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

Percentage Accurate: 99.8% → 99.8%

Time: 17.4s

Alternatives: 22

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. +-commutative 99.9%

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

   2. associate-+r+ 99.9%

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

   3. +-commutative 99.9%

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

   4. associate-+r+ 99.9%

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

   5. +-commutative 99.9%

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

   6. associate-+r+ 99.9%

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

   7. fma-def 99.9%

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

   8. associate-+l+ 99.9%

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

   9. +-commutative 99.9%

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

   10. associate-+r+ 99.9%

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

   11. +-commutative 99.9%

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

   12. associate-+l+ 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 99.8% accurate, 0.7× speedup

Math

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

FPCore

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. +-commutative 99.9%

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

   2. associate-+r+ 99.9%

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

   3. +-commutative 99.9%

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

   4. associate-+r+ 99.9%

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

   5. +-commutative 99.9%

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

   6. associate-+r+ 99.9%

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

   7. fma-def 99.9%

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

   8. associate-+l+ 99.9%

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

   9. +-commutative 99.9%

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

   10. associate-+r+ 99.9%

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

   11. +-commutative 99.9%

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

   12. associate-+l+ 99.9%

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

3. Simplified 99.9%

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

5. Applied egg-rr 99.9%

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

6. Final simplification 99.9%

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

Alternative 3: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

Alternative 4: 95.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+89} \lor \neg \left(x \leq 3.1 \cdot 10^{+135}\right):\\ \;\;\;\;a + \left(t + \left(z + \left(y \cdot i + x \cdot \log y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -4.6e+89) (not (<= x 3.1e+135)))
   (+ a (+ t (+ z (+ (* y i) (* x (log y))))))
   (fma y i (+ a (+ t (+ z (* (log c) (- b 0.5))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -4.6e+89) || !(x <= 3.1e+135)) {
		tmp = a + (t + (z + ((y * i) + (x * log(y)))));
	} else {
		tmp = fma(y, i, (a + (t + (z + (log(c) * (b - 0.5))))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -4.6e+89) || !(x <= 3.1e+135))
		tmp = Float64(a + Float64(t + Float64(z + Float64(Float64(y * i) + Float64(x * log(y))))));
	else
		tmp = fma(y, i, Float64(a + Float64(t + Float64(z + Float64(log(c) * Float64(b - 0.5))))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -4.6e+89], N[Not[LessEqual[x, 3.1e+135]], $MachinePrecision]], N[(a + N[(t + N[(z + N[(N[(y * i), $MachinePrecision] + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * i + N[(a + N[(t + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.5999999999999998e89 or 3.10000000000000022e135 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in b around inf 99.8%

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

      1. *-commutative 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in b around 0 90.9%

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

   if -4.5999999999999998e89 < x < 3.10000000000000022e135

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-+r+ 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+r+ 99.9%

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

      5. +-commutative 99.9%

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

      6. associate-+r+ 99.9%

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

      7. fma-def 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. associate-+r+ 99.9%

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

      11. +-commutative 99.9%

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

      12. associate-+l+ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 98.2%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+89} \lor \neg \left(x \leq 3.1 \cdot 10^{+135}\right):\\ \;\;\;\;a + \left(t + \left(z + \left(y \cdot i + x \cdot \log y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \end{array} \]

Alternative 5: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in b around inf 98.0%

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

   1. *-commutative 98.0%

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

4. Simplified 98.0%

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

5. Final simplification 98.0%

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

Alternative 6: 75.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ t_2 := x \cdot \log y\\ t_3 := \left(z + y \cdot i\right) + \left(a + t\right)\\ \mathbf{if}\;x \leq -2.5 \cdot 10^{+88}:\\ \;\;\;\;t + \left(z + \left(y \cdot i + t_2\right)\right)\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-184}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-268}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+36}:\\ \;\;\;\;t + \left(a + \mathsf{fma}\left(i, y, z\right)\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+115}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+123}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;a + \left(t_2 + \left(z + t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (+ t (+ z (* (log c) (- b 0.5))))))
        (t_2 (* x (log y)))
        (t_3 (+ (+ z (* y i)) (+ a t))))
   (if (<= x -2.5e+88)
     (+ t (+ z (+ (* y i) t_2)))
     (if (<= x -1.5e-184)
       t_3
       (if (<= x 2.05e-268)
         t_1
         (if (<= x 4.4e+36)
           (+ t (+ a (fma i y z)))
           (if (<= x 1.8e+115)
             t_1
             (if (<= x 2.3e+123) t_3 (+ a (+ t_2 (+ z t)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (t + (z + (log(c) * (b - 0.5))));
	double t_2 = x * log(y);
	double t_3 = (z + (y * i)) + (a + t);
	double tmp;
	if (x <= -2.5e+88) {
		tmp = t + (z + ((y * i) + t_2));
	} else if (x <= -1.5e-184) {
		tmp = t_3;
	} else if (x <= 2.05e-268) {
		tmp = t_1;
	} else if (x <= 4.4e+36) {
		tmp = t + (a + fma(i, y, z));
	} else if (x <= 1.8e+115) {
		tmp = t_1;
	} else if (x <= 2.3e+123) {
		tmp = t_3;
	} else {
		tmp = a + (t_2 + (z + t));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(t + Float64(z + Float64(log(c) * Float64(b - 0.5)))))
	t_2 = Float64(x * log(y))
	t_3 = Float64(Float64(z + Float64(y * i)) + Float64(a + t))
	tmp = 0.0
	if (x <= -2.5e+88)
		tmp = Float64(t + Float64(z + Float64(Float64(y * i) + t_2)));
	elseif (x <= -1.5e-184)
		tmp = t_3;
	elseif (x <= 2.05e-268)
		tmp = t_1;
	elseif (x <= 4.4e+36)
		tmp = Float64(t + Float64(a + fma(i, y, z)));
	elseif (x <= 1.8e+115)
		tmp = t_1;
	elseif (x <= 2.3e+123)
		tmp = t_3;
	else
		tmp = Float64(a + Float64(t_2 + Float64(z + t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(t + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision] + N[(a + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.5e+88], N[(t + N[(z + N[(N[(y * i), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.5e-184], t$95$3, If[LessEqual[x, 2.05e-268], t$95$1, If[LessEqual[x, 4.4e+36], N[(t + N[(a + N[(i * y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.8e+115], t$95$1, If[LessEqual[x, 2.3e+123], t$95$3, N[(a + N[(t$95$2 + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -2.49999999999999999e88

