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

Percentage Accurate: 99.8% → 99.8%

Time: 17.3s

Alternatives: 16

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

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

   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. +-commutative 99.9%

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

   4. +-commutative 99.9%

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

   5. associate-+r+ 99.9%

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

   6. associate-+l+ 99.9%

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

   7. +-commutative 99.9%

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

   8. associate-+l+ 99.9%

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

   9. +-commutative 99.9%

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

   10. fma-def 99.9%

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

   11. +-commutative 99.9%

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

   12. fma-def 99.9%

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

   13. sub-neg 99.9%

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

   14. metadata-eval 99.9%

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

   15. +-commutative 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 2: 91.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log c \cdot \left(b - 0.5\right)\\ \mathbf{if}\;x \leq -2.1 \cdot 10^{+88} \lor \neg \left(x \leq 4.5 \cdot 10^{+157}\right):\\ \;\;\;\;y \cdot i + \left(t\_1 + \left(a + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t\_1 + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (log c) (- b 0.5))))
   (if (or (<= x -2.1e+88) (not (<= x 4.5e+157)))
     (+ (* y i) (+ t_1 (+ a (* x (log y)))))
     (+ (* y i) (+ t_1 (+ a (+ z t)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = log(c) * (b - 0.5);
	double tmp;
	if ((x <= -2.1e+88) || !(x <= 4.5e+157)) {
		tmp = (y * i) + (t_1 + (a + (x * log(y))));
	} else {
		tmp = (y * i) + (t_1 + (a + (z + t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = log(c) * (b - 0.5d0)
    if ((x <= (-2.1d+88)) .or. (.not. (x <= 4.5d+157))) then
        tmp = (y * i) + (t_1 + (a + (x * log(y))))
    else
        tmp = (y * i) + (t_1 + (a + (z + t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = Math.log(c) * (b - 0.5);
	double tmp;
	if ((x <= -2.1e+88) || !(x <= 4.5e+157)) {
		tmp = (y * i) + (t_1 + (a + (x * Math.log(y))));
	} else {
		tmp = (y * i) + (t_1 + (a + (z + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = math.log(c) * (b - 0.5)
	tmp = 0
	if (x <= -2.1e+88) or not (x <= 4.5e+157):
		tmp = (y * i) + (t_1 + (a + (x * math.log(y))))
	else:
		tmp = (y * i) + (t_1 + (a + (z + t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(log(c) * Float64(b - 0.5))
	tmp = 0.0
	if ((x <= -2.1e+88) || !(x <= 4.5e+157))
		tmp = Float64(Float64(y * i) + Float64(t_1 + Float64(a + Float64(x * log(y)))));
	else
		tmp = Float64(Float64(y * i) + Float64(t_1 + Float64(a + Float64(z + t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = log(c) * (b - 0.5);
	tmp = 0.0;
	if ((x <= -2.1e+88) || ~((x <= 4.5e+157)))
		tmp = (y * i) + (t_1 + (a + (x * log(y))));
	else
		tmp = (y * i) + (t_1 + (a + (z + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -2.1e+88], N[Not[LessEqual[x, 4.5e+157]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(t$95$1 + N[(a + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(t$95$1 + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.1e88 or 4.49999999999999985e157 < x

   1. Initial program 99.8%

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

      1. associate-+l+ 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+r+ 99.8%

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

      4. fma-udef 99.8%

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

      5. add-sqr-sqrt 60.7%

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

      6. pow2 60.7%

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

   4. Applied egg-rr 60.7%

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

   5. Taylor expanded in t around 0 52.4%

      \[\leadsto \left({\color{blue}{\left(\sqrt{a + \left(z + x \cdot \log y\right)}\right)}}^{2} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   6. Step-by-step derivation

