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

Percentage Accurate: 99.8% → 99.8%

Time: 19.8s

Alternatives: 18

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. associate-+l+ 99.9%

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

   2. associate-+l+ 99.9%

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

   3. +-commutative 99.9%

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

   4. +-commutative 99.9%

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

   5. associate-+r+ 99.9%

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

   6. associate-+l+ 99.9%

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

   7. +-commutative 99.9%

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

   8. associate-+l+ 99.9%

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

   9. +-commutative 99.9%

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

   10. fma-def 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-def 99.9%

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

   13. sub-neg 99.9%

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

   14. metadata-eval 99.9%

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

   15. +-commutative 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 2: 80.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+110} \lor \neg \left(x \leq 1.9 \cdot 10^{+141}\right):\\ \;\;\;\;a + \left(t + \left(z + \left(x \cdot \log y + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, \left(z + a\right) + \left(b + -0.5\right) \cdot \log c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -3.2e+110) (not (<= x 1.9e+141)))
   (+ a (+ t (+ z (+ (* x (log y)) (* (log c) (- b 0.5))))))
   (fma y i (+ (+ z a) (* (+ b -0.5) (log c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -3.2e+110) || !(x <= 1.9e+141)) {
		tmp = a + (t + (z + ((x * log(y)) + (log(c) * (b - 0.5)))));
	} else {
		tmp = fma(y, i, ((z + a) + ((b + -0.5) * log(c))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -3.2e+110) || !(x <= 1.9e+141))
		tmp = Float64(a + Float64(t + Float64(z + Float64(Float64(x * log(y)) + Float64(log(c) * Float64(b - 0.5))))));
	else
		tmp = fma(y, i, Float64(Float64(z + a) + Float64(Float64(b + -0.5) * log(c))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -3.2e+110], N[Not[LessEqual[x, 1.9e+141]], $MachinePrecision]], N[(a + N[(t + N[(z + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * i + N[(N[(z + a), $MachinePrecision] + N[(N[(b + -0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.19999999999999994e110 or 1.89999999999999988e141 < 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 y around 0 80.5%

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

   if -3.19999999999999994e110 < x < 1.89999999999999988e141

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+r+ 99.9%

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

      6. associate-+l+ 99.9%

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

      7. +-commutative 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-def 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-def 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 98.8%

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

      1. fma-udef 98.8%

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

      2. *-commutative 98.8%

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

      3. associate-+r+ 98.8%

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

   7. Applied egg-rr 98.8%

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

   8. Taylor expanded in t around 0 85.3%

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

      1. associate-+r+ 85.3%

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

      2. sub-neg 85.3%

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

      3. metadata-eval 85.3%

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

   10. Simplified 85.3%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+110} \lor \neg \left(x \leq 1.9 \cdot 10^{+141}\right):\\ \;\;\;\;a + \left(t + \left(z + \left(x \cdot \log y + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, \left(z + a\right) + \left(b + -0.5\right) \cdot \log c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+208} \lor \neg \left(x \leq 8 \cdot 10^{+161}\right):\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, \left(z + a\right) + \left(b + -0.5\right) \cdot \log c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -2.7e+208) (not (<= x 8e+161)))
   (+ (* x (log y)) (* y i))
   (fma y i (+ (+ z a) (* (+ b -0.5) (log c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -2.7e+208) || !(x <= 8e+161)) {
		tmp = (x * log(y)) + (y * i);
	} else {
		tmp = fma(y, i, ((z + a) + ((b + -0.5) * log(c))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -2.7e+208) || !(x <= 8e+161))
		tmp = Float64(Float64(x * log(y)) + Float64(y * i));
	else
		tmp = fma(y, i, Float64(Float64(z + a) + Float64(Float64(b + -0.5) * log(c))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -2.7e+208], N[Not[LessEqual[x, 8e+161]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(y * i + N[(N[(z + a), $MachinePrecision] + N[(N[(b + -0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.7e208 or 8.0000000000000003e161 < x

   1. Initial program 99.7%

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

      1. add-cube-cbrt 98.6%

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

   4. Applied egg-rr 98.6%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(\log c, b + -0.5, z + \mathsf{fma}\left(x, \log y, t + a\right)\right)}\right)}^{2} \cdot \sqrt[3]{\mathsf{fma}\left(\log c, b + -0.5, z + \mathsf{fma}\left(x, \log y, t + a\right)\right)}} + y \cdot i \]

   5. Taylor expanded in x around inf 81.5%

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

   if -2.7e208 < x < 8.0000000000000003e161

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+r+ 99.9%

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

      6. associate-+l+ 99.9%

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

      7. +-commutative 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-def 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-def 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 95.9%

