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

Percentage Accurate: 99.8% → 99.8%

Time: 16.5s

Alternatives: 14

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. associate-+l+ 99.9%

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

   2. +-commutative 99.9%

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

   3. associate-+l+ 99.9%

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

   4. associate-+l+ 99.9%

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

   5. +-commutative 99.9%

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

   6. fma-def 99.9%

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

   7. associate-+l+ 99.9%

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

   8. fma-def 99.9%

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

   9. +-commutative 99.9%

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

   10. associate-+l+ 99.9%

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

   11. fma-def 99.9%

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

   12. sub-neg 99.9%

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

   13. metadata-eval 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 99.8% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. associate-+l+ 99.9%

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

   2. associate-+l+ 99.9%

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

   3. fma-def 99.9%

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

   4. sub-neg 99.9%

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

   5. metadata-eval 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 3: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Final simplification 99.9%

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

Alternative 4: 93.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -4 \cdot 10^{+159} \lor \neg \left(b - 0.5 \leq 5 \cdot 10^{+113}\right):\\ \;\;\;\;\left(\left(b + -0.5\right) \cdot \log c + y \cdot i\right) + \left(z + \left(t + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t + \left(x \cdot \log y + \left(a + \left(z + y \cdot i\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (- b 0.5) -4e+159) (not (<= (- b 0.5) 5e+113)))
   (+ (+ (* (+ b -0.5) (log c)) (* y i)) (+ z (+ t a)))
   (+ t (+ (* x (log y)) (+ 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 (((b - 0.5) <= -4e+159) || !((b - 0.5) <= 5e+113)) {
		tmp = (((b + -0.5) * log(c)) + (y * i)) + (z + (t + a));
	} else {
		tmp = t + ((x * log(y)) + (a + (z + (y * i))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((b - 0.5d0) <= (-4d+159)) .or. (.not. ((b - 0.5d0) <= 5d+113))) then
        tmp = (((b + (-0.5d0)) * log(c)) + (y * i)) + (z + (t + a))
    else
        tmp = t + ((x * log(y)) + (a + (z + (y * i))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((b - 0.5) <= -4e+159) || !((b - 0.5) <= 5e+113)) {
		tmp = (((b + -0.5) * Math.log(c)) + (y * i)) + (z + (t + a));
	} else {
		tmp = t + ((x * Math.log(y)) + (a + (z + (y * i))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((b - 0.5) <= -4e+159) or not ((b - 0.5) <= 5e+113):
		tmp = (((b + -0.5) * math.log(c)) + (y * i)) + (z + (t + a))
	else:
		tmp = t + ((x * math.log(y)) + (a + (z + (y * i))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(b - 0.5) <= -4e+159) || !(Float64(b - 0.5) <= 5e+113))
		tmp = Float64(Float64(Float64(Float64(b + -0.5) * log(c)) + Float64(y * i)) + Float64(z + Float64(t + a)));
	else
		tmp = Float64(t + Float64(Float64(x * log(y)) + Float64(a + Float64(z + Float64(y * i)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((b - 0.5) <= -4e+159) || ~(((b - 0.5) <= 5e+113)))
		tmp = (((b + -0.5) * log(c)) + (y * i)) + (z + (t + a));
	else
		tmp = t + ((x * log(y)) + (a + (z + (y * i))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(b - 0.5), $MachinePrecision], -4e+159], N[Not[LessEqual[N[(b - 0.5), $MachinePrecision], 5e+113]], $MachinePrecision]], N[(N[(N[(N[(b + -0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision] + N[(z + N[(t + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(a + N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 b 1/2) < -3.9999999999999997e159 or 5e113 < (-.f64 b 1/2)

   1. Initial program 99.8%

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

      1. associate-+l+ 99.8%

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

      2. associate-+l+ 99.8%

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

      3. fma-def 99.8%

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

      4. sub-neg 99.8%

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

      5. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 95.4%

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

      1. associate-+r+ 95.4%

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

      2. +-commutative 95.4%

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

   6. Simplified 95.4%

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

   if -3.9999999999999997e159 < (-.f64 b 1/2) < 5e113

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. associate-+l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. fma-def 99.9%

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

      7. associate-+l+ 99.9%

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

      8. fma-def 99.9%

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

      9. +-commutative 99.9%

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

      10. associate-+l+ 99.9%

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

      11. fma-def 99.9%

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

      12. sub-neg 99.9%

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

      13. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 97.6%

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

      1. fma-udef 97.6%

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

      2. +-commutative 97.6%

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

   6. Applied egg-rr 97.6%

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

   7. Taylor expanded in a around inf 97.6%

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

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -4 \cdot 10^{+159} \lor \neg \left(b - 0.5 \leq 5 \cdot 10^{+113}\right):\\ \;\;\;\;\left(\left(b + -0.5\right) \cdot \log c + y \cdot i\right) + \left(z + \left(t + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t + \left(x \cdot \log y + \left(a + \left(z + y \cdot i\right)\right)\right)\\ \end{array} \]