      1. associate-+r+ 52.4%

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

      2. +-commutative 52.4%

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

   7. Simplified 52.4%

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

   8. Taylor expanded in z around 0 82.8%

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

   if -2.1e88 < x < 4.49999999999999985e157

   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. Add Preprocessing

   3. Taylor expanded in x around 0 99.4%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+88} \lor \neg \left(x \leq 4.5 \cdot 10^{+157}\right):\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 80.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z + x \cdot \log y\\ \mathbf{if}\;a \leq 0.00025:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(a + \left(t + t\_1\right)\right) + b \cdot \log c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ z (* x (log y)))))
   (if (<= a 0.00025)
     (+ (* y i) (+ (* (log c) (- b 0.5)) t_1))
     (+ (* y i) (+ (+ a (+ t t_1)) (* b (log c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = z + (x * log(y));
	double tmp;
	if (a <= 0.00025) {
		tmp = (y * i) + ((log(c) * (b - 0.5)) + t_1);
	} else {
		tmp = (y * i) + ((a + (t + t_1)) + (b * log(c)));
	}
	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 = z + (x * log(y))
    if (a <= 0.00025d0) then
        tmp = (y * i) + ((log(c) * (b - 0.5d0)) + t_1)
    else
        tmp = (y * i) + ((a + (t + t_1)) + (b * log(c)))
    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 = z + (x * Math.log(y));
	double tmp;
	if (a <= 0.00025) {
		tmp = (y * i) + ((Math.log(c) * (b - 0.5)) + t_1);
	} else {
		tmp = (y * i) + ((a + (t + t_1)) + (b * Math.log(c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = z + (x * math.log(y))
	tmp = 0
	if a <= 0.00025:
		tmp = (y * i) + ((math.log(c) * (b - 0.5)) + t_1)
	else:
		tmp = (y * i) + ((a + (t + t_1)) + (b * math.log(c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(z + Float64(x * log(y)))
	tmp = 0.0
	if (a <= 0.00025)
		tmp = Float64(Float64(y * i) + Float64(Float64(log(c) * Float64(b - 0.5)) + t_1));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(a + Float64(t + t_1)) + Float64(b * log(c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = z + (x * log(y));
	tmp = 0.0;
	if (a <= 0.00025)
		tmp = (y * i) + ((log(c) * (b - 0.5)) + t_1);
	else
		tmp = (y * i) + ((a + (t + t_1)) + (b * log(c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, 0.00025], N[(N[(y * i), $MachinePrecision] + N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(a + N[(t + t$95$1), $MachinePrecision]), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < 2.5000000000000001e-4

   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. Add Preprocessing
   3. Step-by-step derivation

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+r+ 99.9%

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

      4. fma-udef 99.9%

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

      5. add-sqr-sqrt 41.3%

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

      6. pow2 41.3%

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

   4. Applied egg-rr 41.3%

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

   5. Taylor expanded in t around 0 31.6%

      \[\leadsto \left({\color{blue}{\left(\sqrt{a + \left(z + x \cdot \log y\right)}\right)}}^{2} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   6. Step-by-step derivation

      1. associate-+r+ 31.6%

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

      2. +-commutative 31.6%

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

   7. Simplified 31.6%

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

   8. Taylor expanded in a around 0 66.7%

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

   if 2.5000000000000001e-4 < a

   1. Initial program 99.9%

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

   3. Taylor expanded in b around inf 99.9%

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

      1. *-commutative 87.7%

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

   5. Simplified 99.9%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 0.00025:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(z + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right) + b \cdot \log c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 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. Add Preprocessing

3. Final simplification 99.9%

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

Alternative 5: 61.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -1 \cdot 10^{+223} \lor \neg \left(b - 0.5 \leq 5 \cdot 10^{+232}\right):\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + -0.5 \cdot \log c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (- b 0.5) -1e+223) (not (<= (- b 0.5) 5e+232)))
   (+ (* y i) (+ a (* b (log c))))
   (+ (* y i) (+ a (+ z (* -0.5 (log c)))))))

