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

Percentage Accurate: 99.8% → 99.8%

Time: 20.0s

Alternatives: 19

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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. +-commutative 99.8%

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

   2. associate-+r+ 99.8%

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

   3. +-commutative 99.8%

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

   4. associate-+r+ 99.8%

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

   5. +-commutative 99.8%

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

   6. associate-+r+ 99.8%

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

   7. fma-def 99.8%

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

   8. associate-+l+ 99.8%

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

   9. +-commutative 99.8%

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

   10. associate-+r+ 99.8%

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

   11. +-commutative 99.8%

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

   12. associate-+l+ 99.8%

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

3. Simplified 99.8%

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

   1. fma-udef 99.8%

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

   2. fma-udef 99.8%

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

   3. metadata-eval 99.8%

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

   4. sub-neg 99.8%

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

   5. associate-+r+ 99.8%

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

   6. sub-neg 99.8%

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

   7. metadata-eval 99.8%

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

   8. *-commutative 99.8%

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

5. Applied egg-rr 99.8%

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

6. Final simplification 99.8%

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

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 99.8%

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

2. Final simplification 99.8%

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

Alternative 3: 84.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. +-commutative 99.8%

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

   2. associate-+r+ 99.8%

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

   3. +-commutative 99.8%

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

   4. associate-+r+ 99.8%

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

   5. +-commutative 99.8%

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

   6. associate-+r+ 99.8%

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

   7. fma-def 99.8%

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

   8. associate-+l+ 99.8%

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

   9. +-commutative 99.8%

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

   10. associate-+r+ 99.8%

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

   11. +-commutative 99.8%

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

   12. associate-+l+ 99.8%

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

3. Simplified 99.8%

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

4. Taylor expanded in t around 0 85.1%

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

5. Final simplification 85.1%

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

Alternative 4: 94.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+76} \lor \neg \left(x \leq 4 \cdot 10^{+118}\right):\\ \;\;\;\;y \cdot i + \left(\mathsf{fma}\left(x, \log y, a\right) + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -2.2e+76) (not (<= x 4e+118)))
   (+ (* y i) (+ (fma x (log y) a) (+ z t)))
   (+ (* y i) (+ (* (log c) (- b 0.5)) (+ a (+ z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -2.2e+76) || !(x <= 4e+118)) {
		tmp = (y * i) + (fma(x, log(y), a) + (z + t));
	} else {
		tmp = (y * i) + ((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 <= -2.2e+76) || !(x <= 4e+118))
		tmp = Float64(Float64(y * i) + Float64(fma(x, log(y), a) + Float64(z + t)));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(log(c) * Float64(b - 0.5)) + Float64(a + Float64(z + t))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -2.2e+76], N[Not[LessEqual[x, 4e+118]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(N[(x * N[Log[y], $MachinePrecision] + a), $MachinePrecision] + N[(z + t), $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 < -2.2e76 or 3.99999999999999987e118 < x

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-+r+ 99.8%

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

      3. +-commutative 99.8%

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

      4. associate-+r+ 99.8%

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

      5. +-commutative 99.8%

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

      6. associate-+r+ 99.8%

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

      7. fma-def 99.8%

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

      8. associate-+l+ 99.8%

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

      9. +-commutative 99.8%

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

      10. associate-+r+ 99.8%

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

      11. +-commutative 99.8%

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

      12. associate-+l+ 99.8%

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

   3. Simplified 99.8%

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

      1. fma-udef 99.8%

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

      2. fma-udef 99.8%

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

      3. metadata-eval 99.8%

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

      4. sub-neg 99.8%

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

      5. associate-+r+ 99.8%

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

      6. sub-neg 99.8%

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

      7. metadata-eval 99.8%

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

      8. *-commutative 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in y around inf 94.1%

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

   if -2.2e76 < x < 3.99999999999999987e118

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 99.2%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+76} \lor \neg \left(x \leq 4 \cdot 10^{+118}\right):\\ \;\;\;\;y \cdot i + \left(\mathsf{fma}\left(x, \log y, a\right) + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \]

Alternative 5: 88.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+237} \lor \neg \left(x \leq 3.5 \cdot 10^{+243}\right):\\ \;\;\;\;t + \left(z + x \cdot \log y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -4.5e+237) (not (<= x 3.5e+243)))
   (+ t (+ 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 <= -4.5e+237) || !(x <= 3.5e+243)) {
		tmp = t + (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 <= (-4.5d+237)) .or. (.not. (x <= 3.5d+243))) then
        tmp = t + (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 <= -4.5e+237) || !(x <= 3.5e+243)) {
		tmp = t + (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 <= -4.5e+237) or not (x <= 3.5e+243):
		tmp = t + (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 <= -4.5e+237) || !(x <= 3.5e+243))
		tmp = Float64(t + 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 <= -4.5e+237) || ~((x <= 3.5e+243)))
		tmp = t + (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, -4.5e+237], N[Not[LessEqual[x, 3.5e+243]], $MachinePrecision]], N[(t + N[(z + N[(x * N[Log[y], $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 < -4.49999999999999964e237 or 3.49999999999999988e243 < x

