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

Percentage Accurate: 99.8% → 99.8%

Time: 14.7s

Alternatives: 15

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

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

FPCore

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

Python

def code(x, y, z, t, a, b, c, i):
	return (((t + ((x * math.log(y)) + z)) + 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(t + Float64(Float64(x * log(y)) + z)) + 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 = (((t + ((x * log(y)) + z)) + a) + ((b - 0.5) * log(c))) + (y * i);
end

Wolfram

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

Derivation

1. Initial program 99.5%

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

3. Final simplification 99.5%

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

Alternative 2: 93.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y + z\\ \mathbf{if}\;x \leq -1.32 \cdot 10^{+98}:\\ \;\;\;\;y \cdot i + \left(a + t\_1\right)\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+169}:\\ \;\;\;\;a + \left(t + \left(z + \mathsf{fma}\left(\log c, b + -0.5, y \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(\left(t + t\_1\right) + a\right) + \log c \cdot -0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x (log y)) z)))
   (if (<= x -1.32e+98)
     (+ (* y i) (+ a t_1))
     (if (<= x 4e+169)
       (+ a (+ t (+ z (fma (log c) (+ b -0.5) (* y i)))))
       (+ (* y i) (+ (+ (+ t t_1) a) (* (log c) -0.5)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * log(y)) + z;
	double tmp;
	if (x <= -1.32e+98) {
		tmp = (y * i) + (a + t_1);
	} else if (x <= 4e+169) {
		tmp = a + (t + (z + fma(log(c), (b + -0.5), (y * i))));
	} else {
		tmp = (y * i) + (((t + t_1) + a) + (log(c) * -0.5));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * log(y)) + z)
	tmp = 0.0
	if (x <= -1.32e+98)
		tmp = Float64(Float64(y * i) + Float64(a + t_1));
	elseif (x <= 4e+169)
		tmp = Float64(a + Float64(t + Float64(z + fma(log(c), Float64(b + -0.5), Float64(y * i)))));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(Float64(t + t_1) + a) + Float64(log(c) * -0.5)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]}, If[LessEqual[x, -1.32e+98], N[(N[(y * i), $MachinePrecision] + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4e+169], N[(a + N[(t + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(N[(t + t$95$1), $MachinePrecision] + a), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.3200000000000001e98

   1. Initial program 97.5%

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

   3. Taylor expanded in b around 0 99.8%

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

      1. *-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in t around 0 83.8%

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

   7. Taylor expanded in x around inf 83.8%

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

   if -1.3200000000000001e98 < x < 3.99999999999999974e169

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 97.5%

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

      1. +-commutative 97.5%

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

      2. sub-neg 97.5%

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

      3. metadata-eval 97.5%

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

      4. *-commutative 97.5%

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

      5. fma-undefine 97.5%

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

   5. Simplified 97.5%

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

   if 3.99999999999999974e169 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in b around 0 99.8%

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

      1. *-commutative 99.8%

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

   5. Simplified 99.8%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.32 \cdot 10^{+98}:\\ \;\;\;\;y \cdot i + \left(a + \left(x \cdot \log y + z\right)\right)\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+169}:\\ \;\;\;\;a + \left(t + \left(z + \mathsf{fma}\left(\log c, b + -0.5, y \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(\left(t + \left(x \cdot \log y + z\right)\right) + a\right) + \log c \cdot -0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 92.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -4.1 \cdot 10^{+99}:\\ \;\;\;\;y \cdot i + \left(a + \left(t\_1 + z\right)\right)\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+169}:\\ \;\;\;\;a + \left(t + \left(z + \mathsf{fma}\left(\log c, b + -0.5, y \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + \left(t\_1 + \log c \cdot -0.5\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -4.1e+99)
     (+ (* y i) (+ a (+ t_1 z)))
     (if (<= x 4e+169)
       (+ a (+ t (+ z (fma (log c) (+ b -0.5) (* y i)))))
       (+ (* y i) (+ a (+ z (+ t_1 (* (log c) -0.5)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * log(y);
	double tmp;
	if (x <= -4.1e+99) {
		tmp = (y * i) + (a + (t_1 + z));
	} else if (x <= 4e+169) {
		tmp = a + (t + (z + fma(log(c), (b + -0.5), (y * i))));
	} else {
		tmp = (y * i) + (a + (z + (t_1 + (log(c) * -0.5))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -4.1e+99)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(t_1 + z)));
	elseif (x <= 4e+169)
		tmp = Float64(a + Float64(t + Float64(z + fma(log(c), Float64(b + -0.5), Float64(y * i)))));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + Float64(t_1 + Float64(log(c) * -0.5)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.1e+99], N[(N[(y * i), $MachinePrecision] + N[(a + N[(t$95$1 + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4e+169], N[(a + N[(t + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + N[(t$95$1 + N[(N[Log[c], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.09999999999999979e99

