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

Percentage Accurate: 99.8% → 99.9%

Time: 16.7s

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: 99.9% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(z + a), $MachinePrecision] + N[(N[(b + -0.5), $MachinePrecision] * N[Log[c], $MachinePrecision] + N[(y * i + N[(x * N[Log[y], $MachinePrecision] + 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-+l+ 99.9%

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

   3. associate-+r+ 99.9%

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

   4. +-commutative 99.9%

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

   5. associate-+r+ 99.9%

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

   6. associate-+r+ 99.9%

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

   7. associate-+l+ 99.9%

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

   8. +-commutative 99.9%

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

   9. associate-+r+ 99.9%

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

   10. associate-+r+ 99.9%

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

   11. fma-def 99.9%

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

   12. sub-neg 99.9%

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

   13. metadata-eval 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 93.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{+127}:\\ \;\;\;\;a + \left(t + \left(z + \left(y \cdot i - x \cdot \log \left(\frac{1}{y}\right)\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+209}:\\ \;\;\;\;y \cdot i + \mathsf{fma}\left(\log c, b + -0.5, a + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) + \left(x \cdot \log y + \left(t + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -5.4e+127)
   (+ a (+ t (+ z (- (* y i) (* x (log (/ 1.0 y)))))))
   (if (<= x 1.35e+209)
     (+ (* y i) (fma (log c) (+ b -0.5) (+ a (+ z t))))
     (+ (+ z a) (+ (* x (log y)) (+ t (* (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 <= -5.4e+127) {
		tmp = a + (t + (z + ((y * i) - (x * log((1.0 / y))))));
	} else if (x <= 1.35e+209) {
		tmp = (y * i) + fma(log(c), (b + -0.5), (a + (z + t)));
	} else {
		tmp = (z + a) + ((x * log(y)) + (t + (log(c) * (b - 0.5))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -5.4e+127)
		tmp = Float64(a + Float64(t + Float64(z + Float64(Float64(y * i) - Float64(x * log(Float64(1.0 / y)))))));
	elseif (x <= 1.35e+209)
		tmp = Float64(Float64(y * i) + fma(log(c), Float64(b + -0.5), Float64(a + Float64(z + t))));
	else
		tmp = Float64(Float64(z + a) + Float64(Float64(x * log(y)) + Float64(t + Float64(log(c) * Float64(b - 0.5)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -5.4e+127], N[(a + N[(t + N[(z + N[(N[(y * i), $MachinePrecision] - N[(x * N[Log[N[(1.0 / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.35e+209], N[(N[(y * i), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + a), $MachinePrecision] + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(t + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.4000000000000004e127

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. add-cube-cbrt 99.8%

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

      3. fma-def 99.8%

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

      4. pow2 99.8%

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

      5. sub-neg 99.8%

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

      6. metadata-eval 99.8%

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

      7. sub-neg 99.8%

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

      8. metadata-eval 99.8%

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

      9. +-commutative 99.8%

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

      10. +-commutative 99.8%

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

      11. fma-def 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in b around inf 99.8%

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

   5. Taylor expanded in y around inf 99.8%

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

   if -5.4000000000000004e127 < x < 1.35e209

   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 97.9%

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

      1. *-commutative 97.9%

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

      2. fma-def 97.9%

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

      3. sub-neg 97.9%

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

      4. metadata-eval 97.9%

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

      5. +-commutative 97.9%

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

   4. Simplified 97.9%

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

   if 1.35e209 < 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. Step-by-step derivation

      1. +-commutative 99.8%

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

      2. associate-+l+ 99.8%

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

      3. associate-+r+ 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-+r+ 99.8%

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

      6. associate-+r+ 99.8%

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

      7. associate-+l+ 99.8%

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

      8. +-commutative 99.8%

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

      9. associate-+r+ 99.8%

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

      10. associate-+r+ 99.8%

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

      11. fma-def 99.8%

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

      12. sub-neg 99.8%

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

      13. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 95.3%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{+127}:\\ \;\;\;\;a + \left(t + \left(z + \left(y \cdot i - x \cdot \log \left(\frac{1}{y}\right)\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+209}:\\ \;\;\;\;y \cdot i + \mathsf{fma}\left(\log c, b + -0.5, a + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) + \left(x \cdot \log y + \left(t + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \end{array} \]

Alternative 3: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Final simplification 99.9%

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

Alternative 4: 93.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+126}:\\ \;\;\;\;a + \left(t + \left(z + \left(y \cdot i - x \cdot \log \left(\frac{1}{y}\right)\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+209}:\\ \;\;\;\;y \cdot i + \mathsf{fma}\left(\log c, b + -0.5, a + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(x \cdot \log y + \left(z + t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -6e+126)
   (+ a (+ t (+ z (- (* y i) (* x (log (/ 1.0 y)))))))
   (if (<= x 1.35e+209)
     (+ (* y i) (fma (log c) (+ b -0.5) (+ a (+ z t))))
     (+ (* y i) (+ a (+ (* x (log y)) (+ z t)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -6e+126) {
		tmp = a + (t + (z + ((y * i) - (x * log((1.0 / y))))));
	} else if (x <= 1.35e+209) {
		tmp = (y * i) + fma(log(c), (b + -0.5), (a + (z + t)));
	} else {
		tmp = (y * i) + (a + ((x * log(y)) + (z + t)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -6e+126)
		tmp = Float64(a + Float64(t + Float64(z + Float64(Float64(y * i) - Float64(x * log(Float64(1.0 / y)))))));
	elseif (x <= 1.35e+209)
		tmp = Float64(Float64(y * i) + fma(log(c), Float64(b + -0.5), Float64(a + Float64(z + t))));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(Float64(x * log(y)) + Float64(z + t))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -6e+126], N[(a + N[(t + N[(z + N[(N[(y * i), $MachinePrecision] - N[(x * N[Log[N[(1.0 / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.35e+209], N[(N[(y * i), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.0000000000000005e126

