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

Percentage Accurate: 99.8% → 99.8%

Time: 17.2s

Alternatives: 18

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. associate-+l+ 99.9%

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

   2. associate-+l+ 99.9%

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

   3. +-commutative 99.9%

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

   4. associate-+l+ 99.9%

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

   5. +-commutative 99.9%

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

   6. associate-+l+ 99.9%

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

   7. +-commutative 99.9%

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

   8. associate-+l+ 99.9%

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

   9. +-commutative 99.9%

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

   10. fma-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%

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

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. Add Preprocessing

Alternative 2: 90.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+233} \lor \neg \left(x \leq 1.35 \cdot 10^{+233}\right):\\ \;\;\;\;a + \left(t + \left(z + \left(x \cdot \log y + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a + \left(z + t\right)\right) + \mathsf{fma}\left(\log c, b + -0.5, y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -1.2e+233) (not (<= x 1.35e+233)))
   (+ a (+ t (+ z (+ (* x (log y)) (* (log c) (- b 0.5))))))
   (+ (+ a (+ z t)) (fma (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) {
	double tmp;
	if ((x <= -1.2e+233) || !(x <= 1.35e+233)) {
		tmp = a + (t + (z + ((x * log(y)) + (log(c) * (b - 0.5)))));
	} else {
		tmp = (a + (z + t)) + fma(log(c), (b + -0.5), (y * i));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -1.2e+233) || !(x <= 1.35e+233))
		tmp = Float64(a + Float64(t + Float64(z + Float64(Float64(x * log(y)) + Float64(log(c) * Float64(b - 0.5))))));
	else
		tmp = Float64(Float64(a + Float64(z + t)) + fma(log(c), Float64(b + -0.5), Float64(y * i)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -1.2e+233], N[Not[LessEqual[x, 1.35e+233]], $MachinePrecision]], N[(a + N[(t + N[(z + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.20000000000000001e233 or 1.35000000000000004e233 < x

   1. Initial program 99.6%

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

      1. associate-+l+ 99.6%

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

      2. associate-+l+ 99.6%

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

      3. +-commutative 99.6%

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

      4. associate-+l+ 99.6%

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

      5. +-commutative 99.6%

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

      6. associate-+l+ 99.6%

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

      7. +-commutative 99.6%

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

      8. associate-+l+ 99.6%

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

      9. +-commutative 99.6%

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

      10. fma-define 99.6%

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

      11. +-commutative 99.6%

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

      12. fma-define 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around 0 88.1%

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

   if -1.20000000000000001e233 < x < 1.35000000000000004e233

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. associate-+l+ 99.9%

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

      7. +-commutative 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-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%

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

   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 x around 0 96.0%

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

      1. associate-+r+ 96.0%

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

      2. +-commutative 96.0%

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

      3. *-commutative 96.0%

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

      4. sub-neg 96.0%

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

      5. metadata-eval 96.0%

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

      6. associate-+r+ 96.0%

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

      7. +-commutative 96.0%

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

      8. +-commutative 96.0%

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

      9. fma-define 96.0%

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

      10. +-commutative 96.0%

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

   7. Simplified 96.0%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+233} \lor \neg \left(x \leq 1.35 \cdot 10^{+233}\right):\\ \;\;\;\;a + \left(t + \left(z + \left(x \cdot \log y + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a + \left(z + t\right)\right) + \mathsf{fma}\left(\log c, b + -0.5, y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 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 4: 84.3% accurate, 1.0× speedup

