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

Percentage Accurate: 99.8% → 99.8%

Time: 26.0s

Alternatives: 21

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 99.5%

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

   1. associate-+l+ 99.5%

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

   2. +-commutative 99.5%

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

   3. associate-+l+ 99.5%

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

   4. associate-+r+ 99.5%

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

   5. +-commutative 99.5%

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

   6. +-commutative 99.5%

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

   7. associate-+l+ 99.5%

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

   8. associate-+l+ 99.5%

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

   9. +-commutative 99.5%

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

   10. fma-define 99.5%

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

   11. +-commutative 99.5%

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

   12. fma-define 99.5%

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

   13. sub-neg 99.5%

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

   14. metadata-eval 99.5%

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

   15. +-commutative 99.5%

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

3. Simplified 99.5%

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

Alternative 2: 89.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log c \cdot \left(b - 0.5\right)\\ t_2 := y \cdot i + \left(x \cdot \log y + t\_1\right)\\ \mathbf{if}\;x \leq -1.02 \cdot 10^{+228}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 3.25 \cdot 10^{+142}:\\ \;\;\;\;y \cdot i + \left(t\_1 + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.92 \cdot 10^{+177} \lor \neg \left(x \leq 1.3 \cdot 10^{+246}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(z + a\right) + \left(b + -0.5\right) \cdot \log c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (log c) (- b 0.5))) (t_2 (+ (* y i) (+ (* x (log y)) t_1))))
   (if (<= x -1.02e+228)
     t_2
     (if (<= x 3.25e+142)
       (+ (* y i) (+ t_1 (+ a (+ z t))))
       (if (or (<= x 1.92e+177) (not (<= x 1.3e+246)))
         t_2
         (+ (* y i) (+ (+ z a) (* (+ 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 t_1 = log(c) * (b - 0.5);
	double t_2 = (y * i) + ((x * log(y)) + t_1);
	double tmp;
	if (x <= -1.02e+228) {
		tmp = t_2;
	} else if (x <= 3.25e+142) {
		tmp = (y * i) + (t_1 + (a + (z + t)));
	} else if ((x <= 1.92e+177) || !(x <= 1.3e+246)) {
		tmp = t_2;
	} else {
		tmp = (y * i) + ((z + a) + ((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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = log(c) * (b - 0.5d0)
    t_2 = (y * i) + ((x * log(y)) + t_1)
    if (x <= (-1.02d+228)) then
        tmp = t_2
    else if (x <= 3.25d+142) then
        tmp = (y * i) + (t_1 + (a + (z + t)))
    else if ((x <= 1.92d+177) .or. (.not. (x <= 1.3d+246))) then
        tmp = t_2
    else
        tmp = (y * i) + ((z + a) + ((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 t_1 = Math.log(c) * (b - 0.5);
	double t_2 = (y * i) + ((x * Math.log(y)) + t_1);
	double tmp;
	if (x <= -1.02e+228) {
		tmp = t_2;
	} else if (x <= 3.25e+142) {
		tmp = (y * i) + (t_1 + (a + (z + t)));
	} else if ((x <= 1.92e+177) || !(x <= 1.3e+246)) {
		tmp = t_2;
	} else {
		tmp = (y * i) + ((z + a) + ((b + -0.5) * Math.log(c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = math.log(c) * (b - 0.5)
	t_2 = (y * i) + ((x * math.log(y)) + t_1)
	tmp = 0
	if x <= -1.02e+228:
		tmp = t_2
	elif x <= 3.25e+142:
		tmp = (y * i) + (t_1 + (a + (z + t)))
	elif (x <= 1.92e+177) or not (x <= 1.3e+246):
		tmp = t_2
	else:
		tmp = (y * i) + ((z + a) + ((b + -0.5) * math.log(c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(log(c) * Float64(b - 0.5))
	t_2 = Float64(Float64(y * i) + Float64(Float64(x * log(y)) + t_1))
	tmp = 0.0
	if (x <= -1.02e+228)
		tmp = t_2;
	elseif (x <= 3.25e+142)
		tmp = Float64(Float64(y * i) + Float64(t_1 + Float64(a + Float64(z + t))));
	elseif ((x <= 1.92e+177) || !(x <= 1.3e+246))
		tmp = t_2;
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(z + a) + Float64(Float64(b + -0.5) * log(c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = log(c) * (b - 0.5);
	t_2 = (y * i) + ((x * log(y)) + t_1);
	tmp = 0.0;
	if (x <= -1.02e+228)
		tmp = t_2;
	elseif (x <= 3.25e+142)
		tmp = (y * i) + (t_1 + (a + (z + t)));
	elseif ((x <= 1.92e+177) || ~((x <= 1.3e+246)))
		tmp = t_2;
	else
		tmp = (y * i) + ((z + a) + ((b + -0.5) * log(c)));
	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]}, Block[{t$95$2 = N[(N[(y * i), $MachinePrecision] + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.02e+228], t$95$2, If[LessEqual[x, 3.25e+142], N[(N[(y * i), $MachinePrecision] + N[(t$95$1 + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 1.92e+177], N[Not[LessEqual[x, 1.3e+246]], $MachinePrecision]], t$95$2, N[(N[(y * i), $MachinePrecision] + N[(N[(z + a), $MachinePrecision] + N[(N[(b + -0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.02e228 or 3.2499999999999999e142 < x < 1.9200000000000001e177 or 1.30000000000000007e246 < x

   1. Initial program 97.4%

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

      1. associate-+l+ 97.4%

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

      2. +-commutative 97.4%

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

      3. associate-+r+ 97.4%

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

      4. fma-undefine 97.4%

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

      5. add-cube-cbrt 96.2%

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

      6. pow2 96.2%

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

   4. Applied egg-rr 96.2%

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

   5. Taylor expanded in x around inf 92.8%

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

   if -1.02e228 < x < 3.2499999999999999e142

   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 94.8%

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

   if 1.9200000000000001e177 < x < 1.30000000000000007e246

   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 0 84.0%

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

   4. Taylor expanded in t around 0 76.1%

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

      1. associate-+r+ 76.1%

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

      2. sub-neg 76.1%

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

      3. metadata-eval 76.1%

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

   6. Simplified 76.1%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{+228}:\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{elif}\;x \leq 3.25 \cdot 10^{+142}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.92 \cdot 10^{+177} \lor \neg \left(x \leq 1.3 \cdot 10^{+246}\right):\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(z + a\right) + \left(b + -0.5\right) \cdot \log c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log c \cdot \left(b - 0.5\right)\\ t_2 := x \cdot \log y + t\_1\\ t_3 := y \cdot i + t\_2\\ \mathbf{if}\;x \leq -8.2 \cdot 10^{+227}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+95}:\\ \;\;\;\;y \cdot i + \left(t\_1 + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+177}:\\ \;\;\;\;a + \left(t + \left(z + t\_2\right)\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+246}:\\ \;\;\;\;y \cdot i + \left(\left(z + a\right) + \left(b + -0.5\right) \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (log c) (- b 0.5)))
        (t_2 (+ (* x (log y)) t_1))
        (t_3 (+ (* y i) t_2)))
   (if (<= x -8.2e+227)
     t_3
     (if (<= x 5.2e+95)
       (+ (* y i) (+ t_1 (+ a (+ z t))))
       (if (<= x 2.3e+177)
         (+ a (+ t (+ z t_2)))
         (if (<= x 5.2e+246)
           (+ (* y i) (+ (+ z a) (* (+ b -0.5) (log c))))
           t_3))))))