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. add-cube-cbrt 99.8%

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

      3. fma-def 99.8%

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

      4. pow2 99.8%

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

      5. sub-neg 99.8%

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

      6. metadata-eval 99.8%

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

      7. sub-neg 99.8%

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

      8. metadata-eval 99.8%

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

      9. +-commutative 99.8%

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

      10. +-commutative 99.8%

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

      11. fma-def 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in b around inf 99.8%

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

   5. Taylor expanded in y around inf 99.8%

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

   if -6.0000000000000005e126 < x < 1.35e209

   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 97.9%

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

      1. *-commutative 97.9%

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

      2. fma-def 97.9%

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

      3. sub-neg 97.9%

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

      4. metadata-eval 97.9%

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

      5. +-commutative 97.9%

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

   4. Simplified 97.9%

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

   if 1.35e209 < 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. Step-by-step derivation

      1. +-commutative 99.8%

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

      2. add-cube-cbrt 99.8%

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

      3. fma-def 99.8%

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

      4. pow2 99.8%

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

      5. sub-neg 99.8%

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

      6. metadata-eval 99.8%

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

      7. sub-neg 99.8%

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

      8. metadata-eval 99.8%

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

      9. +-commutative 99.8%

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

      10. +-commutative 99.8%

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

      11. fma-def 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in b around inf 94.2%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+126}:\\ \;\;\;\;a + \left(t + \left(z + \left(y \cdot i - x \cdot \log \left(\frac{1}{y}\right)\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+209}:\\ \;\;\;\;y \cdot i + \mathsf{fma}\left(\log c, b + -0.5, a + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(x \cdot \log y + \left(z + t\right)\right)\right)\\ \end{array} \]

Alternative 5: 84.8% accurate, 1.0× speedup

Math

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

FPCore

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

Python

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(z + a), $MachinePrecision] + N[(N[(y * i), $MachinePrecision] + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $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-+l+ 99.9%

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

   3. associate-+r+ 99.9%

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

   4. +-commutative 99.9%

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

   5. associate-+r+ 99.9%

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

   6. associate-+r+ 99.9%

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

   7. associate-+l+ 99.9%

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

   8. +-commutative 99.9%

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

   9. associate-+r+ 99.9%

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

   10. associate-+r+ 99.9%

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

   11. fma-def 99.9%

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

   12. sub-neg 99.9%

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

   13. metadata-eval 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in t around 0 85.5%

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

5. Final simplification 85.5%

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

Alternative 6: 89.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -4 \cdot 10^{+157} \lor \neg \left(b - 0.5 \leq 8 \cdot 10^{+124}\right):\\ \;\;\;\;y \cdot i + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(x \cdot \log y + \left(z + t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (- b 0.5) -4e+157) (not (<= (- b 0.5) 8e+124)))
   (+ (* y i) (+ z (* (log c) (- b 0.5))))
   (+ (* y i) (+ a (+ (* x (log y)) (+ z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((b - 0.5) <= -4e+157) || !((b - 0.5) <= 8e+124)) {
		tmp = (y * i) + (z + (log(c) * (b - 0.5)));
	} else {
		tmp = (y * i) + (a + ((x * log(y)) + (z + t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((b - 0.5d0) <= (-4d+157)) .or. (.not. ((b - 0.5d0) <= 8d+124))) then
        tmp = (y * i) + (z + (log(c) * (b - 0.5d0)))
    else
        tmp = (y * i) + (a + ((x * log(y)) + (z + t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((b - 0.5) <= -4e+157) || !((b - 0.5) <= 8e+124)) {
		tmp = (y * i) + (z + (Math.log(c) * (b - 0.5)));
	} else {
		tmp = (y * i) + (a + ((x * Math.log(y)) + (z + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((b - 0.5) <= -4e+157) or not ((b - 0.5) <= 8e+124):
		tmp = (y * i) + (z + (math.log(c) * (b - 0.5)))
	else:
		tmp = (y * i) + (a + ((x * math.log(y)) + (z + t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(b - 0.5) <= -4e+157) || !(Float64(b - 0.5) <= 8e+124))
		tmp = Float64(Float64(y * i) + Float64(z + Float64(log(c) * Float64(b - 0.5))));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(Float64(x * log(y)) + Float64(z + t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((b - 0.5) <= -4e+157) || ~(((b - 0.5) <= 8e+124)))
		tmp = (y * i) + (z + (log(c) * (b - 0.5)));
	else
		tmp = (y * i) + (a + ((x * log(y)) + (z + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(b - 0.5), $MachinePrecision], -4e+157], N[Not[LessEqual[N[(b - 0.5), $MachinePrecision], 8e+124]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 b 1/2) < -3.99999999999999993e157 or 7.99999999999999959e124 < (-.f64 b 1/2)

   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 91.5%

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

   3. Taylor expanded in a around 0 83.4%

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

      1. fma-def 83.4%

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

      2. sub-neg 83.4%

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

      3. metadata-eval 83.4%

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

      4. +-commutative 83.4%

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

      5. *-commutative 83.4%

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

   5. Simplified 83.4%

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

   6. Taylor expanded in t around 0 77.1%

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

   if -3.99999999999999993e157 < (-.f64 b 1/2) < 7.99999999999999959e124

   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%

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

      2. add-cube-cbrt 99.9%

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

      3. fma-def 99.9%

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

      4. pow2 99.9%

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

      5. sub-neg 99.9%

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

      6. metadata-eval 99.9%

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

      7. sub-neg 99.9%

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

      8. metadata-eval 99.9%

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

      9. +-commutative 99.9%

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

      10. +-commutative 99.9%

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

      11. fma-def 99.9%

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

   3. Applied egg-rr 99.9%

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

   4. Taylor expanded in b around inf 94.4%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -4 \cdot 10^{+157} \lor \neg \left(b - 0.5 \leq 8 \cdot 10^{+124}\right):\\ \;\;\;\;y \cdot i + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(x \cdot \log y + \left(z + t\right)\right)\right)\\ \end{array} \]