   1. Initial program 97.5%

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

   3. Taylor expanded in b around 0 99.8%

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

      1. *-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in t around 0 83.8%

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

   7. Taylor expanded in x around inf 83.8%

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

   if -4.09999999999999979e99 < x < 3.99999999999999974e169

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 97.5%

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

      1. +-commutative 97.5%

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

      2. sub-neg 97.5%

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

      3. metadata-eval 97.5%

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

      4. *-commutative 97.5%

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

      5. fma-undefine 97.5%

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

   5. Simplified 97.5%

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

   if 3.99999999999999974e169 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in b around 0 99.8%

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

      1. *-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in t around 0 96.7%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{+99}:\\ \;\;\;\;y \cdot i + \left(a + \left(x \cdot \log y + z\right)\right)\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+169}:\\ \;\;\;\;a + \left(t + \left(z + \mathsf{fma}\left(\log c, b + -0.5, y \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + \left(x \cdot \log y + \log c \cdot -0.5\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 92.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+100} \lor \neg \left(x \leq 4 \cdot 10^{+169}\right):\\ \;\;\;\;y \cdot i + \left(a + \left(x \cdot \log y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + \mathsf{fma}\left(\log c, b + -0.5, y \cdot i\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -1.05e+100) (not (<= x 4e+169)))
   (+ (* y i) (+ a (+ (* x (log y)) z)))
   (+ a (+ t (+ z (fma (log c) (+ b -0.5) (* y i)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1.05e+100) || !(x <= 4e+169)) {
		tmp = (y * i) + (a + ((x * log(y)) + z));
	} else {
		tmp = a + (t + (z + fma(log(c), (b + -0.5), (y * i))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -1.05e+100) || !(x <= 4e+169))
		tmp = Float64(Float64(y * i) + Float64(a + Float64(Float64(x * log(y)) + z)));
	else
		tmp = Float64(a + Float64(t + Float64(z + fma(log(c), Float64(b + -0.5), Float64(y * i)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -1.05e+100], N[Not[LessEqual[x, 4e+169]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(a + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(t + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.0499999999999999e100 or 3.99999999999999974e169 < x