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

      1. fma-udef 95.8%

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

      2. *-commutative 95.8%

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

      3. associate-+r+ 95.8%

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

   7. Applied egg-rr 95.8%

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

   8. Taylor expanded in t around 0 81.5%

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

      1. associate-+r+ 81.5%

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

      2. sub-neg 81.5%

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

      3. metadata-eval 81.5%

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

   10. Simplified 81.5%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+208} \lor \neg \left(x \leq 8 \cdot 10^{+161}\right):\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, \left(z + a\right) + \left(b + -0.5\right) \cdot \log c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 5: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in b around inf 97.8%

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

   1. *-commutative 97.8%

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

5. Simplified 97.8%

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

6. Final simplification 97.8%

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

Alternative 6: 41.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+192}:\\ \;\;\;\;\mathsf{fma}\left(y, i, z\right)\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{+80} \lor \neg \left(z \leq -8.5 \cdot 10^{-48} \lor \neg \left(z \leq -1.12 \cdot 10^{-187}\right) \land z \leq -3.6 \cdot 10^{-278}\right):\\ \;\;\;\;a + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + \log c \cdot \left(b - 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -1.3e+192)
   (fma y i z)
   (if (or (<= z -4.2e+80)
           (not
            (or (<= z -8.5e-48)
                (and (not (<= z -1.12e-187)) (<= z -3.6e-278)))))
     (+ a (* 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 <= -1.3e+192) {
		tmp = fma(y, i, z);
	} else if ((z <= -4.2e+80) || !((z <= -8.5e-48) || (!(z <= -1.12e-187) && (z <= -3.6e-278)))) {
		tmp = a + (y * i);
	} else {
		tmp = a + (log(c) * (b - 0.5));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -1.3e+192)
		tmp = fma(y, i, z);
	elseif ((z <= -4.2e+80) || !((z <= -8.5e-48) || (!(z <= -1.12e-187) && (z <= -3.6e-278))))
		tmp = Float64(a + Float64(y * i));
	else
		tmp = Float64(a + Float64(log(c) * Float64(b - 0.5)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -1.3e+192], N[(y * i + z), $MachinePrecision], If[Or[LessEqual[z, -4.2e+80], N[Not[Or[LessEqual[z, -8.5e-48], And[N[Not[LessEqual[z, -1.12e-187]], $MachinePrecision], LessEqual[z, -3.6e-278]]]], $MachinePrecision]], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(a + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.30000000000000002e192

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 95.3%

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

      1. +-commutative 95.3%

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

      2. +-commutative 95.3%

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

      3. associate-+l+ 95.3%

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

      4. sub-neg 95.3%

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

      5. metadata-eval 95.3%

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

      6. associate-+r+ 95.3%

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

      7. fma-def 95.3%

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

      8. +-commutative 95.3%

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

      9. +-commutative 95.3%

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

   5. Simplified 95.3%

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

   6. Taylor expanded in t around inf 87.1%

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

   7. Taylor expanded in t around 0 81.5%

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

      1. +-commutative 81.5%

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

      2. *-commutative 81.5%

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

      3. fma-def 81.6%

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

   9. Simplified 81.6%

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

   if -1.30000000000000002e192 < z < -4.20000000000000003e80 or -8.5000000000000004e-48 < z < -1.12e-187 or -3.59999999999999996e-278 < z

   1. Initial program 99.9%

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

      1. add-cube-cbrt 98.7%

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

   4. Applied egg-rr 98.7%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(\log c, b + -0.5, z + \mathsf{fma}\left(x, \log y, t + a\right)\right)}\right)}^{2} \cdot \sqrt[3]{\mathsf{fma}\left(\log c, b + -0.5, z + \mathsf{fma}\left(x, \log y, t + a\right)\right)}} + y \cdot i \]

   5. Taylor expanded in a around inf 45.8%

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

   if -4.20000000000000003e80 < z < -8.5000000000000004e-48 or -1.12e-187 < z < -3.59999999999999996e-278

