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

Percentage Accurate: 99.8% → 99.8%

Time: 33.5s

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 99.4%

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

   1. associate-+l+ 99.4%

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

   2. associate-+l+ 99.4%

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

   3. +-commutative 99.4%

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

   4. associate-+l+ 99.4%

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

   5. +-commutative 99.4%

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

   6. associate-+l+ 99.4%

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

   7. +-commutative 99.4%

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

   8. associate-+l+ 99.4%

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

   9. +-commutative 99.4%

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

   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%

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

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. Final simplification 99.5%

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

Alternative 2: 99.8% accurate, 0.7× speedup

Math

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

FPCore

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

   1. associate-+l+ 99.4%

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

   2. associate-+l+ 99.4%

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

   3. fma-define 99.4%

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

   4. sub-neg 99.4%

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

   5. metadata-eval 99.4%

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

3. Simplified 99.4%

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

5. Final simplification 99.4%

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

Alternative 3: 91.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log c \cdot \left(b - 0.5\right)\\ \mathbf{if}\;x \leq -2.75 \cdot 10^{+240}:\\ \;\;\;\;y \cdot i + x \cdot \left(\log y + \frac{a}{x}\right)\\ \mathbf{elif}\;x \leq 1.76 \cdot 10^{+78}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + t\_1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + \left(x \cdot \log y + t\_1\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (log c) (- b 0.5))))
   (if (<= x -2.75e+240)
     (+ (* y i) (* x (+ (log y) (/ a x))))
     (if (<= x 1.76e+78)
       (+ (* y i) (+ a (+ t (+ z t_1))))
       (+ 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 = log(c) * (b - 0.5);
	double tmp;
	if (x <= -2.75e+240) {
		tmp = (y * i) + (x * (log(y) + (a / x)));
	} else if (x <= 1.76e+78) {
		tmp = (y * i) + (a + (t + (z + t_1)));
	} else {
		tmp = a + (t + (z + ((x * log(y)) + t_1)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = log(c) * (b - 0.5d0)
    if (x <= (-2.75d+240)) then
        tmp = (y * i) + (x * (log(y) + (a / x)))
    else if (x <= 1.76d+78) then
        tmp = (y * i) + (a + (t + (z + t_1)))
    else
        tmp = a + (t + (z + ((x * log(y)) + t_1)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = Math.log(c) * (b - 0.5);
	double tmp;
	if (x <= -2.75e+240) {
		tmp = (y * i) + (x * (Math.log(y) + (a / x)));
	} else if (x <= 1.76e+78) {
		tmp = (y * i) + (a + (t + (z + t_1)));
	} else {
		tmp = a + (t + (z + ((x * Math.log(y)) + t_1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = math.log(c) * (b - 0.5)
	tmp = 0
	if x <= -2.75e+240:
		tmp = (y * i) + (x * (math.log(y) + (a / x)))
	elif x <= 1.76e+78:
		tmp = (y * i) + (a + (t + (z + t_1)))
	else:
		tmp = a + (t + (z + ((x * math.log(y)) + t_1)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(log(c) * Float64(b - 0.5))
	tmp = 0.0
	if (x <= -2.75e+240)
		tmp = Float64(Float64(y * i) + Float64(x * Float64(log(y) + Float64(a / x))));
	elseif (x <= 1.76e+78)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(t + Float64(z + t_1))));
	else
		tmp = Float64(a + Float64(t + Float64(z + Float64(Float64(x * log(y)) + t_1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = log(c) * (b - 0.5);
	tmp = 0.0;
	if (x <= -2.75e+240)
		tmp = (y * i) + (x * (log(y) + (a / x)));
	elseif (x <= 1.76e+78)
		tmp = (y * i) + (a + (t + (z + t_1)));
	else
		tmp = a + (t + (z + ((x * log(y)) + t_1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.75e+240], N[(N[(y * i), $MachinePrecision] + N[(x * N[(N[Log[y], $MachinePrecision] + N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.76e+78], N[(N[(y * i), $MachinePrecision] + N[(a + N[(t + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(t + N[(z + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.75e240

   1. Initial program 99.7%

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

   3. Taylor expanded in x around -inf 99.6%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \log y + -1 \cdot \frac{a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)}{x}\right)\right)} + y \cdot i \]
   4. Step-by-step derivation

      1. mul-1-neg 99.6%

         \[\leadsto \color{blue}{\left(-x \cdot \left(-1 \cdot \log y + -1 \cdot \frac{a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)}{x}\right)\right)} + y \cdot i \]

      2. distribute-lft-out 99.6%

         \[\leadsto \left(-x \cdot \color{blue}{\left(-1 \cdot \left(\log y + \frac{a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)}{x}\right)\right)}\right) + y \cdot i \]

      3. sub-neg 99.6%

         \[\leadsto \left(-x \cdot \left(-1 \cdot \left(\log y + \frac{a + \left(t + \left(z + \log c \cdot \color{blue}{\left(b + \left(-0.5\right)\right)}\right)\right)}{x}\right)\right)\right) + y \cdot i \]

      4. metadata-eval 99.6%

         \[\leadsto \left(-x \cdot \left(-1 \cdot \left(\log y + \frac{a + \left(t + \left(z + \log c \cdot \left(b + \color{blue}{-0.5}\right)\right)\right)}{x}\right)\right)\right) + y \cdot i \]

   5. Simplified 99.6%

      \[\leadsto \color{blue}{\left(-x \cdot \left(-1 \cdot \left(\log y + \frac{a + \left(t + \left(z + \log c \cdot \left(b + -0.5\right)\right)\right)}{x}\right)\right)\right)} + y \cdot i \]

   6. Taylor expanded in a around inf 87.8%

      \[\leadsto \left(-x \cdot \left(-1 \cdot \left(\log y + \color{blue}{\frac{a}{x}}\right)\right)\right) + y \cdot i \]

   if -2.75e240 < x < 1.76e78

   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 95.8%

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

   if 1.76e78 < x

   1. Initial program 97.7%

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

   3. Taylor expanded in y around 0 88.3%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.75 \cdot 10^{+240}:\\ \;\;\;\;y \cdot i + x \cdot \left(\log y + \frac{a}{x}\right)\\ \mathbf{elif}\;x \leq 1.76 \cdot 10^{+78}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + \left(x \cdot \log y + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 91.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log c \cdot \left(b - 0.5\right)\\ \mathbf{if}\;x \leq -3.15 \cdot 10^{+240}:\\ \;\;\;\;y \cdot i + x \cdot \left(\log y + \frac{b \cdot \log c}{x}\right)\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+85}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + t\_1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + \left(x \cdot \log y + t\_1\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (log c) (- b 0.5))))
   (if (<= x -3.15e+240)
     (+ (* y i) (* x (+ (log y) (/ (* b (log c)) x))))
     (if (<= x 4.5e+85)
       (+ (* y i) (+ a (+ t (+ z t_1))))
       (+ 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 = log(c) * (b - 0.5);
	double tmp;
	if (x <= -3.15e+240) {
		tmp = (y * i) + (x * (log(y) + ((b * log(c)) / x)));
	} else if (x <= 4.5e+85) {
		tmp = (y * i) + (a + (t + (z + t_1)));
	} else {
		tmp = a + (t + (z + ((x * log(y)) + t_1)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = log(c) * (b - 0.5d0)
    if (x <= (-3.15d+240)) then
        tmp = (y * i) + (x * (log(y) + ((b * log(c)) / x)))
    else if (x <= 4.5d+85) then
        tmp = (y * i) + (a + (t + (z + t_1)))
    else
        tmp = a + (t + (z + ((x * log(y)) + t_1)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = Math.log(c) * (b - 0.5);
	double tmp;
	if (x <= -3.15e+240) {
		tmp = (y * i) + (x * (Math.log(y) + ((b * Math.log(c)) / x)));
	} else if (x <= 4.5e+85) {
		tmp = (y * i) + (a + (t + (z + t_1)));
	} else {
		tmp = a + (t + (z + ((x * Math.log(y)) + t_1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = math.log(c) * (b - 0.5)
	tmp = 0
	if x <= -3.15e+240:
		tmp = (y * i) + (x * (math.log(y) + ((b * math.log(c)) / x)))
	elif x <= 4.5e+85:
		tmp = (y * i) + (a + (t + (z + t_1)))
	else:
		tmp = a + (t + (z + ((x * math.log(y)) + t_1)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(log(c) * Float64(b - 0.5))
	tmp = 0.0
	if (x <= -3.15e+240)
		tmp = Float64(Float64(y * i) + Float64(x * Float64(log(y) + Float64(Float64(b * log(c)) / x))));
	elseif (x <= 4.5e+85)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(t + Float64(z + t_1))));
	else
		tmp = Float64(a + Float64(t + Float64(z + Float64(Float64(x * log(y)) + t_1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = log(c) * (b - 0.5);
	tmp = 0.0;
	if (x <= -3.15e+240)
		tmp = (y * i) + (x * (log(y) + ((b * log(c)) / x)));
	elseif (x <= 4.5e+85)
		tmp = (y * i) + (a + (t + (z + t_1)));
	else
		tmp = a + (t + (z + ((x * log(y)) + t_1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.15e+240], N[(N[(y * i), $MachinePrecision] + N[(x * N[(N[Log[y], $MachinePrecision] + N[(N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.5e+85], N[(N[(y * i), $MachinePrecision] + N[(a + N[(t + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(t + N[(z + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.14999999999999985e240

   1. Initial program 99.7%

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

   3. Taylor expanded in x around -inf 99.6%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \log y + -1 \cdot \frac{a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)}{x}\right)\right)} + y \cdot i \]
   4. Step-by-step derivation

      1. mul-1-neg 99.6%

         \[\leadsto \color{blue}{\left(-x \cdot \left(-1 \cdot \log y + -1 \cdot \frac{a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)}{x}\right)\right)} + y \cdot i \]

      2. distribute-lft-out 99.6%

         \[\leadsto \left(-x \cdot \color{blue}{\left(-1 \cdot \left(\log y + \frac{a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)}{x}\right)\right)}\right) + y \cdot i \]

      3. sub-neg 99.6%

         \[\leadsto \left(-x \cdot \left(-1 \cdot \left(\log y + \frac{a + \left(t + \left(z + \log c \cdot \color{blue}{\left(b + \left(-0.5\right)\right)}\right)\right)}{x}\right)\right)\right) + y \cdot i \]

      4. metadata-eval 99.6%

         \[\leadsto \left(-x \cdot \left(-1 \cdot \left(\log y + \frac{a + \left(t + \left(z + \log c \cdot \left(b + \color{blue}{-0.5}\right)\right)\right)}{x}\right)\right)\right) + y \cdot i \]

   5. Simplified 99.6%

      \[\leadsto \color{blue}{\left(-x \cdot \left(-1 \cdot \left(\log y + \frac{a + \left(t + \left(z + \log c \cdot \left(b + -0.5\right)\right)\right)}{x}\right)\right)\right)} + y \cdot i \]

   6. Taylor expanded in b around inf 94.8%

      \[\leadsto \left(-x \cdot \left(-1 \cdot \left(\log y + \color{blue}{\frac{b \cdot \log c}{x}}\right)\right)\right) + y \cdot i \]

   if -3.14999999999999985e240 < x < 4.50000000000000007e85

   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 95.8%

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

   if 4.50000000000000007e85 < x

   1. Initial program 97.7%

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

   3. Taylor expanded in y around 0 88.3%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.15 \cdot 10^{+240}:\\ \;\;\;\;y \cdot i + x \cdot \left(\log y + \frac{b \cdot \log c}{x}\right)\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+85}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + \left(x \cdot \log y + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 89.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log c \cdot \left(b - 0.5\right)\\ \mathbf{if}\;a \leq 4.4 \cdot 10^{+123}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + \left(x \cdot \log y + t\_1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + t\_1\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (log c) (- b 0.5))))
   (if (<= a 4.4e+123)
     (+ (* y i) (+ t (+ z (+ (* x (log y)) t_1))))
     (+ (* y i) (+ a (+ t (+ z t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = log(c) * (b - 0.5);
	double tmp;
	if (a <= 4.4e+123) {
		tmp = (y * i) + (t + (z + ((x * log(y)) + t_1)));
	} else {
		tmp = (y * i) + (a + (t + (z + t_1)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = log(c) * (b - 0.5d0)
    if (a <= 4.4d+123) then
        tmp = (y * i) + (t + (z + ((x * log(y)) + t_1)))
    else
        tmp = (y * i) + (a + (t + (z + t_1)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = Math.log(c) * (b - 0.5);
	double tmp;
	if (a <= 4.4e+123) {
		tmp = (y * i) + (t + (z + ((x * Math.log(y)) + t_1)));
	} else {
		tmp = (y * i) + (a + (t + (z + t_1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = math.log(c) * (b - 0.5)
	tmp = 0
	if a <= 4.4e+123:
		tmp = (y * i) + (t + (z + ((x * math.log(y)) + t_1)))
	else:
		tmp = (y * i) + (a + (t + (z + t_1)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(log(c) * Float64(b - 0.5))
	tmp = 0.0
	if (a <= 4.4e+123)
		tmp = Float64(Float64(y * i) + Float64(t + Float64(z + Float64(Float64(x * log(y)) + t_1))));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(t + Float64(z + t_1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = log(c) * (b - 0.5);
	tmp = 0.0;
	if (a <= 4.4e+123)
		tmp = (y * i) + (t + (z + ((x * log(y)) + t_1)));
	else
		tmp = (y * i) + (a + (t + (z + t_1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, 4.4e+123], N[(N[(y * i), $MachinePrecision] + N[(t + N[(z + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(t + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < 4.39999999999999984e123

