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

Percentage Accurate: 99.8% → 99.8%

Time: 17.5s

Alternatives: 17

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = (((((x * log(y)) + z) + t) + a) + ((b - 0.5d0) * log(c))) + (y * i)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = (((((x * log(y)) + z) + t) + a) + ((b - 0.5d0) * log(c))) + (y * i)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \log \left(\frac{1}{c}\right) \cdot \left(0.5 - b\right)\right) + y \cdot i \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (log (/ 1.0 c)) (- 0.5 b))) (* 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) + (log((1.0 / c)) * (0.5 - b))) + (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) + (log((1.0d0 / c)) * (0.5d0 - b))) + (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) + (Math.log((1.0 / c)) * (0.5 - b))) + (y * i);
}

Python

def code(x, y, z, t, a, b, c, i):
	return (((((x * math.log(y)) + z) + t) + a) + (math.log((1.0 / c)) * (0.5 - b))) + (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(log(Float64(1.0 / c)) * Float64(0.5 - b))) + Float64(y * i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = (((((x * log(y)) + z) + t) + a) + (log((1.0 / c)) * (0.5 - b))) + (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[Log[N[(1.0 / c), $MachinePrecision]], $MachinePrecision] * N[(0.5 - b), $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. Taylor expanded in c around inf 99.9%

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

3. Final simplification 99.9%

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

Alternative 2: 93.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -2 \cdot 10^{+130}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + \left(b - 0.5\right) \cdot \log c\right)\right)\\ \mathbf{elif}\;b - 0.5 \leq 10^{+61}:\\ \;\;\;\;y \cdot i + \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \log c \cdot -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(t + a\right) + \mathsf{fma}\left(\log c, b + -0.5, z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (- b 0.5) -2e+130)
   (+ (* y i) (+ a (+ z (* (- b 0.5) (log c)))))
   (if (<= (- b 0.5) 1e+61)
     (+ (* y i) (+ (+ (+ (+ (* x (log y)) z) t) a) (* (log c) -0.5)))
     (+ (* y i) (+ (+ t a) (fma (log c) (+ b -0.5) z))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((b - 0.5) <= -2e+130) {
		tmp = (y * i) + (a + (z + ((b - 0.5) * log(c))));
	} else if ((b - 0.5) <= 1e+61) {
		tmp = (y * i) + (((((x * log(y)) + z) + t) + a) + (log(c) * -0.5));
	} else {
		tmp = (y * i) + ((t + a) + fma(log(c), (b + -0.5), z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(b - 0.5) <= -2e+130)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + Float64(Float64(b - 0.5) * log(c)))));
	elseif (Float64(b - 0.5) <= 1e+61)
		tmp = Float64(Float64(y * i) + Float64(Float64(Float64(Float64(Float64(x * log(y)) + z) + t) + a) + Float64(log(c) * -0.5)));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(t + a) + fma(log(c), Float64(b + -0.5), z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(b - 0.5), $MachinePrecision], -2e+130], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b - 0.5), $MachinePrecision], 1e+61], N[(N[(y * i), $MachinePrecision] + N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(t + a), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 b 1/2) < -2.0000000000000001e130

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0 96.9%

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

      1. associate-+r+ 96.9%

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

      2. sub-neg 96.9%

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

      3. metadata-eval 96.9%

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

      4. +-commutative 96.9%

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

      5. fma-def 96.9%

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

      6. +-commutative 96.9%

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

   4. Simplified 96.9%

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

   5. Taylor expanded in t around 0 85.1%

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

   if -2.0000000000000001e130 < (-.f64 b 1/2) < 9.99999999999999949e60

   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 0 99.7%

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

   if 9.99999999999999949e60 < (-.f64 b 1/2)

   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 96.0%

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

      1. associate-+r+ 96.0%

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

      2. sub-neg 96.0%

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

      3. metadata-eval 96.0%

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

      4. +-commutative 96.0%

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

      5. fma-def 96.0%

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

      6. +-commutative 96.0%

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

   4. Simplified 96.0%

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

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -2 \cdot 10^{+130}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + \left(b - 0.5\right) \cdot \log c\right)\right)\\ \mathbf{elif}\;b - 0.5 \leq 10^{+61}:\\ \;\;\;\;y \cdot i + \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \log c \cdot -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(t + a\right) + \mathsf{fma}\left(\log c, b + -0.5, z\right)\right)\\ \end{array} \]

Alternative 3: 99.8% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (+ (* y i) (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (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 - 0.5) * 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 - 0.5d0) * 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 - 0.5) * 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 - 0.5) * 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(Float64(b - 0.5) * 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 - 0.5) * 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[(N[(b - 0.5), $MachinePrecision] * 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. Final simplification 99.9%

