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

Percentage Accurate: 99.8% → 99.8%

Time: 17.8s

Alternatives: 21

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

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

5. Final simplification 99.9%

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

Alternative 2: 93.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -1.3 \cdot 10^{+112}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\_1\right)\right)\\ \mathbf{elif}\;x \leq 2.45 \cdot 10^{+150}:\\ \;\;\;\;y \cdot i + \left(z + \left(t + \mathsf{fma}\left(\log c, b + -0.5, a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + \left(t\_1 + b \cdot \log c\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -1.3e+112)
     (+ (* y i) (+ a (+ z t_1)))
     (if (<= x 2.45e+150)
       (+ (* y i) (+ z (+ t (fma (log c) (+ b -0.5) a))))
       (+ (* y i) (+ t (+ z (+ 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 <= -1.3e+112) {
		tmp = (y * i) + (a + (z + t_1));
	} else if (x <= 2.45e+150) {
		tmp = (y * i) + (z + (t + fma(log(c), (b + -0.5), a)));
	} else {
		tmp = (y * i) + (t + (z + (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 <= -1.3e+112)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + t_1)));
	elseif (x <= 2.45e+150)
		tmp = Float64(Float64(y * i) + Float64(z + Float64(t + fma(log(c), Float64(b + -0.5), a))));
	else
		tmp = Float64(Float64(y * i) + Float64(t + Float64(z + 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, -1.3e+112], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.45e+150], N[(N[(y * i), $MachinePrecision] + N[(z + N[(t + N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(t + N[(z + N[(t$95$1 + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.3e112

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf 100.0%

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

      1. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in b around 0 97.3%

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

   7. Taylor expanded in t around 0 89.4%

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

   if -1.3e112 < x < 2.45000000000000003e150

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 96.0%

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

      1. +-commutative 96.0%

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

      2. associate-+r+ 96.0%

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

      3. +-commutative 96.0%

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

      4. sub-neg 96.0%

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

      5. metadata-eval 96.0%

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

      6. associate-+r+ 96.0%

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

      7. associate-+l+ 96.0%

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

      8. fma-define 96.0%

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

      9. +-commutative 96.0%

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

   5. Simplified 96.0%

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

   if 2.45000000000000003e150 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in b around inf 99.7%

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

      1. *-commutative 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in a around 0 96.5%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+112}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + x \cdot \log y\right)\right)\\ \mathbf{elif}\;x \leq 2.45 \cdot 10^{+150}:\\ \;\;\;\;y \cdot i + \left(z + \left(t + \mathsf{fma}\left(\log c, b + -0.5, a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + \left(x \cdot \log y + b \cdot \log c\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 91.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+113} \lor \neg \left(x \leq 7 \cdot 10^{+64}\right):\\ \;\;\;\;y \cdot i + \left(a + \left(z + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + \left(t + \mathsf{fma}\left(\log c, b + -0.5, a\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -4e+113) (not (<= x 7e+64)))
   (+ (* y i) (+ a (+ z (* x (log y)))))
   (+ (* y i) (+ z (+ t (fma (log c) (+ b -0.5) a))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -4e+113) || !(x <= 7e+64)) {
		tmp = (y * i) + (a + (z + (x * log(y))));
	} else {
		tmp = (y * i) + (z + (t + fma(log(c), (b + -0.5), a)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -4e+113) || !(x <= 7e+64))
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + Float64(x * log(y)))));
	else
		tmp = Float64(Float64(y * i) + Float64(z + Float64(t + fma(log(c), Float64(b + -0.5), a))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -4e+113], N[Not[LessEqual[x, 7e+64]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(z + N[(t + N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4e113 or 6.9999999999999997e64 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf 99.8%

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

      1. *-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in b around 0 90.9%

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

   7. Taylor expanded in t around 0 80.4%

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

   if -4e113 < x < 6.9999999999999997e64

   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 97.7%

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

      1. +-commutative 97.7%

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

      2. associate-+r+ 97.7%

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

      3. +-commutative 97.7%

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

      4. sub-neg 97.7%

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

      5. metadata-eval 97.7%

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

      6. associate-+r+ 97.7%

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

      7. associate-+l+ 97.7%

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

      8. fma-define 97.7%

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

      9. +-commutative 97.7%

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

   5. Simplified 97.7%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+113} \lor \neg \left(x \leq 7 \cdot 10^{+64}\right):\\ \;\;\;\;y \cdot i + \left(a + \left(z + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + \left(t + \mathsf{fma}\left(\log c, b + -0.5, a\right)\right)\right)\\ \end{array} \]
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: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

Python

def code(x, y, z, t, a, b, c, i):
	return (y * i) + ((a + (t + (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(t + 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 + (t + (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[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $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. Taylor expanded in b around inf 97.7%

