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

Percentage Accurate: 99.8% → 99.8%

Time: 17.6s

Alternatives: 22

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

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (fma y i (fma (+ b -0.5) (log c) (+ z (+ t (fma x (log y) 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 + (t + fma(x, log(y), 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 + Float64(t + fma(x, log(y), 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[(t + N[(x * N[Log[y], $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

   1. associate-+l+ 99.9%

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

   2. +-commutative 99.9%

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

   3. associate-+l+ 99.9%

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

   4. associate-+r+ 99.9%

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

   5. +-commutative 99.9%

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

   6. +-commutative 99.9%

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

   7. associate-+l+ 99.9%

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

   8. associate-+l+ 99.9%

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

   9. +-commutative 99.9%

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

   10. fma-define 99.9%

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

   11. +-commutative 99.9%

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

   12. fma-define 99.9%

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

   13. sub-neg 99.9%

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

   14. metadata-eval 99.9%

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

   15. +-commutative 99.9%

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

3. Simplified 99.9%

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

Alternative 2: 90.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -9 \cdot 10^{+152}:\\ \;\;\;\;a + \left(t\_1 + y \cdot i\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+141}:\\ \;\;\;\;\left(z + \left(t + a\right)\right) + \mathsf{fma}\left(\log c, b + -0.5, y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t\_1 + b \cdot \log c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -9e+152)
     (+ a (+ t_1 (* y i)))
     (if (<= x 5e+141)
       (+ (+ z (+ t a)) (fma (log c) (+ b -0.5) (* y i)))
       (+ (* y i) (+ t_1 (* b (log c))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * log(y);
	double tmp;
	if (x <= -9e+152) {
		tmp = a + (t_1 + (y * i));
	} else if (x <= 5e+141) {
		tmp = (z + (t + a)) + fma(log(c), (b + -0.5), (y * i));
	} else {
		tmp = (y * i) + (t_1 + (b * log(c)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -9e+152)
		tmp = Float64(a + Float64(t_1 + Float64(y * i)));
	elseif (x <= 5e+141)
		tmp = Float64(Float64(z + Float64(t + a)) + fma(log(c), Float64(b + -0.5), Float64(y * i)));
	else
		tmp = Float64(Float64(y * i) + Float64(t_1 + Float64(b * log(c))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9e+152], N[(a + N[(t$95$1 + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5e+141], N[(N[(z + N[(t + a), $MachinePrecision]), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(t$95$1 + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.0000000000000002e152

   1. Initial program 99.7%

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

      1. associate-+l+ 99.7%

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

      2. +-commutative 99.7%

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

      3. associate-+l+ 99.7%

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

      4. associate-+r+ 99.7%

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

      5. +-commutative 99.7%

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

      6. +-commutative 99.7%

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

      7. associate-+l+ 99.7%

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

      8. associate-+l+ 99.7%

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

      9. +-commutative 99.7%

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

      10. fma-define 99.7%

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

      11. +-commutative 99.7%

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

      12. fma-define 99.7%

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

      13. sub-neg 99.7%

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

      14. metadata-eval 99.7%

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

      15. +-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 62.4%

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

   6. Taylor expanded in a around inf 54.3%

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

   7. Taylor expanded in y around 0 85.1%

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

   if -9.0000000000000002e152 < x < 5.00000000000000025e141

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. associate-+r+ 99.9%

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

      5. +-commutative 99.9%

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

      6. +-commutative 99.9%

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

      7. associate-+l+ 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-define 99.9%

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

      13. sub-neg 99.9%

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

      14. metadata-eval 99.9%

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

      15. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 94.7%

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

      1. associate-+r+ 94.7%

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

      2. +-commutative 94.7%

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

      3. *-commutative 94.7%

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

      4. sub-neg 94.7%

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

      5. metadata-eval 94.7%

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

      6. +-commutative 94.7%

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

      7. distribute-rgt-out 94.7%

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

      8. +-commutative 94.7%

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

      9. distribute-rgt-in 94.7%

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

      10. associate-+r+ 94.7%

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

      11. +-commutative 94.7%

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

      12. +-commutative 94.7%

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

      13. +-commutative 94.7%

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

      14. fma-define 94.7%

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

      15. +-commutative 94.7%

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

   7. Simplified 94.7%

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

   if 5.00000000000000025e141 < x

   1. Initial program 99.9%

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

      1. add-cube-cbrt 99.6%

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

      2. pow3 99.6%

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

      3. sub-neg 99.6%

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

      4. metadata-eval 99.6%

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

      5. *-commutative 99.6%

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in b around inf 99.9%

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

      1. *-commutative 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in t around 0 91.4%

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

   9. Taylor expanded in x around inf 83.0%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+152}:\\ \;\;\;\;a + \left(x \cdot \log y + y \cdot i\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+141}:\\ \;\;\;\;\left(z + \left(t + a\right)\right) + \mathsf{fma}\left(\log c, b + -0.5, y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + b \cdot \log c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -2.9 \cdot 10^{+153}:\\ \;\;\;\;a + \left(t\_1 + y \cdot i\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+141}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t\_1 + b \cdot \log c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -2.9e+153)
     (+ a (+ t_1 (* y i)))
     (if (<= x 5e+141)
       (+ (* y i) (+ (* (log c) (- b 0.5)) (+ a (+ z t))))
       (+ (* y i) (+ t_1 (* b (log c))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * log(y);
	double tmp;
	if (x <= -2.9e+153) {
		tmp = a + (t_1 + (y * i));
	} else if (x <= 5e+141) {
		tmp = (y * i) + ((log(c) * (b - 0.5)) + (a + (z + t)));
	} else {
		tmp = (y * i) + (t_1 + (b * log(c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * log(y)
    if (x <= (-2.9d+153)) then
        tmp = a + (t_1 + (y * i))
    else if (x <= 5d+141) then
        tmp = (y * i) + ((log(c) * (b - 0.5d0)) + (a + (z + t)))
    else
        tmp = (y * i) + (t_1 + (b * log(c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * Math.log(y);
	double tmp;
	if (x <= -2.9e+153) {
		tmp = a + (t_1 + (y * i));
	} else if (x <= 5e+141) {
		tmp = (y * i) + ((Math.log(c) * (b - 0.5)) + (a + (z + t)));
	} else {
		tmp = (y * i) + (t_1 + (b * Math.log(c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x * math.log(y)
	tmp = 0
	if x <= -2.9e+153:
		tmp = a + (t_1 + (y * i))
	elif x <= 5e+141:
		tmp = (y * i) + ((math.log(c) * (b - 0.5)) + (a + (z + t)))
	else:
		tmp = (y * i) + (t_1 + (b * math.log(c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -2.9e+153)
		tmp = Float64(a + Float64(t_1 + Float64(y * i)));
	elseif (x <= 5e+141)
		tmp = Float64(Float64(y * i) + Float64(Float64(log(c) * Float64(b - 0.5)) + Float64(a + Float64(z + t))));
	else
		tmp = Float64(Float64(y * i) + Float64(t_1 + Float64(b * log(c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x * log(y);
	tmp = 0.0;
	if (x <= -2.9e+153)
		tmp = a + (t_1 + (y * i));
	elseif (x <= 5e+141)
		tmp = (y * i) + ((log(c) * (b - 0.5)) + (a + (z + t)));
	else
		tmp = (y * i) + (t_1 + (b * log(c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.9e+153], N[(a + N[(t$95$1 + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5e+141], N[(N[(y * i), $MachinePrecision] + N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(t$95$1 + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.90000000000000002e153

   1. Initial program 99.7%

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

      1. associate-+l+ 99.7%

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

      2. +-commutative 99.7%

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

      3. associate-+l+ 99.7%

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

      4. associate-+r+ 99.7%

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

      5. +-commutative 99.7%

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

      6. +-commutative 99.7%

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

      7. associate-+l+ 99.7%

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

      8. associate-+l+ 99.7%

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

      9. +-commutative 99.7%

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

      10. fma-define 99.7%

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

      11. +-commutative 99.7%

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

      12. fma-define 99.7%

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

      13. sub-neg 99.7%

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

      14. metadata-eval 99.7%

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

      15. +-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 62.4%

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

   6. Taylor expanded in a around inf 54.3%

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

   7. Taylor expanded in y around 0 85.1%

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

   if -2.90000000000000002e153 < x < 5.00000000000000025e141

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 94.7%

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

   if 5.00000000000000025e141 < x

   1. Initial program 99.9%

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

      1. add-cube-cbrt 99.6%

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

      2. pow3 99.6%

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

      3. sub-neg 99.6%

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

      4. metadata-eval 99.6%

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

      5. *-commutative 99.6%

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in b around inf 99.9%

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

      1. *-commutative 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in t around 0 91.4%