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) <= -1e+223) || !((b - 0.5) <= 5e+232)) {
		tmp = (y * i) + (a + (b * log(c)));
	} else {
		tmp = (y * i) + (a + (z + (-0.5 * log(c))));
	}
	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) <= (-1d+223)) .or. (.not. ((b - 0.5d0) <= 5d+232))) then
        tmp = (y * i) + (a + (b * log(c)))
    else
        tmp = (y * i) + (a + (z + ((-0.5d0) * log(c))))
    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) <= -1e+223) || !((b - 0.5) <= 5e+232)) {
		tmp = (y * i) + (a + (b * Math.log(c)));
	} else {
		tmp = (y * i) + (a + (z + (-0.5 * Math.log(c))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((b - 0.5) <= -1e+223) or not ((b - 0.5) <= 5e+232):
		tmp = (y * i) + (a + (b * math.log(c)))
	else:
		tmp = (y * i) + (a + (z + (-0.5 * math.log(c))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(b - 0.5) <= -1e+223) || !(Float64(b - 0.5) <= 5e+232))
		tmp = Float64(Float64(y * i) + Float64(a + Float64(b * log(c))));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + Float64(-0.5 * log(c)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((b - 0.5) <= -1e+223) || ~(((b - 0.5) <= 5e+232)))
		tmp = (y * i) + (a + (b * log(c)));
	else
		tmp = (y * i) + (a + (z + (-0.5 * log(c))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(b - 0.5), $MachinePrecision], -1e+223], N[Not[LessEqual[N[(b - 0.5), $MachinePrecision], 5e+232]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(a + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + N[(-0.5 * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 b 1/2) < -1.00000000000000005e223 or 4.99999999999999987e232 < (-.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. Add Preprocessing

   3. Taylor expanded in x around 0 97.3%

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

   4. Taylor expanded in t around 0 95.8%

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

      1. +-commutative 95.8%

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

      2. sub-neg 95.8%

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

      3. metadata-eval 95.8%

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

      4. distribute-lft-in 95.8%

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

      5. distribute-lft-in 95.8%

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

   6. Simplified 95.8%

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

   7. Taylor expanded in b around inf 87.1%

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

      1. *-commutative 87.1%

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

   9. Simplified 87.1%

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

   if -1.00000000000000005e223 < (-.f64 b 1/2) < 4.99999999999999987e232

   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. Add Preprocessing

   3. Taylor expanded in x around 0 84.4%

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

   4. Taylor expanded in t around 0 64.4%

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

      1. +-commutative 64.4%

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

      2. sub-neg 64.4%

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

      3. metadata-eval 64.4%

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

      4. distribute-lft-in 64.4%

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

      5. distribute-lft-in 64.4%

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

   6. Simplified 64.4%

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

   7. Taylor expanded in b around 0 61.3%

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

      1. *-commutative 61.3%

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

   9. Simplified 61.3%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -1 \cdot 10^{+223} \lor \neg \left(b - 0.5 \leq 5 \cdot 10^{+232}\right):\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + -0.5 \cdot \log c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 89.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.32 \cdot 10^{+253} \lor \neg \left(x \leq 2.8 \cdot 10^{+227}\right):\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -1.32e+253) (not (<= x 2.8e+227)))
   (+ (* x (log y)) (* y i))
   (+ (* y i) (+ (* (log c) (- b 0.5)) (+ a (+ z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1.32e+253) || !(x <= 2.8e+227)) {
		tmp = (x * log(y)) + (y * i);
	} else {
		tmp = (y * i) + ((log(c) * (b - 0.5)) + (a + (z + t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-1.32d+253)) .or. (.not. (x <= 2.8d+227))) then
        tmp = (x * log(y)) + (y * i)
    else
        tmp = (y * i) + ((log(c) * (b - 0.5d0)) + (a + (z + t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1.32e+253) || !(x <= 2.8e+227)) {
		tmp = (x * Math.log(y)) + (y * i);
	} else {
		tmp = (y * i) + ((Math.log(c) * (b - 0.5)) + (a + (z + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -1.32e+253) or not (x <= 2.8e+227):
		tmp = (x * math.log(y)) + (y * i)
	else:
		tmp = (y * i) + ((math.log(c) * (b - 0.5)) + (a + (z + t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -1.32e+253) || !(x <= 2.8e+227))
		tmp = Float64(Float64(x * log(y)) + Float64(y * i));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(log(c) * Float64(b - 0.5)) + Float64(a + Float64(z + t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -1.32e+253) || ~((x <= 2.8e+227)))
		tmp = (x * log(y)) + (y * i);
	else
		tmp = (y * i) + ((log(c) * (b - 0.5)) + (a + (z + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -1.32e+253], N[Not[LessEqual[x, 2.8e+227]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.32e253 or 2.79999999999999984e227 < x