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 t_2 = (x * log(y)) + t_1;
	double t_3 = (y * i) + t_2;
	double tmp;
	if (x <= -8.2e+227) {
		tmp = t_3;
	} else if (x <= 5.2e+95) {
		tmp = (y * i) + (t_1 + (a + (z + t)));
	} else if (x <= 2.3e+177) {
		tmp = a + (t + (z + t_2));
	} else if (x <= 5.2e+246) {
		tmp = (y * i) + ((z + a) + ((b + -0.5) * log(c)));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = log(c) * (b - 0.5d0)
    t_2 = (x * log(y)) + t_1
    t_3 = (y * i) + t_2
    if (x <= (-8.2d+227)) then
        tmp = t_3
    else if (x <= 5.2d+95) then
        tmp = (y * i) + (t_1 + (a + (z + t)))
    else if (x <= 2.3d+177) then
        tmp = a + (t + (z + t_2))
    else if (x <= 5.2d+246) then
        tmp = (y * i) + ((z + a) + ((b + (-0.5d0)) * log(c)))
    else
        tmp = t_3
    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 t_2 = (x * Math.log(y)) + t_1;
	double t_3 = (y * i) + t_2;
	double tmp;
	if (x <= -8.2e+227) {
		tmp = t_3;
	} else if (x <= 5.2e+95) {
		tmp = (y * i) + (t_1 + (a + (z + t)));
	} else if (x <= 2.3e+177) {
		tmp = a + (t + (z + t_2));
	} else if (x <= 5.2e+246) {
		tmp = (y * i) + ((z + a) + ((b + -0.5) * Math.log(c)));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = math.log(c) * (b - 0.5)
	t_2 = (x * math.log(y)) + t_1
	t_3 = (y * i) + t_2
	tmp = 0
	if x <= -8.2e+227:
		tmp = t_3
	elif x <= 5.2e+95:
		tmp = (y * i) + (t_1 + (a + (z + t)))
	elif x <= 2.3e+177:
		tmp = a + (t + (z + t_2))
	elif x <= 5.2e+246:
		tmp = (y * i) + ((z + a) + ((b + -0.5) * math.log(c)))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(log(c) * Float64(b - 0.5))
	t_2 = Float64(Float64(x * log(y)) + t_1)
	t_3 = Float64(Float64(y * i) + t_2)
	tmp = 0.0
	if (x <= -8.2e+227)
		tmp = t_3;
	elseif (x <= 5.2e+95)
		tmp = Float64(Float64(y * i) + Float64(t_1 + Float64(a + Float64(z + t))));
	elseif (x <= 2.3e+177)
		tmp = Float64(a + Float64(t + Float64(z + t_2)));
	elseif (x <= 5.2e+246)
		tmp = Float64(Float64(y * i) + Float64(Float64(z + a) + Float64(Float64(b + -0.5) * log(c))));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = log(c) * (b - 0.5);
	t_2 = (x * log(y)) + t_1;
	t_3 = (y * i) + t_2;
	tmp = 0.0;
	if (x <= -8.2e+227)
		tmp = t_3;
	elseif (x <= 5.2e+95)
		tmp = (y * i) + (t_1 + (a + (z + t)));
	elseif (x <= 2.3e+177)
		tmp = a + (t + (z + t_2));
	elseif (x <= 5.2e+246)
		tmp = (y * i) + ((z + a) + ((b + -0.5) * log(c)));
	else
		tmp = t_3;
	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]}, Block[{t$95$2 = N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y * i), $MachinePrecision] + t$95$2), $MachinePrecision]}, If[LessEqual[x, -8.2e+227], t$95$3, If[LessEqual[x, 5.2e+95], N[(N[(y * i), $MachinePrecision] + N[(t$95$1 + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.3e+177], N[(a + N[(t + N[(z + t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.2e+246], N[(N[(y * i), $MachinePrecision] + N[(N[(z + a), $MachinePrecision] + N[(N[(b + -0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -8.19999999999999992e227 or 5.20000000000000028e246 < x

   1. Initial program 97.0%

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

      1. associate-+l+ 97.0%

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

      2. +-commutative 97.0%

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

      3. associate-+r+ 97.0%

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

      4. fma-undefine 97.0%

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

      5. add-cube-cbrt 95.9%

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

      6. pow2 95.9%

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

   4. Applied egg-rr 95.9%

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

   5. Taylor expanded in x around inf 91.7%

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

   if -8.19999999999999992e227 < x < 5.19999999999999981e95

   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 95.9%

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

   if 5.19999999999999981e95 < x < 2.2999999999999999e177

   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. Taylor expanded in y around 0 84.3%

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

   if 2.2999999999999999e177 < x < 5.20000000000000028e246

   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 0 84.0%

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

   4. Taylor expanded in t around 0 76.1%

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

      1. associate-+r+ 76.1%

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

      2. sub-neg 76.1%

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

      3. metadata-eval 76.1%

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

   6. Simplified 76.1%

      \[\leadsto \color{blue}{\left(\left(a + z\right) + \log c \cdot \left(b + -0.5\right)\right)} + y \cdot i \]
3. Recombined 4 regimes into one program.

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+227}:\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+95}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+177}:\\ \;\;\;\;a + \left(t + \left(z + \left(x \cdot \log y + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+246}:\\ \;\;\;\;y \cdot i + \left(\left(z + a\right) + \left(b + -0.5\right) \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + \log c \cdot \left(b - 0.5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 91.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;b \leq -6.6 \cdot 10^{+209}:\\ \;\;\;\;y \cdot i + \left(t\_1 + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{+160}:\\ \;\;\;\;y \cdot i + \left(-0.5 \cdot \log c + \left(a + \left(t + \left(z + t\_1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(z + a\right) + b \cdot \log c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= b -6.6e+209)
     (+ (* y i) (+ t_1 (* (log c) (- b 0.5))))
     (if (<= b 4.8e+160)
       (+ (* y i) (+ (* -0.5 (log c)) (+ a (+ t (+ z t_1)))))
       (+ (* y i) (+ (+ z a) (* 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 = x * log(y);
	double tmp;
	if (b <= -6.6e+209) {
		tmp = (y * i) + (t_1 + (log(c) * (b - 0.5)));
	} else if (b <= 4.8e+160) {
		tmp = (y * i) + ((-0.5 * log(c)) + (a + (t + (z + t_1))));
	} else {
		tmp = (y * i) + ((z + a) + (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 = x * log(y)
    if (b <= (-6.6d+209)) then
        tmp = (y * i) + (t_1 + (log(c) * (b - 0.5d0)))
    else if (b <= 4.8d+160) then
        tmp = (y * i) + (((-0.5d0) * log(c)) + (a + (t + (z + t_1))))
    else
        tmp = (y * i) + ((z + a) + (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 = x * Math.log(y);
	double tmp;
	if (b <= -6.6e+209) {
		tmp = (y * i) + (t_1 + (Math.log(c) * (b - 0.5)));
	} else if (b <= 4.8e+160) {
		tmp = (y * i) + ((-0.5 * Math.log(c)) + (a + (t + (z + t_1))));
	} else {
		tmp = (y * i) + ((z + a) + (b * Math.log(c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x * math.log(y)
	tmp = 0
	if b <= -6.6e+209:
		tmp = (y * i) + (t_1 + (math.log(c) * (b - 0.5)))
	elif b <= 4.8e+160:
		tmp = (y * i) + ((-0.5 * math.log(c)) + (a + (t + (z + t_1))))
	else:
		tmp = (y * i) + ((z + a) + (b * math.log(c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (b <= -6.6e+209)
		tmp = Float64(Float64(y * i) + Float64(t_1 + Float64(log(c) * Float64(b - 0.5))));
	elseif (b <= 4.8e+160)
		tmp = Float64(Float64(y * i) + Float64(Float64(-0.5 * log(c)) + Float64(a + Float64(t + Float64(z + t_1)))));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(z + a) + Float64(b * log(c))));
	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 (b <= -6.6e+209)
		tmp = (y * i) + (t_1 + (log(c) * (b - 0.5)));
	elseif (b <= 4.8e+160)
		tmp = (y * i) + ((-0.5 * log(c)) + (a + (t + (z + t_1))));
	else
		tmp = (y * i) + ((z + a) + (b * log(c)));
	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[b, -6.6e+209], N[(N[(y * i), $MachinePrecision] + N[(t$95$1 + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.8e+160], N[(N[(y * i), $MachinePrecision] + N[(N[(-0.5 * N[Log[c], $MachinePrecision]), $MachinePrecision] + N[(a + N[(t + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(z + a), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.59999999999999961e209

