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

Percentage Accurate: 99.8% → 99.8%

Time: 14.5s

Alternatives: 18

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.7× speedup

Math

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

FPCore

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

Julia

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

Wolfram

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

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

   2. associate-+l+ 99.9%

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

   3. associate-+l+ 99.9%

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

   4. +-commutative 99.9%

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

   5. associate-+l+ 99.9%

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

   6. fma-def 99.9%

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

   7. +-commutative 99.9%

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

   8. sub-neg 99.9%

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

   9. metadata-eval 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Final simplification 99.9%

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

Alternative 3: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in b around inf 97.7%

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

   1. *-commutative 97.7%

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

4. Simplified 97.7%

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

5. Final simplification 97.7%

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

Alternative 4: 92.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+127}:\\ \;\;\;\;y \cdot i + \left(z + \mathsf{fma}\left(x, \log y, a\right)\right)\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+92}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + x \cdot \log y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -2.1e+127)
   (+ (* y i) (+ z (fma x (log y) a)))
   (if (<= x 3.6e+92)
     (+ (* y i) (+ (* (log c) (- b 0.5)) (+ a (+ z t))))
     (+ (* y i) (+ a (+ z (* x (log y))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -2.1e+127) {
		tmp = (y * i) + (z + fma(x, log(y), a));
	} else if (x <= 3.6e+92) {
		tmp = (y * i) + ((log(c) * (b - 0.5)) + (a + (z + t)));
	} else {
		tmp = (y * i) + (a + (z + (x * log(y))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -2.1e+127)
		tmp = Float64(Float64(y * i) + Float64(z + fma(x, log(y), a)));
	elseif (x <= 3.6e+92)
		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(z + Float64(x * log(y)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -2.1e+127], N[(N[(y * i), $MachinePrecision] + N[(z + N[(x * N[Log[y], $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.6e+92], 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[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.09999999999999992e127

   1. Initial program 99.6%

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

      1. associate-+l+ 99.6%

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

      2. associate-+l+ 99.7%

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

      3. associate-+l+ 99.7%

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

      4. +-commutative 99.7%

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

      5. associate-+l+ 99.7%

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

      6. fma-def 99.7%

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

      7. +-commutative 99.7%

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

      8. sub-neg 99.7%

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

      9. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 97.7%

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

      1. *-commutative 97.7%

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

   6. Simplified 97.7%

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

   7. Taylor expanded in t around 0 89.5%

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

      1. +-commutative 89.5%

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

      2. associate-+r+ 89.5%

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

      3. +-commutative 89.5%

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

      4. fma-def 89.5%

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

      5. +-commutative 89.5%

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

   9. Simplified 89.5%

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

   if -2.09999999999999992e127 < x < 3.6e92

   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 97.4%

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

   if 3.6e92 < x

   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. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. associate-+l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+l+ 99.9%

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

      6. fma-def 99.9%

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

      7. +-commutative 99.9%

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

      8. sub-neg 99.9%

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

      9. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 92.4%

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

      1. *-commutative 92.4%

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

   6. Simplified 92.4%

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

   7. Taylor expanded in t around 0 89.3%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+127}:\\ \;\;\;\;y \cdot i + \left(z + \mathsf{fma}\left(x, \log y, a\right)\right)\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+92}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + x \cdot \log y\right)\right)\\ \end{array} \]

Alternative 5: 89.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -2 \cdot 10^{+164} \lor \neg \left(b - 0.5 \leq 2.5 \cdot 10^{+204}\right):\\ \;\;\;\;y \cdot i + \left(z + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (- b 0.5) -2e+164) (not (<= (- b 0.5) 2.5e+204)))
   (+ (* y i) (+ z (* b (log c))))
   (+ (* y i) (+ a (+ t (+ z (* x (log y))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((b - 0.5) <= -2e+164) || !((b - 0.5) <= 2.5e+204)) {
		tmp = (y * i) + (z + (b * log(c)));
	} else {
		tmp = (y * i) + (a + (t + (z + (x * log(y)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((b - 0.5d0) <= (-2d+164)) .or. (.not. ((b - 0.5d0) <= 2.5d+204))) then
        tmp = (y * i) + (z + (b * log(c)))
    else
        tmp = (y * i) + (a + (t + (z + (x * log(y)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((b - 0.5) <= -2e+164) || !((b - 0.5) <= 2.5e+204)) {
		tmp = (y * i) + (z + (b * Math.log(c)));
	} else {
		tmp = (y * i) + (a + (t + (z + (x * Math.log(y)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((b - 0.5) <= -2e+164) or not ((b - 0.5) <= 2.5e+204):
		tmp = (y * i) + (z + (b * math.log(c)))
	else:
		tmp = (y * i) + (a + (t + (z + (x * math.log(y)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(b - 0.5) <= -2e+164) || !(Float64(b - 0.5) <= 2.5e+204))
		tmp = Float64(Float64(y * i) + Float64(z + Float64(b * log(c))));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(t + Float64(z + Float64(x * log(y))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((b - 0.5) <= -2e+164) || ~(((b - 0.5) <= 2.5e+204)))
		tmp = (y * i) + (z + (b * log(c)));
	else
		tmp = (y * i) + (a + (t + (z + (x * log(y)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(b - 0.5), $MachinePrecision], -2e+164], N[Not[LessEqual[N[(b - 0.5), $MachinePrecision], 2.5e+204]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(z + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 b 1/2) < -2e164 or 2.50000000000000004e204 < (-.f64 b 1/2)