   1. Initial program 99.8%

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

   2. Taylor expanded in b around inf 99.8%

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

      1. *-commutative 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in b around 0 85.0%

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

   6. Taylor expanded in a around 0 78.5%

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

   if -2.49999999999999999e88 < x < -1.49999999999999996e-184 or 1.8e115 < x < 2.2999999999999999e123

   1. Initial program 100.0%

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

   2. Taylor expanded in b around inf 97.2%

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

      1. *-commutative 97.2%

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

   4. Simplified 97.2%

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

   5. Taylor expanded in b around 0 88.4%

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

   6. Taylor expanded in x around 0 87.6%

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

      1. associate-+r+ 87.6%

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

      2. +-commutative 87.6%

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

   8. Simplified 87.6%

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

   if -1.49999999999999996e-184 < x < 2.0499999999999999e-268 or 4.40000000000000001e36 < x < 1.8e115

   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 0 97.3%

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

   3. Taylor expanded in i around 0 86.4%

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

   if 2.0499999999999999e-268 < x < 4.40000000000000001e36

   1. Initial program 99.9%

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

   2. Taylor expanded in b around inf 97.8%

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

      1. *-commutative 97.8%

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

   4. Simplified 97.8%

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

   5. Taylor expanded in b around 0 85.4%

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

   6. Taylor expanded in x around 0 85.4%

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

      1. associate-+r+ 85.4%

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

      2. +-commutative 85.4%

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

      3. associate-+l+ 85.4%

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

      4. +-commutative 85.4%

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

      5. fma-def 85.5%

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

   8. Simplified 85.5%

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

   if 2.2999999999999999e123 < x

   1. Initial program 99.7%

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

   2. Taylor expanded in b around inf 99.7%

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

      1. *-commutative 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in b around 0 91.5%

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

   6. Taylor expanded in i around 0 83.8%

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

      1. +-commutative 83.8%

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

      2. associate-+r+ 83.8%

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

   8. Simplified 83.8%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+88}:\\ \;\;\;\;t + \left(z + \left(y \cdot i + x \cdot \log y\right)\right)\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-184}:\\ \;\;\;\;\left(z + y \cdot i\right) + \left(a + t\right)\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-268}:\\ \;\;\;\;a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+36}:\\ \;\;\;\;t + \left(a + \mathsf{fma}\left(i, y, z\right)\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+115}:\\ \;\;\;\;a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+123}:\\ \;\;\;\;\left(z + y \cdot i\right) + \left(a + t\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(x \cdot \log y + \left(z + t\right)\right)\\ \end{array} \]

Alternative 7: 72.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ t_2 := a + \left(x \cdot \log y + \left(z + t\right)\right)\\ \mathbf{if}\;i \leq -1.05 \cdot 10^{+27}:\\ \;\;\;\;\left(z + y \cdot i\right) + \left(a + t\right)\\ \mathbf{elif}\;i \leq -4.9 \cdot 10^{-163}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -6.8 \cdot 10^{-234}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 6.8 \cdot 10^{-44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 5.4 \cdot 10^{+80}:\\ \;\;\;\;a + t_1\\ \mathbf{else}:\\ \;\;\;\;t + \left(a + \mathsf{fma}\left(i, y, z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ t (+ z (* (log c) (- b 0.5)))))
        (t_2 (+ a (+ (* x (log y)) (+ z t)))))
   (if (<= i -1.05e+27)
     (+ (+ z (* y i)) (+ a t))
     (if (<= i -4.9e-163)
       t_2
       (if (<= i -6.8e-234)
         t_1
         (if (<= i 6.8e-44)
           t_2
           (if (<= i 5.4e+80) (+ a t_1) (+ t (+ a (fma i y z))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = t + (z + (log(c) * (b - 0.5)));
	double t_2 = a + ((x * log(y)) + (z + t));
	double tmp;
	if (i <= -1.05e+27) {
		tmp = (z + (y * i)) + (a + t);
	} else if (i <= -4.9e-163) {
		tmp = t_2;
	} else if (i <= -6.8e-234) {
		tmp = t_1;
	} else if (i <= 6.8e-44) {
		tmp = t_2;
	} else if (i <= 5.4e+80) {
		tmp = a + t_1;
	} else {
		tmp = t + (a + fma(i, y, z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(t + Float64(z + Float64(log(c) * Float64(b - 0.5))))
	t_2 = Float64(a + Float64(Float64(x * log(y)) + Float64(z + t)))
	tmp = 0.0
	if (i <= -1.05e+27)
		tmp = Float64(Float64(z + Float64(y * i)) + Float64(a + t));
	elseif (i <= -4.9e-163)
		tmp = t_2;
	elseif (i <= -6.8e-234)
		tmp = t_1;
	elseif (i <= 6.8e-44)
		tmp = t_2;
	elseif (i <= 5.4e+80)
		tmp = Float64(a + t_1);
	else
		tmp = Float64(t + Float64(a + fma(i, y, z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(t + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.05e+27], N[(N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision] + N[(a + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -4.9e-163], t$95$2, If[LessEqual[i, -6.8e-234], t$95$1, If[LessEqual[i, 6.8e-44], t$95$2, If[LessEqual[i, 5.4e+80], N[(a + t$95$1), $MachinePrecision], N[(t + N[(a + N[(i * y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -1.04999999999999997e27