   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. Step-by-step derivation

      1. associate-+l+ 99.6%

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

      2. +-commutative 99.6%

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

      3. associate-+r+ 99.6%

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

      4. fma-undefine 99.6%

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

      5. add-cube-cbrt 99.5%

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

      6. pow2 99.5%

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

   4. Applied egg-rr 99.5%

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

   5. Taylor expanded in x around inf 97.9%

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

   if -6.59999999999999961e209 < b < 4.8000000000000003e160

   1. Initial program 99.4%

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

   3. Taylor expanded in b around 0 97.1%

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

      1. *-commutative 97.1%

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

   5. Simplified 97.1%

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

   if 4.8000000000000003e160 < b

   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 0 91.4%

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

   4. Taylor expanded in t around 0 84.8%

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

      1. associate-+r+ 84.8%

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

      2. sub-neg 84.8%

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

      3. metadata-eval 84.8%

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

   6. Simplified 84.8%

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

   7. Taylor expanded in b around inf 84.8%

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

      1. *-commutative 84.8%

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

   9. Simplified 84.8%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.6 \cdot 10^{+209}:\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{+160}:\\ \;\;\;\;y \cdot i + \left(-0.5 \cdot \log c + \left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(z + a\right) + b \cdot \log c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return ((log(c) * (b - 0.5)) + (a + (t + (z + (x * log(y)))))) + (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 = ((log(c) * (b - 0.5d0)) + (a + (t + (z + (x * log(y)))))) + (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 ((Math.log(c) * (b - 0.5)) + (a + (t + (z + (x * Math.log(y)))))) + (y * i);
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

3. Final simplification 99.5%

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

Alternative 6: 62.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \log c\\ t_2 := y \cdot i + \left(z + a\right)\\ t_3 := a + \left(t + \left(z + x \cdot \log y\right)\right)\\ t_4 := y \cdot i + t\_1\\ \mathbf{if}\;b - 0.5 \leq -1 \cdot 10^{+212}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;b - 0.5 \leq -1 \cdot 10^{+157}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b - 0.5 \leq -5 \cdot 10^{+51}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b - 0.5 \leq -100000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b - 0.5 \leq -0.5:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b - 0.5 \leq 5 \cdot 10^{+173}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b - 0.5 \leq 3 \cdot 10^{+208}:\\ \;\;\;\;a + \left(z + t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* b (log c)))
        (t_2 (+ (* y i) (+ z a)))
        (t_3 (+ a (+ t (+ z (* x (log y))))))
        (t_4 (+ (* y i) t_1)))
   (if (<= (- b 0.5) -1e+212)
     t_4
     (if (<= (- b 0.5) -1e+157)
       t_3
       (if (<= (- b 0.5) -5e+51)
         t_2
         (if (<= (- b 0.5) -100000.0)
           t_3
           (if (<= (- b 0.5) -0.5)
             t_2
             (if (<= (- b 0.5) 5e+173)
               t_3
               (if (<= (- b 0.5) 3e+208) (+ a (+ z t_1)) t_4)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = b * log(c);
	double t_2 = (y * i) + (z + a);
	double t_3 = a + (t + (z + (x * log(y))));
	double t_4 = (y * i) + t_1;
	double tmp;
	if ((b - 0.5) <= -1e+212) {
		tmp = t_4;
	} else if ((b - 0.5) <= -1e+157) {
		tmp = t_3;
	} else if ((b - 0.5) <= -5e+51) {
		tmp = t_2;
	} else if ((b - 0.5) <= -100000.0) {
		tmp = t_3;
	} else if ((b - 0.5) <= -0.5) {
		tmp = t_2;
	} else if ((b - 0.5) <= 5e+173) {
		tmp = t_3;
	} else if ((b - 0.5) <= 3e+208) {
		tmp = a + (z + t_1);
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = b * log(c)
    t_2 = (y * i) + (z + a)
    t_3 = a + (t + (z + (x * log(y))))
    t_4 = (y * i) + t_1
    if ((b - 0.5d0) <= (-1d+212)) then
        tmp = t_4
    else if ((b - 0.5d0) <= (-1d+157)) then
        tmp = t_3
    else if ((b - 0.5d0) <= (-5d+51)) then
        tmp = t_2
    else if ((b - 0.5d0) <= (-100000.0d0)) then
        tmp = t_3
    else if ((b - 0.5d0) <= (-0.5d0)) then
        tmp = t_2
    else if ((b - 0.5d0) <= 5d+173) then
        tmp = t_3
    else if ((b - 0.5d0) <= 3d+208) then
        tmp = a + (z + t_1)
    else
        tmp = t_4
    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 = b * Math.log(c);
	double t_2 = (y * i) + (z + a);
	double t_3 = a + (t + (z + (x * Math.log(y))));
	double t_4 = (y * i) + t_1;
	double tmp;
	if ((b - 0.5) <= -1e+212) {
		tmp = t_4;
	} else if ((b - 0.5) <= -1e+157) {
		tmp = t_3;
	} else if ((b - 0.5) <= -5e+51) {
		tmp = t_2;
	} else if ((b - 0.5) <= -100000.0) {
		tmp = t_3;
	} else if ((b - 0.5) <= -0.5) {
		tmp = t_2;
	} else if ((b - 0.5) <= 5e+173) {
		tmp = t_3;
	} else if ((b - 0.5) <= 3e+208) {
		tmp = a + (z + t_1);
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = b * math.log(c)
	t_2 = (y * i) + (z + a)
	t_3 = a + (t + (z + (x * math.log(y))))
	t_4 = (y * i) + t_1
	tmp = 0
	if (b - 0.5) <= -1e+212:
		tmp = t_4
	elif (b - 0.5) <= -1e+157:
		tmp = t_3
	elif (b - 0.5) <= -5e+51:
		tmp = t_2
	elif (b - 0.5) <= -100000.0:
		tmp = t_3
	elif (b - 0.5) <= -0.5:
		tmp = t_2
	elif (b - 0.5) <= 5e+173:
		tmp = t_3
	elif (b - 0.5) <= 3e+208:
		tmp = a + (z + t_1)
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(b * log(c))
	t_2 = Float64(Float64(y * i) + Float64(z + a))
	t_3 = Float64(a + Float64(t + Float64(z + Float64(x * log(y)))))
	t_4 = Float64(Float64(y * i) + t_1)
	tmp = 0.0
	if (Float64(b - 0.5) <= -1e+212)
		tmp = t_4;
	elseif (Float64(b - 0.5) <= -1e+157)
		tmp = t_3;
	elseif (Float64(b - 0.5) <= -5e+51)
		tmp = t_2;
	elseif (Float64(b - 0.5) <= -100000.0)
		tmp = t_3;
	elseif (Float64(b - 0.5) <= -0.5)
		tmp = t_2;
	elseif (Float64(b - 0.5) <= 5e+173)
		tmp = t_3;
	elseif (Float64(b - 0.5) <= 3e+208)
		tmp = Float64(a + Float64(z + t_1));
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = b * log(c);
	t_2 = (y * i) + (z + a);
	t_3 = a + (t + (z + (x * log(y))));
	t_4 = (y * i) + t_1;
	tmp = 0.0;
	if ((b - 0.5) <= -1e+212)
		tmp = t_4;
	elseif ((b - 0.5) <= -1e+157)
		tmp = t_3;
	elseif ((b - 0.5) <= -5e+51)
		tmp = t_2;
	elseif ((b - 0.5) <= -100000.0)
		tmp = t_3;
	elseif ((b - 0.5) <= -0.5)
		tmp = t_2;
	elseif ((b - 0.5) <= 5e+173)
		tmp = t_3;
	elseif ((b - 0.5) <= 3e+208)
		tmp = a + (z + t_1);
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * i), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a + N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(y * i), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[N[(b - 0.5), $MachinePrecision], -1e+212], t$95$4, If[LessEqual[N[(b - 0.5), $MachinePrecision], -1e+157], t$95$3, If[LessEqual[N[(b - 0.5), $MachinePrecision], -5e+51], t$95$2, If[LessEqual[N[(b - 0.5), $MachinePrecision], -100000.0], t$95$3, If[LessEqual[N[(b - 0.5), $MachinePrecision], -0.5], t$95$2, If[LessEqual[N[(b - 0.5), $MachinePrecision], 5e+173], t$95$3, If[LessEqual[N[(b - 0.5), $MachinePrecision], 3e+208], N[(a + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 b #s(literal 1/2 binary64)) < -9.9999999999999991e211 or 2.99999999999999995e208 < (-.f64 b #s(literal 1/2 binary64))