Alternative 5: 87.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -1.95 \cdot 10^{+159} \lor \neg \left(b - 0.5 \leq 6 \cdot 10^{+171}\right):\\ \;\;\;\;\log c \cdot \left(b - 0.5\right) + \left(a + z\right)\\ \mathbf{else}:\\ \;\;\;\;t + \left(x \cdot \log y + \left(a + \left(z + y \cdot i\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (- b 0.5) -1.95e+159) (not (<= (- b 0.5) 6e+171)))
   (+ (* (log c) (- b 0.5)) (+ a z))
   (+ t (+ (* x (log y)) (+ 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 (((b - 0.5) <= -1.95e+159) || !((b - 0.5) <= 6e+171)) {
		tmp = (log(c) * (b - 0.5)) + (a + z);
	} else {
		tmp = t + ((x * log(y)) + (a + (z + (y * i))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((b - 0.5d0) <= (-1.95d+159)) .or. (.not. ((b - 0.5d0) <= 6d+171))) then
        tmp = (log(c) * (b - 0.5d0)) + (a + z)
    else
        tmp = t + ((x * log(y)) + (a + (z + (y * i))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((b - 0.5) <= -1.95e+159) || !((b - 0.5) <= 6e+171)) {
		tmp = (Math.log(c) * (b - 0.5)) + (a + z);
	} else {
		tmp = t + ((x * Math.log(y)) + (a + (z + (y * i))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((b - 0.5) <= -1.95e+159) or not ((b - 0.5) <= 6e+171):
		tmp = (math.log(c) * (b - 0.5)) + (a + z)
	else:
		tmp = t + ((x * math.log(y)) + (a + (z + (y * i))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(b - 0.5) <= -1.95e+159) || !(Float64(b - 0.5) <= 6e+171))
		tmp = Float64(Float64(log(c) * Float64(b - 0.5)) + Float64(a + z));
	else
		tmp = Float64(t + Float64(Float64(x * log(y)) + Float64(a + Float64(z + Float64(y * i)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((b - 0.5) <= -1.95e+159) || ~(((b - 0.5) <= 6e+171)))
		tmp = (log(c) * (b - 0.5)) + (a + z);
	else
		tmp = t + ((x * log(y)) + (a + (z + (y * i))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(b - 0.5), $MachinePrecision], -1.95e+159], N[Not[LessEqual[N[(b - 0.5), $MachinePrecision], 6e+171]], $MachinePrecision]], N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision] + N[(a + z), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(a + N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 b 1/2) < -1.95e159 or 6.0000000000000002e171 < (-.f64 b 1/2)

   1. Initial program 99.7%

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

      1. associate-+l+ 99.7%

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

      2. associate-+l+ 99.7%

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

      3. fma-def 99.7%

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

      4. sub-neg 99.7%

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

      5. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 96.0%

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

      1. associate-+r+ 96.0%

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

      2. +-commutative 96.0%

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

   6. Simplified 96.0%

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

   7. Taylor expanded in y around 0 79.0%

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

   8. Taylor expanded in t around 0 77.7%

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

   if -1.95e159 < (-.f64 b 1/2) < 6.0000000000000002e171

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. associate-+l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. fma-def 99.9%

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

      7. associate-+l+ 99.9%

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

      8. fma-def 99.9%

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

      9. +-commutative 99.9%

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

      10. associate-+l+ 99.9%

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

      11. fma-def 99.9%

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

      12. sub-neg 99.9%

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

      13. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 96.8%

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

      1. fma-udef 96.8%

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

      2. +-commutative 96.8%

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

   6. Applied egg-rr 96.8%

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

   7. Taylor expanded in a around inf 96.8%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -1.95 \cdot 10^{+159} \lor \neg \left(b - 0.5 \leq 6 \cdot 10^{+171}\right):\\ \;\;\;\;\log c \cdot \left(b - 0.5\right) + \left(a + z\right)\\ \mathbf{else}:\\ \;\;\;\;t + \left(x \cdot \log y + \left(a + \left(z + y \cdot i\right)\right)\right)\\ \end{array} \]

