x, 8e+180]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(t + a), $MachinePrecision] + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.80000000000000001e211 or 8.0000000000000001e180 < x

   1. Initial program 99.6%

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

   2. Taylor expanded in x around inf 80.5%

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

   if -1.80000000000000001e211 < x < 8.0000000000000001e180

   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 96.5%

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

      1. associate-+r+ 96.5%

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

      2. sub-neg 96.5%

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

      3. metadata-eval 96.5%

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

      4. +-commutative 96.5%

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

   4. Simplified 96.5%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+211} \lor \neg \left(x \leq 8 \cdot 10^{+180}\right):\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(t + a\right) + \left(z + \log c \cdot \left(b + -0.5\right)\right)\right)\\ \end{array} \]

Alternative 6: 88.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+211} \lor \neg \left(x \leq 9 \cdot 10^{+180}\right):\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(b \cdot \log c + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -1.8e+211) (not (<= x 9e+180)))
   (+ (* x (log y)) (* y i))
   (+ (* y i) (+ (* b (log c)) (+ a (+ z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1.8e+211) || !(x <= 9e+180)) {
		tmp = (x * log(y)) + (y * i);
	} else {
		tmp = (y * i) + ((b * log(c)) + (a + (z + t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-1.8d+211)) .or. (.not. (x <= 9d+180))) then
        tmp = (x * log(y)) + (y * i)
    else
        tmp = (y * i) + ((b * log(c)) + (a + (z + t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1.8e+211) || !(x <= 9e+180)) {
		tmp = (x * Math.log(y)) + (y * i);
	} else {
		tmp = (y * i) + ((b * Math.log(c)) + (a + (z + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -1.8e+211) or not (x <= 9e+180):
		tmp = (x * math.log(y)) + (y * i)
	else:
		tmp = (y * i) + ((b * math.log(c)) + (a + (z + t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -1.8e+211) || !(x <= 9e+180))
		tmp = Float64(Float64(x * log(y)) + Float64(y * i));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(b * log(c)) + Float64(a + Float64(z + t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -1.8e+211) || ~((x <= 9e+180)))
		tmp = (x * log(y)) + (y * i);
	else
		tmp = (y * i) + ((b * log(c)) + (a + (z + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -1.8e+211], N[Not[LessEqual[x, 9e+180]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.80000000000000001e211 or 8.99999999999999962e180 < x

   1. Initial program 99.6%

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

   2. Taylor expanded in x around inf 80.5%

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

   if -1.80000000000000001e211 < x < 8.99999999999999962e180

   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 98.6%

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

      1. *-commutative 98.6%

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

   4. Simplified 98.6%

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

   5. Taylor expanded in x around 0 95.2%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+211} \lor \neg \left(x \leq 9 \cdot 10^{+180}\right):\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(b \cdot \log c + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \]

Alternative 7: 73.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+211} \lor \neg \left(x \leq 7.8 \cdot 10^{+180}\right):\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -1.8e+211) (not (<= x 7.8e+180)))
   (+ (* x (log y)) (* y i))
   (+ (* y i) (+ t (+ z a)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1.8e+211) || !(x <= 7.8e+180)) {
		tmp = (x * log(y)) + (y * i);
	} else {
		tmp = (y * i) + (t + (z + a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-1.8d+211)) .or. (.not. (x <= 7.8d+180))) then
        tmp = (x * log(y)) + (y * i)
    else
        tmp = (y * i) + (t + (z + a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1.8e+211) || !(x <= 7.8e+180)) {
		tmp = (x * Math.log(y)) + (y * i);
	} else {
		tmp = (y * i) + (t + (z + a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -1.8e+211) or not (x <= 7.8e+180):
		tmp = (x * math.log(y)) + (y * i)
	else:
		tmp = (y * i) + (t + (z + a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -1.8e+211) || !(x <= 7.8e+180))
		tmp = Float64(Float64(x * log(y)) + Float64(y * i));
	else
		tmp = Float64(Float64(y * i) + Float64(t + Float64(z + a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -1.8e+211) || ~((x <= 7.8e+180)))
		tmp = (x * log(y)) + (y * i);
	else
		tmp = (y * i) + (t + (z + a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -1.8e+211], N[Not[LessEqual[x, 7.8e+180]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(t + N[(z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.80000000000000001e211 or 7.8000000000000002e180 < x

   1. Initial program 99.6%

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

   2. Taylor expanded in x around inf 80.5%

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

   if -1.80000000000000001e211 < x < 7.8000000000000002e180

   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 96.5%

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

      1. +-commutative 96.5%

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

      2. associate-+r+ 96.5%

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

      3. +-commutative 96.5%

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

      4. sub-neg 96.5%

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

      5. metadata-eval 96.5%

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

      6. *-commutative 96.5%

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

      7. associate-+r+ 96.5%

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

      8. +-commutative 96.5%

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

      9. +-commutative 96.5%

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

      10. associate-+l+ 96.5%

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

      11. +-commutative 96.5%

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

      12. *-commutative 96.5%

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

      13. fma-def 96.5%

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

      14. +-commutative 96.5%

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

   4. Simplified 96.5%

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

   5. Taylor expanded in a around inf 78.7%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+211} \lor \neg \left(x \leq 7.8 \cdot 10^{+180}\right):\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + a\right)\right)\\ \end{array} \]

