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

Percentage Accurate: 99.8% → 99.8%

Time: 16.5s

Alternatives: 24

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. associate-+l+ 99.9%

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

   2. +-commutative 99.9%

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

   3. associate-+l+ 99.9%

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

   4. associate-+r+ 99.9%

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

   5. +-commutative 99.9%

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

   6. +-commutative 99.9%

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

   7. associate-+l+ 99.9%

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

   8. associate-+l+ 99.9%

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

   9. +-commutative 99.9%

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

   10. fma-define 99.9%

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

   11. +-commutative 99.9%

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

   12. fma-define 99.9%

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

   13. sub-neg 99.9%

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

   14. metadata-eval 99.9%

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

   15. +-commutative 99.9%

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

3. Simplified 99.9%

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

Alternative 2: 90.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{+152} \lor \neg \left(x \leq 5 \cdot 10^{+141}\right):\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + t\right) + \left(a + \mathsf{fma}\left(\log c, b + -0.5, y \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -4.1e+152) (not (<= x 5e+141)))
   (+ (* y i) (+ (* x (log y)) (* b (log c))))
   (+ (+ z t) (+ a (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 <= -4.1e+152) || !(x <= 5e+141)) {
		tmp = (y * i) + ((x * log(y)) + (b * log(c)));
	} else {
		tmp = (z + t) + (a + 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 <= -4.1e+152) || !(x <= 5e+141))
		tmp = Float64(Float64(y * i) + Float64(Float64(x * log(y)) + Float64(b * log(c))));
	else
		tmp = Float64(Float64(z + t) + Float64(a + 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, -4.1e+152], N[Not[LessEqual[x, 5e+141]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + t), $MachinePrecision] + N[(a + N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.0999999999999998e152 or 5.00000000000000025e141 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 91.6%

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

   4. Taylor expanded in b around inf 91.6%

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

      1. *-commutative 91.6%

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

   6. Simplified 91.6%

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

   7. Taylor expanded in x around inf 80.9%

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

   if -4.0999999999999998e152 < x < 5.00000000000000025e141

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. associate-+r+ 99.9%

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

      5. +-commutative 99.9%

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

      6. +-commutative 99.9%

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

      7. associate-+l+ 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-define 99.9%

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

      13. sub-neg 99.9%

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

      14. metadata-eval 99.9%

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

      15. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 94.7%

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

      1. +-commutative 94.7%

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

      2. associate-+r+ 94.7%

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

      3. *-commutative 94.7%

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

      4. sub-neg 94.7%

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

      5. metadata-eval 94.7%

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

      6. +-commutative 94.7%

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

      7. distribute-rgt-out 94.7%

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

      8. +-commutative 94.7%

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

      9. distribute-rgt-in 94.7%

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

      10. associate-+l+ 94.7%

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

      11. +-commutative 94.7%

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

      12. +-commutative 94.7%

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

      13. fma-define 94.7%

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

      14. +-commutative 94.7%

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

   7. Simplified 94.7%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{+152} \lor \neg \left(x \leq 5 \cdot 10^{+141}\right):\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + t\right) + \left(a + \mathsf{fma}\left(\log c, b + -0.5, y \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -1 \cdot 10^{+153}:\\ \;\;\;\;y \cdot i + \left(t\_1 + b \cdot \log c\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+141}:\\ \;\;\;\;\left(z + t\right) + \left(a + \mathsf{fma}\left(\log c, b + -0.5, y \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t\_1 + \log c \cdot \left(b - 0.5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -1e+153)
     (+ (* y i) (+ t_1 (* b (log c))))
     (if (<= x 5e+141)
       (+ (+ z t) (+ a (fma (log c) (+ b -0.5) (* y i))))
       (+ (* y i) (+ t_1 (* (log c) (- b 0.5))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * log(y);
	double tmp;
	if (x <= -1e+153) {
		tmp = (y * i) + (t_1 + (b * log(c)));
	} else if (x <= 5e+141) {
		tmp = (z + t) + (a + fma(log(c), (b + -0.5), (y * i)));
	} else {
		tmp = (y * i) + (t_1 + (log(c) * (b - 0.5)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -1e+153)
		tmp = Float64(Float64(y * i) + Float64(t_1 + Float64(b * log(c))));
	elseif (x <= 5e+141)
		tmp = Float64(Float64(z + t) + Float64(a + fma(log(c), Float64(b + -0.5), Float64(y * i))));
	else
		tmp = Float64(Float64(y * i) + Float64(t_1 + Float64(log(c) * Float64(b - 0.5))));
	end
	return tmp
end

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if x < -1e153

   1. Initial program 99.7%

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

   3. Taylor expanded in t around 0 91.7%

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

   4. Taylor expanded in b around inf 91.7%

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

      1. *-commutative 91.7%

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

   6. Simplified 91.7%

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

   7. Taylor expanded in x around inf 79.2%

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

   if -1e153 < x < 5.00000000000000025e141

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. associate-+r+ 99.9%

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

      5. +-commutative 99.9%

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

      6. +-commutative 99.9%

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

      7. associate-+l+ 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-define 99.9%

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

      13. sub-neg 99.9%

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

      14. metadata-eval 99.9%

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

      15. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 94.7%

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

      1. +-commutative 94.7%

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

      2. associate-+r+ 94.7%

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

      3. *-commutative 94.7%

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

      4. sub-neg 94.7%

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

      5. metadata-eval 94.7%

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

      6. +-commutative 94.7%

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

      7. distribute-rgt-out 94.7%

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

      8. +-commutative 94.7%

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

      9. distribute-rgt-in 94.7%

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

      10. associate-+l+ 94.7%

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

      11. +-commutative 94.7%

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

      12. +-commutative 94.7%

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

      13. fma-define 94.7%

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

      14. +-commutative 94.7%

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

   7. Simplified 94.7%

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

   if 5.00000000000000025e141 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 91.4%

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

   4. Taylor expanded in x around inf 83.0%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+153}:\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + b \cdot \log c\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+141}:\\ \;\;\;\;\left(z + t\right) + \left(a + \mathsf{fma}\left(\log c, b + -0.5, y \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + \log c \cdot \left(b - 0.5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 90.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+153} \lor \neg \left(x \leq 4.7 \cdot 10^{+141}\right):\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -4.8e+153) (not (<= x 4.7e+141)))
   (+ (* y i) (+ (* x (log y)) (* b (log c))))
   (+ (* 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) {
	double tmp;
	if ((x <= -4.8e+153) || !(x <= 4.7e+141)) {
		tmp = (y * i) + ((x * log(y)) + (b * log(c)));
	} else {
		tmp = (y * i) + ((log(c) * (b - 0.5)) + (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 ((x <= (-4.8d+153)) .or. (.not. (x <= 4.7d+141))) then
        tmp = (y * i) + ((x * log(y)) + (b * log(c)))
    else
        tmp = (y * i) + ((log(c) * (b - 0.5d0)) + (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 ((x <= -4.8e+153) || !(x <= 4.7e+141)) {
		tmp = (y * i) + ((x * Math.log(y)) + (b * Math.log(c)));
	} else {
		tmp = (y * i) + ((Math.log(c) * (b - 0.5)) + (a + (z + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -4.8e+153) or not (x <= 4.7e+141):
		tmp = (y * i) + ((x * math.log(y)) + (b * math.log(c)))
	else:
		tmp = (y * i) + ((math.log(c) * (b - 0.5)) + (a + (z + t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -4.8e+153) || !(x <= 4.7e+141))
		tmp = Float64(Float64(y * i) + Float64(Float64(x * log(y)) + Float64(b * log(c))));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(log(c) * Float64(b - 0.5)) + 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 ((x <= -4.8e+153) || ~((x <= 4.7e+141)))
		tmp = (y * i) + ((x * log(y)) + (b * log(c)));
	else
		tmp = (y * i) + ((log(c) * (b - 0.5)) + (a + (z + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -4.8e+153], N[Not[LessEqual[x, 4.7e+141]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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. Split input into 2 regimes

2. if x < -4.79999999999999985e153 or 4.69999999999999979e141 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 91.6%

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

   4. Taylor expanded in b around inf 91.6%

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

      1. *-commutative 91.6%

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

   6. Simplified 91.6%

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

   7. Taylor expanded in x around inf 80.9%

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

   if -4.79999999999999985e153 < x < 4.69999999999999979e141

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 94.7%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+153} \lor \neg \left(x \leq 4.7 \cdot 10^{+141}\right):\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 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 6: 75.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if a < 9.00000000000000087e71

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 84.8%

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

   4. Taylor expanded in b around inf 83.1%

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

      1. *-commutative 83.1%

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

   6. Simplified 83.1%

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

   7. Taylor expanded in a around 0 70.6%

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

   if 9.00000000000000087e71 < a

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. associate-+r+ 99.9%

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

      5. +-commutative 99.9%

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

      6. +-commutative 99.9%

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

      7. associate-+l+ 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-define 99.9%

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

      13. sub-neg 99.9%

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

      14. metadata-eval 99.9%

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

      15. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 94.5%

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

4. Final simplification 75.5%

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

Alternative 7: 75.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 3 \cdot 10^{+73}:\\ \;\;\;\;y \cdot i + \left(\left(z + x \cdot \log y\right) + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 3e+73)
   (+ (* y i) (+ (+ z (* x (log y))) (* b (log c))))
   (+ (* 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) {
	double tmp;
	if (a <= 3e+73) {
		tmp = (y * i) + ((z + (x * log(y))) + (b * log(c)));
	} else {
		tmp = (y * i) + ((log(c) * (b - 0.5)) + (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 <= 3d+73) then
        tmp = (y * i) + ((z + (x * log(y))) + (b * log(c)))
    else
        tmp = (y * i) + ((log(c) * (b - 0.5d0)) + (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 <= 3e+73) {
		tmp = (y * i) + ((z + (x * Math.log(y))) + (b * Math.log(c)));
	} else {
		tmp = (y * i) + ((Math.log(c) * (b - 0.5)) + (a + (z + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 3e+73:
		tmp = (y * i) + ((z + (x * math.log(y))) + (b * math.log(c)))
	else:
		tmp = (y * i) + ((math.log(c) * (b - 0.5)) + (a + (z + t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 3e+73)
		tmp = Float64(Float64(y * i) + Float64(Float64(z + Float64(x * log(y))) + Float64(b * log(c))));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(log(c) * Float64(b - 0.5)) + 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 <= 3e+73)
		tmp = (y * i) + ((z + (x * log(y))) + (b * log(c)));
	else
		tmp = (y * i) + ((log(c) * (b - 0.5)) + (a + (z + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 3e+73], N[(N[(y * i), $MachinePrecision] + N[(N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(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. Split input into 2 regimes

2. if a < 3.00000000000000011e73

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 84.8%

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

   4. Taylor expanded in b around inf 83.1%

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

      1. *-commutative 83.1%

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

   6. Simplified 83.1%

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

   7. Taylor expanded in a around 0 70.6%

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

   if 3.00000000000000011e73 < a

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 94.4%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 3 \cdot 10^{+73}:\\ \;\;\;\;y \cdot i + \left(\left(z + x \cdot \log y\right) + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in t around 0 86.4%

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

4. Final simplification 86.4%

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

Alternative 9: 82.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in t around 0 86.4%

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

4. Taylor expanded in b around inf 85.1%

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

   1. *-commutative 85.1%

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

6. Simplified 85.1%

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

7. Final simplification 85.1%

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

Alternative 10: 88.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.26 \cdot 10^{+224} \lor \neg \left(x \leq 7.5 \cdot 10^{+238}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -1.26e+224) (not (<= x 7.5e+238)))
   (* x (log y))
   (+ (* 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) {
	double tmp;
	if ((x <= -1.26e+224) || !(x <= 7.5e+238)) {
		tmp = x * log(y);
	} else {
		tmp = (y * i) + ((log(c) * (b - 0.5)) + (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 ((x <= (-1.26d+224)) .or. (.not. (x <= 7.5d+238))) then
        tmp = x * log(y)
    else
        tmp = (y * i) + ((log(c) * (b - 0.5d0)) + (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 ((x <= -1.26e+224) || !(x <= 7.5e+238)) {
		tmp = x * Math.log(y);
	} else {
		tmp = (y * i) + ((Math.log(c) * (b - 0.5)) + (a + (z + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -1.26e+224) or not (x <= 7.5e+238):
		tmp = x * math.log(y)
	else:
		tmp = (y * i) + ((math.log(c) * (b - 0.5)) + (a + (z + t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -1.26e+224) || !(x <= 7.5e+238))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(log(c) * Float64(b - 0.5)) + 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 ((x <= -1.26e+224) || ~((x <= 7.5e+238)))
		tmp = x * log(y);
	else
		tmp = (y * i) + ((log(c) * (b - 0.5)) + (a + (z + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -1.26e+224], N[Not[LessEqual[x, 7.5e+238]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], 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. Split input into 2 regimes