   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 0 89.5%

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

   if 4.39999999999999984e123 < a

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 91.3%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 4.4 \cdot 10^{+123}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + \left(x \cdot \log y + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 89.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+149}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b + -0.5\right) \cdot \log c + y \cdot i\right) + \left(\left(t + a\right) + x \cdot \log y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -8e+149)
   (+ (* y i) (+ a (+ t (+ z (* (log c) (- b 0.5))))))
   (+ (+ (* (+ b -0.5) (log c)) (* y i)) (+ (+ t a) (* x (log y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -8e+149) {
		tmp = (y * i) + (a + (t + (z + (log(c) * (b - 0.5)))));
	} else {
		tmp = (((b + -0.5) * log(c)) + (y * i)) + ((t + a) + (x * log(y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-8d+149)) then
        tmp = (y * i) + (a + (t + (z + (log(c) * (b - 0.5d0)))))
    else
        tmp = (((b + (-0.5d0)) * log(c)) + (y * i)) + ((t + a) + (x * log(y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -8e+149) {
		tmp = (y * i) + (a + (t + (z + (Math.log(c) * (b - 0.5)))));
	} else {
		tmp = (((b + -0.5) * Math.log(c)) + (y * i)) + ((t + a) + (x * Math.log(y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -8e+149:
		tmp = (y * i) + (a + (t + (z + (math.log(c) * (b - 0.5)))))
	else:
		tmp = (((b + -0.5) * math.log(c)) + (y * i)) + ((t + a) + (x * math.log(y)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -8e+149)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(t + Float64(z + Float64(log(c) * Float64(b - 0.5))))));
	else
		tmp = Float64(Float64(Float64(Float64(b + -0.5) * log(c)) + Float64(y * i)) + Float64(Float64(t + a) + Float64(x * log(y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -8e+149)
		tmp = (y * i) + (a + (t + (z + (log(c) * (b - 0.5)))));
	else
		tmp = (((b + -0.5) * log(c)) + (y * i)) + ((t + a) + (x * log(y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -8e+149], N[(N[(y * i), $MachinePrecision] + N[(a + N[(t + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(b + -0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision] + N[(N[(t + a), $MachinePrecision] + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.00000000000000039e149

   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 90.5%

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

   if -8.00000000000000039e149 < 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. Step-by-step derivation

      1. associate-+l+ 99.4%

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

      2. associate-+l+ 99.4%

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

      3. fma-define 99.4%

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

      4. sub-neg 99.4%

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

      5. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around inf 89.5%

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

   6. Taylor expanded in z around 0 88.9%

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

      1. associate-+r+ 88.9%

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

   8. Simplified 88.9%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+149}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b + -0.5\right) \cdot \log c + y \cdot i\right) + \left(\left(t + a\right) + x \cdot \log y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

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 + (t + (z + (x * log(y))))));
}

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 + (t + (z + (x * log(y))))))
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 + (t + (z + (x * Math.log(y))))));
}

Python

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

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(t + Float64(z + Float64(x * log(y)))))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = (y * i) + ((log(c) * (b - 0.5)) + (a + (t + (z + (x * log(y))))));
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[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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. Final simplification 99.4%

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

Alternative 8: 62.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \left(t + \left(z + x \cdot \log y\right)\right)\\ t_2 := y \cdot i + b \cdot \log c\\ \mathbf{if}\;b \leq -5 \cdot 10^{+188}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -0.049:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.4 \cdot 10^{-230}:\\ \;\;\;\;y \cdot i + z \cdot \left(\frac{a}{z} + 1\right)\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{-285}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{+95}:\\ \;\;\;\;y \cdot i + a \cdot \left(\left(\frac{t}{a} + \frac{z}{a}\right) + 1\right)\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{+171}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (+ t (+ z (* x (log y)))))) (t_2 (+ (* y i) (* b (log c)))))
   (if (<= b -5e+188)
     t_2
     (if (<= b -0.049)
       t_1
       (if (<= b -1.4e-230)
         (+ (* y i) (* z (+ (/ a z) 1.0)))
         (if (<= b -2.7e-285)
           t_1
           (if (<= b 3.4e+95)
             (+ (* y i) (* a (+ (+ (/ t a) (/ z a)) 1.0)))
             (if (<= b 1.95e+171) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (t + (z + (x * log(y))));
	double t_2 = (y * i) + (b * log(c));
	double tmp;
	if (b <= -5e+188) {
		tmp = t_2;
	} else if (b <= -0.049) {
		tmp = t_1;
	} else if (b <= -1.4e-230) {
		tmp = (y * i) + (z * ((a / z) + 1.0));
	} else if (b <= -2.7e-285) {
		tmp = t_1;
	} else if (b <= 3.4e+95) {
		tmp = (y * i) + (a * (((t / a) + (z / a)) + 1.0));
	} else if (b <= 1.95e+171) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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 = a + (t + (z + (x * log(y))))
    t_2 = (y * i) + (b * log(c))
    if (b <= (-5d+188)) then
        tmp = t_2
    else if (b <= (-0.049d0)) then
        tmp = t_1
    else if (b <= (-1.4d-230)) then
        tmp = (y * i) + (z * ((a / z) + 1.0d0))
    else if (b <= (-2.7d-285)) then
        tmp = t_1
    else if (b <= 3.4d+95) then
        tmp = (y * i) + (a * (((t / a) + (z / a)) + 1.0d0))
    else if (b <= 1.95d+171) then
        tmp = t_1
    else
        tmp = t_2
    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 = a + (t + (z + (x * Math.log(y))));
	double t_2 = (y * i) + (b * Math.log(c));
	double tmp;
	if (b <= -5e+188) {
		tmp = t_2;
	} else if (b <= -0.049) {
		tmp = t_1;
	} else if (b <= -1.4e-230) {
		tmp = (y * i) + (z * ((a / z) + 1.0));
	} else if (b <= -2.7e-285) {
		tmp = t_1;
	} else if (b <= 3.4e+95) {
		tmp = (y * i) + (a * (((t / a) + (z / a)) + 1.0));
	} else if (b <= 1.95e+171) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (t + (z + (x * math.log(y))))
	t_2 = (y * i) + (b * math.log(c))
	tmp = 0
	if b <= -5e+188:
		tmp = t_2
	elif b <= -0.049:
		tmp = t_1
	elif b <= -1.4e-230:
		tmp = (y * i) + (z * ((a / z) + 1.0))
	elif b <= -2.7e-285:
		tmp = t_1
	elif b <= 3.4e+95:
		tmp = (y * i) + (a * (((t / a) + (z / a)) + 1.0))
	elif b <= 1.95e+171:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(t + Float64(z + Float64(x * log(y)))))
	t_2 = Float64(Float64(y * i) + Float64(b * log(c)))
	tmp = 0.0
	if (b <= -5e+188)
		tmp = t_2;
	elseif (b <= -0.049)
		tmp = t_1;
	elseif (b <= -1.4e-230)
		tmp = Float64(Float64(y * i) + Float64(z * Float64(Float64(a / z) + 1.0)));
	elseif (b <= -2.7e-285)
		tmp = t_1;
	elseif (b <= 3.4e+95)
		tmp = Float64(Float64(y * i) + Float64(a * Float64(Float64(Float64(t / a) + Float64(z / a)) + 1.0)));
	elseif (b <= 1.95e+171)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (t + (z + (x * log(y))));
	t_2 = (y * i) + (b * log(c));
	tmp = 0.0;
	if (b <= -5e+188)
		tmp = t_2;
	elseif (b <= -0.049)
		tmp = t_1;
	elseif (b <= -1.4e-230)
		tmp = (y * i) + (z * ((a / z) + 1.0));
	elseif (b <= -2.7e-285)
		tmp = t_1;
	elseif (b <= 3.4e+95)
		tmp = (y * i) + (a * (((t / a) + (z / a)) + 1.0));
	elseif (b <= 1.95e+171)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * i), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5e+188], t$95$2, If[LessEqual[b, -0.049], t$95$1, If[LessEqual[b, -1.4e-230], N[(N[(y * i), $MachinePrecision] + N[(z * N[(N[(a / z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.7e-285], t$95$1, If[LessEqual[b, 3.4e+95], N[(N[(y * i), $MachinePrecision] + N[(a * N[(N[(N[(t / a), $MachinePrecision] + N[(z / a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.95e+171], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -5.0000000000000001e188 or 1.95e171 < b

   1. Initial program 99.7%

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

   3. Taylor expanded in x around -inf 72.3%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \log y + -1 \cdot \frac{a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)}{x}\right)\right)} + y \cdot i \]
   4. Step-by-step derivation

      1. mul-1-neg 72.3%

         \[\leadsto \color{blue}{\left(-x \cdot \left(-1 \cdot \log y + -1 \cdot \frac{a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)}{x}\right)\right)} + y \cdot i \]

      2. distribute-lft-out 72.3%

         \[\leadsto \left(-x \cdot \color{blue}{\left(-1 \cdot \left(\log y + \frac{a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)}{x}\right)\right)}\right) + y \cdot i \]

      3. sub-neg 72.3%

         \[\leadsto \left(-x \cdot \left(-1 \cdot \left(\log y + \frac{a + \left(t + \left(z + \log c \cdot \color{blue}{\left(b + \left(-0.5\right)\right)}\right)\right)}{x}\right)\right)\right) + y \cdot i \]

      4. metadata-eval 72.3%

         \[\leadsto \left(-x \cdot \left(-1 \cdot \left(\log y + \frac{a + \left(t + \left(z + \log c \cdot \left(b + \color{blue}{-0.5}\right)\right)\right)}{x}\right)\right)\right) + y \cdot i \]

   5. Simplified 72.3%

      \[\leadsto \color{blue}{\left(-x \cdot \left(-1 \cdot \left(\log y + \frac{a + \left(t + \left(z + \log c \cdot \left(b + -0.5\right)\right)\right)}{x}\right)\right)\right)} + y \cdot i \]

   6. Taylor expanded in b around inf 74.3%

      \[\leadsto \left(-\color{blue}{-1 \cdot \left(b \cdot \log c\right)}\right) + y \cdot i \]
   7. Step-by-step derivation

      1. mul-1-neg 74.3%

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

      2. *-commutative 74.3%

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

      3. distribute-rgt-neg-in 74.3%

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

   8. Simplified 74.3%

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

   if -5.0000000000000001e188 < b < -0.049000000000000002 or -1.4e-230 < b < -2.6999999999999998e-285 or 3.40000000000000022e95 < b < 1.95e171

   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 78.5%

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

   if -0.049000000000000002 < b < -1.4e-230

   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 74.2%

      \[\leadsto \color{blue}{z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(\frac{x \cdot \log y}{z} + \frac{\log c \cdot \left(b - 0.5\right)}{z}\right)\right)\right)\right)} + y \cdot i \]
   4. Step-by-step derivation

      1. associate-/l* 74.2%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(\color{blue}{x \cdot \frac{\log y}{z}} + \frac{\log c \cdot \left(b - 0.5\right)}{z}\right)\right)\right)\right) + y \cdot i \]

      2. sub-neg 74.2%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \frac{\log c \cdot \color{blue}{\left(b + \left(-0.5\right)\right)}}{z}\right)\right)\right)\right) + y \cdot i \]

      3. metadata-eval 74.2%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \frac{\log c \cdot \left(b + \color{blue}{-0.5}\right)}{z}\right)\right)\right)\right) + y \cdot i \]

      4. associate-/l* 74.2%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \color{blue}{\log c \cdot \frac{b + -0.5}{z}}\right)\right)\right)\right) + y \cdot i \]

   5. Simplified 74.2%

      \[\leadsto \color{blue}{z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \log c \cdot \frac{b + -0.5}{z}\right)\right)\right)\right)} + y \cdot i \]

   6. Taylor expanded in a around inf 61.1%

      \[\leadsto z \cdot \left(1 + \color{blue}{\frac{a}{z}}\right) + y \cdot i \]

   if -2.6999999999999998e-285 < b < 3.40000000000000022e95

   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 a around inf 78.1%

      \[\leadsto \color{blue}{a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(\frac{x \cdot \log y}{a} + \frac{\log c \cdot \left(b - 0.5\right)}{a}\right)\right)\right)\right)} + y \cdot i \]
   4. Step-by-step derivation

      1. associate-/l* 78.1%

         \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(\color{blue}{x \cdot \frac{\log y}{a}} + \frac{\log c \cdot \left(b - 0.5\right)}{a}\right)\right)\right)\right) + y \cdot i \]

      2. sub-neg 78.1%

         \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(x \cdot \frac{\log y}{a} + \frac{\log c \cdot \color{blue}{\left(b + \left(-0.5\right)\right)}}{a}\right)\right)\right)\right) + y \cdot i \]

      3. metadata-eval 78.1%

         \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(x \cdot \frac{\log y}{a} + \frac{\log c \cdot \left(b + \color{blue}{-0.5}\right)}{a}\right)\right)\right)\right) + y \cdot i \]

   5. Simplified 78.1%

      \[\leadsto \color{blue}{a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(x \cdot \frac{\log y}{a} + \frac{\log c \cdot \left(b + -0.5\right)}{a}\right)\right)\right)\right)} + y \cdot i \]

   6. Taylor expanded in z around inf 66.0%

      \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \color{blue}{\frac{z}{a}}\right)\right) + y \cdot i \]
3. Recombined 4 regimes into one program.