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

   1. *-commutative 97.7%

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

5. Simplified 97.7%

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

6. Final simplification 97.7%

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

Alternative 6: 91.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+112} \lor \neg \left(x \leq 5 \cdot 10^{+64}\right):\\ \;\;\;\;y \cdot i + \left(a + \left(z + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -9.5e+112) (not (<= x 5e+64)))
   (+ (* y i) (+ a (+ z (* x (log y)))))
   (+ (* 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 ((x <= -9.5e+112) || !(x <= 5e+64)) {
		tmp = (y * i) + (a + (z + (x * log(y))));
	} else {
		tmp = (y * i) + (a + (t + (z + (log(c) * (b - 0.5)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-9.5d+112)) .or. (.not. (x <= 5d+64))) then
        tmp = (y * i) + (a + (z + (x * log(y))))
    else
        tmp = (y * i) + (a + (t + (z + (log(c) * (b - 0.5d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -9.5e+112) || !(x <= 5e+64)) {
		tmp = (y * i) + (a + (z + (x * Math.log(y))));
	} else {
		tmp = (y * i) + (a + (t + (z + (Math.log(c) * (b - 0.5)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -9.5e+112) or not (x <= 5e+64):
		tmp = (y * i) + (a + (z + (x * math.log(y))))
	else:
		tmp = (y * i) + (a + (t + (z + (math.log(c) * (b - 0.5)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -9.5e+112) || !(x <= 5e+64))
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + Float64(x * log(y)))));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(t + Float64(z + Float64(log(c) * Float64(b - 0.5))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -9.5e+112) || ~((x <= 5e+64)))
		tmp = (y * i) + (a + (z + (x * log(y))));
	else
		tmp = (y * i) + (a + (t + (z + (log(c) * (b - 0.5)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -9.5e+112], N[Not[LessEqual[x, 5e+64]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(t + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.5000000000000008e112 or 5e64 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf 99.8%

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

      1. *-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in b around 0 90.9%

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

   7. Taylor expanded in t around 0 80.4%

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

   if -9.5000000000000008e112 < x < 5e64

   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 97.7%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+112} \lor \neg \left(x \leq 5 \cdot 10^{+64}\right):\\ \;\;\;\;y \cdot i + \left(a + \left(z + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.9 \cdot 10^{+227}:\\ \;\;\;\;b \cdot \log c\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{+257}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + t \cdot \left(\log c \cdot \frac{b}{t} + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= b -3.9e+227)
   (* b (log c))
   (if (<= b 8.2e+257)
     (+ (* y i) (+ a (+ z (* x (log y)))))
     (+ (* y i) (* t (+ (* (log c) (/ b t)) 1.0))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (b <= -3.9e+227) {
		tmp = b * log(c);
	} else if (b <= 8.2e+257) {
		tmp = (y * i) + (a + (z + (x * log(y))));
	} else {
		tmp = (y * i) + (t * ((log(c) * (b / t)) + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (b <= (-3.9d+227)) then
        tmp = b * log(c)
    else if (b <= 8.2d+257) then
        tmp = (y * i) + (a + (z + (x * log(y))))
    else
        tmp = (y * i) + (t * ((log(c) * (b / t)) + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (b <= -3.9e+227) {
		tmp = b * Math.log(c);
	} else if (b <= 8.2e+257) {
		tmp = (y * i) + (a + (z + (x * Math.log(y))));
	} else {
		tmp = (y * i) + (t * ((Math.log(c) * (b / t)) + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if b <= -3.9e+227:
		tmp = b * math.log(c)
	elif b <= 8.2e+257:
		tmp = (y * i) + (a + (z + (x * math.log(y))))
	else:
		tmp = (y * i) + (t * ((math.log(c) * (b / t)) + 1.0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (b <= -3.9e+227)
		tmp = Float64(b * log(c));
	elseif (b <= 8.2e+257)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + Float64(x * log(y)))));
	else
		tmp = Float64(Float64(y * i) + Float64(t * Float64(Float64(log(c) * Float64(b / t)) + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (b <= -3.9e+227)
		tmp = b * log(c);
	elseif (b <= 8.2e+257)
		tmp = (y * i) + (a + (z + (x * log(y))));
	else
		tmp = (y * i) + (t * ((log(c) * (b / t)) + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[b, -3.9e+227], N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.2e+257], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(t * N[(N[(N[Log[c], $MachinePrecision] * N[(b / t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.8999999999999999e227

   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%

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

   5. Taylor expanded in i around -inf 58.6%

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

   6. Taylor expanded in b around inf 65.3%

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

      1. mul-1-neg 65.3%

         \[\leadsto -1 \cdot \color{blue}{\left(-b \cdot \log c\right)} \]

      2. *-commutative 65.3%

         \[\leadsto -1 \cdot \left(-\color{blue}{\log c \cdot b}\right) \]

      3. distribute-rgt-neg-in 65.3%

         \[\leadsto -1 \cdot \color{blue}{\left(\log c \cdot \left(-b\right)\right)} \]