   1. Initial program 99.9%

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

   2. Taylor expanded in b around inf 98.4%

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

      1. *-commutative 98.4%

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

   4. Simplified 98.4%

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

   5. Taylor expanded in b around 0 87.4%

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

   6. Taylor expanded in x around 0 78.4%

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

      1. associate-+r+ 78.4%

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

      2. +-commutative 78.4%

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

   8. Simplified 78.4%

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

   if -1.04999999999999997e27 < i < -4.9000000000000003e-163 or -6.79999999999999971e-234 < i < 6.80000000000000033e-44

   1. Initial program 99.8%

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

   2. Taylor expanded in b around inf 99.0%

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

      1. *-commutative 99.0%

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

   4. Simplified 99.0%

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

   5. Taylor expanded in b around 0 89.1%

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

   6. Taylor expanded in i around 0 84.6%

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

      1. +-commutative 84.6%

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

      2. associate-+r+ 84.6%

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

   8. Simplified 84.6%

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

   if -4.9000000000000003e-163 < i < -6.79999999999999971e-234

   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 88.4%

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

   3. Taylor expanded in a around 0 88.4%

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

   4. Taylor expanded in i around 0 88.4%

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

   if 6.80000000000000033e-44 < i < 5.39999999999999966e80

   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 81.3%

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

   3. Taylor expanded in i around 0 74.5%

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

   if 5.39999999999999966e80 < i

   1. Initial program 99.9%

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

   2. Taylor expanded in b around inf 99.9%

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

      1. *-commutative 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in b around 0 92.4%

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

   6. Taylor expanded in x around 0 87.4%

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

      1. associate-+r+ 87.4%

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

      2. +-commutative 87.4%

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

      3. associate-+l+ 87.4%

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

      4. +-commutative 87.4%

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

      5. fma-def 87.4%

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

   8. Simplified 87.4%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.05 \cdot 10^{+27}:\\ \;\;\;\;\left(z + y \cdot i\right) + \left(a + t\right)\\ \mathbf{elif}\;i \leq -4.9 \cdot 10^{-163}:\\ \;\;\;\;a + \left(x \cdot \log y + \left(z + t\right)\right)\\ \mathbf{elif}\;i \leq -6.8 \cdot 10^{-234}:\\ \;\;\;\;t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{elif}\;i \leq 6.8 \cdot 10^{-44}:\\ \;\;\;\;a + \left(x \cdot \log y + \left(z + t\right)\right)\\ \mathbf{elif}\;i \leq 5.4 \cdot 10^{+80}:\\ \;\;\;\;a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t + \left(a + \mathsf{fma}\left(i, y, z\right)\right)\\ \end{array} \]

Alternative 8: 95.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+95} \lor \neg \left(x \leq 6.3 \cdot 10^{+133}\right):\\ \;\;\;\;a + \left(t + \left(z + \left(y \cdot i + x \cdot \log y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + \left(y \cdot i + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -1.7e+95) (not (<= x 6.3e+133)))
   (+ a (+ t (+ z (+ (* y i) (* x (log y))))))
   (+ a (+ t (+ z (+ (* y i) (* (log c) (- b 0.5))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1.7e+95) || !(x <= 6.3e+133)) {
		tmp = a + (t + (z + ((y * i) + (x * log(y)))));
	} else {
		tmp = a + (t + (z + ((y * i) + (log(c) * (b - 0.5)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-1.7d+95)) .or. (.not. (x <= 6.3d+133))) then
        tmp = a + (t + (z + ((y * i) + (x * log(y)))))
    else
        tmp = a + (t + (z + ((y * i) + (log(c) * (b - 0.5d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1.7e+95) || !(x <= 6.3e+133)) {
		tmp = a + (t + (z + ((y * i) + (x * Math.log(y)))));
	} else {
		tmp = a + (t + (z + ((y * i) + (Math.log(c) * (b - 0.5)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -1.7e+95) or not (x <= 6.3e+133):
		tmp = a + (t + (z + ((y * i) + (x * math.log(y)))))
	else:
		tmp = a + (t + (z + ((y * i) + (math.log(c) * (b - 0.5)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -1.7e+95) || !(x <= 6.3e+133))
		tmp = Float64(a + Float64(t + Float64(z + Float64(Float64(y * i) + Float64(x * log(y))))));
	else
		tmp = Float64(a + Float64(t + Float64(z + Float64(Float64(y * i) + Float64(log(c) * Float64(b - 0.5))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -1.7e+95) || ~((x <= 6.3e+133)))
		tmp = a + (t + (z + ((y * i) + (x * log(y)))));
	else
		tmp = a + (t + (z + ((y * i) + (log(c) * (b - 0.5)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -1.7e+95], N[Not[LessEqual[x, 6.3e+133]], $MachinePrecision]], N[(a + N[(t + N[(z + N[(N[(y * i), $MachinePrecision] + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(t + N[(z + N[(N[(y * i), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.70000000000000011e95 or 6.30000000000000049e133 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in b around inf 99.8%