Alternative 7: 93.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+126} \lor \neg \left(x \leq 1.35 \cdot 10^{+209}\right):\\ \;\;\;\;y \cdot i + \left(a + \left(x \cdot \log y + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -1e+126) (not (<= x 1.35e+209)))
   (+ (* y i) (+ a (+ (* x (log y)) (+ z t))))
   (+ (* y i) (+ (* (log c) (- b 0.5)) (+ a (+ z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1e+126) || !(x <= 1.35e+209)) {
		tmp = (y * i) + (a + ((x * log(y)) + (z + t)));
	} else {
		tmp = (y * i) + ((log(c) * (b - 0.5)) + (a + (z + t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-1d+126)) .or. (.not. (x <= 1.35d+209))) then
        tmp = (y * i) + (a + ((x * log(y)) + (z + t)))
    else
        tmp = (y * i) + ((log(c) * (b - 0.5d0)) + (a + (z + t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1e+126) || !(x <= 1.35e+209)) {
		tmp = (y * i) + (a + ((x * Math.log(y)) + (z + t)));
	} else {
		tmp = (y * i) + ((Math.log(c) * (b - 0.5)) + (a + (z + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -1e+126) or not (x <= 1.35e+209):
		tmp = (y * i) + (a + ((x * math.log(y)) + (z + t)))
	else:
		tmp = (y * i) + ((math.log(c) * (b - 0.5)) + (a + (z + t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -1e+126) || !(x <= 1.35e+209))
		tmp = Float64(Float64(y * i) + Float64(a + Float64(Float64(x * log(y)) + Float64(z + t))));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(log(c) * Float64(b - 0.5)) + Float64(a + Float64(z + t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -1e+126) || ~((x <= 1.35e+209)))
		tmp = (y * i) + (a + ((x * log(y)) + (z + t)));
	else
		tmp = (y * i) + ((log(c) * (b - 0.5)) + (a + (z + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -1e+126], N[Not[LessEqual[x, 1.35e+209]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(a + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.99999999999999925e125 or 1.35e209 < 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. Step-by-step derivation

      1. +-commutative 99.8%

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

      2. add-cube-cbrt 99.8%

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

      3. fma-def 99.8%

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

      4. pow2 99.8%

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

      5. sub-neg 99.8%

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

      6. metadata-eval 99.8%

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

      7. sub-neg 99.8%

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

      8. metadata-eval 99.8%

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

      9. +-commutative 99.8%

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

      10. +-commutative 99.8%

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

      11. fma-def 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in b around inf 97.8%

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

   if -9.99999999999999925e125 < x < 1.35e209

   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 97.9%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+126} \lor \neg \left(x \leq 1.35 \cdot 10^{+209}\right):\\ \;\;\;\;y \cdot i + \left(a + \left(x \cdot \log y + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \]

Alternative 8: 93.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.42 \cdot 10^{+125}:\\ \;\;\;\;a + \left(t + \left(z + \left(y \cdot i - x \cdot \log \left(\frac{1}{y}\right)\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+209}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(x \cdot \log y + \left(z + t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -1.42e+125)
   (+ a (+ t (+ z (- (* y i) (* x (log (/ 1.0 y)))))))
   (if (<= x 1.35e+209)
     (+ (* y i) (+ (* (log c) (- b 0.5)) (+ a (+ z t))))
     (+ (* y i) (+ a (+ (* x (log y)) (+ z t)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -1.42e+125) {
		tmp = a + (t + (z + ((y * i) - (x * log((1.0 / y))))));
	} else if (x <= 1.35e+209) {
		tmp = (y * i) + ((log(c) * (b - 0.5)) + (a + (z + t)));
	} else {
		tmp = (y * i) + (a + ((x * log(y)) + (z + t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (x <= (-1.42d+125)) then
        tmp = a + (t + (z + ((y * i) - (x * log((1.0d0 / y))))))
    else if (x <= 1.35d+209) then
        tmp = (y * i) + ((log(c) * (b - 0.5d0)) + (a + (z + t)))
    else
        tmp = (y * i) + (a + ((x * log(y)) + (z + t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -1.42e+125) {
		tmp = a + (t + (z + ((y * i) - (x * Math.log((1.0 / y))))));
	} else if (x <= 1.35e+209) {
		tmp = (y * i) + ((Math.log(c) * (b - 0.5)) + (a + (z + t)));
	} else {
		tmp = (y * i) + (a + ((x * Math.log(y)) + (z + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if x <= -1.42e+125:
		tmp = a + (t + (z + ((y * i) - (x * math.log((1.0 / y))))))
	elif x <= 1.35e+209:
		tmp = (y * i) + ((math.log(c) * (b - 0.5)) + (a + (z + t)))
	else:
		tmp = (y * i) + (a + ((x * math.log(y)) + (z + t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -1.42e+125)
		tmp = Float64(a + Float64(t + Float64(z + Float64(Float64(y * i) - Float64(x * log(Float64(1.0 / y)))))));
	elseif (x <= 1.35e+209)
		tmp = Float64(Float64(y * i) + Float64(Float64(log(c) * Float64(b - 0.5)) + Float64(a + Float64(z + t))));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(Float64(x * log(y)) + Float64(z + t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (x <= -1.42e+125)
		tmp = a + (t + (z + ((y * i) - (x * log((1.0 / y))))));
	elseif (x <= 1.35e+209)
		tmp = (y * i) + ((log(c) * (b - 0.5)) + (a + (z + t)));
	else
		tmp = (y * i) + (a + ((x * log(y)) + (z + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -1.42e+125], N[(a + N[(t + N[(z + N[(N[(y * i), $MachinePrecision] - N[(x * N[Log[N[(1.0 / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.35e+209], N[(N[(y * i), $MachinePrecision] + N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.4200000000000001e125