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{+188}:\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{elif}\;b \leq -0.049:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{elif}\;b \leq -1.4 \cdot 10^{-230}:\\ \;\;\;\;y \cdot i + z \cdot \left(\frac{a}{z} + 1\right)\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{-285}:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{+95}:\\ \;\;\;\;y \cdot i + a \cdot \left(\left(\frac{t}{a} + \frac{z}{a}\right) + 1\right)\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{+171}:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 63.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \log c\\ t_2 := a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{if}\;b \leq -2.15 \cdot 10^{+185}:\\ \;\;\;\;y \cdot i + t\_1\\ \mathbf{elif}\;b \leq -0.046:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{-230}:\\ \;\;\;\;y \cdot i + z \cdot \left(\frac{a}{z} + 1\right)\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{-285}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 8.4 \cdot 10^{+96}:\\ \;\;\;\;y \cdot i + a \cdot \left(\left(\frac{t}{a} + \frac{z}{a}\right) + 1\right)\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{+170}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t + t\_1\right)\\ \end{array} \end{array} \]

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 -2.15e+185)
     (+ (* y i) t_1)
     (if (<= b -0.046)
       t_2
       (if (<= b -2.1e-230)
         (+ (* y i) (* z (+ (/ a z) 1.0)))
         (if (<= b -2.7e-285)
           t_2
           (if (<= b 8.4e+96)
             (+ (* y i) (* a (+ (+ (/ t a) (/ z a)) 1.0)))
             (if (<= b 6.8e+170) t_2 (+ (* y i) (+ t 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 <= -2.15e+185) {
		tmp = (y * i) + t_1;
	} else if (b <= -0.046) {
		tmp = t_2;
	} else if (b <= -2.1e-230) {
		tmp = (y * i) + (z * ((a / z) + 1.0));
	} else if (b <= -2.7e-285) {
		tmp = t_2;
	} else if (b <= 8.4e+96) {
		tmp = (y * i) + (a * (((t / a) + (z / a)) + 1.0));
	} else if (b <= 6.8e+170) {
		tmp = t_2;
	} else {
		tmp = (y * i) + (t + 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 <= (-2.15d+185)) then
        tmp = (y * i) + t_1
    else if (b <= (-0.046d0)) then
        tmp = t_2
    else if (b <= (-2.1d-230)) then
        tmp = (y * i) + (z * ((a / z) + 1.0d0))
    else if (b <= (-2.7d-285)) then
        tmp = t_2
    else if (b <= 8.4d+96) then
        tmp = (y * i) + (a * (((t / a) + (z / a)) + 1.0d0))
    else if (b <= 6.8d+170) then
        tmp = t_2
    else
        tmp = (y * i) + (t + 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 <= -2.15e+185) {
		tmp = (y * i) + t_1;
	} else if (b <= -0.046) {
		tmp = t_2;
	} else if (b <= -2.1e-230) {
		tmp = (y * i) + (z * ((a / z) + 1.0));
	} else if (b <= -2.7e-285) {
		tmp = t_2;
	} else if (b <= 8.4e+96) {
		tmp = (y * i) + (a * (((t / a) + (z / a)) + 1.0));
	} else if (b <= 6.8e+170) {
		tmp = t_2;
	} else {
		tmp = (y * i) + (t + 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 <= -2.15e+185:
		tmp = (y * i) + t_1
	elif b <= -0.046:
		tmp = t_2
	elif b <= -2.1e-230:
		tmp = (y * i) + (z * ((a / z) + 1.0))
	elif b <= -2.7e-285:
		tmp = t_2
	elif b <= 8.4e+96:
		tmp = (y * i) + (a * (((t / a) + (z / a)) + 1.0))
	elif b <= 6.8e+170:
		tmp = t_2
	else:
		tmp = (y * i) + (t + 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 (b <= -2.15e+185)
		tmp = Float64(Float64(y * i) + t_1);
	elseif (b <= -0.046)
		tmp = t_2;
	elseif (b <= -2.1e-230)
		tmp = Float64(Float64(y * i) + Float64(z * Float64(Float64(a / z) + 1.0)));
	elseif (b <= -2.7e-285)
		tmp = t_2;
	elseif (b <= 8.4e+96)
		tmp = Float64(Float64(y * i) + Float64(a * Float64(Float64(Float64(t / a) + Float64(z / a)) + 1.0)));
	elseif (b <= 6.8e+170)
		tmp = t_2;
	else
		tmp = Float64(Float64(y * i) + Float64(t + 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 <= -2.15e+185)
		tmp = (y * i) + t_1;
	elseif (b <= -0.046)
		tmp = t_2;
	elseif (b <= -2.1e-230)
		tmp = (y * i) + (z * ((a / z) + 1.0));
	elseif (b <= -2.7e-285)
		tmp = t_2;
	elseif (b <= 8.4e+96)
		tmp = (y * i) + (a * (((t / a) + (z / a)) + 1.0));
	elseif (b <= 6.8e+170)
		tmp = t_2;
	else
		tmp = (y * i) + (t + 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[b, -2.15e+185], N[(N[(y * i), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[b, -0.046], t$95$2, If[LessEqual[b, -2.1e-230], N[(N[(y * i), $MachinePrecision] + N[(z * N[(N[(a / z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.7e-285], t$95$2, If[LessEqual[b, 8.4e+96], N[(N[(y * i), $MachinePrecision] + N[(a * N[(N[(N[(t / a), $MachinePrecision] + N[(z / a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.8e+170], t$95$2, N[(N[(y * i), $MachinePrecision] + N[(t + t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -2.15e185

   1. Initial program 99.6%

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

   3. Taylor expanded in x around -inf 74.2%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \log y + -1 \cdot \frac{a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)}{x}\right)\right)} + y \cdot i \]
   4. Step-by-step derivation

      1. mul-1-neg 74.2%

         \[\leadsto \color{blue}{\left(-x \cdot \left(-1 \cdot \log y + -1 \cdot \frac{a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)}{x}\right)\right)} + y \cdot i \]

      2. distribute-lft-out 74.2%

         \[\leadsto \left(-x \cdot \color{blue}{\left(-1 \cdot \left(\log y + \frac{a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)}{x}\right)\right)}\right) + y \cdot i \]

      3. sub-neg 74.2%

         \[\leadsto \left(-x \cdot \left(-1 \cdot \left(\log y + \frac{a + \left(t + \left(z + \log c \cdot \color{blue}{\left(b + \left(-0.5\right)\right)}\right)\right)}{x}\right)\right)\right) + y \cdot i \]

      4. metadata-eval 74.2%

         \[\leadsto \left(-x \cdot \left(-1 \cdot \left(\log y + \frac{a + \left(t + \left(z + \log c \cdot \left(b + \color{blue}{-0.5}\right)\right)\right)}{x}\right)\right)\right) + y \cdot i \]

   5. Simplified 74.2%

      \[\leadsto \color{blue}{\left(-x \cdot \left(-1 \cdot \left(\log y + \frac{a + \left(t + \left(z + \log c \cdot \left(b + -0.5\right)\right)\right)}{x}\right)\right)\right)} + y \cdot i \]

   6. Taylor expanded in b around inf 72.4%

      \[\leadsto \left(-\color{blue}{-1 \cdot \left(b \cdot \log c\right)}\right) + y \cdot i \]
   7. Step-by-step derivation

      1. mul-1-neg 72.4%

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

      2. *-commutative 72.4%

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

      3. distribute-rgt-neg-in 72.4%

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

   8. Simplified 72.4%

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

   if -2.15e185 < b < -0.045999999999999999 or -2.0999999999999998e-230 < b < -2.6999999999999998e-285 or 8.4000000000000005e96 < b < 6.8000000000000003e170

   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 78.5%

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

   if -0.045999999999999999 < b < -2.0999999999999998e-230

   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 74.2%

      \[\leadsto \color{blue}{z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(\frac{x \cdot \log y}{z} + \frac{\log c \cdot \left(b - 0.5\right)}{z}\right)\right)\right)\right)} + y \cdot i \]
   4. Step-by-step derivation

      1. associate-/l* 74.2%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(\color{blue}{x \cdot \frac{\log y}{z}} + \frac{\log c \cdot \left(b - 0.5\right)}{z}\right)\right)\right)\right) + y \cdot i \]

      2. sub-neg 74.2%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \frac{\log c \cdot \color{blue}{\left(b + \left(-0.5\right)\right)}}{z}\right)\right)\right)\right) + y \cdot i \]

      3. metadata-eval 74.2%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \frac{\log c \cdot \left(b + \color{blue}{-0.5}\right)}{z}\right)\right)\right)\right) + y \cdot i \]

      4. associate-/l* 74.2%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \color{blue}{\log c \cdot \frac{b + -0.5}{z}}\right)\right)\right)\right) + y \cdot i \]

   5. Simplified 74.2%

      \[\leadsto \color{blue}{z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \log c \cdot \frac{b + -0.5}{z}\right)\right)\right)\right)} + y \cdot i \]

   6. Taylor expanded in a around inf 61.1%

      \[\leadsto z \cdot \left(1 + \color{blue}{\frac{a}{z}}\right) + y \cdot i \]

   if -2.6999999999999998e-285 < b < 8.4000000000000005e96

   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 a around inf 78.1%

      \[\leadsto \color{blue}{a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(\frac{x \cdot \log y}{a} + \frac{\log c \cdot \left(b - 0.5\right)}{a}\right)\right)\right)\right)} + y \cdot i \]
   4. Step-by-step derivation

      1. associate-/l* 78.1%

         \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(\color{blue}{x \cdot \frac{\log y}{a}} + \frac{\log c \cdot \left(b - 0.5\right)}{a}\right)\right)\right)\right) + y \cdot i \]

      2. sub-neg 78.1%

         \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(x \cdot \frac{\log y}{a} + \frac{\log c \cdot \color{blue}{\left(b + \left(-0.5\right)\right)}}{a}\right)\right)\right)\right) + y \cdot i \]

      3. metadata-eval 78.1%

         \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(x \cdot \frac{\log y}{a} + \frac{\log c \cdot \left(b + \color{blue}{-0.5}\right)}{a}\right)\right)\right)\right) + y \cdot i \]

   5. Simplified 78.1%

      \[\leadsto \color{blue}{a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(x \cdot \frac{\log y}{a} + \frac{\log c \cdot \left(b + -0.5\right)}{a}\right)\right)\right)\right)} + y \cdot i \]

   6. Taylor expanded in z around inf 66.0%

      \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \color{blue}{\frac{z}{a}}\right)\right) + y \cdot i \]

   if 6.8000000000000003e170 < b

   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 a around inf 72.4%

      \[\leadsto \color{blue}{a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(\frac{x \cdot \log y}{a} + \frac{\log c \cdot \left(b - 0.5\right)}{a}\right)\right)\right)\right)} + y \cdot i \]
   4. Step-by-step derivation

      1. associate-/l* 72.4%

         \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(\color{blue}{x \cdot \frac{\log y}{a}} + \frac{\log c \cdot \left(b - 0.5\right)}{a}\right)\right)\right)\right) + y \cdot i \]

      2. sub-neg 72.4%

         \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(x \cdot \frac{\log y}{a} + \frac{\log c \cdot \color{blue}{\left(b + \left(-0.5\right)\right)}}{a}\right)\right)\right)\right) + y \cdot i \]

      3. metadata-eval 72.4%

         \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(x \cdot \frac{\log y}{a} + \frac{\log c \cdot \left(b + \color{blue}{-0.5}\right)}{a}\right)\right)\right)\right) + y \cdot i \]

   5. Simplified 72.4%

      \[\leadsto \color{blue}{a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(x \cdot \frac{\log y}{a} + \frac{\log c \cdot \left(b + -0.5\right)}{a}\right)\right)\right)\right)} + y \cdot i \]

   6. Taylor expanded in b around inf 67.2%

      \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \color{blue}{\frac{b \cdot \log c}{a}}\right)\right)\right) + y \cdot i \]
   7. Step-by-step derivation

      1. *-commutative 67.2%

         \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \frac{\color{blue}{\log c \cdot b}}{a}\right)\right)\right) + y \cdot i \]

   8. Simplified 67.2%

      \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \color{blue}{\frac{\log c \cdot b}{a}}\right)\right)\right) + y \cdot i \]

   9. Taylor expanded in z around 0 67.2%

      \[\leadsto \color{blue}{a \cdot \left(1 + \left(\frac{t}{a} + \frac{b \cdot \log c}{a}\right)\right)} + y \cdot i \]
   10. Step-by-step derivation

       1. *-commutative 67.2%

          \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \frac{\color{blue}{\log c \cdot b}}{a}\right)\right) + y \cdot i \]

       2. associate-*r/ 67.1%

          \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \color{blue}{\log c \cdot \frac{b}{a}}\right)\right) + y \cdot i \]

   11. Simplified 67.1%

       \[\leadsto \color{blue}{a \cdot \left(1 + \left(\frac{t}{a} + \log c \cdot \frac{b}{a}\right)\right)} + y \cdot i \]