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

      1. *-commutative 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in b around 0 90.9%

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

   if -1.70000000000000011e95 < x < 6.30000000000000049e133

   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 98.2%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+95} \lor \neg \left(x \leq 6.3 \cdot 10^{+133}\right):\\ \;\;\;\;a + \left(t + \left(z + \left(y \cdot i + x \cdot \log y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + \left(y \cdot i + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \end{array} \]

Alternative 9: 72.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \left(x \cdot \log y + \left(z + t\right)\right)\\ \mathbf{if}\;i \leq -1.4 \cdot 10^{+25}:\\ \;\;\;\;\left(z + y \cdot i\right) + \left(a + t\right)\\ \mathbf{elif}\;i \leq -2.3 \cdot 10^{-159}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -1.9 \cdot 10^{-233}:\\ \;\;\;\;t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{elif}\;i \leq 9.5 \cdot 10^{+77}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \left(a + \mathsf{fma}\left(i, y, z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (+ (* x (log y)) (+ z t)))))
   (if (<= i -1.4e+25)
     (+ (+ z (* y i)) (+ a t))
     (if (<= i -2.3e-159)
       t_1
       (if (<= i -1.9e-233)
         (+ t (+ z (* (log c) (- b 0.5))))
         (if (<= i 9.5e+77) t_1 (+ t (+ a (fma i y z)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + ((x * log(y)) + (z + t));
	double tmp;
	if (i <= -1.4e+25) {
		tmp = (z + (y * i)) + (a + t);
	} else if (i <= -2.3e-159) {
		tmp = t_1;
	} else if (i <= -1.9e-233) {
		tmp = t + (z + (log(c) * (b - 0.5)));
	} else if (i <= 9.5e+77) {
		tmp = t_1;
	} else {
		tmp = t + (a + fma(i, y, z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(Float64(x * log(y)) + Float64(z + t)))
	tmp = 0.0
	if (i <= -1.4e+25)
		tmp = Float64(Float64(z + Float64(y * i)) + Float64(a + t));
	elseif (i <= -2.3e-159)
		tmp = t_1;
	elseif (i <= -1.9e-233)
		tmp = Float64(t + Float64(z + Float64(log(c) * Float64(b - 0.5))));
	elseif (i <= 9.5e+77)
		tmp = t_1;
	else
		tmp = Float64(t + Float64(a + fma(i, y, z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.4e+25], N[(N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision] + N[(a + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -2.3e-159], t$95$1, If[LessEqual[i, -1.9e-233], N[(t + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 9.5e+77], t$95$1, N[(t + N[(a + N[(i * y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -1.4000000000000001e25

   1. Initial program 99.9%

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

   2. Taylor expanded in b around inf 98.4%

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

      1. *-commutative 98.4%

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

   4. Simplified 98.4%

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

   5. Taylor expanded in b around 0 87.4%

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

   6. Taylor expanded in x around 0 78.4%

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

      1. associate-+r+ 78.4%

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

      2. +-commutative 78.4%

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

   8. Simplified 78.4%

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

   if -1.4000000000000001e25 < i < -2.29999999999999978e-159 or -1.9e-233 < i < 9.4999999999999998e77

   1. Initial program 99.8%

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

   2. Taylor expanded in b around inf 99.1%

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

      1. *-commutative 99.1%

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

   4. Simplified 99.1%

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

   5. Taylor expanded in b around 0 84.3%

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

   6. Taylor expanded in i around 0 79.7%

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

      1. +-commutative 79.7%

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

      2. associate-+r+ 79.7%

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

   8. Simplified 79.7%

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

   if -2.29999999999999978e-159 < i < -1.9e-233

   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 88.4%

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

   3. Taylor expanded in a around 0 88.4%

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

   4. Taylor expanded in i around 0 88.4%

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

   if 9.4999999999999998e77 < i

   1. Initial program 99.9%

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

   2. Taylor expanded in b around inf 99.9%

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

      1. *-commutative 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in b around 0 92.4%

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

   6. Taylor expanded in x around 0 87.4%

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

      1. associate-+r+ 87.4%

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

      2. +-commutative 87.4%

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

      3. associate-+l+ 87.4%

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

      4. +-commutative 87.4%

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

      5. fma-def 87.4%

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

   8. Simplified 87.4%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.4 \cdot 10^{+25}:\\ \;\;\;\;\left(z + y \cdot i\right) + \left(a + t\right)\\ \mathbf{elif}\;i \leq -2.3 \cdot 10^{-159}:\\ \;\;\;\;a + \left(x \cdot \log y + \left(z + t\right)\right)\\ \mathbf{elif}\;i \leq -1.9 \cdot 10^{-233}:\\ \;\;\;\;t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{elif}\;i \leq 9.5 \cdot 10^{+77}:\\ \;\;\;\;a + \left(x \cdot \log y + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t + \left(a + \mathsf{fma}\left(i, y, z\right)\right)\\ \end{array} \]