2. if x < -1.2600000000000001e224 or 7.4999999999999996e238 < x

   1. Initial program 99.7%

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

      1. associate-+l+ 99.7%

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

      2. +-commutative 99.7%

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

      3. associate-+l+ 99.7%

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

      4. associate-+r+ 99.7%

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

      5. +-commutative 99.7%

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

      6. +-commutative 99.7%

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

      7. associate-+l+ 99.7%

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

      8. associate-+l+ 99.7%

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

      9. +-commutative 99.7%

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

      10. fma-define 99.7%

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

      11. +-commutative 99.7%

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

      12. fma-define 99.7%

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

      13. sub-neg 99.7%

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

      14. metadata-eval 99.7%

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

      15. +-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 99.6%

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

      1. associate-+r+ 99.6%

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

      2. associate-+r+ 99.6%

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

      3. associate-+r+ 99.6%

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

      4. associate-+r+ 99.6%

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

      5. +-commutative 99.6%

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

      6. +-commutative 99.6%

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

      7. associate-+l+ 99.6%

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

      8. +-commutative 99.6%

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

      9. +-commutative 99.6%

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

   7. Simplified 99.6%

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

   8. Taylor expanded in x around inf 68.7%

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

   if -1.2600000000000001e224 < x < 7.4999999999999996e238

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 91.5%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.26 \cdot 10^{+224} \lor \neg \left(x \leq 7.5 \cdot 10^{+238}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 80.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -2.2 \cdot 10^{-20} \lor \neg \left(i \leq 2.2 \cdot 10^{-132}\right):\\ \;\;\;\;\left(z + t\right) + \left(a + i \cdot \left(y + b \cdot \frac{\log c}{i}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + t\right) + \left(a + b \cdot \log c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= i -2.2e-20) (not (<= i 2.2e-132)))
   (+ (+ z t) (+ a (* i (+ y (* b (/ (log c) i))))))
   (+ (+ z t) (+ a (* b (log c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((i <= -2.2e-20) || !(i <= 2.2e-132)) {
		tmp = (z + t) + (a + (i * (y + (b * (log(c) / i)))));
	} else {
		tmp = (z + t) + (a + (b * log(c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((i <= (-2.2d-20)) .or. (.not. (i <= 2.2d-132))) then
        tmp = (z + t) + (a + (i * (y + (b * (log(c) / i)))))
    else
        tmp = (z + t) + (a + (b * log(c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((i <= -2.2e-20) || !(i <= 2.2e-132)) {
		tmp = (z + t) + (a + (i * (y + (b * (Math.log(c) / i)))));
	} else {
		tmp = (z + t) + (a + (b * Math.log(c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (i <= -2.2e-20) or not (i <= 2.2e-132):
		tmp = (z + t) + (a + (i * (y + (b * (math.log(c) / i)))))
	else:
		tmp = (z + t) + (a + (b * math.log(c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((i <= -2.2e-20) || !(i <= 2.2e-132))
		tmp = Float64(Float64(z + t) + Float64(a + Float64(i * Float64(y + Float64(b * Float64(log(c) / i))))));
	else
		tmp = Float64(Float64(z + t) + Float64(a + Float64(b * log(c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((i <= -2.2e-20) || ~((i <= 2.2e-132)))
		tmp = (z + t) + (a + (i * (y + (b * (log(c) / i)))));
	else
		tmp = (z + t) + (a + (b * log(c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[i, -2.2e-20], N[Not[LessEqual[i, 2.2e-132]], $MachinePrecision]], N[(N[(z + t), $MachinePrecision] + N[(a + N[(i * N[(y + N[(b * N[(N[Log[c], $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + t), $MachinePrecision] + N[(a + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -2.19999999999999991e-20 or 2.19999999999999991e-132 < i

   1. Initial program 99.8%

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

      1. associate-+l+ 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+l+ 99.8%

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

      4. associate-+r+ 99.8%

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

      5. +-commutative 99.8%

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

      6. +-commutative 99.8%

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

      7. associate-+l+ 99.8%

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

      8. associate-+l+ 99.8%

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

      9. +-commutative 99.8%

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

      10. fma-define 99.8%

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

      11. +-commutative 99.8%

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

      12. fma-define 99.9%

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

      13. sub-neg 99.9%

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

      14. metadata-eval 99.9%

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

      15. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 88.4%

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

      1. +-commutative 88.4%

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

      2. associate-+r+ 88.4%

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

      3. *-commutative 88.4%

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

      4. sub-neg 88.4%

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

      5. metadata-eval 88.4%

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

      6. +-commutative 88.4%

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

      7. distribute-rgt-out 88.4%

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

      8. +-commutative 88.4%

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

      9. distribute-rgt-in 88.4%

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

      10. associate-+l+ 88.4%

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

      11. +-commutative 88.4%

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

      12. +-commutative 88.4%

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

      13. fma-define 88.4%

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

      14. +-commutative 88.4%

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

   7. Simplified 88.4%

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

   8. Taylor expanded in y around inf 79.1%

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

   9. Taylor expanded in b around inf 79.0%

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

       1. *-commutative 79.0%

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

   11. Simplified 79.0%

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

   12. Taylor expanded in i around inf 86.5%

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

       1. associate-/l* 86.5%

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

   14. Simplified 86.5%

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

   if -2.19999999999999991e-20 < i < 2.19999999999999991e-132

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. associate-+r+ 99.9%

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

      5. +-commutative 99.9%

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

      6. +-commutative 99.9%

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

      7. associate-+l+ 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-define 99.9%

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

      13. sub-neg 99.9%

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

      14. metadata-eval 99.9%

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

      15. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 80.0%

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

      1. +-commutative 80.0%

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

      2. associate-+r+ 80.0%

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

      3. *-commutative 80.0%

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

      4. sub-neg 80.0%

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

      5. metadata-eval 80.0%

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

      6. +-commutative 80.0%

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

      7. distribute-rgt-out 80.0%

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

      8. +-commutative 80.0%

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

      9. distribute-rgt-in 80.0%

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

      10. associate-+l+ 80.0%

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

      11. +-commutative 80.0%

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

      12. +-commutative 80.0%

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

      13. fma-define 80.0%

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

      14. +-commutative 80.0%

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

   7. Simplified 80.0%

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

   8. Taylor expanded in b around inf 77.4%

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

      1. *-commutative 77.4%

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

   10. Simplified 77.4%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.2 \cdot 10^{-20} \lor \neg \left(i \leq 2.2 \cdot 10^{-132}\right):\\ \;\;\;\;\left(z + t\right) + \left(a + i \cdot \left(y + b \cdot \frac{\log c}{i}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + t\right) + \left(a + b \cdot \log c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 60.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + b \cdot \log c\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{+99}:\\ \;\;\;\;\left(z + t\right) + \left(a + y \cdot i\right)\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+73}:\\ \;\;\;\;\left(z + t\right) + t\_1\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+21}:\\ \;\;\;\;\left(z + t\right) + y \cdot \left(i + \frac{a}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b (log c)))))
   (if (<= z -9.5e+99)
     (+ (+ z t) (+ a (* y i)))
     (if (<= z -1.05e+73)
       (+ (+ z t) t_1)
       (if (<= z -2.6e+21) (+ (+ z t) (* y (+ i (/ a y)))) (+ (* y i) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * log(c));
	double tmp;
	if (z <= -9.5e+99) {
		tmp = (z + t) + (a + (y * i));
	} else if (z <= -1.05e+73) {
		tmp = (z + t) + t_1;
	} else if (z <= -2.6e+21) {
		tmp = (z + t) + (y * (i + (a / y)));
	} else {
		tmp = (y * i) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a + (b * log(c))
    if (z <= (-9.5d+99)) then
        tmp = (z + t) + (a + (y * i))
    else if (z <= (-1.05d+73)) then
        tmp = (z + t) + t_1
    else if (z <= (-2.6d+21)) then
        tmp = (z + t) + (y * (i + (a / y)))
    else
        tmp = (y * i) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * Math.log(c));
	double tmp;
	if (z <= -9.5e+99) {
		tmp = (z + t) + (a + (y * i));
	} else if (z <= -1.05e+73) {
		tmp = (z + t) + t_1;
	} else if (z <= -2.6e+21) {
		tmp = (z + t) + (y * (i + (a / y)));
	} else {
		tmp = (y * i) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (b * math.log(c))
	tmp = 0
	if z <= -9.5e+99:
		tmp = (z + t) + (a + (y * i))
	elif z <= -1.05e+73:
		tmp = (z + t) + t_1
	elif z <= -2.6e+21:
		tmp = (z + t) + (y * (i + (a / y)))
	else:
		tmp = (y * i) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(b * log(c)))
	tmp = 0.0
	if (z <= -9.5e+99)
		tmp = Float64(Float64(z + t) + Float64(a + Float64(y * i)));
	elseif (z <= -1.05e+73)
		tmp = Float64(Float64(z + t) + t_1);
	elseif (z <= -2.6e+21)
		tmp = Float64(Float64(z + t) + Float64(y * Float64(i + Float64(a / y))));
	else
		tmp = Float64(Float64(y * i) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (b * log(c));
	tmp = 0.0;
	if (z <= -9.5e+99)
		tmp = (z + t) + (a + (y * i));
	elseif (z <= -1.05e+73)
		tmp = (z + t) + t_1;
	elseif (z <= -2.6e+21)
		tmp = (z + t) + (y * (i + (a / y)));
	else
		tmp = (y * i) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.5e+99], N[(N[(z + t), $MachinePrecision] + N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.05e+73], N[(N[(z + t), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[z, -2.6e+21], N[(N[(z + t), $MachinePrecision] + N[(y * N[(i + N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.49999999999999908e99

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+l+ 100.0%

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

      4. associate-+r+ 100.0%

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

      5. +-commutative 100.0%

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

      6. +-commutative 100.0%

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

      7. associate-+l+ 100.0%

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

      8. associate-+l+ 100.0%

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

      9. +-commutative 100.0%

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

      10. fma-define 100.0%

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

      11. +-commutative 100.0%

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

      12. fma-define 100.0%

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

      13. sub-neg 100.0%

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

      14. metadata-eval 100.0%

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

      15. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 89.6%

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

      1. +-commutative 89.6%

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

      2. associate-+r+ 89.6%

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

      3. *-commutative 89.6%

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

      4. sub-neg 89.6%

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

      5. metadata-eval 89.6%

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

      6. +-commutative 89.6%

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

      7. distribute-rgt-out 89.6%

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

      8. +-commutative 89.6%

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

      9. distribute-rgt-in 89.6%

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

      10. associate-+l+ 89.6%

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

      11. +-commutative 89.6%

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

      12. +-commutative 89.6%

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

      13. fma-define 89.6%

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

      14. +-commutative 89.6%

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

   7. Simplified 89.6%

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

   8. Taylor expanded in y around inf 84.5%

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

      1. *-commutative 84.5%

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

   10. Simplified 84.5%

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

   if -9.49999999999999908e99 < z < -1.0500000000000001e73

   1. Initial program 99.7%

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

      1. associate-+l+ 99.7%

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

      2. +-commutative 99.7%

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

      3. associate-+l+ 99.7%

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

      4. associate-+r+ 99.7%

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

      5. +-commutative 99.7%

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

      6. +-commutative 99.7%

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

      7. associate-+l+ 99.7%

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

      8. associate-+l+ 99.7%

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

      9. +-commutative 99.7%

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

      10. fma-define 99.7%

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

      11. +-commutative 99.7%

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

      12. fma-define 99.7%

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

      13. sub-neg 99.7%

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

      14. metadata-eval 99.7%

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

      15. +-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-+r+ 99.7%

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

      3. *-commutative 99.7%

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

      4. sub-neg 99.7%

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

      5. metadata-eval 99.7%

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

      6. +-commutative 99.7%

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

      7. distribute-rgt-out 99.7%

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

      8. +-commutative 99.7%

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

      9. distribute-rgt-in 99.7%

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

      10. associate-+l+ 99.7%

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

      11. +-commutative 99.7%

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

      12. +-commutative 99.7%

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

      13. fma-define 99.7%

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

      14. +-commutative 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in b around inf 97.3%