   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 95.0%

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

   4. Taylor expanded in b around inf 86.2%

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

      1. *-commutative 86.2%

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

   6. Simplified 86.2%

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

   if -9.9999999999999991e211 < (-.f64 b #s(literal 1/2 binary64)) < -9.99999999999999983e156 or -5e51 < (-.f64 b #s(literal 1/2 binary64)) < -1e5 or -0.5 < (-.f64 b #s(literal 1/2 binary64)) < 5.00000000000000034e173

   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. Taylor expanded in y around 0 89.4%

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

   4. Taylor expanded in x around inf 84.1%

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

   if -9.99999999999999983e156 < (-.f64 b #s(literal 1/2 binary64)) < -5e51 or -1e5 < (-.f64 b #s(literal 1/2 binary64)) < -0.5

   1. Initial program 99.3%

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

   3. Taylor expanded in x around 0 85.0%

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

   4. Taylor expanded in t around 0 70.1%

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

      1. associate-+r+ 70.1%

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

      2. sub-neg 70.1%

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

      3. metadata-eval 70.1%

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

   6. Simplified 70.1%

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

   7. Taylor expanded in b around inf 67.9%

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

      1. *-commutative 67.9%

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

   9. Simplified 67.9%

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

   10. Taylor expanded in b around 0 66.7%

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

       1. +-commutative 66.7%

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

   12. Simplified 66.7%

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

   if 5.00000000000000034e173 < (-.f64 b #s(literal 1/2 binary64)) < 2.99999999999999995e208

   1. Initial program 99.4%

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

   3. Taylor expanded in x around 0 99.4%

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

   4. Taylor expanded in t around 0 87.8%

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

      1. associate-+r+ 87.8%

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

      2. sub-neg 87.8%

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

      3. metadata-eval 87.8%

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

   6. Simplified 87.8%

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

   7. Taylor expanded in b around inf 87.8%

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

      1. *-commutative 87.8%

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

   9. Simplified 87.8%

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

   10. Taylor expanded in i around inf 50.5%

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

       1. associate-+r+ 50.5%

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

       2. associate-/l* 50.5%

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

   12. Simplified 50.5%

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

   13. Taylor expanded in i around 0 75.3%

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

       1. *-commutative 75.3%

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

   15. Simplified 75.3%

       \[\leadsto \color{blue}{a + \left(z + \log c \cdot b\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -1 \cdot 10^{+212}:\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{elif}\;b - 0.5 \leq -1 \cdot 10^{+157}:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{elif}\;b - 0.5 \leq -5 \cdot 10^{+51}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \mathbf{elif}\;b - 0.5 \leq -100000:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{elif}\;b - 0.5 \leq -0.5:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \mathbf{elif}\;b - 0.5 \leq 5 \cdot 10^{+173}:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{elif}\;b - 0.5 \leq 3 \cdot 10^{+208}:\\ \;\;\;\;a + \left(z + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 62.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \log c\\ t_2 := a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{if}\;b - 0.5 \leq -1 \cdot 10^{+212}:\\ \;\;\;\;y \cdot i + t\_1\\ \mathbf{elif}\;b - 0.5 \leq -5 \cdot 10^{+155}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b - 0.5 \leq -0.5:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \mathbf{elif}\;b - 0.5 \leq 5 \cdot 10^{+173}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b - 0.5 \leq 3 \cdot 10^{+208}:\\ \;\;\;\;a + \left(z + t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* b (log c))) (t_2 (+ a (+ t (+ z (* x (log y)))))))
   (if (<= (- b 0.5) -1e+212)
     (+ (* y i) t_1)
     (if (<= (- b 0.5) -5e+155)
       t_2
       (if (<= (- b 0.5) -0.5)
         (+ (* y i) (+ z a))
         (if (<= (- b 0.5) 5e+173)
           t_2
           (if (<= (- b 0.5) 3e+208)
             (+ a (+ z t_1))
             (+ (* y i) (+ a t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = b * log(c);
	double t_2 = a + (t + (z + (x * log(y))));
	double tmp;
	if ((b - 0.5) <= -1e+212) {
		tmp = (y * i) + t_1;
	} else if ((b - 0.5) <= -5e+155) {
		tmp = t_2;
	} else if ((b - 0.5) <= -0.5) {
		tmp = (y * i) + (z + a);
	} else if ((b - 0.5) <= 5e+173) {
		tmp = t_2;
	} else if ((b - 0.5) <= 3e+208) {
		tmp = a + (z + t_1);
	} else {
		tmp = (y * i) + (a + t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * log(c)
    t_2 = a + (t + (z + (x * log(y))))
    if ((b - 0.5d0) <= (-1d+212)) then
        tmp = (y * i) + t_1
    else if ((b - 0.5d0) <= (-5d+155)) then
        tmp = t_2
    else if ((b - 0.5d0) <= (-0.5d0)) then
        tmp = (y * i) + (z + a)
    else if ((b - 0.5d0) <= 5d+173) then
        tmp = t_2
    else if ((b - 0.5d0) <= 3d+208) then
        tmp = a + (z + t_1)
    else
        tmp = (y * i) + (a + t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = b * Math.log(c);
	double t_2 = a + (t + (z + (x * Math.log(y))));
	double tmp;
	if ((b - 0.5) <= -1e+212) {
		tmp = (y * i) + t_1;
	} else if ((b - 0.5) <= -5e+155) {
		tmp = t_2;
	} else if ((b - 0.5) <= -0.5) {
		tmp = (y * i) + (z + a);
	} else if ((b - 0.5) <= 5e+173) {
		tmp = t_2;
	} else if ((b - 0.5) <= 3e+208) {
		tmp = a + (z + t_1);
	} else {
		tmp = (y * i) + (a + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = b * math.log(c)
	t_2 = a + (t + (z + (x * math.log(y))))
	tmp = 0
	if (b - 0.5) <= -1e+212:
		tmp = (y * i) + t_1
	elif (b - 0.5) <= -5e+155:
		tmp = t_2
	elif (b - 0.5) <= -0.5:
		tmp = (y * i) + (z + a)
	elif (b - 0.5) <= 5e+173:
		tmp = t_2
	elif (b - 0.5) <= 3e+208:
		tmp = a + (z + t_1)
	else:
		tmp = (y * i) + (a + t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(b * log(c))
	t_2 = Float64(a + Float64(t + Float64(z + Float64(x * log(y)))))
	tmp = 0.0
	if (Float64(b - 0.5) <= -1e+212)
		tmp = Float64(Float64(y * i) + t_1);
	elseif (Float64(b - 0.5) <= -5e+155)
		tmp = t_2;
	elseif (Float64(b - 0.5) <= -0.5)
		tmp = Float64(Float64(y * i) + Float64(z + a));
	elseif (Float64(b - 0.5) <= 5e+173)
		tmp = t_2;
	elseif (Float64(b - 0.5) <= 3e+208)
		tmp = Float64(a + Float64(z + t_1));
	else
		tmp = Float64(Float64(y * i) + Float64(a + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = b * log(c);
	t_2 = a + (t + (z + (x * log(y))));
	tmp = 0.0;
	if ((b - 0.5) <= -1e+212)
		tmp = (y * i) + t_1;
	elseif ((b - 0.5) <= -5e+155)
		tmp = t_2;
	elseif ((b - 0.5) <= -0.5)
		tmp = (y * i) + (z + a);
	elseif ((b - 0.5) <= 5e+173)
		tmp = t_2;
	elseif ((b - 0.5) <= 3e+208)
		tmp = a + (z + t_1);
	else
		tmp = (y * i) + (a + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a + N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b - 0.5), $MachinePrecision], -1e+212], N[(N[(y * i), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[N[(b - 0.5), $MachinePrecision], -5e+155], t$95$2, If[LessEqual[N[(b - 0.5), $MachinePrecision], -0.5], N[(N[(y * i), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b - 0.5), $MachinePrecision], 5e+173], t$95$2, If[LessEqual[N[(b - 0.5), $MachinePrecision], 3e+208], N[(a + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (-.f64 b #s(literal 1/2 binary64)) < -9.9999999999999991e211