   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 80.9%

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

   4. Taylor expanded in t around 0 62.4%

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

   5. Taylor expanded in z around 0 61.4%

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

      1. +-commutative 61.4%

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

      2. fma-def 61.4%

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

      3. sub-neg 61.4%

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

      4. metadata-eval 61.4%

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

      5. +-commutative 61.4%

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

   7. Simplified 61.4%

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

   8. Taylor expanded in i around 0 46.4%

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

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+192}:\\ \;\;\;\;\mathsf{fma}\left(y, i, z\right)\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{+80} \lor \neg \left(z \leq -8.5 \cdot 10^{-48} \lor \neg \left(z \leq -1.12 \cdot 10^{-187}\right) \land z \leq -3.6 \cdot 10^{-278}\right):\\ \;\;\;\;a + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + \log c \cdot \left(b - 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 54.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;i \leq -6.6 \cdot 10^{+227}:\\ \;\;\;\;t\_1 + y \cdot i\\ \mathbf{elif}\;i \leq -3.8 \cdot 10^{+150}:\\ \;\;\;\;a + \left(t + \left(z + t\_1\right)\right)\\ \mathbf{elif}\;i \leq -750000000 \lor \neg \left(i \leq 3.1 \cdot 10^{+44}\right):\\ \;\;\;\;a + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= i -6.6e+227)
     (+ t_1 (* y i))
     (if (<= i -3.8e+150)
       (+ a (+ t (+ z t_1)))
       (if (or (<= i -750000000.0) (not (<= i 3.1e+44)))
         (+ a (* y i))
         (+ a (+ 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 t_1 = x * log(y);
	double tmp;
	if (i <= -6.6e+227) {
		tmp = t_1 + (y * i);
	} else if (i <= -3.8e+150) {
		tmp = a + (t + (z + t_1));
	} else if ((i <= -750000000.0) || !(i <= 3.1e+44)) {
		tmp = a + (y * i);
	} else {
		tmp = a + (z + (log(c) * (b - 0.5)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * log(y)
    if (i <= (-6.6d+227)) then
        tmp = t_1 + (y * i)
    else if (i <= (-3.8d+150)) then
        tmp = a + (t + (z + t_1))
    else if ((i <= (-750000000.0d0)) .or. (.not. (i <= 3.1d+44))) then
        tmp = a + (y * i)
    else
        tmp = a + (z + (log(c) * (b - 0.5d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * Math.log(y);
	double tmp;
	if (i <= -6.6e+227) {
		tmp = t_1 + (y * i);
	} else if (i <= -3.8e+150) {
		tmp = a + (t + (z + t_1));
	} else if ((i <= -750000000.0) || !(i <= 3.1e+44)) {
		tmp = a + (y * i);
	} else {
		tmp = a + (z + (Math.log(c) * (b - 0.5)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x * math.log(y)
	tmp = 0
	if i <= -6.6e+227:
		tmp = t_1 + (y * i)
	elif i <= -3.8e+150:
		tmp = a + (t + (z + t_1))
	elif (i <= -750000000.0) or not (i <= 3.1e+44):
		tmp = a + (y * i)
	else:
		tmp = a + (z + (math.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 (i <= -6.6e+227)
		tmp = Float64(t_1 + Float64(y * i));
	elseif (i <= -3.8e+150)
		tmp = Float64(a + Float64(t + Float64(z + t_1)));
	elseif ((i <= -750000000.0) || !(i <= 3.1e+44))
		tmp = Float64(a + Float64(y * i));
	else
		tmp = Float64(a + Float64(z + Float64(log(c) * Float64(b - 0.5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x * log(y);
	tmp = 0.0;
	if (i <= -6.6e+227)
		tmp = t_1 + (y * i);
	elseif (i <= -3.8e+150)
		tmp = a + (t + (z + t_1));
	elseif ((i <= -750000000.0) || ~((i <= 3.1e+44)))
		tmp = a + (y * i);
	else
		tmp = a + (z + (log(c) * (b - 0.5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -6.6e+227], N[(t$95$1 + N[(y * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -3.8e+150], N[(a + N[(t + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[i, -750000000.0], N[Not[LessEqual[i, 3.1e+44]], $MachinePrecision]], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(a + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -6.5999999999999998e227

   1. Initial program 99.9%

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

      1. add-cube-cbrt 99.3%

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

   4. Applied egg-rr 99.3%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(\log c, b + -0.5, z + \mathsf{fma}\left(x, \log y, t + a\right)\right)}\right)}^{2} \cdot \sqrt[3]{\mathsf{fma}\left(\log c, b + -0.5, z + \mathsf{fma}\left(x, \log y, t + a\right)\right)}} + y \cdot i \]

   5. Taylor expanded in x around inf 73.2%

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

   if -6.5999999999999998e227 < i < -3.79999999999999989e150

   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 y around 0 83.6%

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

   4. Taylor expanded in x around inf 72.1%

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

   if -3.79999999999999989e150 < i < -7.5e8 or 3.09999999999999996e44 < 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. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 99.1%

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

   4. Applied egg-rr 99.1%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(\log c, b + -0.5, z + \mathsf{fma}\left(x, \log y, t + a\right)\right)}\right)}^{2} \cdot \sqrt[3]{\mathsf{fma}\left(\log c, b + -0.5, z + \mathsf{fma}\left(x, \log y, t + a\right)\right)}} + y \cdot i \]