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

Alternative 4: 87.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2.6 \cdot 10^{+175}:\\ \;\;\;\;a + \left(\left(z + t\right) + \mathsf{fma}\left(y, i, \log c \cdot \left(b + -0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x 2.6e+175)
   (+ a (+ (+ z t) (fma y i (* (log c) (+ b -0.5)))))
   (+ (* x (log y)) (* y i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= 2.6e+175) {
		tmp = a + ((z + t) + fma(y, i, (log(c) * (b + -0.5))));
	} else {
		tmp = (x * log(y)) + (y * i);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= 2.6e+175)
		tmp = Float64(a + Float64(Float64(z + t) + fma(y, i, Float64(log(c) * Float64(b + -0.5)))));
	else
		tmp = Float64(Float64(x * log(y)) + Float64(y * i));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, 2.6e+175], N[(a + N[(N[(z + t), $MachinePrecision] + N[(y * i + N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2.6e175

   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 92.6%

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

      1. associate-+r+ 92.6%

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

      2. sub-neg 92.6%

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

      3. metadata-eval 92.6%

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

      4. *-commutative 92.6%

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

      5. fma-def 92.6%

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

      6. +-commutative 92.6%

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

   4. Simplified 92.6%

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

   if 2.6e175 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 85.0%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2.6 \cdot 10^{+175}:\\ \;\;\;\;a + \left(\left(z + t\right) + \mathsf{fma}\left(y, i, \log c \cdot \left(b + -0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \end{array} \]

Alternative 5: 87.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2.6 \cdot 10^{+175}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \left(b - 0.5\right) \cdot \log c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x 2.6e+175)
   (+ (* y i) (+ a (+ t (+ z (* (- b 0.5) (log c))))))
   (+ (* x (log y)) (* y i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= 2.6e+175) {
		tmp = (y * i) + (a + (t + (z + ((b - 0.5) * log(c)))));
	} else {
		tmp = (x * log(y)) + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (x <= 2.6d+175) then
        tmp = (y * i) + (a + (t + (z + ((b - 0.5d0) * log(c)))))
    else
        tmp = (x * log(y)) + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= 2.6e+175) {
		tmp = (y * i) + (a + (t + (z + ((b - 0.5) * Math.log(c)))));
	} else {
		tmp = (x * Math.log(y)) + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if x <= 2.6e+175:
		tmp = (y * i) + (a + (t + (z + ((b - 0.5) * math.log(c)))))
	else:
		tmp = (x * math.log(y)) + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= 2.6e+175)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(t + Float64(z + Float64(Float64(b - 0.5) * log(c))))));
	else
		tmp = Float64(Float64(x * log(y)) + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (x <= 2.6e+175)
		tmp = (y * i) + (a + (t + (z + ((b - 0.5) * log(c)))));
	else
		tmp = (x * log(y)) + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, 2.6e+175], N[(N[(y * i), $MachinePrecision] + N[(a + N[(t + N[(z + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2.6e175

   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 92.6%

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

   if 2.6e175 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 85.0%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2.6 \cdot 10^{+175}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \left(b - 0.5\right) \cdot \log c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \end{array} \]