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 95.8%

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

      1. +-commutative 95.8%

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

      2. associate-+l+ 95.8%

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

      3. +-commutative 95.8%

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

      4. sub-neg 95.8%

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

      5. metadata-eval 95.8%

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

      6. associate-+r+ 95.8%

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

      7. fma-def 95.8%

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

      8. fma-def 95.8%

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

      9. +-commutative 95.8%

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

   4. Simplified 95.8%

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

   5. Taylor expanded in b around inf 85.8%

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

      1. *-commutative 85.8%

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

   7. Simplified 85.8%

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

   if -2e164 < (-.f64 b 1/2) < 2.50000000000000004e204

   1. Initial program 99.9%

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

   2. Taylor expanded in b around inf 97.2%

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

      1. *-commutative 97.2%

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

   4. Simplified 97.2%

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

   5. Taylor expanded in b around 0 93.7%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -2 \cdot 10^{+164} \lor \neg \left(b - 0.5 \leq 2.5 \cdot 10^{+204}\right):\\ \;\;\;\;y \cdot i + \left(z + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right)\\ \end{array} \]

Alternative 6: 76.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -2 \cdot 10^{+164} \lor \neg \left(b - 0.5 \leq 2.5 \cdot 10^{+204}\right):\\ \;\;\;\;y \cdot i + \left(z + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + x \cdot \log y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (- b 0.5) -2e+164) (not (<= (- b 0.5) 2.5e+204)))
   (+ (* y i) (+ z (* b (log c))))
   (+ (* y i) (+ a (+ z (* x (log y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((b - 0.5) <= -2e+164) || !((b - 0.5) <= 2.5e+204)) {
		tmp = (y * i) + (z + (b * log(c)));
	} else {
		tmp = (y * i) + (a + (z + (x * log(y))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((b - 0.5d0) <= (-2d+164)) .or. (.not. ((b - 0.5d0) <= 2.5d+204))) then
        tmp = (y * i) + (z + (b * log(c)))
    else
        tmp = (y * i) + (a + (z + (x * log(y))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((b - 0.5) <= -2e+164) || !((b - 0.5) <= 2.5e+204)) {
		tmp = (y * i) + (z + (b * Math.log(c)));
	} else {
		tmp = (y * i) + (a + (z + (x * Math.log(y))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((b - 0.5) <= -2e+164) or not ((b - 0.5) <= 2.5e+204):
		tmp = (y * i) + (z + (b * math.log(c)))
	else:
		tmp = (y * i) + (a + (z + (x * math.log(y))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(b - 0.5) <= -2e+164) || !(Float64(b - 0.5) <= 2.5e+204))
		tmp = Float64(Float64(y * i) + Float64(z + Float64(b * log(c))));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + Float64(x * log(y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((b - 0.5) <= -2e+164) || ~(((b - 0.5) <= 2.5e+204)))
		tmp = (y * i) + (z + (b * log(c)));
	else
		tmp = (y * i) + (a + (z + (x * log(y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(b - 0.5), $MachinePrecision], -2e+164], N[Not[LessEqual[N[(b - 0.5), $MachinePrecision], 2.5e+204]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(z + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 b 1/2) < -2e164 or 2.50000000000000004e204 < (-.f64 b 1/2)

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 95.8%

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

      1. +-commutative 95.8%

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

      2. associate-+l+ 95.8%

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

      3. +-commutative 95.8%

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

      4. sub-neg 95.8%

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

      5. metadata-eval 95.8%

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

      6. associate-+r+ 95.8%

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

      7. fma-def 95.8%

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

      8. fma-def 95.8%

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

      9. +-commutative 95.8%

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

   4. Simplified 95.8%

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

   5. Taylor expanded in b around inf 85.8%

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

      1. *-commutative 85.8%

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

   7. Simplified 85.8%

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

   if -2e164 < (-.f64 b 1/2) < 2.50000000000000004e204

   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. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. associate-+l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+l+ 99.9%