Alternative 10: 87.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{+214} \lor \neg \left(b \leq 1.5 \cdot 10^{+56}\right):\\ \;\;\;\;z + \left(y \cdot i + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + \left(y \cdot i + x \cdot \log y\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= b -7.2e+214) (not (<= b 1.5e+56)))
   (+ z (+ (* y i) (* (log c) (- b 0.5))))
   (+ a (+ t (+ z (+ (* y i) (* x (log y))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((b <= -7.2e+214) || !(b <= 1.5e+56)) {
		tmp = z + ((y * i) + (log(c) * (b - 0.5)));
	} else {
		tmp = a + (t + (z + ((y * i) + (x * log(y)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((b <= (-7.2d+214)) .or. (.not. (b <= 1.5d+56))) then
        tmp = z + ((y * i) + (log(c) * (b - 0.5d0)))
    else
        tmp = a + (t + (z + ((y * i) + (x * log(y)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((b <= -7.2e+214) || !(b <= 1.5e+56)) {
		tmp = z + ((y * i) + (Math.log(c) * (b - 0.5)));
	} else {
		tmp = a + (t + (z + ((y * i) + (x * Math.log(y)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (b <= -7.2e+214) or not (b <= 1.5e+56):
		tmp = z + ((y * i) + (math.log(c) * (b - 0.5)))
	else:
		tmp = a + (t + (z + ((y * i) + (x * math.log(y)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((b <= -7.2e+214) || !(b <= 1.5e+56))
		tmp = Float64(z + Float64(Float64(y * i) + Float64(log(c) * Float64(b - 0.5))));
	else
		tmp = Float64(a + Float64(t + Float64(z + Float64(Float64(y * i) + Float64(x * log(y))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((b <= -7.2e+214) || ~((b <= 1.5e+56)))
		tmp = z + ((y * i) + (log(c) * (b - 0.5)));
	else
		tmp = a + (t + (z + ((y * i) + (x * log(y)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[b, -7.2e+214], N[Not[LessEqual[b, 1.5e+56]], $MachinePrecision]], N[(z + N[(N[(y * i), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(t + N[(z + N[(N[(y * i), $MachinePrecision] + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -7.2000000000000002e214 or 1.50000000000000003e56 < b

   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 90.7%

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

   3. Taylor expanded in a around 0 79.2%

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

   4. Taylor expanded in t around 0 70.5%

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

   if -7.2000000000000002e214 < b < 1.50000000000000003e56

   1. Initial program 99.9%

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

   2. Taylor expanded in b around inf 97.3%

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

      1. *-commutative 97.3%

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

   4. Simplified 97.3%

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

   5. Taylor expanded in b around 0 95.8%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{+214} \lor \neg \left(b \leq 1.5 \cdot 10^{+56}\right):\\ \;\;\;\;z + \left(y \cdot i + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + \left(y \cdot i + x \cdot \log y\right)\right)\right)\\ \end{array} \]

Alternative 11: 83.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.3 \cdot 10^{+88} \lor \neg \left(x \leq 2.5 \cdot 10^{+132}\right):\\ \;\;\;\;a + \left(t + \left(z + \left(y \cdot i + x \cdot \log y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(z + \left(y \cdot i + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -5.3e+88) (not (<= x 2.5e+132)))
   (+ a (+ t (+ z (+ (* y i) (* x (log y))))))
   (+ a (+ z (+ (* y i) (* (log c) (- b 0.5)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -5.3e+88) || !(x <= 2.5e+132)) {
		tmp = a + (t + (z + ((y * i) + (x * log(y)))));
	} else {
		tmp = a + (z + ((y * i) + (log(c) * (b - 0.5))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-5.3d+88)) .or. (.not. (x <= 2.5d+132))) then
        tmp = a + (t + (z + ((y * i) + (x * log(y)))))
    else
        tmp = a + (z + ((y * i) + (log(c) * (b - 0.5d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -5.3e+88) || !(x <= 2.5e+132)) {
		tmp = a + (t + (z + ((y * i) + (x * Math.log(y)))));
	} else {
		tmp = a + (z + ((y * i) + (Math.log(c) * (b - 0.5))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -5.3e+88) or not (x <= 2.5e+132):
		tmp = a + (t + (z + ((y * i) + (x * math.log(y)))))
	else:
		tmp = a + (z + ((y * i) + (math.log(c) * (b - 0.5))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -5.3e+88) || !(x <= 2.5e+132))
		tmp = Float64(a + Float64(t + Float64(z + Float64(Float64(y * i) + Float64(x * log(y))))));
	else
		tmp = Float64(a + Float64(z + Float64(Float64(y * i) + Float64(log(c) * Float64(b - 0.5)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -5.3e+88) || ~((x <= 2.5e+132)))
		tmp = a + (t + (z + ((y * i) + (x * log(y)))));
	else
		tmp = a + (z + ((y * i) + (log(c) * (b - 0.5))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -5.3e+88], N[Not[LessEqual[x, 2.5e+132]], $MachinePrecision]], N[(a + N[(t + N[(z + N[(N[(y * i), $MachinePrecision] + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(z + N[(N[(y * i), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.29999999999999987e88 or 2.5000000000000001e132 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in b around inf 99.8%

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

      1. *-commutative 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in b around 0 90.9%

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

   if -5.29999999999999987e88 < x < 2.5000000000000001e132

   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 98.2%

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

   3. Taylor expanded in t around 0 83.8%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.3 \cdot 10^{+88} \lor \neg \left(x \leq 2.5 \cdot 10^{+132}\right):\\ \;\;\;\;a + \left(t + \left(z + \left(y \cdot i + x \cdot \log y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(z + \left(y \cdot i + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \end{array} \]