   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. +-commutative 99.6%

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

      2. associate-+r+ 99.6%

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

      3. +-commutative 99.6%

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

      4. associate-+r+ 99.6%

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

      5. +-commutative 99.6%

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

      6. associate-+r+ 99.6%

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

      7. fma-def 99.6%

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

      8. associate-+l+ 99.6%

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

      9. +-commutative 99.6%

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

      10. associate-+r+ 99.6%

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

      11. +-commutative 99.6%

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

      12. associate-+l+ 99.6%

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

   3. Simplified 99.6%

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

      1. fma-udef 99.6%

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

      2. fma-udef 99.6%

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

      3. metadata-eval 99.6%

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

      4. sub-neg 99.6%

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

      5. associate-+r+ 99.6%

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

      6. sub-neg 99.6%

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

      7. metadata-eval 99.6%

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

      8. *-commutative 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in y around 0 81.1%

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

   7. Taylor expanded in a around 0 72.7%

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

   8. Taylor expanded in x around inf 72.7%

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

   if -4.49999999999999964e237 < x < 3.49999999999999988e243

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 93.4%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+237} \lor \neg \left(x \leq 3.5 \cdot 10^{+243}\right):\\ \;\;\;\;t + \left(z + x \cdot \log y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \]

Alternative 6: 87.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+237} \lor \neg \left(x \leq 2.3 \cdot 10^{+244}\right):\\ \;\;\;\;t + \left(z + x \cdot \log y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(a + \left(z + t\right)\right) + \log c \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -4e+237) (not (<= x 2.3e+244)))
   (+ t (+ z (* x (log y))))
   (+ (* y i) (+ (+ a (+ z t)) (* (log c) b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -4e+237) || !(x <= 2.3e+244)) {
		tmp = t + (z + (x * log(y)));
	} else {
		tmp = (y * i) + ((a + (z + t)) + (log(c) * b));
	}
	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 <= (-4d+237)) .or. (.not. (x <= 2.3d+244))) then
        tmp = t + (z + (x * log(y)))
    else
        tmp = (y * i) + ((a + (z + t)) + (log(c) * b))
    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 <= -4e+237) || !(x <= 2.3e+244)) {
		tmp = t + (z + (x * Math.log(y)));
	} else {
		tmp = (y * i) + ((a + (z + t)) + (Math.log(c) * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -4e+237) or not (x <= 2.3e+244):
		tmp = t + (z + (x * math.log(y)))
	else:
		tmp = (y * i) + ((a + (z + t)) + (math.log(c) * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -4e+237) || !(x <= 2.3e+244))
		tmp = Float64(t + Float64(z + Float64(x * log(y))));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(a + Float64(z + t)) + Float64(log(c) * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -4e+237) || ~((x <= 2.3e+244)))
		tmp = t + (z + (x * log(y)));
	else
		tmp = (y * i) + ((a + (z + t)) + (log(c) * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -4e+237], N[Not[LessEqual[x, 2.3e+244]], $MachinePrecision]], N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.99999999999999976e237 or 2.2999999999999999e244 < x

   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. +-commutative 99.6%

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

      2. associate-+r+ 99.6%

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

      3. +-commutative 99.6%

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

      4. associate-+r+ 99.6%

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

      5. +-commutative 99.6%

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

      6. associate-+r+ 99.6%

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

      7. fma-def 99.6%

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

      8. associate-+l+ 99.6%

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

      9. +-commutative 99.6%

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

      10. associate-+r+ 99.6%

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

      11. +-commutative 99.6%

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

      12. associate-+l+ 99.6%

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

   3. Simplified 99.6%

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

      1. fma-udef 99.6%

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

      2. fma-udef 99.6%

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

      3. metadata-eval 99.6%

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

      4. sub-neg 99.6%

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

      5. associate-+r+ 99.6%

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

      6. sub-neg 99.6%

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

      7. metadata-eval 99.6%

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

      8. *-commutative 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in y around 0 81.1%

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

   7. Taylor expanded in a around 0 72.7%

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

   8. Taylor expanded in x around inf 72.7%

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

   if -3.99999999999999976e237 < x < 2.2999999999999999e244

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 93.4%

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

   3. Taylor expanded in b around inf 92.1%

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

      1. *-commutative 92.1%

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

   5. Simplified 92.1%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+237} \lor \neg \left(x \leq 2.3 \cdot 10^{+244}\right):\\ \;\;\;\;t + \left(z + x \cdot \log y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(a + \left(z + t\right)\right) + \log c \cdot b\right)\\ \end{array} \]