   8. Simplified 65.3%

      \[\leadsto -1 \cdot \color{blue}{\left(\log c \cdot \left(-b\right)\right)} \]

   if -3.8999999999999999e227 < b < 8.20000000000000038e257

   1. Initial program 99.9%

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

   3. Taylor expanded in b around inf 97.4%

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

      1. *-commutative 97.4%

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

   5. Simplified 97.4%

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

   6. Taylor expanded in b around 0 91.8%

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

   7. Taylor expanded in t around 0 78.0%

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

   if 8.20000000000000038e257 < b

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 99.7%

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

      1. +-commutative 99.7%

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

      2. sub-neg 99.7%

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

      3. metadata-eval 99.7%

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

      4. fma-define 99.7%

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

      5. +-commutative 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in t around inf 99.7%

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

      1. associate-/l* 99.5%

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

      2. sub-neg 99.5%

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

      3. metadata-eval 99.5%

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

   8. Simplified 99.5%

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

   9. Taylor expanded in b around inf 99.7%

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

       1. *-commutative 99.7%

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

       2. associate-/l* 99.5%

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

   11. Simplified 99.5%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.9 \cdot 10^{+227}:\\ \;\;\;\;b \cdot \log c\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{+257}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + t \cdot \left(\log c \cdot \frac{b}{t} + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.7 \cdot 10^{+226}:\\ \;\;\;\;b \cdot \log c\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{+255}:\\ \;\;\;\;\left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + t \cdot \left(\log c \cdot \frac{b}{t} + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= b -6.7e+226)
   (* b (log c))
   (if (<= b 6.2e+255)
     (+ (+ a (+ t (+ z (* x (log y))))) (* y i))
     (+ (* y i) (* t (+ (* (log c) (/ b t)) 1.0))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (b <= -6.7e+226) {
		tmp = b * log(c);
	} else if (b <= 6.2e+255) {
		tmp = (a + (t + (z + (x * log(y))))) + (y * i);
	} else {
		tmp = (y * i) + (t * ((log(c) * (b / t)) + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (b <= (-6.7d+226)) then
        tmp = b * log(c)
    else if (b <= 6.2d+255) then
        tmp = (a + (t + (z + (x * log(y))))) + (y * i)
    else
        tmp = (y * i) + (t * ((log(c) * (b / t)) + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (b <= -6.7e+226) {
		tmp = b * Math.log(c);
	} else if (b <= 6.2e+255) {
		tmp = (a + (t + (z + (x * Math.log(y))))) + (y * i);
	} else {
		tmp = (y * i) + (t * ((Math.log(c) * (b / t)) + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if b <= -6.7e+226:
		tmp = b * math.log(c)
	elif b <= 6.2e+255:
		tmp = (a + (t + (z + (x * math.log(y))))) + (y * i)
	else:
		tmp = (y * i) + (t * ((math.log(c) * (b / t)) + 1.0))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (b <= -6.7e+226)
		tmp = Float64(b * log(c));
	elseif (b <= 6.2e+255)
		tmp = Float64(Float64(a + Float64(t + Float64(z + Float64(x * log(y))))) + Float64(y * i));
	else
		tmp = Float64(Float64(y * i) + Float64(t * Float64(Float64(log(c) * Float64(b / t)) + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (b <= -6.7e+226)
		tmp = b * log(c);
	elseif (b <= 6.2e+255)
		tmp = (a + (t + (z + (x * log(y))))) + (y * i);
	else
		tmp = (y * i) + (t * ((log(c) * (b / t)) + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[b, -6.7e+226], N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.2e+255], N[(N[(a + N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(t * N[(N[(N[Log[c], $MachinePrecision] * N[(b / t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.69999999999999957e226

   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%

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

   5. Taylor expanded in i around -inf 58.6%

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

   6. Taylor expanded in b around inf 65.3%

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

      1. mul-1-neg 65.3%

         \[\leadsto -1 \cdot \color{blue}{\left(-b \cdot \log c\right)} \]

      2. *-commutative 65.3%

         \[\leadsto -1 \cdot \left(-\color{blue}{\log c \cdot b}\right) \]

      3. distribute-rgt-neg-in 65.3%

         \[\leadsto -1 \cdot \color{blue}{\left(\log c \cdot \left(-b\right)\right)} \]

   8. Simplified 65.3%

      \[\leadsto -1 \cdot \color{blue}{\left(\log c \cdot \left(-b\right)\right)} \]

   if -6.69999999999999957e226 < b < 6.2000000000000004e255

   1. Initial program 99.9%

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

   3. Taylor expanded in b around inf 97.4%

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

      1. *-commutative 97.4%

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

   5. Simplified 97.4%

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

   6. Taylor expanded in b around 0 91.8%

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

   if 6.2000000000000004e255 < b

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 99.7%

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

      1. +-commutative 99.7%

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

      2. sub-neg 99.7%

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

      3. metadata-eval 99.7%

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

      4. fma-define 99.7%

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

      5. +-commutative 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in t around inf 99.7%