   5. Taylor expanded in a around inf 66.3%

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

   if -7.5e8 < i < 3.09999999999999996e44

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 82.1%

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

   4. Taylor expanded in t around 0 68.3%

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

   5. Taylor expanded in y around 0 66.1%

      \[\leadsto \color{blue}{a + \left(z + \log c \cdot \left(b - 0.5\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -6.6 \cdot 10^{+227}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{elif}\;i \leq -3.8 \cdot 10^{+150}:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{elif}\;i \leq -750000000 \lor \neg \left(i \leq 3.1 \cdot 10^{+44}\right):\\ \;\;\;\;a + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 53.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1.65 \cdot 10^{+227}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{elif}\;i \leq -7.2 \cdot 10^{+196} \lor \neg \left(i \leq -52000000\right) \land i \leq 7.6 \cdot 10^{+42}:\\ \;\;\;\;a + \left(z + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= i -1.65e+227)
   (+ (* x (log y)) (* y i))
   (if (or (<= i -7.2e+196) (and (not (<= i -52000000.0)) (<= i 7.6e+42)))
     (+ a (+ z (* b (log c))))
     (+ a (* y i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (i <= -1.65e+227) {
		tmp = (x * log(y)) + (y * i);
	} else if ((i <= -7.2e+196) || (!(i <= -52000000.0) && (i <= 7.6e+42))) {
		tmp = a + (z + (b * log(c)));
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (i <= (-1.65d+227)) then
        tmp = (x * log(y)) + (y * i)
    else if ((i <= (-7.2d+196)) .or. (.not. (i <= (-52000000.0d0))) .and. (i <= 7.6d+42)) then
        tmp = a + (z + (b * log(c)))
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (i <= -1.65e+227) {
		tmp = (x * Math.log(y)) + (y * i);
	} else if ((i <= -7.2e+196) || (!(i <= -52000000.0) && (i <= 7.6e+42))) {
		tmp = a + (z + (b * Math.log(c)));
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if i <= -1.65e+227:
		tmp = (x * math.log(y)) + (y * i)
	elif (i <= -7.2e+196) or (not (i <= -52000000.0) and (i <= 7.6e+42)):
		tmp = a + (z + (b * math.log(c)))
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (i <= -1.65e+227)
		tmp = Float64(Float64(x * log(y)) + Float64(y * i));
	elseif ((i <= -7.2e+196) || (!(i <= -52000000.0) && (i <= 7.6e+42)))
		tmp = Float64(a + Float64(z + Float64(b * log(c))));
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (i <= -1.65e+227)
		tmp = (x * log(y)) + (y * i);
	elseif ((i <= -7.2e+196) || (~((i <= -52000000.0)) && (i <= 7.6e+42)))
		tmp = a + (z + (b * log(c)));
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[i, -1.65e+227], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[i, -7.2e+196], And[N[Not[LessEqual[i, -52000000.0]], $MachinePrecision], LessEqual[i, 7.6e+42]]], N[(a + N[(z + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if i < -1.6499999999999999e227

   1. Initial program 99.9%

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

      1. add-cube-cbrt 99.3%

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

   4. Applied egg-rr 99.3%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(\log c, b + -0.5, z + \mathsf{fma}\left(x, \log y, t + a\right)\right)}\right)}^{2} \cdot \sqrt[3]{\mathsf{fma}\left(\log c, b + -0.5, z + \mathsf{fma}\left(x, \log y, t + a\right)\right)}} + y \cdot i \]

   5. Taylor expanded in x around inf 73.2%

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

   if -1.6499999999999999e227 < i < -7.20000000000000015e196 or -5.2e7 < i < 7.5999999999999997e42

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 83.2%

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

   4. Taylor expanded in t around 0 68.2%

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

   5. Taylor expanded in y around 0 65.4%

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

   6. Taylor expanded in b around inf 62.3%

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

      1. *-commutative 62.3%

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

   8. Simplified 62.3%

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

   if -7.20000000000000015e196 < i < -5.2e7 or 7.5999999999999997e42 < 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. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 99.0%

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

   4. Applied egg-rr 99.0%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(\log c, b + -0.5, z + \mathsf{fma}\left(x, \log y, t + a\right)\right)}\right)}^{2} \cdot \sqrt[3]{\mathsf{fma}\left(\log c, b + -0.5, z + \mathsf{fma}\left(x, \log y, t + a\right)\right)}} + y \cdot i \]