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

      1. *-commutative 97.3%

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

   10. Simplified 97.3%

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

   if -1.0500000000000001e73 < z < -2.6e21

   1. Initial program 99.7%

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

      1. associate-+l+ 99.7%

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

      2. +-commutative 99.7%

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

      3. associate-+l+ 99.7%

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

      4. associate-+r+ 99.7%

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

      5. +-commutative 99.7%

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

      6. +-commutative 99.7%

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

      7. associate-+l+ 99.7%

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

      8. associate-+l+ 99.7%

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

      9. +-commutative 99.7%

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

      10. fma-define 99.7%

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

      11. +-commutative 99.7%

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

      12. fma-define 99.7%

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

      13. sub-neg 99.7%

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

      14. metadata-eval 99.7%

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

      15. +-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 56.7%

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

      1. +-commutative 56.7%

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

      2. associate-+r+ 56.7%

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

      3. *-commutative 56.7%

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

      4. sub-neg 56.7%

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

      5. metadata-eval 56.7%

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

      6. +-commutative 56.7%

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

      7. distribute-rgt-out 56.7%

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

      8. +-commutative 56.7%

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

      9. distribute-rgt-in 56.7%

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

      10. associate-+l+ 56.7%

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

      11. +-commutative 56.7%

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

      12. +-commutative 56.7%

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

      13. fma-define 56.7%

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

      14. +-commutative 56.7%

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

   7. Simplified 56.7%

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

   8. Taylor expanded in y around inf 56.2%

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

      1. *-commutative 56.2%

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

   10. Simplified 56.2%

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

   11. Taylor expanded in y around inf 56.2%

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

   if -2.6e21 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 85.1%

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

   4. Taylor expanded in b around inf 83.4%

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

      1. *-commutative 83.4%

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

   6. Simplified 83.4%

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

   7. Taylor expanded in a around inf 61.4%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+99}:\\ \;\;\;\;\left(z + t\right) + \left(a + y \cdot i\right)\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+73}:\\ \;\;\;\;\left(z + t\right) + \left(a + b \cdot \log c\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+21}:\\ \;\;\;\;\left(z + t\right) + y \cdot \left(i + \frac{a}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 60.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+147}:\\ \;\;\;\;\left(z + t\right) + \left(a + y \cdot i\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+21}:\\ \;\;\;\;y \cdot i + \left(z + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \log c \cdot \left(b - 0.5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -3.6e+147)
   (+ (+ z t) (+ a (* y i)))
   (if (<= z -2.6e+21)
     (+ (* y i) (+ z (* b (log c))))
     (+ (* y i) (+ a (* (log c) (- b 0.5)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -3.6e+147) {
		tmp = (z + t) + (a + (y * i));
	} else if (z <= -2.6e+21) {
		tmp = (y * i) + (z + (b * log(c)));
	} else {
		tmp = (y * i) + (a + (log(c) * (b - 0.5)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-3.6d+147)) then
        tmp = (z + t) + (a + (y * i))
    else if (z <= (-2.6d+21)) then
        tmp = (y * i) + (z + (b * log(c)))
    else
        tmp = (y * i) + (a + (log(c) * (b - 0.5d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -3.6e+147) {
		tmp = (z + t) + (a + (y * i));
	} else if (z <= -2.6e+21) {
		tmp = (y * i) + (z + (b * Math.log(c)));
	} else {
		tmp = (y * i) + (a + (Math.log(c) * (b - 0.5)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -3.6e+147:
		tmp = (z + t) + (a + (y * i))
	elif z <= -2.6e+21:
		tmp = (y * i) + (z + (b * math.log(c)))
	else:
		tmp = (y * i) + (a + (math.log(c) * (b - 0.5)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -3.6e+147)
		tmp = Float64(Float64(z + t) + Float64(a + Float64(y * i)));
	elseif (z <= -2.6e+21)
		tmp = Float64(Float64(y * i) + Float64(z + Float64(b * log(c))));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(log(c) * Float64(b - 0.5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -3.6e+147)
		tmp = (z + t) + (a + (y * i));
	elseif (z <= -2.6e+21)
		tmp = (y * i) + (z + (b * log(c)));
	else
		tmp = (y * i) + (a + (log(c) * (b - 0.5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -3.6e+147], N[(N[(z + t), $MachinePrecision] + N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.6e+21], N[(N[(y * i), $MachinePrecision] + N[(z + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.6000000000000002e147

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+l+ 100.0%

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

      4. associate-+r+ 100.0%

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

      5. +-commutative 100.0%

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

      6. +-commutative 100.0%

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

      7. associate-+l+ 100.0%

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

      8. associate-+l+ 100.0%

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

      9. +-commutative 100.0%

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

      10. fma-define 100.0%

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

      11. +-commutative 100.0%

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

      12. fma-define 100.0%

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

      13. sub-neg 100.0%

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

      14. metadata-eval 100.0%

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

      15. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 90.9%

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

      1. +-commutative 90.9%

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

      2. associate-+r+ 90.9%

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

      3. *-commutative 90.9%

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

      4. sub-neg 90.9%

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

      5. metadata-eval 90.9%

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

      6. +-commutative 90.9%

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

      7. distribute-rgt-out 90.9%

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

      8. +-commutative 90.9%

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

      9. distribute-rgt-in 90.9%

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

      10. associate-+l+ 90.9%

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

      11. +-commutative 90.9%

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

      12. +-commutative 90.9%

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

      13. fma-define 90.9%

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

      14. +-commutative 90.9%

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

   7. Simplified 90.9%

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

   8. Taylor expanded in y around inf 88.0%

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

      1. *-commutative 88.0%

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

   10. Simplified 88.0%

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

   if -3.6000000000000002e147 < z < -2.6e21

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 91.8%

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

   4. Taylor expanded in b around inf 91.8%

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

      1. *-commutative 91.8%

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

   6. Simplified 91.8%

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

   7. Taylor expanded in z around inf 65.5%

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

   if -2.6e21 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf 62.8%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+147}:\\ \;\;\;\;\left(z + t\right) + \left(a + y \cdot i\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+21}:\\ \;\;\;\;y \cdot i + \left(z + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \log c \cdot \left(b - 0.5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 81.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3 \cdot 10^{-55}:\\ \;\;\;\;\left(z + t\right) + \left(a + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + t\right) + \left(a + y \cdot \left(i + \log c \cdot \frac{b}{y}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 3e-55)
   (+ (+ z t) (+ a (* b (log c))))
   (+ (+ z t) (+ a (* y (+ i (* (log c) (/ b y))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 3e-55) {
		tmp = (z + t) + (a + (b * log(c)));
	} else {
		tmp = (z + t) + (a + (y * (i + (log(c) * (b / y)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= 3d-55) then
        tmp = (z + t) + (a + (b * log(c)))
    else
        tmp = (z + t) + (a + (y * (i + (log(c) * (b / y)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 3e-55) {
		tmp = (z + t) + (a + (b * Math.log(c)));
	} else {
		tmp = (z + t) + (a + (y * (i + (Math.log(c) * (b / y)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 3e-55:
		tmp = (z + t) + (a + (b * math.log(c)))
	else:
		tmp = (z + t) + (a + (y * (i + (math.log(c) * (b / y)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 3e-55)
		tmp = Float64(Float64(z + t) + Float64(a + Float64(b * log(c))));
	else
		tmp = Float64(Float64(z + t) + Float64(a + Float64(y * Float64(i + Float64(log(c) * Float64(b / y))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= 3e-55)
		tmp = (z + t) + (a + (b * log(c)));
	else
		tmp = (z + t) + (a + (y * (i + (log(c) * (b / y)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 3e-55], N[(N[(z + t), $MachinePrecision] + N[(a + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + t), $MachinePrecision] + N[(a + N[(y * N[(i + N[(N[Log[c], $MachinePrecision] * N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.00000000000000016e-55

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. associate-+r+ 99.9%

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

      5. +-commutative 99.9%

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

      6. +-commutative 99.9%

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

      7. associate-+l+ 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-define 99.9%

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

      13. sub-neg 99.9%

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

      14. metadata-eval 99.9%

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

      15. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 75.8%

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

      1. +-commutative 75.8%

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

      2. associate-+r+ 75.8%

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

      3. *-commutative 75.8%

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

      4. sub-neg 75.8%

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

      5. metadata-eval 75.8%

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

      6. +-commutative 75.8%

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

      7. distribute-rgt-out 75.8%

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

      8. +-commutative 75.8%

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

      9. distribute-rgt-in 75.8%

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

      10. associate-+l+ 75.8%

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

      11. +-commutative 75.8%

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

      12. +-commutative 75.8%

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

      13. fma-define 75.8%

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

      14. +-commutative 75.8%

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

   7. Simplified 75.8%

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

   8. Taylor expanded in b around inf 72.2%

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

      1. *-commutative 72.2%

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

   10. Simplified 72.2%

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

   if 3.00000000000000016e-55 < y

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. associate-+r+ 99.9%

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

      5. +-commutative 99.9%

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

      6. +-commutative 99.9%

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

      7. associate-+l+ 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-define 99.9%

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

      13. sub-neg 99.9%

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

      14. metadata-eval 99.9%

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

      15. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 89.8%

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

      1. +-commutative 89.8%

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

      2. associate-+r+ 89.8%

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

      3. *-commutative 89.8%

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

      4. sub-neg 89.8%

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

      5. metadata-eval 89.8%

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

      6. +-commutative 89.8%

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

      7. distribute-rgt-out 89.8%

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

      8. +-commutative 89.8%

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

      9. distribute-rgt-in 89.8%

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

      10. associate-+l+ 89.8%

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

      11. +-commutative 89.8%

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

      12. +-commutative 89.8%

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

      13. fma-define 89.8%

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

      14. +-commutative 89.8%

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

   7. Simplified 89.8%

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

   8. Taylor expanded in y around inf 89.3%

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

   9. Taylor expanded in b around inf 88.7%

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

       1. *-commutative 88.7%

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

       2. associate-/l* 88.7%

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

   11. Simplified 88.7%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3 \cdot 10^{-55}:\\ \;\;\;\;\left(z + t\right) + \left(a + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + t\right) + \left(a + y \cdot \left(i + \log c \cdot \frac{b}{y}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 58.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \log c\\ \mathbf{if}\;z \leq -3.7 \cdot 10^{+146}:\\ \;\;\;\;\left(z + t\right) + \left(a + y \cdot i\right)\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{+21}:\\ \;\;\;\;y \cdot i + \left(z + t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* b (log c))))
   (if (<= z -3.7e+146)
     (+ (+ z t) (+ a (* y i)))
     (if (<= z -2.45e+21) (+ (* y i) (+ z t_1)) (+ (* y i) (+ a t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = b * log(c);
	double tmp;
	if (z <= -3.7e+146) {
		tmp = (z + t) + (a + (y * i));
	} else if (z <= -2.45e+21) {
		tmp = (y * i) + (z + t_1);
	} else {
		tmp = (y * i) + (a + t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * log(c)
    if (z <= (-3.7d+146)) then
        tmp = (z + t) + (a + (y * i))
    else if (z <= (-2.45d+21)) then
        tmp = (y * i) + (z + t_1)
    else
        tmp = (y * i) + (a + t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = b * Math.log(c);
	double tmp;
	if (z <= -3.7e+146) {
		tmp = (z + t) + (a + (y * i));
	} else if (z <= -2.45e+21) {
		tmp = (y * i) + (z + t_1);
	} else {
		tmp = (y * i) + (a + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = b * math.log(c)
	tmp = 0
	if z <= -3.7e+146:
		tmp = (z + t) + (a + (y * i))
	elif z <= -2.45e+21:
		tmp = (y * i) + (z + t_1)
	else:
		tmp = (y * i) + (a + t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(b * log(c))
	tmp = 0.0
	if (z <= -3.7e+146)
		tmp = Float64(Float64(z + t) + Float64(a + Float64(y * i)));
	elseif (z <= -2.45e+21)
		tmp = Float64(Float64(y * i) + Float64(z + t_1));
	else
		tmp = Float64(Float64(y * i) + Float64(a + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = b * log(c);
	tmp = 0.0;
	if (z <= -3.7e+146)
		tmp = (z + t) + (a + (y * i));
	elseif (z <= -2.45e+21)
		tmp = (y * i) + (z + t_1);
	else
		tmp = (y * i) + (a + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.7e+146], N[(N[(z + t), $MachinePrecision] + N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.45e+21], N[(N[(y * i), $MachinePrecision] + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.70000000000000004e146

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+l+ 100.0%

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

      4. associate-+r+ 100.0%

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

      5. +-commutative 100.0%

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

      6. +-commutative 100.0%

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

      7. associate-+l+ 100.0%

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

      8. associate-+l+ 100.0%

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

      9. +-commutative 100.0%

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

      10. fma-define 100.0%

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

      11. +-commutative 100.0%

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

      12. fma-define 100.0%

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

      13. sub-neg 100.0%

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

      14. metadata-eval 100.0%

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

      15. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 90.9%

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

      1. +-commutative 90.9%

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

      2. associate-+r+ 90.9%

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

      3. *-commutative 90.9%

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

      4. sub-neg 90.9%

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

      5. metadata-eval 90.9%

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

      6. +-commutative 90.9%

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

      7. distribute-rgt-out 90.9%

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

      8. +-commutative 90.9%

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

      9. distribute-rgt-in 90.9%

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

      10. associate-+l+ 90.9%

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

      11. +-commutative 90.9%

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

      12. +-commutative 90.9%

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

      13. fma-define 90.9%

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

      14. +-commutative 90.9%

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

   7. Simplified 90.9%

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

   8. Taylor expanded in y around inf 88.0%

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

      1. *-commutative 88.0%

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

   10. Simplified 88.0%

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

   if -3.70000000000000004e146 < z < -2.45e21

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 91.8%

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

   4. Taylor expanded in b around inf 91.8%

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

      1. *-commutative 91.8%

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

   6. Simplified 91.8%

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

   7. Taylor expanded in z around inf 65.5%

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

   if -2.45e21 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 85.1%

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

   4. Taylor expanded in b around inf 83.4%

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

      1. *-commutative 83.4%

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

   6. Simplified 83.4%

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

   7. Taylor expanded in a around inf 61.4%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+146}:\\ \;\;\;\;\left(z + t\right) + \left(a + y \cdot i\right)\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{+21}:\\ \;\;\;\;y \cdot i + \left(z + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 70.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+216} \lor \neg \left(x \leq 2 \cdot 10^{+157}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(z + t\right) + \mathsf{fma}\left(y, i, a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -2.4e+216) (not (<= x 2e+157)))
   (* x (log y))
   (+ (+ z t) (fma 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 ((x <= -2.4e+216) || !(x <= 2e+157)) {
		tmp = x * log(y);
	} else {
		tmp = (z + t) + fma(y, i, a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -2.4e+216) || !(x <= 2e+157))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(Float64(z + t) + fma(y, i, a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -2.4e+216], N[Not[LessEqual[x, 2e+157]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(N[(z + t), $MachinePrecision] + N[(y * i + a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.3999999999999999e216 or 1.99999999999999997e157 < x