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. add-cube-cbrt 99.8%

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

      3. fma-def 99.8%

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

      4. pow2 99.8%

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

      5. sub-neg 99.8%

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

      6. metadata-eval 99.8%

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

      7. sub-neg 99.8%

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

      8. metadata-eval 99.8%

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

      9. +-commutative 99.8%

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

      10. +-commutative 99.8%

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

      11. fma-def 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in b around inf 99.8%

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

   5. Taylor expanded in y around inf 99.8%

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

   if -1.4200000000000001e125 < x < 1.35e209

   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 97.9%

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

   if 1.35e209 < 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. Step-by-step derivation

      1. +-commutative 99.8%

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

      2. add-cube-cbrt 99.8%

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

      3. fma-def 99.8%

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

      4. pow2 99.8%

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

      5. sub-neg 99.8%

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

      6. metadata-eval 99.8%

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

      7. sub-neg 99.8%

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

      8. metadata-eval 99.8%

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

      9. +-commutative 99.8%

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

      10. +-commutative 99.8%

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

      11. fma-def 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in b around inf 94.2%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.42 \cdot 10^{+125}:\\ \;\;\;\;a + \left(t + \left(z + \left(y \cdot i - x \cdot \log \left(\frac{1}{y}\right)\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+209}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(x \cdot \log y + \left(z + t\right)\right)\right)\\ \end{array} \]

Alternative 9: 61.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 6.1 \cdot 10^{+29}:\\ \;\;\;\;y \cdot i + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a + t\right) + \left(z + y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 6.1e+29)
   (+ (* y i) (+ z (* (log c) (- b 0.5))))
   (+ (+ a t) (+ z (* y i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 6.1e+29) {
		tmp = (y * i) + (z + (log(c) * (b - 0.5)));
	} else {
		tmp = (a + t) + (z + (y * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 6.1d+29) then
        tmp = (y * i) + (z + (log(c) * (b - 0.5d0)))
    else
        tmp = (a + t) + (z + (y * i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 6.1e+29) {
		tmp = (y * i) + (z + (Math.log(c) * (b - 0.5)));
	} else {
		tmp = (a + t) + (z + (y * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 6.1e+29:
		tmp = (y * i) + (z + (math.log(c) * (b - 0.5)))
	else:
		tmp = (a + t) + (z + (y * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 6.1e+29)
		tmp = Float64(Float64(y * i) + Float64(z + Float64(log(c) * Float64(b - 0.5))));
	else
		tmp = Float64(Float64(a + t) + Float64(z + Float64(y * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 6.1e+29)
		tmp = (y * i) + (z + (log(c) * (b - 0.5)));
	else
		tmp = (a + t) + (z + (y * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 6.1e+29], N[(N[(y * i), $MachinePrecision] + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a + t), $MachinePrecision] + N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 6.0999999999999998e29

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 85.0%

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

   3. Taylor expanded in a around 0 76.5%

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

      1. fma-def 76.5%

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

      2. sub-neg 76.5%

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

      3. metadata-eval 76.5%

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

      4. +-commutative 76.5%

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

      5. *-commutative 76.5%

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

   5. Simplified 76.5%

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

   6. Taylor expanded in t around 0 59.6%

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

   if 6.0999999999999998e29 < a

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. add-cube-cbrt 99.7%

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

      3. fma-def 99.7%

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

      4. pow2 99.7%

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

      5. sub-neg 99.7%

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

      6. metadata-eval 99.7%

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

      7. sub-neg 99.7%

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

      8. metadata-eval 99.7%

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

      9. +-commutative 99.7%

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

      10. +-commutative 99.7%

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

      11. fma-def 99.7%

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

   3. Applied egg-rr 99.7%

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

   4. Taylor expanded in b around inf 89.3%

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

   5. Taylor expanded in x around 0 79.9%

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

      1. associate-+r+ 79.9%

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

      2. *-commutative 79.9%

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

   7. Simplified 79.9%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 6.1 \cdot 10^{+29}:\\ \;\;\;\;y \cdot i + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a + t\right) + \left(z + y \cdot i\right)\\ \end{array} \]

Alternative 10: 72.7% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+144} \lor \neg \left(x \leq 8 \cdot 10^{+211}\right):\\ \;\;\;\;y \cdot i + x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(a + t\right) + \left(z + y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -5.2e+144) (not (<= x 8e+211)))
   (+ (* y i) (* x (log y)))
   (+ (+ a t) (+ z (* y i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -5.2e+144) || !(x <= 8e+211)) {
		tmp = (y * i) + (x * log(y));
	} else {
		tmp = (a + t) + (z + (y * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-5.2d+144)) .or. (.not. (x <= 8d+211))) then
        tmp = (y * i) + (x * log(y))
    else
        tmp = (a + t) + (z + (y * i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -5.2e+144) || !(x <= 8e+211)) {
		tmp = (y * i) + (x * Math.log(y));
	} else {
		tmp = (a + t) + (z + (y * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -5.2e+144) or not (x <= 8e+211):
		tmp = (y * i) + (x * math.log(y))
	else:
		tmp = (a + t) + (z + (y * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -5.2e+144) || !(x <= 8e+211))
		tmp = Float64(Float64(y * i) + Float64(x * log(y)));
	else
		tmp = Float64(Float64(a + t) + Float64(z + Float64(y * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -5.2e+144) || ~((x <= 8e+211)))
		tmp = (y * i) + (x * log(y));
	else
		tmp = (a + t) + (z + (y * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -5.2e+144], N[Not[LessEqual[x, 8e+211]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a + t), $MachinePrecision] + N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.1999999999999998e144 or 7.9999999999999997e211 < 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. Step-by-step derivation