Math

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

FPCore

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. associate-+l+ 99.9%

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

   2. associate-+l+ 99.9%

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

   3. +-commutative 99.9%

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

   4. associate-+l+ 99.9%

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

   5. +-commutative 99.9%

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

   6. associate-+l+ 99.9%

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

   7. +-commutative 99.9%

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

   8. associate-+l+ 99.9%

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

   9. +-commutative 99.9%

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

   10. fma-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%

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

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 x around 0 84.8%

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

   1. associate-+r+ 84.8%

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

   2. +-commutative 84.8%

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

   3. *-commutative 84.8%

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

   4. sub-neg 84.8%

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

   5. metadata-eval 84.8%

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

   6. associate-+r+ 84.8%

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

   7. +-commutative 84.8%

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

   8. +-commutative 84.8%

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

   9. fma-define 84.8%

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

   10. +-commutative 84.8%

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

7. Simplified 84.8%

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

8. Final simplification 84.8%

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

Alternative 5: 74.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \left(z + t\right)\\ \mathbf{if}\;i \leq -4.5 \cdot 10^{-42} \lor \neg \left(i \leq 8 \cdot 10^{+54}\right):\\ \;\;\;\;y \cdot i + t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_1 + b \cdot \log c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (+ z t))))
   (if (or (<= i -4.5e-42) (not (<= i 8e+54)))
     (+ (* y i) t_1)
     (+ 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 = a + (z + t);
	double tmp;
	if ((i <= -4.5e-42) || !(i <= 8e+54)) {
		tmp = (y * i) + t_1;
	} else {
		tmp = t_1 + (b * log(c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a + (z + t)
    if ((i <= (-4.5d-42)) .or. (.not. (i <= 8d+54))) then
        tmp = (y * i) + t_1
    else
        tmp = t_1 + (b * log(c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (z + t);
	double tmp;
	if ((i <= -4.5e-42) || !(i <= 8e+54)) {
		tmp = (y * i) + t_1;
	} else {
		tmp = t_1 + (b * Math.log(c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (z + t)
	tmp = 0
	if (i <= -4.5e-42) or not (i <= 8e+54):
		tmp = (y * i) + t_1
	else:
		tmp = t_1 + (b * math.log(c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(z + t))
	tmp = 0.0
	if ((i <= -4.5e-42) || !(i <= 8e+54))
		tmp = Float64(Float64(y * i) + t_1);
	else
		tmp = Float64(t_1 + Float64(b * log(c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (z + t);
	tmp = 0.0;
	if ((i <= -4.5e-42) || ~((i <= 8e+54)))
		tmp = (y * i) + t_1;
	else
		tmp = t_1 + (b * log(c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[i, -4.5e-42], N[Not[LessEqual[i, 8e+54]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + t$95$1), $MachinePrecision], N[(t$95$1 + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if i < -4.5e-42 or 8.0000000000000006e54 < i

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. associate-+l+ 99.9%

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

      7. +-commutative 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-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%

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

   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 x around 0 88.0%

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

      1. associate-+r+ 88.0%

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

      2. +-commutative 88.0%

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

      3. *-commutative 88.0%

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

      4. sub-neg 88.0%

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

      5. metadata-eval 88.0%

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

      6. associate-+r+ 88.0%

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

      7. +-commutative 88.0%

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

      8. +-commutative 88.0%

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

      9. fma-define 88.0%

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

      10. +-commutative 88.0%

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

   7. Simplified 88.0%

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

   8. Taylor expanded in y around inf 79.1%

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

      1. *-commutative 79.1%

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

   10. Simplified 79.1%

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

   if -4.5e-42 < i < 8.0000000000000006e54

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. associate-+l+ 99.9%

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

      7. +-commutative 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-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%

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

   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 x around 0 81.8%

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

      1. associate-+r+ 81.8%

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

      2. +-commutative 81.8%

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

      3. *-commutative 81.8%

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

      4. sub-neg 81.8%

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

      5. metadata-eval 81.8%

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

      6. associate-+r+ 81.8%

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

      7. +-commutative 81.8%

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

      8. +-commutative 81.8%

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

      9. fma-define 81.8%

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

      10. +-commutative 81.8%

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

   7. Simplified 81.8%

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

   8. Taylor expanded in b around inf 79.5%

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

      1. *-commutative 79.5%

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

   10. Simplified 79.5%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4.5 \cdot 10^{-42} \lor \neg \left(i \leq 8 \cdot 10^{+54}\right):\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a + \left(z + t\right)\right) + b \cdot \log c\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 1.25 \cdot 10^{+94}:\\ \;\;\;\;y \cdot i + \left(z + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a + \left(z + t\right)\right) + \left(y \cdot i + -0.5 \cdot \log c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 1.25e+94)
   (+ (* y i) (+ z (* b (log c))))
   (+ (+ a (+ z t)) (+ (* y i) (* -0.5 (log c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 1.25e+94) {
		tmp = (y * i) + (z + (b * log(c)));
	} else {
		tmp = (a + (z + t)) + ((y * i) + (-0.5 * log(c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 1.25d+94) then
        tmp = (y * i) + (z + (b * log(c)))
    else
        tmp = (a + (z + t)) + ((y * i) + ((-0.5d0) * log(c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 1.25e+94) {
		tmp = (y * i) + (z + (b * Math.log(c)));
	} else {
		tmp = (a + (z + t)) + ((y * i) + (-0.5 * Math.log(c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 1.25e+94:
		tmp = (y * i) + (z + (b * math.log(c)))
	else:
		tmp = (a + (z + t)) + ((y * i) + (-0.5 * math.log(c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 1.25e+94)
		tmp = Float64(Float64(y * i) + Float64(z + Float64(b * log(c))));
	else
		tmp = Float64(Float64(a + Float64(z + t)) + Float64(Float64(y * i) + Float64(-0.5 * log(c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 1.25e+94)
		tmp = (y * i) + (z + (b * log(c)));
	else
		tmp = (a + (z + t)) + ((y * i) + (-0.5 * log(c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 1.25e+94], N[(N[(y * i), $MachinePrecision] + N[(z + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision] + N[(N[(y * i), $MachinePrecision] + N[(-0.5 * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 1.25000000000000003e94