Alternative 12: 62.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 2.1 \cdot 10^{+17}:\\ \;\;\;\;z + \left(y \cdot i + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+174}:\\ \;\;\;\;t + \left(z + \left(y \cdot i + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + y \cdot i\right) + \left(a + t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 2.1e+17)
   (+ z (+ (* y i) (* (log c) (- b 0.5))))
   (if (<= a 1.55e+174)
     (+ t (+ z (+ (* y i) (* x (log y)))))
     (+ (+ z (* y i)) (+ a t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 2.1e+17) {
		tmp = z + ((y * i) + (log(c) * (b - 0.5)));
	} else if (a <= 1.55e+174) {
		tmp = t + (z + ((y * i) + (x * log(y))));
	} else {
		tmp = (z + (y * i)) + (a + 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 (a <= 2.1d+17) then
        tmp = z + ((y * i) + (log(c) * (b - 0.5d0)))
    else if (a <= 1.55d+174) then
        tmp = t + (z + ((y * i) + (x * log(y))))
    else
        tmp = (z + (y * i)) + (a + 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 (a <= 2.1e+17) {
		tmp = z + ((y * i) + (Math.log(c) * (b - 0.5)));
	} else if (a <= 1.55e+174) {
		tmp = t + (z + ((y * i) + (x * Math.log(y))));
	} else {
		tmp = (z + (y * i)) + (a + t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 2.1e+17:
		tmp = z + ((y * i) + (math.log(c) * (b - 0.5)))
	elif a <= 1.55e+174:
		tmp = t + (z + ((y * i) + (x * math.log(y))))
	else:
		tmp = (z + (y * i)) + (a + t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 2.1e+17)
		tmp = Float64(z + Float64(Float64(y * i) + Float64(log(c) * Float64(b - 0.5))));
	elseif (a <= 1.55e+174)
		tmp = Float64(t + Float64(z + Float64(Float64(y * i) + Float64(x * log(y)))));
	else
		tmp = Float64(Float64(z + Float64(y * i)) + Float64(a + t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 2.1e+17)
		tmp = z + ((y * i) + (log(c) * (b - 0.5)));
	elseif (a <= 1.55e+174)
		tmp = t + (z + ((y * i) + (x * log(y))));
	else
		tmp = (z + (y * i)) + (a + t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 2.1e+17], N[(z + N[(N[(y * i), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.55e+174], N[(t + N[(z + N[(N[(y * i), $MachinePrecision] + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision] + N[(a + t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < 2.1e17

   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 84.7%

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

   3. Taylor expanded in a around 0 74.7%

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

   4. Taylor expanded in t around 0 60.9%

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

   if 2.1e17 < a < 1.55e174

   1. Initial program 99.7%

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

   2. Taylor expanded in b around inf 99.7%

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

      1. *-commutative 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in b around 0 93.7%

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

   6. Taylor expanded in a around 0 84.3%

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

   if 1.55e174 < a

   1. Initial program 100.0%

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

   2. Taylor expanded in b around inf 100.0%

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

      1. *-commutative 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in b around 0 100.0%

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

   6. Taylor expanded in x around 0 95.1%

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

      1. associate-+r+ 95.1%

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

      2. +-commutative 95.1%

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

   8. Simplified 95.1%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 2.1 \cdot 10^{+17}:\\ \;\;\;\;z + \left(y \cdot i + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+174}:\\ \;\;\;\;t + \left(z + \left(y \cdot i + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + y \cdot i\right) + \left(a + t\right)\\ \end{array} \]

Alternative 13: 73.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+197} \lor \neg \left(x \leq 3.5 \cdot 10^{+197}\right):\\ \;\;\;\;a + x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;t + \left(a + \mathsf{fma}\left(i, y, z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -1.35e+197) (not (<= x 3.5e+197)))
   (+ a (* x (log y)))
   (+ t (+ a (fma i y z)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1.35e+197) || !(x <= 3.5e+197)) {
		tmp = a + (x * log(y));
	} else {
		tmp = t + (a + fma(i, y, z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -1.35e+197) || !(x <= 3.5e+197))
		tmp = Float64(a + Float64(x * log(y)));
	else
		tmp = Float64(t + Float64(a + fma(i, y, z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -1.35e+197], N[Not[LessEqual[x, 3.5e+197]], $MachinePrecision]], N[(a + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(a + N[(i * y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.35e197 or 3.49999999999999999e197 < x

   1. Initial program 99.7%

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

   2. Taylor expanded in b around inf 99.7%

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

      1. *-commutative 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in b around 0 90.8%

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

   6. Taylor expanded in x around inf 70.3%

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

   if -1.35e197 < x < 3.49999999999999999e197

   1. Initial program 99.9%

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

   2. Taylor expanded in b around inf 97.6%

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

      1. *-commutative 97.6%

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

   4. Simplified 97.6%

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

   5. Taylor expanded in b around 0 82.4%

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

   6. Taylor expanded in x around 0 77.7%

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

      1. associate-+r+ 77.7%

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

      2. +-commutative 77.7%

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

      3. associate-+l+ 77.7%

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

      4. +-commutative 77.7%

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

      5. fma-def 77.7%

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

   8. Simplified 77.7%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+197} \lor \neg \left(x \leq 3.5 \cdot 10^{+197}\right):\\ \;\;\;\;a + x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;t + \left(a + \mathsf{fma}\left(i, y, z\right)\right)\\ \end{array} \]