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

      6. fma-def 99.9%

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

      7. +-commutative 99.9%

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

      8. sub-neg 99.9%

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

      9. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 93.8%

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

      1. *-commutative 93.8%

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

   6. Simplified 93.8%

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

   7. Taylor expanded in t around 0 78.6%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -2 \cdot 10^{+164} \lor \neg \left(b - 0.5 \leq 2.5 \cdot 10^{+204}\right):\\ \;\;\;\;y \cdot i + \left(z + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + x \cdot \log y\right)\right)\\ \end{array} \]

Alternative 7: 92.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.34 \cdot 10^{+132} \lor \neg \left(x \leq 1.5 \cdot 10^{+91}\right):\\ \;\;\;\;y \cdot i + \left(a + \left(z + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -1.34e+132) (not (<= x 1.5e+91)))
   (+ (* y i) (+ a (+ z (* x (log y)))))
   (+ (* 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 <= -1.34e+132) || !(x <= 1.5e+91)) {
		tmp = (y * i) + (a + (z + (x * log(y))));
	} 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 <= (-1.34d+132)) .or. (.not. (x <= 1.5d+91))) then
        tmp = (y * i) + (a + (z + (x * log(y))))
    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 <= -1.34e+132) || !(x <= 1.5e+91)) {
		tmp = (y * i) + (a + (z + (x * Math.log(y))));
	} 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 <= -1.34e+132) or not (x <= 1.5e+91):
		tmp = (y * i) + (a + (z + (x * math.log(y))))
	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 <= -1.34e+132) || !(x <= 1.5e+91))
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + Float64(x * log(y)))));
	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 <= -1.34e+132) || ~((x <= 1.5e+91)))
		tmp = (y * i) + (a + (z + (x * log(y))));
	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, -1.34e+132], N[Not[LessEqual[x, 1.5e+91]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + N[(x * N[Log[y], $MachinePrecision]), $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 < -1.34000000000000002e132 or 1.50000000000000003e91 < 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. associate-+l+ 99.8%

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

      2. associate-+l+ 99.8%

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

      3. associate-+l+ 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-+l+ 99.8%

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

      6. fma-def 99.8%

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

      7. +-commutative 99.8%

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

      8. sub-neg 99.8%

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

      9. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 94.7%

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

      1. *-commutative 94.7%

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

   6. Simplified 94.7%

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

   7. Taylor expanded in t around 0 89.4%

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

   if -1.34000000000000002e132 < x < 1.50000000000000003e91

   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 97.4%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.34 \cdot 10^{+132} \lor \neg \left(x \leq 1.5 \cdot 10^{+91}\right):\\ \;\;\;\;y \cdot i + \left(a + \left(z + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \]

Alternative 8: 80.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+126} \lor \neg \left(x \leq 2.8 \cdot 10^{+90}\right):\\ \;\;\;\;y \cdot i + \left(a + \left(z + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(b + -0.5\right) \cdot \log c + \left(z + a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -9e+126) (not (<= x 2.8e+90)))
   (+ (* y i) (+ a (+ z (* x (log y)))))
   (+ (* y i) (+ (* (+ b -0.5) (log c)) (+ z a)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -9e+126) || !(x <= 2.8e+90)) {
		tmp = (y * i) + (a + (z + (x * log(y))));
	} else {
		tmp = (y * i) + (((b + -0.5) * log(c)) + (z + a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-9d+126)) .or. (.not. (x <= 2.8d+90))) then
        tmp = (y * i) + (a + (z + (x * log(y))))
    else
        tmp = (y * i) + (((b + (-0.5d0)) * log(c)) + (z + a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -9e+126) || !(x <= 2.8e+90)) {
		tmp = (y * i) + (a + (z + (x * Math.log(y))));
	} else {
		tmp = (y * i) + (((b + -0.5) * Math.log(c)) + (z + a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -9e+126) or not (x <= 2.8e+90):
		tmp = (y * i) + (a + (z + (x * math.log(y))))
	else:
		tmp = (y * i) + (((b + -0.5) * math.log(c)) + (z + a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -9e+126) || !(x <= 2.8e+90))
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + Float64(x * log(y)))));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(Float64(b + -0.5) * log(c)) + Float64(z + a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -9e+126) || ~((x <= 2.8e+90)))
		tmp = (y * i) + (a + (z + (x * log(y))));
	else
		tmp = (y * i) + (((b + -0.5) * log(c)) + (z + a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -9e+126], N[Not[LessEqual[x, 2.8e+90]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(N[(b + -0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.99999999999999947e126 or 2.8e90 < 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. associate-+l+ 99.8%