   12. Taylor expanded in a around 0 80.6%

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

       1. +-commutative 80.6%

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

   14. Simplified 80.6%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.15 \cdot 10^{+185}:\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{elif}\;b \leq -0.046:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{-230}:\\ \;\;\;\;y \cdot i + z \cdot \left(\frac{a}{z} + 1\right)\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{-285}:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{elif}\;b \leq 8.4 \cdot 10^{+96}:\\ \;\;\;\;y \cdot i + a \cdot \left(\left(\frac{t}{a} + \frac{z}{a}\right) + 1\right)\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{+170}:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t + b \cdot \log c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 67.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{if}\;i \leq -2.35 \cdot 10^{+29}:\\ \;\;\;\;y \cdot i + a \cdot \left(\left(\frac{t}{a} + \frac{z}{a}\right) + 1\right)\\ \mathbf{elif}\;i \leq 5.1 \cdot 10^{+109}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 9.5 \cdot 10^{+191}:\\ \;\;\;\;y \cdot i + x \cdot \log y\\ \mathbf{elif}\;i \leq 9 \cdot 10^{+269}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (+ t (+ z (* (log c) (- b 0.5)))))))
   (if (<= i -2.35e+29)
     (+ (* y i) (* a (+ (+ (/ t a) (/ z a)) 1.0)))
     (if (<= i 5.1e+109)
       t_1
       (if (<= i 9.5e+191)
         (+ (* y i) (* x (log y)))
         (if (<= i 9e+269) t_1 (+ (* y i) (* 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 = a + (t + (z + (log(c) * (b - 0.5))));
	double tmp;
	if (i <= -2.35e+29) {
		tmp = (y * i) + (a * (((t / a) + (z / a)) + 1.0));
	} else if (i <= 5.1e+109) {
		tmp = t_1;
	} else if (i <= 9.5e+191) {
		tmp = (y * i) + (x * log(y));
	} else if (i <= 9e+269) {
		tmp = t_1;
	} else {
		tmp = (y * i) + (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 = a + (t + (z + (log(c) * (b - 0.5d0))))
    if (i <= (-2.35d+29)) then
        tmp = (y * i) + (a * (((t / a) + (z / a)) + 1.0d0))
    else if (i <= 5.1d+109) then
        tmp = t_1
    else if (i <= 9.5d+191) then
        tmp = (y * i) + (x * log(y))
    else if (i <= 9d+269) then
        tmp = t_1
    else
        tmp = (y * i) + (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 = a + (t + (z + (Math.log(c) * (b - 0.5))));
	double tmp;
	if (i <= -2.35e+29) {
		tmp = (y * i) + (a * (((t / a) + (z / a)) + 1.0));
	} else if (i <= 5.1e+109) {
		tmp = t_1;
	} else if (i <= 9.5e+191) {
		tmp = (y * i) + (x * Math.log(y));
	} else if (i <= 9e+269) {
		tmp = t_1;
	} else {
		tmp = (y * i) + (b * Math.log(c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (t + (z + (math.log(c) * (b - 0.5))))
	tmp = 0
	if i <= -2.35e+29:
		tmp = (y * i) + (a * (((t / a) + (z / a)) + 1.0))
	elif i <= 5.1e+109:
		tmp = t_1
	elif i <= 9.5e+191:
		tmp = (y * i) + (x * math.log(y))
	elif i <= 9e+269:
		tmp = t_1
	else:
		tmp = (y * i) + (b * math.log(c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(t + Float64(z + Float64(log(c) * Float64(b - 0.5)))))
	tmp = 0.0
	if (i <= -2.35e+29)
		tmp = Float64(Float64(y * i) + Float64(a * Float64(Float64(Float64(t / a) + Float64(z / a)) + 1.0)));
	elseif (i <= 5.1e+109)
		tmp = t_1;
	elseif (i <= 9.5e+191)
		tmp = Float64(Float64(y * i) + Float64(x * log(y)));
	elseif (i <= 9e+269)
		tmp = t_1;
	else
		tmp = Float64(Float64(y * i) + Float64(b * log(c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (t + (z + (log(c) * (b - 0.5))));
	tmp = 0.0;
	if (i <= -2.35e+29)
		tmp = (y * i) + (a * (((t / a) + (z / a)) + 1.0));
	elseif (i <= 5.1e+109)
		tmp = t_1;
	elseif (i <= 9.5e+191)
		tmp = (y * i) + (x * log(y));
	elseif (i <= 9e+269)
		tmp = t_1;
	else
		tmp = (y * i) + (b * log(c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(t + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2.35e+29], N[(N[(y * i), $MachinePrecision] + N[(a * N[(N[(N[(t / a), $MachinePrecision] + N[(z / a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5.1e+109], t$95$1, If[LessEqual[i, 9.5e+191], N[(N[(y * i), $MachinePrecision] + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 9e+269], t$95$1, N[(N[(y * i), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -2.3500000000000001e29

   1. Initial program 98.0%

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

   3. Taylor expanded in a around inf 67.1%

      \[\leadsto \color{blue}{a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(\frac{x \cdot \log y}{a} + \frac{\log c \cdot \left(b - 0.5\right)}{a}\right)\right)\right)\right)} + y \cdot i \]
   4. Step-by-step derivation

      1. associate-/l* 67.1%

         \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(\color{blue}{x \cdot \frac{\log y}{a}} + \frac{\log c \cdot \left(b - 0.5\right)}{a}\right)\right)\right)\right) + y \cdot i \]

      2. sub-neg 67.1%

         \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(x \cdot \frac{\log y}{a} + \frac{\log c \cdot \color{blue}{\left(b + \left(-0.5\right)\right)}}{a}\right)\right)\right)\right) + y \cdot i \]

      3. metadata-eval 67.1%

         \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(x \cdot \frac{\log y}{a} + \frac{\log c \cdot \left(b + \color{blue}{-0.5}\right)}{a}\right)\right)\right)\right) + y \cdot i \]

   5. Simplified 67.1%

      \[\leadsto \color{blue}{a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(x \cdot \frac{\log y}{a} + \frac{\log c \cdot \left(b + -0.5\right)}{a}\right)\right)\right)\right)} + y \cdot i \]

   6. Taylor expanded in z around inf 63.2%

      \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \color{blue}{\frac{z}{a}}\right)\right) + y \cdot i \]

   if -2.3500000000000001e29 < i < 5.0999999999999999e109 or 9.4999999999999998e191 < i < 9.0000000000000004e269

   1. Initial program 99.8%

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

      1. associate-+l+ 99.8%

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

      2. associate-+l+ 99.8%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 87.2%

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

   6. Taylor expanded in x around 0 85.7%

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

      1. associate-+r+ 85.7%

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

   8. Simplified 85.7%

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

   9. Taylor expanded in y around 0 78.3%

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

   if 5.0999999999999999e109 < i < 9.4999999999999998e191

   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 -inf 92.6%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \log y + -1 \cdot \frac{a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)}{x}\right)\right)} + y \cdot i \]
   4. Step-by-step derivation

      1. mul-1-neg 92.6%

         \[\leadsto \color{blue}{\left(-x \cdot \left(-1 \cdot \log y + -1 \cdot \frac{a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)}{x}\right)\right)} + y \cdot i \]

      2. distribute-lft-out 92.6%

         \[\leadsto \left(-x \cdot \color{blue}{\left(-1 \cdot \left(\log y + \frac{a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)}{x}\right)\right)}\right) + y \cdot i \]

      3. sub-neg 92.6%

         \[\leadsto \left(-x \cdot \left(-1 \cdot \left(\log y + \frac{a + \left(t + \left(z + \log c \cdot \color{blue}{\left(b + \left(-0.5\right)\right)}\right)\right)}{x}\right)\right)\right) + y \cdot i \]

      4. metadata-eval 92.6%

         \[\leadsto \left(-x \cdot \left(-1 \cdot \left(\log y + \frac{a + \left(t + \left(z + \log c \cdot \left(b + \color{blue}{-0.5}\right)\right)\right)}{x}\right)\right)\right) + y \cdot i \]

   5. Simplified 92.6%

      \[\leadsto \color{blue}{\left(-x \cdot \left(-1 \cdot \left(\log y + \frac{a + \left(t + \left(z + \log c \cdot \left(b + -0.5\right)\right)\right)}{x}\right)\right)\right)} + y \cdot i \]

   6. Taylor expanded in x around inf 82.7%

      \[\leadsto \left(-\color{blue}{-1 \cdot \left(x \cdot \log y\right)}\right) + y \cdot i \]
   7. Step-by-step derivation

      1. associate-*r* 82.7%

         \[\leadsto \left(-\color{blue}{\left(-1 \cdot x\right) \cdot \log y}\right) + y \cdot i \]

      2. neg-mul-1 82.7%

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

   8. Simplified 82.7%

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

   if 9.0000000000000004e269 < i

   1. Initial program 99.7%

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

   3. Taylor expanded in x around -inf 83.7%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \log y + -1 \cdot \frac{a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)}{x}\right)\right)} + y \cdot i \]
   4. Step-by-step derivation

      1. mul-1-neg 83.7%

         \[\leadsto \color{blue}{\left(-x \cdot \left(-1 \cdot \log y + -1 \cdot \frac{a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)}{x}\right)\right)} + y \cdot i \]

      2. distribute-lft-out 83.7%

         \[\leadsto \left(-x \cdot \color{blue}{\left(-1 \cdot \left(\log y + \frac{a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)}{x}\right)\right)}\right) + y \cdot i \]

      3. sub-neg 83.7%

         \[\leadsto \left(-x \cdot \left(-1 \cdot \left(\log y + \frac{a + \left(t + \left(z + \log c \cdot \color{blue}{\left(b + \left(-0.5\right)\right)}\right)\right)}{x}\right)\right)\right) + y \cdot i \]

      4. metadata-eval 83.7%

         \[\leadsto \left(-x \cdot \left(-1 \cdot \left(\log y + \frac{a + \left(t + \left(z + \log c \cdot \left(b + \color{blue}{-0.5}\right)\right)\right)}{x}\right)\right)\right) + y \cdot i \]

   5. Simplified 83.7%

      \[\leadsto \color{blue}{\left(-x \cdot \left(-1 \cdot \left(\log y + \frac{a + \left(t + \left(z + \log c \cdot \left(b + -0.5\right)\right)\right)}{x}\right)\right)\right)} + y \cdot i \]

   6. Taylor expanded in b around inf 97.3%

      \[\leadsto \left(-\color{blue}{-1 \cdot \left(b \cdot \log c\right)}\right) + y \cdot i \]
   7. Step-by-step derivation

      1. mul-1-neg 97.3%

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

      2. *-commutative 97.3%

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

      3. distribute-rgt-neg-in 97.3%

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

   8. Simplified 97.3%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.35 \cdot 10^{+29}:\\ \;\;\;\;y \cdot i + a \cdot \left(\left(\frac{t}{a} + \frac{z}{a}\right) + 1\right)\\ \mathbf{elif}\;i \leq 5.1 \cdot 10^{+109}:\\ \;\;\;\;a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{elif}\;i \leq 9.5 \cdot 10^{+191}:\\ \;\;\;\;y \cdot i + x \cdot \log y\\ \mathbf{elif}\;i \leq 9 \cdot 10^{+269}:\\ \;\;\;\;a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 67.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -4 \cdot 10^{+181}:\\ \;\;\;\;y \cdot i + x \cdot \left(\log y + \frac{z}{x}\right)\\ \mathbf{elif}\;i \leq -3.6 \cdot 10^{+30}:\\ \;\;\;\;y \cdot i + z \cdot \left(\frac{a}{z} + 1\right)\\ \mathbf{elif}\;i \leq 7 \cdot 10^{+34}:\\ \;\;\;\;a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + z \cdot \left(b \cdot \frac{\log c}{z} + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= i -4e+181)
   (+ (* y i) (* x (+ (log y) (/ z x))))
   (if (<= i -3.6e+30)
     (+ (* y i) (* z (+ (/ a z) 1.0)))
     (if (<= i 7e+34)
       (+ a (+ t (+ z (* (log c) (- b 0.5)))))
       (+ (* y i) (* z (+ (* b (/ (log c) z)) 1.0)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (i <= -4e+181) {
		tmp = (y * i) + (x * (log(y) + (z / x)));
	} else if (i <= -3.6e+30) {
		tmp = (y * i) + (z * ((a / z) + 1.0));
	} else if (i <= 7e+34) {
		tmp = a + (t + (z + (log(c) * (b - 0.5))));
	} else {
		tmp = (y * i) + (z * ((b * (log(c) / z)) + 1.0));
	}
	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 <= (-4d+181)) then
        tmp = (y * i) + (x * (log(y) + (z / x)))
    else if (i <= (-3.6d+30)) then
        tmp = (y * i) + (z * ((a / z) + 1.0d0))
    else if (i <= 7d+34) then
        tmp = a + (t + (z + (log(c) * (b - 0.5d0))))
    else
        tmp = (y * i) + (z * ((b * (log(c) / z)) + 1.0d0))
    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 <= -4e+181) {
		tmp = (y * i) + (x * (Math.log(y) + (z / x)));
	} else if (i <= -3.6e+30) {
		tmp = (y * i) + (z * ((a / z) + 1.0));
	} else if (i <= 7e+34) {
		tmp = a + (t + (z + (Math.log(c) * (b - 0.5))));
	} else {
		tmp = (y * i) + (z * ((b * (Math.log(c) / z)) + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if i <= -4e+181:
		tmp = (y * i) + (x * (math.log(y) + (z / x)))
	elif i <= -3.6e+30:
		tmp = (y * i) + (z * ((a / z) + 1.0))
	elif i <= 7e+34:
		tmp = a + (t + (z + (math.log(c) * (b - 0.5))))
	else:
		tmp = (y * i) + (z * ((b * (math.log(c) / z)) + 1.0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (i <= -4e+181)
		tmp = Float64(Float64(y * i) + Float64(x * Float64(log(y) + Float64(z / x))));
	elseif (i <= -3.6e+30)
		tmp = Float64(Float64(y * i) + Float64(z * Float64(Float64(a / z) + 1.0)));
	elseif (i <= 7e+34)
		tmp = Float64(a + Float64(t + Float64(z + Float64(log(c) * Float64(b - 0.5)))));
	else
		tmp = Float64(Float64(y * i) + Float64(z * Float64(Float64(b * Float64(log(c) / z)) + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (i <= -4e+181)
		tmp = (y * i) + (x * (log(y) + (z / x)));
	elseif (i <= -3.6e+30)
		tmp = (y * i) + (z * ((a / z) + 1.0));
	elseif (i <= 7e+34)
		tmp = a + (t + (z + (log(c) * (b - 0.5))));
	else
		tmp = (y * i) + (z * ((b * (log(c) / z)) + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[i, -4e+181], N[(N[(y * i), $MachinePrecision] + N[(x * N[(N[Log[y], $MachinePrecision] + N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -3.6e+30], N[(N[(y * i), $MachinePrecision] + N[(z * N[(N[(a / z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 7e+34], N[(a + N[(t + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(z * N[(N[(b * N[(N[Log[c], $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if i < -3.9999999999999997e181