   1. Initial program 99.7%

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

      1. associate-+l+ 99.7%

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

      2. +-commutative 99.7%

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

      3. associate-+l+ 99.7%

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

      4. associate-+r+ 99.7%

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

      5. +-commutative 99.7%

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

      6. +-commutative 99.7%

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

      7. associate-+l+ 99.7%

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

      8. associate-+l+ 99.7%

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

      9. +-commutative 99.7%

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

      10. fma-define 99.7%

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

      11. +-commutative 99.7%

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

      12. fma-define 99.7%

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

      13. sub-neg 99.7%

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

      14. metadata-eval 99.7%

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

      15. +-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 99.6%

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

      1. associate-+r+ 99.6%

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

      2. associate-+r+ 99.6%

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

      3. associate-+r+ 99.6%

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

      4. associate-+r+ 99.6%

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

      5. +-commutative 99.6%

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

      6. +-commutative 99.6%

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

      7. associate-+l+ 99.6%

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

      8. +-commutative 99.6%

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

      9. +-commutative 99.6%

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

   7. Simplified 99.5%

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

   8. Taylor expanded in x around inf 61.7%

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

   if -2.3999999999999999e216 < x < 1.99999999999999997e157

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. associate-+r+ 99.9%

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

      5. +-commutative 99.9%

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

      6. +-commutative 99.9%

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

      7. associate-+l+ 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-define 99.9%

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

      13. sub-neg 99.9%

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

      14. metadata-eval 99.9%

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

      15. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 92.8%

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

      1. +-commutative 92.8%

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

      2. associate-+r+ 92.8%

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

      3. *-commutative 92.8%

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

      4. sub-neg 92.8%

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

      5. metadata-eval 92.8%

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

      6. +-commutative 92.8%

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

      7. distribute-rgt-out 92.8%

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

      8. +-commutative 92.8%

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

      9. distribute-rgt-in 92.8%

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

      10. associate-+l+ 92.8%

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

      11. +-commutative 92.8%

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

      12. +-commutative 92.8%

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

      13. fma-define 92.8%

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

      14. +-commutative 92.8%

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

   7. Simplified 92.8%

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

   8. Taylor expanded in y around inf 76.5%

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

      1. *-commutative 76.5%

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

   10. Simplified 76.5%

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

       1. fma-define 76.5%

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

   12. Applied egg-rr 76.5%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+216} \lor \neg \left(x \leq 2 \cdot 10^{+157}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(z + t\right) + \mathsf{fma}\left(y, i, a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 60.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{+21}:\\ \;\;\;\;\left(z + t\right) + \left(a + y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -2.45e+21)
   (+ (+ z t) (+ a (* y i)))
   (+ (* y i) (+ a (* b (log c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -2.45e+21) {
		tmp = (z + t) + (a + (y * i));
	} else {
		tmp = (y * i) + (a + (b * log(c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-2.45d+21)) then
        tmp = (z + t) + (a + (y * i))
    else
        tmp = (y * i) + (a + (b * log(c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -2.45e+21) {
		tmp = (z + t) + (a + (y * i));
	} else {
		tmp = (y * i) + (a + (b * Math.log(c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -2.45e+21:
		tmp = (z + t) + (a + (y * i))
	else:
		tmp = (y * i) + (a + (b * math.log(c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -2.45e+21)
		tmp = Float64(Float64(z + t) + Float64(a + Float64(y * i)));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(b * log(c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -2.45e+21)
		tmp = (z + t) + (a + (y * i));
	else
		tmp = (y * i) + (a + (b * log(c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -2.45e+21], N[(N[(z + t), $MachinePrecision] + N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.45e21

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. associate-+r+ 99.9%

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

      5. +-commutative 99.9%

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

      6. +-commutative 99.9%

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

      7. associate-+l+ 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-define 99.9%

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

      13. sub-neg 99.9%

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

      14. metadata-eval 99.9%

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

      15. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in 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. +-commutative 81.8%

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

      2. associate-+r+ 81.8%

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

      3. *-commutative 81.8%

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

      4. sub-neg 81.8%

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

      5. metadata-eval 81.8%

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

      6. +-commutative 81.8%

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

      7. distribute-rgt-out 81.8%

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

      8. +-commutative 81.8%

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

      9. distribute-rgt-in 81.8%

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

      10. associate-+l+ 81.8%

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

      11. +-commutative 81.8%

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

      12. +-commutative 81.8%

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

      13. fma-define 81.8%

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

      14. +-commutative 81.8%

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

   7. Simplified 81.8%

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

   8. Taylor expanded in y around inf 73.3%

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

      1. *-commutative 73.3%

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

   10. Simplified 73.3%

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

   if -2.45e21 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 85.1%

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

   4. Taylor expanded in b around inf 83.4%

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

      1. *-commutative 83.4%

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

   6. Simplified 83.4%

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

   7. Taylor expanded in a around inf 61.4%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{+21}:\\ \;\;\;\;\left(z + t\right) + \left(a + y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 70.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{+223} \lor \neg \left(x \leq 2 \cdot 10^{+157}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(z + t\right) + \left(a + y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -2.05e+223) (not (<= x 2e+157)))
   (* x (log y))
   (+ (+ z t) (+ a (* y i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -2.05e+223) || !(x <= 2e+157)) {
		tmp = x * log(y);
	} else {
		tmp = (z + t) + (a + (y * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-2.05d+223)) .or. (.not. (x <= 2d+157))) then
        tmp = x * log(y)
    else
        tmp = (z + t) + (a + (y * i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -2.05e+223) || !(x <= 2e+157)) {
		tmp = x * Math.log(y);
	} else {
		tmp = (z + t) + (a + (y * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -2.05e+223) or not (x <= 2e+157):
		tmp = x * math.log(y)
	else:
		tmp = (z + t) + (a + (y * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -2.05e+223) || !(x <= 2e+157))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(Float64(z + t) + Float64(a + Float64(y * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -2.05e+223) || ~((x <= 2e+157)))
		tmp = x * log(y);
	else
		tmp = (z + t) + (a + (y * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -2.05e+223], N[Not[LessEqual[x, 2e+157]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(N[(z + t), $MachinePrecision] + N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.05e223 or 1.99999999999999997e157 < x

   1. Initial program 99.7%

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

      1. associate-+l+ 99.7%

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

      2. +-commutative 99.7%

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

      3. associate-+l+ 99.7%

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

      4. associate-+r+ 99.7%

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

      5. +-commutative 99.7%

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

      6. +-commutative 99.7%

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

      7. associate-+l+ 99.7%

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

      8. associate-+l+ 99.7%

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

      9. +-commutative 99.7%

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

      10. fma-define 99.7%

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

      11. +-commutative 99.7%

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

      12. fma-define 99.7%

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

      13. sub-neg 99.7%

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

      14. metadata-eval 99.7%

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

      15. +-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 99.6%

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

      1. associate-+r+ 99.6%

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

      2. associate-+r+ 99.6%

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

      3. associate-+r+ 99.6%

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

      4. associate-+r+ 99.6%

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

      5. +-commutative 99.6%

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

      6. +-commutative 99.6%

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

      7. associate-+l+ 99.6%

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

      8. +-commutative 99.6%

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

      9. +-commutative 99.6%

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

   7. Simplified 99.5%

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

   8. Taylor expanded in x around inf 61.7%

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

   if -2.05e223 < x < 1.99999999999999997e157

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. associate-+r+ 99.9%

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

      5. +-commutative 99.9%

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

      6. +-commutative 99.9%

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

      7. associate-+l+ 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-define 99.9%

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

      13. sub-neg 99.9%

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

      14. metadata-eval 99.9%

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

      15. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 92.8%

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

      1. +-commutative 92.8%

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

      2. associate-+r+ 92.8%

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

      3. *-commutative 92.8%

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

      4. sub-neg 92.8%

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

      5. metadata-eval 92.8%

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

      6. +-commutative 92.8%

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

      7. distribute-rgt-out 92.8%

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

      8. +-commutative 92.8%

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

      9. distribute-rgt-in 92.8%

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

      10. associate-+l+ 92.8%

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

      11. +-commutative 92.8%

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

      12. +-commutative 92.8%

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

      13. fma-define 92.8%

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

      14. +-commutative 92.8%

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

   7. Simplified 92.8%

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

   8. Taylor expanded in y around inf 76.5%

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

      1. *-commutative 76.5%

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

   10. Simplified 76.5%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{+223} \lor \neg \left(x \leq 2 \cdot 10^{+157}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(z + t\right) + \left(a + y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 60.1% accurate, 12.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -6.2 \cdot 10^{-12} \lor \neg \left(i \leq 0.0105\right):\\ \;\;\;\;y \cdot i + \left(z + t\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(z + t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= i -6.2e-12) (not (<= i 0.0105)))
   (+ (* y i) (+ z t))
   (+ 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 ((i <= -6.2e-12) || !(i <= 0.0105)) {
		tmp = (y * i) + (z + t);
	} else {
		tmp = 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 ((i <= (-6.2d-12)) .or. (.not. (i <= 0.0105d0))) then
        tmp = (y * i) + (z + t)
    else
        tmp = 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 ((i <= -6.2e-12) || !(i <= 0.0105)) {
		tmp = (y * i) + (z + t);
	} else {
		tmp = a + (z + t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (i <= -6.2e-12) or not (i <= 0.0105):
		tmp = (y * i) + (z + t)
	else:
		tmp = a + (z + t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((i <= -6.2e-12) || !(i <= 0.0105))
		tmp = Float64(Float64(y * i) + Float64(z + t));
	else
		tmp = 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 ((i <= -6.2e-12) || ~((i <= 0.0105)))
		tmp = (y * i) + (z + t);
	else
		tmp = a + (z + t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[i, -6.2e-12], N[Not[LessEqual[i, 0.0105]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(z + t), $MachinePrecision]), $MachinePrecision], N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -6.2000000000000002e-12 or 0.0105000000000000007 < i

   1. Initial program 99.8%

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

      1. associate-+l+ 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+l+ 99.8%

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

      4. associate-+r+ 99.8%

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

      5. +-commutative 99.8%

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

      6. +-commutative 99.8%

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

      7. associate-+l+ 99.8%

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

      8. associate-+l+ 99.8%

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

      9. +-commutative 99.8%

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

      10. fma-define 99.8%

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

      11. +-commutative 99.8%

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

      12. fma-define 99.9%

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

      13. sub-neg 99.9%

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

      14. metadata-eval 99.9%

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

      15. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 88.9%

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

      1. +-commutative 88.9%

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

      2. associate-+r+ 88.9%

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

      3. *-commutative 88.9%

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

      4. sub-neg 88.9%

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

      5. metadata-eval 88.9%

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

      6. +-commutative 88.9%

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

      7. distribute-rgt-out 88.9%

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

      8. +-commutative 88.9%

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

      9. distribute-rgt-in 88.9%

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

      10. associate-+l+ 88.9%

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

      11. +-commutative 88.9%

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

      12. +-commutative 88.9%

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

      13. fma-define 88.9%

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

      14. +-commutative 88.9%

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

   7. Simplified 88.9%

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

   8. Taylor expanded in y around inf 76.6%

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

      1. *-commutative 76.6%

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

   10. Simplified 76.6%

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

   11. Taylor expanded in y around inf 66.4%

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

   if -6.2000000000000002e-12 < i < 0.0105000000000000007

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+l+ 99.9%

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

      4. associate-+r+ 99.9%

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

      5. +-commutative 99.9%

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

      6. +-commutative 99.9%

         \[\leadsto \left(\color{blue}{\left(x \cdot \log y + a\right)} + \left(t + z\right)\right) + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

      7. associate-+l+ 99.9%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right)} + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

      8. associate-+l+ 99.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i} \]

      9. +-commutative 99.9%

         \[\leadsto \color{blue}{y \cdot i + \left(\left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right) + \left(b - 0.5\right) \cdot \log c\right)} \]

      10. fma-define 99.9%

          \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right) + \left(b - 0.5\right) \cdot \log c\right)} \]

      11. +-commutative 99.9%

          \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\left(b - 0.5\right) \cdot \log c + \left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right)}\right) \]

      12. fma-define 99.9%

          \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\mathsf{fma}\left(b - 0.5, \log c, \left(\left(x \cdot \log y + a\right) + t\right) + z\right)}\right) \]

      13. sub-neg 99.9%

          \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\color{blue}{b + \left(-0.5\right)}, \log c, \left(\left(x \cdot \log y + a\right) + t\right) + z\right)\right) \]

      14. metadata-eval 99.9%

          \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + \color{blue}{-0.5}, \log c, \left(\left(x \cdot \log y + a\right) + t\right) + z\right)\right) \]

      15. +-commutative 99.9%

          \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + -0.5, \log c, \color{blue}{z + \left(\left(x \cdot \log y + a\right) + t\right)}\right)\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \mathsf{fma}\left(b + -0.5, \log c, z + \mathsf{fma}\left(x, \log y, t + a\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 80.9%

      \[\leadsto \color{blue}{a + \left(t + \left(z + \left(i \cdot y + \log c \cdot \left(b - 0.5\right)\right)\right)\right)} \]
   6. Step-by-step derivation

      1. +-commutative 80.9%

         \[\leadsto \color{blue}{\left(t + \left(z + \left(i \cdot y + \log c \cdot \left(b - 0.5\right)\right)\right)\right) + a} \]