   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 0 93.6%

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

   4. Taylor expanded in b around inf 92.0%

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

      1. *-commutative 92.0%

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

   6. Simplified 92.0%

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

   if -9.9999999999999991e211 < (-.f64 b #s(literal 1/2 binary64)) < -4.9999999999999999e155 or -0.5 < (-.f64 b #s(literal 1/2 binary64)) < 5.00000000000000034e173

   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. Taylor expanded in y around 0 87.8%

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

   4. Taylor expanded in x around inf 83.5%

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

   if -4.9999999999999999e155 < (-.f64 b #s(literal 1/2 binary64)) < -0.5

   1. Initial program 99.3%

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

   3. Taylor expanded in x around 0 83.3%

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

   4. Taylor expanded in t around 0 69.1%

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

      1. associate-+r+ 69.1%

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

      2. sub-neg 69.1%

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

      3. metadata-eval 69.1%

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

   6. Simplified 69.1%

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

   7. Taylor expanded in b around inf 67.1%

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

      1. *-commutative 67.1%

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

   9. Simplified 67.1%

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

   10. Taylor expanded in b around 0 65.3%

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

       1. +-commutative 65.3%

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

   12. Simplified 65.3%

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

   if 5.00000000000000034e173 < (-.f64 b #s(literal 1/2 binary64)) < 2.99999999999999995e208

   1. Initial program 99.4%

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

   3. Taylor expanded in x around 0 99.4%

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

   4. Taylor expanded in t around 0 87.8%

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

      1. associate-+r+ 87.8%

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

      2. sub-neg 87.8%

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

      3. metadata-eval 87.8%

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

   6. Simplified 87.8%

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

   7. Taylor expanded in b around inf 87.8%

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

      1. *-commutative 87.8%

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

   9. Simplified 87.8%

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

   10. Taylor expanded in i around inf 50.5%

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

       1. associate-+r+ 50.5%

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

       2. associate-/l* 50.5%

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

   12. Simplified 50.5%

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

   13. Taylor expanded in i around 0 75.3%

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

       1. *-commutative 75.3%

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

   15. Simplified 75.3%

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

   if 2.99999999999999995e208 < (-.f64 b #s(literal 1/2 binary64))

   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. Taylor expanded in x around 0 95.9%

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

   4. Taylor expanded in t around 0 90.4%

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

      1. associate-+r+ 90.4%

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

      2. sub-neg 90.4%

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

      3. metadata-eval 90.4%

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

   6. Simplified 90.4%

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

   7. Taylor expanded in b around inf 90.4%

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

      1. *-commutative 90.4%

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

   9. Simplified 90.4%

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

   10. Taylor expanded in z around 0 90.4%

       \[\leadsto \color{blue}{\left(a + b \cdot \log c\right)} + y \cdot i \]
3. Recombined 5 regimes into one program.

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -1 \cdot 10^{+212}:\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{elif}\;b - 0.5 \leq -5 \cdot 10^{+155}:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{elif}\;b - 0.5 \leq -0.5:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \mathbf{elif}\;b - 0.5 \leq 5 \cdot 10^{+173}:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{elif}\;b - 0.5 \leq 3 \cdot 10^{+208}:\\ \;\;\;\;a + \left(z + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 63.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot i + \left(z + b \cdot \log c\right)\\ \mathbf{if}\;b - 0.5 \leq -1 \cdot 10^{+212}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b - 0.5 \leq -0.499998:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \mathbf{elif}\;b - 0.5 \leq 10^{+137}:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y i) (+ z (* b (log c))))))
   (if (<= (- b 0.5) -1e+212)
     t_1
     (if (<= (- b 0.5) -0.499998)
       (+ (* y i) (+ z a))
       (if (<= (- b 0.5) 1e+137) (+ a (+ t (+ z (* x (log y))))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * i) + (z + (b * log(c)));
	double tmp;
	if ((b - 0.5) <= -1e+212) {
		tmp = t_1;
	} else if ((b - 0.5) <= -0.499998) {
		tmp = (y * i) + (z + a);
	} else if ((b - 0.5) <= 1e+137) {
		tmp = a + (t + (z + (x * log(y))));
	} 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 = (y * i) + (z + (b * log(c)))
    if ((b - 0.5d0) <= (-1d+212)) then
        tmp = t_1
    else if ((b - 0.5d0) <= (-0.499998d0)) then
        tmp = (y * i) + (z + a)
    else if ((b - 0.5d0) <= 1d+137) then
        tmp = a + (t + (z + (x * log(y))))
    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 = (y * i) + (z + (b * Math.log(c)));
	double tmp;
	if ((b - 0.5) <= -1e+212) {
		tmp = t_1;
	} else if ((b - 0.5) <= -0.499998) {
		tmp = (y * i) + (z + a);
	} else if ((b - 0.5) <= 1e+137) {
		tmp = a + (t + (z + (x * Math.log(y))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y * i) + (z + (b * math.log(c)))
	tmp = 0
	if (b - 0.5) <= -1e+212:
		tmp = t_1
	elif (b - 0.5) <= -0.499998:
		tmp = (y * i) + (z + a)
	elif (b - 0.5) <= 1e+137:
		tmp = a + (t + (z + (x * math.log(y))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * i) + Float64(z + Float64(b * log(c))))
	tmp = 0.0
	if (Float64(b - 0.5) <= -1e+212)
		tmp = t_1;
	elseif (Float64(b - 0.5) <= -0.499998)
		tmp = Float64(Float64(y * i) + Float64(z + a));
	elseif (Float64(b - 0.5) <= 1e+137)
		tmp = Float64(a + Float64(t + Float64(z + Float64(x * log(y)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y * i) + (z + (b * log(c)));
	tmp = 0.0;
	if ((b - 0.5) <= -1e+212)
		tmp = t_1;
	elseif ((b - 0.5) <= -0.499998)
		tmp = (y * i) + (z + a);
	elseif ((b - 0.5) <= 1e+137)
		tmp = a + (t + (z + (x * log(y))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(y * i), $MachinePrecision] + N[(z + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b - 0.5), $MachinePrecision], -1e+212], t$95$1, If[LessEqual[N[(b - 0.5), $MachinePrecision], -0.499998], N[(N[(y * i), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b - 0.5), $MachinePrecision], 1e+137], N[(a + N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 b #s(literal 1/2 binary64)) < -9.9999999999999991e211 or 1e137 < (-.f64 b #s(literal 1/2 binary64))

   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 89.1%

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

   4. Taylor expanded in t around 0 83.7%

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

      1. associate-+r+ 83.7%

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

      2. sub-neg 83.7%

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

      3. metadata-eval 83.7%

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

   6. Simplified 83.7%

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

   7. Taylor expanded in b around inf 83.7%

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

      1. *-commutative 83.7%

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

   9. Simplified 83.7%

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

   10. Taylor expanded in a around 0 74.4%

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

   if -9.9999999999999991e211 < (-.f64 b #s(literal 1/2 binary64)) < -0.499997999999999998