   1. Initial program 99.9%

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

      1. add-cbrt-cube 99.8%

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

      2. pow3 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in b around inf 99.7%

      \[\leadsto \left(\left(\left(\left(x \cdot \sqrt[3]{{\log y}^{3}} + z\right) + t\right) + a\right) + \color{blue}{b \cdot \log c}\right) + y \cdot i \]
   6. Step-by-step derivation

      1. *-commutative 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in z around inf 60.3%

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

   if 1.25000000000000003e94 < a

   1. Initial program 99.8%

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

      1. associate-+l+ 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. associate-+l+ 99.8%

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

      5. +-commutative 99.8%

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

      6. associate-+l+ 99.8%

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

      7. +-commutative 99.8%

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

      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%

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

   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 x around 0 82.4%

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

      1. associate-+r+ 82.4%

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

      2. +-commutative 82.4%

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

      3. *-commutative 82.4%

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

      4. sub-neg 82.4%

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

      5. metadata-eval 82.4%

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

      6. associate-+r+ 82.4%

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

      7. +-commutative 82.4%

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

      8. +-commutative 82.4%

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

      9. fma-define 82.4%

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

      10. +-commutative 82.4%

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

   7. Simplified 82.4%

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

   8. Taylor expanded in b around 0 64.8%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.25 \cdot 10^{+94}:\\ \;\;\;\;y \cdot i + \left(z + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a + \left(z + t\right)\right) + \left(y \cdot i + -0.5 \cdot \log c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{+151} \lor \neg \left(b \leq 1.55 \cdot 10^{+188}\right):\\ \;\;\;\;b \cdot \log c + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= b -1.55e+151) (not (<= b 1.55e+188)))
   (+ (* b (log c)) (+ z a))
   (+ (* y i) (+ a (+ z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((b <= -1.55e+151) || !(b <= 1.55e+188)) {
		tmp = (b * log(c)) + (z + a);
	} else {
		tmp = (y * i) + (a + (z + t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((b <= (-1.55d+151)) .or. (.not. (b <= 1.55d+188))) then
        tmp = (b * log(c)) + (z + a)
    else
        tmp = (y * i) + (a + (z + t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((b <= -1.55e+151) || !(b <= 1.55e+188)) {
		tmp = (b * Math.log(c)) + (z + a);
	} else {
		tmp = (y * i) + (a + (z + t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (b <= -1.55e+151) or not (b <= 1.55e+188):
		tmp = (b * math.log(c)) + (z + a)
	else:
		tmp = (y * i) + (a + (z + t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((b <= -1.55e+151) || !(b <= 1.55e+188))
		tmp = Float64(Float64(b * log(c)) + Float64(z + a));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((b <= -1.55e+151) || ~((b <= 1.55e+188)))
		tmp = (b * log(c)) + (z + a);
	else
		tmp = (y * i) + (a + (z + t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[b, -1.55e+151], N[Not[LessEqual[b, 1.55e+188]], $MachinePrecision]], N[(N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision] + N[(z + a), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.5500000000000001e151 or 1.5500000000000001e188 < 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. Step-by-step derivation

      1. associate-+l+ 99.7%

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

      2. associate-+l+ 99.7%

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

      3. +-commutative 99.7%

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

      4. associate-+l+ 99.7%

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

      5. +-commutative 99.7%

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

      6. associate-+l+ 99.7%

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

      7. +-commutative 99.7%

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

      8. associate-+l+ 99.7%

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

      9. +-commutative 99.7%

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

      10. fma-define 99.7%

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

      11. +-commutative 99.7%

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

      12. fma-define 99.7%

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

   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 x around 0 95.2%

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

      1. associate-+r+ 95.2%

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

      2. +-commutative 95.2%

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

      3. *-commutative 95.2%

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

      4. sub-neg 95.2%

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

      5. metadata-eval 95.2%

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

      6. associate-+r+ 95.2%

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

      7. +-commutative 95.2%

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

      8. +-commutative 95.2%

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

      9. fma-define 95.2%

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

      10. +-commutative 95.2%

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

   7. Simplified 95.2%

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

   8. Taylor expanded in b around inf 83.1%

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

      1. *-commutative 83.1%

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

   10. Simplified 83.1%

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

   11. Taylor expanded in t around 0 73.4%

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

   if -1.5500000000000001e151 < b < 1.5500000000000001e188

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. associate-+l+ 99.9%

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

      7. +-commutative 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-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%