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

      1. associate-/l* 99.5%

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

      2. sub-neg 99.5%

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

      3. metadata-eval 99.5%

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

   8. Simplified 99.5%

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

   9. Taylor expanded in b around inf 99.7%

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

       1. *-commutative 99.7%

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

       2. associate-/l* 99.5%

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

   11. Simplified 99.5%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.7 \cdot 10^{+226}:\\ \;\;\;\;b \cdot \log c\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{+255}:\\ \;\;\;\;\left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + t \cdot \left(\log c \cdot \frac{b}{t} + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 81.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z + x \cdot \log y\\ \mathbf{if}\;x \leq -1.3 \cdot 10^{+112}:\\ \;\;\;\;y \cdot i + \left(a + t\_1\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+15}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a + \left(t + t\_1\right)\right) + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ z (* x (log y)))))
   (if (<= x -1.3e+112)
     (+ (* y i) (+ a t_1))
     (if (<= x 6.5e+15)
       (+ (* y i) (+ a (+ z (* (log c) (- b 0.5)))))
       (+ (+ a (+ t t_1)) (* y i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = z + (x * log(y));
	double tmp;
	if (x <= -1.3e+112) {
		tmp = (y * i) + (a + t_1);
	} else if (x <= 6.5e+15) {
		tmp = (y * i) + (a + (z + (log(c) * (b - 0.5))));
	} else {
		tmp = (a + (t + t_1)) + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z + (x * log(y))
    if (x <= (-1.3d+112)) then
        tmp = (y * i) + (a + t_1)
    else if (x <= 6.5d+15) then
        tmp = (y * i) + (a + (z + (log(c) * (b - 0.5d0))))
    else
        tmp = (a + (t + t_1)) + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = z + (x * Math.log(y));
	double tmp;
	if (x <= -1.3e+112) {
		tmp = (y * i) + (a + t_1);
	} else if (x <= 6.5e+15) {
		tmp = (y * i) + (a + (z + (Math.log(c) * (b - 0.5))));
	} else {
		tmp = (a + (t + t_1)) + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = z + (x * math.log(y))
	tmp = 0
	if x <= -1.3e+112:
		tmp = (y * i) + (a + t_1)
	elif x <= 6.5e+15:
		tmp = (y * i) + (a + (z + (math.log(c) * (b - 0.5))))
	else:
		tmp = (a + (t + t_1)) + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(z + Float64(x * log(y)))
	tmp = 0.0
	if (x <= -1.3e+112)
		tmp = Float64(Float64(y * i) + Float64(a + t_1));
	elseif (x <= 6.5e+15)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + Float64(log(c) * Float64(b - 0.5)))));
	else
		tmp = Float64(Float64(a + Float64(t + t_1)) + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = z + (x * log(y));
	tmp = 0.0;
	if (x <= -1.3e+112)
		tmp = (y * i) + (a + t_1);
	elseif (x <= 6.5e+15)
		tmp = (y * i) + (a + (z + (log(c) * (b - 0.5))));
	else
		tmp = (a + (t + t_1)) + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.3e+112], N[(N[(y * i), $MachinePrecision] + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.5e+15], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a + N[(t + t$95$1), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.3e112