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

   9. Taylor expanded in x around inf 83.0%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+153}:\\ \;\;\;\;a + \left(x \cdot \log y + y \cdot i\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+141}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + b \cdot \log c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 5: 75.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 9 \cdot 10^{+71}:\\ \;\;\;\;y \cdot i + \left(\left(z + x \cdot \log y\right) + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 9e+71)
   (+ (* y i) (+ (+ z (* x (log y))) (* b (log c))))
   (fma y i (+ a (+ t (+ z (* (log c) (- b 0.5))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 9e+71) {
		tmp = (y * i) + ((z + (x * log(y))) + (b * log(c)));
	} else {
		tmp = fma(y, i, (a + (t + (z + (log(c) * (b - 0.5))))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 9e+71)
		tmp = Float64(Float64(y * i) + Float64(Float64(z + Float64(x * log(y))) + Float64(b * log(c))));
	else
		tmp = fma(y, i, Float64(a + Float64(t + Float64(z + Float64(log(c) * Float64(b - 0.5))))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 9e+71], N[(N[(y * i), $MachinePrecision] + N[(N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * i + N[(a + N[(t + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 9.00000000000000087e71

   1. Initial program 99.9%

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

      1. add-cube-cbrt 99.6%

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

      2. pow3 99.6%

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

      3. sub-neg 99.6%

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

      4. metadata-eval 99.6%

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

      5. *-commutative 99.6%

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in b around inf 98.2%

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

      1. *-commutative 98.2%

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

   7. Simplified 98.2%

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

   8. Taylor expanded in t around 0 83.1%

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

   9. Taylor expanded in a around 0 70.6%

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

   if 9.00000000000000087e71 < a

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. associate-+r+ 99.9%

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

      5. +-commutative 99.9%

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

      6. +-commutative 99.9%

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

      7. associate-+l+ 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-define 99.9%

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

      13. sub-neg 99.9%

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

      14. metadata-eval 99.9%

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

      15. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 94.5%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 9 \cdot 10^{+71}:\\ \;\;\;\;y \cdot i + \left(\left(z + x \cdot \log y\right) + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \log c\\ \mathbf{if}\;a \leq 3 \cdot 10^{+73}:\\ \;\;\;\;y \cdot i + \left(\left(z + x \cdot \log y\right) + t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t\_1 + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* b (log c))))
   (if (<= a 3e+73)
     (+ (* y i) (+ (+ z (* x (log y))) t_1))
     (+ (* y i) (+ t_1 (+ a (+ z t)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = b * log(c);
	double tmp;
	if (a <= 3e+73) {
		tmp = (y * i) + ((z + (x * log(y))) + t_1);
	} else {
		tmp = (y * i) + (t_1 + (a + (z + t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * log(c)
    if (a <= 3d+73) then
        tmp = (y * i) + ((z + (x * log(y))) + t_1)
    else
        tmp = (y * i) + (t_1 + (a + (z + t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = b * Math.log(c);
	double tmp;
	if (a <= 3e+73) {
		tmp = (y * i) + ((z + (x * Math.log(y))) + t_1);
	} else {
		tmp = (y * i) + (t_1 + (a + (z + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = b * math.log(c)
	tmp = 0
	if a <= 3e+73:
		tmp = (y * i) + ((z + (x * math.log(y))) + t_1)
	else:
		tmp = (y * i) + (t_1 + (a + (z + t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(b * log(c))
	tmp = 0.0
	if (a <= 3e+73)
		tmp = Float64(Float64(y * i) + Float64(Float64(z + Float64(x * log(y))) + t_1));
	else
		tmp = Float64(Float64(y * i) + Float64(t_1 + Float64(a + Float64(z + t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = b * log(c);
	tmp = 0.0;
	if (a <= 3e+73)
		tmp = (y * i) + ((z + (x * log(y))) + t_1);
	else
		tmp = (y * i) + (t_1 + (a + (z + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, 3e+73], N[(N[(y * i), $MachinePrecision] + N[(N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(t$95$1 + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < 3.00000000000000011e73

   1. Initial program 99.9%

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

      1. add-cube-cbrt 99.6%

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

      2. pow3 99.6%

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

      3. sub-neg 99.6%

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

      4. metadata-eval 99.6%

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

      5. *-commutative 99.6%

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in b around inf 98.2%

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

      1. *-commutative 98.2%

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

   7. Simplified 98.2%

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

   8. Taylor expanded in t around 0 83.1%

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

   9. Taylor expanded in a around 0 70.6%

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

   if 3.00000000000000011e73 < 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. Step-by-step derivation

      1. add-cube-cbrt 99.8%

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

      2. pow3 99.8%

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

      3. sub-neg 99.8%

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

      4. metadata-eval 99.8%

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

      5. *-commutative 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in b around inf 99.9%

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

      1. *-commutative 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in x around 0 94.4%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 3 \cdot 10^{+73}:\\ \;\;\;\;y \cdot i + \left(\left(z + x \cdot \log y\right) + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(b \cdot \log c + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.1% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (+ (* y i) (+ (* (log c) (- b 0.5)) (+ a (+ z (* 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 + (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 + (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 + (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 + (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(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 + (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[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in t around 0 86.4%

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

4. Final simplification 86.4%

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

Alternative 8: 82.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. add-cube-cbrt 99.7%

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

   2. pow3 99.6%

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

   3. sub-neg 99.6%

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

   4. metadata-eval 99.6%

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

   5. *-commutative 99.6%

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

4. Applied egg-rr 99.6%

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

5. Taylor expanded in b around inf 98.6%

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

   1. *-commutative 98.6%

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

7. Simplified 98.6%

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

8. Taylor expanded in t around 0 85.1%

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

9. Final simplification 85.1%

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

Alternative 9: 56.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+264}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+135}:\\ \;\;\;\;y \cdot \left(i + \left(\frac{a}{y} + \left(\frac{t}{y} + \frac{z}{y}\right)\right)\right)\\ \mathbf{elif}\;z \leq -8 \cdot 10^{+69} \lor \neg \left(z \leq -1400000000000\right) \land z \leq -1.1 \cdot 10^{-131}:\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(x \cdot \log y + y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -2.2e+264)
   z
   (if (<= z -3e+135)
     (* y (+ i (+ (/ a y) (+ (/ t y) (/ z y)))))
     (if (or (<= z -8e+69)
             (and (not (<= z -1400000000000.0)) (<= z -1.1e-131)))
       (+ (* y i) (+ a (* b (log c))))
       (+ a (+ (* x (log y)) (* 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 <= -2.2e+264) {
		tmp = z;
	} else if (z <= -3e+135) {
		tmp = y * (i + ((a / y) + ((t / y) + (z / y))));
	} else if ((z <= -8e+69) || (!(z <= -1400000000000.0) && (z <= -1.1e-131))) {
		tmp = (y * i) + (a + (b * log(c)));
	} else {
		tmp = a + ((x * log(y)) + (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 <= (-2.2d+264)) then
        tmp = z
    else if (z <= (-3d+135)) then
        tmp = y * (i + ((a / y) + ((t / y) + (z / y))))
    else if ((z <= (-8d+69)) .or. (.not. (z <= (-1400000000000.0d0))) .and. (z <= (-1.1d-131))) then
        tmp = (y * i) + (a + (b * log(c)))
    else
        tmp = a + ((x * log(y)) + (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 <= -2.2e+264) {
		tmp = z;
	} else if (z <= -3e+135) {
		tmp = y * (i + ((a / y) + ((t / y) + (z / y))));
	} else if ((z <= -8e+69) || (!(z <= -1400000000000.0) && (z <= -1.1e-131))) {
		tmp = (y * i) + (a + (b * Math.log(c)));
	} else {
		tmp = a + ((x * Math.log(y)) + (y * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -2.2e+264:
		tmp = z
	elif z <= -3e+135:
		tmp = y * (i + ((a / y) + ((t / y) + (z / y))))
	elif (z <= -8e+69) or (not (z <= -1400000000000.0) and (z <= -1.1e-131)):
		tmp = (y * i) + (a + (b * math.log(c)))
	else:
		tmp = a + ((x * math.log(y)) + (y * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -2.2e+264)
		tmp = z;
	elseif (z <= -3e+135)
		tmp = Float64(y * Float64(i + Float64(Float64(a / y) + Float64(Float64(t / y) + Float64(z / y)))));
	elseif ((z <= -8e+69) || (!(z <= -1400000000000.0) && (z <= -1.1e-131)))
		tmp = Float64(Float64(y * i) + Float64(a + Float64(b * log(c))));
	else
		tmp = Float64(a + Float64(Float64(x * log(y)) + 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 <= -2.2e+264)
		tmp = z;
	elseif (z <= -3e+135)
		tmp = y * (i + ((a / y) + ((t / y) + (z / y))));
	elseif ((z <= -8e+69) || (~((z <= -1400000000000.0)) && (z <= -1.1e-131)))
		tmp = (y * i) + (a + (b * log(c)));
	else
		tmp = a + ((x * log(y)) + (y * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -2.2e+264], z, If[LessEqual[z, -3e+135], N[(y * N[(i + N[(N[(a / y), $MachinePrecision] + N[(N[(t / y), $MachinePrecision] + N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -8e+69], And[N[Not[LessEqual[z, -1400000000000.0]], $MachinePrecision], LessEqual[z, -1.1e-131]]], N[(N[(y * i), $MachinePrecision] + N[(a + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.2e264