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

      2. associate-+l+ 99.8%

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

      3. associate-+l+ 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-+l+ 99.8%

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

      6. fma-def 99.8%

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

      7. +-commutative 99.8%

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

      8. sub-neg 99.8%

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

      9. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 94.7%

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

      1. *-commutative 94.7%

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

   6. Simplified 94.7%

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

   7. Taylor expanded in t around 0 89.4%

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

   if -8.99999999999999947e126 < x < 2.8e90

   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 t around 0 82.6%

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

      1. +-commutative 82.6%

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

      2. associate-+l+ 82.6%

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

      3. +-commutative 82.6%

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

      4. sub-neg 82.6%

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

      5. metadata-eval 82.6%

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

      6. associate-+r+ 82.6%

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

      7. fma-def 82.6%

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

      8. fma-def 82.6%

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

      9. +-commutative 82.6%

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

   4. Simplified 82.6%

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

   5. Taylor expanded in x around 0 80.5%

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

      1. associate-+r+ 80.5%

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

      2. sub-neg 80.5%

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

      3. metadata-eval 80.5%

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

   7. Simplified 80.5%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+126} \lor \neg \left(x \leq 2.8 \cdot 10^{+90}\right):\\ \;\;\;\;y \cdot i + \left(a + \left(z + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(b + -0.5\right) \cdot \log c + \left(z + a\right)\right)\\ \end{array} \]

Alternative 9: 58.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 1.85 \cdot 10^{+101}:\\ \;\;\;\;y \cdot i + \left(z + x \cdot \log y\right)\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+209}:\\ \;\;\;\;y \cdot i + \left(a + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 1.85e+101)
   (+ (* y i) (+ z (* x (log y))))
   (if (<= a 6.5e+209)
     (+ (* y i) (+ a (* (log c) (- b 0.5))))
     (+ (* y i) (+ z a)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 1.85e+101) {
		tmp = (y * i) + (z + (x * log(y)));
	} else if (a <= 6.5e+209) {
		tmp = (y * i) + (a + (log(c) * (b - 0.5)));
	} else {
		tmp = (y * i) + (z + a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 1.85d+101) then
        tmp = (y * i) + (z + (x * log(y)))
    else if (a <= 6.5d+209) then
        tmp = (y * i) + (a + (log(c) * (b - 0.5d0)))
    else
        tmp = (y * i) + (z + a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 1.85e+101) {
		tmp = (y * i) + (z + (x * Math.log(y)));
	} else if (a <= 6.5e+209) {
		tmp = (y * i) + (a + (Math.log(c) * (b - 0.5)));
	} else {
		tmp = (y * i) + (z + a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 1.85e+101:
		tmp = (y * i) + (z + (x * math.log(y)))
	elif a <= 6.5e+209:
		tmp = (y * i) + (a + (math.log(c) * (b - 0.5)))
	else:
		tmp = (y * i) + (z + a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 1.85e+101)
		tmp = Float64(Float64(y * i) + Float64(z + Float64(x * log(y))));
	elseif (a <= 6.5e+209)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(log(c) * Float64(b - 0.5))));
	else
		tmp = Float64(Float64(y * i) + Float64(z + a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 1.85e+101)
		tmp = (y * i) + (z + (x * log(y)));
	elseif (a <= 6.5e+209)
		tmp = (y * i) + (a + (log(c) * (b - 0.5)));
	else
		tmp = (y * i) + (z + a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 1.85e+101], N[(N[(y * i), $MachinePrecision] + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.5e+209], N[(N[(y * i), $MachinePrecision] + N[(a + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < 1.8499999999999999e101

   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 t around 0 85.0%

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

      1. +-commutative 85.0%

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

      2. associate-+l+ 85.0%

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

      3. +-commutative 85.0%

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

      4. sub-neg 85.0%

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

      5. metadata-eval 85.0%

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

      6. associate-+r+ 85.0%

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

      7. fma-def 85.0%

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

      8. fma-def 85.0%

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

      9. +-commutative 85.0%

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

   4. Simplified 85.0%

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

   5. Taylor expanded in x around inf 60.1%

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

   if 1.8499999999999999e101 < a < 6.49999999999999975e209

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 93.3%

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

      1. +-commutative 93.3%

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

      2. associate-+l+ 93.3%

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

      3. +-commutative 93.3%

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

      4. sub-neg 93.3%

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

      5. metadata-eval 93.3%

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

      6. associate-+r+ 93.3%

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

      7. fma-def 93.3%

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

      8. fma-def 93.3%

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

      9. +-commutative 93.3%

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

   4. Simplified 93.3%

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

   5. Taylor expanded in x around 0 93.3%

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

      1. associate-+r+ 93.3%

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

      2. sub-neg 93.3%

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

      3. metadata-eval 93.3%

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

   7. Simplified 93.3%

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

   8. Taylor expanded in z around 0 93.3%

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

   if 6.49999999999999975e209 < a

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 95.2%

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

      1. +-commutative 95.2%

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

      2. associate-+l+ 95.2%

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

      3. +-commutative 95.2%

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

      4. sub-neg 95.2%

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

      5. metadata-eval 95.2%

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

      6. associate-+r+ 95.2%

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

      7. fma-def 95.2%

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

      8. fma-def 95.2%

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

      9. +-commutative 95.2%

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

   4. Simplified 95.2%

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

   5. Taylor expanded in a around inf 90.2%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.85 \cdot 10^{+101}:\\ \;\;\;\;y \cdot i + \left(z + x \cdot \log y\right)\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+209}:\\ \;\;\;\;y \cdot i + \left(a + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \end{array} \]