   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 -inf 59.0%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \log y + -1 \cdot \frac{a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)}{x}\right)\right)} + y \cdot i \]
   4. Step-by-step derivation

      1. mul-1-neg 59.0%

         \[\leadsto \color{blue}{\left(-x \cdot \left(-1 \cdot \log y + -1 \cdot \frac{a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)}{x}\right)\right)} + y \cdot i \]

      2. distribute-lft-out 59.0%

         \[\leadsto \left(-x \cdot \color{blue}{\left(-1 \cdot \left(\log y + \frac{a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)}{x}\right)\right)}\right) + y \cdot i \]

      3. sub-neg 59.0%

         \[\leadsto \left(-x \cdot \left(-1 \cdot \left(\log y + \frac{a + \left(t + \left(z + \log c \cdot \color{blue}{\left(b + \left(-0.5\right)\right)}\right)\right)}{x}\right)\right)\right) + y \cdot i \]

      4. metadata-eval 59.0%

         \[\leadsto \left(-x \cdot \left(-1 \cdot \left(\log y + \frac{a + \left(t + \left(z + \log c \cdot \left(b + \color{blue}{-0.5}\right)\right)\right)}{x}\right)\right)\right) + y \cdot i \]

   5. Simplified 59.0%

      \[\leadsto \color{blue}{\left(-x \cdot \left(-1 \cdot \left(\log y + \frac{a + \left(t + \left(z + \log c \cdot \left(b + -0.5\right)\right)\right)}{x}\right)\right)\right)} + y \cdot i \]

   6. Taylor expanded in z around inf 71.0%

      \[\leadsto \left(-x \cdot \left(-1 \cdot \left(\log y + \color{blue}{\frac{z}{x}}\right)\right)\right) + y \cdot i \]

   if -3.9999999999999997e181 < i < -3.6000000000000002e30

   1. Initial program 96.1%

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

   3. Taylor expanded in z around inf 77.1%

      \[\leadsto \color{blue}{z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(\frac{x \cdot \log y}{z} + \frac{\log c \cdot \left(b - 0.5\right)}{z}\right)\right)\right)\right)} + y \cdot i \]
   4. Step-by-step derivation

      1. associate-/l* 77.1%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(\color{blue}{x \cdot \frac{\log y}{z}} + \frac{\log c \cdot \left(b - 0.5\right)}{z}\right)\right)\right)\right) + y \cdot i \]

      2. sub-neg 77.1%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \frac{\log c \cdot \color{blue}{\left(b + \left(-0.5\right)\right)}}{z}\right)\right)\right)\right) + y \cdot i \]

      3. metadata-eval 77.1%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \frac{\log c \cdot \left(b + \color{blue}{-0.5}\right)}{z}\right)\right)\right)\right) + y \cdot i \]

      4. associate-/l* 77.1%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \color{blue}{\log c \cdot \frac{b + -0.5}{z}}\right)\right)\right)\right) + y \cdot i \]

   5. Simplified 77.1%

      \[\leadsto \color{blue}{z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \log c \cdot \frac{b + -0.5}{z}\right)\right)\right)\right)} + y \cdot i \]

   6. Taylor expanded in a around inf 68.6%

      \[\leadsto z \cdot \left(1 + \color{blue}{\frac{a}{z}}\right) + y \cdot i \]

   if -3.6000000000000002e30 < i < 6.99999999999999996e34

   1. Initial program 99.8%

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

      1. associate-+l+ 99.8%

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

      2. associate-+l+ 99.8%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 84.1%

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

   6. Taylor expanded in x around 0 84.8%

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

      1. associate-+r+ 84.8%

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

   8. Simplified 84.8%

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

   9. Taylor expanded in y around 0 79.9%

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

   if 6.99999999999999996e34 < i

   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 a around inf 76.2%

      \[\leadsto \color{blue}{a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(\frac{x \cdot \log y}{a} + \frac{\log c \cdot \left(b - 0.5\right)}{a}\right)\right)\right)\right)} + y \cdot i \]
   4. Step-by-step derivation

      1. associate-/l* 76.2%

         \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(\color{blue}{x \cdot \frac{\log y}{a}} + \frac{\log c \cdot \left(b - 0.5\right)}{a}\right)\right)\right)\right) + y \cdot i \]

      2. sub-neg 76.2%

         \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(x \cdot \frac{\log y}{a} + \frac{\log c \cdot \color{blue}{\left(b + \left(-0.5\right)\right)}}{a}\right)\right)\right)\right) + y \cdot i \]

      3. metadata-eval 76.2%

         \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(x \cdot \frac{\log y}{a} + \frac{\log c \cdot \left(b + \color{blue}{-0.5}\right)}{a}\right)\right)\right)\right) + y \cdot i \]

   5. Simplified 76.2%

      \[\leadsto \color{blue}{a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(x \cdot \frac{\log y}{a} + \frac{\log c \cdot \left(b + -0.5\right)}{a}\right)\right)\right)\right)} + y \cdot i \]

   6. Taylor expanded in b around inf 70.9%

      \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \color{blue}{\frac{b \cdot \log c}{a}}\right)\right)\right) + y \cdot i \]
   7. Step-by-step derivation

      1. *-commutative 70.9%

         \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \frac{\color{blue}{\log c \cdot b}}{a}\right)\right)\right) + y \cdot i \]

   8. Simplified 70.9%

      \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \color{blue}{\frac{\log c \cdot b}{a}}\right)\right)\right) + y \cdot i \]

   9. Taylor expanded in z around inf 52.4%

      \[\leadsto \color{blue}{z \cdot \left(1 + \frac{a \cdot \left(1 + \left(\frac{t}{a} + \frac{b \cdot \log c}{a}\right)\right)}{z}\right)} + y \cdot i \]
   10. Step-by-step derivation

       1. associate-/l* 49.2%

          \[\leadsto z \cdot \left(1 + \color{blue}{a \cdot \frac{1 + \left(\frac{t}{a} + \frac{b \cdot \log c}{a}\right)}{z}}\right) + y \cdot i \]

       2. *-commutative 49.2%

          \[\leadsto z \cdot \left(1 + a \cdot \frac{1 + \left(\frac{t}{a} + \frac{\color{blue}{\log c \cdot b}}{a}\right)}{z}\right) + y \cdot i \]

       3. associate-*r/ 49.2%

          \[\leadsto z \cdot \left(1 + a \cdot \frac{1 + \left(\frac{t}{a} + \color{blue}{\log c \cdot \frac{b}{a}}\right)}{z}\right) + y \cdot i \]

   11. Simplified 49.2%

       \[\leadsto \color{blue}{z \cdot \left(1 + a \cdot \frac{1 + \left(\frac{t}{a} + \log c \cdot \frac{b}{a}\right)}{z}\right)} + y \cdot i \]

   12. Taylor expanded in b around inf 56.3%

       \[\leadsto z \cdot \left(1 + \color{blue}{\frac{b \cdot \log c}{z}}\right) + y \cdot i \]
   13. Step-by-step derivation

       1. associate-/l* 56.3%

          \[\leadsto z \cdot \left(1 + \color{blue}{b \cdot \frac{\log c}{z}}\right) + y \cdot i \]

   14. Simplified 56.3%

       \[\leadsto z \cdot \left(1 + \color{blue}{b \cdot \frac{\log c}{z}}\right) + y \cdot i \]
3. Recombined 4 regimes into one program.

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4 \cdot 10^{+181}:\\ \;\;\;\;y \cdot i + x \cdot \left(\log y + \frac{z}{x}\right)\\ \mathbf{elif}\;i \leq -3.6 \cdot 10^{+30}:\\ \;\;\;\;y \cdot i + z \cdot \left(\frac{a}{z} + 1\right)\\ \mathbf{elif}\;i \leq 7 \cdot 10^{+34}:\\ \;\;\;\;a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + z \cdot \left(b \cdot \frac{\log c}{z} + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 90.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.3 \cdot 10^{+240}:\\ \;\;\;\;y \cdot i + x \cdot \left(\log y + \frac{a}{x}\right)\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+225}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -6.3e+240)
   (+ (* y i) (* x (+ (log y) (/ a x))))
   (if (<= x 1.25e+225)
     (+ (* y i) (+ a (+ t (+ z (* (log c) (- b 0.5))))))
     (+ a (+ t (+ z (* x (log y))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -6.3e+240) {
		tmp = (y * i) + (x * (log(y) + (a / x)));
	} else if (x <= 1.25e+225) {
		tmp = (y * i) + (a + (t + (z + (log(c) * (b - 0.5)))));
	} else {
		tmp = a + (t + (z + (x * log(y))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (x <= (-6.3d+240)) then
        tmp = (y * i) + (x * (log(y) + (a / x)))
    else if (x <= 1.25d+225) then
        tmp = (y * i) + (a + (t + (z + (log(c) * (b - 0.5d0)))))
    else
        tmp = a + (t + (z + (x * log(y))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -6.3e+240) {
		tmp = (y * i) + (x * (Math.log(y) + (a / x)));
	} else if (x <= 1.25e+225) {
		tmp = (y * i) + (a + (t + (z + (Math.log(c) * (b - 0.5)))));
	} else {
		tmp = a + (t + (z + (x * Math.log(y))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if x <= -6.3e+240:
		tmp = (y * i) + (x * (math.log(y) + (a / x)))
	elif x <= 1.25e+225:
		tmp = (y * i) + (a + (t + (z + (math.log(c) * (b - 0.5)))))
	else:
		tmp = a + (t + (z + (x * math.log(y))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -6.3e+240)
		tmp = Float64(Float64(y * i) + Float64(x * Float64(log(y) + Float64(a / x))));
	elseif (x <= 1.25e+225)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(t + Float64(z + Float64(log(c) * Float64(b - 0.5))))));
	else
		tmp = Float64(a + Float64(t + Float64(z + Float64(x * log(y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (x <= -6.3e+240)
		tmp = (y * i) + (x * (log(y) + (a / x)));
	elseif (x <= 1.25e+225)
		tmp = (y * i) + (a + (t + (z + (log(c) * (b - 0.5)))));
	else
		tmp = a + (t + (z + (x * log(y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -6.3e+240], N[(N[(y * i), $MachinePrecision] + N[(x * N[(N[Log[y], $MachinePrecision] + N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.25e+225], N[(N[(y * i), $MachinePrecision] + N[(a + N[(t + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.2999999999999997e240

   1. Initial program 99.7%

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

   3. Taylor expanded in x around -inf 99.6%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \log y + -1 \cdot \frac{a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)}{x}\right)\right)} + y \cdot i \]
   4. Step-by-step derivation

      1. mul-1-neg 99.6%

         \[\leadsto \color{blue}{\left(-x \cdot \left(-1 \cdot \log y + -1 \cdot \frac{a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)}{x}\right)\right)} + y \cdot i \]

      2. distribute-lft-out 99.6%

         \[\leadsto \left(-x \cdot \color{blue}{\left(-1 \cdot \left(\log y + \frac{a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)}{x}\right)\right)}\right) + y \cdot i \]

      3. sub-neg 99.6%

         \[\leadsto \left(-x \cdot \left(-1 \cdot \left(\log y + \frac{a + \left(t + \left(z + \log c \cdot \color{blue}{\left(b + \left(-0.5\right)\right)}\right)\right)}{x}\right)\right)\right) + y \cdot i \]

      4. metadata-eval 99.6%

         \[\leadsto \left(-x \cdot \left(-1 \cdot \left(\log y + \frac{a + \left(t + \left(z + \log c \cdot \left(b + \color{blue}{-0.5}\right)\right)\right)}{x}\right)\right)\right) + y \cdot i \]

   5. Simplified 99.6%

      \[\leadsto \color{blue}{\left(-x \cdot \left(-1 \cdot \left(\log y + \frac{a + \left(t + \left(z + \log c \cdot \left(b + -0.5\right)\right)\right)}{x}\right)\right)\right)} + y \cdot i \]