Alternative 7: 72.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -3.7 \cdot 10^{+169} \lor \neg \left(b - 0.5 \leq 6.6 \cdot 10^{+220}\right):\\ \;\;\;\;a + \log c \cdot \left(b - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (- b 0.5) -3.7e+169) (not (<= (- b 0.5) 6.6e+220)))
   (+ a (* (log c) (- b 0.5)))
   (+ (* y i) (+ 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 (((b - 0.5) <= -3.7e+169) || !((b - 0.5) <= 6.6e+220)) {
		tmp = a + (log(c) * (b - 0.5));
	} else {
		tmp = (y * i) + (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 (((b - 0.5d0) <= (-3.7d+169)) .or. (.not. ((b - 0.5d0) <= 6.6d+220))) then
        tmp = a + (log(c) * (b - 0.5d0))
    else
        tmp = (y * i) + (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 (((b - 0.5) <= -3.7e+169) || !((b - 0.5) <= 6.6e+220)) {
		tmp = a + (Math.log(c) * (b - 0.5));
	} else {
		tmp = (y * i) + (a + (z + t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((b - 0.5) <= -3.7e+169) or not ((b - 0.5) <= 6.6e+220):
		tmp = a + (math.log(c) * (b - 0.5))
	else:
		tmp = (y * i) + (a + (z + t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(b - 0.5) <= -3.7e+169) || !(Float64(b - 0.5) <= 6.6e+220))
		tmp = Float64(a + Float64(log(c) * Float64(b - 0.5)));
	else
		tmp = Float64(Float64(y * i) + 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 (((b - 0.5) <= -3.7e+169) || ~(((b - 0.5) <= 6.6e+220)))
		tmp = a + (log(c) * (b - 0.5));
	else
		tmp = (y * i) + (a + (z + t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(b - 0.5), $MachinePrecision], -3.7e+169], N[Not[LessEqual[N[(b - 0.5), $MachinePrecision], 6.6e+220]], $MachinePrecision]], N[(a + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 b 1/2) < -3.70000000000000001e169 or 6.60000000000000043e220 < (-.f64 b 1/2)

   1. Initial program 99.5%

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

   2. Taylor expanded in a around inf 84.2%

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

   3. Taylor expanded in y around 0 69.1%

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

   if -3.70000000000000001e169 < (-.f64 b 1/2) < 6.60000000000000043e220

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 84.0%

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

   3. Taylor expanded in b around inf 82.5%

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

      1. *-commutative 82.5%

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

   5. Simplified 82.5%

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

   6. Taylor expanded in b around 0 74.4%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -3.7 \cdot 10^{+169} \lor \neg \left(b - 0.5 \leq 6.6 \cdot 10^{+220}\right):\\ \;\;\;\;a + \log c \cdot \left(b - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \end{array} \]

Alternative 8: 73.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log c \cdot \left(b - 0.5\right)\\ \mathbf{if}\;b - 0.5 \leq -5.1 \cdot 10^{+185}:\\ \;\;\;\;t + \left(z + t_1\right)\\ \mathbf{elif}\;b - 0.5 \leq 7 \cdot 10^{+216}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (log c) (- b 0.5))))
   (if (<= (- b 0.5) -5.1e+185)
     (+ t (+ z t_1))
     (if (<= (- b 0.5) 7e+216) (+ (* y i) (+ a (+ z t))) (+ 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 = log(c) * (b - 0.5);
	double tmp;
	if ((b - 0.5) <= -5.1e+185) {
		tmp = t + (z + t_1);
	} else if ((b - 0.5) <= 7e+216) {
		tmp = (y * i) + (a + (z + t));
	} else {
		tmp = a + 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 = log(c) * (b - 0.5d0)
    if ((b - 0.5d0) <= (-5.1d+185)) then
        tmp = t + (z + t_1)
    else if ((b - 0.5d0) <= 7d+216) then
        tmp = (y * i) + (a + (z + t))
    else
        tmp = a + 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 = Math.log(c) * (b - 0.5);
	double tmp;
	if ((b - 0.5) <= -5.1e+185) {
		tmp = t + (z + t_1);
	} else if ((b - 0.5) <= 7e+216) {
		tmp = (y * i) + (a + (z + t));
	} else {
		tmp = a + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = math.log(c) * (b - 0.5)
	tmp = 0
	if (b - 0.5) <= -5.1e+185:
		tmp = t + (z + t_1)
	elif (b - 0.5) <= 7e+216:
		tmp = (y * i) + (a + (z + t))
	else:
		tmp = a + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(log(c) * Float64(b - 0.5))
	tmp = 0.0
	if (Float64(b - 0.5) <= -5.1e+185)
		tmp = Float64(t + Float64(z + t_1));
	elseif (Float64(b - 0.5) <= 7e+216)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + t)));
	else
		tmp = Float64(a + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = log(c) * (b - 0.5);
	tmp = 0.0;
	if ((b - 0.5) <= -5.1e+185)
		tmp = t + (z + t_1);
	elseif ((b - 0.5) <= 7e+216)
		tmp = (y * i) + (a + (z + t));
	else
		tmp = a + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b - 0.5), $MachinePrecision], -5.1e+185], N[(t + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b - 0.5), $MachinePrecision], 7e+216], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 b 1/2) < -5.09999999999999996e185