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+l+ 100.0%

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

      4. associate-+r+ 100.0%

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

      5. +-commutative 100.0%

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

      6. +-commutative 100.0%

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

      7. associate-+l+ 100.0%

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

      8. associate-+l+ 100.0%

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

      9. +-commutative 100.0%

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

      10. fma-define 100.0%

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

      11. +-commutative 100.0%

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

      12. fma-define 100.0%

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

      13. sub-neg 100.0%

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

      14. metadata-eval 100.0%

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

      15. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 100.0%

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

   6. Taylor expanded in z around inf 88.7%

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

   if -2.2e264 < z < -3e135

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. associate-+r+ 99.9%

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

      5. +-commutative 99.9%

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

      6. +-commutative 99.9%

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

      7. associate-+l+ 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-define 99.9%

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

      13. sub-neg 99.9%

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

      14. metadata-eval 99.9%

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

      15. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 88.3%

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

   6. Taylor expanded in y around inf 69.1%

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

   7. Taylor expanded in z around inf 65.4%

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

   if -3e135 < z < -8.0000000000000006e69 or -1.4e12 < z < -1.1e-131

   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. Step-by-step derivation

      1. add-cube-cbrt 99.1%

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

      2. pow3 99.1%

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

      3. sub-neg 99.1%

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

      4. metadata-eval 99.1%

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

      5. *-commutative 99.1%

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

   4. Applied egg-rr 99.1%

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

   5. Taylor expanded in b around inf 97.1%

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

      1. *-commutative 97.1%

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

   7. Simplified 97.1%

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

   8. Taylor expanded in a around inf 74.3%

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

   if -8.0000000000000006e69 < z < -1.4e12 or -1.1e-131 < z

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. associate-+r+ 99.9%

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

      5. +-commutative 99.9%

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

      6. +-commutative 99.9%

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

      7. associate-+l+ 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-define 99.9%

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

      13. sub-neg 99.9%

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

      14. metadata-eval 99.9%

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

      15. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 74.3%

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

   6. Taylor expanded in a around inf 50.5%

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

   7. Taylor expanded in y around 0 63.0%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+264}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+135}:\\ \;\;\;\;y \cdot \left(i + \left(\frac{a}{y} + \left(\frac{t}{y} + \frac{z}{y}\right)\right)\right)\\ \mathbf{elif}\;z \leq -8 \cdot 10^{+69} \lor \neg \left(z \leq -1400000000000\right) \land z \leq -1.1 \cdot 10^{-131}:\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(x \cdot \log y + y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 60.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log c \cdot \left(b - 0.5\right)\\ t_2 := a + \left(x \cdot \log y + y \cdot i\right)\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{+72}:\\ \;\;\;\;t + \left(z + \left(t\_1 + y \cdot i\right)\right)\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{+14}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-135}:\\ \;\;\;\;y \cdot i + \left(a + t\_1\right)\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-271}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (log c) (- b 0.5))) (t_2 (+ a (+ (* x (log y)) (* y i)))))
   (if (<= z -1.6e+72)
     (+ t (+ z (+ t_1 (* y i))))
     (if (<= z -1.12e+14)
       t_2
       (if (<= z -6.2e-135)
         (+ (* y i) (+ a t_1))
         (if (<= z -3.5e-271) t_2 (+ (* y i) (+ a (* b (log c))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = log(c) * (b - 0.5);
	double t_2 = a + ((x * log(y)) + (y * i));
	double tmp;
	if (z <= -1.6e+72) {
		tmp = t + (z + (t_1 + (y * i)));
	} else if (z <= -1.12e+14) {
		tmp = t_2;
	} else if (z <= -6.2e-135) {
		tmp = (y * i) + (a + t_1);
	} else if (z <= -3.5e-271) {
		tmp = t_2;
	} else {
		tmp = (y * i) + (a + (b * log(c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = log(c) * (b - 0.5d0)
    t_2 = a + ((x * log(y)) + (y * i))
    if (z <= (-1.6d+72)) then
        tmp = t + (z + (t_1 + (y * i)))
    else if (z <= (-1.12d+14)) then
        tmp = t_2
    else if (z <= (-6.2d-135)) then
        tmp = (y * i) + (a + t_1)
    else if (z <= (-3.5d-271)) then
        tmp = t_2
    else
        tmp = (y * i) + (a + (b * log(c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = Math.log(c) * (b - 0.5);
	double t_2 = a + ((x * Math.log(y)) + (y * i));
	double tmp;
	if (z <= -1.6e+72) {
		tmp = t + (z + (t_1 + (y * i)));
	} else if (z <= -1.12e+14) {
		tmp = t_2;
	} else if (z <= -6.2e-135) {
		tmp = (y * i) + (a + t_1);
	} else if (z <= -3.5e-271) {
		tmp = t_2;
	} else {
		tmp = (y * i) + (a + (b * Math.log(c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = math.log(c) * (b - 0.5)
	t_2 = a + ((x * math.log(y)) + (y * i))
	tmp = 0
	if z <= -1.6e+72:
		tmp = t + (z + (t_1 + (y * i)))
	elif z <= -1.12e+14:
		tmp = t_2
	elif z <= -6.2e-135:
		tmp = (y * i) + (a + t_1)
	elif z <= -3.5e-271:
		tmp = t_2
	else:
		tmp = (y * i) + (a + (b * math.log(c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(log(c) * Float64(b - 0.5))
	t_2 = Float64(a + Float64(Float64(x * log(y)) + Float64(y * i)))
	tmp = 0.0
	if (z <= -1.6e+72)
		tmp = Float64(t + Float64(z + Float64(t_1 + Float64(y * i))));
	elseif (z <= -1.12e+14)
		tmp = t_2;
	elseif (z <= -6.2e-135)
		tmp = Float64(Float64(y * i) + Float64(a + t_1));
	elseif (z <= -3.5e-271)
		tmp = t_2;
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(b * log(c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = log(c) * (b - 0.5);
	t_2 = a + ((x * log(y)) + (y * i));
	tmp = 0.0;
	if (z <= -1.6e+72)
		tmp = t + (z + (t_1 + (y * i)));
	elseif (z <= -1.12e+14)
		tmp = t_2;
	elseif (z <= -6.2e-135)
		tmp = (y * i) + (a + t_1);
	elseif (z <= -3.5e-271)
		tmp = t_2;
	else
		tmp = (y * i) + (a + (b * log(c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.6e+72], N[(t + N[(z + N[(t$95$1 + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.12e+14], t$95$2, If[LessEqual[z, -6.2e-135], N[(N[(y * i), $MachinePrecision] + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.5e-271], t$95$2, N[(N[(y * i), $MachinePrecision] + N[(a + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.6000000000000001e72

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. associate-+r+ 99.9%

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

      5. +-commutative 99.9%

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

      6. +-commutative 99.9%

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

      7. associate-+l+ 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-define 99.9%

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

      13. sub-neg 99.9%

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

      14. metadata-eval 99.9%

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

      15. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 88.7%

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

   6. Taylor expanded in a around 0 77.8%

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

   if -1.6000000000000001e72 < z < -1.12e14 or -6.2000000000000001e-135 < z < -3.4999999999999999e-271

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. associate-+r+ 99.9%

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

      5. +-commutative 99.9%

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

      6. +-commutative 99.9%

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

      7. associate-+l+ 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-define 99.9%

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

      13. sub-neg 99.9%

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

      14. metadata-eval 99.9%

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

      15. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 66.1%

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

   6. Taylor expanded in a around inf 54.0%

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

   7. Taylor expanded in y around 0 74.4%

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

   if -1.12e14 < z < -6.2000000000000001e-135

   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 a around inf 86.1%

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

   if -3.4999999999999999e-271 < z

   1. Initial program 99.9%

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

      1. add-cube-cbrt 99.7%

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

      2. pow3 99.7%

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

      3. sub-neg 99.7%

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

      4. metadata-eval 99.7%

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

      5. *-commutative 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in b around inf 98.3%