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf 87.2%

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

   if -1.32e253 < x < 2.79999999999999984e227

   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. Add Preprocessing

   3. Taylor expanded in x around 0 93.9%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.32 \cdot 10^{+253} \lor \neg \left(x \leq 2.8 \cdot 10^{+227}\right):\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 88.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.32 \cdot 10^{+253} \lor \neg \left(x \leq 5.9 \cdot 10^{+225}\right):\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(b \cdot \log c + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -1.32e+253) (not (<= x 5.9e+225)))
   (+ (* x (log y)) (* y i))
   (+ (* y i) (+ (* b (log c)) (+ a (+ z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1.32e+253) || !(x <= 5.9e+225)) {
		tmp = (x * log(y)) + (y * i);
	} else {
		tmp = (y * i) + ((b * log(c)) + (a + (z + t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-1.32d+253)) .or. (.not. (x <= 5.9d+225))) then
        tmp = (x * log(y)) + (y * i)
    else
        tmp = (y * i) + ((b * log(c)) + (a + (z + t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1.32e+253) || !(x <= 5.9e+225)) {
		tmp = (x * Math.log(y)) + (y * i);
	} else {
		tmp = (y * i) + ((b * Math.log(c)) + (a + (z + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -1.32e+253) or not (x <= 5.9e+225):
		tmp = (x * math.log(y)) + (y * i)
	else:
		tmp = (y * i) + ((b * math.log(c)) + (a + (z + t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -1.32e+253) || !(x <= 5.9e+225))
		tmp = Float64(Float64(x * log(y)) + Float64(y * i));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(b * log(c)) + Float64(a + Float64(z + t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -1.32e+253) || ~((x <= 5.9e+225)))
		tmp = (x * log(y)) + (y * i);
	else
		tmp = (y * i) + ((b * log(c)) + (a + (z + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -1.32e+253], N[Not[LessEqual[x, 5.9e+225]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.32e253 or 5.8999999999999998e225 < x

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf 87.2%

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

   if -1.32e253 < x < 5.8999999999999998e225

   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. Add Preprocessing

   3. Taylor expanded in x around 0 93.9%

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

   4. Taylor expanded in b around inf 91.3%

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

      1. *-commutative 91.3%

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

   6. Simplified 91.3%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.32 \cdot 10^{+253} \lor \neg \left(x \leq 5.9 \cdot 10^{+225}\right):\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(b \cdot \log c + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.38 \cdot 10^{+253} \lor \neg \left(x \leq 1.25 \cdot 10^{+227}\right):\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + \left(b + -0.5\right) \cdot \log c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -1.38e+253) (not (<= x 1.25e+227)))
   (+ (* x (log y)) (* y i))
   (+ (* y i) (+ a (+ z (* (+ b -0.5) (log c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1.38e+253) || !(x <= 1.25e+227)) {
		tmp = (x * log(y)) + (y * i);
	} else {
		tmp = (y * i) + (a + (z + ((b + -0.5) * log(c))));
	}
	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 <= (-1.38d+253)) .or. (.not. (x <= 1.25d+227))) then
        tmp = (x * log(y)) + (y * i)
    else
        tmp = (y * i) + (a + (z + ((b + (-0.5d0)) * log(c))))
    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 <= -1.38e+253) || !(x <= 1.25e+227)) {
		tmp = (x * Math.log(y)) + (y * i);
	} else {
		tmp = (y * i) + (a + (z + ((b + -0.5) * Math.log(c))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -1.38e+253) or not (x <= 1.25e+227):
		tmp = (x * math.log(y)) + (y * i)
	else:
		tmp = (y * i) + (a + (z + ((b + -0.5) * math.log(c))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -1.38e+253) || !(x <= 1.25e+227))
		tmp = Float64(Float64(x * log(y)) + Float64(y * i));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + Float64(Float64(b + -0.5) * log(c)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -1.38e+253) || ~((x <= 1.25e+227)))
		tmp = (x * log(y)) + (y * i);
	else
		tmp = (y * i) + (a + (z + ((b + -0.5) * log(c))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -1.38e+253], N[Not[LessEqual[x, 1.25e+227]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + N[(N[(b + -0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.38e253 or 1.2499999999999999e227 < x