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf 100.0%

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

      1. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in b around 0 97.3%

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

   7. Taylor expanded in t around 0 89.4%

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

   if -1.3e112 < x < 6.5e15

   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 98.7%

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

      1. +-commutative 98.7%

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

      2. sub-neg 98.7%

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

      3. metadata-eval 98.7%

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

      4. fma-define 98.7%

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

      5. +-commutative 98.7%

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

   5. Simplified 98.7%

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

   6. Taylor expanded in t around 0 85.0%

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

   if 6.5e15 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf 99.8%

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

      1. *-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in b around 0 87.5%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+112}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + x \cdot \log y\right)\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+15}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right) + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 74.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+187} \lor \neg \left(x \leq 8.5 \cdot 10^{+64}\right):\\ \;\;\;\;y \cdot i + x \cdot \left(\log y + \frac{a}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -4.8e+187) (not (<= x 8.5e+64)))
   (+ (* y i) (* x (+ (log y) (/ a x))))
   (+ (* y i) (+ t (+ z a)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -4.8e+187) || !(x <= 8.5e+64)) {
		tmp = (y * i) + (x * (log(y) + (a / x)));
	} else {
		tmp = (y * i) + (t + (z + a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-4.8d+187)) .or. (.not. (x <= 8.5d+64))) then
        tmp = (y * i) + (x * (log(y) + (a / x)))
    else
        tmp = (y * i) + (t + (z + a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -4.8e+187) || !(x <= 8.5e+64)) {
		tmp = (y * i) + (x * (Math.log(y) + (a / x)));
	} else {
		tmp = (y * i) + (t + (z + a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -4.8e+187) or not (x <= 8.5e+64):
		tmp = (y * i) + (x * (math.log(y) + (a / x)))
	else:
		tmp = (y * i) + (t + (z + a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -4.8e+187) || !(x <= 8.5e+64))
		tmp = Float64(Float64(y * i) + Float64(x * Float64(log(y) + Float64(a / x))));
	else
		tmp = Float64(Float64(y * i) + Float64(t + Float64(z + a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -4.8e+187) || ~((x <= 8.5e+64)))
		tmp = (y * i) + (x * (log(y) + (a / x)));
	else
		tmp = (y * i) + (t + (z + a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -4.8e+187], N[Not[LessEqual[x, 8.5e+64]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(x * N[(N[Log[y], $MachinePrecision] + N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(t + N[(z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.79999999999999971e187 or 8.4999999999999998e64 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 99.6%

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

   4. Taylor expanded in a around inf 73.5%

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

   if -4.79999999999999971e187 < x < 8.4999999999999998e64

   1. Initial program 99.9%

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

   3. Taylor expanded in b around inf 96.8%

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

      1. *-commutative 96.8%

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

   5. Simplified 96.8%

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

   6. Taylor expanded in b around 0 81.6%

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

   7. Taylor expanded in x around 0 77.5%

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

      1. associate-+r+ 77.5%

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

      2. +-commutative 77.5%

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

      3. associate-+l+ 77.5%

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

   9. Simplified 77.5%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+187} \lor \neg \left(x \leq 8.5 \cdot 10^{+64}\right):\\ \;\;\;\;y \cdot i + x \cdot \left(\log y + \frac{a}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 76.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+114} \lor \neg \left(x \leq 2.05 \cdot 10^{+151}\right):\\ \;\;\;\;y \cdot i + x \cdot \left(\log y + \frac{z}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -2.3e+114) (not (<= x 2.05e+151)))
   (+ (* y i) (* x (+ (log y) (/ z x))))
   (+ (* y i) (+ t (+ z a)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -2.3e+114) || !(x <= 2.05e+151)) {
		tmp = (y * i) + (x * (log(y) + (z / x)));
	} else {
		tmp = (y * i) + (t + (z + a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-2.3d+114)) .or. (.not. (x <= 2.05d+151))) then
        tmp = (y * i) + (x * (log(y) + (z / x)))
    else
        tmp = (y * i) + (t + (z + a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -2.3e+114) || !(x <= 2.05e+151)) {
		tmp = (y * i) + (x * (Math.log(y) + (z / x)));
	} else {
		tmp = (y * i) + (t + (z + a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -2.3e+114) or not (x <= 2.05e+151):
		tmp = (y * i) + (x * (math.log(y) + (z / x)))
	else:
		tmp = (y * i) + (t + (z + a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -2.3e+114) || !(x <= 2.05e+151))
		tmp = Float64(Float64(y * i) + Float64(x * Float64(log(y) + Float64(z / x))));
	else
		tmp = Float64(Float64(y * i) + Float64(t + Float64(z + a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -2.3e+114) || ~((x <= 2.05e+151)))
		tmp = (y * i) + (x * (log(y) + (z / x)));
	else
		tmp = (y * i) + (t + (z + a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -2.3e+114], N[Not[LessEqual[x, 2.05e+151]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(x * N[(N[Log[y], $MachinePrecision] + N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(t + N[(z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.3e114 or 2.0499999999999999e151 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 99.7%