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

      1. *-commutative 98.3%

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

   7. Simplified 98.3%

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

   8. Taylor expanded in a around inf 58.4%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+72}:\\ \;\;\;\;t + \left(z + \left(\log c \cdot \left(b - 0.5\right) + y \cdot i\right)\right)\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{+14}:\\ \;\;\;\;a + \left(x \cdot \log y + y \cdot i\right)\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-135}:\\ \;\;\;\;y \cdot i + \left(a + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-271}:\\ \;\;\;\;a + \left(x \cdot \log y + y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \log c\\ t_2 := a + \left(x \cdot \log y + y \cdot i\right)\\ \mathbf{if}\;z \leq -5.5 \cdot 10^{+73}:\\ \;\;\;\;y \cdot i + \left(z + t\_1\right)\\ \mathbf{elif}\;z \leq -125000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-135}:\\ \;\;\;\;y \cdot i + \left(a + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-272}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* b (log c))) (t_2 (+ a (+ (* x (log y)) (* y i)))))
   (if (<= z -5.5e+73)
     (+ (* y i) (+ z t_1))
     (if (<= z -125000000000.0)
       t_2
       (if (<= z -2.9e-135)
         (+ (* y i) (+ a (* (log c) (- b 0.5))))
         (if (<= z -2.3e-272) t_2 (+ (* y i) (+ a t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = b * log(c);
	double t_2 = a + ((x * log(y)) + (y * i));
	double tmp;
	if (z <= -5.5e+73) {
		tmp = (y * i) + (z + t_1);
	} else if (z <= -125000000000.0) {
		tmp = t_2;
	} else if (z <= -2.9e-135) {
		tmp = (y * i) + (a + (log(c) * (b - 0.5)));
	} else if (z <= -2.3e-272) {
		tmp = t_2;
	} else {
		tmp = (y * i) + (a + t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * log(c)
    t_2 = a + ((x * log(y)) + (y * i))
    if (z <= (-5.5d+73)) then
        tmp = (y * i) + (z + t_1)
    else if (z <= (-125000000000.0d0)) then
        tmp = t_2
    else if (z <= (-2.9d-135)) then
        tmp = (y * i) + (a + (log(c) * (b - 0.5d0)))
    else if (z <= (-2.3d-272)) then
        tmp = t_2
    else
        tmp = (y * i) + (a + t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = b * Math.log(c);
	double t_2 = a + ((x * Math.log(y)) + (y * i));
	double tmp;
	if (z <= -5.5e+73) {
		tmp = (y * i) + (z + t_1);
	} else if (z <= -125000000000.0) {
		tmp = t_2;
	} else if (z <= -2.9e-135) {
		tmp = (y * i) + (a + (Math.log(c) * (b - 0.5)));
	} else if (z <= -2.3e-272) {
		tmp = t_2;
	} else {
		tmp = (y * i) + (a + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = b * math.log(c)
	t_2 = a + ((x * math.log(y)) + (y * i))
	tmp = 0
	if z <= -5.5e+73:
		tmp = (y * i) + (z + t_1)
	elif z <= -125000000000.0:
		tmp = t_2
	elif z <= -2.9e-135:
		tmp = (y * i) + (a + (math.log(c) * (b - 0.5)))
	elif z <= -2.3e-272:
		tmp = t_2
	else:
		tmp = (y * i) + (a + t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(b * log(c))
	t_2 = Float64(a + Float64(Float64(x * log(y)) + Float64(y * i)))
	tmp = 0.0
	if (z <= -5.5e+73)
		tmp = Float64(Float64(y * i) + Float64(z + t_1));
	elseif (z <= -125000000000.0)
		tmp = t_2;
	elseif (z <= -2.9e-135)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(log(c) * Float64(b - 0.5))));
	elseif (z <= -2.3e-272)
		tmp = t_2;
	else
		tmp = Float64(Float64(y * i) + Float64(a + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = b * log(c);
	t_2 = a + ((x * log(y)) + (y * i));
	tmp = 0.0;
	if (z <= -5.5e+73)
		tmp = (y * i) + (z + t_1);
	elseif (z <= -125000000000.0)
		tmp = t_2;
	elseif (z <= -2.9e-135)
		tmp = (y * i) + (a + (log(c) * (b - 0.5)));
	elseif (z <= -2.3e-272)
		tmp = t_2;
	else
		tmp = (y * i) + (a + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.5e+73], N[(N[(y * i), $MachinePrecision] + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -125000000000.0], t$95$2, If[LessEqual[z, -2.9e-135], N[(N[(y * i), $MachinePrecision] + N[(a + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.3e-272], t$95$2, N[(N[(y * i), $MachinePrecision] + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.5000000000000003e73

   1. Initial program 99.9%

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

      1. add-cube-cbrt 99.8%

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

      2. pow3 99.8%

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

      3. sub-neg 99.8%

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

      4. metadata-eval 99.8%

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

      5. *-commutative 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in b around inf 99.9%

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

      1. *-commutative 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in t around 0 93.1%

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

   9. Taylor expanded in z around inf 72.6%

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

   if -5.5000000000000003e73 < z < -1.25e11 or -2.9000000000000002e-135 < z < -2.29999999999999989e-272

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. associate-+r+ 99.9%

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

      5. +-commutative 99.9%

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

      6. +-commutative 99.9%

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

      7. associate-+l+ 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-define 99.9%

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

      13. sub-neg 99.9%

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

      14. metadata-eval 99.9%

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

      15. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 63.8%

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

   6. Taylor expanded in a around inf 51.7%

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

   7. Taylor expanded in y around 0 74.4%

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

   if -1.25e11 < z < -2.9000000000000002e-135

   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 a around inf 86.6%

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

   if -2.29999999999999989e-272 < z

   1. Initial program 99.9%

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

      1. add-cube-cbrt 99.7%

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

      2. pow3 99.7%

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

      3. sub-neg 99.7%

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

      4. metadata-eval 99.7%

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

      5. *-commutative 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in b around inf 98.3%

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

      1. *-commutative 98.3%

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

   7. Simplified 98.3%

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

   8. Taylor expanded in a around inf 58.4%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+73}:\\ \;\;\;\;y \cdot i + \left(z + b \cdot \log c\right)\\ \mathbf{elif}\;z \leq -125000000000:\\ \;\;\;\;a + \left(x \cdot \log y + y \cdot i\right)\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-135}:\\ \;\;\;\;y \cdot i + \left(a + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-272}:\\ \;\;\;\;a + \left(x \cdot \log y + y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 90.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y + y \cdot i\\ \mathbf{if}\;x \leq -1.15 \cdot 10^{+154}:\\ \;\;\;\;a + t\_1\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+237}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x (log y)) (* y i))))
   (if (<= x -1.15e+154)
     (+ a t_1)
     (if (<= x 6e+237)
       (+ (* y i) (+ (* (log c) (- b 0.5)) (+ a (+ z 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 = (x * log(y)) + (y * i);
	double tmp;
	if (x <= -1.15e+154) {
		tmp = a + t_1;
	} else if (x <= 6e+237) {
		tmp = (y * i) + ((log(c) * (b - 0.5)) + (a + (z + t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * log(y)) + (y * i)
    if (x <= (-1.15d+154)) then
        tmp = a + t_1
    else if (x <= 6d+237) then
        tmp = (y * i) + ((log(c) * (b - 0.5d0)) + (a + (z + t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * Math.log(y)) + (y * i);
	double tmp;
	if (x <= -1.15e+154) {
		tmp = a + t_1;
	} else if (x <= 6e+237) {
		tmp = (y * i) + ((Math.log(c) * (b - 0.5)) + (a + (z + t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * math.log(y)) + (y * i)
	tmp = 0
	if x <= -1.15e+154:
		tmp = a + t_1
	elif x <= 6e+237:
		tmp = (y * i) + ((math.log(c) * (b - 0.5)) + (a + (z + t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * log(y)) + Float64(y * i))
	tmp = 0.0
	if (x <= -1.15e+154)
		tmp = Float64(a + t_1);
	elseif (x <= 6e+237)
		tmp = Float64(Float64(y * i) + Float64(Float64(log(c) * Float64(b - 0.5)) + Float64(a + Float64(z + t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * log(y)) + (y * i);
	tmp = 0.0;
	if (x <= -1.15e+154)
		tmp = a + t_1;
	elseif (x <= 6e+237)
		tmp = (y * i) + ((log(c) * (b - 0.5)) + (a + (z + t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.15e+154], N[(a + t$95$1), $MachinePrecision], If[LessEqual[x, 6e+237], N[(N[(y * i), $MachinePrecision] + N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.15e154