   5. Taylor expanded in a around inf 63.9%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.65 \cdot 10^{+227}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{elif}\;i \leq -7.2 \cdot 10^{+196} \lor \neg \left(i \leq -52000000\right) \land i \leq 7.6 \cdot 10^{+42}:\\ \;\;\;\;a + \left(z + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 53.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;i \leq -1.65 \cdot 10^{+227}:\\ \;\;\;\;t\_1 + y \cdot i\\ \mathbf{elif}\;i \leq -5.5 \cdot 10^{+150}:\\ \;\;\;\;a + \left(t + \left(z + t\_1\right)\right)\\ \mathbf{elif}\;i \leq -400000000 \lor \neg \left(i \leq 1.32 \cdot 10^{+41}\right):\\ \;\;\;\;a + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + \left(z + b \cdot \log c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= i -1.65e+227)
     (+ t_1 (* y i))
     (if (<= i -5.5e+150)
       (+ a (+ t (+ z t_1)))
       (if (or (<= i -400000000.0) (not (<= i 1.32e+41)))
         (+ a (* y i))
         (+ a (+ z (* b (log c)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * log(y);
	double tmp;
	if (i <= -1.65e+227) {
		tmp = t_1 + (y * i);
	} else if (i <= -5.5e+150) {
		tmp = a + (t + (z + t_1));
	} else if ((i <= -400000000.0) || !(i <= 1.32e+41)) {
		tmp = a + (y * i);
	} else {
		tmp = a + (z + (b * log(c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * log(y)
    if (i <= (-1.65d+227)) then
        tmp = t_1 + (y * i)
    else if (i <= (-5.5d+150)) then
        tmp = a + (t + (z + t_1))
    else if ((i <= (-400000000.0d0)) .or. (.not. (i <= 1.32d+41))) then
        tmp = a + (y * i)
    else
        tmp = a + (z + (b * log(c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * Math.log(y);
	double tmp;
	if (i <= -1.65e+227) {
		tmp = t_1 + (y * i);
	} else if (i <= -5.5e+150) {
		tmp = a + (t + (z + t_1));
	} else if ((i <= -400000000.0) || !(i <= 1.32e+41)) {
		tmp = a + (y * i);
	} else {
		tmp = a + (z + (b * Math.log(c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x * math.log(y)
	tmp = 0
	if i <= -1.65e+227:
		tmp = t_1 + (y * i)
	elif i <= -5.5e+150:
		tmp = a + (t + (z + t_1))
	elif (i <= -400000000.0) or not (i <= 1.32e+41):
		tmp = a + (y * i)
	else:
		tmp = a + (z + (b * math.log(c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (i <= -1.65e+227)
		tmp = Float64(t_1 + Float64(y * i));
	elseif (i <= -5.5e+150)
		tmp = Float64(a + Float64(t + Float64(z + t_1)));
	elseif ((i <= -400000000.0) || !(i <= 1.32e+41))
		tmp = Float64(a + Float64(y * i));
	else
		tmp = Float64(a + Float64(z + Float64(b * log(c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x * log(y);
	tmp = 0.0;
	if (i <= -1.65e+227)
		tmp = t_1 + (y * i);
	elseif (i <= -5.5e+150)
		tmp = a + (t + (z + t_1));
	elseif ((i <= -400000000.0) || ~((i <= 1.32e+41)))
		tmp = a + (y * i);
	else
		tmp = a + (z + (b * log(c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.65e+227], N[(t$95$1 + N[(y * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -5.5e+150], N[(a + N[(t + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[i, -400000000.0], N[Not[LessEqual[i, 1.32e+41]], $MachinePrecision]], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(a + N[(z + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -1.6499999999999999e227

   1. Initial program 99.9%

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

      1. add-cube-cbrt 99.3%

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

   4. Applied egg-rr 99.3%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(\log c, b + -0.5, z + \mathsf{fma}\left(x, \log y, t + a\right)\right)}\right)}^{2} \cdot \sqrt[3]{\mathsf{fma}\left(\log c, b + -0.5, z + \mathsf{fma}\left(x, \log y, t + a\right)\right)}} + y \cdot i \]

   5. Taylor expanded in x around inf 73.2%

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

   if -1.6499999999999999e227 < i < -5.50000000000000017e150

   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 y around 0 83.6%

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

   4. Taylor expanded in x around inf 72.1%

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

   if -5.50000000000000017e150 < i < -4e8 or 1.3199999999999999e41 < 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. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 99.1%

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

   4. Applied egg-rr 99.1%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(\log c, b + -0.5, z + \mathsf{fma}\left(x, \log y, t + a\right)\right)}\right)}^{2} \cdot \sqrt[3]{\mathsf{fma}\left(\log c, b + -0.5, z + \mathsf{fma}\left(x, \log y, t + a\right)\right)}} + y \cdot i \]