      1. +-commutative 99.8%

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

      2. add-cube-cbrt 99.7%

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

      3. fma-def 99.7%

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

      4. pow2 99.7%

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

      5. sub-neg 99.7%

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

      6. metadata-eval 99.7%

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

      7. sub-neg 99.7%

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

      8. metadata-eval 99.7%

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

      9. +-commutative 99.7%

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

      10. +-commutative 99.7%

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

      11. fma-def 99.7%

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

   3. Applied egg-rr 99.7%

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

   4. Taylor expanded in x around inf 72.6%

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

   if -5.1999999999999998e144 < x < 7.9999999999999997e211

   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%

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

      2. add-cube-cbrt 99.6%

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

      3. fma-def 99.6%

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

      4. pow2 99.6%

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

      5. sub-neg 99.6%

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

      6. metadata-eval 99.6%

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

      7. sub-neg 99.6%

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

      8. metadata-eval 99.6%

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

      9. +-commutative 99.6%

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

      10. +-commutative 99.6%

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

      11. fma-def 99.6%

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

   3. Applied egg-rr 99.6%

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

   4. Taylor expanded in b around inf 79.8%

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

   5. Taylor expanded in x around 0 77.3%

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

      1. associate-+r+ 77.3%

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

      2. *-commutative 77.3%

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

   7. Simplified 77.3%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+144} \lor \neg \left(x \leq 8 \cdot 10^{+211}\right):\\ \;\;\;\;y \cdot i + x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(a + t\right) + \left(z + y \cdot i\right)\\ \end{array} \]

Alternative 11: 73.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 135000:\\ \;\;\;\;a + \left(x \cdot \log y + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a + t\right) + \left(z + y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 135000.0)
   (+ a (+ (* x (log y)) (+ z t)))
   (+ (+ a t) (+ z (* y i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 135000.0) {
		tmp = a + ((x * log(y)) + (z + t));
	} else {
		tmp = (a + t) + (z + (y * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= 135000.0d0) then
        tmp = a + ((x * log(y)) + (z + t))
    else
        tmp = (a + t) + (z + (y * i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 135000.0) {
		tmp = a + ((x * Math.log(y)) + (z + t));
	} else {
		tmp = (a + t) + (z + (y * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 135000.0:
		tmp = a + ((x * math.log(y)) + (z + t))
	else:
		tmp = (a + t) + (z + (y * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 135000.0)
		tmp = Float64(a + Float64(Float64(x * log(y)) + Float64(z + t)));
	else
		tmp = Float64(Float64(a + t) + Float64(z + Float64(y * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= 135000.0)
		tmp = a + ((x * log(y)) + (z + t));
	else
		tmp = (a + t) + (z + (y * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 135000.0], N[(a + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a + t), $MachinePrecision] + N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 135000

   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%

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

      2. add-cube-cbrt 99.6%

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

      3. fma-def 99.6%

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

      4. pow2 99.6%

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

      5. sub-neg 99.6%

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

      6. metadata-eval 99.6%

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

      7. sub-neg 99.6%

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

      8. metadata-eval 99.6%

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

      9. +-commutative 99.6%

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

      10. +-commutative 99.6%

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

      11. fma-def 99.6%

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

   3. Applied egg-rr 99.6%

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

   4. Taylor expanded in b around inf 79.5%

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

   5. Taylor expanded in y around 0 77.1%

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

   if 135000 < y

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. add-cube-cbrt 99.7%

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

      3. fma-def 99.7%

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

      4. pow2 99.7%

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

      5. sub-neg 99.7%

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

      6. metadata-eval 99.7%

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

      7. sub-neg 99.7%

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

      8. metadata-eval 99.7%

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

      9. +-commutative 99.7%

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

      10. +-commutative 99.7%

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

      11. fma-def 99.7%

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

   3. Applied egg-rr 99.7%

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

   4. Taylor expanded in b around inf 86.4%

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

   5. Taylor expanded in x around 0 78.8%

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

      1. associate-+r+ 78.8%

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

      2. *-commutative 78.8%

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

   7. Simplified 78.8%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 135000:\\ \;\;\;\;a + \left(x \cdot \log y + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a + t\right) + \left(z + y \cdot i\right)\\ \end{array} \]

Alternative 12: 72.7% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.3 \cdot 10^{+157} \lor \neg \left(b \leq 7.6 \cdot 10^{+230}\right):\\ \;\;\;\;z + b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;\left(a + t\right) + \left(z + y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= b -4.3e+157) (not (<= b 7.6e+230)))
   (+ z (* b (log c)))
   (+ (+ a t) (+ z (* y i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((b <= -4.3e+157) || !(b <= 7.6e+230)) {
		tmp = z + (b * log(c));
	} else {
		tmp = (a + t) + (z + (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 ((b <= (-4.3d+157)) .or. (.not. (b <= 7.6d+230))) then
        tmp = z + (b * log(c))
    else
        tmp = (a + t) + (z + (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 ((b <= -4.3e+157) || !(b <= 7.6e+230)) {
		tmp = z + (b * Math.log(c));
	} else {
		tmp = (a + t) + (z + (y * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (b <= -4.3e+157) or not (b <= 7.6e+230):
		tmp = z + (b * math.log(c))
	else:
		tmp = (a + t) + (z + (y * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((b <= -4.3e+157) || !(b <= 7.6e+230))
		tmp = Float64(z + Float64(b * log(c)));
	else
		tmp = Float64(Float64(a + t) + Float64(z + Float64(y * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((b <= -4.3e+157) || ~((b <= 7.6e+230)))
		tmp = z + (b * log(c));
	else
		tmp = (a + t) + (z + (y * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[b, -4.3e+157], N[Not[LessEqual[b, 7.6e+230]], $MachinePrecision]], N[(z + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a + t), $MachinePrecision] + N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.3e157 or 7.6e230 < 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. Step-by-step derivation