   1. Initial program 99.7%

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

      1. associate-+l+ 99.7%

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

      2. +-commutative 99.7%

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

      3. associate-+l+ 99.7%

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

      4. associate-+r+ 99.7%

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

      5. +-commutative 99.7%

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

      6. +-commutative 99.7%

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

      7. associate-+l+ 99.7%

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

      8. associate-+l+ 99.7%

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

      9. +-commutative 99.7%

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

      10. fma-define 99.7%

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

      11. +-commutative 99.7%

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

      12. fma-define 99.7%

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

      13. sub-neg 99.7%

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

      14. metadata-eval 99.7%

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

      15. +-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 62.4%

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

   6. Taylor expanded in a around inf 54.3%

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

   7. Taylor expanded in y around 0 85.1%

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

   if -1.15e154 < x < 6e237

   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 93.3%

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

   if 6e237 < x

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+l+ 100.0%

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

      4. associate-+r+ 100.0%

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

      5. +-commutative 100.0%

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

      6. +-commutative 100.0%

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

      7. associate-+l+ 100.0%

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

      8. associate-+l+ 100.0%

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

      9. +-commutative 100.0%

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

      10. fma-define 100.0%

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

      11. +-commutative 100.0%

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

      12. fma-define 100.0%

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

      13. sub-neg 100.0%

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

      14. metadata-eval 100.0%

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

      15. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 62.1%

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

   6. Taylor expanded in x around inf 53.3%

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

      1. mul-1-neg 53.3%

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

      2. log-rec 53.3%

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

      3. distribute-rgt-neg-out 53.3%

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

      4. distribute-frac-neg 53.3%

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

      5. remove-double-neg 53.3%

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

      6. associate-/l* 53.3%

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

   8. Simplified 53.3%

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

   9. Taylor expanded in y around 0 90.0%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+154}:\\ \;\;\;\;a + \left(x \cdot \log y + y \cdot i\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+237}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 57.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \log c\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{+72}:\\ \;\;\;\;y \cdot i + \left(z + t\_1\right)\\ \mathbf{elif}\;z \leq -200000000000 \lor \neg \left(z \leq -2.15 \cdot 10^{-130}\right):\\ \;\;\;\;a + \left(x \cdot \log y + y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* b (log c))))
   (if (<= z -5.8e+72)
     (+ (* y i) (+ z t_1))
     (if (or (<= z -200000000000.0) (not (<= z -2.15e-130)))
       (+ a (+ (* x (log y)) (* y i)))
       (+ (* y i) (+ a t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = b * log(c);
	double tmp;
	if (z <= -5.8e+72) {
		tmp = (y * i) + (z + t_1);
	} else if ((z <= -200000000000.0) || !(z <= -2.15e-130)) {
		tmp = a + ((x * log(y)) + (y * i));
	} else {
		tmp = (y * i) + (a + t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * log(c)
    if (z <= (-5.8d+72)) then
        tmp = (y * i) + (z + t_1)
    else if ((z <= (-200000000000.0d0)) .or. (.not. (z <= (-2.15d-130)))) then
        tmp = a + ((x * log(y)) + (y * i))
    else
        tmp = (y * i) + (a + t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = b * Math.log(c);
	double tmp;
	if (z <= -5.8e+72) {
		tmp = (y * i) + (z + t_1);
	} else if ((z <= -200000000000.0) || !(z <= -2.15e-130)) {
		tmp = a + ((x * Math.log(y)) + (y * i));
	} else {
		tmp = (y * i) + (a + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = b * math.log(c)
	tmp = 0
	if z <= -5.8e+72:
		tmp = (y * i) + (z + t_1)
	elif (z <= -200000000000.0) or not (z <= -2.15e-130):
		tmp = a + ((x * math.log(y)) + (y * i))
	else:
		tmp = (y * i) + (a + t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(b * log(c))
	tmp = 0.0
	if (z <= -5.8e+72)
		tmp = Float64(Float64(y * i) + Float64(z + t_1));
	elseif ((z <= -200000000000.0) || !(z <= -2.15e-130))
		tmp = Float64(a + Float64(Float64(x * log(y)) + Float64(y * i)));
	else
		tmp = Float64(Float64(y * i) + Float64(a + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = b * log(c);
	tmp = 0.0;
	if (z <= -5.8e+72)
		tmp = (y * i) + (z + t_1);
	elseif ((z <= -200000000000.0) || ~((z <= -2.15e-130)))
		tmp = a + ((x * log(y)) + (y * i));
	else
		tmp = (y * i) + (a + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.8e+72], N[(N[(y * i), $MachinePrecision] + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -200000000000.0], N[Not[LessEqual[z, -2.15e-130]], $MachinePrecision]], N[(a + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.80000000000000034e72

   1. Initial program 99.9%

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

      1. add-cube-cbrt 99.8%

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

      2. pow3 99.8%

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

      3. sub-neg 99.8%

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

      4. metadata-eval 99.8%

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

      5. *-commutative 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in b around inf 99.9%

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

      1. *-commutative 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in t around 0 93.1%

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

   9. Taylor expanded in z around inf 72.6%

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

   if -5.80000000000000034e72 < z < -2e11 or -2.15000000000000014e-130 < z

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. associate-+r+ 99.9%

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

      5. +-commutative 99.9%

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

      6. +-commutative 99.9%

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

      7. associate-+l+ 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-define 99.9%

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

      13. sub-neg 99.9%

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

      14. metadata-eval 99.9%

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

      15. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 73.9%

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

   6. Taylor expanded in a around inf 50.3%

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

   7. Taylor expanded in y around 0 63.1%

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

   if -2e11 < z < -2.15000000000000014e-130

   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. Step-by-step derivation

      1. add-cube-cbrt 99.0%

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

      2. pow3 99.1%

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

      3. sub-neg 99.1%

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

      4. metadata-eval 99.1%

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

      5. *-commutative 99.1%

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

   4. Applied egg-rr 99.1%

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

   5. Taylor expanded in b around inf 96.2%

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

      1. *-commutative 96.2%

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

   7. Simplified 96.2%

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

   8. Taylor expanded in a around inf 82.2%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+72}:\\ \;\;\;\;y \cdot i + \left(z + b \cdot \log c\right)\\ \mathbf{elif}\;z \leq -200000000000 \lor \neg \left(z \leq -2.15 \cdot 10^{-130}\right):\\ \;\;\;\;a + \left(x \cdot \log y + y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 89.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y + y \cdot i\\ \mathbf{if}\;x \leq -9.6 \cdot 10^{+153}:\\ \;\;\;\;a + t\_1\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{+236}:\\ \;\;\;\;y \cdot i + \left(b \cdot \log c + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* x (log y)) (* y i))))
   (if (<= x -9.6e+153)
     (+ a t_1)
     (if (<= x 6.6e+236) (+ (* y i) (+ (* b (log c)) (+ a (+ z 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 = (x * log(y)) + (y * i);
	double tmp;
	if (x <= -9.6e+153) {
		tmp = a + t_1;
	} else if (x <= 6.6e+236) {
		tmp = (y * i) + ((b * log(c)) + (a + (z + t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * log(y)) + (y * i)
    if (x <= (-9.6d+153)) then
        tmp = a + t_1
    else if (x <= 6.6d+236) then
        tmp = (y * i) + ((b * log(c)) + (a + (z + t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x * Math.log(y)) + (y * i);
	double tmp;
	if (x <= -9.6e+153) {
		tmp = a + t_1;
	} else if (x <= 6.6e+236) {
		tmp = (y * i) + ((b * Math.log(c)) + (a + (z + t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x * math.log(y)) + (y * i)
	tmp = 0
	if x <= -9.6e+153:
		tmp = a + t_1
	elif x <= 6.6e+236:
		tmp = (y * i) + ((b * math.log(c)) + (a + (z + t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x * log(y)) + Float64(y * i))
	tmp = 0.0
	if (x <= -9.6e+153)
		tmp = Float64(a + t_1);
	elseif (x <= 6.6e+236)
		tmp = Float64(Float64(y * i) + Float64(Float64(b * log(c)) + Float64(a + Float64(z + t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x * log(y)) + (y * i);
	tmp = 0.0;
	if (x <= -9.6e+153)
		tmp = a + t_1;
	elseif (x <= 6.6e+236)
		tmp = (y * i) + ((b * log(c)) + (a + (z + t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9.6e+153], N[(a + t$95$1), $MachinePrecision], If[LessEqual[x, 6.6e+236], N[(N[(y * i), $MachinePrecision] + N[(N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.5999999999999997e153