   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. +-commutative 99.6%

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

      2. associate-+r+ 99.6%

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

      3. +-commutative 99.6%

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

      4. associate-+r+ 99.6%

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

      5. +-commutative 99.6%

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

      6. associate-+r+ 99.6%

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

      7. fma-def 99.6%

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

      8. associate-+l+ 99.6%

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

      9. +-commutative 99.6%

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

      10. associate-+r+ 99.6%

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

      11. +-commutative 99.6%

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

      12. associate-+l+ 99.6%

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

   3. Simplified 99.6%

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

      1. fma-udef 99.6%

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

      2. fma-udef 99.6%

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

      3. metadata-eval 99.6%

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

      4. sub-neg 99.6%

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

      5. associate-+r+ 99.6%

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

      6. sub-neg 99.6%

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

      7. metadata-eval 99.6%

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

      8. *-commutative 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in y around 0 79.9%

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

   7. Taylor expanded in a around 0 70.2%

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

   8. Taylor expanded in x around 0 68.5%

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

   if -5.09999999999999996e185 < (-.f64 b 1/2) < 6.99999999999999984e216

   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 83.8%

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

   3. Taylor expanded in b around inf 82.3%

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

      1. *-commutative 82.3%

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

   5. Simplified 82.3%

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

   6. Taylor expanded in b around 0 73.8%

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

   if 6.99999999999999984e216 < (-.f64 b 1/2)

   1. Initial program 99.5%

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

   2. Taylor expanded in a around inf 90.0%

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

   3. Taylor expanded in y around 0 85.3%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -5.1 \cdot 10^{+185}:\\ \;\;\;\;t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{elif}\;b - 0.5 \leq 7 \cdot 10^{+216}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \log c \cdot \left(b - 0.5\right)\\ \end{array} \]

Alternative 9: 74.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -2.75 \cdot 10^{-11} \lor \neg \left(i \leq 155\right):\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a + t\right) + \left(z + \log c \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= i -2.75e-11) (not (<= i 155.0)))
   (+ (* y i) (+ a (+ z t)))
   (+ (+ a t) (+ z (* (log c) b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((i <= -2.75e-11) || !(i <= 155.0)) {
		tmp = (y * i) + (a + (z + t));
	} else {
		tmp = (a + t) + (z + (log(c) * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((i <= (-2.75d-11)) .or. (.not. (i <= 155.0d0))) then
        tmp = (y * i) + (a + (z + t))
    else
        tmp = (a + t) + (z + (log(c) * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((i <= -2.75e-11) || !(i <= 155.0)) {
		tmp = (y * i) + (a + (z + t));
	} else {
		tmp = (a + t) + (z + (Math.log(c) * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (i <= -2.75e-11) or not (i <= 155.0):
		tmp = (y * i) + (a + (z + t))
	else:
		tmp = (a + t) + (z + (math.log(c) * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((i <= -2.75e-11) || !(i <= 155.0))
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + t)));
	else
		tmp = Float64(Float64(a + t) + Float64(z + Float64(log(c) * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((i <= -2.75e-11) || ~((i <= 155.0)))
		tmp = (y * i) + (a + (z + t));
	else
		tmp = (a + t) + (z + (log(c) * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[i, -2.75e-11], N[Not[LessEqual[i, 155.0]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a + t), $MachinePrecision] + N[(z + N[(N[Log[c], $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -2.74999999999999987e-11 or 155 < i

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 89.5%

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

   3. Taylor expanded in b around inf 88.0%

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

      1. *-commutative 88.0%

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

   5. Simplified 88.0%

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

   6. Taylor expanded in b around 0 76.0%

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

   if -2.74999999999999987e-11 < i < 155

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0 82.2%

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

   3. Taylor expanded in b around inf 81.3%

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

      1. *-commutative 81.3%

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

   5. Simplified 81.3%

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

   6. Taylor expanded in y around 0 76.5%

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

      1. associate-+r+ 76.5%

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

   8. Simplified 76.5%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.75 \cdot 10^{-11} \lor \neg \left(i \leq 155\right):\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a + t\right) + \left(z + \log c \cdot b\right)\\ \end{array} \]