      1. +-commutative 99.7%

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

      2. associate-+l+ 99.7%

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

      3. associate-+r+ 99.7%

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

      4. +-commutative 99.7%

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

      5. associate-+r+ 99.7%

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

      6. associate-+r+ 99.7%

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

      7. associate-+l+ 99.7%

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

      8. +-commutative 99.7%

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

      9. associate-+r+ 99.7%

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

      10. associate-+r+ 99.7%

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

      11. fma-def 99.7%

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

      12. sub-neg 99.7%

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

      13. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in b around inf 62.8%

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

   5. Taylor expanded in a around 0 55.5%

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

   if -4.3e157 < b < 7.6e230

   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%

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

      2. add-cube-cbrt 99.8%

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

      3. fma-def 99.8%

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

      4. pow2 99.8%

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

      5. sub-neg 99.8%

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

      6. metadata-eval 99.8%

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

      7. sub-neg 99.8%

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

      8. metadata-eval 99.8%

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

      9. +-commutative 99.8%

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

      10. +-commutative 99.8%

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

      11. fma-def 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in b around inf 91.1%

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

   5. Taylor expanded in x around 0 76.8%

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

      1. associate-+r+ 76.8%

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

      2. *-commutative 76.8%

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

   7. Simplified 76.8%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.3 \cdot 10^{+157} \lor \neg \left(b \leq 7.6 \cdot 10^{+230}\right):\\ \;\;\;\;z + b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;\left(a + t\right) + \left(z + y \cdot i\right)\\ \end{array} \]

Alternative 13: 64.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 11200:\\ \;\;\;\;\left(z + a\right) + b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;\left(a + t\right) + \left(z + y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 11200.0) (+ (+ z a) (* b (log c))) (+ (+ a t) (+ z (* y i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 11200.0) {
		tmp = (z + a) + (b * log(c));
	} else {
		tmp = (a + t) + (z + (y * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= 11200.0d0) then
        tmp = (z + a) + (b * log(c))
    else
        tmp = (a + t) + (z + (y * i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 11200.0) {
		tmp = (z + a) + (b * Math.log(c));
	} else {
		tmp = (a + t) + (z + (y * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 11200.0:
		tmp = (z + a) + (b * math.log(c))
	else:
		tmp = (a + t) + (z + (y * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 11200.0)
		tmp = Float64(Float64(z + a) + Float64(b * log(c)));
	else
		tmp = Float64(Float64(a + t) + Float64(z + Float64(y * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= 11200.0)
		tmp = (z + a) + (b * log(c));
	else
		tmp = (a + t) + (z + (y * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 11200.0], N[(N[(z + a), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a + t), $MachinePrecision] + N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 11200

   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-+l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+r+ 99.9%

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

      6. associate-+r+ 99.9%

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

      7. associate-+l+ 99.9%

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

      8. +-commutative 99.9%

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

      9. associate-+r+ 99.9%

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

      10. associate-+r+ 99.9%

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

      11. fma-def 99.9%

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

      12. sub-neg 99.9%

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

      13. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in b around inf 53.2%

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

   if 11200 < y

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. add-cube-cbrt 99.7%

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

      3. fma-def 99.7%

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

      4. pow2 99.7%

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

      5. sub-neg 99.7%

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

      6. metadata-eval 99.7%

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

      7. sub-neg 99.7%

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

      8. metadata-eval 99.7%

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

      9. +-commutative 99.7%

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

      10. +-commutative 99.7%

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

      11. fma-def 99.7%

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

   3. Applied egg-rr 99.7%

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

   4. Taylor expanded in b around inf 86.4%

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

   5. Taylor expanded in x around 0 78.8%

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

      1. associate-+r+ 78.8%

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

      2. *-commutative 78.8%

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

   7. Simplified 78.8%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 11200:\\ \;\;\;\;\left(z + a\right) + b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;\left(a + t\right) + \left(z + y \cdot i\right)\\ \end{array} \]

Alternative 14: 68.8% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.6 \cdot 10^{+233}:\\ \;\;\;\;b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;\left(a + t\right) + \left(z + y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= b -2.6e+233) (* b (log c)) (+ (+ a t) (+ z (* y i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (b <= -2.6e+233) {
		tmp = b * log(c);
	} else {
		tmp = (a + t) + (z + (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 (b <= (-2.6d+233)) then
        tmp = b * log(c)
    else
        tmp = (a + t) + (z + (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 (b <= -2.6e+233) {
		tmp = b * Math.log(c);
	} else {
		tmp = (a + t) + (z + (y * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if b <= -2.6e+233:
		tmp = b * math.log(c)
	else:
		tmp = (a + t) + (z + (y * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (b <= -2.6e+233)
		tmp = Float64(b * log(c));
	else
		tmp = Float64(Float64(a + t) + Float64(z + Float64(y * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (b <= -2.6e+233)
		tmp = b * log(c);
	else
		tmp = (a + t) + (z + (y * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[b, -2.6e+233], N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision], N[(N[(a + t), $MachinePrecision] + N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.60000000000000006e233

   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. Step-by-step derivation

      1. +-commutative 100.0%

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

      2. associate-+l+ 100.0%

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

      3. associate-+r+ 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-+r+ 100.0%

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

      6. associate-+r+ 100.0%

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

      7. associate-+l+ 100.0%

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

      8. +-commutative 100.0%

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

      9. associate-+r+ 100.0%

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

      10. associate-+r+ 100.0%

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

      11. fma-def 100.0%

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

      12. sub-neg 100.0%

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

      13. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in b around inf 77.8%

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

   5. Taylor expanded in b around inf 77.8%

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

   if -2.60000000000000006e233 < b

   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%

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

      2. add-cube-cbrt 99.7%

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

      3. fma-def 99.7%

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

      4. pow2 99.7%

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

      5. sub-neg 99.7%

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

      6. metadata-eval 99.7%

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

      7. sub-neg 99.7%

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

      8. metadata-eval 99.7%

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

      9. +-commutative 99.7%

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

      10. +-commutative 99.7%

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

      11. fma-def 99.7%

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

   3. Applied egg-rr 99.7%

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

   4. Taylor expanded in b around inf 85.7%

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

   5. Taylor expanded in x around 0 72.4%

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

      1. associate-+r+ 72.4%

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

      2. *-commutative 72.4%

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

   7. Simplified 72.4%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.6 \cdot 10^{+233}:\\ \;\;\;\;b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;\left(a + t\right) + \left(z + y \cdot i\right)\\ \end{array} \]