      2. associate-+r+ 80.9%

         \[\leadsto \color{blue}{\left(\left(t + z\right) + \left(i \cdot y + \log c \cdot \left(b - 0.5\right)\right)\right)} + a \]

      3. *-commutative 80.9%

         \[\leadsto \left(\left(t + z\right) + \left(\color{blue}{y \cdot i} + \log c \cdot \left(b - 0.5\right)\right)\right) + a \]

      4. sub-neg 80.9%

         \[\leadsto \left(\left(t + z\right) + \left(y \cdot i + \log c \cdot \color{blue}{\left(b + \left(-0.5\right)\right)}\right)\right) + a \]

      5. metadata-eval 80.9%

         \[\leadsto \left(\left(t + z\right) + \left(y \cdot i + \log c \cdot \left(b + \color{blue}{-0.5}\right)\right)\right) + a \]

      6. +-commutative 80.9%

         \[\leadsto \left(\left(t + z\right) + \left(y \cdot i + \log c \cdot \color{blue}{\left(-0.5 + b\right)}\right)\right) + a \]

      7. distribute-rgt-out 80.9%

         \[\leadsto \left(\left(t + z\right) + \left(y \cdot i + \color{blue}{\left(-0.5 \cdot \log c + b \cdot \log c\right)}\right)\right) + a \]

      8. +-commutative 80.9%

         \[\leadsto \left(\left(t + z\right) + \left(y \cdot i + \color{blue}{\left(b \cdot \log c + -0.5 \cdot \log c\right)}\right)\right) + a \]

      9. distribute-rgt-in 80.9%

         \[\leadsto \left(\left(t + z\right) + \left(y \cdot i + \color{blue}{\log c \cdot \left(b + -0.5\right)}\right)\right) + a \]

      10. associate-+l+ 80.9%

          \[\leadsto \color{blue}{\left(t + z\right) + \left(\left(y \cdot i + \log c \cdot \left(b + -0.5\right)\right) + a\right)} \]

      11. +-commutative 80.9%

          \[\leadsto \color{blue}{\left(z + t\right)} + \left(\left(y \cdot i + \log c \cdot \left(b + -0.5\right)\right) + a\right) \]

      12. +-commutative 80.9%

          \[\leadsto \left(z + t\right) + \left(\color{blue}{\left(\log c \cdot \left(b + -0.5\right) + y \cdot i\right)} + a\right) \]

      13. fma-define 80.9%

          \[\leadsto \left(z + t\right) + \left(\color{blue}{\mathsf{fma}\left(\log c, b + -0.5, y \cdot i\right)} + a\right) \]

      14. +-commutative 80.9%

          \[\leadsto \left(z + t\right) + \left(\mathsf{fma}\left(\log c, \color{blue}{-0.5 + b}, y \cdot i\right) + a\right) \]

   7. Simplified 80.9%

      \[\leadsto \color{blue}{\left(z + t\right) + \left(\mathsf{fma}\left(\log c, -0.5 + b, y \cdot i\right) + a\right)} \]

   8. Taylor expanded in y around inf 63.1%

      \[\leadsto \left(z + t\right) + \left(\color{blue}{i \cdot y} + a\right) \]
   9. Step-by-step derivation

      1. *-commutative 63.1%

         \[\leadsto \left(z + t\right) + \left(\color{blue}{y \cdot i} + a\right) \]

   10. Simplified 63.1%

       \[\leadsto \left(z + t\right) + \left(\color{blue}{y \cdot i} + a\right) \]

   11. Taylor expanded in y around 0 60.7%

       \[\leadsto \left(z + t\right) + \color{blue}{a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -6.2 \cdot 10^{-12} \lor \neg \left(i \leq 0.0105\right):\\ \;\;\;\;y \cdot i + \left(z + t\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(z + t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 51.6% accurate, 14.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1.8 \cdot 10^{+141} \lor \neg \left(i \leq 1.1 \cdot 10^{+74}\right):\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + \left(z + t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= i -1.8e+141) (not (<= i 1.1e+74))) (* 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 ((i <= -1.8e+141) || !(i <= 1.1e+74)) {
		tmp = y * i;
	} else {
		tmp = 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 ((i <= (-1.8d+141)) .or. (.not. (i <= 1.1d+74))) then
        tmp = y * i
    else
        tmp = 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 ((i <= -1.8e+141) || !(i <= 1.1e+74)) {
		tmp = y * i;
	} else {
		tmp = a + (z + t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (i <= -1.8e+141) or not (i <= 1.1e+74):
		tmp = y * i
	else:
		tmp = a + (z + t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((i <= -1.8e+141) || !(i <= 1.1e+74))
		tmp = Float64(y * i);
	else
		tmp = 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 ((i <= -1.8e+141) || ~((i <= 1.1e+74)))
		tmp = y * i;
	else
		tmp = a + (z + t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[i, -1.8e+141], N[Not[LessEqual[i, 1.1e+74]], $MachinePrecision]], N[(y * i), $MachinePrecision], N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -1.8000000000000001e141 or 1.1000000000000001e74 < 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. +-commutative 99.9%

         \[\leadsto \color{blue}{\left(a + \left(\left(x \cdot \log y + z\right) + t\right)\right)} + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

      3. associate-+l+ 99.9%

         \[\leadsto \left(a + \color{blue}{\left(x \cdot \log y + \left(z + t\right)\right)}\right) + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

      4. associate-+r+ 99.9%

         \[\leadsto \color{blue}{\left(\left(a + x \cdot \log y\right) + \left(z + t\right)\right)} + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

      5. +-commutative 99.9%

         \[\leadsto \left(\left(a + x \cdot \log y\right) + \color{blue}{\left(t + z\right)}\right) + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

      6. +-commutative 99.9%

         \[\leadsto \left(\color{blue}{\left(x \cdot \log y + a\right)} + \left(t + z\right)\right) + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

      7. associate-+l+ 99.9%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right)} + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

      8. associate-+l+ 99.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i} \]

      9. +-commutative 99.9%

         \[\leadsto \color{blue}{y \cdot i + \left(\left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right) + \left(b - 0.5\right) \cdot \log c\right)} \]

      10. fma-define 99.9%

          \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right) + \left(b - 0.5\right) \cdot \log c\right)} \]

      11. +-commutative 99.9%

          \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\left(b - 0.5\right) \cdot \log c + \left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right)}\right) \]

      12. fma-define 99.9%

          \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\mathsf{fma}\left(b - 0.5, \log c, \left(\left(x \cdot \log y + a\right) + t\right) + z\right)}\right) \]

      13. sub-neg 99.9%

          \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\color{blue}{b + \left(-0.5\right)}, \log c, \left(\left(x \cdot \log y + a\right) + t\right) + z\right)\right) \]

      14. metadata-eval 99.9%

          \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + \color{blue}{-0.5}, \log c, \left(\left(x \cdot \log y + a\right) + t\right) + z\right)\right) \]

      15. +-commutative 99.9%

          \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + -0.5, \log c, \color{blue}{z + \left(\left(x \cdot \log y + a\right) + t\right)}\right)\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \mathsf{fma}\left(b + -0.5, \log c, z + \mathsf{fma}\left(x, \log y, t + a\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 63.5%

      \[\leadsto \color{blue}{i \cdot y} \]
   6. Step-by-step derivation

      1. *-commutative 63.5%

         \[\leadsto \color{blue}{y \cdot i} \]

   7. Simplified 63.5%

      \[\leadsto \color{blue}{y \cdot i} \]

   if -1.8000000000000001e141 < i < 1.1000000000000001e74

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Step-by-step derivation

      1. associate-+l+ 99.9%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right)} \]

      2. +-commutative 99.9%

         \[\leadsto \color{blue}{\left(a + \left(\left(x \cdot \log y + z\right) + t\right)\right)} + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

      3. associate-+l+ 99.9%

         \[\leadsto \left(a + \color{blue}{\left(x \cdot \log y + \left(z + t\right)\right)}\right) + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

      4. associate-+r+ 99.9%

         \[\leadsto \color{blue}{\left(\left(a + x \cdot \log y\right) + \left(z + t\right)\right)} + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

      5. +-commutative 99.9%

         \[\leadsto \left(\left(a + x \cdot \log y\right) + \color{blue}{\left(t + z\right)}\right) + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

      6. +-commutative 99.9%

         \[\leadsto \left(\color{blue}{\left(x \cdot \log y + a\right)} + \left(t + z\right)\right) + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

      7. associate-+l+ 99.9%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right)} + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

      8. associate-+l+ 99.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i} \]

      9. +-commutative 99.9%

         \[\leadsto \color{blue}{y \cdot i + \left(\left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right) + \left(b - 0.5\right) \cdot \log c\right)} \]

      10. fma-define 99.9%

          \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right) + \left(b - 0.5\right) \cdot \log c\right)} \]

      11. +-commutative 99.9%

          \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\left(b - 0.5\right) \cdot \log c + \left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right)}\right) \]

      12. fma-define 99.9%

          \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\mathsf{fma}\left(b - 0.5, \log c, \left(\left(x \cdot \log y + a\right) + t\right) + z\right)}\right) \]

      13. sub-neg 99.9%

          \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\color{blue}{b + \left(-0.5\right)}, \log c, \left(\left(x \cdot \log y + a\right) + t\right) + z\right)\right) \]

      14. metadata-eval 99.9%

          \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + \color{blue}{-0.5}, \log c, \left(\left(x \cdot \log y + a\right) + t\right) + z\right)\right) \]

      15. +-commutative 99.9%

          \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + -0.5, \log c, \color{blue}{z + \left(\left(x \cdot \log y + a\right) + t\right)}\right)\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \mathsf{fma}\left(b + -0.5, \log c, z + \mathsf{fma}\left(x, \log y, t + a\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in 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. +-commutative 82.8%

         \[\leadsto \color{blue}{\left(t + \left(z + \left(i \cdot y + \log c \cdot \left(b - 0.5\right)\right)\right)\right) + a} \]

      2. associate-+r+ 82.8%

         \[\leadsto \color{blue}{\left(\left(t + z\right) + \left(i \cdot y + \log c \cdot \left(b - 0.5\right)\right)\right)} + a \]

      3. *-commutative 82.8%

         \[\leadsto \left(\left(t + z\right) + \left(\color{blue}{y \cdot i} + \log c \cdot \left(b - 0.5\right)\right)\right) + a \]

      4. sub-neg 82.8%

         \[\leadsto \left(\left(t + z\right) + \left(y \cdot i + \log c \cdot \color{blue}{\left(b + \left(-0.5\right)\right)}\right)\right) + a \]

      5. metadata-eval 82.8%

         \[\leadsto \left(\left(t + z\right) + \left(y \cdot i + \log c \cdot \left(b + \color{blue}{-0.5}\right)\right)\right) + a \]

      6. +-commutative 82.8%

         \[\leadsto \left(\left(t + z\right) + \left(y \cdot i + \log c \cdot \color{blue}{\left(-0.5 + b\right)}\right)\right) + a \]

      7. distribute-rgt-out 82.8%

         \[\leadsto \left(\left(t + z\right) + \left(y \cdot i + \color{blue}{\left(-0.5 \cdot \log c + b \cdot \log c\right)}\right)\right) + a \]

      8. +-commutative 82.8%

         \[\leadsto \left(\left(t + z\right) + \left(y \cdot i + \color{blue}{\left(b \cdot \log c + -0.5 \cdot \log c\right)}\right)\right) + a \]

      9. distribute-rgt-in 82.8%

         \[\leadsto \left(\left(t + z\right) + \left(y \cdot i + \color{blue}{\log c \cdot \left(b + -0.5\right)}\right)\right) + a \]

      10. associate-+l+ 82.8%

          \[\leadsto \color{blue}{\left(t + z\right) + \left(\left(y \cdot i + \log c \cdot \left(b + -0.5\right)\right) + a\right)} \]

      11. +-commutative 82.8%

          \[\leadsto \color{blue}{\left(z + t\right)} + \left(\left(y \cdot i + \log c \cdot \left(b + -0.5\right)\right) + a\right) \]

      12. +-commutative 82.8%

          \[\leadsto \left(z + t\right) + \left(\color{blue}{\left(\log c \cdot \left(b + -0.5\right) + y \cdot i\right)} + a\right) \]

      13. fma-define 82.8%

          \[\leadsto \left(z + t\right) + \left(\color{blue}{\mathsf{fma}\left(\log c, b + -0.5, y \cdot i\right)} + a\right) \]

      14. +-commutative 82.8%

          \[\leadsto \left(z + t\right) + \left(\mathsf{fma}\left(\log c, \color{blue}{-0.5 + b}, y \cdot i\right) + a\right) \]

   7. Simplified 82.8%

      \[\leadsto \color{blue}{\left(z + t\right) + \left(\mathsf{fma}\left(\log c, -0.5 + b, y \cdot i\right) + a\right)} \]

   8. Taylor expanded in y around inf 65.2%

      \[\leadsto \left(z + t\right) + \left(\color{blue}{i \cdot y} + a\right) \]
   9. Step-by-step derivation

      1. *-commutative 65.2%

         \[\leadsto \left(z + t\right) + \left(\color{blue}{y \cdot i} + a\right) \]

   10. Simplified 65.2%

       \[\leadsto \left(z + t\right) + \left(\color{blue}{y \cdot i} + a\right) \]