Alternative 6: 55.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot i + \left(z + t\right)\\ \mathbf{if}\;a \leq 3.9 \cdot 10^{-179}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-121}:\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{elif}\;a \leq 9.3 \cdot 10^{-63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+99}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t + a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y i) (+ z t))))
   (if (<= a 3.9e-179)
     t_1
     (if (<= a 1.1e-121)
       (+ (* y i) (* b (log c)))
       (if (<= a 9.3e-63)
         t_1
         (if (<= a 4.4e+33)
           (+ (* x (log y)) (* y i))
           (if (<= a 4.2e+99) (+ z (* y i)) (+ (* y i) (+ t a)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * i) + (z + t);
	double tmp;
	if (a <= 3.9e-179) {
		tmp = t_1;
	} else if (a <= 1.1e-121) {
		tmp = (y * i) + (b * log(c));
	} else if (a <= 9.3e-63) {
		tmp = t_1;
	} else if (a <= 4.4e+33) {
		tmp = (x * log(y)) + (y * i);
	} else if (a <= 4.2e+99) {
		tmp = z + (y * i);
	} else {
		tmp = (y * i) + (t + 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) :: t_1
    real(8) :: tmp
    t_1 = (y * i) + (z + t)
    if (a <= 3.9d-179) then
        tmp = t_1
    else if (a <= 1.1d-121) then
        tmp = (y * i) + (b * log(c))
    else if (a <= 9.3d-63) then
        tmp = t_1
    else if (a <= 4.4d+33) then
        tmp = (x * log(y)) + (y * i)
    else if (a <= 4.2d+99) then
        tmp = z + (y * i)
    else
        tmp = (y * i) + (t + 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 t_1 = (y * i) + (z + t);
	double tmp;
	if (a <= 3.9e-179) {
		tmp = t_1;
	} else if (a <= 1.1e-121) {
		tmp = (y * i) + (b * Math.log(c));
	} else if (a <= 9.3e-63) {
		tmp = t_1;
	} else if (a <= 4.4e+33) {
		tmp = (x * Math.log(y)) + (y * i);
	} else if (a <= 4.2e+99) {
		tmp = z + (y * i);
	} else {
		tmp = (y * i) + (t + a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y * i) + (z + t)
	tmp = 0
	if a <= 3.9e-179:
		tmp = t_1
	elif a <= 1.1e-121:
		tmp = (y * i) + (b * math.log(c))
	elif a <= 9.3e-63:
		tmp = t_1
	elif a <= 4.4e+33:
		tmp = (x * math.log(y)) + (y * i)
	elif a <= 4.2e+99:
		tmp = z + (y * i)
	else:
		tmp = (y * i) + (t + a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * i) + Float64(z + t))
	tmp = 0.0
	if (a <= 3.9e-179)
		tmp = t_1;
	elseif (a <= 1.1e-121)
		tmp = Float64(Float64(y * i) + Float64(b * log(c)));
	elseif (a <= 9.3e-63)
		tmp = t_1;
	elseif (a <= 4.4e+33)
		tmp = Float64(Float64(x * log(y)) + Float64(y * i));
	elseif (a <= 4.2e+99)
		tmp = Float64(z + Float64(y * i));
	else
		tmp = Float64(Float64(y * i) + Float64(t + a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y * i) + (z + t);
	tmp = 0.0;
	if (a <= 3.9e-179)
		tmp = t_1;
	elseif (a <= 1.1e-121)
		tmp = (y * i) + (b * log(c));
	elseif (a <= 9.3e-63)
		tmp = t_1;
	elseif (a <= 4.4e+33)
		tmp = (x * log(y)) + (y * i);
	elseif (a <= 4.2e+99)
		tmp = z + (y * i);
	else
		tmp = (y * i) + (t + a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(y * i), $MachinePrecision] + N[(z + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, 3.9e-179], t$95$1, If[LessEqual[a, 1.1e-121], N[(N[(y * i), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.3e-63], t$95$1, If[LessEqual[a, 4.4e+33], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.2e+99], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(t + a), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < 3.9000000000000003e-179 or 1.10000000000000011e-121 < a < 9.30000000000000007e-63

   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 89.0%

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

      1. associate-+r+ 89.0%

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

      2. sub-neg 89.0%

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

      3. metadata-eval 89.0%

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

      4. +-commutative 89.0%

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

      5. fma-def 89.0%

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

      6. +-commutative 89.0%

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

   4. Simplified 89.0%

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

   5. Taylor expanded in a around 0 77.8%

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

      1. +-commutative 77.8%

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

      2. sub-neg 77.8%

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

      3. metadata-eval 77.8%

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

      4. +-commutative 77.8%

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

      5. distribute-rgt-out 77.8%

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

      6. +-commutative 77.8%

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

      7. distribute-rgt-in 77.8%

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

      8. fma-def 77.8%

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

   7. Simplified 77.8%

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

   8. Taylor expanded in z around inf 58.6%

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

   if 3.9000000000000003e-179 < a < 1.10000000000000011e-121

   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 c around inf 99.6%

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

   3. Taylor expanded in b around inf 52.2%

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

      1. *-commutative 52.2%

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

      2. associate-*r* 52.2%

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

      3. log-rec 52.2%

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

      4. neg-mul-1 52.2%

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

      5. associate-*r* 52.2%

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

      6. metadata-eval 52.2%

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

      7. *-lft-identity 52.2%

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

   5. Simplified 52.2%

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

   if 9.30000000000000007e-63 < a < 4.39999999999999988e33

   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 inf 58.2%

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

   if 4.39999999999999988e33 < a < 4.2000000000000002e99

   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 51.8%

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

   if 4.2000000000000002e99 < 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 x around 0 85.4%

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

      1. associate-+r+ 85.4%

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

      2. sub-neg 85.4%

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

      3. metadata-eval 85.4%

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

      4. +-commutative 85.4%

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

      5. fma-def 85.4%

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

      6. +-commutative 85.4%

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

   4. Simplified 85.4%

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

   5. Taylor expanded in b around inf 75.5%

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

   6. Taylor expanded in b around 0 65.1%

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

      1. +-commutative 65.1%

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

   8. Simplified 65.1%

      \[\leadsto \color{blue}{\left(t + a\right)} + y \cdot i \]
3. Recombined 5 regimes into one program.