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

   4. Taylor expanded in z around inf 78.4%

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

   if -2.3e114 < x < 2.0499999999999999e151

   1. Initial program 99.9%

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

   3. Taylor expanded in b around inf 96.9%

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

      1. *-commutative 96.9%

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

   5. Simplified 96.9%

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

   6. Taylor expanded in b around 0 81.4%

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

   7. Taylor expanded in x around 0 77.5%

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

      1. associate-+r+ 77.5%

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

      2. +-commutative 77.5%

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

      3. associate-+l+ 77.5%

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

   9. Simplified 77.5%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+114} \lor \neg \left(x \leq 2.05 \cdot 10^{+151}\right):\\ \;\;\;\;y \cdot i + x \cdot \left(\log y + \frac{z}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 71.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.7 \cdot 10^{+226} \lor \neg \left(b \leq 5.6 \cdot 10^{+262}\right):\\ \;\;\;\;b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + x \cdot \log y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= b -6.7e+226) (not (<= b 5.6e+262)))
   (* b (log c))
   (+ (* y i) (+ a (+ z (* x (log y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((b <= -6.7e+226) || !(b <= 5.6e+262)) {
		tmp = b * log(c);
	} else {
		tmp = (y * i) + (a + (z + (x * log(y))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((b <= (-6.7d+226)) .or. (.not. (b <= 5.6d+262))) then
        tmp = b * log(c)
    else
        tmp = (y * i) + (a + (z + (x * log(y))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((b <= -6.7e+226) || !(b <= 5.6e+262)) {
		tmp = b * Math.log(c);
	} else {
		tmp = (y * i) + (a + (z + (x * Math.log(y))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (b <= -6.7e+226) or not (b <= 5.6e+262):
		tmp = b * math.log(c)
	else:
		tmp = (y * i) + (a + (z + (x * math.log(y))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((b <= -6.7e+226) || !(b <= 5.6e+262))
		tmp = Float64(b * log(c));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + Float64(x * log(y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((b <= -6.7e+226) || ~((b <= 5.6e+262)))
		tmp = b * log(c);
	else
		tmp = (y * i) + (a + (z + (x * log(y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[b, -6.7e+226], N[Not[LessEqual[b, 5.6e+262]], $MachinePrecision]], N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -6.69999999999999957e226 or 5.59999999999999995e262 < b

   1. Initial program 99.8%

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

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

   5. Taylor expanded in i around -inf 69.6%

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

   6. Taylor expanded in b around inf 68.3%

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

      1. mul-1-neg 68.3%

         \[\leadsto -1 \cdot \color{blue}{\left(-b \cdot \log c\right)} \]

      2. *-commutative 68.3%

         \[\leadsto -1 \cdot \left(-\color{blue}{\log c \cdot b}\right) \]

      3. distribute-rgt-neg-in 68.3%

         \[\leadsto -1 \cdot \color{blue}{\left(\log c \cdot \left(-b\right)\right)} \]

   8. Simplified 68.3%

      \[\leadsto -1 \cdot \color{blue}{\left(\log c \cdot \left(-b\right)\right)} \]

   if -6.69999999999999957e226 < b < 5.59999999999999995e262

   1. Initial program 99.9%

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

   3. Taylor expanded in b around inf 97.4%

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

      1. *-commutative 97.4%

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

   5. Simplified 97.4%

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

   6. Taylor expanded in b around 0 91.9%

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

   7. Taylor expanded in t around 0 78.1%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.7 \cdot 10^{+226} \lor \neg \left(b \leq 5.6 \cdot 10^{+262}\right):\\ \;\;\;\;b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + x \cdot \log y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 74.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+190} \lor \neg \left(x \leq 2.15 \cdot 10^{+151}\right):\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -1e+190) (not (<= x 2.15e+151)))
   (+ (* x (log y)) (* y i))
   (+ (* y i) (+ t (+ z a)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1e+190) || !(x <= 2.15e+151)) {
		tmp = (x * log(y)) + (y * i);
	} else {
		tmp = (y * i) + (t + (z + a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-1d+190)) .or. (.not. (x <= 2.15d+151))) then
        tmp = (x * log(y)) + (y * i)
    else
        tmp = (y * i) + (t + (z + a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1e+190) || !(x <= 2.15e+151)) {
		tmp = (x * Math.log(y)) + (y * i);
	} else {
		tmp = (y * i) + (t + (z + a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -1e+190) or not (x <= 2.15e+151):
		tmp = (x * math.log(y)) + (y * i)
	else:
		tmp = (y * i) + (t + (z + a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -1e+190) || !(x <= 2.15e+151))
		tmp = Float64(Float64(x * log(y)) + Float64(y * i));
	else
		tmp = Float64(Float64(y * i) + Float64(t + Float64(z + a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -1e+190) || ~((x <= 2.15e+151)))
		tmp = (x * log(y)) + (y * i);
	else
		tmp = (y * i) + (t + (z + a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -1e+190], N[Not[LessEqual[x, 2.15e+151]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(t + N[(z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.0000000000000001e190 or 2.14999999999999991e151 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 75.3%