   1. Initial program 98.5%

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

   3. Taylor expanded in b around 0 99.8%

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

      1. *-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in t around 0 89.0%

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

   7. Taylor expanded in x around inf 89.0%

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

   if -1.0499999999999999e100 < x < 3.99999999999999974e169

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 97.5%

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

      1. +-commutative 97.5%

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

      2. sub-neg 97.5%

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

      3. metadata-eval 97.5%

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

      4. *-commutative 97.5%

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

      5. fma-undefine 97.5%

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

   5. Simplified 97.5%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+100} \lor \neg \left(x \leq 4 \cdot 10^{+169}\right):\\ \;\;\;\;y \cdot i + \left(a + \left(x \cdot \log y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + \mathsf{fma}\left(\log c, b + -0.5, y \cdot i\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 92.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+99} \lor \neg \left(x \leq 1.65 \cdot 10^{+174}\right):\\ \;\;\;\;y \cdot i + \left(a + \left(x \cdot \log y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -1.8e+99) (not (<= x 1.65e+174)))
   (+ (* y i) (+ a (+ (* x (log y)) z)))
   (+ (* y i) (+ (* (- b 0.5) (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+99) || !(x <= 1.65e+174)) {
		tmp = (y * i) + (a + ((x * log(y)) + z));
	} else {
		tmp = (y * i) + (((b - 0.5) * 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+99)) .or. (.not. (x <= 1.65d+174))) then
        tmp = (y * i) + (a + ((x * log(y)) + z))
    else
        tmp = (y * i) + (((b - 0.5d0) * 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+99) || !(x <= 1.65e+174)) {
		tmp = (y * i) + (a + ((x * Math.log(y)) + z));
	} else {
		tmp = (y * i) + (((b - 0.5) * 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+99) or not (x <= 1.65e+174):
		tmp = (y * i) + (a + ((x * math.log(y)) + z))
	else:
		tmp = (y * i) + (((b - 0.5) * 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+99) || !(x <= 1.65e+174))
		tmp = Float64(Float64(y * i) + Float64(a + Float64(Float64(x * log(y)) + z)));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(Float64(b - 0.5) * 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+99) || ~((x <= 1.65e+174)))
		tmp = (y * i) + (a + ((x * log(y)) + z));
	else
		tmp = (y * i) + (((b - 0.5) * 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+99], N[Not[LessEqual[x, 1.65e+174]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(a + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.8000000000000001e99 or 1.65e174 < x

   1. Initial program 98.5%

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

   3. Taylor expanded in b around 0 99.8%

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

      1. *-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in t around 0 89.0%

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

   7. Taylor expanded in x around inf 89.0%

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

   if -1.8000000000000001e99 < x < 1.65e174

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 94.0%

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

      1. +-commutative 94.0%

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

      2. associate-/l* 93.5%

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

      3. fma-define 93.5%

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

   5. Simplified 93.5%

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

   6. Taylor expanded in z around inf 97.5%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+99} \lor \neg \left(x \leq 1.65 \cdot 10^{+174}\right):\\ \;\;\;\;y \cdot i + \left(a + \left(x \cdot \log y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 92.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+99} \lor \neg \left(x \leq 4 \cdot 10^{+169}\right):\\ \;\;\;\;y \cdot i + \left(a + \left(x \cdot \log y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -8.5e+99) (not (<= x 4e+169)))
   (+ (* y i) (+ a (+ (* x (log y)) z)))
   (+ a (+ t (+ z (+ (* (- b 0.5) (log c)) (* y i)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -8.5e+99) || !(x <= 4e+169)) {
		tmp = (y * i) + (a + ((x * log(y)) + z));
	} else {
		tmp = a + (t + (z + (((b - 0.5) * log(c)) + (y * i))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-8.5d+99)) .or. (.not. (x <= 4d+169))) then
        tmp = (y * i) + (a + ((x * log(y)) + z))
    else
        tmp = a + (t + (z + (((b - 0.5d0) * log(c)) + (y * i))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -8.5e+99) || !(x <= 4e+169)) {
		tmp = (y * i) + (a + ((x * Math.log(y)) + z));
	} else {
		tmp = a + (t + (z + (((b - 0.5) * Math.log(c)) + (y * i))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -8.5e+99) or not (x <= 4e+169):
		tmp = (y * i) + (a + ((x * math.log(y)) + z))
	else:
		tmp = a + (t + (z + (((b - 0.5) * math.log(c)) + (y * i))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -8.5e+99) || !(x <= 4e+169))
		tmp = Float64(Float64(y * i) + Float64(a + Float64(Float64(x * log(y)) + z)));
	else
		tmp = Float64(a + Float64(t + Float64(z + Float64(Float64(Float64(b - 0.5) * log(c)) + Float64(y * i)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -8.5e+99) || ~((x <= 4e+169)))
		tmp = (y * i) + (a + ((x * log(y)) + z));
	else
		tmp = a + (t + (z + (((b - 0.5) * log(c)) + (y * i))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -8.5e+99], N[Not[LessEqual[x, 4e+169]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(a + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(t + N[(z + N[(N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.49999999999999984e99 or 3.99999999999999974e169 < x