   11. Taylor expanded in y around 0 56.3%

       \[\leadsto \left(z + t\right) + \color{blue}{a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.8 \cdot 10^{+141} \lor \neg \left(i \leq 1.1 \cdot 10^{+74}\right):\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + \left(z + t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 30.9% accurate, 16.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -5.8 \cdot 10^{-31} \lor \neg \left(i \leq 2.6 \cdot 10^{+15}\right):\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= i -5.8e-31) (not (<= i 2.6e+15))) (* 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 ((i <= -5.8e-31) || !(i <= 2.6e+15)) {
		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 ((i <= (-5.8d-31)) .or. (.not. (i <= 2.6d+15))) 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 ((i <= -5.8e-31) || !(i <= 2.6e+15)) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (i <= -5.8e-31) or not (i <= 2.6e+15):
		tmp = y * i
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((i <= -5.8e-31) || !(i <= 2.6e+15))
		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 ((i <= -5.8e-31) || ~((i <= 2.6e+15)))
		tmp = y * i;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[i, -5.8e-31], N[Not[LessEqual[i, 2.6e+15]], $MachinePrecision]], N[(y * i), $MachinePrecision], a]

Derivation

1. Split input into 2 regimes

2. if i < -5.8000000000000001e-31 or 2.6e15 < i

   1. Initial program 99.8%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Step-by-step derivation

      1. associate-+l+ 99.8%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right)} \]

      2. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(a + \left(\left(x \cdot \log y + z\right) + t\right)\right)} + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

      3. associate-+l+ 99.8%

         \[\leadsto \left(a + \color{blue}{\left(x \cdot \log y + \left(z + t\right)\right)}\right) + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

      4. associate-+r+ 99.8%

         \[\leadsto \color{blue}{\left(\left(a + x \cdot \log y\right) + \left(z + t\right)\right)} + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

      5. +-commutative 99.8%

         \[\leadsto \left(\left(a + x \cdot \log y\right) + \color{blue}{\left(t + z\right)}\right) + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

      6. +-commutative 99.8%

         \[\leadsto \left(\color{blue}{\left(x \cdot \log y + a\right)} + \left(t + z\right)\right) + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

      7. associate-+l+ 99.8%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right)} + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

      8. associate-+l+ 99.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i} \]

      9. +-commutative 99.8%

         \[\leadsto \color{blue}{y \cdot i + \left(\left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right) + \left(b - 0.5\right) \cdot \log c\right)} \]

      10. fma-define 99.8%

          \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right) + \left(b - 0.5\right) \cdot \log c\right)} \]

      11. +-commutative 99.8%

          \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\left(b - 0.5\right) \cdot \log c + \left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right)}\right) \]

      12. fma-define 99.9%

          \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\mathsf{fma}\left(b - 0.5, \log c, \left(\left(x \cdot \log y + a\right) + t\right) + z\right)}\right) \]

      13. sub-neg 99.9%

          \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\color{blue}{b + \left(-0.5\right)}, \log c, \left(\left(x \cdot \log y + a\right) + t\right) + z\right)\right) \]

      14. metadata-eval 99.9%

          \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + \color{blue}{-0.5}, \log c, \left(\left(x \cdot \log y + a\right) + t\right) + z\right)\right) \]

      15. +-commutative 99.9%

          \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + -0.5, \log c, \color{blue}{z + \left(\left(x \cdot \log y + a\right) + t\right)}\right)\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \mathsf{fma}\left(b + -0.5, \log c, z + \mathsf{fma}\left(x, \log y, t + a\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 50.0%

      \[\leadsto \color{blue}{i \cdot y} \]
   6. Step-by-step derivation

      1. *-commutative 50.0%

         \[\leadsto \color{blue}{y \cdot i} \]

   7. Simplified 50.0%

      \[\leadsto \color{blue}{y \cdot i} \]

   if -5.8000000000000001e-31 < i < 2.6e15

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Step-by-step derivation

      1. associate-+l+ 99.9%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right)} \]

      2. +-commutative 99.9%

         \[\leadsto \color{blue}{\left(a + \left(\left(x \cdot \log y + z\right) + t\right)\right)} + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

      3. associate-+l+ 99.9%

         \[\leadsto \left(a + \color{blue}{\left(x \cdot \log y + \left(z + t\right)\right)}\right) + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

      4. associate-+r+ 99.9%

         \[\leadsto \color{blue}{\left(\left(a + x \cdot \log y\right) + \left(z + t\right)\right)} + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

      5. +-commutative 99.9%

         \[\leadsto \left(\left(a + x \cdot \log y\right) + \color{blue}{\left(t + z\right)}\right) + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

      6. +-commutative 99.9%

         \[\leadsto \left(\color{blue}{\left(x \cdot \log y + a\right)} + \left(t + z\right)\right) + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

      7. associate-+l+ 99.9%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right)} + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

      8. associate-+l+ 99.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i} \]

      9. +-commutative 99.9%

         \[\leadsto \color{blue}{y \cdot i + \left(\left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right) + \left(b - 0.5\right) \cdot \log c\right)} \]

      10. fma-define 99.9%

          \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right) + \left(b - 0.5\right) \cdot \log c\right)} \]

      11. +-commutative 99.9%

          \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\left(b - 0.5\right) \cdot \log c + \left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right)}\right) \]

      12. fma-define 99.9%

          \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\mathsf{fma}\left(b - 0.5, \log c, \left(\left(x \cdot \log y + a\right) + t\right) + z\right)}\right) \]

      13. sub-neg 99.9%

          \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\color{blue}{b + \left(-0.5\right)}, \log c, \left(\left(x \cdot \log y + a\right) + t\right) + z\right)\right) \]

      14. metadata-eval 99.9%

          \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + \color{blue}{-0.5}, \log c, \left(\left(x \cdot \log y + a\right) + t\right) + z\right)\right) \]

      15. +-commutative 99.9%

          \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + -0.5, \log c, \color{blue}{z + \left(\left(x \cdot \log y + a\right) + t\right)}\right)\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \mathsf{fma}\left(b + -0.5, \log c, z + \mathsf{fma}\left(x, \log y, t + a\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 67.9%

      \[\leadsto \color{blue}{x \cdot \left(\log y + \left(\frac{a}{x} + \left(\frac{t}{x} + \left(\frac{z}{x} + \left(\frac{i \cdot y}{x} + \frac{\log c \cdot \left(b - 0.5\right)}{x}\right)\right)\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-+r+ 67.9%

         \[\leadsto x \cdot \color{blue}{\left(\left(\log y + \frac{a}{x}\right) + \left(\frac{t}{x} + \left(\frac{z}{x} + \left(\frac{i \cdot y}{x} + \frac{\log c \cdot \left(b - 0.5\right)}{x}\right)\right)\right)\right)} \]

      2. associate-+r+ 67.9%

         \[\leadsto x \cdot \left(\left(\log y + \frac{a}{x}\right) + \color{blue}{\left(\left(\frac{t}{x} + \frac{z}{x}\right) + \left(\frac{i \cdot y}{x} + \frac{\log c \cdot \left(b - 0.5\right)}{x}\right)\right)}\right) \]

      3. associate-+r+ 67.9%

         \[\leadsto x \cdot \color{blue}{\left(\left(\left(\log y + \frac{a}{x}\right) + \left(\frac{t}{x} + \frac{z}{x}\right)\right) + \left(\frac{i \cdot y}{x} + \frac{\log c \cdot \left(b - 0.5\right)}{x}\right)\right)} \]

      4. associate-+r+ 67.9%

         \[\leadsto x \cdot \left(\color{blue}{\left(\log y + \left(\frac{a}{x} + \left(\frac{t}{x} + \frac{z}{x}\right)\right)\right)} + \left(\frac{i \cdot y}{x} + \frac{\log c \cdot \left(b - 0.5\right)}{x}\right)\right) \]

      5. +-commutative 67.9%

         \[\leadsto x \cdot \left(\left(\log y + \color{blue}{\left(\left(\frac{t}{x} + \frac{z}{x}\right) + \frac{a}{x}\right)}\right) + \left(\frac{i \cdot y}{x} + \frac{\log c \cdot \left(b - 0.5\right)}{x}\right)\right) \]

      6. +-commutative 67.9%

         \[\leadsto x \cdot \left(\left(\log y + \left(\color{blue}{\left(\frac{z}{x} + \frac{t}{x}\right)} + \frac{a}{x}\right)\right) + \left(\frac{i \cdot y}{x} + \frac{\log c \cdot \left(b - 0.5\right)}{x}\right)\right) \]

      7. associate-+l+ 67.9%

         \[\leadsto x \cdot \left(\left(\log y + \color{blue}{\left(\frac{z}{x} + \left(\frac{t}{x} + \frac{a}{x}\right)\right)}\right) + \left(\frac{i \cdot y}{x} + \frac{\log c \cdot \left(b - 0.5\right)}{x}\right)\right) \]

      8. +-commutative 67.9%

         \[\leadsto x \cdot \left(\left(\log y + \left(\frac{z}{x} + \color{blue}{\left(\frac{a}{x} + \frac{t}{x}\right)}\right)\right) + \left(\frac{i \cdot y}{x} + \frac{\log c \cdot \left(b - 0.5\right)}{x}\right)\right) \]

      9. +-commutative 67.9%

         \[\leadsto x \cdot \left(\left(\log y + \left(\frac{z}{x} + \left(\frac{a}{x} + \frac{t}{x}\right)\right)\right) + \color{blue}{\left(\frac{\log c \cdot \left(b - 0.5\right)}{x} + \frac{i \cdot y}{x}\right)}\right) \]

   7. Simplified 67.9%

      \[\leadsto \color{blue}{x \cdot \left(\left(\log y + \left(\frac{z}{x} + \left(\frac{a}{x} + \frac{t}{x}\right)\right)\right) + \mathsf{fma}\left(\log c, \frac{-0.5 + b}{x}, \frac{y \cdot i}{x}\right)\right)} \]

   8. Taylor expanded in a around inf 15.3%

      \[\leadsto x \cdot \color{blue}{\frac{a}{x}} \]

   9. Taylor expanded in x around 0 23.1%

      \[\leadsto \color{blue}{a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 36.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -5.8 \cdot 10^{-31} \lor \neg \left(i \leq 2.6 \cdot 10^{+15}\right):\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 28.2% accurate, 16.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.6 \cdot 10^{-178}:\\ \;\;\;\;x \cdot \frac{z}{x}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+94}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 2.6e-178) (* x (/ z x)) (if (<= y 5e+94) a (* y i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 2.6e-178) {
		tmp = x * (z / x);
	} else if (y <= 5e+94) {
		tmp = a;
	} else {
		tmp = y * i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= 2.6d-178) then
        tmp = x * (z / x)
    else if (y <= 5d+94) then
        tmp = a
    else
        tmp = y * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 2.6e-178) {
		tmp = x * (z / x);
	} else if (y <= 5e+94) {
		tmp = a;
	} else {
		tmp = y * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 2.6e-178:
		tmp = x * (z / x)
	elif y <= 5e+94:
		tmp = a
	else:
		tmp = y * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 2.6e-178)
		tmp = Float64(x * Float64(z / x));
	elseif (y <= 5e+94)
		tmp = a;
	else
		tmp = Float64(y * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= 2.6e-178)
		tmp = x * (z / x);
	elseif (y <= 5e+94)
		tmp = a;
	else
		tmp = y * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 2.6e-178], N[(x * N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5e+94], a, N[(y * i), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 2.59999999999999998e-178

   1. Initial program 99.8%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Step-by-step derivation

      1. associate-+l+ 99.8%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right)} \]

      2. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(a + \left(\left(x \cdot \log y + z\right) + t\right)\right)} + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

      3. associate-+l+ 99.8%

         \[\leadsto \left(a + \color{blue}{\left(x \cdot \log y + \left(z + t\right)\right)}\right) + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

      4. associate-+r+ 99.8%

         \[\leadsto \color{blue}{\left(\left(a + x \cdot \log y\right) + \left(z + t\right)\right)} + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

      5. +-commutative 99.8%

         \[\leadsto \left(\left(a + x \cdot \log y\right) + \color{blue}{\left(t + z\right)}\right) + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

      6. +-commutative 99.8%

         \[\leadsto \left(\color{blue}{\left(x \cdot \log y + a\right)} + \left(t + z\right)\right) + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

      7. associate-+l+ 99.8%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right)} + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

      8. associate-+l+ 99.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i} \]

      9. +-commutative 99.8%

         \[\leadsto \color{blue}{y \cdot i + \left(\left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right) + \left(b - 0.5\right) \cdot \log c\right)} \]

      10. fma-define 99.8%

          \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right) + \left(b - 0.5\right) \cdot \log c\right)} \]

      11. +-commutative 99.8%

          \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\left(b - 0.5\right) \cdot \log c + \left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right)}\right) \]

      12. fma-define 99.8%

          \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\mathsf{fma}\left(b - 0.5, \log c, \left(\left(x \cdot \log y + a\right) + t\right) + z\right)}\right) \]

      13. sub-neg 99.8%

          \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\color{blue}{b + \left(-0.5\right)}, \log c, \left(\left(x \cdot \log y + a\right) + t\right) + z\right)\right) \]

      14. metadata-eval 99.8%

          \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + \color{blue}{-0.5}, \log c, \left(\left(x \cdot \log y + a\right) + t\right) + z\right)\right) \]