Alternative 14: 73.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+198} \lor \neg \left(x \leq 4.1 \cdot 10^{+197}\right):\\ \;\;\;\;a + x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(z + y \cdot i\right) + \left(a + t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -2.3e+198) (not (<= x 4.1e+197)))
   (+ a (* x (log y)))
   (+ (+ z (* y i)) (+ a t))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -2.3e+198) || !(x <= 4.1e+197)) {
		tmp = a + (x * log(y));
	} else {
		tmp = (z + (y * i)) + (a + t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-2.3d+198)) .or. (.not. (x <= 4.1d+197))) then
        tmp = a + (x * log(y))
    else
        tmp = (z + (y * i)) + (a + t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -2.3e+198) || !(x <= 4.1e+197)) {
		tmp = a + (x * Math.log(y));
	} else {
		tmp = (z + (y * i)) + (a + t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -2.3e+198) or not (x <= 4.1e+197):
		tmp = a + (x * math.log(y))
	else:
		tmp = (z + (y * i)) + (a + t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -2.3e+198) || !(x <= 4.1e+197))
		tmp = Float64(a + Float64(x * log(y)));
	else
		tmp = Float64(Float64(z + Float64(y * i)) + Float64(a + t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -2.3e+198) || ~((x <= 4.1e+197)))
		tmp = a + (x * log(y));
	else
		tmp = (z + (y * i)) + (a + t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -2.3e+198], N[Not[LessEqual[x, 4.1e+197]], $MachinePrecision]], N[(a + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision] + N[(a + t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.3000000000000001e198 or 4.1000000000000003e197 < x

   1. Initial program 99.7%

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

   2. Taylor expanded in b around inf 99.7%

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

      1. *-commutative 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in b around 0 90.8%

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

   6. Taylor expanded in x around inf 70.3%

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

   if -2.3000000000000001e198 < x < 4.1000000000000003e197

   1. Initial program 99.9%

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

   2. Taylor expanded in b around inf 97.6%

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

      1. *-commutative 97.6%

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

   4. Simplified 97.6%

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

   5. Taylor expanded in b around 0 82.4%

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

   6. Taylor expanded in x around 0 77.7%

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

      1. associate-+r+ 77.7%

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

      2. +-commutative 77.7%

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

   8. Simplified 77.7%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+198} \lor \neg \left(x \leq 4.1 \cdot 10^{+197}\right):\\ \;\;\;\;a + x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(z + y \cdot i\right) + \left(a + t\right)\\ \end{array} \]

Alternative 15: 71.9% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+198} \lor \neg \left(x \leq 3.3 \cdot 10^{+198}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(z + y \cdot i\right) + \left(a + t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -3.5e+198) (not (<= x 3.3e+198)))
   (* x (log y))
   (+ (+ z (* y i)) (+ a t))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -3.5e+198) || !(x <= 3.3e+198)) {
		tmp = x * log(y);
	} else {
		tmp = (z + (y * i)) + (a + t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-3.5d+198)) .or. (.not. (x <= 3.3d+198))) then
        tmp = x * log(y)
    else
        tmp = (z + (y * i)) + (a + t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -3.5e+198) || !(x <= 3.3e+198)) {
		tmp = x * Math.log(y);
	} else {
		tmp = (z + (y * i)) + (a + t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -3.5e+198) or not (x <= 3.3e+198):
		tmp = x * math.log(y)
	else:
		tmp = (z + (y * i)) + (a + t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -3.5e+198) || !(x <= 3.3e+198))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(Float64(z + Float64(y * i)) + Float64(a + t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -3.5e+198) || ~((x <= 3.3e+198)))
		tmp = x * log(y);
	else
		tmp = (z + (y * i)) + (a + t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -3.5e+198], N[Not[LessEqual[x, 3.3e+198]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision] + N[(a + t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.50000000000000013e198 or 3.29999999999999994e198 < x

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 63.8%

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

   if -3.50000000000000013e198 < x < 3.29999999999999994e198

   1. Initial program 99.9%

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

   2. Taylor expanded in b around inf 97.6%

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

      1. *-commutative 97.6%

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

   4. Simplified 97.6%

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

   5. Taylor expanded in b around 0 82.5%

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

   6. Taylor expanded in x around 0 77.6%

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

      1. associate-+r+ 77.6%

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

      2. +-commutative 77.6%

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

   8. Simplified 77.6%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+198} \lor \neg \left(x \leq 3.3 \cdot 10^{+198}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(z + y \cdot i\right) + \left(a + t\right)\\ \end{array} \]

Alternative 16: 67.5% accurate, 24.3× speedup

Math

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

FPCore

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

C

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

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 + (y * i)) + (a + t)
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 + (y * i)) + (a + t);
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in b around inf 98.0%

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

   1. *-commutative 98.0%

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

4. Simplified 98.0%

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

5. Taylor expanded in b around 0 83.8%

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

6. Taylor expanded in x around 0 68.7%

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

   1. associate-+r+ 68.7%

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

   2. +-commutative 68.7%

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

8. Simplified 68.7%

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

9. Final simplification 68.7%

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

Alternative 17: 39.6% accurate, 30.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1.12 \cdot 10^{+106} \lor \neg \left(i \leq 6.6 \cdot 10^{+201}\right):\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= i -1.12e+106) (not (<= i 6.6e+201))) (* y i) (+ a z)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((i <= -1.12e+106) || !(i <= 6.6e+201)) {
		tmp = y * i;
	} else {
		tmp = a + z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((i <= (-1.12d+106)) .or. (.not. (i <= 6.6d+201))) then
        tmp = y * i
    else
        tmp = a + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((i <= -1.12e+106) || !(i <= 6.6e+201)) {
		tmp = y * i;
	} else {
		tmp = a + z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (i <= -1.12e+106) or not (i <= 6.6e+201):
		tmp = y * i
	else:
		tmp = a + z
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((i <= -1.12e+106) || !(i <= 6.6e+201))
		tmp = Float64(y * i);
	else
		tmp = Float64(a + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((i <= -1.12e+106) || ~((i <= 6.6e+201)))
		tmp = y * i;
	else
		tmp = a + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[i, -1.12e+106], N[Not[LessEqual[i, 6.6e+201]], $MachinePrecision]], N[(y * i), $MachinePrecision], N[(a + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -1.1200000000000001e106 or 6.6e201 < i