   1. Initial program 99.3%

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

   3. Taylor expanded in x around 0 82.4%

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

   4. Taylor expanded in t around 0 68.3%

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

      1. associate-+r+ 68.3%

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

      2. sub-neg 68.3%

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

      3. metadata-eval 68.3%

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

   6. Simplified 68.3%

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

   7. Taylor expanded in b around inf 66.4%

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

      1. *-commutative 66.4%

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

   9. Simplified 66.4%

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

   10. Taylor expanded in b around 0 63.7%

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

       1. +-commutative 63.7%

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

   12. Simplified 63.7%

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

   if -0.499997999999999998 < (-.f64 b #s(literal 1/2 binary64)) < 1e137

   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 y around 0 91.4%

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

   4. Taylor expanded in x around inf 90.3%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -1 \cdot 10^{+212}:\\ \;\;\;\;y \cdot i + \left(z + b \cdot \log c\right)\\ \mathbf{elif}\;b - 0.5 \leq -0.499998:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \mathbf{elif}\;b - 0.5 \leq 10^{+137}:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + b \cdot \log c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 61.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \log c\\ \mathbf{if}\;b - 0.5 \leq -5 \cdot 10^{+242}:\\ \;\;\;\;y \cdot i + t\_1\\ \mathbf{elif}\;b - 0.5 \leq -2 \cdot 10^{+156} \lor \neg \left(b - 0.5 \leq 2 \cdot 10^{+142}\right):\\ \;\;\;\;a + \left(z + t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* b (log c))))
   (if (<= (- b 0.5) -5e+242)
     (+ (* y i) t_1)
     (if (or (<= (- b 0.5) -2e+156) (not (<= (- b 0.5) 2e+142)))
       (+ a (+ z t_1))
       (+ (* y i) (+ z a))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = b * log(c);
	double tmp;
	if ((b - 0.5) <= -5e+242) {
		tmp = (y * i) + t_1;
	} else if (((b - 0.5) <= -2e+156) || !((b - 0.5) <= 2e+142)) {
		tmp = a + (z + t_1);
	} else {
		tmp = (y * i) + (z + a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * log(c)
    if ((b - 0.5d0) <= (-5d+242)) then
        tmp = (y * i) + t_1
    else if (((b - 0.5d0) <= (-2d+156)) .or. (.not. ((b - 0.5d0) <= 2d+142))) then
        tmp = a + (z + t_1)
    else
        tmp = (y * i) + (z + a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = b * Math.log(c);
	double tmp;
	if ((b - 0.5) <= -5e+242) {
		tmp = (y * i) + t_1;
	} else if (((b - 0.5) <= -2e+156) || !((b - 0.5) <= 2e+142)) {
		tmp = a + (z + t_1);
	} else {
		tmp = (y * i) + (z + a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = b * math.log(c)
	tmp = 0
	if (b - 0.5) <= -5e+242:
		tmp = (y * i) + t_1
	elif ((b - 0.5) <= -2e+156) or not ((b - 0.5) <= 2e+142):
		tmp = a + (z + t_1)
	else:
		tmp = (y * i) + (z + a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(b * log(c))
	tmp = 0.0
	if (Float64(b - 0.5) <= -5e+242)
		tmp = Float64(Float64(y * i) + t_1);
	elseif ((Float64(b - 0.5) <= -2e+156) || !(Float64(b - 0.5) <= 2e+142))
		tmp = Float64(a + Float64(z + t_1));
	else
		tmp = Float64(Float64(y * i) + Float64(z + a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = b * log(c);
	tmp = 0.0;
	if ((b - 0.5) <= -5e+242)
		tmp = (y * i) + t_1;
	elseif (((b - 0.5) <= -2e+156) || ~(((b - 0.5) <= 2e+142)))
		tmp = a + (z + t_1);
	else
		tmp = (y * i) + (z + a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b - 0.5), $MachinePrecision], -5e+242], N[(N[(y * i), $MachinePrecision] + t$95$1), $MachinePrecision], If[Or[LessEqual[N[(b - 0.5), $MachinePrecision], -2e+156], N[Not[LessEqual[N[(b - 0.5), $MachinePrecision], 2e+142]], $MachinePrecision]], N[(a + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 b #s(literal 1/2 binary64)) < -5.0000000000000004e242

   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 0 92.7%

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

   4. Taylor expanded in b around inf 90.8%

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

      1. *-commutative 90.8%

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

   6. Simplified 90.8%

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

   if -5.0000000000000004e242 < (-.f64 b #s(literal 1/2 binary64)) < -2e156 or 2.0000000000000001e142 < (-.f64 b #s(literal 1/2 binary64))

   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 85.8%

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

   4. Taylor expanded in t around 0 76.0%

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

      1. associate-+r+ 76.0%

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

      2. sub-neg 76.0%

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

      3. metadata-eval 76.0%

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

   6. Simplified 76.0%

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

   7. Taylor expanded in b around inf 76.0%

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

      1. *-commutative 76.0%

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

   9. Simplified 76.0%

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

   10. Taylor expanded in i around inf 41.9%

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

       1. associate-+r+ 41.9%

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

       2. associate-/l* 41.8%

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

   12. Simplified 41.8%

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

   13. Taylor expanded in i around 0 65.0%

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

       1. *-commutative 65.0%

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

   15. Simplified 65.0%

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

   if -2e156 < (-.f64 b #s(literal 1/2 binary64)) < 2.0000000000000001e142

   1. Initial program 99.4%

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

   3. Taylor expanded in x around 0 81.4%

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

   4. Taylor expanded in t around 0 67.5%

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

      1. associate-+r+ 67.5%

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

      2. sub-neg 67.5%

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

      3. metadata-eval 67.5%

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

   6. Simplified 67.5%

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

   7. Taylor expanded in b around inf 65.8%

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

      1. *-commutative 65.8%

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

   9. Simplified 65.8%

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

   10. Taylor expanded in b around 0 64.2%

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

       1. +-commutative 64.2%

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

   12. Simplified 64.2%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -5 \cdot 10^{+242}:\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{elif}\;b - 0.5 \leq -2 \cdot 10^{+156} \lor \neg \left(b - 0.5 \leq 2 \cdot 10^{+142}\right):\\ \;\;\;\;a + \left(z + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot i + \left(z + a\right)\\ \mathbf{if}\;i \leq -12500000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 7.6 \cdot 10^{-116}:\\ \;\;\;\;a + \left(z + b \cdot \log c\right)\\ \mathbf{elif}\;i \leq 4.7 \cdot 10^{-85}:\\ \;\;\;\;x \cdot \left(\log y + \frac{z}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y i) (+ z a))))
   (if (<= i -12500000000.0)
     t_1
     (if (<= i 7.6e-116)
       (+ a (+ z (* b (log c))))
       (if (<= i 4.7e-85) (* x (+ (log y) (/ z x))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * i) + (z + a);
	double tmp;
	if (i <= -12500000000.0) {
		tmp = t_1;
	} else if (i <= 7.6e-116) {
		tmp = a + (z + (b * log(c)));
	} else if (i <= 4.7e-85) {
		tmp = x * (log(y) + (z / x));
	} 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 = (y * i) + (z + a)
    if (i <= (-12500000000.0d0)) then
        tmp = t_1
    else if (i <= 7.6d-116) then
        tmp = a + (z + (b * log(c)))
    else if (i <= 4.7d-85) then
        tmp = x * (log(y) + (z / x))
    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 = (y * i) + (z + a);
	double tmp;
	if (i <= -12500000000.0) {
		tmp = t_1;
	} else if (i <= 7.6e-116) {
		tmp = a + (z + (b * Math.log(c)));
	} else if (i <= 4.7e-85) {
		tmp = x * (Math.log(y) + (z / x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y * i) + (z + a)
	tmp = 0
	if i <= -12500000000.0:
		tmp = t_1
	elif i <= 7.6e-116:
		tmp = a + (z + (b * math.log(c)))
	elif i <= 4.7e-85:
		tmp = x * (math.log(y) + (z / x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * i) + Float64(z + a))
	tmp = 0.0
	if (i <= -12500000000.0)
		tmp = t_1;
	elseif (i <= 7.6e-116)
		tmp = Float64(a + Float64(z + Float64(b * log(c))));
	elseif (i <= 4.7e-85)
		tmp = Float64(x * Float64(log(y) + Float64(z / x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y * i) + (z + a);
	tmp = 0.0;
	if (i <= -12500000000.0)
		tmp = t_1;
	elseif (i <= 7.6e-116)
		tmp = a + (z + (b * log(c)));
	elseif (i <= 4.7e-85)
		tmp = x * (log(y) + (z / x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(y * i), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -12500000000.0], t$95$1, If[LessEqual[i, 7.6e-116], N[(a + N[(z + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4.7e-85], N[(x * N[(N[Log[y], $MachinePrecision] + N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if i < -1.25e10 or 4.70000000000000009e-85 < i

   1. Initial program 99.2%

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

   3. Taylor expanded in x around 0 86.7%

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

   4. Taylor expanded in t around 0 77.8%

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

      1. associate-+r+ 77.8%

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

      2. sub-neg 77.8%

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

      3. metadata-eval 77.8%

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

   6. Simplified 77.8%

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

   7. Taylor expanded in b around inf 76.5%

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

      1. *-commutative 76.5%

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

   9. Simplified 76.5%

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

   10. Taylor expanded in b around 0 66.7%

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

       1. +-commutative 66.7%

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

   12. Simplified 66.7%

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

   if -1.25e10 < i < 7.6000000000000003e-116

   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. Taylor expanded in x around 0 81.9%