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

   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 x around 0 81.3%

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

      1. associate-+r+ 81.3%

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

      2. +-commutative 81.3%

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

      3. *-commutative 81.3%

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

      4. sub-neg 81.3%

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

      5. metadata-eval 81.3%

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

      6. associate-+r+ 81.3%

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

      7. +-commutative 81.3%

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

      8. +-commutative 81.3%

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

      9. fma-define 81.3%

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

      10. +-commutative 81.3%

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

   7. Simplified 81.3%

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

   8. Taylor expanded in y around inf 77.9%

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

      1. *-commutative 77.9%

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

   10. Simplified 77.9%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{+151} \lor \neg \left(b \leq 1.55 \cdot 10^{+188}\right):\\ \;\;\;\;b \cdot \log c + \left(z + a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 73.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.8 \cdot 10^{+225} \lor \neg \left(b \leq 6 \cdot 10^{+221}\right):\\ \;\;\;\;\left(t + a\right) + b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= b -1.8e+225) (not (<= b 6e+221)))
   (+ (+ t a) (* b (log c)))
   (+ (* y i) (+ a (+ z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((b <= -1.8e+225) || !(b <= 6e+221)) {
		tmp = (t + a) + (b * log(c));
	} else {
		tmp = (y * i) + (a + (z + t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((b <= (-1.8d+225)) .or. (.not. (b <= 6d+221))) then
        tmp = (t + a) + (b * log(c))
    else
        tmp = (y * i) + (a + (z + t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((b <= -1.8e+225) || !(b <= 6e+221)) {
		tmp = (t + a) + (b * Math.log(c));
	} else {
		tmp = (y * i) + (a + (z + t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (b <= -1.8e+225) or not (b <= 6e+221):
		tmp = (t + a) + (b * math.log(c))
	else:
		tmp = (y * i) + (a + (z + t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((b <= -1.8e+225) || !(b <= 6e+221))
		tmp = Float64(Float64(t + a) + Float64(b * log(c)));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((b <= -1.8e+225) || ~((b <= 6e+221)))
		tmp = (t + a) + (b * log(c));
	else
		tmp = (y * i) + (a + (z + t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[b, -1.8e+225], N[Not[LessEqual[b, 6e+221]], $MachinePrecision]], N[(N[(t + a), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.7999999999999999e225 or 6.0000000000000003e221 < 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. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. associate-+l+ 99.8%

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

      5. +-commutative 99.8%

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

      6. associate-+l+ 99.8%

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

      7. +-commutative 99.8%

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

      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%

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

   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 x around 0 99.8%

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

      1. associate-+r+ 99.8%

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

      2. +-commutative 99.8%

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

      3. *-commutative 99.8%

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

      4. sub-neg 99.8%

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

      5. metadata-eval 99.8%

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

      6. associate-+r+ 99.8%

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

      7. +-commutative 99.8%

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

      8. +-commutative 99.8%

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

      9. fma-define 99.8%

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

      10. +-commutative 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in b around inf 91.4%

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

      1. *-commutative 91.4%

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

   10. Simplified 91.4%

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

   11. Taylor expanded in z around 0 84.9%

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

   if -1.7999999999999999e225 < b < 6.0000000000000003e221

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. associate-+l+ 99.9%

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

      7. +-commutative 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-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%