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 3.9 \cdot 10^{-179}:\\ \;\;\;\;y \cdot i + \left(z + t\right)\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-121}:\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{elif}\;a \leq 9.3 \cdot 10^{-63}:\\ \;\;\;\;y \cdot i + \left(z + t\right)\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+99}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t + a\right)\\ \end{array} \]

Alternative 7: 57.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+214}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;z \leq -5 \cdot 10^{+187} \lor \neg \left(z \leq -2 \cdot 10^{+135}\right):\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -1.5e+214)
   (+ z (* y i))
   (if (or (<= z -5e+187) (not (<= z -2e+135)))
     (+ (* y i) (+ a (* b (log c))))
     (+ (* y i) (+ z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -1.5e+214) {
		tmp = z + (y * i);
	} else if ((z <= -5e+187) || !(z <= -2e+135)) {
		tmp = (y * i) + (a + (b * log(c)));
	} else {
		tmp = (y * i) + (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 (z <= (-1.5d+214)) then
        tmp = z + (y * i)
    else if ((z <= (-5d+187)) .or. (.not. (z <= (-2d+135)))) then
        tmp = (y * i) + (a + (b * log(c)))
    else
        tmp = (y * i) + (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 (z <= -1.5e+214) {
		tmp = z + (y * i);
	} else if ((z <= -5e+187) || !(z <= -2e+135)) {
		tmp = (y * i) + (a + (b * Math.log(c)));
	} else {
		tmp = (y * i) + (z + t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -1.5e+214:
		tmp = z + (y * i)
	elif (z <= -5e+187) or not (z <= -2e+135):
		tmp = (y * i) + (a + (b * math.log(c)))
	else:
		tmp = (y * i) + (z + t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -1.5e+214)
		tmp = Float64(z + Float64(y * i));
	elseif ((z <= -5e+187) || !(z <= -2e+135))
		tmp = Float64(Float64(y * i) + Float64(a + Float64(b * log(c))));
	else
		tmp = Float64(Float64(y * i) + Float64(z + t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -1.5e+214)
		tmp = z + (y * i);
	elseif ((z <= -5e+187) || ~((z <= -2e+135)))
		tmp = (y * i) + (a + (b * log(c)));
	else
		tmp = (y * i) + (z + t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -1.5e+214], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -5e+187], N[Not[LessEqual[z, -2e+135]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(a + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(z + t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.5000000000000001e214

   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 z around inf 73.3%

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

   if -1.5000000000000001e214 < z < -5.0000000000000001e187 or -1.99999999999999992e135 < 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 x around 0 85.8%

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

      1. associate-+r+ 85.8%

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

      2. sub-neg 85.8%

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

      3. metadata-eval 85.8%

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

      4. +-commutative 85.8%

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

      5. fma-def 85.8%

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

      6. +-commutative 85.8%

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

   4. Simplified 85.8%

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

   5. Taylor expanded in b around inf 69.7%

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

   6. Taylor expanded in t around 0 52.1%

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

      1. *-commutative 52.1%

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

   8. Simplified 52.1%

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

   if -5.0000000000000001e187 < z < -1.99999999999999992e135

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 99.9%

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

      1. associate-+r+ 99.9%

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

      2. sub-neg 99.9%

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

      3. metadata-eval 99.9%

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

      4. +-commutative 99.9%

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

      5. fma-def 99.9%

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

      6. +-commutative 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in a around 0 85.7%

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

      1. +-commutative 85.7%

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

      2. sub-neg 85.7%

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

      3. metadata-eval 85.7%

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

      4. +-commutative 85.7%

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

      5. distribute-rgt-out 85.7%

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

      6. +-commutative 85.7%

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

      7. distribute-rgt-in 85.7%

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

      8. fma-def 85.7%

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

   7. Simplified 85.7%

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

   8. Taylor expanded in z around inf 71.0%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+214}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;z \leq -5 \cdot 10^{+187} \lor \neg \left(z \leq -2 \cdot 10^{+135}\right):\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + t\right)\\ \end{array} \]