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 58.9%

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

      1. *-commutative 58.9%

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

   4. Simplified 58.9%

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

   if -1.1200000000000001e106 < i < 6.6e201

   1. Initial program 99.8%

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

   2. Taylor expanded in b around inf 97.8%

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

      1. *-commutative 97.8%

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

   4. Simplified 97.8%

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

   5. Taylor expanded in b around 0 81.2%

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

   6. Taylor expanded in z around inf 37.9%

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

4. Final simplification 43.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.12 \cdot 10^{+106} \lor \neg \left(i \leq 6.6 \cdot 10^{+201}\right):\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + z\\ \end{array} \]

Alternative 18: 23.4% accurate, 30.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+97}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-185}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -7e+97) z (if (<= z -1.6e-185) (* y i) a)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -7e+97) {
		tmp = z;
	} else if (z <= -1.6e-185) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-7d+97)) then
        tmp = z
    else if (z <= (-1.6d-185)) then
        tmp = y * i
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -7e+97) {
		tmp = z;
	} else if (z <= -1.6e-185) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -7e+97:
		tmp = z
	elif z <= -1.6e-185:
		tmp = y * i
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -7e+97)
		tmp = z;
	elseif (z <= -1.6e-185)
		tmp = Float64(y * i);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -7e+97)
		tmp = z;
	elseif (z <= -1.6e-185)
		tmp = y * i;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -7e+97], z, If[LessEqual[z, -1.6e-185], N[(y * i), $MachinePrecision], a]]

Derivation

1. Split input into 3 regimes

2. if z < -7.0000000000000001e97

   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 43.0%

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

   if -7.0000000000000001e97 < z < -1.5999999999999999e-185

   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 y around inf 25.0%

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

      1. *-commutative 25.0%

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

   4. Simplified 25.0%

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

   if -1.5999999999999999e-185 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in a around inf 20.6%

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

4. Final simplification 25.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+97}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-185}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 19: 31.6% accurate, 30.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+97}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -1.44 \cdot 10^{-185}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -3.8e+97) z (if (<= z -1.44e-185) (* y i) (+ a t))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -3.8e+97) {
		tmp = z;
	} else if (z <= -1.44e-185) {
		tmp = y * i;
	} else {
		tmp = a + 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 <= (-3.8d+97)) then
        tmp = z
    else if (z <= (-1.44d-185)) then
        tmp = y * i
    else
        tmp = a + 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 <= -3.8e+97) {
		tmp = z;
	} else if (z <= -1.44e-185) {
		tmp = y * i;
	} else {
		tmp = a + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -3.8e+97:
		tmp = z
	elif z <= -1.44e-185:
		tmp = y * i
	else:
		tmp = a + t
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -3.8e+97)
		tmp = z;
	elseif (z <= -1.44e-185)
		tmp = Float64(y * i);
	else
		tmp = Float64(a + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -3.8e+97)
		tmp = z;
	elseif (z <= -1.44e-185)
		tmp = y * i;
	else
		tmp = a + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -3.8e+97], z, If[LessEqual[z, -1.44e-185], N[(y * i), $MachinePrecision], N[(a + t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.80000000000000036e97

   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 43.0%

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

   if -3.80000000000000036e97 < z < -1.4399999999999999e-185

   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 y around inf 25.0%

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

      1. *-commutative 25.0%

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

   4. Simplified 25.0%

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

   if -1.4399999999999999e-185 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in b around inf 98.6%

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

      1. *-commutative 98.6%

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

   4. Simplified 98.6%

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

   5. Taylor expanded in b around 0 85.4%

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

   6. Taylor expanded in t around inf 34.2%

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

4. Final simplification 33.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+97}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -1.44 \cdot 10^{-185}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + t\\ \end{array} \]

Alternative 20: 43.2% accurate, 31.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+97}:\\ \;\;\;\;a + z\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -3.8e+97) (+ a 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 <= -3.8e+97) {
		tmp = a + 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 <= (-3.8d+97)) then
        tmp = a + 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 <= -3.8e+97) {
		tmp = a + z;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -3.8e+97:
		tmp = a + z
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -3.8e+97)
		tmp = Float64(a + 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 <= -3.8e+97)
		tmp = a + z;
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -3.8e+97], N[(a + z), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.80000000000000036e97

   1. Initial program 99.9%

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

   2. Taylor expanded in b around inf 99.9%

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

      1. *-commutative 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in b around 0 87.4%

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

   6. Taylor expanded in z around inf 56.2%

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

   if -3.80000000000000036e97 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in b around inf 97.6%

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

      1. *-commutative 97.6%

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

   4. Simplified 97.6%

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

   5. Taylor expanded in b around 0 83.1%

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

   6. Taylor expanded in i around inf 42.6%

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

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+97}:\\ \;\;\;\;a + z\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]

Alternative 21: 21.5% accurate, 71.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+97}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (if (<= z -2e+97) z a))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -2e+97) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-2d+97)) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -2e+97) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -2e+97:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -2e+97)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -2e+97)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -2e+97], z, a]

Derivation

1. Split input into 2 regimes

2. if z < -2.0000000000000001e97

   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 41.4%

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

   if -2.0000000000000001e97 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in a around inf 19.1%

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

4. Final simplification 23.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+97}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 22: 16.7% accurate, 219.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in a around inf 18.7%

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

3. Final simplification 18.7%

   \[\leadsto a \]

Reproduce

herbie shell --seed 2023336 
(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)))