Alternative 10: 57.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 2.1 \cdot 10^{+56}:\\ \;\;\;\;y \cdot i + \left(z + x \cdot \log y\right)\\ \mathbf{elif}\;a \leq 5.7 \cdot 10^{+153} \lor \neg \left(a \leq 1.95 \cdot 10^{+180}\right):\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;a + \log c \cdot \left(b - 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 2.1e+56)
   (+ (* y i) (+ z (* x (log y))))
   (if (or (<= a 5.7e+153) (not (<= a 1.95e+180)))
     (+ (* y i) (+ z a))
     (+ a (* (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 (a <= 2.1e+56) {
		tmp = (y * i) + (z + (x * log(y)));
	} else if ((a <= 5.7e+153) || !(a <= 1.95e+180)) {
		tmp = (y * i) + (z + a);
	} else {
		tmp = a + (log(c) * (b - 0.5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 2.1d+56) then
        tmp = (y * i) + (z + (x * log(y)))
    else if ((a <= 5.7d+153) .or. (.not. (a <= 1.95d+180))) then
        tmp = (y * i) + (z + a)
    else
        tmp = a + (log(c) * (b - 0.5d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 2.1e+56) {
		tmp = (y * i) + (z + (x * Math.log(y)));
	} else if ((a <= 5.7e+153) || !(a <= 1.95e+180)) {
		tmp = (y * i) + (z + a);
	} else {
		tmp = a + (Math.log(c) * (b - 0.5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 2.1e+56:
		tmp = (y * i) + (z + (x * math.log(y)))
	elif (a <= 5.7e+153) or not (a <= 1.95e+180):
		tmp = (y * i) + (z + a)
	else:
		tmp = a + (math.log(c) * (b - 0.5))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 2.1e+56)
		tmp = Float64(Float64(y * i) + Float64(z + Float64(x * log(y))));
	elseif ((a <= 5.7e+153) || !(a <= 1.95e+180))
		tmp = Float64(Float64(y * i) + Float64(z + a));
	else
		tmp = Float64(a + Float64(log(c) * Float64(b - 0.5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 2.1e+56)
		tmp = (y * i) + (z + (x * log(y)));
	elseif ((a <= 5.7e+153) || ~((a <= 1.95e+180)))
		tmp = (y * i) + (z + a);
	else
		tmp = a + (log(c) * (b - 0.5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 2.1e+56], N[(N[(y * i), $MachinePrecision] + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, 5.7e+153], N[Not[LessEqual[a, 1.95e+180]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision], N[(a + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < 2.10000000000000017e56

   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 t around 0 85.1%

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

      1. +-commutative 85.1%

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

      2. associate-+l+ 85.1%

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

      3. +-commutative 85.1%

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

      4. sub-neg 85.1%

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

      5. metadata-eval 85.1%

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

      6. associate-+r+ 85.1%

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

      7. fma-def 85.1%

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

      8. fma-def 85.1%

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

      9. +-commutative 85.1%

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

   4. Simplified 85.1%

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

   5. Taylor expanded in x around inf 60.3%

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

   if 2.10000000000000017e56 < a < 5.69999999999999987e153 or 1.95e180 < a

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 91.1%

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

      1. +-commutative 91.1%

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

      2. associate-+l+ 91.1%

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

      3. +-commutative 91.1%

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

      4. sub-neg 91.1%

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

      5. metadata-eval 91.1%

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

      6. associate-+r+ 91.1%

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

      7. fma-def 91.1%

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

      8. fma-def 91.1%

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

      9. +-commutative 91.1%

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

   4. Simplified 91.1%

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

   5. Taylor expanded in a around inf 86.6%

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

   if 5.69999999999999987e153 < a < 1.95e180

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. associate-+r+ 100.0%

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

      7. fma-def 100.0%

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

      8. fma-def 100.0%

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

      9. +-commutative 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in x around 0 100.0%

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

      1. associate-+r+ 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in z around 0 100.0%

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

   9. Taylor expanded in y around 0 100.0%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 2.1 \cdot 10^{+56}:\\ \;\;\;\;y \cdot i + \left(z + x \cdot \log y\right)\\ \mathbf{elif}\;a \leq 5.7 \cdot 10^{+153} \lor \neg \left(a \leq 1.95 \cdot 10^{+180}\right):\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;a + \log c \cdot \left(b - 0.5\right)\\ \end{array} \]