   1. Initial program 98.5%

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

   3. Taylor expanded in b around 0 99.8%

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

      1. *-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in t around 0 89.0%

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

   7. Taylor expanded in x around inf 89.0%

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

   if -8.49999999999999984e99 < x < 3.99999999999999974e169

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 97.5%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+99} \lor \neg \left(x \leq 4 \cdot 10^{+169}\right):\\ \;\;\;\;y \cdot i + \left(a + \left(x \cdot \log y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{+222} \lor \neg \left(b \leq 1.4 \cdot 10^{+207}\right):\\ \;\;\;\;b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(x \cdot \log y + z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= b -2.5e+222) (not (<= b 1.4e+207)))
   (* b (log c))
   (+ (* y i) (+ a (+ (* x (log y)) z)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((b <= -2.5e+222) || !(b <= 1.4e+207)) {
		tmp = b * log(c);
	} else {
		tmp = (y * i) + (a + ((x * log(y)) + 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 <= (-2.5d+222)) .or. (.not. (b <= 1.4d+207))) then
        tmp = b * log(c)
    else
        tmp = (y * i) + (a + ((x * log(y)) + 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 <= -2.5e+222) || !(b <= 1.4e+207)) {
		tmp = b * Math.log(c);
	} else {
		tmp = (y * i) + (a + ((x * Math.log(y)) + z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (b <= -2.5e+222) or not (b <= 1.4e+207):
		tmp = b * math.log(c)
	else:
		tmp = (y * i) + (a + ((x * math.log(y)) + z))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((b <= -2.5e+222) || !(b <= 1.4e+207))
		tmp = Float64(b * log(c));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(Float64(x * log(y)) + z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((b <= -2.5e+222) || ~((b <= 1.4e+207)))
		tmp = b * log(c);
	else
		tmp = (y * i) + (a + ((x * log(y)) + z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[b, -2.5e+222], N[Not[LessEqual[b, 1.4e+207]], $MachinePrecision]], N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.50000000000000012e222 or 1.40000000000000005e207 < b

   1. Initial program 96.1%

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

   3. Taylor expanded in b around inf 78.6%

      \[\leadsto \color{blue}{b \cdot \log c} \]
   4. Step-by-step derivation

      1. *-commutative 78.6%

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

   5. Simplified 78.6%

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

   if -2.50000000000000012e222 < b < 1.40000000000000005e207

   1. Initial program 99.9%

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

   3. Taylor expanded in b around 0 93.9%

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

      1. *-commutative 93.9%

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

   5. Simplified 93.9%

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

   6. Taylor expanded in t around 0 77.5%

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

   7. Taylor expanded in x around inf 75.5%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{+222} \lor \neg \left(b \leq 1.4 \cdot 10^{+207}\right):\\ \;\;\;\;b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(x \cdot \log y + z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 70.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \log c\\ \mathbf{if}\;b \leq -1.42 \cdot 10^{+222}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{+207}:\\ \;\;\;\;y \cdot i + \left(a + \left(x \cdot \log y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\frac{t\_1}{z} + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* b (log c))))
   (if (<= b -1.42e+222)
     t_1
     (if (<= b 1.3e+207)
       (+ (* y i) (+ a (+ (* x (log y)) z)))
       (* z (+ (/ t_1 z) 1.0))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = b * log(c);
	double tmp;
	if (b <= -1.42e+222) {
		tmp = t_1;
	} else if (b <= 1.3e+207) {
		tmp = (y * i) + (a + ((x * log(y)) + z));
	} else {
		tmp = z * ((t_1 / z) + 1.0);
	}
	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 = b * log(c)
    if (b <= (-1.42d+222)) then
        tmp = t_1
    else if (b <= 1.3d+207) then
        tmp = (y * i) + (a + ((x * log(y)) + z))
    else
        tmp = z * ((t_1 / z) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = b * Math.log(c);
	double tmp;
	if (b <= -1.42e+222) {
		tmp = t_1;
	} else if (b <= 1.3e+207) {
		tmp = (y * i) + (a + ((x * Math.log(y)) + z));
	} else {
		tmp = z * ((t_1 / z) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = b * math.log(c)
	tmp = 0
	if b <= -1.42e+222:
		tmp = t_1
	elif b <= 1.3e+207:
		tmp = (y * i) + (a + ((x * math.log(y)) + z))
	else:
		tmp = z * ((t_1 / z) + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(b * log(c))
	tmp = 0.0
	if (b <= -1.42e+222)
		tmp = t_1;
	elseif (b <= 1.3e+207)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(Float64(x * log(y)) + z)));
	else
		tmp = Float64(z * Float64(Float64(t_1 / z) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = b * log(c);
	tmp = 0.0;
	if (b <= -1.42e+222)
		tmp = t_1;
	elseif (b <= 1.3e+207)
		tmp = (y * i) + (a + ((x * log(y)) + z));
	else
		tmp = z * ((t_1 / z) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.42e+222], t$95$1, If[LessEqual[b, 1.3e+207], N[(N[(y * i), $MachinePrecision] + N[(a + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(t$95$1 / z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.41999999999999997e222