   1. Initial program 99.7%

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

      1. associate-+l+ 99.7%

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

      2. +-commutative 99.7%

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

      3. associate-+l+ 99.7%

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

      4. associate-+r+ 99.7%

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

      5. +-commutative 99.7%

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

      6. +-commutative 99.7%

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

      7. associate-+l+ 99.7%

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

      8. associate-+l+ 99.7%

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

      9. +-commutative 99.7%

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

      10. fma-define 99.7%

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

      11. +-commutative 99.7%

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

      12. fma-define 99.7%

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

      13. sub-neg 99.7%

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

      14. metadata-eval 99.7%

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

      15. +-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 62.4%

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

   6. Taylor expanded in a around inf 54.3%

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

   7. Taylor expanded in y around 0 85.1%

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

   if -9.5999999999999997e153 < x < 6.5999999999999998e236

   1. Initial program 99.9%

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

      1. add-cube-cbrt 99.6%

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

      2. pow3 99.6%

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

      3. sub-neg 99.6%

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

      4. metadata-eval 99.6%

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

      5. *-commutative 99.6%

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in b around inf 98.4%

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

      1. *-commutative 98.4%

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

   7. Simplified 98.4%

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

   8. Taylor expanded in x around 0 92.0%

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

   if 6.5999999999999998e236 < x

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+l+ 100.0%

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

      4. associate-+r+ 100.0%

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

      5. +-commutative 100.0%

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

      6. +-commutative 100.0%

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

      7. associate-+l+ 100.0%

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

      8. associate-+l+ 100.0%

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

      9. +-commutative 100.0%

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

      10. fma-define 100.0%

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

      11. +-commutative 100.0%

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

      12. fma-define 100.0%

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

      13. sub-neg 100.0%

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

      14. metadata-eval 100.0%

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

      15. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 62.1%

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

   6. Taylor expanded in x around inf 53.3%

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

      1. mul-1-neg 53.3%

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

      2. log-rec 53.3%

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

      3. distribute-rgt-neg-out 53.3%

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

      4. distribute-frac-neg 53.3%

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

      5. remove-double-neg 53.3%

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

      6. associate-/l* 53.3%

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

   8. Simplified 53.3%

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

   9. Taylor expanded in y around 0 90.0%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.6 \cdot 10^{+153}:\\ \;\;\;\;a + \left(x \cdot \log y + y \cdot i\right)\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{+236}:\\ \;\;\;\;y \cdot i + \left(b \cdot \log c + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 55.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+263}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+71}:\\ \;\;\;\;y \cdot \left(i + \left(\frac{a}{y} + \left(\frac{t}{y} + \frac{z}{y}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(x \cdot \log y + y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -6.2e+263)
   z
   (if (<= z -6e+71)
     (* y (+ i (+ (/ a y) (+ (/ t y) (/ z y)))))
     (+ a (+ (* x (log y)) (* 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 <= -6.2e+263) {
		tmp = z;
	} else if (z <= -6e+71) {
		tmp = y * (i + ((a / y) + ((t / y) + (z / y))));
	} else {
		tmp = a + ((x * log(y)) + (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 <= (-6.2d+263)) then
        tmp = z
    else if (z <= (-6d+71)) then
        tmp = y * (i + ((a / y) + ((t / y) + (z / y))))
    else
        tmp = a + ((x * log(y)) + (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 <= -6.2e+263) {
		tmp = z;
	} else if (z <= -6e+71) {
		tmp = y * (i + ((a / y) + ((t / y) + (z / y))));
	} else {
		tmp = a + ((x * Math.log(y)) + (y * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -6.2e+263:
		tmp = z
	elif z <= -6e+71:
		tmp = y * (i + ((a / y) + ((t / y) + (z / y))))
	else:
		tmp = a + ((x * math.log(y)) + (y * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -6.2e+263)
		tmp = z;
	elseif (z <= -6e+71)
		tmp = Float64(y * Float64(i + Float64(Float64(a / y) + Float64(Float64(t / y) + Float64(z / y)))));
	else
		tmp = Float64(a + Float64(Float64(x * log(y)) + 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 <= -6.2e+263)
		tmp = z;
	elseif (z <= -6e+71)
		tmp = y * (i + ((a / y) + ((t / y) + (z / y))));
	else
		tmp = a + ((x * log(y)) + (y * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -6.2e+263], z, If[LessEqual[z, -6e+71], N[(y * N[(i + N[(N[(a / y), $MachinePrecision] + N[(N[(t / y), $MachinePrecision] + N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.2000000000000005e263

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+l+ 100.0%

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

      4. associate-+r+ 100.0%

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

      5. +-commutative 100.0%

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

      6. +-commutative 100.0%

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

      7. associate-+l+ 100.0%

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

      8. associate-+l+ 100.0%

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

      9. +-commutative 100.0%

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

      10. fma-define 100.0%

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

      11. +-commutative 100.0%

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

      12. fma-define 100.0%

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

      13. sub-neg 100.0%

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

      14. metadata-eval 100.0%

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

      15. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 100.0%

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

   6. Taylor expanded in z around inf 88.7%

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

   if -6.2000000000000005e263 < z < -6.00000000000000025e71

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. associate-+r+ 99.9%

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

      5. +-commutative 99.9%

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

      6. +-commutative 99.9%

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

      7. associate-+l+ 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-define 99.9%

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

      13. sub-neg 99.9%

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

      14. metadata-eval 99.9%

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

      15. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 86.1%

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

   6. Taylor expanded in y around inf 67.2%

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

   7. Taylor expanded in z around inf 58.8%

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

   if -6.00000000000000025e71 < z

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. associate-+r+ 99.9%

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

      5. +-commutative 99.9%

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

      6. +-commutative 99.9%

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

      7. associate-+l+ 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-define 99.9%

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

      13. sub-neg 99.9%

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

      14. metadata-eval 99.9%

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

      15. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 74.2%

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

   6. Taylor expanded in a around inf 49.0%

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

   7. Taylor expanded in y around 0 60.6%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+263}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+71}:\\ \;\;\;\;y \cdot \left(i + \left(\frac{a}{y} + \left(\frac{t}{y} + \frac{z}{y}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(x \cdot \log y + y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 59.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 6 \cdot 10^{-52}:\\ \;\;\;\;a + \log c \cdot \left(b - 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i + \left(\frac{a}{y} + \left(\frac{t}{y} + \frac{z}{y}\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 6e-52)
   (+ a (* (log c) (- b 0.5)))
   (* y (+ i (+ (/ a y) (+ (/ t y) (/ z y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 6e-52) {
		tmp = a + (log(c) * (b - 0.5));
	} else {
		tmp = y * (i + ((a / y) + ((t / y) + (z / 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 (y <= 6d-52) then
        tmp = a + (log(c) * (b - 0.5d0))
    else
        tmp = y * (i + ((a / y) + ((t / y) + (z / 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 (y <= 6e-52) {
		tmp = a + (Math.log(c) * (b - 0.5));
	} else {
		tmp = y * (i + ((a / y) + ((t / y) + (z / y))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 6e-52:
		tmp = a + (math.log(c) * (b - 0.5))
	else:
		tmp = y * (i + ((a / y) + ((t / y) + (z / y))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 6e-52)
		tmp = Float64(a + Float64(log(c) * Float64(b - 0.5)));
	else
		tmp = Float64(y * Float64(i + Float64(Float64(a / y) + Float64(Float64(t / y) + Float64(z / y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= 6e-52)
		tmp = a + (log(c) * (b - 0.5));
	else
		tmp = y * (i + ((a / y) + ((t / y) + (z / y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 6e-52], N[(a + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(i + N[(N[(a / y), $MachinePrecision] + N[(N[(t / y), $MachinePrecision] + N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 6e-52

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf 43.5%

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

   4. Taylor expanded in y around 0 42.1%

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

   if 6e-52 < y

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. associate-+r+ 99.9%

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

      5. +-commutative 99.9%

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

      6. +-commutative 99.9%

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

      7. associate-+l+ 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-define 99.9%