Alternative 8: 72.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2.6 \cdot 10^{+175}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + \left(b - 0.5\right) \cdot \log c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x 2.6e+175)
   (+ (* y i) (+ a (+ z (* (- b 0.5) (log c)))))
   (+ (* x (log y)) (* y i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= 2.6e+175) {
		tmp = (y * i) + (a + (z + ((b - 0.5) * log(c))));
	} else {
		tmp = (x * log(y)) + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (x <= 2.6d+175) then
        tmp = (y * i) + (a + (z + ((b - 0.5d0) * log(c))))
    else
        tmp = (x * log(y)) + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= 2.6e+175) {
		tmp = (y * i) + (a + (z + ((b - 0.5) * Math.log(c))));
	} else {
		tmp = (x * Math.log(y)) + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if x <= 2.6e+175:
		tmp = (y * i) + (a + (z + ((b - 0.5) * math.log(c))))
	else:
		tmp = (x * math.log(y)) + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= 2.6e+175)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + Float64(Float64(b - 0.5) * log(c)))));
	else
		tmp = Float64(Float64(x * log(y)) + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (x <= 2.6e+175)
		tmp = (y * i) + (a + (z + ((b - 0.5) * log(c))));
	else
		tmp = (x * log(y)) + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, 2.6e+175], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2.6e175

   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 92.6%

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

      1. associate-+r+ 92.6%

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

      2. sub-neg 92.6%

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

      3. metadata-eval 92.6%

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

      4. +-commutative 92.6%

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

      5. fma-def 92.6%

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

      6. +-commutative 92.6%

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

   4. Simplified 92.6%

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

   5. Taylor expanded in t around 0 74.1%

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

   if 2.6e175 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 85.0%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2.6 \cdot 10^{+175}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + \left(b - 0.5\right) \cdot \log c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \end{array} \]

Alternative 9: 59.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 9.5 \cdot 10^{+97}:\\ \;\;\;\;z + \left(y \cdot i + \left(b - 0.5\right) \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 9.5e+97)
   (+ z (+ (* y i) (* (- b 0.5) (log c))))
   (+ (* 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 (a <= 9.5e+97) {
		tmp = z + ((y * i) + ((b - 0.5) * log(c)));
	} 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 (a <= 9.5d+97) then
        tmp = z + ((y * i) + ((b - 0.5d0) * log(c)))
    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 (a <= 9.5e+97) {
		tmp = z + ((y * i) + ((b - 0.5) * Math.log(c)));
	} 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 a <= 9.5e+97:
		tmp = z + ((y * i) + ((b - 0.5) * math.log(c)))
	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 (a <= 9.5e+97)
		tmp = Float64(z + Float64(Float64(y * i) + Float64(Float64(b - 0.5) * log(c))));
	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 (a <= 9.5e+97)
		tmp = z + ((y * i) + ((b - 0.5) * log(c)));
	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[a, 9.5e+97], N[(z + N[(N[(y * i), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $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 a < 9.49999999999999975e97

   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 87.0%

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

      1. associate-+r+ 87.0%

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

      2. sub-neg 87.0%

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

      3. metadata-eval 87.0%

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

      4. +-commutative 87.0%

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

      5. fma-def 87.0%

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

      6. +-commutative 87.0%

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

   4. Simplified 87.0%

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

   5. Taylor expanded in a around 0 77.8%

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

      1. +-commutative 77.8%

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

      2. sub-neg 77.8%

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

      3. metadata-eval 77.8%

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

      4. +-commutative 77.8%

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

      5. distribute-rgt-out 77.8%

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

      6. +-commutative 77.8%

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

      7. distribute-rgt-in 77.8%

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

      8. fma-def 77.8%

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

   7. Simplified 77.8%

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

   8. Taylor expanded in t around 0 59.2%

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

   if 9.49999999999999975e97 < 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 x around 0 85.4%

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

      1. associate-+r+ 85.4%

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

      2. sub-neg 85.4%

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

      3. metadata-eval 85.4%

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

      4. +-commutative 85.4%

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

      5. fma-def 85.4%

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

      6. +-commutative 85.4%

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

   4. Simplified 85.4%

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

   5. Taylor expanded in b around inf 75.5%

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

   6. Taylor expanded in t around 0 65.8%

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

      1. *-commutative 65.8%

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

   8. Simplified 65.8%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 9.5 \cdot 10^{+97}:\\ \;\;\;\;z + \left(y \cdot i + \left(b - 0.5\right) \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \end{array} \]