      15. +-commutative 99.8%

          \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + -0.5, \log c, \color{blue}{z + \left(\left(x \cdot \log y + a\right) + t\right)}\right)\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \mathsf{fma}\left(b + -0.5, \log c, z + \mathsf{fma}\left(x, \log y, t + a\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 77.5%

      \[\leadsto \color{blue}{x \cdot \left(\log y + \left(\frac{a}{x} + \left(\frac{t}{x} + \left(\frac{z}{x} + \left(\frac{i \cdot y}{x} + \frac{\log c \cdot \left(b - 0.5\right)}{x}\right)\right)\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-+r+ 77.5%

         \[\leadsto x \cdot \color{blue}{\left(\left(\log y + \frac{a}{x}\right) + \left(\frac{t}{x} + \left(\frac{z}{x} + \left(\frac{i \cdot y}{x} + \frac{\log c \cdot \left(b - 0.5\right)}{x}\right)\right)\right)\right)} \]

      2. associate-+r+ 77.5%

         \[\leadsto x \cdot \left(\left(\log y + \frac{a}{x}\right) + \color{blue}{\left(\left(\frac{t}{x} + \frac{z}{x}\right) + \left(\frac{i \cdot y}{x} + \frac{\log c \cdot \left(b - 0.5\right)}{x}\right)\right)}\right) \]

      3. associate-+r+ 77.5%

         \[\leadsto x \cdot \color{blue}{\left(\left(\left(\log y + \frac{a}{x}\right) + \left(\frac{t}{x} + \frac{z}{x}\right)\right) + \left(\frac{i \cdot y}{x} + \frac{\log c \cdot \left(b - 0.5\right)}{x}\right)\right)} \]

      4. associate-+r+ 77.5%

         \[\leadsto x \cdot \left(\color{blue}{\left(\log y + \left(\frac{a}{x} + \left(\frac{t}{x} + \frac{z}{x}\right)\right)\right)} + \left(\frac{i \cdot y}{x} + \frac{\log c \cdot \left(b - 0.5\right)}{x}\right)\right) \]

      5. +-commutative 77.5%

         \[\leadsto x \cdot \left(\left(\log y + \color{blue}{\left(\left(\frac{t}{x} + \frac{z}{x}\right) + \frac{a}{x}\right)}\right) + \left(\frac{i \cdot y}{x} + \frac{\log c \cdot \left(b - 0.5\right)}{x}\right)\right) \]

      6. +-commutative 77.5%

         \[\leadsto x \cdot \left(\left(\log y + \left(\color{blue}{\left(\frac{z}{x} + \frac{t}{x}\right)} + \frac{a}{x}\right)\right) + \left(\frac{i \cdot y}{x} + \frac{\log c \cdot \left(b - 0.5\right)}{x}\right)\right) \]

      7. associate-+l+ 77.5%

         \[\leadsto x \cdot \left(\left(\log y + \color{blue}{\left(\frac{z}{x} + \left(\frac{t}{x} + \frac{a}{x}\right)\right)}\right) + \left(\frac{i \cdot y}{x} + \frac{\log c \cdot \left(b - 0.5\right)}{x}\right)\right) \]

      8. +-commutative 77.5%

         \[\leadsto x \cdot \left(\left(\log y + \left(\frac{z}{x} + \color{blue}{\left(\frac{a}{x} + \frac{t}{x}\right)}\right)\right) + \left(\frac{i \cdot y}{x} + \frac{\log c \cdot \left(b - 0.5\right)}{x}\right)\right) \]

      9. +-commutative 77.5%

         \[\leadsto x \cdot \left(\left(\log y + \left(\frac{z}{x} + \left(\frac{a}{x} + \frac{t}{x}\right)\right)\right) + \color{blue}{\left(\frac{\log c \cdot \left(b - 0.5\right)}{x} + \frac{i \cdot y}{x}\right)}\right) \]

   7. Simplified 77.5%

      \[\leadsto \color{blue}{x \cdot \left(\left(\log y + \left(\frac{z}{x} + \left(\frac{a}{x} + \frac{t}{x}\right)\right)\right) + \mathsf{fma}\left(\log c, \frac{-0.5 + b}{x}, \frac{y \cdot i}{x}\right)\right)} \]

   8. Taylor expanded in z around inf 17.0%

      \[\leadsto x \cdot \color{blue}{\frac{z}{x}} \]

   if 2.59999999999999998e-178 < y < 5.0000000000000001e94

   1. Initial program 99.8%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Step-by-step derivation

      1. associate-+l+ 99.8%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right)} \]

      2. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(a + \left(\left(x \cdot \log y + z\right) + t\right)\right)} + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

      3. associate-+l+ 99.8%

         \[\leadsto \left(a + \color{blue}{\left(x \cdot \log y + \left(z + t\right)\right)}\right) + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

      4. associate-+r+ 99.8%

         \[\leadsto \color{blue}{\left(\left(a + x \cdot \log y\right) + \left(z + t\right)\right)} + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

      5. +-commutative 99.8%

         \[\leadsto \left(\left(a + x \cdot \log y\right) + \color{blue}{\left(t + z\right)}\right) + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

      6. +-commutative 99.8%

         \[\leadsto \left(\color{blue}{\left(x \cdot \log y + a\right)} + \left(t + z\right)\right) + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

      7. associate-+l+ 99.8%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right)} + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

      8. associate-+l+ 99.8%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i} \]

      9. +-commutative 99.8%

         \[\leadsto \color{blue}{y \cdot i + \left(\left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right) + \left(b - 0.5\right) \cdot \log c\right)} \]

      10. fma-define 99.9%

          \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right) + \left(b - 0.5\right) \cdot \log c\right)} \]

      11. +-commutative 99.9%

          \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\left(b - 0.5\right) \cdot \log c + \left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right)}\right) \]

      12. fma-define 99.9%

          \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\mathsf{fma}\left(b - 0.5, \log c, \left(\left(x \cdot \log y + a\right) + t\right) + z\right)}\right) \]

      13. sub-neg 99.9%

          \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\color{blue}{b + \left(-0.5\right)}, \log c, \left(\left(x \cdot \log y + a\right) + t\right) + z\right)\right) \]

      14. metadata-eval 99.9%

          \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + \color{blue}{-0.5}, \log c, \left(\left(x \cdot \log y + a\right) + t\right) + z\right)\right) \]

      15. +-commutative 99.9%

          \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + -0.5, \log c, \color{blue}{z + \left(\left(x \cdot \log y + a\right) + t\right)}\right)\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \mathsf{fma}\left(b + -0.5, \log c, z + \mathsf{fma}\left(x, \log y, t + a\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 74.5%

      \[\leadsto \color{blue}{x \cdot \left(\log y + \left(\frac{a}{x} + \left(\frac{t}{x} + \left(\frac{z}{x} + \left(\frac{i \cdot y}{x} + \frac{\log c \cdot \left(b - 0.5\right)}{x}\right)\right)\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-+r+ 74.5%

         \[\leadsto x \cdot \color{blue}{\left(\left(\log y + \frac{a}{x}\right) + \left(\frac{t}{x} + \left(\frac{z}{x} + \left(\frac{i \cdot y}{x} + \frac{\log c \cdot \left(b - 0.5\right)}{x}\right)\right)\right)\right)} \]

      2. associate-+r+ 74.5%

         \[\leadsto x \cdot \left(\left(\log y + \frac{a}{x}\right) + \color{blue}{\left(\left(\frac{t}{x} + \frac{z}{x}\right) + \left(\frac{i \cdot y}{x} + \frac{\log c \cdot \left(b - 0.5\right)}{x}\right)\right)}\right) \]

      3. associate-+r+ 74.5%

         \[\leadsto x \cdot \color{blue}{\left(\left(\left(\log y + \frac{a}{x}\right) + \left(\frac{t}{x} + \frac{z}{x}\right)\right) + \left(\frac{i \cdot y}{x} + \frac{\log c \cdot \left(b - 0.5\right)}{x}\right)\right)} \]

      4. associate-+r+ 74.5%

         \[\leadsto x \cdot \left(\color{blue}{\left(\log y + \left(\frac{a}{x} + \left(\frac{t}{x} + \frac{z}{x}\right)\right)\right)} + \left(\frac{i \cdot y}{x} + \frac{\log c \cdot \left(b - 0.5\right)}{x}\right)\right) \]

      5. +-commutative 74.5%

         \[\leadsto x \cdot \left(\left(\log y + \color{blue}{\left(\left(\frac{t}{x} + \frac{z}{x}\right) + \frac{a}{x}\right)}\right) + \left(\frac{i \cdot y}{x} + \frac{\log c \cdot \left(b - 0.5\right)}{x}\right)\right) \]

      6. +-commutative 74.5%

         \[\leadsto x \cdot \left(\left(\log y + \left(\color{blue}{\left(\frac{z}{x} + \frac{t}{x}\right)} + \frac{a}{x}\right)\right) + \left(\frac{i \cdot y}{x} + \frac{\log c \cdot \left(b - 0.5\right)}{x}\right)\right) \]

      7. associate-+l+ 74.5%

         \[\leadsto x \cdot \left(\left(\log y + \color{blue}{\left(\frac{z}{x} + \left(\frac{t}{x} + \frac{a}{x}\right)\right)}\right) + \left(\frac{i \cdot y}{x} + \frac{\log c \cdot \left(b - 0.5\right)}{x}\right)\right) \]

      8. +-commutative 74.5%

         \[\leadsto x \cdot \left(\left(\log y + \left(\frac{z}{x} + \color{blue}{\left(\frac{a}{x} + \frac{t}{x}\right)}\right)\right) + \left(\frac{i \cdot y}{x} + \frac{\log c \cdot \left(b - 0.5\right)}{x}\right)\right) \]

      9. +-commutative 74.5%

         \[\leadsto x \cdot \left(\left(\log y + \left(\frac{z}{x} + \left(\frac{a}{x} + \frac{t}{x}\right)\right)\right) + \color{blue}{\left(\frac{\log c \cdot \left(b - 0.5\right)}{x} + \frac{i \cdot y}{x}\right)}\right) \]

   7. Simplified 74.5%

      \[\leadsto \color{blue}{x \cdot \left(\left(\log y + \left(\frac{z}{x} + \left(\frac{a}{x} + \frac{t}{x}\right)\right)\right) + \mathsf{fma}\left(\log c, \frac{-0.5 + b}{x}, \frac{y \cdot i}{x}\right)\right)} \]

   8. Taylor expanded in a around inf 14.9%

      \[\leadsto x \cdot \color{blue}{\frac{a}{x}} \]

   9. Taylor expanded in x around 0 19.2%

      \[\leadsto \color{blue}{a} \]

   if 5.0000000000000001e94 < y

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Step-by-step derivation

      1. associate-+l+ 99.9%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right)} \]

      2. +-commutative 99.9%

         \[\leadsto \color{blue}{\left(a + \left(\left(x \cdot \log y + z\right) + t\right)\right)} + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

      3. associate-+l+ 99.9%

         \[\leadsto \left(a + \color{blue}{\left(x \cdot \log y + \left(z + t\right)\right)}\right) + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

      4. associate-+r+ 99.9%

         \[\leadsto \color{blue}{\left(\left(a + x \cdot \log y\right) + \left(z + t\right)\right)} + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

      5. +-commutative 99.9%

         \[\leadsto \left(\left(a + x \cdot \log y\right) + \color{blue}{\left(t + z\right)}\right) + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

      6. +-commutative 99.9%

         \[\leadsto \left(\color{blue}{\left(x \cdot \log y + a\right)} + \left(t + z\right)\right) + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

      7. associate-+l+ 99.9%

         \[\leadsto \color{blue}{\left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right)} + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

      8. associate-+l+ 99.9%

         \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i} \]

      9. +-commutative 99.9%

         \[\leadsto \color{blue}{y \cdot i + \left(\left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right) + \left(b - 0.5\right) \cdot \log c\right)} \]

      10. fma-define 99.9%

          \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right) + \left(b - 0.5\right) \cdot \log c\right)} \]

      11. +-commutative 99.9%

          \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\left(b - 0.5\right) \cdot \log c + \left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right)}\right) \]

      12. fma-define 99.9%

          \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\mathsf{fma}\left(b - 0.5, \log c, \left(\left(x \cdot \log y + a\right) + t\right) + z\right)}\right) \]

      13. sub-neg 99.9%

          \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\color{blue}{b + \left(-0.5\right)}, \log c, \left(\left(x \cdot \log y + a\right) + t\right) + z\right)\right) \]

      14. metadata-eval 99.9%

          \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + \color{blue}{-0.5}, \log c, \left(\left(x \cdot \log y + a\right) + t\right) + z\right)\right) \]

      15. +-commutative 99.9%

          \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + -0.5, \log c, \color{blue}{z + \left(\left(x \cdot \log y + a\right) + t\right)}\right)\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \mathsf{fma}\left(b + -0.5, \log c, z + \mathsf{fma}\left(x, \log y, t + a\right)\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 56.3%

      \[\leadsto \color{blue}{i \cdot y} \]
   6. Step-by-step derivation

      1. *-commutative 56.3%

         \[\leadsto \color{blue}{y \cdot i} \]

   7. Simplified 56.3%

      \[\leadsto \color{blue}{y \cdot i} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 23: 67.6% accurate, 24.3× speedup