   6. Taylor expanded in a around inf 87.8%

      \[\leadsto \left(-x \cdot \left(-1 \cdot \left(\log y + \color{blue}{\frac{a}{x}}\right)\right)\right) + y \cdot i \]

   if -6.2999999999999997e240 < x < 1.24999999999999995e225

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 93.7%

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

   if 1.24999999999999995e225 < x

   1. Initial program 92.5%

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

   3. Taylor expanded in y around 0 92.5%

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

   4. Taylor expanded in x around inf 85.9%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.3 \cdot 10^{+240}:\\ \;\;\;\;y \cdot i + x \cdot \left(\log y + \frac{a}{x}\right)\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+225}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 68.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1.04 \cdot 10^{+33}:\\ \;\;\;\;y \cdot i + a \cdot \left(\left(\frac{t}{a} + \frac{z}{a}\right) + 1\right)\\ \mathbf{elif}\;i \leq 6.8 \cdot 10^{+34}:\\ \;\;\;\;a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + z \cdot \left(b \cdot \frac{\log c}{z} + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= i -1.04e+33)
   (+ (* y i) (* a (+ (+ (/ t a) (/ z a)) 1.0)))
   (if (<= i 6.8e+34)
     (+ a (+ t (+ z (* (log c) (- b 0.5)))))
     (+ (* y i) (* z (+ (* b (/ (log c) z)) 1.0))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (i <= -1.04e+33) {
		tmp = (y * i) + (a * (((t / a) + (z / a)) + 1.0));
	} else if (i <= 6.8e+34) {
		tmp = a + (t + (z + (log(c) * (b - 0.5))));
	} else {
		tmp = (y * i) + (z * ((b * (log(c) / z)) + 1.0));
	}
	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 <= (-1.04d+33)) then
        tmp = (y * i) + (a * (((t / a) + (z / a)) + 1.0d0))
    else if (i <= 6.8d+34) then
        tmp = a + (t + (z + (log(c) * (b - 0.5d0))))
    else
        tmp = (y * i) + (z * ((b * (log(c) / z)) + 1.0d0))
    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 <= -1.04e+33) {
		tmp = (y * i) + (a * (((t / a) + (z / a)) + 1.0));
	} else if (i <= 6.8e+34) {
		tmp = a + (t + (z + (Math.log(c) * (b - 0.5))));
	} else {
		tmp = (y * i) + (z * ((b * (Math.log(c) / z)) + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if i <= -1.04e+33:
		tmp = (y * i) + (a * (((t / a) + (z / a)) + 1.0))
	elif i <= 6.8e+34:
		tmp = a + (t + (z + (math.log(c) * (b - 0.5))))
	else:
		tmp = (y * i) + (z * ((b * (math.log(c) / z)) + 1.0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (i <= -1.04e+33)
		tmp = Float64(Float64(y * i) + Float64(a * Float64(Float64(Float64(t / a) + Float64(z / a)) + 1.0)));
	elseif (i <= 6.8e+34)
		tmp = Float64(a + Float64(t + Float64(z + Float64(log(c) * Float64(b - 0.5)))));
	else
		tmp = Float64(Float64(y * i) + Float64(z * Float64(Float64(b * Float64(log(c) / z)) + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (i <= -1.04e+33)
		tmp = (y * i) + (a * (((t / a) + (z / a)) + 1.0));
	elseif (i <= 6.8e+34)
		tmp = a + (t + (z + (log(c) * (b - 0.5))));
	else
		tmp = (y * i) + (z * ((b * (log(c) / z)) + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[i, -1.04e+33], N[(N[(y * i), $MachinePrecision] + N[(a * N[(N[(N[(t / a), $MachinePrecision] + N[(z / a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 6.8e+34], N[(a + N[(t + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(z * N[(N[(b * N[(N[Log[c], $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if i < -1.0400000000000001e33

   1. Initial program 98.0%

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

   3. Taylor expanded in a around inf 67.1%

      \[\leadsto \color{blue}{a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(\frac{x \cdot \log y}{a} + \frac{\log c \cdot \left(b - 0.5\right)}{a}\right)\right)\right)\right)} + y \cdot i \]
   4. Step-by-step derivation

      1. associate-/l* 67.1%

         \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(\color{blue}{x \cdot \frac{\log y}{a}} + \frac{\log c \cdot \left(b - 0.5\right)}{a}\right)\right)\right)\right) + y \cdot i \]

      2. sub-neg 67.1%

         \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(x \cdot \frac{\log y}{a} + \frac{\log c \cdot \color{blue}{\left(b + \left(-0.5\right)\right)}}{a}\right)\right)\right)\right) + y \cdot i \]

      3. metadata-eval 67.1%

         \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(x \cdot \frac{\log y}{a} + \frac{\log c \cdot \left(b + \color{blue}{-0.5}\right)}{a}\right)\right)\right)\right) + y \cdot i \]

   5. Simplified 67.1%

      \[\leadsto \color{blue}{a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(x \cdot \frac{\log y}{a} + \frac{\log c \cdot \left(b + -0.5\right)}{a}\right)\right)\right)\right)} + y \cdot i \]

   6. Taylor expanded in z around inf 63.2%

      \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \color{blue}{\frac{z}{a}}\right)\right) + y \cdot i \]

   if -1.0400000000000001e33 < i < 6.7999999999999999e34

   1. Initial program 99.8%

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

      1. associate-+l+ 99.8%

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

      2. associate-+l+ 99.8%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 84.1%

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

   6. Taylor expanded in x around 0 84.8%

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

      1. associate-+r+ 84.8%

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

   8. Simplified 84.8%

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

   9. Taylor expanded in y around 0 79.9%

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

   if 6.7999999999999999e34 < i

   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 a around inf 76.2%

      \[\leadsto \color{blue}{a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(\frac{x \cdot \log y}{a} + \frac{\log c \cdot \left(b - 0.5\right)}{a}\right)\right)\right)\right)} + y \cdot i \]
   4. Step-by-step derivation

      1. associate-/l* 76.2%

         \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(\color{blue}{x \cdot \frac{\log y}{a}} + \frac{\log c \cdot \left(b - 0.5\right)}{a}\right)\right)\right)\right) + y \cdot i \]

      2. sub-neg 76.2%

         \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(x \cdot \frac{\log y}{a} + \frac{\log c \cdot \color{blue}{\left(b + \left(-0.5\right)\right)}}{a}\right)\right)\right)\right) + y \cdot i \]

      3. metadata-eval 76.2%

         \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(x \cdot \frac{\log y}{a} + \frac{\log c \cdot \left(b + \color{blue}{-0.5}\right)}{a}\right)\right)\right)\right) + y \cdot i \]

   5. Simplified 76.2%

      \[\leadsto \color{blue}{a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(x \cdot \frac{\log y}{a} + \frac{\log c \cdot \left(b + -0.5\right)}{a}\right)\right)\right)\right)} + y \cdot i \]

   6. Taylor expanded in b around inf 70.9%

      \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \color{blue}{\frac{b \cdot \log c}{a}}\right)\right)\right) + y \cdot i \]
   7. Step-by-step derivation

      1. *-commutative 70.9%

         \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \frac{\color{blue}{\log c \cdot b}}{a}\right)\right)\right) + y \cdot i \]

   8. Simplified 70.9%

      \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \color{blue}{\frac{\log c \cdot b}{a}}\right)\right)\right) + y \cdot i \]

   9. Taylor expanded in z around inf 52.4%

      \[\leadsto \color{blue}{z \cdot \left(1 + \frac{a \cdot \left(1 + \left(\frac{t}{a} + \frac{b \cdot \log c}{a}\right)\right)}{z}\right)} + y \cdot i \]
   10. Step-by-step derivation

       1. associate-/l* 49.2%

          \[\leadsto z \cdot \left(1 + \color{blue}{a \cdot \frac{1 + \left(\frac{t}{a} + \frac{b \cdot \log c}{a}\right)}{z}}\right) + y \cdot i \]

       2. *-commutative 49.2%

          \[\leadsto z \cdot \left(1 + a \cdot \frac{1 + \left(\frac{t}{a} + \frac{\color{blue}{\log c \cdot b}}{a}\right)}{z}\right) + y \cdot i \]

       3. associate-*r/ 49.2%

          \[\leadsto z \cdot \left(1 + a \cdot \frac{1 + \left(\frac{t}{a} + \color{blue}{\log c \cdot \frac{b}{a}}\right)}{z}\right) + y \cdot i \]

   11. Simplified 49.2%

       \[\leadsto \color{blue}{z \cdot \left(1 + a \cdot \frac{1 + \left(\frac{t}{a} + \log c \cdot \frac{b}{a}\right)}{z}\right)} + y \cdot i \]

   12. Taylor expanded in b around inf 56.3%

       \[\leadsto z \cdot \left(1 + \color{blue}{\frac{b \cdot \log c}{z}}\right) + y \cdot i \]
   13. Step-by-step derivation

       1. associate-/l* 56.3%

          \[\leadsto z \cdot \left(1 + \color{blue}{b \cdot \frac{\log c}{z}}\right) + y \cdot i \]

   14. Simplified 56.3%

       \[\leadsto z \cdot \left(1 + \color{blue}{b \cdot \frac{\log c}{z}}\right) + y \cdot i \]
3. Recombined 3 regimes into one program.

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.04 \cdot 10^{+33}:\\ \;\;\;\;y \cdot i + a \cdot \left(\left(\frac{t}{a} + \frac{z}{a}\right) + 1\right)\\ \mathbf{elif}\;i \leq 6.8 \cdot 10^{+34}:\\ \;\;\;\;a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + z \cdot \left(b \cdot \frac{\log c}{z} + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 66.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1.72 \cdot 10^{-43}:\\ \;\;\;\;y \cdot i + a \cdot \left(\left(\frac{t}{a} + \frac{z}{a}\right) + 1\right)\\ \mathbf{elif}\;i \leq 1.2 \cdot 10^{+34}:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + z \cdot \left(\frac{a}{z} + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= i -1.72e-43)
   (+ (* y i) (* a (+ (+ (/ t a) (/ z a)) 1.0)))
   (if (<= i 1.2e+34)
     (+ a (+ t (+ z (* x (log y)))))
     (+ (* y i) (* z (+ (/ a z) 1.0))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (i <= -1.72e-43) {
		tmp = (y * i) + (a * (((t / a) + (z / a)) + 1.0));
	} else if (i <= 1.2e+34) {
		tmp = a + (t + (z + (x * log(y))));
	} else {
		tmp = (y * i) + (z * ((a / z) + 1.0));
	}
	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 <= (-1.72d-43)) then
        tmp = (y * i) + (a * (((t / a) + (z / a)) + 1.0d0))
    else if (i <= 1.2d+34) then
        tmp = a + (t + (z + (x * log(y))))
    else
        tmp = (y * i) + (z * ((a / z) + 1.0d0))
    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 <= -1.72e-43) {
		tmp = (y * i) + (a * (((t / a) + (z / a)) + 1.0));
	} else if (i <= 1.2e+34) {
		tmp = a + (t + (z + (x * Math.log(y))));
	} else {
		tmp = (y * i) + (z * ((a / z) + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if i <= -1.72e-43:
		tmp = (y * i) + (a * (((t / a) + (z / a)) + 1.0))
	elif i <= 1.2e+34:
		tmp = a + (t + (z + (x * math.log(y))))
	else:
		tmp = (y * i) + (z * ((a / z) + 1.0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (i <= -1.72e-43)
		tmp = Float64(Float64(y * i) + Float64(a * Float64(Float64(Float64(t / a) + Float64(z / a)) + 1.0)));
	elseif (i <= 1.2e+34)
		tmp = Float64(a + Float64(t + Float64(z + Float64(x * log(y)))));
	else
		tmp = Float64(Float64(y * i) + Float64(z * Float64(Float64(a / z) + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (i <= -1.72e-43)
		tmp = (y * i) + (a * (((t / a) + (z / a)) + 1.0));
	elseif (i <= 1.2e+34)
		tmp = a + (t + (z + (x * log(y))));
	else
		tmp = (y * i) + (z * ((a / z) + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[i, -1.72e-43], N[(N[(y * i), $MachinePrecision] + N[(a * N[(N[(N[(t / a), $MachinePrecision] + N[(z / a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.2e+34], N[(a + N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(z * N[(N[(a / z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if i < -1.72000000000000005e-43

   1. Initial program 98.4%

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

   3. Taylor expanded in a around inf 70.4%

      \[\leadsto \color{blue}{a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(\frac{x \cdot \log y}{a} + \frac{\log c \cdot \left(b - 0.5\right)}{a}\right)\right)\right)\right)} + y \cdot i \]
   4. Step-by-step derivation

      1. associate-/l* 70.4%

         \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(\color{blue}{x \cdot \frac{\log y}{a}} + \frac{\log c \cdot \left(b - 0.5\right)}{a}\right)\right)\right)\right) + y \cdot i \]

      2. sub-neg 70.4%

         \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(x \cdot \frac{\log y}{a} + \frac{\log c \cdot \color{blue}{\left(b + \left(-0.5\right)\right)}}{a}\right)\right)\right)\right) + y \cdot i \]

      3. metadata-eval 70.4%

         \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(x \cdot \frac{\log y}{a} + \frac{\log c \cdot \left(b + \color{blue}{-0.5}\right)}{a}\right)\right)\right)\right) + y \cdot i \]

   5. Simplified 70.4%

      \[\leadsto \color{blue}{a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(x \cdot \frac{\log y}{a} + \frac{\log c \cdot \left(b + -0.5\right)}{a}\right)\right)\right)\right)} + y \cdot i \]

   6. Taylor expanded in z around inf 61.4%

      \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \color{blue}{\frac{z}{a}}\right)\right) + y \cdot i \]

   if -1.72000000000000005e-43 < i < 1.19999999999999993e34

   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 96.1%

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

   4. Taylor expanded in x around inf 70.2%

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

   if 1.19999999999999993e34 < i

   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 z around inf 65.1%

      \[\leadsto \color{blue}{z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(\frac{x \cdot \log y}{z} + \frac{\log c \cdot \left(b - 0.5\right)}{z}\right)\right)\right)\right)} + y \cdot i \]
   4. Step-by-step derivation

      1. associate-/l* 65.0%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(\color{blue}{x \cdot \frac{\log y}{z}} + \frac{\log c \cdot \left(b - 0.5\right)}{z}\right)\right)\right)\right) + y \cdot i \]

      2. sub-neg 65.0%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \frac{\log c \cdot \color{blue}{\left(b + \left(-0.5\right)\right)}}{z}\right)\right)\right)\right) + y \cdot i \]

      3. metadata-eval 65.0%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \frac{\log c \cdot \left(b + \color{blue}{-0.5}\right)}{z}\right)\right)\right)\right) + y \cdot i \]

      4. associate-/l* 65.0%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \color{blue}{\log c \cdot \frac{b + -0.5}{z}}\right)\right)\right)\right) + y \cdot i \]

   5. Simplified 65.0%

      \[\leadsto \color{blue}{z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \log c \cdot \frac{b + -0.5}{z}\right)\right)\right)\right)} + y \cdot i \]

   6. Taylor expanded in a around inf 43.6%

      \[\leadsto z \cdot \left(1 + \color{blue}{\frac{a}{z}}\right) + y \cdot i \]
3. Recombined 3 regimes into one program.