Alternative 6: 91.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -4 \cdot 10^{+159} \lor \neg \left(b - 0.5 \leq 2 \cdot 10^{+150}\right):\\ \;\;\;\;\left(\left(b + -0.5\right) \cdot \log c + y \cdot i\right) + \left(t + z\right)\\ \mathbf{else}:\\ \;\;\;\;t + \left(x \cdot \log y + \left(a + \left(z + y \cdot i\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (- b 0.5) -4e+159) (not (<= (- b 0.5) 2e+150)))
   (+ (+ (* (+ b -0.5) (log c)) (* y i)) (+ t z))
   (+ t (+ (* x (log y)) (+ 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 (((b - 0.5) <= -4e+159) || !((b - 0.5) <= 2e+150)) {
		tmp = (((b + -0.5) * log(c)) + (y * i)) + (t + z);
	} else {
		tmp = t + ((x * log(y)) + (a + (z + (y * i))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((b - 0.5d0) <= (-4d+159)) .or. (.not. ((b - 0.5d0) <= 2d+150))) then
        tmp = (((b + (-0.5d0)) * log(c)) + (y * i)) + (t + z)
    else
        tmp = t + ((x * log(y)) + (a + (z + (y * i))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((b - 0.5) <= -4e+159) || !((b - 0.5) <= 2e+150)) {
		tmp = (((b + -0.5) * Math.log(c)) + (y * i)) + (t + z);
	} else {
		tmp = t + ((x * Math.log(y)) + (a + (z + (y * i))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((b - 0.5) <= -4e+159) or not ((b - 0.5) <= 2e+150):
		tmp = (((b + -0.5) * math.log(c)) + (y * i)) + (t + z)
	else:
		tmp = t + ((x * math.log(y)) + (a + (z + (y * i))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(b - 0.5) <= -4e+159) || !(Float64(b - 0.5) <= 2e+150))
		tmp = Float64(Float64(Float64(Float64(b + -0.5) * log(c)) + Float64(y * i)) + Float64(t + z));
	else
		tmp = Float64(t + Float64(Float64(x * log(y)) + Float64(a + Float64(z + Float64(y * i)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((b - 0.5) <= -4e+159) || ~(((b - 0.5) <= 2e+150)))
		tmp = (((b + -0.5) * log(c)) + (y * i)) + (t + z);
	else
		tmp = t + ((x * log(y)) + (a + (z + (y * i))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(b - 0.5), $MachinePrecision], -4e+159], N[Not[LessEqual[N[(b - 0.5), $MachinePrecision], 2e+150]], $MachinePrecision]], N[(N[(N[(N[(b + -0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision] + N[(t + z), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(a + N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 b 1/2) < -3.9999999999999997e159 or 1.99999999999999996e150 < (-.f64 b 1/2)

   1. Initial program 99.7%

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

      1. associate-+l+ 99.7%

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

      2. associate-+l+ 99.7%

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

      3. fma-def 99.7%

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

      4. sub-neg 99.7%

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

      5. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 96.1%

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

      1. associate-+r+ 96.1%

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

      2. +-commutative 96.1%

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

   6. Simplified 96.1%

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

   7. Taylor expanded in a around 0 86.4%

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

   if -3.9999999999999997e159 < (-.f64 b 1/2) < 1.99999999999999996e150

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. associate-+l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. fma-def 99.9%

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

      7. associate-+l+ 99.9%

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

      8. fma-def 99.9%

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

      9. +-commutative 99.9%

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

      10. associate-+l+ 99.9%

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

      11. fma-def 99.9%

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

      12. sub-neg 99.9%

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

      13. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 96.8%

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

      1. fma-udef 96.8%

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

      2. +-commutative 96.8%

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

   6. Applied egg-rr 96.8%

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

   7. Taylor expanded in a around inf 96.8%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -4 \cdot 10^{+159} \lor \neg \left(b - 0.5 \leq 2 \cdot 10^{+150}\right):\\ \;\;\;\;\left(\left(b + -0.5\right) \cdot \log c + y \cdot i\right) + \left(t + z\right)\\ \mathbf{else}:\\ \;\;\;\;t + \left(x \cdot \log y + \left(a + \left(z + y \cdot i\right)\right)\right)\\ \end{array} \]