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

   4. Taylor expanded in t around 0 65.2%

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

      1. associate-+r+ 65.2%

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

      2. sub-neg 65.2%

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

      3. metadata-eval 65.2%

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

   6. Simplified 65.2%

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

   7. Taylor expanded in b around inf 64.4%

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

      1. *-commutative 64.4%

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

   9. Simplified 64.4%

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

   10. Taylor expanded in i around inf 21.6%

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

       1. associate-+r+ 21.6%

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

       2. associate-/l* 21.6%

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

   12. Simplified 21.6%

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

   13. Taylor expanded in i around 0 58.9%

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

       1. *-commutative 58.9%

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

   15. Simplified 58.9%

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

   if 7.6000000000000003e-116 < i < 4.70000000000000009e-85

   1. Initial program 99.4%

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

      1. associate-+l+ 99.4%

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

      2. +-commutative 99.4%

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

      3. associate-+r+ 99.4%

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

      4. fma-undefine 99.4%

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

      5. add-cube-cbrt 98.0%

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

      6. pow2 98.0%

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

   4. Applied egg-rr 98.0%

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

   5. Taylor expanded in x around inf 99.2%

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

      1. associate-+r+ 99.2%

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

      2. associate-+r+ 99.2%

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

      3. *-commutative 99.2%

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

      4. associate-/l* 99.2%

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

      5. sub-neg 99.2%

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

      6. metadata-eval 99.2%

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

   7. Simplified 99.2%

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

   8. Taylor expanded in z around inf 63.7%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -12500000000:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \mathbf{elif}\;i \leq 7.6 \cdot 10^{-116}:\\ \;\;\;\;a + \left(z + b \cdot \log c\right)\\ \mathbf{elif}\;i \leq 4.7 \cdot 10^{-85}:\\ \;\;\;\;x \cdot \left(\log y + \frac{z}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 74.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4 \cdot 10^{-31}:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(z + a\right) + b \cdot \log c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 4e-31)
   (+ a (+ t (+ z (* x (log y)))))
   (+ (* y i) (+ (+ z a) (* b (log c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 4e-31) {
		tmp = a + (t + (z + (x * log(y))));
	} else {
		tmp = (y * i) + ((z + a) + (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) :: tmp
    if (y <= 4d-31) then
        tmp = a + (t + (z + (x * log(y))))
    else
        tmp = (y * i) + ((z + a) + (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 tmp;
	if (y <= 4e-31) {
		tmp = a + (t + (z + (x * Math.log(y))));
	} else {
		tmp = (y * i) + ((z + a) + (b * Math.log(c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 4e-31:
		tmp = a + (t + (z + (x * math.log(y))))
	else:
		tmp = (y * i) + ((z + a) + (b * math.log(c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 4e-31)
		tmp = Float64(a + Float64(t + Float64(z + Float64(x * log(y)))));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(z + a) + Float64(b * log(c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= 4e-31)
		tmp = a + (t + (z + (x * log(y))));
	else
		tmp = (y * i) + ((z + a) + (b * log(c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 4e-31], N[(a + N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(z + a), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 4e-31

   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. Taylor expanded in y around 0 95.5%

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

   4. Taylor expanded in x around inf 82.1%

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

   if 4e-31 < y

   1. Initial program 99.2%

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

   3. Taylor expanded in x around 0 88.5%

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

   4. Taylor expanded in t around 0 80.0%

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

      1. associate-+r+ 80.0%

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

      2. sub-neg 80.0%

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

      3. metadata-eval 80.0%

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

   6. Simplified 80.0%

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

   7. Taylor expanded in b around inf 79.0%

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

      1. *-commutative 79.0%

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

   9. Simplified 79.0%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4 \cdot 10^{-31}:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(z + a\right) + b \cdot \log c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 84.8% accurate, 1.9× speedup

Math

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

FPCore

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := 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. Initial program 99.5%

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

3. Taylor expanded in x around 0 82.9%

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

4. Final simplification 82.9%

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

Alternative 13: 69.7% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

3. Taylor expanded in x around 0 82.9%

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

4. Taylor expanded in t around 0 70.6%

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

   1. associate-+r+ 70.6%

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

   2. sub-neg 70.6%

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

   3. metadata-eval 70.6%

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

6. Simplified 70.6%

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

7. Final simplification 70.6%

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

Alternative 14: 55.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b - 0.5 \leq 2 \cdot 10^{+151}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \log c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= (- b 0.5) 2e+151) (+ (* y i) (+ z a)) (* b (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) <= 2e+151) {
		tmp = (y * i) + (z + a);
	} else {
		tmp = 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) :: tmp
    if ((b - 0.5d0) <= 2d+151) then
        tmp = (y * i) + (z + a)
    else
        tmp = 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 tmp;
	if ((b - 0.5) <= 2e+151) {
		tmp = (y * i) + (z + a);
	} else {
		tmp = b * Math.log(c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (b - 0.5) <= 2e+151:
		tmp = (y * i) + (z + a)
	else:
		tmp = b * math.log(c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(b - 0.5) <= 2e+151)
		tmp = Float64(Float64(y * i) + Float64(z + a));
	else
		tmp = Float64(b * 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) <= 2e+151)
		tmp = (y * i) + (z + a);
	else
		tmp = b * log(c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(b - 0.5), $MachinePrecision], 2e+151], N[(N[(y * i), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision], N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 b #s(literal 1/2 binary64)) < 2.00000000000000003e151

   1. Initial program 99.4%

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

   3. Taylor expanded in x around 0 81.8%

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

   4. Taylor expanded in t around 0 68.6%

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

      1. associate-+r+ 68.6%

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

      2. sub-neg 68.6%

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

      3. metadata-eval 68.6%

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

   6. Simplified 68.6%

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

   7. Taylor expanded in b around inf 67.1%

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

      1. *-commutative 67.1%

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

   9. Simplified 67.1%

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

   10. Taylor expanded in b around 0 60.7%

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

       1. +-commutative 60.7%

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

   12. Simplified 60.7%

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

   if 2.00000000000000003e151 < (-.f64 b #s(literal 1/2 binary64))

   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 b around inf 58.9%

      \[\leadsto \color{blue}{b \cdot \log c} \]
   4. Step-by-step derivation

      1. *-commutative 58.9%

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

   5. Simplified 58.9%

      \[\leadsto \color{blue}{\log c \cdot b} \]
3. Recombined 2 regimes into one program.

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b - 0.5 \leq 2 \cdot 10^{+151}:\\ \;\;\;\;y \cdot i + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \log c\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 42.6% accurate, 10.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 4 \cdot 10^{+34}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;a \leq 1.36 \cdot 10^{+160} \lor \neg \left(a \leq 4.5 \cdot 10^{+265}\right):\\ \;\;\;\;a + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 4e+34)
   (+ z (* y i))
   (if (or (<= a 1.36e+160) (not (<= a 4.5e+265))) (+ a (* y i)) (+ z a))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 4e+34) {
		tmp = z + (y * i);
	} else if ((a <= 1.36e+160) || !(a <= 4.5e+265)) {
		tmp = a + (y * i);
	} else {
		tmp = z + a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 4d+34) then
        tmp = z + (y * i)
    else if ((a <= 1.36d+160) .or. (.not. (a <= 4.5d+265))) then
        tmp = a + (y * i)
    else
        tmp = z + a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 4e+34) {
		tmp = z + (y * i);
	} else if ((a <= 1.36e+160) || !(a <= 4.5e+265)) {
		tmp = a + (y * i);
	} else {
		tmp = z + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 4e+34:
		tmp = z + (y * i)
	elif (a <= 1.36e+160) or not (a <= 4.5e+265):
		tmp = a + (y * i)
	else:
		tmp = z + a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 4e+34)
		tmp = Float64(z + Float64(y * i));
	elseif ((a <= 1.36e+160) || !(a <= 4.5e+265))
		tmp = Float64(a + Float64(y * i));
	else
		tmp = Float64(z + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 4e+34)
		tmp = z + (y * i);
	elseif ((a <= 1.36e+160) || ~((a <= 4.5e+265)))
		tmp = a + (y * i);
	else
		tmp = z + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 4e+34], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, 1.36e+160], N[Not[LessEqual[a, 4.5e+265]], $MachinePrecision]], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(z + a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < 3.99999999999999978e34