Math

\[\begin{array}{l} \\ \left(z + t\right) + \left(a + y \cdot i\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (+ (+ z t) (+ a (* y i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (z + t) + (a + (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 = (z + t) + (a + (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 (z + t) + (a + (y * i));
}

Python

def code(x, y, z, t, a, b, c, i):
	return (z + t) + (a + (y * i))

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(z + t) + Float64(a + Float64(y * i)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = (z + t) + (a + (y * i));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(z + t), $MachinePrecision] + N[(a + 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. +-commutative 99.9%

      \[\leadsto \color{blue}{\left(a + \left(\left(x \cdot \log y + z\right) + t\right)\right)} + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

   3. associate-+l+ 99.9%

      \[\leadsto \left(a + \color{blue}{\left(x \cdot \log y + \left(z + t\right)\right)}\right) + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

   4. associate-+r+ 99.9%

      \[\leadsto \color{blue}{\left(\left(a + x \cdot \log y\right) + \left(z + t\right)\right)} + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

   5. +-commutative 99.9%

      \[\leadsto \left(\left(a + x \cdot \log y\right) + \color{blue}{\left(t + z\right)}\right) + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

   6. +-commutative 99.9%

      \[\leadsto \left(\color{blue}{\left(x \cdot \log y + a\right)} + \left(t + z\right)\right) + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

   7. associate-+l+ 99.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right)} + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

   8. associate-+l+ 99.9%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i} \]

   9. +-commutative 99.9%

      \[\leadsto \color{blue}{y \cdot i + \left(\left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right) + \left(b - 0.5\right) \cdot \log c\right)} \]

   10. fma-define 99.9%

       \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right) + \left(b - 0.5\right) \cdot \log c\right)} \]

   11. +-commutative 99.9%

       \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\left(b - 0.5\right) \cdot \log c + \left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right)}\right) \]

   12. fma-define 99.9%

       \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\mathsf{fma}\left(b - 0.5, \log c, \left(\left(x \cdot \log y + a\right) + t\right) + z\right)}\right) \]

   13. sub-neg 99.9%

       \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\color{blue}{b + \left(-0.5\right)}, \log c, \left(\left(x \cdot \log y + a\right) + t\right) + z\right)\right) \]

   14. metadata-eval 99.9%

       \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + \color{blue}{-0.5}, \log c, \left(\left(x \cdot \log y + a\right) + t\right) + z\right)\right) \]

   15. +-commutative 99.9%

       \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + -0.5, \log c, \color{blue}{z + \left(\left(x \cdot \log y + a\right) + t\right)}\right)\right) \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \mathsf{fma}\left(b + -0.5, \log c, z + \mathsf{fma}\left(x, \log y, t + a\right)\right)\right)} \]
4. Add Preprocessing

5. Taylor expanded in 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. +-commutative 84.8%

      \[\leadsto \color{blue}{\left(t + \left(z + \left(i \cdot y + \log c \cdot \left(b - 0.5\right)\right)\right)\right) + a} \]

   2. associate-+r+ 84.8%

      \[\leadsto \color{blue}{\left(\left(t + z\right) + \left(i \cdot y + \log c \cdot \left(b - 0.5\right)\right)\right)} + a \]

   3. *-commutative 84.8%

      \[\leadsto \left(\left(t + z\right) + \left(\color{blue}{y \cdot i} + \log c \cdot \left(b - 0.5\right)\right)\right) + a \]

   4. sub-neg 84.8%

      \[\leadsto \left(\left(t + z\right) + \left(y \cdot i + \log c \cdot \color{blue}{\left(b + \left(-0.5\right)\right)}\right)\right) + a \]

   5. metadata-eval 84.8%

      \[\leadsto \left(\left(t + z\right) + \left(y \cdot i + \log c \cdot \left(b + \color{blue}{-0.5}\right)\right)\right) + a \]

   6. +-commutative 84.8%

      \[\leadsto \left(\left(t + z\right) + \left(y \cdot i + \log c \cdot \color{blue}{\left(-0.5 + b\right)}\right)\right) + a \]

   7. distribute-rgt-out 84.8%

      \[\leadsto \left(\left(t + z\right) + \left(y \cdot i + \color{blue}{\left(-0.5 \cdot \log c + b \cdot \log c\right)}\right)\right) + a \]

   8. +-commutative 84.8%

      \[\leadsto \left(\left(t + z\right) + \left(y \cdot i + \color{blue}{\left(b \cdot \log c + -0.5 \cdot \log c\right)}\right)\right) + a \]

   9. distribute-rgt-in 84.8%

      \[\leadsto \left(\left(t + z\right) + \left(y \cdot i + \color{blue}{\log c \cdot \left(b + -0.5\right)}\right)\right) + a \]

   10. associate-+l+ 84.8%

       \[\leadsto \color{blue}{\left(t + z\right) + \left(\left(y \cdot i + \log c \cdot \left(b + -0.5\right)\right) + a\right)} \]

   11. +-commutative 84.8%

       \[\leadsto \color{blue}{\left(z + t\right)} + \left(\left(y \cdot i + \log c \cdot \left(b + -0.5\right)\right) + a\right) \]

   12. +-commutative 84.8%

       \[\leadsto \left(z + t\right) + \left(\color{blue}{\left(\log c \cdot \left(b + -0.5\right) + y \cdot i\right)} + a\right) \]

   13. fma-define 84.8%

       \[\leadsto \left(z + t\right) + \left(\color{blue}{\mathsf{fma}\left(\log c, b + -0.5, y \cdot i\right)} + a\right) \]

   14. +-commutative 84.8%

       \[\leadsto \left(z + t\right) + \left(\mathsf{fma}\left(\log c, \color{blue}{-0.5 + b}, y \cdot i\right) + a\right) \]

7. Simplified 84.8%

   \[\leadsto \color{blue}{\left(z + t\right) + \left(\mathsf{fma}\left(\log c, -0.5 + b, y \cdot i\right) + a\right)} \]

8. Taylor expanded in y around inf 69.7%

   \[\leadsto \left(z + t\right) + \left(\color{blue}{i \cdot y} + a\right) \]
9. Step-by-step derivation

   1. *-commutative 69.7%

      \[\leadsto \left(z + t\right) + \left(\color{blue}{y \cdot i} + a\right) \]

10. Simplified 69.7%

    \[\leadsto \left(z + t\right) + \left(\color{blue}{y \cdot i} + a\right) \]

11. Final simplification 69.7%

    \[\leadsto \left(z + t\right) + \left(a + y \cdot i\right) \]
12. Add Preprocessing

Alternative 24: 15.7% accurate, 219.0× speedup

Math

\[\begin{array}{l} \\ a \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 a)

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return a;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = a
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return a;
}

Python

def code(x, y, z, t, a, b, c, i):
	return a

Julia

function code(x, y, z, t, a, b, c, i)
	return a
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = a;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := a

Derivation

1. Initial program 99.9%

   \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
2. Step-by-step derivation

   1. associate-+l+ 99.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right)} \]

   2. +-commutative 99.9%

      \[\leadsto \color{blue}{\left(a + \left(\left(x \cdot \log y + z\right) + t\right)\right)} + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

   3. associate-+l+ 99.9%

      \[\leadsto \left(a + \color{blue}{\left(x \cdot \log y + \left(z + t\right)\right)}\right) + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

   4. associate-+r+ 99.9%

      \[\leadsto \color{blue}{\left(\left(a + x \cdot \log y\right) + \left(z + t\right)\right)} + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

   5. +-commutative 99.9%

      \[\leadsto \left(\left(a + x \cdot \log y\right) + \color{blue}{\left(t + z\right)}\right) + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

   6. +-commutative 99.9%

      \[\leadsto \left(\color{blue}{\left(x \cdot \log y + a\right)} + \left(t + z\right)\right) + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

   7. associate-+l+ 99.9%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right)} + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

   8. associate-+l+ 99.9%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i} \]

   9. +-commutative 99.9%

      \[\leadsto \color{blue}{y \cdot i + \left(\left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right) + \left(b - 0.5\right) \cdot \log c\right)} \]

   10. fma-define 99.9%

       \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right) + \left(b - 0.5\right) \cdot \log c\right)} \]

   11. +-commutative 99.9%

       \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\left(b - 0.5\right) \cdot \log c + \left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right)}\right) \]

   12. fma-define 99.9%

       \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\mathsf{fma}\left(b - 0.5, \log c, \left(\left(x \cdot \log y + a\right) + t\right) + z\right)}\right) \]

   13. sub-neg 99.9%

       \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\color{blue}{b + \left(-0.5\right)}, \log c, \left(\left(x \cdot \log y + a\right) + t\right) + z\right)\right) \]

   14. metadata-eval 99.9%

       \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + \color{blue}{-0.5}, \log c, \left(\left(x \cdot \log y + a\right) + t\right) + z\right)\right) \]

   15. +-commutative 99.9%

       \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + -0.5, \log c, \color{blue}{z + \left(\left(x \cdot \log y + a\right) + t\right)}\right)\right) \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \mathsf{fma}\left(b + -0.5, \log c, z + \mathsf{fma}\left(x, \log y, t + a\right)\right)\right)} \]
4. Add Preprocessing

5. Taylor expanded in x around inf 66.1%

   \[\leadsto \color{blue}{x \cdot \left(\log y + \left(\frac{a}{x} + \left(\frac{t}{x} + \left(\frac{z}{x} + \left(\frac{i \cdot y}{x} + \frac{\log c \cdot \left(b - 0.5\right)}{x}\right)\right)\right)\right)\right)} \]
6. Step-by-step derivation

   1. associate-+r+ 66.1%

      \[\leadsto x \cdot \color{blue}{\left(\left(\log y + \frac{a}{x}\right) + \left(\frac{t}{x} + \left(\frac{z}{x} + \left(\frac{i \cdot y}{x} + \frac{\log c \cdot \left(b - 0.5\right)}{x}\right)\right)\right)\right)} \]

   2. associate-+r+ 66.1%

      \[\leadsto x \cdot \left(\left(\log y + \frac{a}{x}\right) + \color{blue}{\left(\left(\frac{t}{x} + \frac{z}{x}\right) + \left(\frac{i \cdot y}{x} + \frac{\log c \cdot \left(b - 0.5\right)}{x}\right)\right)}\right) \]

   3. associate-+r+ 66.1%

      \[\leadsto x \cdot \color{blue}{\left(\left(\left(\log y + \frac{a}{x}\right) + \left(\frac{t}{x} + \frac{z}{x}\right)\right) + \left(\frac{i \cdot y}{x} + \frac{\log c \cdot \left(b - 0.5\right)}{x}\right)\right)} \]

   4. associate-+r+ 66.1%

      \[\leadsto x \cdot \left(\color{blue}{\left(\log y + \left(\frac{a}{x} + \left(\frac{t}{x} + \frac{z}{x}\right)\right)\right)} + \left(\frac{i \cdot y}{x} + \frac{\log c \cdot \left(b - 0.5\right)}{x}\right)\right) \]

   5. +-commutative 66.1%

      \[\leadsto x \cdot \left(\left(\log y + \color{blue}{\left(\left(\frac{t}{x} + \frac{z}{x}\right) + \frac{a}{x}\right)}\right) + \left(\frac{i \cdot y}{x} + \frac{\log c \cdot \left(b - 0.5\right)}{x}\right)\right) \]

   6. +-commutative 66.1%

      \[\leadsto x \cdot \left(\left(\log y + \left(\color{blue}{\left(\frac{z}{x} + \frac{t}{x}\right)} + \frac{a}{x}\right)\right) + \left(\frac{i \cdot y}{x} + \frac{\log c \cdot \left(b - 0.5\right)}{x}\right)\right) \]

   7. associate-+l+ 66.1%

      \[\leadsto x \cdot \left(\left(\log y + \color{blue}{\left(\frac{z}{x} + \left(\frac{t}{x} + \frac{a}{x}\right)\right)}\right) + \left(\frac{i \cdot y}{x} + \frac{\log c \cdot \left(b - 0.5\right)}{x}\right)\right) \]

   8. +-commutative 66.1%

      \[\leadsto x \cdot \left(\left(\log y + \left(\frac{z}{x} + \color{blue}{\left(\frac{a}{x} + \frac{t}{x}\right)}\right)\right) + \left(\frac{i \cdot y}{x} + \frac{\log c \cdot \left(b - 0.5\right)}{x}\right)\right) \]

   9. +-commutative 66.1%

      \[\leadsto x \cdot \left(\left(\log y + \left(\frac{z}{x} + \left(\frac{a}{x} + \frac{t}{x}\right)\right)\right) + \color{blue}{\left(\frac{\log c \cdot \left(b - 0.5\right)}{x} + \frac{i \cdot y}{x}\right)}\right) \]

7. Simplified 66.1%

   \[\leadsto \color{blue}{x \cdot \left(\left(\log y + \left(\frac{z}{x} + \left(\frac{a}{x} + \frac{t}{x}\right)\right)\right) + \mathsf{fma}\left(\log c, \frac{-0.5 + b}{x}, \frac{y \cdot i}{x}\right)\right)} \]

8. Taylor expanded in a around inf 14.5%

   \[\leadsto x \cdot \color{blue}{\frac{a}{x}} \]

9. Taylor expanded in x around 0 17.8%

   \[\leadsto \color{blue}{a} \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2024096 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, B"
  :precision binary64
  (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i)))