Alternative 7: 72.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(x \cdot \log y + y \cdot i\right)\\ \mathbf{if}\;x \leq -1.52 \cdot 10^{+181}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -27000:\\ \;\;\;\;\log c \cdot \left(b - 0.5\right) + \left(a + z\right)\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+183}:\\ \;\;\;\;t + \left(y \cdot i + \left(a + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ t (+ (* x (log y)) (* y i)))))
   (if (<= x -1.52e+181)
     t_1
     (if (<= x -27000.0)
       (+ (* (log c) (- b 0.5)) (+ a z))
       (if (<= x 1.55e+183) (+ t (+ (* y i) (+ a z))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = t + ((x * log(y)) + (y * i));
	double tmp;
	if (x <= -1.52e+181) {
		tmp = t_1;
	} else if (x <= -27000.0) {
		tmp = (log(c) * (b - 0.5)) + (a + z);
	} else if (x <= 1.55e+183) {
		tmp = t + ((y * i) + (a + z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + ((x * log(y)) + (y * i))
    if (x <= (-1.52d+181)) then
        tmp = t_1
    else if (x <= (-27000.0d0)) then
        tmp = (log(c) * (b - 0.5d0)) + (a + z)
    else if (x <= 1.55d+183) then
        tmp = t + ((y * i) + (a + z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = t + ((x * Math.log(y)) + (y * i));
	double tmp;
	if (x <= -1.52e+181) {
		tmp = t_1;
	} else if (x <= -27000.0) {
		tmp = (Math.log(c) * (b - 0.5)) + (a + z);
	} else if (x <= 1.55e+183) {
		tmp = t + ((y * i) + (a + z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = t + ((x * math.log(y)) + (y * i))
	tmp = 0
	if x <= -1.52e+181:
		tmp = t_1
	elif x <= -27000.0:
		tmp = (math.log(c) * (b - 0.5)) + (a + z)
	elif x <= 1.55e+183:
		tmp = t + ((y * i) + (a + z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(t + Float64(Float64(x * log(y)) + Float64(y * i)))
	tmp = 0.0
	if (x <= -1.52e+181)
		tmp = t_1;
	elseif (x <= -27000.0)
		tmp = Float64(Float64(log(c) * Float64(b - 0.5)) + Float64(a + z));
	elseif (x <= 1.55e+183)
		tmp = Float64(t + Float64(Float64(y * i) + Float64(a + z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = t + ((x * log(y)) + (y * i));
	tmp = 0.0;
	if (x <= -1.52e+181)
		tmp = t_1;
	elseif (x <= -27000.0)
		tmp = (log(c) * (b - 0.5)) + (a + z);
	elseif (x <= 1.55e+183)
		tmp = t + ((y * i) + (a + z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(t + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.52e+181], t$95$1, If[LessEqual[x, -27000.0], N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision] + N[(a + z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.55e+183], N[(t + N[(N[(y * i), $MachinePrecision] + N[(a + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.52e181 or 1.5499999999999999e183 < x

   1. Initial program 99.7%

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

      1. associate-+l+ 99.7%

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

      2. +-commutative 99.7%

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

      3. associate-+l+ 99.7%

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

      4. associate-+l+ 99.7%

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

      5. +-commutative 99.7%

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

      6. fma-def 99.7%

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

      7. associate-+l+ 99.7%

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

      8. fma-def 99.7%

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

      9. +-commutative 99.7%

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

      10. associate-+l+ 99.7%

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

      11. fma-def 99.7%

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

      12. sub-neg 99.7%

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

      13. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 74.7%

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

   5. Taylor expanded in y around 0 74.7%

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

   if -1.52e181 < x < -27000

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. fma-def 99.9%

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

      4. sub-neg 99.9%

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

      5. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 93.3%

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

      1. associate-+r+ 93.3%

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

      2. +-commutative 93.3%

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

   6. Simplified 93.3%

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

   7. Taylor expanded in y around 0 79.8%

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

   8. Taylor expanded in t around 0 58.0%

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

   if -27000 < x < 1.5499999999999999e183

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. associate-+l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. fma-def 99.9%

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

      7. associate-+l+ 99.9%

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

      8. fma-def 100.0%

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

      9. +-commutative 100.0%

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

      10. associate-+l+ 100.0%

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

      11. fma-def 100.0%

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

      12. sub-neg 100.0%

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

      13. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 85.2%

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

      1. fma-udef 85.2%

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

      2. +-commutative 85.2%

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

   6. Applied egg-rr 85.2%

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

   7. Taylor expanded in x around 0 82.7%

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

      1. associate-+r+ 82.7%

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

      2. *-commutative 82.7%

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

   9. Simplified 82.7%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.52 \cdot 10^{+181}:\\ \;\;\;\;t + \left(x \cdot \log y + y \cdot i\right)\\ \mathbf{elif}\;x \leq -27000:\\ \;\;\;\;\log c \cdot \left(b - 0.5\right) + \left(a + z\right)\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+183}:\\ \;\;\;\;t + \left(y \cdot i + \left(a + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t + \left(x \cdot \log y + y \cdot i\right)\\ \end{array} \]