Alternative 10: 61.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 1.6 \cdot 10^{+98}:\\ \;\;\;\;z + \left(y \cdot i + \left(b - 0.5\right) \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(t + a\right) + b \cdot \log c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 1.6e+98)
   (+ z (+ (* y i) (* (- b 0.5) (log c))))
   (+ (* y i) (+ (+ t 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 (a <= 1.6e+98) {
		tmp = z + ((y * i) + ((b - 0.5) * log(c)));
	} else {
		tmp = (y * i) + ((t + 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 (a <= 1.6d+98) then
        tmp = z + ((y * i) + ((b - 0.5d0) * log(c)))
    else
        tmp = (y * i) + ((t + 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 (a <= 1.6e+98) {
		tmp = z + ((y * i) + ((b - 0.5) * Math.log(c)));
	} else {
		tmp = (y * i) + ((t + a) + (b * Math.log(c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 1.6e+98:
		tmp = z + ((y * i) + ((b - 0.5) * math.log(c)))
	else:
		tmp = (y * i) + ((t + a) + (b * math.log(c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 1.6e+98)
		tmp = Float64(z + Float64(Float64(y * i) + Float64(Float64(b - 0.5) * log(c))));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(t + 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 (a <= 1.6e+98)
		tmp = z + ((y * i) + ((b - 0.5) * log(c)));
	else
		tmp = (y * i) + ((t + a) + (b * log(c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 1.6e+98], N[(z + N[(N[(y * i), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(t + a), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 1.6000000000000001e98

   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 87.0%

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

      1. associate-+r+ 87.0%

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

      2. sub-neg 87.0%

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

      3. metadata-eval 87.0%

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

      4. +-commutative 87.0%

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

      5. fma-def 87.0%

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

      6. +-commutative 87.0%

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

   4. Simplified 87.0%

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

   5. Taylor expanded in a around 0 77.8%

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

      1. +-commutative 77.8%

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

      2. sub-neg 77.8%

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

      3. metadata-eval 77.8%

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

      4. +-commutative 77.8%

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

      5. distribute-rgt-out 77.8%

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

      6. +-commutative 77.8%

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

      7. distribute-rgt-in 77.8%

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

      8. fma-def 77.8%

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

   7. Simplified 77.8%

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

   8. Taylor expanded in t around 0 59.2%

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

   if 1.6000000000000001e98 < 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 x around 0 85.4%

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

      1. associate-+r+ 85.4%

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

      2. sub-neg 85.4%

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

      3. metadata-eval 85.4%

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

      4. +-commutative 85.4%

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

      5. fma-def 85.4%

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

      6. +-commutative 85.4%

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

   4. Simplified 85.4%

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

   5. Taylor expanded in b around inf 75.5%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.6 \cdot 10^{+98}:\\ \;\;\;\;z + \left(y \cdot i + \left(b - 0.5\right) \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(t + a\right) + b \cdot \log c\right)\\ \end{array} \]

Alternative 11: 56.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 1.72 \cdot 10^{-62}:\\ \;\;\;\;y \cdot i + \left(z + t\right)\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+32}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{+100}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t + a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 1.72e-62)
   (+ (* y i) (+ z t))
   (if (<= a 3.6e+32)
     (+ (* x (log y)) (* y i))
     (if (<= a 5.6e+100) (+ z (* y i)) (+ (* y i) (+ t a))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 1.72e-62) {
		tmp = (y * i) + (z + t);
	} else if (a <= 3.6e+32) {
		tmp = (x * log(y)) + (y * i);
	} else if (a <= 5.6e+100) {
		tmp = z + (y * i);
	} else {
		tmp = (y * i) + (t + 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 <= 1.72d-62) then
        tmp = (y * i) + (z + t)
    else if (a <= 3.6d+32) then
        tmp = (x * log(y)) + (y * i)
    else if (a <= 5.6d+100) then
        tmp = z + (y * i)
    else
        tmp = (y * i) + (t + 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 <= 1.72e-62) {
		tmp = (y * i) + (z + t);
	} else if (a <= 3.6e+32) {
		tmp = (x * Math.log(y)) + (y * i);
	} else if (a <= 5.6e+100) {
		tmp = z + (y * i);
	} else {
		tmp = (y * i) + (t + a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 1.72e-62:
		tmp = (y * i) + (z + t)
	elif a <= 3.6e+32:
		tmp = (x * math.log(y)) + (y * i)
	elif a <= 5.6e+100:
		tmp = z + (y * i)
	else:
		tmp = (y * i) + (t + a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 1.72e-62)
		tmp = Float64(Float64(y * i) + Float64(z + t));
	elseif (a <= 3.6e+32)
		tmp = Float64(Float64(x * log(y)) + Float64(y * i));
	elseif (a <= 5.6e+100)
		tmp = Float64(z + Float64(y * i));
	else
		tmp = Float64(Float64(y * i) + Float64(t + a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 1.72e-62)
		tmp = (y * i) + (z + t);
	elseif (a <= 3.6e+32)
		tmp = (x * log(y)) + (y * i);
	elseif (a <= 5.6e+100)
		tmp = z + (y * i);
	else
		tmp = (y * i) + (t + a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 1.72e-62], N[(N[(y * i), $MachinePrecision] + N[(z + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.6e+32], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.6e+100], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(t + a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < 1.7199999999999999e-62