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

   if -1.0000000000000001e190 < x < 2.14999999999999991e151

   1. Initial program 99.9%

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

   3. Taylor expanded in b around inf 97.1%

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

      1. *-commutative 97.1%

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

   5. Simplified 97.1%

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

   6. Taylor expanded in b around 0 82.1%

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

   7. Taylor expanded in x around 0 76.6%

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

      1. associate-+r+ 76.6%

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

      2. +-commutative 76.6%

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

      3. associate-+l+ 76.6%

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

   9. Simplified 76.6%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+190} \lor \neg \left(x \leq 2.15 \cdot 10^{+151}\right):\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 72.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{+262} \lor \neg \left(x \leq 5.35 \cdot 10^{+244}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -6.6e+262) (not (<= x 5.35e+244)))
   (* x (log y))
   (+ (* y i) (+ t (+ z a)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -6.6e+262) || !(x <= 5.35e+244)) {
		tmp = x * log(y);
	} else {
		tmp = (y * i) + (t + (z + a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-6.6d+262)) .or. (.not. (x <= 5.35d+244))) then
        tmp = x * log(y)
    else
        tmp = (y * i) + (t + (z + a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -6.6e+262) || !(x <= 5.35e+244)) {
		tmp = x * Math.log(y);
	} else {
		tmp = (y * i) + (t + (z + a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -6.6e+262) or not (x <= 5.35e+244):
		tmp = x * math.log(y)
	else:
		tmp = (y * i) + (t + (z + a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -6.6e+262) || !(x <= 5.35e+244))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(Float64(y * i) + Float64(t + Float64(z + a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -6.6e+262) || ~((x <= 5.35e+244)))
		tmp = x * log(y);
	else
		tmp = (y * i) + (t + (z + a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -6.6e+262], N[Not[LessEqual[x, 5.35e+244]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(t + N[(z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.59999999999999997e262 or 5.3500000000000001e244 < x

   1. Initial program 99.8%

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

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

   5. Taylor expanded in i around -inf 60.4%

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

   6. Taylor expanded in x around inf 68.0%

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

      1. mul-1-neg 68.0%

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

      2. *-commutative 68.0%

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

      3. distribute-rgt-neg-in 68.0%

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

   8. Simplified 68.0%

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

   if -6.59999999999999997e262 < x < 5.3500000000000001e244

   1. Initial program 99.9%

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

   3. Taylor expanded in b around inf 97.4%

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

      1. *-commutative 97.4%

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

   5. Simplified 97.4%

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

   6. Taylor expanded in b around 0 83.2%

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

   7. Taylor expanded in x around 0 73.5%

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

      1. associate-+r+ 73.5%

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

      2. +-commutative 73.5%

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

      3. associate-+l+ 73.5%

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

   9. Simplified 73.5%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{+262} \lor \neg \left(x \leq 5.35 \cdot 10^{+244}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 70.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -8.5 \cdot 10^{+227}:\\ \;\;\;\;b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= b -8.5e+227) (* b (log c)) (+ (* y i) (+ t (+ z a)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (b <= -8.5e+227) {
		tmp = b * log(c);
	} else {
		tmp = (y * i) + (t + (z + a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (b <= (-8.5d+227)) then
        tmp = b * log(c)
    else
        tmp = (y * i) + (t + (z + a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (b <= -8.5e+227) {
		tmp = b * Math.log(c);
	} else {
		tmp = (y * i) + (t + (z + a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if b <= -8.5e+227:
		tmp = b * math.log(c)
	else:
		tmp = (y * i) + (t + (z + a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (b <= -8.5e+227)
		tmp = Float64(b * log(c));
	else
		tmp = Float64(Float64(y * i) + Float64(t + Float64(z + a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (b <= -8.5e+227)
		tmp = b * log(c);
	else
		tmp = (y * i) + (t + (z + a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[b, -8.5e+227], N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(t + N[(z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -8.4999999999999995e227

   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%

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

   5. Taylor expanded in i around -inf 58.6%

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

   6. Taylor expanded in b around inf 65.3%

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

      1. mul-1-neg 65.3%

         \[\leadsto -1 \cdot \color{blue}{\left(-b \cdot \log c\right)} \]

      2. *-commutative 65.3%

         \[\leadsto -1 \cdot \left(-\color{blue}{\log c \cdot b}\right) \]

      3. distribute-rgt-neg-in 65.3%

         \[\leadsto -1 \cdot \color{blue}{\left(\log c \cdot \left(-b\right)\right)} \]

   8. Simplified 65.3%

      \[\leadsto -1 \cdot \color{blue}{\left(\log c \cdot \left(-b\right)\right)} \]

   if -8.4999999999999995e227 < b

   1. Initial program 99.9%

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

   3. Taylor expanded in b around inf 97.5%

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

      1. *-commutative 97.5%

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

   5. Simplified 97.5%

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

   6. Taylor expanded in b around 0 89.6%

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

   7. Taylor expanded in x around 0 71.3%

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

      1. associate-+r+ 71.3%

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

      2. +-commutative 71.3%

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

      3. associate-+l+ 71.3%

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

   9. Simplified 71.3%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.5 \cdot 10^{+227}:\\ \;\;\;\;b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 29.4% accurate, 16.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.7 \cdot 10^{-195}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+72}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 3.7e-195) z (if (<= y 1.4e+72) 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 (y <= 3.7e-195) {
		tmp = z;
	} else if (y <= 1.4e+72) {
		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 (y <= 3.7d-195) then
        tmp = z
    else if (y <= 1.4d+72) 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 (y <= 3.7e-195) {
		tmp = z;
	} else if (y <= 1.4e+72) {
		tmp = a;
	} else {
		tmp = y * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 3.7e-195:
		tmp = z
	elif y <= 1.4e+72:
		tmp = a
	else:
		tmp = y * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 3.7e-195)
		tmp = z;
	elseif (y <= 1.4e+72)
		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 (y <= 3.7e-195)
		tmp = z;
	elseif (y <= 1.4e+72)
		tmp = a;
	else
		tmp = y * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 3.7e-195], z, If[LessEqual[y, 1.4e+72], a, N[(y * i), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 3.69999999999999962e-195