Alternative 10: 59.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+148}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \log c \cdot \left(b - 0.5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -6e+148)
   (+ (* y i) (+ a (+ z t)))
   (+ (* y i) (+ 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 (z <= -6e+148) {
		tmp = (y * i) + (a + (z + t));
	} else {
		tmp = (y * i) + (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 (z <= (-6d+148)) then
        tmp = (y * i) + (a + (z + t))
    else
        tmp = (y * i) + (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 (z <= -6e+148) {
		tmp = (y * i) + (a + (z + t));
	} else {
		tmp = (y * i) + (a + (Math.log(c) * (b - 0.5)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -6e+148:
		tmp = (y * i) + (a + (z + t))
	else:
		tmp = (y * i) + (a + (math.log(c) * (b - 0.5)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -6e+148)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + t)));
	else
		tmp = Float64(Float64(y * i) + 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 (z <= -6e+148)
		tmp = (y * i) + (a + (z + t));
	else
		tmp = (y * i) + (a + (log(c) * (b - 0.5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -6e+148], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.00000000000000029e148

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 91.2%

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

   3. Taylor expanded in b around inf 91.2%

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

      1. *-commutative 91.2%

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

   5. Simplified 91.2%

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

   6. Taylor expanded in b around 0 82.4%

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

   if -6.00000000000000029e148 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in a around inf 60.9%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+148}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \log c \cdot \left(b - 0.5\right)\right)\\ \end{array} \]

Alternative 11: 58.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+148}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \log c \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -6.2e+148)
   (+ (* y i) (+ a (+ z t)))
   (+ (* y i) (+ a (* (log c) b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -6.2e+148) {
		tmp = (y * i) + (a + (z + t));
	} else {
		tmp = (y * i) + (a + (log(c) * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-6.2d+148)) then
        tmp = (y * i) + (a + (z + t))
    else
        tmp = (y * i) + (a + (log(c) * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -6.2e+148) {
		tmp = (y * i) + (a + (z + t));
	} else {
		tmp = (y * i) + (a + (Math.log(c) * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -6.2e+148:
		tmp = (y * i) + (a + (z + t))
	else:
		tmp = (y * i) + (a + (math.log(c) * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -6.2e+148)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + t)));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(log(c) * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -6.2e+148)
		tmp = (y * i) + (a + (z + t));
	else
		tmp = (y * i) + (a + (log(c) * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -6.2e+148], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(N[Log[c], $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.19999999999999951e148

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 91.2%

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

   3. Taylor expanded in b around inf 91.2%

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

      1. *-commutative 91.2%

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

   5. Simplified 91.2%

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

   6. Taylor expanded in b around 0 82.4%

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

   if -6.19999999999999951e148 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in a around inf 60.9%

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

   3. Taylor expanded in b around inf 59.5%

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

      1. *-commutative 83.7%

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

   5. Simplified 59.5%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+148}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \log c \cdot b\right)\\ \end{array} \]

Alternative 12: 70.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+238} \lor \neg \left(x \leq 3.1 \cdot 10^{+266}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -1.85e+238) (not (<= x 3.1e+266)))
   (* x (log y))
   (+ (* y i) (+ 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 <= -1.85e+238) || !(x <= 3.1e+266)) {
		tmp = x * log(y);
	} else {
		tmp = (y * i) + (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 <= (-1.85d+238)) .or. (.not. (x <= 3.1d+266))) then
        tmp = x * log(y)
    else
        tmp = (y * i) + (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 <= -1.85e+238) || !(x <= 3.1e+266)) {
		tmp = x * Math.log(y);
	} else {
		tmp = (y * i) + (a + (z + t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -1.85e+238) or not (x <= 3.1e+266):
		tmp = x * math.log(y)
	else:
		tmp = (y * i) + (a + (z + t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -1.85e+238) || !(x <= 3.1e+266))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(Float64(y * i) + 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 <= -1.85e+238) || ~((x <= 3.1e+266)))
		tmp = x * log(y);
	else
		tmp = (y * i) + (a + (z + t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -1.85e+238], N[Not[LessEqual[x, 3.1e+266]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.85e238 or 3.1e266 < x