   1. Initial program 99.6%

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

   3. Taylor expanded in b around inf 83.5%

      \[\leadsto \color{blue}{b \cdot \log c} \]
   4. Step-by-step derivation

      1. *-commutative 83.5%

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

   5. Simplified 83.5%

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

   if -1.41999999999999997e222 < b < 1.2999999999999999e207

   1. Initial program 99.9%

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

   3. Taylor expanded in b around 0 93.9%

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

      1. *-commutative 93.9%

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

   5. Simplified 93.9%

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

   6. Taylor expanded in t around 0 77.5%

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

   7. Taylor expanded in x around inf 75.5%

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

   if 1.2999999999999999e207 < b

   1. Initial program 93.6%

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

   3. Taylor expanded in z around -inf 56.2%

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

   4. Taylor expanded in b around inf 44.4%

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

      1. *-commutative 44.4%

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

   6. Simplified 44.4%

      \[\leadsto -1 \cdot \left(z \cdot \left(-1 \cdot \color{blue}{\frac{\log c \cdot b}{z}} - 1\right)\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.42 \cdot 10^{+222}:\\ \;\;\;\;b \cdot \log c\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{+207}:\\ \;\;\;\;y \cdot i + \left(a + \left(x \cdot \log y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\frac{b \cdot \log c}{z} + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 62.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.6 \cdot 10^{+131} \lor \neg \left(x \leq 4.7 \cdot 10^{+82}\right):\\ \;\;\;\;z + \left(x \cdot \log y + y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -9.6e+131) (not (<= x 4.7e+82)))
   (+ z (+ (* x (log y)) (* y i)))
   (+ (* y i) (+ 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 <= -9.6e+131) || !(x <= 4.7e+82)) {
		tmp = z + ((x * log(y)) + (y * i));
	} else {
		tmp = (y * i) + (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 <= (-9.6d+131)) .or. (.not. (x <= 4.7d+82))) then
        tmp = z + ((x * log(y)) + (y * i))
    else
        tmp = (y * i) + (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 <= -9.6e+131) || !(x <= 4.7e+82)) {
		tmp = z + ((x * Math.log(y)) + (y * i));
	} else {
		tmp = (y * i) + (z + a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -9.6e+131) or not (x <= 4.7e+82):
		tmp = z + ((x * math.log(y)) + (y * i))
	else:
		tmp = (y * i) + (z + a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -9.6e+131) || !(x <= 4.7e+82))
		tmp = Float64(z + Float64(Float64(x * log(y)) + Float64(y * i)));
	else
		tmp = Float64(Float64(y * i) + 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 <= -9.6e+131) || ~((x <= 4.7e+82)))
		tmp = z + ((x * log(y)) + (y * i));
	else
		tmp = (y * i) + (z + a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -9.6e+131], N[Not[LessEqual[x, 4.7e+82]], $MachinePrecision]], N[(z + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.5999999999999998e131 or 4.7e82 < x