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf 87.2%

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

   if -1.38e253 < x < 1.2499999999999999e227

   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. Add Preprocessing

   3. Taylor expanded in x around 0 93.9%

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

   4. Taylor expanded in t around 0 75.4%

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

      1. +-commutative 75.4%

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

      2. sub-neg 75.4%

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

      3. metadata-eval 75.4%

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

      4. distribute-lft-in 75.4%

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

      5. distribute-lft-in 75.4%

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

   6. Simplified 75.4%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.38 \cdot 10^{+253} \lor \neg \left(x \leq 1.25 \cdot 10^{+227}\right):\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + \left(b + -0.5\right) \cdot \log c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 73.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.6 \cdot 10^{+218} \lor \neg \left(b \leq 2.6 \cdot 10^{+232}\right):\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + \left(t + a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= b -6.6e+218) (not (<= b 2.6e+232)))
   (+ (* y i) (+ a (* b (log c))))
   (+ (* y i) (+ z (+ t a)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((b <= -6.6e+218) || !(b <= 2.6e+232)) {
		tmp = (y * i) + (a + (b * log(c)));
	} else {
		tmp = (y * i) + (z + (t + 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 ((b <= (-6.6d+218)) .or. (.not. (b <= 2.6d+232))) then
        tmp = (y * i) + (a + (b * log(c)))
    else
        tmp = (y * i) + (z + (t + 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 ((b <= -6.6e+218) || !(b <= 2.6e+232)) {
		tmp = (y * i) + (a + (b * Math.log(c)));
	} else {
		tmp = (y * i) + (z + (t + a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (b <= -6.6e+218) or not (b <= 2.6e+232):
		tmp = (y * i) + (a + (b * math.log(c)))
	else:
		tmp = (y * i) + (z + (t + a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((b <= -6.6e+218) || !(b <= 2.6e+232))
		tmp = Float64(Float64(y * i) + Float64(a + Float64(b * log(c))));
	else
		tmp = Float64(Float64(y * i) + Float64(z + Float64(t + a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((b <= -6.6e+218) || ~((b <= 2.6e+232)))
		tmp = (y * i) + (a + (b * log(c)));
	else
		tmp = (y * i) + (z + (t + a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[b, -6.6e+218], N[Not[LessEqual[b, 2.6e+232]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(a + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(z + N[(t + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -6.59999999999999996e218 or 2.59999999999999973e232 < b