Alternative 8: 71.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+205}:\\ \;\;\;\;t + \left(y \cdot i + \left(a + z\right)\right)\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{+107}:\\ \;\;\;\;\log c \cdot \left(b - 0.5\right) + \left(a + z\right)\\ \mathbf{else}:\\ \;\;\;\;t + \left(x \cdot \log y + \left(a + y \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -7.5e+205)
   (+ t (+ (* y i) (+ a z)))
   (if (<= z -9.5e+107)
     (+ (* (log c) (- b 0.5)) (+ a z))
     (+ t (+ (* x (log y)) (+ a (* y i)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -7.5e+205) {
		tmp = t + ((y * i) + (a + z));
	} else if (z <= -9.5e+107) {
		tmp = (log(c) * (b - 0.5)) + (a + z);
	} else {
		tmp = t + ((x * log(y)) + (a + (y * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-7.5d+205)) then
        tmp = t + ((y * i) + (a + z))
    else if (z <= (-9.5d+107)) then
        tmp = (log(c) * (b - 0.5d0)) + (a + z)
    else
        tmp = t + ((x * log(y)) + (a + (y * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -7.5e+205) {
		tmp = t + ((y * i) + (a + z));
	} else if (z <= -9.5e+107) {
		tmp = (Math.log(c) * (b - 0.5)) + (a + z);
	} else {
		tmp = t + ((x * Math.log(y)) + (a + (y * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -7.5e+205:
		tmp = t + ((y * i) + (a + z))
	elif z <= -9.5e+107:
		tmp = (math.log(c) * (b - 0.5)) + (a + z)
	else:
		tmp = t + ((x * math.log(y)) + (a + (y * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -7.5e+205)
		tmp = Float64(t + Float64(Float64(y * i) + Float64(a + z)));
	elseif (z <= -9.5e+107)
		tmp = Float64(Float64(log(c) * Float64(b - 0.5)) + Float64(a + z));
	else
		tmp = Float64(t + Float64(Float64(x * log(y)) + Float64(a + Float64(y * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -7.5e+205)
		tmp = t + ((y * i) + (a + z));
	elseif (z <= -9.5e+107)
		tmp = (log(c) * (b - 0.5)) + (a + z);
	else
		tmp = t + ((x * log(y)) + (a + (y * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -7.5e+205], N[(t + N[(N[(y * i), $MachinePrecision] + N[(a + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9.5e+107], N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision] + N[(a + z), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.5000000000000003e205

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+l+ 100.0%

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

      4. associate-+l+ 100.0%

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

      5. +-commutative 100.0%

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

      6. fma-def 100.0%

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

      7. associate-+l+ 100.0%

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

      8. fma-def 100.0%

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

      9. +-commutative 100.0%

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

      10. associate-+l+ 100.0%

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

      11. fma-def 100.0%

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

      12. sub-neg 100.0%

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

      13. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 95.9%

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

      1. fma-udef 95.9%

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

      2. +-commutative 95.9%

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

   6. Applied egg-rr 95.9%

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

   7. Taylor expanded in x around 0 92.3%

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

      1. associate-+r+ 92.3%

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

      2. *-commutative 92.3%

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

   9. Simplified 92.3%

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

   if -7.5000000000000003e205 < z < -9.50000000000000019e107

   1. Initial program 99.8%

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

      1. associate-+l+ 99.8%

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

      2. associate-+l+ 99.8%

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

      3. fma-def 99.8%

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

      4. sub-neg 99.8%

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

      5. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 91.3%

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

      1. associate-+r+ 91.3%

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

      2. +-commutative 91.3%

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

   6. Simplified 91.3%

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

   7. Taylor expanded in y around 0 77.0%

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

   8. Taylor expanded in t around 0 70.7%

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

   if -9.50000000000000019e107 < z

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. associate-+l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. fma-def 99.9%

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

      7. associate-+l+ 99.9%

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

      8. fma-def 99.9%

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

      9. +-commutative 99.9%

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

      10. associate-+l+ 99.9%

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

      11. fma-def 99.9%

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

      12. sub-neg 99.9%

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

      13. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 85.4%

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

      1. fma-udef 85.4%

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

      2. +-commutative 85.4%

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

   6. Applied egg-rr 85.4%

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

   7. Taylor expanded in z around 0 75.5%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+205}:\\ \;\;\;\;t + \left(y \cdot i + \left(a + z\right)\right)\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{+107}:\\ \;\;\;\;\log c \cdot \left(b - 0.5\right) + \left(a + z\right)\\ \mathbf{else}:\\ \;\;\;\;t + \left(x \cdot \log y + \left(a + y \cdot i\right)\right)\\ \end{array} \]