   1. Initial program 99.4%

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

   3. Taylor expanded in x around 0 82.7%

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

   4. Taylor expanded in z around inf 44.1%

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

   if 3.99999999999999978e34 < a < 1.35999999999999997e160 or 4.49999999999999985e265 < a

   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. Add Preprocessing

   3. Taylor expanded in x around 0 81.8%

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

   4. Taylor expanded in a around inf 56.7%

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

   if 1.35999999999999997e160 < a < 4.49999999999999985e265

   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. Taylor expanded in t around 0 80.4%

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

      1. associate-+r+ 80.4%

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

      2. sub-neg 80.4%

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

      3. metadata-eval 80.4%

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

   6. Simplified 80.4%

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

   7. Taylor expanded in b around inf 80.4%

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

      1. *-commutative 80.4%

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

   9. Simplified 80.4%

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

   10. Taylor expanded in b around 0 80.4%

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

       1. +-commutative 80.4%

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

   12. Simplified 80.4%

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

   13. Taylor expanded in y around 0 73.8%

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

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 4 \cdot 10^{+34}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;a \leq 1.36 \cdot 10^{+160} \lor \neg \left(a \leq 4.5 \cdot 10^{+265}\right):\\ \;\;\;\;a + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 23.2% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.7 \cdot 10^{+159}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{+119}:\\ \;\;\;\;a\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-199}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -5.7e+159)
   z
   (if (<= z -2.05e+119) a (if (<= z -7e-199) (* y i) a))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -5.7e+159) {
		tmp = z;
	} else if (z <= -2.05e+119) {
		tmp = a;
	} else if (z <= -7e-199) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-5.7d+159)) then
        tmp = z
    else if (z <= (-2.05d+119)) then
        tmp = a
    else if (z <= (-7d-199)) then
        tmp = y * i
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -5.7e+159) {
		tmp = z;
	} else if (z <= -2.05e+119) {
		tmp = a;
	} else if (z <= -7e-199) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -5.7e+159:
		tmp = z
	elif z <= -2.05e+119:
		tmp = a
	elif z <= -7e-199:
		tmp = y * i
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -5.7e+159)
		tmp = z;
	elseif (z <= -2.05e+119)
		tmp = a;
	elseif (z <= -7e-199)
		tmp = Float64(y * i);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -5.7e+159)
		tmp = z;
	elseif (z <= -2.05e+119)
		tmp = a;
	elseif (z <= -7e-199)
		tmp = y * i;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -5.7e+159], z, If[LessEqual[z, -2.05e+119], a, If[LessEqual[z, -7e-199], N[(y * i), $MachinePrecision], a]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.6999999999999999e159

   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 42.1%

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

   if -5.6999999999999999e159 < z < -2.0499999999999999e119 or -6.9999999999999998e-199 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf 15.7%

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

   if -2.0499999999999999e119 < z < -6.9999999999999998e-199

   1. Initial program 97.9%

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

   3. Taylor expanded in y around inf 47.7%

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

      1. *-commutative 47.7%

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

   5. Simplified 47.7%

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

Alternative 17: 39.0% accurate, 16.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1.7 \cdot 10^{+170} \lor \neg \left(i \leq 1.7 \cdot 10^{-34}\right):\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= i -1.7e+170) (not (<= i 1.7e-34))) (* y i) (+ z a)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((i <= -1.7e+170) || !(i <= 1.7e-34)) {
		tmp = y * i;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((i <= (-1.7d+170)) .or. (.not. (i <= 1.7d-34))) then
        tmp = y * i
    else
        tmp = z + a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((i <= -1.7e+170) || !(i <= 1.7e-34)) {
		tmp = y * i;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (i <= -1.7e+170) or not (i <= 1.7e-34):
		tmp = y * i
	else:
		tmp = z + a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((i <= -1.7e+170) || !(i <= 1.7e-34))
		tmp = Float64(y * i);
	else
		tmp = Float64(z + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((i <= -1.7e+170) || ~((i <= 1.7e-34)))
		tmp = y * i;
	else
		tmp = z + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[i, -1.7e+170], N[Not[LessEqual[i, 1.7e-34]], $MachinePrecision]], N[(y * i), $MachinePrecision], N[(z + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -1.7000000000000001e170 or 1.7e-34 < i

   1. Initial program 98.8%

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

   3. Taylor expanded in y around inf 53.0%

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

      1. *-commutative 53.0%

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

   5. Simplified 53.0%

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

   if -1.7000000000000001e170 < i < 1.7e-34

   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. Taylor expanded in x around 0 80.6%

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

   4. Taylor expanded in t around 0 64.3%

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

      1. associate-+r+ 64.3%

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

      2. sub-neg 64.3%

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

      3. metadata-eval 64.3%

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

   6. Simplified 64.3%

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

   7. Taylor expanded in b around inf 62.8%

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

      1. *-commutative 62.8%

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

   9. Simplified 62.8%

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

   10. Taylor expanded in b around 0 49.1%

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

       1. +-commutative 49.1%

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

   12. Simplified 49.1%

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

   13. Taylor expanded in y around 0 38.2%

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

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.7 \cdot 10^{+170} \lor \neg \left(i \leq 1.7 \cdot 10^{-34}\right):\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 42.2% accurate, 21.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+155}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -4.5e+155) (+ z a) (+ a (* y i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -4.5e+155) {
		tmp = z + a;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-4.5d+155)) then
        tmp = z + a
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -4.5e+155) {
		tmp = z + a;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -4.5e+155:
		tmp = z + a
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -4.5e+155)
		tmp = Float64(z + a);
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -4.5e+155)
		tmp = z + a;
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -4.5e+155], N[(z + a), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.49999999999999973e155

   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 85.2%

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

   4. Taylor expanded in t around 0 70.1%

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

      1. associate-+r+ 70.1%

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

      2. sub-neg 70.1%

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

      3. metadata-eval 70.1%

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

   6. Simplified 70.1%

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

   7. Taylor expanded in b around inf 70.1%

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

      1. *-commutative 70.1%

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

   9. Simplified 70.1%

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

   10. Taylor expanded in b around 0 62.6%

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

       1. +-commutative 62.6%

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

   12. Simplified 62.6%

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

   13. Taylor expanded in y around 0 49.8%

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

   if -4.49999999999999973e155 < z

   1. Initial program 99.4%

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

   3. Taylor expanded in x around 0 82.5%

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

   4. Taylor expanded in a around inf 42.7%

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

4. Final simplification 43.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+155}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 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 99.5%

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

3. Taylor expanded in x around 0 82.9%

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

4. Taylor expanded in t around 0 70.6%

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

   1. associate-+r+ 70.6%

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

   2. sub-neg 70.6%

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

   3. metadata-eval 70.6%

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

6. Simplified 70.6%

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

7. Taylor expanded in b around inf 69.3%

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

   1. *-commutative 69.3%

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

9. Simplified 69.3%

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

10. Taylor expanded in b around 0 55.9%

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

    1. +-commutative 55.9%

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

12. Simplified 55.9%

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

13. Final simplification 55.9%

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

Alternative 20: 20.8% accurate, 36.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+159}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (if (<= z -3.5e+159) 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 <= -3.5e+159) {
		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 <= (-3.5d+159)) 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 <= -3.5e+159) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -3.5e+159:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -3.5e+159)
		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 <= -3.5e+159)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -3.5e+159], z, a]

Derivation

1. Split input into 2 regimes

2. if z < -3.4999999999999999e159

   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 42.1%

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

   if -3.4999999999999999e159 < z

   1. Initial program 99.4%

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

   3. Taylor expanded in a around inf 15.1%

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

Alternative 21: 15.9% 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 99.5%

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

3. Taylor expanded in a around inf 14.0%

   \[\leadsto \color{blue}{a} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024105 
(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)))