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

   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 x around 0 82.4%

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

      1. associate-+r+ 82.4%

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

      2. +-commutative 82.4%

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

      3. *-commutative 82.4%

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

      4. sub-neg 82.4%

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

      5. metadata-eval 82.4%

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

      6. associate-+r+ 82.4%

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

      7. +-commutative 82.4%

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

      8. +-commutative 82.4%

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

      9. fma-define 82.4%

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

      10. +-commutative 82.4%

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

   7. Simplified 82.4%

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

   8. Taylor expanded in y around inf 76.2%

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

      1. *-commutative 76.2%

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

   10. Simplified 76.2%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.8 \cdot 10^{+225} \lor \neg \left(b \leq 6 \cdot 10^{+221}\right):\\ \;\;\;\;\left(t + a\right) + b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 67.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{+223}:\\ \;\;\;\;y \cdot \left(b \cdot \frac{\log c}{y}\right)\\ \mathbf{elif}\;b \leq 5.1 \cdot 10^{+223}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(b \cdot \frac{\log c}{i}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= b -1e+223)
   (* y (* b (/ (log c) y)))
   (if (<= b 5.1e+223) (+ (* y i) (+ a (+ z t))) (* i (* b (/ (log c) i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (b <= -1e+223) {
		tmp = y * (b * (log(c) / y));
	} else if (b <= 5.1e+223) {
		tmp = (y * i) + (a + (z + t));
	} else {
		tmp = i * (b * (log(c) / 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 (b <= (-1d+223)) then
        tmp = y * (b * (log(c) / y))
    else if (b <= 5.1d+223) then
        tmp = (y * i) + (a + (z + t))
    else
        tmp = i * (b * (log(c) / 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 (b <= -1e+223) {
		tmp = y * (b * (Math.log(c) / y));
	} else if (b <= 5.1e+223) {
		tmp = (y * i) + (a + (z + t));
	} else {
		tmp = i * (b * (Math.log(c) / i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if b <= -1e+223:
		tmp = y * (b * (math.log(c) / y))
	elif b <= 5.1e+223:
		tmp = (y * i) + (a + (z + t))
	else:
		tmp = i * (b * (math.log(c) / i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (b <= -1e+223)
		tmp = Float64(y * Float64(b * Float64(log(c) / y)));
	elseif (b <= 5.1e+223)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + t)));
	else
		tmp = Float64(i * Float64(b * Float64(log(c) / i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (b <= -1e+223)
		tmp = y * (b * (log(c) / y));
	elseif (b <= 5.1e+223)
		tmp = (y * i) + (a + (z + t));
	else
		tmp = i * (b * (log(c) / i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[b, -1e+223], N[(y * N[(b * N[(N[Log[c], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.1e+223], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(b * N[(N[Log[c], $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.00000000000000005e223

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. associate-+l+ 99.9%

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

      7. +-commutative 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-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%

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

   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 x around 0 94.5%

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

      1. associate-+r+ 94.5%

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

      2. +-commutative 94.5%

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

      3. *-commutative 94.5%

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

      4. sub-neg 94.5%

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

      5. metadata-eval 94.5%

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

      6. associate-+r+ 94.5%

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

      7. +-commutative 94.5%

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

      8. +-commutative 94.5%

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

      9. fma-define 94.5%

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

      10. +-commutative 94.5%

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

   7. Simplified 94.5%

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

   8. Taylor expanded in y around inf 58.3%

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

      1. associate-+r+ 58.3%

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

      2. associate-+r+ 58.3%

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

      3. associate-/l* 58.3%

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

      4. sub-neg 58.3%

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

      5. metadata-eval 58.3%

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

   10. Simplified 58.3%

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

   11. Taylor expanded in b around inf 42.9%

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

       1. associate-/l* 42.8%

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

   13. Simplified 42.8%

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

   if -1.00000000000000005e223 < b < 5.09999999999999966e223

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. associate-+l+ 99.9%

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

      7. +-commutative 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-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%

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

   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 x around 0 82.8%

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

      1. associate-+r+ 82.8%

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

      2. +-commutative 82.8%

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

      3. *-commutative 82.8%

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

      4. sub-neg 82.8%

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

      5. metadata-eval 82.8%

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

      6. associate-+r+ 82.8%

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

      7. +-commutative 82.8%

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

      8. +-commutative 82.8%

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

      9. fma-define 82.8%

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

      10. +-commutative 82.8%

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

   7. Simplified 82.8%

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

   8. Taylor expanded in y around inf 76.6%

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

      1. *-commutative 76.6%

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

   10. Simplified 76.6%

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

   if 5.09999999999999966e223 < b

   1. Initial program 99.6%

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

      1. associate-+l+ 99.6%

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

      2. associate-+l+ 99.6%

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

      3. +-commutative 99.6%

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

      4. associate-+l+ 99.6%

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

      5. +-commutative 99.6%

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

      6. associate-+l+ 99.6%

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

      7. +-commutative 99.6%

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

      8. associate-+l+ 99.6%

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

      9. +-commutative 99.6%

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

      10. fma-define 99.6%

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

      11. +-commutative 99.6%

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

      12. fma-define 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0 99.6%

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

      1. associate-+r+ 99.6%

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

      2. +-commutative 99.6%

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

      3. *-commutative 99.6%

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

      4. sub-neg 99.6%

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

      5. metadata-eval 99.6%

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

      6. associate-+r+ 99.6%

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

      7. +-commutative 99.6%

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

      8. +-commutative 99.6%

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

      9. fma-define 99.7%

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

      10. +-commutative 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in i around inf 71.3%

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

      1. associate-+r+ 71.3%

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

      2. associate-+r+ 71.3%

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

      3. associate-/l* 71.6%

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

      4. sub-neg 71.6%

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

      5. metadata-eval 71.6%

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

   10. Simplified 71.6%

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

   11. Taylor expanded in b around inf 55.8%

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

       1. associate-/l* 55.9%

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

   13. Simplified 55.9%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{+223}:\\ \;\;\;\;y \cdot \left(b \cdot \frac{\log c}{y}\right)\\ \mathbf{elif}\;b \leq 5.1 \cdot 10^{+223}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(b \cdot \frac{\log c}{i}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 84.2% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in x around 0 84.8%