   5. Taylor expanded in a around inf 66.3%

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

   if -4e8 < i < 1.3199999999999999e41

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 82.1%

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

   4. Taylor expanded in t around 0 68.3%

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

   5. Taylor expanded in y around 0 66.1%

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

   6. Taylor expanded in b around inf 62.8%

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

      1. *-commutative 62.8%

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

   8. Simplified 62.8%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.65 \cdot 10^{+227}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{elif}\;i \leq -5.5 \cdot 10^{+150}:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{elif}\;i \leq -400000000 \lor \neg \left(i \leq 1.32 \cdot 10^{+41}\right):\\ \;\;\;\;a + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + \left(z + b \cdot \log c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 75.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+208} \lor \neg \left(x \leq 5.2 \cdot 10^{+151}\right):\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -1.5e+208) (not (<= x 5.2e+151)))
   (+ (* x (log y)) (* y i))
   (+ (* y i) (+ a (+ z (* (log c) (- b 0.5)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1.5e+208) || !(x <= 5.2e+151)) {
		tmp = (x * log(y)) + (y * i);
	} else {
		tmp = (y * i) + (a + (z + (log(c) * (b - 0.5))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-1.5d+208)) .or. (.not. (x <= 5.2d+151))) then
        tmp = (x * log(y)) + (y * i)
    else
        tmp = (y * i) + (a + (z + (log(c) * (b - 0.5d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1.5e+208) || !(x <= 5.2e+151)) {
		tmp = (x * Math.log(y)) + (y * i);
	} else {
		tmp = (y * i) + (a + (z + (Math.log(c) * (b - 0.5))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -1.5e+208) or not (x <= 5.2e+151):
		tmp = (x * math.log(y)) + (y * i)
	else:
		tmp = (y * i) + (a + (z + (math.log(c) * (b - 0.5))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -1.5e+208) || !(x <= 5.2e+151))
		tmp = Float64(Float64(x * log(y)) + Float64(y * i));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + Float64(log(c) * Float64(b - 0.5)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -1.5e+208) || ~((x <= 5.2e+151)))
		tmp = (x * log(y)) + (y * i);
	else
		tmp = (y * i) + (a + (z + (log(c) * (b - 0.5))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -1.5e+208], N[Not[LessEqual[x, 5.2e+151]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.49999999999999997e208 or 5.20000000000000026e151 < x

   1. Initial program 99.7%

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

      1. add-cube-cbrt 98.6%

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

   4. Applied egg-rr 98.6%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(\log c, b + -0.5, z + \mathsf{fma}\left(x, \log y, t + a\right)\right)}\right)}^{2} \cdot \sqrt[3]{\mathsf{fma}\left(\log c, b + -0.5, z + \mathsf{fma}\left(x, \log y, t + a\right)\right)}} + y \cdot i \]

   5. Taylor expanded in x around inf 81.5%

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

   if -1.49999999999999997e208 < x < 5.20000000000000026e151

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 95.8%

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

   4. Taylor expanded in t around 0 81.5%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+208} \lor \neg \left(x \leq 5.2 \cdot 10^{+151}\right):\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 74.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+208} \lor \neg \left(x \leq 8 \cdot 10^{+161}\right):\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + b \cdot \log c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -1.75e+208) (not (<= x 8e+161)))
   (+ (* x (log y)) (* y i))
   (+ (* y i) (+ a (+ z (* 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 ((x <= -1.75e+208) || !(x <= 8e+161)) {
		tmp = (x * log(y)) + (y * i);
	} else {
		tmp = (y * i) + (a + (z + (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 ((x <= (-1.75d+208)) .or. (.not. (x <= 8d+161))) then
        tmp = (x * log(y)) + (y * i)
    else
        tmp = (y * i) + (a + (z + (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 ((x <= -1.75e+208) || !(x <= 8e+161)) {
		tmp = (x * Math.log(y)) + (y * i);
	} else {
		tmp = (y * i) + (a + (z + (b * Math.log(c))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -1.75e+208) or not (x <= 8e+161):
		tmp = (x * math.log(y)) + (y * i)
	else:
		tmp = (y * i) + (a + (z + (b * math.log(c))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -1.75e+208) || !(x <= 8e+161))
		tmp = Float64(Float64(x * log(y)) + Float64(y * i));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + 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 ((x <= -1.75e+208) || ~((x <= 8e+161)))
		tmp = (x * log(y)) + (y * i);
	else
		tmp = (y * i) + (a + (z + (b * log(c))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -1.75e+208], N[Not[LessEqual[x, 8e+161]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.75000000000000008e208 or 8.0000000000000003e161 < x

   1. Initial program 99.7%

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

      1. add-cube-cbrt 98.6%

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

   4. Applied egg-rr 98.6%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(\log c, b + -0.5, z + \mathsf{fma}\left(x, \log y, t + a\right)\right)}\right)}^{2} \cdot \sqrt[3]{\mathsf{fma}\left(\log c, b + -0.5, z + \mathsf{fma}\left(x, \log y, t + a\right)\right)}} + y \cdot i \]