   1. Initial program 99.5%

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

      1. +-commutative 99.5%

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

      2. associate-+r+ 99.5%

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

      3. +-commutative 99.5%

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

      4. associate-+r+ 99.5%

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

      5. +-commutative 99.5%

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

      6. associate-+r+ 99.5%

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

      7. fma-def 99.5%

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

      8. associate-+l+ 99.5%

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

      9. +-commutative 99.5%

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

      10. associate-+r+ 99.5%

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

      11. +-commutative 99.5%

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

      12. associate-+l+ 99.5%

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

   3. Simplified 99.5%

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

      1. fma-udef 99.5%

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

      2. fma-udef 99.5%

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

      3. metadata-eval 99.5%

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

      4. sub-neg 99.5%

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

      5. associate-+r+ 99.5%

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

      6. sub-neg 99.5%

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

      7. metadata-eval 99.5%

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

      8. *-commutative 99.5%

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

   5. Applied egg-rr 99.5%

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

   6. Taylor expanded in x around inf 74.0%

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

   if -1.85e238 < x < 3.1e266

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 92.5%

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

   3. Taylor expanded in b around inf 91.2%

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

      1. *-commutative 91.2%

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

   5. Simplified 91.2%

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

   6. Taylor expanded in b around 0 68.8%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+238} \lor \neg \left(x \leq 3.1 \cdot 10^{+266}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \end{array} \]

Alternative 13: 25.9% accurate, 23.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 2.25 \cdot 10^{-291}:\\ \;\;\;\;y \cdot i\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{-106}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 9.7 \cdot 10^{+197}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 2.25e-291)
   (* y i)
   (if (<= a 1.95e-106) z (if (<= a 9.7e+197) (* y i) a))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 2.25e-291) {
		tmp = y * i;
	} else if (a <= 1.95e-106) {
		tmp = z;
	} else if (a <= 9.7e+197) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 2.25d-291) then
        tmp = y * i
    else if (a <= 1.95d-106) then
        tmp = z
    else if (a <= 9.7d+197) then
        tmp = y * i
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 2.25e-291) {
		tmp = y * i;
	} else if (a <= 1.95e-106) {
		tmp = z;
	} else if (a <= 9.7e+197) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 2.25e-291:
		tmp = y * i
	elif a <= 1.95e-106:
		tmp = z
	elif a <= 9.7e+197:
		tmp = y * i
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 2.25e-291)
		tmp = Float64(y * i);
	elseif (a <= 1.95e-106)
		tmp = z;
	elseif (a <= 9.7e+197)
		tmp = Float64(y * i);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 2.25e-291)
		tmp = y * i;
	elseif (a <= 1.95e-106)
		tmp = z;
	elseif (a <= 9.7e+197)
		tmp = y * i;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 2.25e-291], N[(y * i), $MachinePrecision], If[LessEqual[a, 1.95e-106], z, If[LessEqual[a, 9.7e+197], N[(y * i), $MachinePrecision], a]]]

Derivation

1. Split input into 3 regimes

2. if a < 2.24999999999999987e-291 or 1.95000000000000005e-106 < a < 9.69999999999999936e197

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-+r+ 99.8%

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

      3. +-commutative 99.8%

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

      4. associate-+r+ 99.8%

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

      5. +-commutative 99.8%

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

      6. associate-+r+ 99.8%

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

      7. fma-def 99.8%

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

      8. associate-+l+ 99.8%

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

      9. +-commutative 99.8%

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

      10. associate-+r+ 99.8%

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

      11. +-commutative 99.8%

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

      12. associate-+l+ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 31.1%

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

      1. *-commutative 31.1%

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

   6. Simplified 31.1%

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

   if 2.24999999999999987e-291 < a < 1.95000000000000005e-106

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-+r+ 99.7%

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

      3. +-commutative 99.7%

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

      4. associate-+r+ 99.7%

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

      5. +-commutative 99.7%

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

      6. associate-+r+ 99.7%

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

      7. fma-def 99.7%

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

      8. associate-+l+ 99.7%

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

      9. +-commutative 99.7%

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

      10. associate-+r+ 99.7%

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

      11. +-commutative 99.7%

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

      12. associate-+l+ 99.7%

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

   3. Simplified 99.7%

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

      1. fma-udef 99.7%

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

      2. fma-udef 99.7%

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

      3. metadata-eval 99.7%

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

      4. sub-neg 99.7%

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

      5. associate-+r+ 99.7%

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

      6. sub-neg 99.7%

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

      7. metadata-eval 99.7%

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

      8. *-commutative 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in z around inf 26.2%

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

   if 9.69999999999999936e197 < a

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-+r+ 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+r+ 99.9%

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

      5. +-commutative 99.9%

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

      6. associate-+r+ 99.9%

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

      7. fma-def 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. associate-+r+ 99.9%

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

      11. +-commutative 99.9%

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

      12. associate-+l+ 99.9%

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

   3. Simplified 99.9%

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

      1. fma-udef 99.9%

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

      2. fma-udef 99.9%

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

      3. metadata-eval 99.9%

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

      4. sub-neg 99.9%

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

      5. associate-+r+ 99.9%

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

      6. sub-neg 99.9%

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

      7. metadata-eval 99.9%

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

      8. *-commutative 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in a around inf 53.4%