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

      13. sub-neg 99.9%

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

      14. metadata-eval 99.9%

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

      15. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 89.8%

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

   6. Taylor expanded in y around inf 87.4%

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

   7. Taylor expanded in z around inf 76.9%

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

Alternative 17: 50.3% accurate, 10.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.95 \cdot 10^{-44}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i + \left(\frac{a}{y} + \left(\frac{t}{y} + \frac{z}{y}\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 1.95e-44) z (* y (+ i (+ (/ a y) (+ (/ t y) (/ z y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 1.95e-44) {
		tmp = z;
	} else {
		tmp = y * (i + ((a / y) + ((t / y) + (z / 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 (y <= 1.95d-44) then
        tmp = z
    else
        tmp = y * (i + ((a / y) + ((t / y) + (z / 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 (y <= 1.95e-44) {
		tmp = z;
	} else {
		tmp = y * (i + ((a / y) + ((t / y) + (z / y))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 1.95e-44:
		tmp = z
	else:
		tmp = y * (i + ((a / y) + ((t / y) + (z / y))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 1.95e-44)
		tmp = z;
	else
		tmp = Float64(y * Float64(i + Float64(Float64(a / y) + Float64(Float64(t / y) + Float64(z / y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= 1.95e-44)
		tmp = z;
	else
		tmp = y * (i + ((a / y) + ((t / y) + (z / y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 1.95e-44], z, N[(y * N[(i + N[(N[(a / y), $MachinePrecision] + N[(N[(t / y), $MachinePrecision] + N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.9500000000000001e-44

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. associate-+r+ 99.9%

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

      5. +-commutative 99.9%

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

      6. +-commutative 99.9%

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

      7. associate-+l+ 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-define 99.9%

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

      13. sub-neg 99.9%

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

      14. metadata-eval 99.9%

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

      15. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 75.5%

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

   6. Taylor expanded in z around inf 20.1%

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

   if 1.9500000000000001e-44 < y

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. associate-+r+ 99.9%

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

      5. +-commutative 99.9%

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

      6. +-commutative 99.9%

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

      7. associate-+l+ 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-define 99.9%

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

      13. sub-neg 99.9%

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

      14. metadata-eval 99.9%

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

      15. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 90.3%

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

   6. Taylor expanded in y around inf 88.4%

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

   7. Taylor expanded in z around inf 77.7%

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

Alternative 18: 30.7% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1.4 \cdot 10^{+75}:\\ \;\;\;\;y \cdot i\\ \mathbf{elif}\;i \leq 3 \cdot 10^{-271}:\\ \;\;\;\;z\\ \mathbf{elif}\;i \leq 95000000000000:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= i -1.4e+75)
   (* y i)
   (if (<= i 3e-271) z (if (<= i 95000000000000.0) 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 (i <= -1.4e+75) {
		tmp = y * i;
	} else if (i <= 3e-271) {
		tmp = z;
	} else if (i <= 95000000000000.0) {
		tmp = a;
	} else {
		tmp = y * i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (i <= (-1.4d+75)) then
        tmp = y * i
    else if (i <= 3d-271) then
        tmp = z
    else if (i <= 95000000000000.0d0) then
        tmp = a
    else
        tmp = y * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (i <= -1.4e+75) {
		tmp = y * i;
	} else if (i <= 3e-271) {
		tmp = z;
	} else if (i <= 95000000000000.0) {
		tmp = a;
	} else {
		tmp = y * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if i <= -1.4e+75:
		tmp = y * i
	elif i <= 3e-271:
		tmp = z
	elif i <= 95000000000000.0:
		tmp = a
	else:
		tmp = y * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (i <= -1.4e+75)
		tmp = Float64(y * i);
	elseif (i <= 3e-271)
		tmp = z;
	elseif (i <= 95000000000000.0)
		tmp = a;
	else
		tmp = Float64(y * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (i <= -1.4e+75)
		tmp = y * i;
	elseif (i <= 3e-271)
		tmp = z;
	elseif (i <= 95000000000000.0)
		tmp = a;
	else
		tmp = y * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[i, -1.4e+75], N[(y * i), $MachinePrecision], If[LessEqual[i, 3e-271], z, If[LessEqual[i, 95000000000000.0], a, N[(y * i), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if i < -1.40000000000000006e75 or 9.5e13 < 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. 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. +-commutative 99.8%

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

      3. associate-+l+ 99.8%

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

      4. associate-+r+ 99.8%

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

      5. +-commutative 99.8%

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

      6. +-commutative 99.8%

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

      7. associate-+l+ 99.8%

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

      8. associate-+l+ 99.8%

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

      9. +-commutative 99.8%

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

      10. fma-define 99.8%

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

      11. +-commutative 99.8%

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

      12. fma-define 99.8%

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

      13. sub-neg 99.8%

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

      14. metadata-eval 99.8%

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

      15. +-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 56.1%

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

      1. *-commutative 56.1%

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

   7. Simplified 56.1%

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

   if -1.40000000000000006e75 < i < 3.00000000000000002e-271

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. associate-+r+ 99.9%

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

      5. +-commutative 99.9%

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

      6. +-commutative 99.9%

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

      7. associate-+l+ 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-define 99.9%

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

      13. sub-neg 99.9%

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

      14. metadata-eval 99.9%

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

      15. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 85.9%

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

   6. Taylor expanded in z around inf 23.1%

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

   if 3.00000000000000002e-271 < i < 9.5e13

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. associate-+r+ 99.9%

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

      5. +-commutative 99.9%

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

      6. +-commutative 99.9%

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

      7. associate-+l+ 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-define 99.9%

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

      13. sub-neg 99.9%

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

      14. metadata-eval 99.9%

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

      15. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 73.1%

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

   6. Taylor expanded in a around inf 18.0%

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

Alternative 19: 36.2% accurate, 12.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+248}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+16}:\\ \;\;\;\;y \cdot \left(i + \frac{z}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i + \frac{a}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -1.35e+248)
   z
   (if (<= z -3e+16) (* y (+ i (/ z y))) (* y (+ i (/ a y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -1.35e+248) {
		tmp = z;
	} else if (z <= -3e+16) {
		tmp = y * (i + (z / y));
	} else {
		tmp = y * (i + (a / 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 <= (-1.35d+248)) then
        tmp = z
    else if (z <= (-3d+16)) then
        tmp = y * (i + (z / y))
    else
        tmp = y * (i + (a / 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 <= -1.35e+248) {
		tmp = z;
	} else if (z <= -3e+16) {
		tmp = y * (i + (z / y));
	} else {
		tmp = y * (i + (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -1.35e+248:
		tmp = z
	elif z <= -3e+16:
		tmp = y * (i + (z / y))
	else:
		tmp = y * (i + (a / y))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -1.35e+248)
		tmp = z;
	elseif (z <= -3e+16)
		tmp = Float64(y * Float64(i + Float64(z / y)));
	else
		tmp = Float64(y * Float64(i + Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -1.35e+248)
		tmp = z;
	elseif (z <= -3e+16)
		tmp = y * (i + (z / y));
	else
		tmp = y * (i + (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -1.35e+248], z, If[LessEqual[z, -3e+16], N[(y * N[(i + N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(i + N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.34999999999999994e248

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+l+ 100.0%

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

      4. associate-+r+ 100.0%

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

      5. +-commutative 100.0%

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

      6. +-commutative 100.0%

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

      7. associate-+l+ 100.0%

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

      8. associate-+l+ 100.0%

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

      9. +-commutative 100.0%

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

      10. fma-define 100.0%

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

      11. +-commutative 100.0%

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

      12. fma-define 100.0%

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

      13. sub-neg 100.0%

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

      14. metadata-eval 100.0%

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

      15. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 100.0%

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

   6. Taylor expanded in z around inf 79.6%

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

   if -1.34999999999999994e248 < z < -3e16

   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. +-commutative 99.8%

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

      3. associate-+l+ 99.8%

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

      4. associate-+r+ 99.8%

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

      5. +-commutative 99.8%

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

      6. +-commutative 99.8%

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

      7. associate-+l+ 99.8%

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

      8. associate-+l+ 99.8%

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

      9. +-commutative 99.8%

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

      10. fma-define 99.8%

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

      11. +-commutative 99.8%

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

      12. fma-define 99.8%

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

      13. sub-neg 99.8%

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

      14. metadata-eval 99.8%

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

      15. +-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 76.8%

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

   6. Taylor expanded in y around inf 62.9%

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

   7. Taylor expanded in z around inf 46.7%

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

   if -3e16 < z

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. associate-+r+ 99.9%

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

      5. +-commutative 99.9%

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

      6. +-commutative 99.9%

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

      7. associate-+l+ 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-define 99.9%

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

      13. sub-neg 99.9%

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

      14. metadata-eval 99.9%

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

      15. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 86.1%

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

   6. Taylor expanded in y around inf 65.9%

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

   7. Taylor expanded in a around inf 40.1%

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

Alternative 20: 35.5% accurate, 18.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+135}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i + \frac{a}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -2.8e+135) z (* y (+ i (/ a y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -2.8e+135) {
		tmp = z;
	} else {
		tmp = y * (i + (a / 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 <= (-2.8d+135)) then
        tmp = z
    else
        tmp = y * (i + (a / 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 <= -2.8e+135) {
		tmp = z;
	} else {
		tmp = y * (i + (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -2.8e+135:
		tmp = z
	else:
		tmp = y * (i + (a / y))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -2.8e+135)
		tmp = z;
	else
		tmp = Float64(y * Float64(i + Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -2.8e+135)
		tmp = z;
	else
		tmp = y * (i + (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -2.8e+135], z, N[(y * N[(i + N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.80000000000000002e135