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

4. Final simplification 84.8%

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

Alternative 11: 60.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 1.6 \cdot 10^{+94}:\\ \;\;\;\;y \cdot i + \left(z + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 1.6e+94) (+ (* y i) (+ z (* b (log c)))) (+ (* y i) (+ a (+ z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 1.6e+94) {
		tmp = (y * i) + (z + (b * log(c)));
	} else {
		tmp = (y * i) + (a + (z + t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 1.6d+94) then
        tmp = (y * i) + (z + (b * log(c)))
    else
        tmp = (y * i) + (a + (z + t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 1.6e+94) {
		tmp = (y * i) + (z + (b * Math.log(c)));
	} else {
		tmp = (y * i) + (a + (z + t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 1.6e+94:
		tmp = (y * i) + (z + (b * math.log(c)))
	else:
		tmp = (y * i) + (a + (z + t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 1.6e+94)
		tmp = Float64(Float64(y * i) + Float64(z + Float64(b * log(c))));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 1.6e+94)
		tmp = (y * i) + (z + (b * log(c)));
	else
		tmp = (y * i) + (a + (z + t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 1.6e+94], N[(N[(y * i), $MachinePrecision] + N[(z + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 1.60000000000000007e94

   1. Initial program 99.9%

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

      1. add-cbrt-cube 99.8%

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

      2. pow3 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in b around inf 99.7%

      \[\leadsto \left(\left(\left(\left(x \cdot \sqrt[3]{{\log y}^{3}} + z\right) + t\right) + a\right) + \color{blue}{b \cdot \log c}\right) + y \cdot i \]
   6. Step-by-step derivation

      1. *-commutative 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in z around inf 60.3%

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

   if 1.60000000000000007e94 < a

   1. Initial program 99.8%

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

      1. associate-+l+ 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. associate-+l+ 99.8%

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

      5. +-commutative 99.8%

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

      6. associate-+l+ 99.8%

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

      7. +-commutative 99.8%

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

      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%

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

   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 x around 0 82.4%

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

      1. associate-+r+ 82.4%

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

      2. +-commutative 82.4%

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

      3. *-commutative 82.4%

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

      4. sub-neg 82.4%

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

      5. metadata-eval 82.4%

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

      6. associate-+r+ 82.4%

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

      7. +-commutative 82.4%

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

      8. +-commutative 82.4%

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

      9. fma-define 82.4%

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

      10. +-commutative 82.4%

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

   7. Simplified 82.4%

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

   8. Taylor expanded in y around inf 64.8%

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

      1. *-commutative 64.8%

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

   10. Simplified 64.8%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.6 \cdot 10^{+94}:\\ \;\;\;\;y \cdot i + \left(z + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 67.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 5.1 \cdot 10^{+223}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(b \cdot \frac{\log c}{i}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= b 5.1e+223) (+ (* y i) (+ a (+ z t))) (* i (* b (/ (log c) i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (b <= 5.1e+223) {
		tmp = (y * i) + (a + (z + t));
	} else {
		tmp = i * (b * (log(c) / 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 (b <= 5.1d+223) then
        tmp = (y * i) + (a + (z + t))
    else
        tmp = i * (b * (log(c) / 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 (b <= 5.1e+223) {
		tmp = (y * i) + (a + (z + t));
	} else {
		tmp = i * (b * (Math.log(c) / i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if b <= 5.1e+223:
		tmp = (y * i) + (a + (z + t))
	else:
		tmp = i * (b * (math.log(c) / i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (b <= 5.1e+223)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + t)));
	else
		tmp = Float64(i * Float64(b * Float64(log(c) / i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (b <= 5.1e+223)
		tmp = (y * i) + (a + (z + t));
	else
		tmp = i * (b * (log(c) / i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[b, 5.1e+223], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(b * N[(N[Log[c], $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 5.09999999999999966e223

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. associate-+l+ 99.9%

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

      7. +-commutative 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-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%