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 97.3%

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

   4. Taylor expanded in t around 0 95.8%

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

      1. +-commutative 95.8%

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

      2. sub-neg 95.8%

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

      3. metadata-eval 95.8%

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

      4. distribute-lft-in 95.8%

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

      5. distribute-lft-in 95.8%

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

   6. Simplified 95.8%

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

   7. Taylor expanded in b around inf 87.1%

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

      1. *-commutative 87.1%

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

   9. Simplified 87.1%

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

   if -6.59999999999999996e218 < b < 2.59999999999999973e232

   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. Add Preprocessing

   3. Taylor expanded in x around 0 84.4%

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

      1. add-cube-cbrt 84.3%

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

      2. pow3 84.3%

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

      3. sub-neg 84.3%

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

      4. metadata-eval 84.3%

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

      5. *-commutative 84.3%

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

   5. Applied egg-rr 84.3%

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

   6. Taylor expanded in b around inf 78.5%

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

      1. associate-+r+ 78.5%

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

      2. +-commutative 78.5%

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

   8. Simplified 78.5%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.6 \cdot 10^{+218} \lor \neg \left(b \leq 2.6 \cdot 10^{+232}\right):\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + \left(t + a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 73.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+137} \lor \neg \left(x \leq 5.4 \cdot 10^{+225}\right):\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + \left(t + a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -2.9e+137) (not (<= x 5.4e+225)))
   (+ (* x (log y)) (* y i))
   (+ (* y i) (+ z (+ t a)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -2.9e+137) || !(x <= 5.4e+225)) {
		tmp = (x * log(y)) + (y * i);
	} else {
		tmp = (y * i) + (z + (t + a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-2.9d+137)) .or. (.not. (x <= 5.4d+225))) then
        tmp = (x * log(y)) + (y * i)
    else
        tmp = (y * i) + (z + (t + a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -2.9e+137) || !(x <= 5.4e+225)) {
		tmp = (x * Math.log(y)) + (y * i);
	} else {
		tmp = (y * i) + (z + (t + a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -2.9e+137) or not (x <= 5.4e+225):
		tmp = (x * math.log(y)) + (y * i)
	else:
		tmp = (y * i) + (z + (t + a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -2.9e+137) || !(x <= 5.4e+225))
		tmp = Float64(Float64(x * log(y)) + Float64(y * i));
	else
		tmp = Float64(Float64(y * i) + Float64(z + Float64(t + a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -2.9e+137) || ~((x <= 5.4e+225)))
		tmp = (x * log(y)) + (y * i);
	else
		tmp = (y * i) + (z + (t + a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -2.9e+137], N[Not[LessEqual[x, 5.4e+225]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(z + N[(t + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.89999999999999985e137 or 5.3999999999999997e225 < 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. Add Preprocessing

   3. Taylor expanded in x around inf 73.1%

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

   if -2.89999999999999985e137 < x < 5.3999999999999997e225

   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. Add Preprocessing

   3. Taylor expanded in x around 0 96.1%

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

      1. add-cube-cbrt 95.8%

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

      2. pow3 95.8%

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

      3. sub-neg 95.8%

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

      4. metadata-eval 95.8%

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

      5. *-commutative 95.8%

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

   5. Applied egg-rr 95.8%

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

   6. Taylor expanded in b around inf 79.1%

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

      1. associate-+r+ 79.1%

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

      2. +-commutative 79.1%

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

   8. Simplified 79.1%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+137} \lor \neg \left(x \leq 5.4 \cdot 10^{+225}\right):\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + \left(t + a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 61.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 1.15 \cdot 10^{+23}:\\ \;\;\;\;y \cdot i + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + \left(t + a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 1.15e+23)
   (+ (* y i) (+ z (* (log c) (- b 0.5))))
   (+ (* y i) (+ z (+ t a)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 1.15e+23) {
		tmp = (y * i) + (z + (log(c) * (b - 0.5)));
	} else {
		tmp = (y * i) + (z + (t + a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 1.15d+23) then
        tmp = (y * i) + (z + (log(c) * (b - 0.5d0)))
    else
        tmp = (y * i) + (z + (t + a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 1.15e+23) {
		tmp = (y * i) + (z + (Math.log(c) * (b - 0.5)));
	} else {
		tmp = (y * i) + (z + (t + a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 1.15e+23:
		tmp = (y * i) + (z + (math.log(c) * (b - 0.5)))
	else:
		tmp = (y * i) + (z + (t + a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 1.15e+23)
		tmp = Float64(Float64(y * i) + Float64(z + Float64(log(c) * Float64(b - 0.5))));
	else
		tmp = Float64(Float64(y * i) + Float64(z + Float64(t + a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 1.15e+23)
		tmp = (y * i) + (z + (log(c) * (b - 0.5)));
	else
		tmp = (y * i) + (z + (t + a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 1.15e+23], N[(N[(y * i), $MachinePrecision] + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(z + N[(t + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 1.15e23