Alternative 15: 22.5% accurate, 19.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+176}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{+134}:\\ \;\;\;\;a\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{+113}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-199}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -1.4e+176)
   z
   (if (<= z -1.4e+134)
     a
     (if (<= z -5.3e+113) z (if (<= z -4.1e-199) (* 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 <= -1.4e+176) {
		tmp = z;
	} else if (z <= -1.4e+134) {
		tmp = a;
	} else if (z <= -5.3e+113) {
		tmp = z;
	} else if (z <= -4.1e-199) {
		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 <= (-1.4d+176)) then
        tmp = z
    else if (z <= (-1.4d+134)) then
        tmp = a
    else if (z <= (-5.3d+113)) then
        tmp = z
    else if (z <= (-4.1d-199)) 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 <= -1.4e+176) {
		tmp = z;
	} else if (z <= -1.4e+134) {
		tmp = a;
	} else if (z <= -5.3e+113) {
		tmp = z;
	} else if (z <= -4.1e-199) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -1.4e+176:
		tmp = z
	elif z <= -1.4e+134:
		tmp = a
	elif z <= -5.3e+113:
		tmp = z
	elif z <= -4.1e-199:
		tmp = y * i
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -1.4e+176)
		tmp = z;
	elseif (z <= -1.4e+134)
		tmp = a;
	elseif (z <= -5.3e+113)
		tmp = z;
	elseif (z <= -4.1e-199)
		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 <= -1.4e+176)
		tmp = z;
	elseif (z <= -1.4e+134)
		tmp = a;
	elseif (z <= -5.3e+113)
		tmp = z;
	elseif (z <= -4.1e-199)
		tmp = y * i;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -1.4e+176], z, If[LessEqual[z, -1.4e+134], a, If[LessEqual[z, -5.3e+113], z, If[LessEqual[z, -4.1e-199], N[(y * i), $MachinePrecision], a]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.4000000000000001e176 or -1.3999999999999999e134 < z < -5.29999999999999967e113

   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-+l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+r+ 99.9%

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

      6. associate-+r+ 99.9%

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

      7. associate-+l+ 99.9%

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

      8. +-commutative 99.9%

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

      9. associate-+r+ 99.9%

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

      10. associate-+r+ 99.9%

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

      11. fma-def 99.9%

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

      12. sub-neg 99.9%

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

      13. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 55.0%

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

   if -1.4000000000000001e176 < z < -1.3999999999999999e134 or -4.10000000000000022e-199 < z

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. 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-+l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+r+ 99.9%

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

      6. associate-+r+ 99.9%

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

      7. associate-+l+ 99.9%

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

      8. +-commutative 99.9%

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

      9. associate-+r+ 99.9%

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

      10. associate-+r+ 99.9%

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

      11. fma-def 99.9%

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

      12. sub-neg 99.9%

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

      13. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around inf 17.7%

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

   if -5.29999999999999967e113 < z < -4.10000000000000022e-199

   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 82.5%

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

   3. Taylor expanded in y around inf 30.5%

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

      1. *-commutative 30.5%

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

   5. Simplified 30.5%

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

4. Final simplification 26.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+176}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{+134}:\\ \;\;\;\;a\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{+113}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-199}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 16: 66.2% accurate, 24.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

   2. add-cube-cbrt 99.7%

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

   3. fma-def 99.7%

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

   4. pow2 99.7%

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

   5. sub-neg 99.7%

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

   6. metadata-eval 99.7%

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

   7. sub-neg 99.7%

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

   8. metadata-eval 99.7%

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

   9. +-commutative 99.7%

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

   10. +-commutative 99.7%

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

   11. fma-def 99.7%

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

3. Applied egg-rr 99.7%

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

4. Taylor expanded in b around inf 83.2%

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

5. Taylor expanded in x around 0 70.1%

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

   1. associate-+r+ 70.1%

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

   2. *-commutative 70.1%

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

7. Simplified 70.1%

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

8. Final simplification 70.1%

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

Alternative 17: 41.0% accurate, 31.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+111}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -4.1e+111) (+ z a) (+ 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 <= -4.1e+111) {
		tmp = z + a;
	} 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 <= (-4.1d+111)) then
        tmp = z + a
    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 <= -4.1e+111) {
		tmp = z + a;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -4.1e+111:
		tmp = z + a
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -4.1e+111)
		tmp = Float64(z + a);
	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 <= -4.1e+111)
		tmp = z + a;
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -4.1e+111], N[(z + a), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.09999999999999986e111

   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-+l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+r+ 99.9%

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

      6. associate-+r+ 99.9%

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

      7. associate-+l+ 99.9%

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

      8. +-commutative 99.9%

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

      9. associate-+r+ 99.9%

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

      10. associate-+r+ 99.9%

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

      11. fma-def 99.9%

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

      12. sub-neg 99.9%

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

      13. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in b around inf 61.0%

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

   5. Taylor expanded in b around 0 56.3%

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

   if -4.09999999999999986e111 < z

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. add-cube-cbrt 99.6%

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

      3. fma-def 99.6%

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

      4. pow2 99.6%

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

      5. sub-neg 99.6%

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

      6. metadata-eval 99.6%

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

      7. sub-neg 99.6%

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

      8. metadata-eval 99.6%

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

      9. +-commutative 99.6%

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

      10. +-commutative 99.6%

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

      11. fma-def 99.6%

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

   3. Applied egg-rr 99.6%

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

   4. Taylor expanded in a around inf 44.0%

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

4. Final simplification 46.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+111}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]