   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 88.9%

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

      1. associate-+r+ 88.9%

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

      2. sub-neg 88.9%

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

      3. metadata-eval 88.9%

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

      4. +-commutative 88.9%

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

      5. fma-def 88.9%

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

      6. +-commutative 88.9%

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

   4. Simplified 88.9%

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

   5. Taylor expanded in a around 0 78.3%

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

      1. +-commutative 78.3%

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

      2. sub-neg 78.3%

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

      3. metadata-eval 78.3%

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

      4. +-commutative 78.3%

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

      5. distribute-rgt-out 78.3%

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

      6. +-commutative 78.3%

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

      7. distribute-rgt-in 78.3%

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

      8. fma-def 78.3%

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

   7. Simplified 78.3%

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

   8. Taylor expanded in z around inf 58.6%

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

   if 1.7199999999999999e-62 < a < 3.5999999999999997e32

   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 inf 58.2%

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

   if 3.5999999999999997e32 < a < 5.5999999999999996e100

   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 51.8%

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

   if 5.5999999999999996e100 < 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 x around 0 85.4%

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

      1. associate-+r+ 85.4%

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

      2. sub-neg 85.4%

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

      3. metadata-eval 85.4%

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

      4. +-commutative 85.4%

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

      5. fma-def 85.4%

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

      6. +-commutative 85.4%

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

   4. Simplified 85.4%

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

   5. Taylor expanded in b around inf 75.5%

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

   6. Taylor expanded in b around 0 65.1%

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

      1. +-commutative 65.1%

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

   8. Simplified 65.1%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.72 \cdot 10^{-62}:\\ \;\;\;\;y \cdot i + \left(z + t\right)\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+32}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{+100}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t + a\right)\\ \end{array} \]

Alternative 12: 46.0% accurate, 24.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 1.42 \cdot 10^{+100}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t + a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 1.42e+100) (+ z (* y i)) (+ (* y i) (+ t a))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 1.42e+100) {
		tmp = z + (y * i);
	} else {
		tmp = (y * i) + (t + 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 <= 1.42d+100) then
        tmp = z + (y * i)
    else
        tmp = (y * i) + (t + 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 <= 1.42e+100) {
		tmp = z + (y * i);
	} else {
		tmp = (y * i) + (t + a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 1.42e+100:
		tmp = z + (y * i)
	else:
		tmp = (y * i) + (t + a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 1.42e+100)
		tmp = Float64(z + Float64(y * i));
	else
		tmp = Float64(Float64(y * i) + Float64(t + a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 1.42e+100)
		tmp = z + (y * i);
	else
		tmp = (y * i) + (t + a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 1.42e+100], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(t + a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 1.41999999999999999e100

   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 39.7%

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

   if 1.41999999999999999e100 < 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 x around 0 85.4%

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

      1. associate-+r+ 85.4%

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

      2. sub-neg 85.4%

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

      3. metadata-eval 85.4%

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

      4. +-commutative 85.4%

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

      5. fma-def 85.4%

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

      6. +-commutative 85.4%

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

   4. Simplified 85.4%

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

   5. Taylor expanded in b around inf 75.5%

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

   6. Taylor expanded in b around 0 65.1%

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

      1. +-commutative 65.1%

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

   8. Simplified 65.1%

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

4. Final simplification 43.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.42 \cdot 10^{+100}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t + a\right)\\ \end{array} \]

Alternative 13: 59.1% accurate, 24.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 6.6 \cdot 10^{+101}:\\ \;\;\;\;y \cdot i + \left(z + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t + a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 6.6e+101) (+ (* y i) (+ z t)) (+ (* y i) (+ t a))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 6.6e+101) {
		tmp = (y * i) + (z + t);
	} else {
		tmp = (y * i) + (t + a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 6.6d+101) then
        tmp = (y * i) + (z + t)
    else
        tmp = (y * i) + (t + a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 6.6e+101) {
		tmp = (y * i) + (z + t);
	} else {
		tmp = (y * i) + (t + a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 6.6e+101:
		tmp = (y * i) + (z + t)
	else:
		tmp = (y * i) + (t + a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 6.6e+101)
		tmp = Float64(Float64(y * i) + Float64(z + t));
	else
		tmp = Float64(Float64(y * i) + Float64(t + a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 6.6e+101)
		tmp = (y * i) + (z + t);
	else
		tmp = (y * i) + (t + a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 6.6e+101], N[(N[(y * i), $MachinePrecision] + N[(z + t), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(t + a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 6.60000000000000022e101