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.72 \cdot 10^{-43}:\\ \;\;\;\;y \cdot i + a \cdot \left(\left(\frac{t}{a} + \frac{z}{a}\right) + 1\right)\\ \mathbf{elif}\;i \leq 1.2 \cdot 10^{+34}:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + z \cdot \left(\frac{a}{z} + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 40.6% accurate, 10.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+206} \lor \neg \left(z \leq -6.6 \cdot 10^{+174}\right) \land z \leq -1.18 \cdot 10^{+151}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= z -4.9e+206) (and (not (<= z -6.6e+174)) (<= z -1.18e+151)))
   z
   (+ 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 <= -4.9e+206) || (!(z <= -6.6e+174) && (z <= -1.18e+151))) {
		tmp = z;
	} 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 <= (-4.9d+206)) .or. (.not. (z <= (-6.6d+174))) .and. (z <= (-1.18d+151))) then
        tmp = z
    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 <= -4.9e+206) || (!(z <= -6.6e+174) && (z <= -1.18e+151))) {
		tmp = z;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (z <= -4.9e+206) or (not (z <= -6.6e+174) and (z <= -1.18e+151)):
		tmp = z
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((z <= -4.9e+206) || (!(z <= -6.6e+174) && (z <= -1.18e+151)))
		tmp = z;
	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 <= -4.9e+206) || (~((z <= -6.6e+174)) && (z <= -1.18e+151)))
		tmp = z;
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[z, -4.9e+206], And[N[Not[LessEqual[z, -6.6e+174]], $MachinePrecision], LessEqual[z, -1.18e+151]]], z, N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.9e206 or -6.6000000000000001e174 < z < -1.18000000000000005e151

   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 54.3%

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

   if -4.9e206 < z < -6.6000000000000001e174 or -1.18000000000000005e151 < 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 -inf 75.3%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \log y + -1 \cdot \frac{a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)}{x}\right)\right)} + y \cdot i \]
   4. Step-by-step derivation

      1. mul-1-neg 75.3%

         \[\leadsto \color{blue}{\left(-x \cdot \left(-1 \cdot \log y + -1 \cdot \frac{a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)}{x}\right)\right)} + y \cdot i \]

      2. distribute-lft-out 75.3%

         \[\leadsto \left(-x \cdot \color{blue}{\left(-1 \cdot \left(\log y + \frac{a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)}{x}\right)\right)}\right) + y \cdot i \]

      3. sub-neg 75.3%

         \[\leadsto \left(-x \cdot \left(-1 \cdot \left(\log y + \frac{a + \left(t + \left(z + \log c \cdot \color{blue}{\left(b + \left(-0.5\right)\right)}\right)\right)}{x}\right)\right)\right) + y \cdot i \]

      4. metadata-eval 75.3%

         \[\leadsto \left(-x \cdot \left(-1 \cdot \left(\log y + \frac{a + \left(t + \left(z + \log c \cdot \left(b + \color{blue}{-0.5}\right)\right)\right)}{x}\right)\right)\right) + y \cdot i \]

   5. Simplified 75.3%

      \[\leadsto \color{blue}{\left(-x \cdot \left(-1 \cdot \left(\log y + \frac{a + \left(t + \left(z + \log c \cdot \left(b + -0.5\right)\right)\right)}{x}\right)\right)\right)} + y \cdot i \]

   6. Taylor expanded in a around inf 39.1%

      \[\leadsto \left(-\color{blue}{-1 \cdot a}\right) + y \cdot i \]
   7. Step-by-step derivation

      1. mul-1-neg 39.1%

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

   8. Simplified 39.1%

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

4. Final simplification 40.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+206} \lor \neg \left(z \leq -6.6 \cdot 10^{+174}\right) \land z \leq -1.18 \cdot 10^{+151}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 55.7% accurate, 10.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+143}:\\ \;\;\;\;y \cdot i + z \cdot \left(a \cdot \frac{1}{z} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + a \cdot \left(\left(\frac{t}{a} + \frac{z}{a}\right) + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -3.1e+143)
   (+ (* y i) (* z (+ (* a (/ 1.0 z)) 1.0)))
   (+ (* y i) (* a (+ (+ (/ t a) (/ z a)) 1.0)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -3.1e+143) {
		tmp = (y * i) + (z * ((a * (1.0 / z)) + 1.0));
	} else {
		tmp = (y * i) + (a * (((t / a) + (z / a)) + 1.0));
	}
	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 <= (-3.1d+143)) then
        tmp = (y * i) + (z * ((a * (1.0d0 / z)) + 1.0d0))
    else
        tmp = (y * i) + (a * (((t / a) + (z / a)) + 1.0d0))
    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 <= -3.1e+143) {
		tmp = (y * i) + (z * ((a * (1.0 / z)) + 1.0));
	} else {
		tmp = (y * i) + (a * (((t / a) + (z / a)) + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -3.1e+143:
		tmp = (y * i) + (z * ((a * (1.0 / z)) + 1.0))
	else:
		tmp = (y * i) + (a * (((t / a) + (z / a)) + 1.0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -3.1e+143)
		tmp = Float64(Float64(y * i) + Float64(z * Float64(Float64(a * Float64(1.0 / z)) + 1.0)));
	else
		tmp = Float64(Float64(y * i) + Float64(a * Float64(Float64(Float64(t / a) + Float64(z / a)) + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -3.1e+143)
		tmp = (y * i) + (z * ((a * (1.0 / z)) + 1.0));
	else
		tmp = (y * i) + (a * (((t / a) + (z / a)) + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -3.1e+143], N[(N[(y * i), $MachinePrecision] + N[(z * N[(N[(a * N[(1.0 / z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a * N[(N[(N[(t / a), $MachinePrecision] + N[(z / a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.0999999999999999e143

   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 50.6%

      \[\leadsto \color{blue}{a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(\frac{x \cdot \log y}{a} + \frac{\log c \cdot \left(b - 0.5\right)}{a}\right)\right)\right)\right)} + y \cdot i \]
   4. Step-by-step derivation

      1. associate-/l* 50.6%

         \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(\color{blue}{x \cdot \frac{\log y}{a}} + \frac{\log c \cdot \left(b - 0.5\right)}{a}\right)\right)\right)\right) + y \cdot i \]

      2. sub-neg 50.6%

         \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(x \cdot \frac{\log y}{a} + \frac{\log c \cdot \color{blue}{\left(b + \left(-0.5\right)\right)}}{a}\right)\right)\right)\right) + y \cdot i \]

      3. metadata-eval 50.6%

         \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(x \cdot \frac{\log y}{a} + \frac{\log c \cdot \left(b + \color{blue}{-0.5}\right)}{a}\right)\right)\right)\right) + y \cdot i \]

   5. Simplified 50.6%

      \[\leadsto \color{blue}{a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(x \cdot \frac{\log y}{a} + \frac{\log c \cdot \left(b + -0.5\right)}{a}\right)\right)\right)\right)} + y \cdot i \]

   6. Taylor expanded in b around inf 44.2%

      \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \color{blue}{\frac{b \cdot \log c}{a}}\right)\right)\right) + y \cdot i \]
   7. Step-by-step derivation

      1. *-commutative 44.2%

         \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \frac{\color{blue}{\log c \cdot b}}{a}\right)\right)\right) + y \cdot i \]

   8. Simplified 44.2%

      \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \color{blue}{\frac{\log c \cdot b}{a}}\right)\right)\right) + y \cdot i \]

   9. Taylor expanded in z around inf 75.0%

      \[\leadsto \color{blue}{z \cdot \left(1 + \frac{a \cdot \left(1 + \left(\frac{t}{a} + \frac{b \cdot \log c}{a}\right)\right)}{z}\right)} + y \cdot i \]
   10. Step-by-step derivation

       1. associate-/l* 75.0%

          \[\leadsto z \cdot \left(1 + \color{blue}{a \cdot \frac{1 + \left(\frac{t}{a} + \frac{b \cdot \log c}{a}\right)}{z}}\right) + y \cdot i \]

       2. *-commutative 75.0%

          \[\leadsto z \cdot \left(1 + a \cdot \frac{1 + \left(\frac{t}{a} + \frac{\color{blue}{\log c \cdot b}}{a}\right)}{z}\right) + y \cdot i \]

       3. associate-*r/ 75.0%

          \[\leadsto z \cdot \left(1 + a \cdot \frac{1 + \left(\frac{t}{a} + \color{blue}{\log c \cdot \frac{b}{a}}\right)}{z}\right) + y \cdot i \]

   11. Simplified 75.0%

       \[\leadsto \color{blue}{z \cdot \left(1 + a \cdot \frac{1 + \left(\frac{t}{a} + \log c \cdot \frac{b}{a}\right)}{z}\right)} + y \cdot i \]

   12. Taylor expanded in a around inf 76.5%

       \[\leadsto z \cdot \left(1 + a \cdot \color{blue}{\frac{1}{z}}\right) + y \cdot i \]

   if -3.0999999999999999e143 < 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 74.5%

      \[\leadsto \color{blue}{a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(\frac{x \cdot \log y}{a} + \frac{\log c \cdot \left(b - 0.5\right)}{a}\right)\right)\right)\right)} + y \cdot i \]
   4. Step-by-step derivation

      1. associate-/l* 74.5%

         \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(\color{blue}{x \cdot \frac{\log y}{a}} + \frac{\log c \cdot \left(b - 0.5\right)}{a}\right)\right)\right)\right) + y \cdot i \]

      2. sub-neg 74.5%

         \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(x \cdot \frac{\log y}{a} + \frac{\log c \cdot \color{blue}{\left(b + \left(-0.5\right)\right)}}{a}\right)\right)\right)\right) + y \cdot i \]

      3. metadata-eval 74.5%

         \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(x \cdot \frac{\log y}{a} + \frac{\log c \cdot \left(b + \color{blue}{-0.5}\right)}{a}\right)\right)\right)\right) + y \cdot i \]

   5. Simplified 74.5%

      \[\leadsto \color{blue}{a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(x \cdot \frac{\log y}{a} + \frac{\log c \cdot \left(b + -0.5\right)}{a}\right)\right)\right)\right)} + y \cdot i \]

   6. Taylor expanded in z around inf 51.2%

      \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \color{blue}{\frac{z}{a}}\right)\right) + y \cdot i \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+143}:\\ \;\;\;\;y \cdot i + z \cdot \left(a \cdot \frac{1}{z} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + a \cdot \left(\left(\frac{t}{a} + \frac{z}{a}\right) + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 49.5% accurate, 13.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+143}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + a \cdot \left(\frac{t}{a} + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -2.25e+143) (+ z (* y i)) (+ (* y i) (* a (+ (/ t a) 1.0)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -2.25e+143) {
		tmp = z + (y * i);
	} else {
		tmp = (y * i) + (a * ((t / a) + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-2.25d+143)) then
        tmp = z + (y * i)
    else
        tmp = (y * i) + (a * ((t / a) + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -2.25e+143) {
		tmp = z + (y * i);
	} else {
		tmp = (y * i) + (a * ((t / a) + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -2.25e+143:
		tmp = z + (y * i)
	else:
		tmp = (y * i) + (a * ((t / a) + 1.0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -2.25e+143)
		tmp = Float64(z + Float64(y * i));
	else
		tmp = Float64(Float64(y * i) + Float64(a * Float64(Float64(t / a) + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -2.25e+143)
		tmp = z + (y * i);
	else
		tmp = (y * i) + (a * ((t / a) + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -2.25e+143], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a * N[(N[(t / a), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2499999999999998e143

   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 -inf 68.3%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \log y + -1 \cdot \frac{a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)}{x}\right)\right)} + y \cdot i \]
   4. Step-by-step derivation

      1. mul-1-neg 68.3%

         \[\leadsto \color{blue}{\left(-x \cdot \left(-1 \cdot \log y + -1 \cdot \frac{a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)}{x}\right)\right)} + y \cdot i \]

      2. distribute-lft-out 68.3%

         \[\leadsto \left(-x \cdot \color{blue}{\left(-1 \cdot \left(\log y + \frac{a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)}{x}\right)\right)}\right) + y \cdot i \]

      3. sub-neg 68.3%

         \[\leadsto \left(-x \cdot \left(-1 \cdot \left(\log y + \frac{a + \left(t + \left(z + \log c \cdot \color{blue}{\left(b + \left(-0.5\right)\right)}\right)\right)}{x}\right)\right)\right) + y \cdot i \]

      4. metadata-eval 68.3%

         \[\leadsto \left(-x \cdot \left(-1 \cdot \left(\log y + \frac{a + \left(t + \left(z + \log c \cdot \left(b + \color{blue}{-0.5}\right)\right)\right)}{x}\right)\right)\right) + y \cdot i \]

   5. Simplified 68.3%

      \[\leadsto \color{blue}{\left(-x \cdot \left(-1 \cdot \left(\log y + \frac{a + \left(t + \left(z + \log c \cdot \left(b + -0.5\right)\right)\right)}{x}\right)\right)\right)} + y \cdot i \]