   1. Initial program 98.7%

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

   3. Taylor expanded in b around 0 95.6%

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

      1. *-commutative 95.6%

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

   5. Simplified 95.6%

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

   6. Taylor expanded in t around 0 85.4%

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

   7. Taylor expanded in x around inf 85.4%

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

   8. Taylor expanded in a around 0 79.1%

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

   if -9.5999999999999998e131 < x < 4.7e82

   1. Initial program 99.9%

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

   3. Taylor expanded in b around 0 80.5%

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

      1. *-commutative 80.5%

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

   5. Simplified 80.5%

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

   6. Taylor expanded in t around 0 63.0%

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

   7. Taylor expanded in x around inf 60.1%

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

   8. Taylor expanded in z around inf 59.4%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.6 \cdot 10^{+131} \lor \neg \left(x \leq 4.7 \cdot 10^{+82}\right):\\ \;\;\;\;z + \left(x \cdot \log y + y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 60.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+144} \lor \neg \left(x \leq 3.3 \cdot 10^{+195}\right):\\ \;\;\;\;a + \left(x \cdot \log y + z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -1.55e+144) (not (<= x 3.3e+195)))
   (+ a (+ (* x (log y)) z))
   (+ (* y i) (+ 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 <= -1.55e+144) || !(x <= 3.3e+195)) {
		tmp = a + ((x * log(y)) + z);
	} else {
		tmp = (y * i) + (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 <= (-1.55d+144)) .or. (.not. (x <= 3.3d+195))) then
        tmp = a + ((x * log(y)) + z)
    else
        tmp = (y * i) + (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 <= -1.55e+144) || !(x <= 3.3e+195)) {
		tmp = a + ((x * Math.log(y)) + z);
	} else {
		tmp = (y * i) + (z + a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -1.55e+144) or not (x <= 3.3e+195):
		tmp = a + ((x * math.log(y)) + z)
	else:
		tmp = (y * i) + (z + a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -1.55e+144) || !(x <= 3.3e+195))
		tmp = Float64(a + Float64(Float64(x * log(y)) + z));
	else
		tmp = Float64(Float64(y * i) + 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 <= -1.55e+144) || ~((x <= 3.3e+195)))
		tmp = a + ((x * log(y)) + z);
	else
		tmp = (y * i) + (z + a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -1.55e+144], N[Not[LessEqual[x, 3.3e+195]], $MachinePrecision]], N[(a + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.5500000000000001e144 or 3.3e195 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in b around 0 99.8%

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

      1. *-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in t around 0 91.1%

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

   7. Taylor expanded in x around inf 91.1%

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

   8. Taylor expanded in y around 0 75.3%

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

   if -1.5500000000000001e144 < x < 3.3e195

   1. Initial program 99.3%

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

   3. Taylor expanded in b around 0 81.4%

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

      1. *-commutative 81.4%

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

   5. Simplified 81.4%

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

   6. Taylor expanded in t around 0 64.5%

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

   7. Taylor expanded in x around inf 62.1%

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

   8. Taylor expanded in z around inf 59.3%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+144} \lor \neg \left(x \leq 3.3 \cdot 10^{+195}\right):\\ \;\;\;\;a + \left(x \cdot \log y + z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 57.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+214} \lor \neg \left(x \leq 4.6 \cdot 10^{+233}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -4.8e+214) (not (<= x 4.6e+233)))
   (* x (log y))
   (+ (* y i) (+ 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 <= -4.8e+214) || !(x <= 4.6e+233)) {
		tmp = x * log(y);
	} else {
		tmp = (y * i) + (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 <= (-4.8d+214)) .or. (.not. (x <= 4.6d+233))) then
        tmp = x * log(y)
    else
        tmp = (y * i) + (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 <= -4.8e+214) || !(x <= 4.6e+233)) {
		tmp = x * Math.log(y);
	} else {
		tmp = (y * i) + (z + a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -4.8e+214) or not (x <= 4.6e+233):
		tmp = x * math.log(y)
	else:
		tmp = (y * i) + (z + a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -4.8e+214) || !(x <= 4.6e+233))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(Float64(y * i) + 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 <= -4.8e+214) || ~((x <= 4.6e+233)))
		tmp = x * log(y);
	else
		tmp = (y * i) + (z + a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -4.8e+214], N[Not[LessEqual[x, 4.6e+233]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.8000000000000002e214 or 4.60000000000000001e233 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 79.9%