Alternative 11: 72.5% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := z + t_1\\ \mathbf{if}\;x \leq -3.8 \cdot 10^{+229}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{+207}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{+185}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+221}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (+ z t_1)))
   (if (<= x -3.8e+229)
     t_2
     (if (<= x -1.4e+207)
       (+ (* y i) (+ z a))
       (if (<= x -5.5e+185)
         t_2
         (if (<= x 7.5e+221) (+ (* y i) (+ t (+ z a))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * log(y);
	double t_2 = z + t_1;
	double tmp;
	if (x <= -3.8e+229) {
		tmp = t_2;
	} else if (x <= -1.4e+207) {
		tmp = (y * i) + (z + a);
	} else if (x <= -5.5e+185) {
		tmp = t_2;
	} else if (x <= 7.5e+221) {
		tmp = (y * i) + (t + (z + a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * log(y)
    t_2 = z + t_1
    if (x <= (-3.8d+229)) then
        tmp = t_2
    else if (x <= (-1.4d+207)) then
        tmp = (y * i) + (z + a)
    else if (x <= (-5.5d+185)) then
        tmp = t_2
    else if (x <= 7.5d+221) then
        tmp = (y * i) + (t + (z + a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * Math.log(y);
	double t_2 = z + t_1;
	double tmp;
	if (x <= -3.8e+229) {
		tmp = t_2;
	} else if (x <= -1.4e+207) {
		tmp = (y * i) + (z + a);
	} else if (x <= -5.5e+185) {
		tmp = t_2;
	} else if (x <= 7.5e+221) {
		tmp = (y * i) + (t + (z + a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x * math.log(y)
	t_2 = z + t_1
	tmp = 0
	if x <= -3.8e+229:
		tmp = t_2
	elif x <= -1.4e+207:
		tmp = (y * i) + (z + a)
	elif x <= -5.5e+185:
		tmp = t_2
	elif x <= 7.5e+221:
		tmp = (y * i) + (t + (z + a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * log(y))
	t_2 = Float64(z + t_1)
	tmp = 0.0
	if (x <= -3.8e+229)
		tmp = t_2;
	elseif (x <= -1.4e+207)
		tmp = Float64(Float64(y * i) + Float64(z + a));
	elseif (x <= -5.5e+185)
		tmp = t_2;
	elseif (x <= 7.5e+221)
		tmp = Float64(Float64(y * i) + Float64(t + Float64(z + a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x * log(y);
	t_2 = z + t_1;
	tmp = 0.0;
	if (x <= -3.8e+229)
		tmp = t_2;
	elseif (x <= -1.4e+207)
		tmp = (y * i) + (z + a);
	elseif (x <= -5.5e+185)
		tmp = t_2;
	elseif (x <= 7.5e+221)
		tmp = (y * i) + (t + (z + a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z + t$95$1), $MachinePrecision]}, If[LessEqual[x, -3.8e+229], t$95$2, If[LessEqual[x, -1.4e+207], N[(N[(y * i), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.5e+185], t$95$2, If[LessEqual[x, 7.5e+221], N[(N[(y * i), $MachinePrecision] + N[(t + N[(z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.80000000000000018e229 or -1.40000000000000005e207 < x < -5.4999999999999996e185

   1. Initial program 99.3%

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

   2. Taylor expanded in t around 0 91.9%

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

      1. +-commutative 91.9%

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

      2. associate-+l+ 91.9%

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

      3. +-commutative 91.9%

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

      4. sub-neg 91.9%

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

      5. metadata-eval 91.9%

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

      6. associate-+r+ 91.9%

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

      7. fma-def 91.9%

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

      8. fma-def 91.9%

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

      9. +-commutative 91.9%

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

   4. Simplified 91.9%

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

   5. Taylor expanded in x around inf 84.9%

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

   6. Taylor expanded in y around 0 84.9%

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

   if -3.80000000000000018e229 < x < -1.40000000000000005e207

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. associate-+r+ 100.0%

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

      7. fma-def 100.0%

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

      8. fma-def 100.0%

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

      9. +-commutative 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in a around inf 87.6%

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

   if -5.4999999999999996e185 < x < 7.50000000000000035e221

   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. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. associate-+l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+l+ 99.9%

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

      6. fma-def 99.9%

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

      7. +-commutative 99.9%

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

      8. sub-neg 99.9%

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

      9. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 83.1%

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

      1. *-commutative 83.1%

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

   6. Simplified 83.1%

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

   7. Taylor expanded in x around 0 78.5%

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

      1. +-commutative 78.5%

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

      2. associate-+l+ 78.5%

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

   9. Simplified 78.5%

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

   if 7.50000000000000035e221 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. sub-neg 99.8%