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

4. Final simplification 32.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 2.25 \cdot 10^{-291}:\\ \;\;\;\;y \cdot i\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{-106}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 9.7 \cdot 10^{+197}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 14: 59.0% accurate, 24.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.7 \cdot 10^{-9}:\\ \;\;\;\;t + \left(a + z\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(y \cdot i + t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 4.7e-9) (+ t (+ a z)) (+ a (+ (* y i) t))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 4.7e-9) {
		tmp = t + (a + z);
	} else {
		tmp = a + ((y * i) + 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 (y <= 4.7d-9) then
        tmp = t + (a + z)
    else
        tmp = a + ((y * i) + 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 (y <= 4.7e-9) {
		tmp = t + (a + z);
	} else {
		tmp = a + ((y * i) + t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 4.7e-9:
		tmp = t + (a + z)
	else:
		tmp = a + ((y * i) + t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 4.7e-9)
		tmp = Float64(t + Float64(a + z));
	else
		tmp = Float64(a + Float64(Float64(y * i) + t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= 4.7e-9)
		tmp = t + (a + z);
	else
		tmp = a + ((y * i) + t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 4.7e-9], N[(t + N[(a + z), $MachinePrecision]), $MachinePrecision], N[(a + N[(N[(y * i), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 4.6999999999999999e-9

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 81.4%

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

   3. Taylor expanded in b around inf 78.7%

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

      1. *-commutative 78.7%

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

   5. Simplified 78.7%

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

   6. Taylor expanded in b around 0 54.4%

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

   7. Taylor expanded in y around 0 49.1%

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

      1. +-commutative 49.1%

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

      2. associate-+l+ 49.1%

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

   9. Simplified 49.1%

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

   if 4.6999999999999999e-9 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 89.1%

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

   3. Taylor expanded in b around inf 89.1%

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

      1. *-commutative 89.1%

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

   5. Simplified 89.1%

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

   6. Taylor expanded in b around 0 72.3%

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

   7. Taylor expanded in z around 0 61.5%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.7 \cdot 10^{-9}:\\ \;\;\;\;t + \left(a + z\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(y \cdot i + t\right)\\ \end{array} \]

Alternative 15: 57.5% accurate, 24.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 3.8 \cdot 10^{+143}:\\ \;\;\;\;y \cdot i + \left(z + t\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(y \cdot i + t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 3.8e+143) (+ (* y i) (+ z t)) (+ a (+ (* y i) t))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 3.8e+143) {
		tmp = (y * i) + (z + t);
	} else {
		tmp = a + ((y * i) + t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 3.8d+143) then
        tmp = (y * i) + (z + t)
    else
        tmp = a + ((y * i) + t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 3.8e+143) {
		tmp = (y * i) + (z + t);
	} else {
		tmp = a + ((y * i) + t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 3.8e+143:
		tmp = (y * i) + (z + t)
	else:
		tmp = a + ((y * i) + t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 3.8e+143)
		tmp = Float64(Float64(y * i) + Float64(z + t));
	else
		tmp = Float64(a + Float64(Float64(y * i) + t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 3.8e+143)
		tmp = (y * i) + (z + t);
	else
		tmp = a + ((y * i) + t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 3.8e+143], N[(N[(y * i), $MachinePrecision] + N[(z + t), $MachinePrecision]), $MachinePrecision], N[(a + N[(N[(y * i), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 3.8e143

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 85.1%

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

   3. Taylor expanded in b around inf 83.8%

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

      1. *-commutative 83.8%

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

   5. Simplified 83.8%

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

   6. Taylor expanded in b around 0 61.2%

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

   7. Taylor expanded in a around 0 55.6%

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

      1. associate-+r+ 55.6%

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

   9. Simplified 55.6%

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

   if 3.8e143 < a

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 89.7%

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

   3. Taylor expanded in b around inf 89.7%

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

      1. *-commutative 89.7%

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

   5. Simplified 89.7%

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

   6. Taylor expanded in b around 0 84.4%

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

   7. Taylor expanded in z around 0 79.1%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 3.8 \cdot 10^{+143}:\\ \;\;\;\;y \cdot i + \left(z + t\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(y \cdot i + t\right)\\ \end{array} \]

Alternative 16: 66.7% accurate, 24.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in x around 0 85.8%