   6. Taylor expanded in z around inf 66.3%

      \[\leadsto \left(-\color{blue}{-1 \cdot z}\right) + y \cdot i \]
   7. Step-by-step derivation

      1. mul-1-neg 66.3%

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

   8. Simplified 66.3%

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

   if -2.2499999999999998e143 < 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 74.4%

      \[\leadsto \color{blue}{a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(\frac{x \cdot \log y}{a} + \frac{\log c \cdot \left(b - 0.5\right)}{a}\right)\right)\right)\right)} + y \cdot i \]
   4. Step-by-step derivation

      1. associate-/l* 74.4%

         \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(\color{blue}{x \cdot \frac{\log y}{a}} + \frac{\log c \cdot \left(b - 0.5\right)}{a}\right)\right)\right)\right) + y \cdot i \]

      2. sub-neg 74.4%

         \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(x \cdot \frac{\log y}{a} + \frac{\log c \cdot \color{blue}{\left(b + \left(-0.5\right)\right)}}{a}\right)\right)\right)\right) + y \cdot i \]

      3. metadata-eval 74.4%

         \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(x \cdot \frac{\log y}{a} + \frac{\log c \cdot \left(b + \color{blue}{-0.5}\right)}{a}\right)\right)\right)\right) + y \cdot i \]

   5. Simplified 74.4%

      \[\leadsto \color{blue}{a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(x \cdot \frac{\log y}{a} + \frac{\log c \cdot \left(b + -0.5\right)}{a}\right)\right)\right)\right)} + y \cdot i \]

   6. Taylor expanded in b around inf 64.3%

      \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \color{blue}{\frac{b \cdot \log c}{a}}\right)\right)\right) + y \cdot i \]
   7. Step-by-step derivation

      1. *-commutative 64.3%

         \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \frac{\color{blue}{\log c \cdot b}}{a}\right)\right)\right) + y \cdot i \]

   8. Simplified 64.3%

      \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \color{blue}{\frac{\log c \cdot b}{a}}\right)\right)\right) + y \cdot i \]

   9. Taylor expanded in z around 0 56.1%

      \[\leadsto \color{blue}{a \cdot \left(1 + \left(\frac{t}{a} + \frac{b \cdot \log c}{a}\right)\right)} + y \cdot i \]
   10. Step-by-step derivation

       1. *-commutative 56.1%

          \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \frac{\color{blue}{\log c \cdot b}}{a}\right)\right) + y \cdot i \]

       2. associate-*r/ 56.1%

          \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \color{blue}{\log c \cdot \frac{b}{a}}\right)\right) + y \cdot i \]

   11. Simplified 56.1%

       \[\leadsto \color{blue}{a \cdot \left(1 + \left(\frac{t}{a} + \log c \cdot \frac{b}{a}\right)\right)} + y \cdot i \]

   12. Taylor expanded in b around 0 43.5%

       \[\leadsto \color{blue}{a \cdot \left(1 + \frac{t}{a}\right)} + y \cdot i \]
3. Recombined 2 regimes into one program.

4. Final simplification 46.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+143}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + a \cdot \left(\frac{t}{a} + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 50.9% accurate, 13.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -860000000:\\ \;\;\;\;y \cdot i + z \cdot \left(\frac{a}{z} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + a \cdot \left(\frac{t}{a} + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -860000000.0)
   (+ (* y i) (* z (+ (/ a z) 1.0)))
   (+ (* y i) (* a (+ (/ t a) 1.0)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -860000000.0) {
		tmp = (y * i) + (z * ((a / z) + 1.0));
	} else {
		tmp = (y * i) + (a * ((t / a) + 1.0));
	}
	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 <= (-860000000.0d0)) then
        tmp = (y * i) + (z * ((a / z) + 1.0d0))
    else
        tmp = (y * i) + (a * ((t / a) + 1.0d0))
    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 <= -860000000.0) {
		tmp = (y * i) + (z * ((a / z) + 1.0));
	} else {
		tmp = (y * i) + (a * ((t / a) + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -860000000.0:
		tmp = (y * i) + (z * ((a / z) + 1.0))
	else:
		tmp = (y * i) + (a * ((t / a) + 1.0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -860000000.0)
		tmp = Float64(Float64(y * i) + Float64(z * Float64(Float64(a / z) + 1.0)));
	else
		tmp = Float64(Float64(y * i) + Float64(a * Float64(Float64(t / a) + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -860000000.0)
		tmp = (y * i) + (z * ((a / z) + 1.0));
	else
		tmp = (y * i) + (a * ((t / a) + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -860000000.0], N[(N[(y * i), $MachinePrecision] + N[(z * N[(N[(a / z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a * N[(N[(t / a), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.6e8

   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 99.8%

      \[\leadsto \color{blue}{z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(\frac{x \cdot \log y}{z} + \frac{\log c \cdot \left(b - 0.5\right)}{z}\right)\right)\right)\right)} + y \cdot i \]
   4. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(\color{blue}{x \cdot \frac{\log y}{z}} + \frac{\log c \cdot \left(b - 0.5\right)}{z}\right)\right)\right)\right) + y \cdot i \]

      2. sub-neg 99.8%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \frac{\log c \cdot \color{blue}{\left(b + \left(-0.5\right)\right)}}{z}\right)\right)\right)\right) + y \cdot i \]

      3. metadata-eval 99.8%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \frac{\log c \cdot \left(b + \color{blue}{-0.5}\right)}{z}\right)\right)\right)\right) + y \cdot i \]

      4. associate-/l* 99.8%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \color{blue}{\log c \cdot \frac{b + -0.5}{z}}\right)\right)\right)\right) + y \cdot i \]

   5. Simplified 99.8%

      \[\leadsto \color{blue}{z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \log c \cdot \frac{b + -0.5}{z}\right)\right)\right)\right)} + y \cdot i \]

   6. Taylor expanded in a around inf 69.7%

      \[\leadsto z \cdot \left(1 + \color{blue}{\frac{a}{z}}\right) + y \cdot i \]

   if -8.6e8 < z

   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 a around inf 74.0%

      \[\leadsto \color{blue}{a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(\frac{x \cdot \log y}{a} + \frac{\log c \cdot \left(b - 0.5\right)}{a}\right)\right)\right)\right)} + y \cdot i \]
   4. Step-by-step derivation

      1. associate-/l* 74.0%

         \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(\color{blue}{x \cdot \frac{\log y}{a}} + \frac{\log c \cdot \left(b - 0.5\right)}{a}\right)\right)\right)\right) + y \cdot i \]

      2. sub-neg 74.0%

         \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(x \cdot \frac{\log y}{a} + \frac{\log c \cdot \color{blue}{\left(b + \left(-0.5\right)\right)}}{a}\right)\right)\right)\right) + y \cdot i \]

      3. metadata-eval 74.0%

         \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(x \cdot \frac{\log y}{a} + \frac{\log c \cdot \left(b + \color{blue}{-0.5}\right)}{a}\right)\right)\right)\right) + y \cdot i \]

   5. Simplified 74.0%

      \[\leadsto \color{blue}{a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \left(x \cdot \frac{\log y}{a} + \frac{\log c \cdot \left(b + -0.5\right)}{a}\right)\right)\right)\right)} + y \cdot i \]

   6. Taylor expanded in b around inf 62.4%

      \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \color{blue}{\frac{b \cdot \log c}{a}}\right)\right)\right) + y \cdot i \]
   7. Step-by-step derivation

      1. *-commutative 62.4%

         \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \frac{\color{blue}{\log c \cdot b}}{a}\right)\right)\right) + y \cdot i \]

   8. Simplified 62.4%

      \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \color{blue}{\frac{\log c \cdot b}{a}}\right)\right)\right) + y \cdot i \]

   9. Taylor expanded in z around 0 54.2%

      \[\leadsto \color{blue}{a \cdot \left(1 + \left(\frac{t}{a} + \frac{b \cdot \log c}{a}\right)\right)} + y \cdot i \]
   10. Step-by-step derivation

       1. *-commutative 54.2%

          \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \frac{\color{blue}{\log c \cdot b}}{a}\right)\right) + y \cdot i \]

       2. associate-*r/ 54.2%

          \[\leadsto a \cdot \left(1 + \left(\frac{t}{a} + \color{blue}{\log c \cdot \frac{b}{a}}\right)\right) + y \cdot i \]

   11. Simplified 54.2%

       \[\leadsto \color{blue}{a \cdot \left(1 + \left(\frac{t}{a} + \log c \cdot \frac{b}{a}\right)\right)} + y \cdot i \]

   12. Taylor expanded in b around 0 42.1%

       \[\leadsto \color{blue}{a \cdot \left(1 + \frac{t}{a}\right)} + y \cdot i \]
3. Recombined 2 regimes into one program.

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -860000000:\\ \;\;\;\;y \cdot i + z \cdot \left(\frac{a}{z} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + a \cdot \left(\frac{t}{a} + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 42.8% accurate, 21.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+149}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -8.2e+149) (+ z (* y i)) (+ a (* y i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -8.2e+149) {
		tmp = z + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-8.2d+149)) then
        tmp = z + (y * i)
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -8.2e+149) {
		tmp = z + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -8.2e+149:
		tmp = z + (y * i)
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -8.2e+149)
		tmp = Float64(z + Float64(y * i));
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -8.2e+149)
		tmp = z + (y * i);
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -8.2e+149], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.1999999999999992e149

   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 -inf 67.2%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \log y + -1 \cdot \frac{a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)}{x}\right)\right)} + y \cdot i \]
   4. Step-by-step derivation

      1. mul-1-neg 67.2%

         \[\leadsto \color{blue}{\left(-x \cdot \left(-1 \cdot \log y + -1 \cdot \frac{a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)}{x}\right)\right)} + y \cdot i \]

      2. distribute-lft-out 67.2%

         \[\leadsto \left(-x \cdot \color{blue}{\left(-1 \cdot \left(\log y + \frac{a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)}{x}\right)\right)}\right) + y \cdot i \]

      3. sub-neg 67.2%

         \[\leadsto \left(-x \cdot \left(-1 \cdot \left(\log y + \frac{a + \left(t + \left(z + \log c \cdot \color{blue}{\left(b + \left(-0.5\right)\right)}\right)\right)}{x}\right)\right)\right) + y \cdot i \]

      4. metadata-eval 67.2%

         \[\leadsto \left(-x \cdot \left(-1 \cdot \left(\log y + \frac{a + \left(t + \left(z + \log c \cdot \left(b + \color{blue}{-0.5}\right)\right)\right)}{x}\right)\right)\right) + y \cdot i \]

   5. Simplified 67.2%

      \[\leadsto \color{blue}{\left(-x \cdot \left(-1 \cdot \left(\log y + \frac{a + \left(t + \left(z + \log c \cdot \left(b + -0.5\right)\right)\right)}{x}\right)\right)\right)} + y \cdot i \]

   6. Taylor expanded in z around inf 68.3%

      \[\leadsto \left(-\color{blue}{-1 \cdot z}\right) + y \cdot i \]
   7. Step-by-step derivation

      1. mul-1-neg 68.3%

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

   8. Simplified 68.3%

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

   if -8.1999999999999992e149 < 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 -inf 74.7%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \log y + -1 \cdot \frac{a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)}{x}\right)\right)} + y \cdot i \]
   4. Step-by-step derivation

      1. mul-1-neg 74.7%

         \[\leadsto \color{blue}{\left(-x \cdot \left(-1 \cdot \log y + -1 \cdot \frac{a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)}{x}\right)\right)} + y \cdot i \]

      2. distribute-lft-out 74.7%

         \[\leadsto \left(-x \cdot \color{blue}{\left(-1 \cdot \left(\log y + \frac{a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)}{x}\right)\right)}\right) + y \cdot i \]

      3. sub-neg 74.7%

         \[\leadsto \left(-x \cdot \left(-1 \cdot \left(\log y + \frac{a + \left(t + \left(z + \log c \cdot \color{blue}{\left(b + \left(-0.5\right)\right)}\right)\right)}{x}\right)\right)\right) + y \cdot i \]

      4. metadata-eval 74.7%

         \[\leadsto \left(-x \cdot \left(-1 \cdot \left(\log y + \frac{a + \left(t + \left(z + \log c \cdot \left(b + \color{blue}{-0.5}\right)\right)\right)}{x}\right)\right)\right) + y \cdot i \]

   5. Simplified 74.7%

      \[\leadsto \color{blue}{\left(-x \cdot \left(-1 \cdot \left(\log y + \frac{a + \left(t + \left(z + \log c \cdot \left(b + -0.5\right)\right)\right)}{x}\right)\right)\right)} + y \cdot i \]

   6. Taylor expanded in a around inf 39.3%

      \[\leadsto \left(-\color{blue}{-1 \cdot a}\right) + y \cdot i \]
   7. Step-by-step derivation

      1. mul-1-neg 39.3%

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

   8. Simplified 39.3%

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

4. Final simplification 42.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+149}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 21.1% accurate, 36.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 4.5 \cdot 10^{+131}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (if (<= a 4.5e+131) 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 <= 4.5e+131) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 4.5d+131) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 4.5e+131) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 4.5e+131:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 4.5e+131)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 4.5e+131)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 4.5e+131], z, a]

Derivation

1. Split input into 2 regimes

2. if a < 4.5000000000000002e131

   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 z around inf 17.7%

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

   if 4.5000000000000002e131 < a

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf 50.1%

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

4. Final simplification 23.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 4.5 \cdot 10^{+131}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 16.0% accurate, 219.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

3. Taylor expanded in a around inf 17.0%

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

4. Final simplification 17.0%

   \[\leadsto a \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024076 
(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)))