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

   if -4.8000000000000002e214 < x < 4.60000000000000001e233

   1. Initial program 99.4%

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

   3. Taylor expanded in b around 0 83.6%

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

      1. *-commutative 83.6%

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

   5. Simplified 83.6%

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

   6. Taylor expanded in t around 0 67.8%

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

   7. Taylor expanded in x around inf 65.7%

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

   8. Taylor expanded in z around inf 58.6%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+214} \lor \neg \left(x \leq 4.6 \cdot 10^{+233}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 30.6% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.45 \cdot 10^{-181}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-88}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-26}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 1.45e-181) a (if (<= y 3.1e-88) z (if (<= y 4.8e-26) a (* y i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 1.45e-181) {
		tmp = a;
	} else if (y <= 3.1e-88) {
		tmp = z;
	} else if (y <= 4.8e-26) {
		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 (y <= 1.45d-181) then
        tmp = a
    else if (y <= 3.1d-88) then
        tmp = z
    else if (y <= 4.8d-26) 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 (y <= 1.45e-181) {
		tmp = a;
	} else if (y <= 3.1e-88) {
		tmp = z;
	} else if (y <= 4.8e-26) {
		tmp = a;
	} else {
		tmp = y * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 1.45e-181:
		tmp = a
	elif y <= 3.1e-88:
		tmp = z
	elif y <= 4.8e-26:
		tmp = a
	else:
		tmp = y * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 1.45e-181)
		tmp = a;
	elseif (y <= 3.1e-88)
		tmp = z;
	elseif (y <= 4.8e-26)
		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 (y <= 1.45e-181)
		tmp = a;
	elseif (y <= 3.1e-88)
		tmp = z;
	elseif (y <= 4.8e-26)
		tmp = a;
	else
		tmp = y * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 1.45e-181], a, If[LessEqual[y, 3.1e-88], z, If[LessEqual[y, 4.8e-26], a, N[(y * i), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < 1.4499999999999999e-181 or 3.0999999999999998e-88 < y < 4.8000000000000002e-26

   1. Initial program 99.8%

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

   3. Taylor expanded in a around inf 22.0%

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

   if 1.4499999999999999e-181 < y < 3.0999999999999998e-88

   1. Initial program 99.6%

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

   3. Taylor expanded in z around inf 18.9%

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

   if 4.8000000000000002e-26 < y

   1. Initial program 99.2%

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

   3. Taylor expanded in y around inf 48.7%

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

      1. *-commutative 48.7%

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

   5. Simplified 48.7%

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

Alternative 13: 51.4% accurate, 31.3× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. Add Preprocessing

3. Taylor expanded in b around 0 85.8%

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

   1. *-commutative 85.8%

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

5. Simplified 85.8%

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

6. Taylor expanded in t around 0 71.0%

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

7. Taylor expanded in x around inf 69.1%

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

8. Taylor expanded in z around inf 51.9%

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

9. Final simplification 51.9%

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

Alternative 14: 20.7% accurate, 36.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 3.55 \cdot 10^{+112}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (if (<= a 3.55e+112) z a))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 3.55e+112) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 3.55d+112) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 3.55e+112) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 3.55e+112:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 3.55e+112)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 3.55e+112)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 3.55e+112], z, a]

Derivation

1. Split input into 2 regimes

2. if a < 3.55e112

   1. Initial program 99.4%

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

   3. Taylor expanded in z around inf 15.2%

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

   if 3.55e112 < a

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf 45.9%

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

Alternative 15: 16.3% accurate, 219.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

3. Taylor expanded in a around inf 14.3%

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

Reproduce

herbie shell --seed 2024103 
(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)))