Alternative 8: 59.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+113}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -4e+113) (+ (* y i) (+ t (+ z a))) (+ (* 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 tmp;
	if (z <= -4e+113) {
		tmp = (y * i) + (t + (z + a));
	} 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) :: tmp
    if (z <= (-4d+113)) then
        tmp = (y * i) + (t + (z + a))
    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 tmp;
	if (z <= -4e+113) {
		tmp = (y * i) + (t + (z + a));
	} else {
		tmp = (y * i) + (a + (b * Math.log(c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -4e+113:
		tmp = (y * i) + (t + (z + a))
	else:
		tmp = (y * i) + (a + (b * math.log(c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -4e+113)
		tmp = Float64(Float64(y * i) + Float64(t + Float64(z + a)));
	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)
	tmp = 0.0;
	if (z <= -4e+113)
		tmp = (y * i) + (t + (z + a));
	else
		tmp = (y * i) + (a + (b * log(c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -4e+113], N[(N[(y * i), $MachinePrecision] + N[(t + N[(z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4e113

   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 x around 0 92.9%

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

      1. +-commutative 92.9%

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

      2. associate-+r+ 92.9%

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

      3. +-commutative 92.9%

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

      4. sub-neg 92.9%

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

      5. metadata-eval 92.9%

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

      6. *-commutative 92.9%

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

      7. associate-+r+ 92.9%

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

      8. +-commutative 92.9%

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

      9. +-commutative 92.9%

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

      10. associate-+l+ 92.9%

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

      11. +-commutative 92.9%

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

      12. *-commutative 92.9%

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

      13. fma-def 92.9%

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

      14. +-commutative 92.9%

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

   4. Simplified 92.9%

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

   5. Taylor expanded in a around inf 83.4%

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

   if -4e113 < 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. Taylor expanded in b around inf 98.5%

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

      1. *-commutative 98.5%

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

   4. Simplified 98.5%

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

   5. Taylor expanded in a around inf 55.0%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+113}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \end{array} \]

Alternative 9: 66.2% accurate, 24.3× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(y * i), $MachinePrecision] + N[(t + N[(z + a), $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. Taylor expanded in x around 0 86.5%

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

   1. +-commutative 86.5%

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

   2. associate-+r+ 86.5%

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

   3. +-commutative 86.5%

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

   4. sub-neg 86.5%

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

   5. metadata-eval 86.5%

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

   6. *-commutative 86.5%

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

   7. associate-+r+ 86.5%

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

   8. +-commutative 86.5%

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

   9. +-commutative 86.5%

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

   10. associate-+l+ 86.5%

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

   11. +-commutative 86.5%

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

   12. *-commutative 86.5%

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

   13. fma-def 86.4%

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

   14. +-commutative 86.4%

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

4. Simplified 86.4%

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

5. Taylor expanded in a around inf 70.3%

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

6. Final simplification 70.3%

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

Alternative 10: 42.0% accurate, 31.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.46 \cdot 10^{+78}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -1.46e+78) (+ z (* y i)) (+ a (* y i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -1.46e+78) {
		tmp = z + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-1.46d+78)) then
        tmp = z + (y * i)
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -1.46e+78) {
		tmp = z + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -1.46e+78:
		tmp = z + (y * i)
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -1.46e+78)
		tmp = Float64(z + Float64(y * i));
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -1.46e+78)
		tmp = z + (y * i);
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -1.46e+78], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.46000000000000005e78

   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 z around inf 62.2%

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

   if -1.46000000000000005e78 < 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. Taylor expanded in a around inf 40.0%

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

4. Final simplification 44.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.46 \cdot 10^{+78}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]

Alternative 11: 27.1% accurate, 43.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 1.16 \cdot 10^{+107}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (if (<= a 1.16e+107) (* y i) a))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 1.16e+107) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 1.16d+107) then
        tmp = y * i
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 1.16e+107) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 1.16e+107:
		tmp = y * i
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 1.16e+107)
		tmp = Float64(y * i);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 1.16e+107)
		tmp = y * i;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 1.16e+107], N[(y * i), $MachinePrecision], a]

Derivation

1. Split input into 2 regimes

2. if a < 1.1600000000000001e107

   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 y around inf 24.6%

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

      1. *-commutative 24.6%

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

   4. Simplified 24.6%

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

   if 1.1600000000000001e107 < 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 62.0%

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

   3. Taylor expanded in a around inf 44.7%

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

4. Final simplification 28.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.16 \cdot 10^{+107}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 12: 37.7% accurate, 43.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in a around inf 39.2%

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

3. Final simplification 39.2%

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

Alternative 13: 15.7% 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. Taylor expanded in a around inf 39.2%

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

3. Taylor expanded in a around inf 17.9%

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

4. Final simplification 17.9%

   \[\leadsto a \]

Reproduce

herbie shell --seed 2023275 
(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)))