   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 87.0%

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

      1. associate-+r+ 87.0%

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

      2. sub-neg 87.0%

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

      3. metadata-eval 87.0%

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

      4. +-commutative 87.0%

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

      5. fma-def 87.0%

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

      6. +-commutative 87.0%

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

   4. Simplified 87.0%

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

   5. Taylor expanded in a around 0 77.8%

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

      1. +-commutative 77.8%

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

      2. sub-neg 77.8%

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

      3. metadata-eval 77.8%

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

      4. +-commutative 77.8%

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

      5. distribute-rgt-out 77.8%

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

      6. +-commutative 77.8%

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

      7. distribute-rgt-in 77.8%

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

      8. fma-def 77.8%

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

   7. Simplified 77.8%

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

   8. Taylor expanded in z around inf 57.5%

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

   if 6.60000000000000022e101 < 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 x around 0 85.4%

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

      1. associate-+r+ 85.4%

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

      2. sub-neg 85.4%

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

      3. metadata-eval 85.4%

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

      4. +-commutative 85.4%

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

      5. fma-def 85.4%

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

      6. +-commutative 85.4%

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

   4. Simplified 85.4%

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

   5. Taylor expanded in b around inf 75.5%

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

   6. Taylor expanded in b around 0 65.1%

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

      1. +-commutative 65.1%

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

   8. Simplified 65.1%

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

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 6.6 \cdot 10^{+101}:\\ \;\;\;\;y \cdot i + \left(z + t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t + a\right)\\ \end{array} \]

Alternative 14: 41.4% accurate, 31.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+134}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -5.5e+134) z (+ 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 <= -5.5e+134) {
		tmp = z;
	} 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 <= (-5.5d+134)) then
        tmp = z
    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 <= -5.5e+134) {
		tmp = z;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -5.5e+134:
		tmp = z
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -5.5e+134)
		tmp = z;
	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 <= -5.5e+134)
		tmp = z;
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -5.5e+134], z, N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.4999999999999999e134

   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 57.0%

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

   3. Taylor expanded in z around inf 37.5%

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

   if -5.4999999999999999e134 < 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 36.2%

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

4. Final simplification 36.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+134}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]

Alternative 15: 44.3% accurate, 31.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 4.9 \cdot 10^{+101}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 4.9e+101) (+ z (* y i)) (+ a (* y i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 4.9e+101) {
		tmp = z + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 4.9d+101) then
        tmp = z + (y * i)
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 4.9e+101) {
		tmp = z + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 4.9e+101:
		tmp = z + (y * i)
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 4.9e+101)
		tmp = Float64(z + Float64(y * i));
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 4.9e+101)
		tmp = z + (y * i);
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 4.9e+101], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 4.89999999999999983e101

   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 39.7%

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

   if 4.89999999999999983e101 < 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 55.4%

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

4. Final simplification 42.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 4.9 \cdot 10^{+101}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]

Alternative 16: 31.3% accurate, 43.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.52 \cdot 10^{+33}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (if (<= y 2.52e+33) z (* y i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 2.52e+33) {
		tmp = z;
	} 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 <= 2.52d+33) then
        tmp = z
    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 <= 2.52e+33) {
		tmp = z;
	} else {
		tmp = y * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 2.52e+33:
		tmp = z
	else:
		tmp = y * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 2.52e+33)
		tmp = z;
	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 <= 2.52e+33)
		tmp = z;
	else
		tmp = y * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 2.52e+33], z, N[(y * i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.5200000000000001e33

   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 29.0%

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

   3. Taylor expanded in z around inf 25.9%

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

   if 2.5200000000000001e33 < y

   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 42.9%

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

      1. *-commutative 42.9%

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

   4. Simplified 42.9%

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

4. Final simplification 33.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.52 \cdot 10^{+33}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \]

Alternative 17: 16.6% accurate, 219.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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 z around inf 38.7%

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

3. Taylor expanded in z around inf 18.4%

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

4. Final simplification 18.4%

   \[\leadsto z \]

Reproduce

herbie shell --seed 2023334 
(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)))