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

      5. metadata-eval 99.8%

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

      6. associate-+r+ 99.8%

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

      7. fma-def 99.8%

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

      8. fma-def 99.8%

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

      9. +-commutative 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in x around inf 96.9%

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

   6. Taylor expanded in z around 0 96.9%

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

   7. Taylor expanded in x around inf 74.4%

      \[\leadsto \color{blue}{x \cdot \log y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+229}:\\ \;\;\;\;z + x \cdot \log y\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{+207}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{+185}:\\ \;\;\;\;z + x \cdot \log y\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+221}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \]

Alternative 12: 74.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -1.6 \cdot 10^{+227}:\\ \;\;\;\;z + t_1\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+215}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -1.6e+227)
     (+ z t_1)
     (if (<= x 3.2e+215) (+ (* y i) (+ t (+ z a))) (+ (* y i) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * log(y);
	double tmp;
	if (x <= -1.6e+227) {
		tmp = z + t_1;
	} else if (x <= 3.2e+215) {
		tmp = (y * i) + (t + (z + a));
	} else {
		tmp = (y * i) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * log(y)
    if (x <= (-1.6d+227)) then
        tmp = z + t_1
    else if (x <= 3.2d+215) then
        tmp = (y * i) + (t + (z + a))
    else
        tmp = (y * i) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * Math.log(y);
	double tmp;
	if (x <= -1.6e+227) {
		tmp = z + t_1;
	} else if (x <= 3.2e+215) {
		tmp = (y * i) + (t + (z + a));
	} else {
		tmp = (y * i) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x * math.log(y)
	tmp = 0
	if x <= -1.6e+227:
		tmp = z + t_1
	elif x <= 3.2e+215:
		tmp = (y * i) + (t + (z + a))
	else:
		tmp = (y * i) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -1.6e+227)
		tmp = Float64(z + t_1);
	elseif (x <= 3.2e+215)
		tmp = Float64(Float64(y * i) + Float64(t + Float64(z + a)));
	else
		tmp = Float64(Float64(y * i) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x * log(y);
	tmp = 0.0;
	if (x <= -1.6e+227)
		tmp = z + t_1;
	elseif (x <= 3.2e+215)
		tmp = (y * i) + (t + (z + a));
	else
		tmp = (y * i) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.6e+227], N[(z + t$95$1), $MachinePrecision], If[LessEqual[x, 3.2e+215], N[(N[(y * i), $MachinePrecision] + N[(t + N[(z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.59999999999999994e227

   1. Initial program 99.4%

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

   2. Taylor expanded in t around 0 97.1%

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

      1. +-commutative 97.1%

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

      2. associate-+l+ 97.1%

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

      3. +-commutative 97.1%

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

      4. sub-neg 97.1%

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

      5. metadata-eval 97.1%

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

      6. associate-+r+ 97.1%

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

      7. fma-def 97.1%

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

      8. fma-def 97.1%

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

      9. +-commutative 97.1%

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

   4. Simplified 97.1%

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

   5. Taylor expanded in x around inf 83.2%

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

   6. Taylor expanded in y around 0 83.2%

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

   if -1.59999999999999994e227 < x < 3.1999999999999999e215

   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. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. associate-+l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+l+ 99.9%

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

      6. fma-def 99.9%

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

      7. +-commutative 99.9%

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

      8. sub-neg 99.9%

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

      9. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 84.1%

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

      1. *-commutative 84.1%

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

   6. Simplified 84.1%

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

   7. Taylor expanded in x around 0 77.2%

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

      1. +-commutative 77.2%

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

      2. associate-+l+ 77.2%

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

   9. Simplified 77.2%

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

   if 3.1999999999999999e215 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. sub-neg 99.8%

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

      5. metadata-eval 99.8%

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

      6. associate-+r+ 99.8%

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

      7. fma-def 99.8%

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

      8. fma-def 99.8%

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

      9. +-commutative 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in x around inf 97.3%

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

   6. Taylor expanded in z around 0 97.3%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+227}:\\ \;\;\;\;z + x \cdot \log y\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+215}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + x \cdot \log y\\ \end{array} \]