Alternative 9: 72.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;z \leq -4.9 \cdot 10^{+166}:\\ \;\;\;\;t + \left(t_1 + \left(z + y \cdot i\right)\right)\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{+109}:\\ \;\;\;\;\log c \cdot \left(b - 0.5\right) + \left(a + z\right)\\ \mathbf{else}:\\ \;\;\;\;t + \left(t_1 + \left(a + y \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= z -4.9e+166)
     (+ t (+ t_1 (+ z (* y i))))
     (if (<= z -5.8e+109)
       (+ (* (log c) (- b 0.5)) (+ a z))
       (+ t (+ t_1 (+ a (* y i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * log(y);
	double tmp;
	if (z <= -4.9e+166) {
		tmp = t + (t_1 + (z + (y * i)));
	} else if (z <= -5.8e+109) {
		tmp = (log(c) * (b - 0.5)) + (a + z);
	} else {
		tmp = t + (t_1 + (a + (y * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * log(y)
    if (z <= (-4.9d+166)) then
        tmp = t + (t_1 + (z + (y * i)))
    else if (z <= (-5.8d+109)) then
        tmp = (log(c) * (b - 0.5d0)) + (a + z)
    else
        tmp = t + (t_1 + (a + (y * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * Math.log(y);
	double tmp;
	if (z <= -4.9e+166) {
		tmp = t + (t_1 + (z + (y * i)));
	} else if (z <= -5.8e+109) {
		tmp = (Math.log(c) * (b - 0.5)) + (a + z);
	} else {
		tmp = t + (t_1 + (a + (y * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x * math.log(y)
	tmp = 0
	if z <= -4.9e+166:
		tmp = t + (t_1 + (z + (y * i)))
	elif z <= -5.8e+109:
		tmp = (math.log(c) * (b - 0.5)) + (a + z)
	else:
		tmp = t + (t_1 + (a + (y * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (z <= -4.9e+166)
		tmp = Float64(t + Float64(t_1 + Float64(z + Float64(y * i))));
	elseif (z <= -5.8e+109)
		tmp = Float64(Float64(log(c) * Float64(b - 0.5)) + Float64(a + z));
	else
		tmp = Float64(t + Float64(t_1 + Float64(a + Float64(y * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x * log(y);
	tmp = 0.0;
	if (z <= -4.9e+166)
		tmp = t + (t_1 + (z + (y * i)));
	elseif (z <= -5.8e+109)
		tmp = (log(c) * (b - 0.5)) + (a + z);
	else
		tmp = t + (t_1 + (a + (y * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.9e+166], N[(t + N[(t$95$1 + N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.8e+109], N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision] + N[(a + z), $MachinePrecision]), $MachinePrecision], N[(t + N[(t$95$1 + N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.89999999999999969e166

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+l+ 100.0%

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

      4. associate-+l+ 100.0%

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

      5. +-commutative 100.0%

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

      6. fma-def 100.0%

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

      7. associate-+l+ 100.0%

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

      8. fma-def 100.0%

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

      9. +-commutative 100.0%

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

      10. associate-+l+ 100.0%

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

      11. fma-def 100.0%

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

      12. sub-neg 100.0%

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

      13. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 84.8%

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

      1. fma-udef 84.8%

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

      2. +-commutative 84.8%

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

   6. Applied egg-rr 84.8%

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

   7. Taylor expanded in a around 0 83.8%

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

   if -4.89999999999999969e166 < z < -5.8e109

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. fma-def 99.9%

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

      4. sub-neg 99.9%

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

      5. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 99.5%

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

      1. associate-+r+ 99.5%

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

      2. +-commutative 99.5%

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

   6. Simplified 99.5%

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

   7. Taylor expanded in y around 0 90.5%

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

   8. Taylor expanded in t around 0 81.4%

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

   if -5.8e109 < z

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. associate-+l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. fma-def 99.9%

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

      7. associate-+l+ 99.9%

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

      8. fma-def 99.9%

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

      9. +-commutative 99.9%

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

      10. associate-+l+ 99.9%

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

      11. fma-def 99.9%

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

      12. sub-neg 99.9%

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

      13. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 85.4%

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

      1. fma-udef 85.4%

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

      2. +-commutative 85.4%

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

   6. Applied egg-rr 85.4%

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

   7. Taylor expanded in z around 0 75.5%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+166}:\\ \;\;\;\;t + \left(x \cdot \log y + \left(z + y \cdot i\right)\right)\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{+109}:\\ \;\;\;\;\log c \cdot \left(b - 0.5\right) + \left(a + z\right)\\ \mathbf{else}:\\ \;\;\;\;t + \left(x \cdot \log y + \left(a + y \cdot i\right)\right)\\ \end{array} \]