   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%

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

   5. Taylor expanded in i around -inf 69.7%

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

   6. Taylor expanded in z around inf 24.5%

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

      1. mul-1-neg 24.5%

         \[\leadsto -1 \cdot \color{blue}{\left(-z\right)} \]

   8. Simplified 24.5%

      \[\leadsto -1 \cdot \color{blue}{\left(-z\right)} \]

   if 3.69999999999999962e-195 < y < 1.4e72

   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%

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

   5. Taylor expanded in i around -inf 74.7%

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

   6. Taylor expanded in a around inf 18.4%

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

      1. mul-1-neg 18.4%

         \[\leadsto -1 \cdot \color{blue}{\left(-a\right)} \]

   8. Simplified 18.4%

      \[\leadsto -1 \cdot \color{blue}{\left(-a\right)} \]

   if 1.4e72 < 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 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%

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

   5. Taylor expanded in y around inf 52.9%

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

      1. *-commutative 52.9%

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

   7. Simplified 52.9%

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

4. Final simplification 32.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.7 \cdot 10^{-195}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+72}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 41.4% accurate, 21.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+232}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -4.2e+232) z (+ a (* y i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -4.2e+232) {
		tmp = z;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-4.2d+232)) then
        tmp = z
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -4.2e+232) {
		tmp = z;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -4.2e+232:
		tmp = z
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -4.2e+232)
		tmp = z;
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -4.2e+232)
		tmp = z;
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -4.2e+232], z, N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.19999999999999982e232

   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%

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

   5. Taylor expanded in i around -inf 73.5%

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

   6. Taylor expanded in z around inf 47.7%

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

      1. mul-1-neg 47.7%

         \[\leadsto -1 \cdot \color{blue}{\left(-z\right)} \]

   8. Simplified 47.7%

      \[\leadsto -1 \cdot \color{blue}{\left(-z\right)} \]

   if -4.19999999999999982e232 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf 40.9%

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

4. Final simplification 41.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+232}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 43.0% accurate, 21.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 7.8 \cdot 10^{+145}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 7.8e+145) (+ z (* y i)) (+ a (* y i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 7.8e+145) {
		tmp = z + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 7.8d+145) then
        tmp = z + (y * i)
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 7.8e+145) {
		tmp = z + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 7.8e+145:
		tmp = z + (y * i)
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 7.8e+145)
		tmp = Float64(z + Float64(y * i));
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 7.8e+145)
		tmp = z + (y * i);
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 7.8e+145], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 7.7999999999999995e145

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 40.5%

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

   if 7.7999999999999995e145 < a

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf 71.4%

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

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 7.8 \cdot 10^{+145}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 68.0% accurate, 24.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in b around inf 97.7%

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

   1. *-commutative 97.7%

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

5. Simplified 97.7%

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

6. Taylor expanded in b around 0 84.2%

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

7. Taylor expanded in x around 0 67.4%

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

   1. associate-+r+ 67.4%

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

   2. +-commutative 67.4%

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

   3. associate-+l+ 67.4%

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

9. Simplified 67.4%

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

10. Final simplification 67.4%

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

Alternative 20: 29.4% accurate, 27.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.4 \cdot 10^{+72}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (if (<= y 2.4e+72) 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 (y <= 2.4e+72) {
		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 (y <= 2.4d+72) 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 (y <= 2.4e+72) {
		tmp = a;
	} else {
		tmp = y * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 2.4e+72:
		tmp = a
	else:
		tmp = y * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 2.4e+72)
		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 (y <= 2.4e+72)
		tmp = a;
	else
		tmp = y * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 2.4e+72], a, N[(y * i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.4000000000000001e72

   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%

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

   5. Taylor expanded in i around -inf 73.1%

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

   6. Taylor expanded in a around inf 20.8%

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

      1. mul-1-neg 20.8%

         \[\leadsto -1 \cdot \color{blue}{\left(-a\right)} \]

   8. Simplified 20.8%

      \[\leadsto -1 \cdot \color{blue}{\left(-a\right)} \]

   if 2.4000000000000001e72 < 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 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%

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

   5. Taylor expanded in y around inf 52.9%

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

      1. *-commutative 52.9%

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

   7. Simplified 52.9%

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

4. Final simplification 32.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.4 \cdot 10^{+72}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 23.8% accurate, 73.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

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

5. Taylor expanded in y around inf 24.0%

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

   1. *-commutative 24.0%

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

7. Simplified 24.0%

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

8. Final simplification 24.0%

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

Reproduce

herbie shell --seed 2024077 
(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)))