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+l+ 100.0%

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

      4. associate-+r+ 100.0%

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

      5. +-commutative 100.0%

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

      6. +-commutative 100.0%

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

      7. associate-+l+ 100.0%

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

      8. associate-+l+ 100.0%

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

      9. +-commutative 100.0%

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

      10. fma-define 100.0%

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

      11. +-commutative 100.0%

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

      12. fma-define 100.0%

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

      13. sub-neg 100.0%

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

      14. metadata-eval 100.0%

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

      15. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 91.1%

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

   6. Taylor expanded in z around inf 44.2%

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

   if -2.80000000000000002e135 < z

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. associate-+r+ 99.9%

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

      5. +-commutative 99.9%

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

      6. +-commutative 99.9%

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

      7. associate-+l+ 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-define 99.9%

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

      13. sub-neg 99.9%

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

      14. metadata-eval 99.9%

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

      15. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 83.9%

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

   6. Taylor expanded in y around inf 65.1%

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

   7. Taylor expanded in a around inf 38.6%

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

Alternative 21: 20.1% accurate, 36.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+21}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (if (<= z -2.6e+21) z a))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -2.6e+21) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-2.6d+21)) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -2.6e+21) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -2.6e+21:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -2.6e+21)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -2.6e+21)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -2.6e+21], z, a]

Derivation

1. Split input into 2 regimes

2. if z < -2.6e21

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. associate-+r+ 99.9%

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

      5. +-commutative 99.9%

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

      6. +-commutative 99.9%

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

      7. associate-+l+ 99.9%

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

      8. associate-+l+ 99.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i} \]

      9. +-commutative 99.9%

         \[\leadsto \color{blue}{y \cdot i + \left(\left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right) + \left(b - 0.5\right) \cdot \log c\right)} \]

      10. fma-define 99.9%

          \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right) + \left(b - 0.5\right) \cdot \log c\right)} \]

      11. +-commutative 99.9%

          \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\left(b - 0.5\right) \cdot \log c + \left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right)}\right) \]

      12. fma-define 99.9%

          \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\mathsf{fma}\left(b - 0.5, \log c, \left(\left(x \cdot \log y + a\right) + t\right) + z\right)}\right) \]

      13. sub-neg 99.9%

          \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\color{blue}{b + \left(-0.5\right)}, \log c, \left(\left(x \cdot \log y + a\right) + t\right) + z\right)\right) \]

      14. metadata-eval 99.9%

          \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + \color{blue}{-0.5}, \log c, \left(\left(x \cdot \log y + a\right) + t\right) + z\right)\right) \]

      15. +-commutative 99.9%

          \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + -0.5, \log c, \color{blue}{z + \left(\left(x \cdot \log y + a\right) + t\right)}\right)\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \mathsf{fma}\left(b + -0.5, \log c, z + \left(t + \mathsf{fma}\left(x, \log y, a\right)\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 81.8%

      \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)}\right) \]

   6. Taylor expanded in z around inf 35.0%

      \[\leadsto \color{blue}{z} \]

   if -2.6e21 < z

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Step-by-step derivation

      1. associate-+l+ 99.9%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right)} \]

      2. +-commutative 99.9%

         \[\leadsto \color{blue}{\left(a + \left(\left(x \cdot \log y + z\right) + t\right)\right)} + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

      3. associate-+l+ 99.9%

         \[\leadsto \left(a + \color{blue}{\left(x \cdot \log y + \left(z + t\right)\right)}\right) + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

      4. associate-+r+ 99.9%

         \[\leadsto \color{blue}{\left(\left(a + x \cdot \log y\right) + \left(z + t\right)\right)} + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

      5. +-commutative 99.9%

         \[\leadsto \left(\left(a + x \cdot \log y\right) + \color{blue}{\left(t + z\right)}\right) + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

      6. +-commutative 99.9%

         \[\leadsto \left(\color{blue}{\left(x \cdot \log y + a\right)} + \left(t + z\right)\right) + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

      7. associate-+l+ 99.9%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right)} + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

      8. associate-+l+ 99.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i} \]

      9. +-commutative 99.9%

         \[\leadsto \color{blue}{y \cdot i + \left(\left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right) + \left(b - 0.5\right) \cdot \log c\right)} \]

      10. fma-define 99.9%

          \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right) + \left(b - 0.5\right) \cdot \log c\right)} \]

      11. +-commutative 99.9%

          \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\left(b - 0.5\right) \cdot \log c + \left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right)}\right) \]

      12. fma-define 99.9%

          \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\mathsf{fma}\left(b - 0.5, \log c, \left(\left(x \cdot \log y + a\right) + t\right) + z\right)}\right) \]

      13. sub-neg 99.9%

          \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\color{blue}{b + \left(-0.5\right)}, \log c, \left(\left(x \cdot \log y + a\right) + t\right) + z\right)\right) \]

      14. metadata-eval 99.9%

          \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + \color{blue}{-0.5}, \log c, \left(\left(x \cdot \log y + a\right) + t\right) + z\right)\right) \]

      15. +-commutative 99.9%

          \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + -0.5, \log c, \color{blue}{z + \left(\left(x \cdot \log y + a\right) + t\right)}\right)\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \mathsf{fma}\left(b + -0.5, \log c, z + \left(t + \mathsf{fma}\left(x, \log y, a\right)\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 85.7%

      \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)}\right) \]

   6. Taylor expanded in a around inf 19.6%

      \[\leadsto \color{blue}{a} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 22: 15.7% accurate, 219.0× speedup

Math

\[\begin{array}{l} \\ a \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 a)

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return a;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = a
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return a;
}

Python

def code(x, y, z, t, a, b, c, i):
	return a

Julia

function code(x, y, z, t, a, b, c, i)
	return a
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = a;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := a

Derivation

1. Initial program 99.9%

   \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
2. Step-by-step derivation

   1. associate-+l+ 99.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right)} \]

   2. +-commutative 99.9%

      \[\leadsto \color{blue}{\left(a + \left(\left(x \cdot \log y + z\right) + t\right)\right)} + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

   3. associate-+l+ 99.9%

      \[\leadsto \left(a + \color{blue}{\left(x \cdot \log y + \left(z + t\right)\right)}\right) + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

   4. associate-+r+ 99.9%

      \[\leadsto \color{blue}{\left(\left(a + x \cdot \log y\right) + \left(z + t\right)\right)} + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

   5. +-commutative 99.9%

      \[\leadsto \left(\left(a + x \cdot \log y\right) + \color{blue}{\left(t + z\right)}\right) + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

   6. +-commutative 99.9%

      \[\leadsto \left(\color{blue}{\left(x \cdot \log y + a\right)} + \left(t + z\right)\right) + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

   7. associate-+l+ 99.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right)} + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

   8. associate-+l+ 99.9%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i} \]

   9. +-commutative 99.9%

      \[\leadsto \color{blue}{y \cdot i + \left(\left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right) + \left(b - 0.5\right) \cdot \log c\right)} \]

   10. fma-define 99.9%

       \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right) + \left(b - 0.5\right) \cdot \log c\right)} \]

   11. +-commutative 99.9%

       \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\left(b - 0.5\right) \cdot \log c + \left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right)}\right) \]

   12. fma-define 99.9%

       \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\mathsf{fma}\left(b - 0.5, \log c, \left(\left(x \cdot \log y + a\right) + t\right) + z\right)}\right) \]

   13. sub-neg 99.9%

       \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\color{blue}{b + \left(-0.5\right)}, \log c, \left(\left(x \cdot \log y + a\right) + t\right) + z\right)\right) \]

   14. metadata-eval 99.9%

       \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + \color{blue}{-0.5}, \log c, \left(\left(x \cdot \log y + a\right) + t\right) + z\right)\right) \]

   15. +-commutative 99.9%

       \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + -0.5, \log c, \color{blue}{z + \left(\left(x \cdot \log y + a\right) + t\right)}\right)\right) \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \mathsf{fma}\left(b + -0.5, \log c, z + \left(t + \mathsf{fma}\left(x, \log y, a\right)\right)\right)\right)} \]
4. Add Preprocessing

5. Taylor expanded in x around 0 84.8%

   \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)}\right) \]

6. Taylor expanded in a around inf 17.8%

   \[\leadsto \color{blue}{a} \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024096 
(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)))