Alternative 10: 76.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+185} \lor \neg \left(x \leq 4.2 \cdot 10^{+183}\right):\\ \;\;\;\;t + \left(x \cdot \log y + y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t + \left(y \cdot i + \left(a + z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -1.7e+185) (not (<= x 4.2e+183)))
   (+ t (+ (* x (log y)) (* y i)))
   (+ t (+ (* y i) (+ a z)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1.7e+185) || !(x <= 4.2e+183)) {
		tmp = t + ((x * log(y)) + (y * i));
	} else {
		tmp = t + ((y * i) + (a + z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-1.7d+185)) .or. (.not. (x <= 4.2d+183))) then
        tmp = t + ((x * log(y)) + (y * i))
    else
        tmp = t + ((y * i) + (a + z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1.7e+185) || !(x <= 4.2e+183)) {
		tmp = t + ((x * Math.log(y)) + (y * i));
	} else {
		tmp = t + ((y * i) + (a + z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -1.7e+185) or not (x <= 4.2e+183):
		tmp = t + ((x * math.log(y)) + (y * i))
	else:
		tmp = t + ((y * i) + (a + z))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -1.7e+185) || !(x <= 4.2e+183))
		tmp = Float64(t + Float64(Float64(x * log(y)) + Float64(y * i)));
	else
		tmp = Float64(t + Float64(Float64(y * i) + Float64(a + z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -1.7e+185) || ~((x <= 4.2e+183)))
		tmp = t + ((x * log(y)) + (y * i));
	else
		tmp = t + ((y * i) + (a + z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -1.7e+185], N[Not[LessEqual[x, 4.2e+183]], $MachinePrecision]], N[(t + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(y * i), $MachinePrecision] + N[(a + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.70000000000000009e185 or 4.2e183 < x

   1. Initial program 99.7%

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

      1. associate-+l+ 99.7%

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

      2. +-commutative 99.7%

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

      3. associate-+l+ 99.7%

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

      4. associate-+l+ 99.7%

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

      5. +-commutative 99.7%

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

      6. fma-def 99.7%

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

      7. associate-+l+ 99.7%

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

      8. fma-def 99.7%

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

      9. +-commutative 99.7%

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

      10. associate-+l+ 99.7%

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

      11. fma-def 99.7%

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

      12. sub-neg 99.7%

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

      13. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 74.7%

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

   5. Taylor expanded in y around 0 74.7%

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

   if -1.70000000000000009e185 < x < 4.2e183

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. associate-+l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. fma-def 99.9%

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

      7. associate-+l+ 99.9%

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

      8. fma-def 99.9%

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

      9. +-commutative 99.9%

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

      10. associate-+l+ 99.9%

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

      11. fma-def 99.9%

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

      12. sub-neg 99.9%

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

      13. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 82.9%

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

      1. fma-udef 82.9%

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

      2. +-commutative 82.9%

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

   6. Applied egg-rr 82.9%

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

   7. Taylor expanded in x around 0 79.5%

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

      1. associate-+r+ 79.5%

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

      2. *-commutative 79.5%

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

   9. Simplified 79.5%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+185} \lor \neg \left(x \leq 4.2 \cdot 10^{+183}\right):\\ \;\;\;\;t + \left(x \cdot \log y + y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t + \left(y \cdot i + \left(a + z\right)\right)\\ \end{array} \]

Alternative 11: 71.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+267} \lor \neg \left(x \leq 4.8 \cdot 10^{+228}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;t + \left(y \cdot i + \left(a + z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -2.7e+267) (not (<= x 4.8e+228)))
   (* x (log y))
   (+ t (+ (* y i) (+ a z)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -2.7e+267) || !(x <= 4.8e+228)) {
		tmp = x * log(y);
	} else {
		tmp = t + ((y * i) + (a + z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-2.7d+267)) .or. (.not. (x <= 4.8d+228))) then
        tmp = x * log(y)
    else
        tmp = t + ((y * i) + (a + z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -2.7e+267) || !(x <= 4.8e+228)) {
		tmp = x * Math.log(y);
	} else {
		tmp = t + ((y * i) + (a + z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -2.7e+267) or not (x <= 4.8e+228):
		tmp = x * math.log(y)
	else:
		tmp = t + ((y * i) + (a + z))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -2.7e+267) || !(x <= 4.8e+228))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(t + Float64(Float64(y * i) + Float64(a + z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -2.7e+267) || ~((x <= 4.8e+228)))
		tmp = x * log(y);
	else
		tmp = t + ((y * i) + (a + z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -2.7e+267], N[Not[LessEqual[x, 4.8e+228]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(y * i), $MachinePrecision] + N[(a + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.7000000000000001e267 or 4.79999999999999977e228 < x