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

3. Taylor expanded in b around inf 84.6%

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

   1. *-commutative 84.6%

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

5. Simplified 84.6%

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

6. Taylor expanded in b around 0 64.5%

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

7. Final simplification 64.5%

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

Alternative 17: 52.4% accurate, 31.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.8 \cdot 10^{+148}:\\ \;\;\;\;t + \left(a + z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 1.8e+148) (+ t (+ a z)) (* y i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 1.8e+148) {
		tmp = t + (a + z);
	} else {
		tmp = y * i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= 1.8d+148) then
        tmp = t + (a + z)
    else
        tmp = y * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 1.8e+148) {
		tmp = t + (a + z);
	} else {
		tmp = y * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 1.8e+148:
		tmp = t + (a + z)
	else:
		tmp = y * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 1.8e+148)
		tmp = Float64(t + Float64(a + z));
	else
		tmp = Float64(y * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= 1.8e+148)
		tmp = t + (a + z);
	else
		tmp = y * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 1.8e+148], N[(t + N[(a + z), $MachinePrecision]), $MachinePrecision], N[(y * i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.80000000000000003e148

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 85.1%

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

   3. Taylor expanded in b around inf 83.4%

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

      1. *-commutative 83.4%

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

   5. Simplified 83.4%

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

   6. Taylor expanded in b around 0 60.3%

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

   7. Taylor expanded in y around 0 47.9%

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

      1. +-commutative 47.9%

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

      2. associate-+l+ 47.9%

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

   9. Simplified 47.9%

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

   if 1.80000000000000003e148 < y

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-+r+ 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+r+ 99.9%

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

      5. +-commutative 99.9%

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

      6. associate-+r+ 99.9%

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

      7. fma-def 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. associate-+r+ 99.9%

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

      11. +-commutative 99.9%

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

      12. associate-+l+ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 58.5%

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

      1. *-commutative 58.5%

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

   6. Simplified 58.5%

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

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.8 \cdot 10^{+148}:\\ \;\;\;\;t + \left(a + z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \]

Alternative 18: 21.1% accurate, 71.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 2.85 \cdot 10^{+143}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (if (<= a 2.85e+143) 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 <= 2.85e+143) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 2.85d+143) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 2.85e+143) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 2.85e+143:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 2.85e+143)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 2.85e+143)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 2.85e+143], z, a]

Derivation

1. Split input into 2 regimes

2. if a < 2.85000000000000011e143

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-+r+ 99.8%

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

      3. +-commutative 99.8%

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

      4. associate-+r+ 99.8%

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

      5. +-commutative 99.8%

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

      6. associate-+r+ 99.8%

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

      7. fma-def 99.8%

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

      8. associate-+l+ 99.8%

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

      9. +-commutative 99.8%

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

      10. associate-+r+ 99.8%

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

      11. +-commutative 99.8%

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

      12. associate-+l+ 99.8%

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

   3. Simplified 99.8%

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

      1. fma-udef 99.8%

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

      2. fma-udef 99.8%

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

      3. metadata-eval 99.8%

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

      4. sub-neg 99.8%

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

      5. associate-+r+ 99.8%

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

      6. sub-neg 99.8%

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

      7. metadata-eval 99.8%

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

      8. *-commutative 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in z around inf 15.7%

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

   if 2.85000000000000011e143 < a

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-+r+ 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+r+ 99.9%

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

      5. +-commutative 99.9%

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

      6. associate-+r+ 99.9%

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

      7. fma-def 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. associate-+r+ 99.9%

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

      11. +-commutative 99.9%

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

      12. associate-+l+ 99.9%

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

   3. Simplified 100.0%

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

      1. fma-udef 100.0%

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

      2. fma-udef 100.0%

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

      3. metadata-eval 100.0%

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

      4. sub-neg 100.0%

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

      5. associate-+r+ 100.0%

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

      6. sub-neg 100.0%

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

      7. metadata-eval 100.0%

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

      8. *-commutative 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in a around inf 44.7%

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

4. Final simplification 19.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 2.85 \cdot 10^{+143}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 19: 16.1% accurate, 219.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. +-commutative 99.8%

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

   2. associate-+r+ 99.8%

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

   3. +-commutative 99.8%

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

   4. associate-+r+ 99.8%

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

   5. +-commutative 99.8%

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

   6. associate-+r+ 99.8%

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

   7. fma-def 99.8%

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

   8. associate-+l+ 99.8%

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

   9. +-commutative 99.8%

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

   10. associate-+r+ 99.8%

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

   11. +-commutative 99.8%

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

   12. associate-+l+ 99.8%

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

3. Simplified 99.8%

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

   1. fma-udef 99.8%

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

   2. fma-udef 99.8%

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

   3. metadata-eval 99.8%

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

   4. sub-neg 99.8%

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

   5. associate-+r+ 99.8%

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

   6. sub-neg 99.8%

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

   7. metadata-eval 99.8%

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

   8. *-commutative 99.8%

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

5. Applied egg-rr 99.8%

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

6. Taylor expanded in a around inf 12.6%

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

7. Final simplification 12.6%

   \[\leadsto a \]

Reproduce

herbie shell --seed 2023308 
(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)))