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

   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 x around 0 83.7%

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

      1. associate-+r+ 83.7%

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

      2. +-commutative 83.7%

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

      3. *-commutative 83.7%

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

      4. sub-neg 83.7%

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

      5. metadata-eval 83.7%

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

      6. associate-+r+ 83.7%

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

      7. +-commutative 83.7%

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

      8. +-commutative 83.7%

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

      9. fma-define 83.7%

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

      10. +-commutative 83.7%

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

   7. Simplified 83.7%

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

   8. Taylor expanded in y around inf 72.3%

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

      1. *-commutative 72.3%

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

   10. Simplified 72.3%

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

   if 5.09999999999999966e223 < b

   1. Initial program 99.6%

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

      1. associate-+l+ 99.6%

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

      2. associate-+l+ 99.6%

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

      3. +-commutative 99.6%

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

      4. associate-+l+ 99.6%

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

      5. +-commutative 99.6%

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

      6. associate-+l+ 99.6%

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

      7. +-commutative 99.6%

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

      8. associate-+l+ 99.6%

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

      9. +-commutative 99.6%

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

      10. fma-define 99.6%

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

      11. +-commutative 99.6%

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

      12. fma-define 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0 99.6%

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

      1. associate-+r+ 99.6%

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

      2. +-commutative 99.6%

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

      3. *-commutative 99.6%

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

      4. sub-neg 99.6%

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

      5. metadata-eval 99.6%

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

      6. associate-+r+ 99.6%

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

      7. +-commutative 99.6%

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

      8. +-commutative 99.6%

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

      9. fma-define 99.7%

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

      10. +-commutative 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in i around inf 71.3%

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

      1. associate-+r+ 71.3%

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

      2. associate-+r+ 71.3%

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

      3. associate-/l* 71.6%

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

      4. sub-neg 71.6%

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

      5. metadata-eval 71.6%

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

   10. Simplified 71.6%

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

   11. Taylor expanded in b around inf 55.8%

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

       1. associate-/l* 55.9%

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

   13. Simplified 55.9%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 5.1 \cdot 10^{+223}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(b \cdot \frac{\log c}{i}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 37.0% accurate, 12.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -65000 \lor \neg \left(i \leq 5.8 \cdot 10^{-8}\right):\\ \;\;\;\;i \cdot \left(y + \frac{a}{i}\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= i -65000.0) (not (<= i 5.8e-8))) (* i (+ y (/ a i))) z))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((i <= -65000.0) || !(i <= 5.8e-8)) {
		tmp = i * (y + (a / i));
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((i <= (-65000.0d0)) .or. (.not. (i <= 5.8d-8))) then
        tmp = i * (y + (a / i))
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((i <= -65000.0) || !(i <= 5.8e-8)) {
		tmp = i * (y + (a / i));
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (i <= -65000.0) or not (i <= 5.8e-8):
		tmp = i * (y + (a / i))
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((i <= -65000.0) || !(i <= 5.8e-8))
		tmp = Float64(i * Float64(y + Float64(a / i)));
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((i <= -65000.0) || ~((i <= 5.8e-8)))
		tmp = i * (y + (a / i));
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[i, -65000.0], N[Not[LessEqual[i, 5.8e-8]], $MachinePrecision]], N[(i * N[(y + N[(a / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if i < -65000 or 5.8000000000000003e-8 < i

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. associate-+l+ 99.9%

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

      7. +-commutative 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-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%

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

   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 99.7%

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

      1. associate-/l* 99.7%

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

      2. sub-neg 99.7%

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

      3. metadata-eval 99.7%

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

      4. associate-/l* 99.7%

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

      5. +-commutative 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in a around inf 59.0%

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

   if -65000 < i < 5.8000000000000003e-8

   1. Initial program 99.8%

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

      1. associate-+l+ 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. associate-+l+ 99.8%

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

      5. +-commutative 99.8%

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

      6. associate-+l+ 99.8%

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

      7. +-commutative 99.8%

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

      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%

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

   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 z around inf 22.4%

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

4. Final simplification 41.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -65000 \lor \neg \left(i \leq 5.8 \cdot 10^{-8}\right):\\ \;\;\;\;i \cdot \left(y + \frac{a}{i}\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 25.1% accurate, 16.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{-128}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+91}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a -5e-128) z (if (<= a 4e+91) (* y i) a)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= -5e-128) {
		tmp = z;
	} else if (a <= 4e+91) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= (-5d-128)) then
        tmp = z
    else if (a <= 4d+91) then
        tmp = y * i
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= -5e-128) {
		tmp = z;
	} else if (a <= 4e+91) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= -5e-128:
		tmp = z
	elif a <= 4e+91:
		tmp = y * i
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= -5e-128)
		tmp = z;
	elseif (a <= 4e+91)
		tmp = Float64(y * i);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= -5e-128)
		tmp = z;
	elseif (a <= 4e+91)
		tmp = y * i;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, -5e-128], z, If[LessEqual[a, 4e+91], N[(y * i), $MachinePrecision], a]]

Derivation

1. Split input into 3 regimes

2. if a < -5.0000000000000001e-128

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. associate-+l+ 99.9%

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

      7. +-commutative 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-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%

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

   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 z around inf 18.4%

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

   if -5.0000000000000001e-128 < a < 4.00000000000000032e91

   1. Initial program 99.8%

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

      1. associate-+l+ 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. associate-+l+ 99.8%