   5. Taylor expanded in x around inf 81.5%

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

   if -1.75000000000000008e208 < x < 8.0000000000000003e161

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 95.8%

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

   4. Taylor expanded in t around 0 81.5%

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

   5. Taylor expanded in b around inf 78.9%

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

      1. *-commutative 53.5%

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

   7. Simplified 78.9%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+208} \lor \neg \left(x \leq 8 \cdot 10^{+161}\right):\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + b \cdot \log c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 54.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -30000000 \lor \neg \left(i \leq 1.4 \cdot 10^{+44}\right):\\ \;\;\;\;a + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + \left(z + b \cdot \log c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= i -30000000.0) (not (<= i 1.4e+44)))
   (+ a (* y i))
   (+ a (+ z (* 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 <= -30000000.0) || !(i <= 1.4e+44)) {
		tmp = a + (y * i);
	} else {
		tmp = a + (z + (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 <= (-30000000.0d0)) .or. (.not. (i <= 1.4d+44))) then
        tmp = a + (y * i)
    else
        tmp = a + (z + (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 <= -30000000.0) || !(i <= 1.4e+44)) {
		tmp = a + (y * i);
	} else {
		tmp = a + (z + (b * Math.log(c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (i <= -30000000.0) or not (i <= 1.4e+44):
		tmp = a + (y * i)
	else:
		tmp = a + (z + (b * math.log(c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((i <= -30000000.0) || !(i <= 1.4e+44))
		tmp = Float64(a + Float64(y * i));
	else
		tmp = Float64(a + Float64(z + 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 <= -30000000.0) || ~((i <= 1.4e+44)))
		tmp = a + (y * i);
	else
		tmp = a + (z + (b * log(c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[i, -30000000.0], N[Not[LessEqual[i, 1.4e+44]], $MachinePrecision]], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(a + N[(z + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -3e7 or 1.4e44 < 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. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 99.0%

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

   4. Applied egg-rr 99.0%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(\log c, b + -0.5, z + \mathsf{fma}\left(x, \log y, t + a\right)\right)}\right)}^{2} \cdot \sqrt[3]{\mathsf{fma}\left(\log c, b + -0.5, z + \mathsf{fma}\left(x, \log y, t + a\right)\right)}} + y \cdot i \]

   5. Taylor expanded in a around inf 63.1%

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

   if -3e7 < i < 1.4e44

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 82.1%

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

   4. Taylor expanded in t around 0 68.3%

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

   5. Taylor expanded in y around 0 66.1%

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

   6. Taylor expanded in b around inf 62.8%

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

      1. *-commutative 62.8%

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

   8. Simplified 62.8%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -30000000 \lor \neg \left(i \leq 1.4 \cdot 10^{+44}\right):\\ \;\;\;\;a + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + \left(z + b \cdot \log c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 42.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+192}:\\ \;\;\;\;\mathsf{fma}\left(y, i, z\right)\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -1.8e+192) (fma y i z) (+ a (* y i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -1.8e+192) {
		tmp = fma(y, i, z);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -1.8e+192)
		tmp = fma(y, i, z);
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -1.8e+192], N[(y * i + z), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8000000000000001e192

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 95.3%

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

      1. +-commutative 95.3%

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

      2. +-commutative 95.3%

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

      3. associate-+l+ 95.3%

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

      4. sub-neg 95.3%

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

      5. metadata-eval 95.3%

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

      6. associate-+r+ 95.3%

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

      7. fma-def 95.3%

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

      8. +-commutative 95.3%

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

      9. +-commutative 95.3%

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

   5. Simplified 95.3%

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

   6. Taylor expanded in t around inf 87.1%

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

   7. Taylor expanded in t around 0 81.5%

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

      1. +-commutative 81.5%

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

      2. *-commutative 81.5%

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

      3. fma-def 81.6%

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

   9. Simplified 81.6%

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

   if -1.8000000000000001e192 < z

   1. Initial program 99.9%

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

      1. add-cube-cbrt 98.6%

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

   4. Applied egg-rr 98.6%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(\log c, b + -0.5, z + \mathsf{fma}\left(x, \log y, t + a\right)\right)}\right)}^{2} \cdot \sqrt[3]{\mathsf{fma}\left(\log c, b + -0.5, z + \mathsf{fma}\left(x, \log y, t + a\right)\right)}} + y \cdot i \]

   5. Taylor expanded in a around inf 43.4%

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

4. Final simplification 46.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+192}:\\ \;\;\;\;\mathsf{fma}\left(y, i, z\right)\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 23.4% accurate, 9.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 3.4 \cdot 10^{-212}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+145} \lor \neg \left(a \leq 9.6 \cdot 10^{+160}\right) \land a \leq 1.2 \cdot 10^{+182}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 3.4e-212)
   z
   (if (or (<= a 4e+145) (and (not (<= a 9.6e+160)) (<= a 1.2e+182)))
     (* y i)
     a)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 3.4e-212) {
		tmp = z;
	} else if ((a <= 4e+145) || (!(a <= 9.6e+160) && (a <= 1.2e+182))) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 3.4d-212) then
        tmp = z
    else if ((a <= 4d+145) .or. (.not. (a <= 9.6d+160)) .and. (a <= 1.2d+182)) then
        tmp = y * i
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 3.4e-212) {
		tmp = z;
	} else if ((a <= 4e+145) || (!(a <= 9.6e+160) && (a <= 1.2e+182))) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 3.4e-212:
		tmp = z
	elif (a <= 4e+145) or (not (a <= 9.6e+160) and (a <= 1.2e+182)):
		tmp = y * i
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 3.4e-212)
		tmp = z;
	elseif ((a <= 4e+145) || (!(a <= 9.6e+160) && (a <= 1.2e+182)))
		tmp = Float64(y * i);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 3.4e-212)
		tmp = z;
	elseif ((a <= 4e+145) || (~((a <= 9.6e+160)) && (a <= 1.2e+182)))
		tmp = y * i;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 3.4e-212], z, If[Or[LessEqual[a, 4e+145], And[N[Not[LessEqual[a, 9.6e+160]], $MachinePrecision], LessEqual[a, 1.2e+182]]], N[(y * i), $MachinePrecision], a]]