   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. Add Preprocessing

   3. Taylor expanded in x around 0 86.3%

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

   4. Taylor expanded in a around 0 72.6%

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

      1. associate-+r+ 72.6%

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

      2. sub-neg 72.6%

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

      3. metadata-eval 72.6%

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

      4. +-commutative 72.6%

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

      5. distribute-lft-out 72.6%

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

      6. +-commutative 72.6%

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

      7. distribute-lft-in 72.6%

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

      8. +-commutative 72.6%

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

      9. fma-def 72.6%

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

   6. Simplified 72.6%

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

   7. Taylor expanded in t around 0 53.9%

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

   if 1.15e23 < a

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 87.1%

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

      1. add-cube-cbrt 86.8%

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

      2. pow3 86.8%

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

      3. sub-neg 86.8%

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

      4. metadata-eval 86.8%

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

      5. *-commutative 86.8%

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

   5. Applied egg-rr 86.8%

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

   6. Taylor expanded in b around inf 71.3%

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

      1. associate-+r+ 71.3%

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

      2. +-commutative 71.3%

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

   8. Simplified 71.3%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.15 \cdot 10^{+23}:\\ \;\;\;\;y \cdot i + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + \left(t + a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 43.1% accurate, 21.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+87}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -9.8e+87) (+ z (* y i)) (+ a (* y i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -9.8e+87) {
		tmp = z + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-9.8d+87)) then
        tmp = z + (y * i)
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -9.8e+87) {
		tmp = z + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -9.8e+87:
		tmp = z + (y * i)
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -9.8e+87)
		tmp = Float64(z + Float64(y * i));
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -9.8e+87)
		tmp = z + (y * i);
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -9.8e+87], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.79999999999999943e87

   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. Add Preprocessing

   3. Taylor expanded in z around inf 59.8%

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

   if -9.79999999999999943e87 < 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. Add Preprocessing

   3. Taylor expanded in a around inf 43.2%

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

4. Final simplification 45.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+87}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 67.0% accurate, 24.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in x around 0 86.5%

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

   1. add-cube-cbrt 86.2%

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

   2. pow3 86.2%

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

   3. sub-neg 86.2%

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

   4. metadata-eval 86.2%

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

   5. *-commutative 86.2%

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

5. Applied egg-rr 86.2%

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

6. Taylor expanded in b around inf 71.2%

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

   1. associate-+r+ 71.2%

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

   2. +-commutative 71.2%

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

8. Simplified 71.2%

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

9. Final simplification 71.2%

   \[\leadsto y \cdot i + \left(z + \left(t + a\right)\right) \]
10. Add Preprocessing

Alternative 14: 52.8% accurate, 31.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in x around 0 86.5%

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

4. Taylor expanded in t around 0 69.6%

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

   1. +-commutative 69.6%

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

   2. sub-neg 69.6%

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

   3. metadata-eval 69.6%

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

   4. distribute-lft-in 69.6%

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

   5. distribute-lft-in 69.6%

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

6. Simplified 69.6%

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

7. Taylor expanded in z around inf 54.5%

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

8. Final simplification 54.5%

   \[\leadsto y \cdot i + \left(z + a\right) \]
9. Add Preprocessing

Alternative 15: 38.4% accurate, 43.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in a around inf 41.2%

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

4. Final simplification 41.2%

   \[\leadsto a + y \cdot i \]
5. Add Preprocessing

Alternative 16: 23.9% accurate, 73.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in x around 0 86.5%

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

4. Taylor expanded in a around 0 68.7%

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

   1. associate-+r+ 68.7%

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

   2. sub-neg 68.7%

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

   3. metadata-eval 68.7%

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

   4. +-commutative 68.7%

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

   5. distribute-lft-out 68.7%

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

   6. +-commutative 68.7%

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

   7. distribute-lft-in 68.7%

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

   8. +-commutative 68.7%

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

   9. fma-def 68.7%

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

6. Simplified 68.7%

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

7. Taylor expanded in y around inf 24.7%

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

8. Final simplification 24.7%

   \[\leadsto y \cdot i \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024026 
(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)))