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

      5. +-commutative 99.8%

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

      6. associate-+l+ 99.8%

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

      7. +-commutative 99.8%

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

      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%

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

   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 y around inf 28.4%

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

      1. *-commutative 28.4%

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

   7. Simplified 28.4%

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

   if 4.00000000000000032e91 < a

   1. Initial program 99.8%

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

      1. associate-+l+ 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. associate-+l+ 99.8%

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

      5. +-commutative 99.8%

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

      6. associate-+l+ 99.8%

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

      7. +-commutative 99.8%

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

      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%

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

   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 a around inf 39.3%

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

Alternative 15: 36.0% accurate, 18.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 1.6 \cdot 10^{+167}:\\ \;\;\;\;i \cdot \left(y + \frac{z}{i}\right)\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 1.6e+167) (* i (+ y (/ z i))) a))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 1.6e+167) {
		tmp = i * (y + (z / i));
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 1.6d+167) then
        tmp = i * (y + (z / i))
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 1.6e+167) {
		tmp = i * (y + (z / i));
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 1.6e+167:
		tmp = i * (y + (z / i))
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 1.6e+167)
		tmp = Float64(i * Float64(y + Float64(z / i)));
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 1.6e+167)
		tmp = i * (y + (z / i));
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 1.6e+167], N[(i * N[(y + N[(z / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], a]

Derivation

1. Split input into 2 regimes

2. if a < 1.5999999999999999e167

   1. Initial program 99.8%

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

      1. associate-+l+ 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. associate-+l+ 99.8%

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

      5. +-commutative 99.8%

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

      6. associate-+l+ 99.8%

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

      7. +-commutative 99.8%

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

      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%

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

   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 69.2%

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

      1. associate-/l* 69.2%

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

      2. sub-neg 69.2%

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

      3. metadata-eval 69.2%

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

      4. associate-/l* 69.2%

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

      5. +-commutative 69.2%

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

   7. Simplified 69.2%

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

   8. Taylor expanded in z around inf 38.3%

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

   if 1.5999999999999999e167 < a

   1. Initial program 100.0%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. 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. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. associate-+l+ 100.0%

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

      5. +-commutative 100.0%

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

      6. associate-+l+ 100.0%

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

      7. +-commutative 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%

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

   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 a around inf 45.8%

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

Alternative 16: 67.2% accurate, 24.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. associate-+l+ 99.9%

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

   2. associate-+l+ 99.9%

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

   3. +-commutative 99.9%

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

   4. associate-+l+ 99.9%

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

   5. +-commutative 99.9%

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

   6. associate-+l+ 99.9%

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

   7. +-commutative 99.9%

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

   8. associate-+l+ 99.9%

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

   9. +-commutative 99.9%

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

   10. fma-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%

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

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 x around 0 84.8%

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

   1. associate-+r+ 84.8%

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

   2. +-commutative 84.8%

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

   3. *-commutative 84.8%

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

   4. sub-neg 84.8%

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

   5. metadata-eval 84.8%

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

   6. associate-+r+ 84.8%

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

   7. +-commutative 84.8%

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

   8. +-commutative 84.8%

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

   9. fma-define 84.8%

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

   10. +-commutative 84.8%

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

7. Simplified 84.8%

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

8. Taylor expanded in y around inf 69.1%

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

   1. *-commutative 69.1%

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

10. Simplified 69.1%

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

11. Final simplification 69.1%

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

Alternative 17: 21.7% accurate, 36.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 8.2 \cdot 10^{+113}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (if (<= a 8.2e+113) z a))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 8.2e+113) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 8.2d+113) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 8.2e+113) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 8.2e+113:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 8.2e+113)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 8.2e+113)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 8.2e+113], z, a]

Derivation

1. Split input into 2 regimes

2. if a < 8.19999999999999985e113

   1. Initial program 99.8%

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

      1. associate-+l+ 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. associate-+l+ 99.8%

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

      5. +-commutative 99.8%

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

      6. associate-+l+ 99.8%

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

      7. +-commutative 99.8%

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

      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 99.9%

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

      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%

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

   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 z around inf 20.3%

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

   if 8.19999999999999985e113 < a

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. associate-+l+ 99.9%

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

      7. +-commutative 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-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%

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

   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 a around inf 42.2%

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

Alternative 18: 16.1% accurate, 219.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. associate-+l+ 99.9%

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

   2. associate-+l+ 99.9%

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

   3. +-commutative 99.9%

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

   4. associate-+l+ 99.9%

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

   5. +-commutative 99.9%

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

   6. associate-+l+ 99.9%

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

   7. +-commutative 99.9%

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

   8. associate-+l+ 99.9%

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

   9. +-commutative 99.9%

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

   10. fma-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%

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

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 a around inf 15.6%

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

Reproduce

herbie shell --seed 2024181 
(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)))