Alternative 18: 41.8% accurate, 31.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.95 \cdot 10^{+175}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -2.95e+175) (+ z (* y i)) (+ a (* y i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -2.95e+175) {
		tmp = z + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-2.95d+175)) then
        tmp = z + (y * i)
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -2.95e+175) {
		tmp = z + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -2.95e+175:
		tmp = z + (y * i)
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -2.95e+175)
		tmp = Float64(z + Float64(y * i));
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -2.95e+175)
		tmp = z + (y * i);
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -2.95e+175], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.95000000000000015e175

   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%

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

      2. add-cube-cbrt 99.7%

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

      3. fma-def 99.7%

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

      4. pow2 99.7%

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

      5. sub-neg 99.7%

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

      6. metadata-eval 99.7%

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

      7. sub-neg 99.7%

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

      8. metadata-eval 99.7%

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

      9. +-commutative 99.7%

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

      10. +-commutative 99.7%

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

      11. fma-def 99.7%

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

   3. Applied egg-rr 99.7%

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

   4. Taylor expanded in z around inf 74.7%

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

   if -2.95000000000000015e175 < z

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. add-cube-cbrt 99.7%

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

      3. fma-def 99.7%

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

      4. pow2 99.7%

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

      5. sub-neg 99.7%

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

      6. metadata-eval 99.7%

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

      7. sub-neg 99.7%

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

      8. metadata-eval 99.7%

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

      9. +-commutative 99.7%

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

      10. +-commutative 99.7%

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

      11. fma-def 99.7%

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

   3. Applied egg-rr 99.7%

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

   4. Taylor expanded in a around inf 43.4%

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

4. Final simplification 47.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.95 \cdot 10^{+175}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]

Alternative 19: 51.8% accurate, 31.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

   \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
2. 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-+l+ 99.9%

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

   3. associate-+r+ 99.9%

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

   4. +-commutative 99.9%

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

   5. associate-+r+ 99.9%

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

   6. associate-+r+ 99.9%

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

   7. associate-+l+ 99.9%

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

   8. +-commutative 99.9%

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

   9. associate-+r+ 99.9%

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

   10. associate-+r+ 99.9%

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

   11. fma-def 99.9%

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

   12. sub-neg 99.9%

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

   13. metadata-eval 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in y around inf 56.3%

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

   1. *-commutative 56.3%

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

6. Simplified 56.3%

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

7. Final simplification 56.3%

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

Alternative 20: 39.9% accurate, 43.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 9 \cdot 10^{+88}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 9e+88) (+ 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 (y <= 9e+88) {
		tmp = z + a;
	} else {
		tmp = y * i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= 9d+88) then
        tmp = z + a
    else
        tmp = y * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 9e+88) {
		tmp = z + a;
	} else {
		tmp = y * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 9e+88:
		tmp = z + a
	else:
		tmp = y * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 9e+88)
		tmp = Float64(z + a);
	else
		tmp = Float64(y * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= 9e+88)
		tmp = z + a;
	else
		tmp = y * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 9e+88], N[(z + a), $MachinePrecision], N[(y * i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 9e88

   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-+l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+r+ 99.9%

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

      6. associate-+r+ 99.9%

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

      7. associate-+l+ 99.9%

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

      8. +-commutative 99.9%

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

      9. associate-+r+ 99.9%

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

      10. associate-+r+ 99.9%

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

      11. fma-def 99.9%

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

      12. sub-neg 99.9%

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

      13. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in b around inf 51.4%

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

   5. Taylor expanded in b around 0 36.0%

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

   if 9e88 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 91.9%

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

   3. Taylor expanded in y around inf 54.6%

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

      1. *-commutative 54.6%

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

   5. Simplified 54.6%

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

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 9 \cdot 10^{+88}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \]

Alternative 21: 20.5% accurate, 71.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+175}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (if (<= z -6.2e+175) 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 <= -6.2e+175) {
		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 <= (-6.2d+175)) 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 <= -6.2e+175) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -6.2e+175:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -6.2e+175)
		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 <= -6.2e+175)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -6.2e+175], z, a]

Derivation

1. Split input into 2 regimes

2. if z < -6.19999999999999968e175

   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-+l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+r+ 99.9%

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

      6. associate-+r+ 99.9%

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

      7. associate-+l+ 99.9%

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

      8. +-commutative 99.9%

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

      9. associate-+r+ 99.9%

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

      10. associate-+r+ 99.9%

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

      11. fma-def 99.9%

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

      12. sub-neg 99.9%

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

      13. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 54.1%

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

   if -6.19999999999999968e175 < z

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. 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-+l+ 99.9%

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

      3. associate-+r+ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+r+ 99.9%

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

      6. associate-+r+ 99.9%

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

      7. associate-+l+ 99.9%

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

      8. +-commutative 99.9%

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

      9. associate-+r+ 99.9%

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

      10. associate-+r+ 99.9%

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

      11. fma-def 99.9%

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

      12. sub-neg 99.9%

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

      13. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around inf 17.9%

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

4. Final simplification 22.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+175}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 22: 15.6% 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. 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-+l+ 99.9%

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

   3. associate-+r+ 99.9%

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

   4. +-commutative 99.9%

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

   5. associate-+r+ 99.9%

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

   6. associate-+r+ 99.9%

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

   7. associate-+l+ 99.9%

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

   8. +-commutative 99.9%

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

   9. associate-+r+ 99.9%

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

   10. associate-+r+ 99.9%

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

   11. fma-def 99.9%

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

   12. sub-neg 99.9%

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

   13. metadata-eval 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in a around inf 16.1%

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

5. Final simplification 16.1%

   \[\leadsto a \]

Reproduce

herbie shell --seed 2023242 
(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)))