Derivation

1. Split input into 3 regimes

2. if a < 3.39999999999999998e-212

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 18.2%

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

   if 3.39999999999999998e-212 < a < 4e145 or 9.6000000000000006e160 < a < 1.20000000000000005e182

   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 y around inf 28.6%

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

      1. *-commutative 28.6%

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

   5. Simplified 28.6%

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

   if 4e145 < a < 9.6000000000000006e160 or 1.20000000000000005e182 < a

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf 58.3%

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

4. Final simplification 26.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 3.4 \cdot 10^{-212}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+145} \lor \neg \left(a \leq 9.6 \cdot 10^{+160}\right) \land a \leq 1.2 \cdot 10^{+182}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 40.8% accurate, 21.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+224}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -8e+224) z (+ a (* y i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -8e+224) {
		tmp = z;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-8d+224)) then
        tmp = z
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -8e+224) {
		tmp = z;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -8e+224:
		tmp = z
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -8e+224)
		tmp = z;
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -8e+224)
		tmp = z;
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -8e+224], z, N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.99999999999999976e224

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 81.8%

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

   if -7.99999999999999976e224 < z

   1. Initial program 99.9%

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

      1. add-cube-cbrt 98.6%

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

   4. Applied egg-rr 98.6%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(\log c, b + -0.5, z + \mathsf{fma}\left(x, \log y, t + a\right)\right)}\right)}^{2} \cdot \sqrt[3]{\mathsf{fma}\left(\log c, b + -0.5, z + \mathsf{fma}\left(x, \log y, t + a\right)\right)}} + y \cdot i \]

   5. Taylor expanded in a around inf 43.2%

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

4. Final simplification 44.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+224}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 42.6% accurate, 21.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+192}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -1.55e+192) (+ z (* y i)) (+ a (* y i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -1.55e+192) {
		tmp = z + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-1.55d+192)) then
        tmp = z + (y * i)
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -1.55e+192) {
		tmp = z + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -1.55e+192:
		tmp = z + (y * i)
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -1.55e+192)
		tmp = Float64(z + Float64(y * i));
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -1.55e+192)
		tmp = z + (y * i);
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -1.55e+192], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.5499999999999999e192

   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. Step-by-step derivation

      1. add-cube-cbrt 98.3%

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

   4. Applied egg-rr 98.3%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(\log c, b + -0.5, z + \mathsf{fma}\left(x, \log y, t + a\right)\right)}\right)}^{2} \cdot \sqrt[3]{\mathsf{fma}\left(\log c, b + -0.5, z + \mathsf{fma}\left(x, \log y, t + a\right)\right)}} + y \cdot i \]

   5. Taylor expanded in z around inf 81.5%

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

   if -1.5499999999999999e192 < z

   1. Initial program 99.9%

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

      1. add-cube-cbrt 98.6%

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

   4. Applied egg-rr 98.6%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(\log c, b + -0.5, z + \mathsf{fma}\left(x, \log y, t + a\right)\right)}\right)}^{2} \cdot \sqrt[3]{\mathsf{fma}\left(\log c, b + -0.5, z + \mathsf{fma}\left(x, \log y, t + a\right)\right)}} + y \cdot i \]

   5. Taylor expanded in a around inf 43.4%

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

4. Final simplification 46.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+192}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 21.0% accurate, 36.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+188}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (if (<= z -1.05e+188) z a))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -1.05e+188) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-1.05d+188)) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -1.05e+188) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -1.05e+188:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -1.05e+188)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -1.05e+188)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -1.05e+188], z, a]

Derivation

1. Split input into 2 regimes

2. if z < -1.04999999999999993e188

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 63.2%

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

   if -1.04999999999999993e188 < 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 18.2%

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

4. Final simplification 21.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+188}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 16.2% 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. Add Preprocessing

3. Taylor expanded in a around inf 17.0%

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

4. Final simplification 17.0%

   \[\leadsto a \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024036 
(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)))