Alternative 13: 72.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+250} \lor \neg \left(x \leq 1.35 \cdot 10^{+223}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -5e+250) (not (<= x 1.35e+223)))
   (* x (log y))
   (+ (* y i) (+ t (+ z a)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -5e+250) || !(x <= 1.35e+223)) {
		tmp = x * log(y);
	} else {
		tmp = (y * i) + (t + (z + a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-5d+250)) .or. (.not. (x <= 1.35d+223))) then
        tmp = x * log(y)
    else
        tmp = (y * i) + (t + (z + a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -5e+250) || !(x <= 1.35e+223)) {
		tmp = x * Math.log(y);
	} else {
		tmp = (y * i) + (t + (z + a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -5e+250) or not (x <= 1.35e+223):
		tmp = x * math.log(y)
	else:
		tmp = (y * i) + (t + (z + a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -5e+250) || !(x <= 1.35e+223))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(Float64(y * i) + Float64(t + Float64(z + a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -5e+250) || ~((x <= 1.35e+223)))
		tmp = x * log(y);
	else
		tmp = (y * i) + (t + (z + a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -5e+250], N[Not[LessEqual[x, 1.35e+223]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(t + N[(z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.0000000000000002e250 or 1.35e223 < x

   1. Initial program 99.7%

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

   2. Taylor expanded in t around 0 98.9%

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

      1. +-commutative 98.9%

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

      2. associate-+l+ 98.9%

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

      3. +-commutative 98.9%

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

      4. sub-neg 98.9%

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

      5. metadata-eval 98.9%

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

      6. associate-+r+ 98.9%

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

      7. fma-def 98.9%

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

      8. fma-def 98.9%

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

      9. +-commutative 98.9%

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

   4. Simplified 98.9%

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

   5. Taylor expanded in x around inf 96.4%

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

   6. Taylor expanded in z around 0 96.4%

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

   7. Taylor expanded in x around inf 80.4%

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

   if -5.0000000000000002e250 < x < 1.35e223

   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. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. associate-+l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+l+ 99.9%

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

      6. fma-def 99.9%

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

      7. +-commutative 99.9%

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

      8. sub-neg 99.9%

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

      9. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 84.3%

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

      1. *-commutative 84.3%

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

   6. Simplified 84.3%

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

   7. Taylor expanded in x around 0 77.4%

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

      1. +-commutative 77.4%

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

      2. associate-+l+ 77.4%

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

   9. Simplified 77.4%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+250} \lor \neg \left(x \leq 1.35 \cdot 10^{+223}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + a\right)\right)\\ \end{array} \]

Alternative 14: 67.7% accurate, 24.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. associate-+l+ 99.9%

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

   2. associate-+l+ 99.9%

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

   3. associate-+l+ 99.9%

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

   4. +-commutative 99.9%

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

   5. associate-+l+ 99.9%

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

   6. fma-def 99.9%

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

   7. +-commutative 99.9%

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

   8. sub-neg 99.9%

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

   9. metadata-eval 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in y around inf 85.5%

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

   1. *-commutative 85.5%

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

6. Simplified 85.5%

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

7. Taylor expanded in x around 0 72.0%

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

   1. +-commutative 72.0%

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

   2. associate-+l+ 72.0%

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

9. Simplified 72.0%

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

10. Final simplification 72.0%

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

Alternative 15: 44.6% accurate, 31.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+79}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -3.4e+79) (+ 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 <= -3.4e+79) {
		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 <= (-3.4d+79)) 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 <= -3.4e+79) {
		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 <= -3.4e+79:
		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 <= -3.4e+79)
		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 <= -3.4e+79)
		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, -3.4e+79], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.40000000000000032e79

   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 t around 0 98.7%

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

      1. +-commutative 98.7%

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

      2. associate-+l+ 98.7%

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

      3. +-commutative 98.7%

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

      4. sub-neg 98.7%

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

      5. metadata-eval 98.7%

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

      6. associate-+r+ 98.7%

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

      7. fma-def 98.7%

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

      8. fma-def 98.7%

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

      9. +-commutative 98.7%

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

   4. Simplified 98.7%

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

   5. Taylor expanded in z around inf 61.9%

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

   if -3.40000000000000032e79 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in a around inf 46.6%

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

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+79}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]

Alternative 16: 53.6% accurate, 31.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in t around 0 86.3%

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

   1. +-commutative 86.3%

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

   2. associate-+l+ 86.3%

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

   3. +-commutative 86.3%

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

   4. sub-neg 86.3%

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

   5. metadata-eval 86.3%

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

   6. associate-+r+ 86.3%

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

   7. fma-def 86.3%

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

   8. fma-def 86.3%

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

   9. +-commutative 86.3%

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

4. Simplified 86.3%

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

5. Taylor expanded in a around inf 59.2%

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

6. Final simplification 59.2%

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

Alternative 17: 40.4% accurate, 43.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in a around inf 43.3%

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

3. Final simplification 43.3%

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

Alternative 18: 25.9% accurate, 73.0× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in a around inf 43.3%

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

3. Taylor expanded in a around 0 27.0%

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

   1. *-commutative 27.0%

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

5. Simplified 27.0%

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

6. Final simplification 27.0%

   \[\leadsto y \cdot i \]

Reproduce

herbie shell --seed 2023333 
(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)))