   1. Initial program 99.7%

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

      1. associate-+l+ 99.7%

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

      2. +-commutative 99.7%

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

      3. associate-+l+ 99.7%

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

      4. associate-+l+ 99.7%

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

      5. +-commutative 99.7%

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

      6. fma-def 99.7%

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

      7. associate-+l+ 99.7%

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

      8. fma-def 99.7%

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

      9. +-commutative 99.7%

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

      10. associate-+l+ 99.7%

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

      11. fma-def 99.7%

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

      12. sub-neg 99.7%

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

      13. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 88.4%

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

   5. Taylor expanded in y around 0 81.6%

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

   6. Taylor expanded in t around 0 81.6%

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

   if -2.7000000000000001e267 < x < 4.79999999999999977e228

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. associate-+l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. fma-def 99.9%

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

      7. associate-+l+ 99.9%

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

      8. fma-def 99.9%

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

      9. +-commutative 99.9%

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

      10. associate-+l+ 99.9%

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

      11. fma-def 99.9%

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

      12. sub-neg 99.9%

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

      13. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 83.4%

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

      1. fma-udef 83.4%

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

      2. +-commutative 83.4%

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

   6. Applied egg-rr 83.4%

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

   7. Taylor expanded in x around 0 75.3%

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

      1. associate-+r+ 75.3%

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

      2. *-commutative 75.3%

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

   9. Simplified 75.3%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+267} \lor \neg \left(x \leq 4.8 \cdot 10^{+228}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;t + \left(y \cdot i + \left(a + z\right)\right)\\ \end{array} \]

Alternative 12: 67.3% accurate, 24.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. associate-+l+ 99.9%

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

   2. +-commutative 99.9%

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

   3. associate-+l+ 99.9%

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

   4. associate-+l+ 99.9%

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

   5. +-commutative 99.9%

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

   6. fma-def 99.9%

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

   7. associate-+l+ 99.9%

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

   8. fma-def 99.9%

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

   9. +-commutative 99.9%

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

   10. associate-+l+ 99.9%

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

   11. fma-def 99.9%

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

   12. sub-neg 99.9%

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

   13. metadata-eval 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in z around inf 84.8%

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

   1. fma-udef 84.8%

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

   2. +-commutative 84.8%

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

6. Applied egg-rr 84.8%

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

7. Taylor expanded in x around 0 69.2%

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

   1. associate-+r+ 69.2%

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

   2. *-commutative 69.2%

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

9. Simplified 69.2%

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

10. Final simplification 69.2%

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

Alternative 13: 20.6% accurate, 71.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+99}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (if (<= z -2.9e+99) z a))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -2.9e+99) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-2.9d+99)) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -2.9e+99) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -2.9e+99:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -2.9e+99)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -2.9e+99)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -2.9e+99], z, a]

Derivation

1. Split input into 2 regimes

2. if z < -2.9000000000000002e99

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. fma-def 99.9%

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

      4. sub-neg 99.9%

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

      5. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 94.3%

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

      1. associate-+r+ 94.3%

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

      2. +-commutative 94.3%

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

   6. Simplified 94.3%

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

   7. Taylor expanded in z around inf 50.0%

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

   if -2.9000000000000002e99 < z

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. fma-def 99.9%

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

      4. sub-neg 99.9%

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

      5. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 82.2%

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

      1. associate-+r+ 82.2%

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

      2. +-commutative 82.2%

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

   6. Simplified 82.2%

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

   7. Taylor expanded in a around inf 17.8%

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

4. Final simplification 23.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+99}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 14: 16.0% accurate, 219.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. associate-+l+ 99.9%

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

   2. associate-+l+ 99.9%

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

   3. fma-def 99.9%

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

   4. sub-neg 99.9%

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

   5. metadata-eval 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in x around 0 84.3%

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

   1. associate-+r+ 84.3%

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

   2. +-commutative 84.3%

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

6. Simplified 84.3%

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

7. Taylor expanded in a around inf 16.0%

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

8. Final simplification 16.0%

   \[\leadsto a \]

Reproduce

herbie shell --seed 2023200 
(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)))