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

Percentage Accurate: 99.8% → 99.8%

Time: 18.5s

Alternatives: 19

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, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. associate-+l+ 99.8%

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

   2. +-commutative 99.8%

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

   3. +-commutative 99.8%

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

   4. associate-+l+ 99.8%

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

   5. fma-def 99.8%

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

   6. sub-neg 99.8%

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

   7. metadata-eval 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 2: 93.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+50} \lor \neg \left(x \leq 4 \cdot 10^{-6}\right):\\ \;\;\;\;y \cdot i + \left(a + \left(z + \left(x \cdot \log y + b \cdot \log c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -4.5e+50) (not (<= x 4e-6)))
   (+ (* y i) (+ a (+ z (+ (* x (log y)) (* b (log c))))))
   (+ (* y i) (+ (* (log c) (- b 0.5)) (+ a (+ z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -4.5e+50) || !(x <= 4e-6)) {
		tmp = (y * i) + (a + (z + ((x * log(y)) + (b * log(c)))));
	} else {
		tmp = (y * i) + ((log(c) * (b - 0.5)) + (a + (z + t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-4.5d+50)) .or. (.not. (x <= 4d-6))) then
        tmp = (y * i) + (a + (z + ((x * log(y)) + (b * log(c)))))
    else
        tmp = (y * i) + ((log(c) * (b - 0.5d0)) + (a + (z + t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -4.5e+50) || !(x <= 4e-6)) {
		tmp = (y * i) + (a + (z + ((x * Math.log(y)) + (b * Math.log(c)))));
	} else {
		tmp = (y * i) + ((Math.log(c) * (b - 0.5)) + (a + (z + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -4.5e+50) or not (x <= 4e-6):
		tmp = (y * i) + (a + (z + ((x * math.log(y)) + (b * math.log(c)))))
	else:
		tmp = (y * i) + ((math.log(c) * (b - 0.5)) + (a + (z + t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -4.5e+50) || !(x <= 4e-6))
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + Float64(Float64(x * log(y)) + Float64(b * log(c))))));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(log(c) * Float64(b - 0.5)) + Float64(a + Float64(z + t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -4.5e+50) || ~((x <= 4e-6)))
		tmp = (y * i) + (a + (z + ((x * log(y)) + (b * log(c)))));
	else
		tmp = (y * i) + ((log(c) * (b - 0.5)) + (a + (z + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -4.5e+50], N[Not[LessEqual[x, 4e-6]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.50000000000000014e50 or 3.99999999999999982e-6 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 88.2%

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

   4. Taylor expanded in b around inf 88.2%

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

   if -4.50000000000000014e50 < x < 3.99999999999999982e-6

   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 99.5%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+50} \lor \neg \left(x \leq 4 \cdot 10^{-6}\right):\\ \;\;\;\;y \cdot i + \left(a + \left(z + \left(x \cdot \log y + b \cdot \log c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+59} \lor \neg \left(x \leq 8.5 \cdot 10^{+139}\right):\\ \;\;\;\;\left(\mathsf{fma}\left(x, \log y, z\right) + \left(t + a\right)\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -2.5e+59) (not (<= x 8.5e+139)))
   (+ (+ (fma x (log y) z) (+ t a)) (* y i))
   (+ (* y i) (+ (* (log c) (- b 0.5)) (+ a (+ z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -2.5e+59) || !(x <= 8.5e+139)) {
		tmp = (fma(x, log(y), z) + (t + a)) + (y * i);
	} else {
		tmp = (y * i) + ((log(c) * (b - 0.5)) + (a + (z + t)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -2.5e+59) || !(x <= 8.5e+139))
		tmp = Float64(Float64(fma(x, log(y), z) + Float64(t + a)) + Float64(y * i));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(log(c) * Float64(b - 0.5)) + Float64(a + Float64(z + t))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -2.5e+59], N[Not[LessEqual[x, 8.5e+139]], $MachinePrecision]], N[(N[(N[(x * N[Log[y], $MachinePrecision] + z), $MachinePrecision] + N[(t + a), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.4999999999999999e59 or 8.5e139 < x

   1. Initial program 99.7%

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

      1. associate-+l+ 99.7%

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

      2. +-commutative 99.7%

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

      3. +-commutative 99.7%

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

      4. associate-+l+ 99.7%

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

      5. fma-def 99.8%

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

      6. sub-neg 99.8%

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

      7. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 94.0%

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

      1. *-commutative 94.0%

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

   7. Simplified 94.0%

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

   if -2.4999999999999999e59 < x < 8.5e139

   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 99.6%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+59} \lor \neg \left(x \leq 8.5 \cdot 10^{+139}\right):\\ \;\;\;\;\left(\mathsf{fma}\left(x, \log y, z\right) + \left(t + a\right)\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. Final simplification 99.8%

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

Alternative 5: 84.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in t around 0 86.9%

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

4. Final simplification 86.9%

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

Alternative 6: 91.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+55} \lor \neg \left(x \leq 8.6 \cdot 10^{+139}\right):\\ \;\;\;\;y \cdot i + \left(a + \left(z + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -2.6e+55) (not (<= x 8.6e+139)))
   (+ (* y i) (+ a (+ z (* x (log y)))))
   (+ (* y i) (+ (* (log c) (- b 0.5)) (+ a (+ z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -2.6e+55) || !(x <= 8.6e+139)) {
		tmp = (y * i) + (a + (z + (x * log(y))));
	} else {
		tmp = (y * i) + ((log(c) * (b - 0.5)) + (a + (z + t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-2.6d+55)) .or. (.not. (x <= 8.6d+139))) then
        tmp = (y * i) + (a + (z + (x * log(y))))
    else
        tmp = (y * i) + ((log(c) * (b - 0.5d0)) + (a + (z + t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -2.6e+55) || !(x <= 8.6e+139)) {
		tmp = (y * i) + (a + (z + (x * Math.log(y))));
	} else {
		tmp = (y * i) + ((Math.log(c) * (b - 0.5)) + (a + (z + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -2.6e+55) or not (x <= 8.6e+139):
		tmp = (y * i) + (a + (z + (x * math.log(y))))
	else:
		tmp = (y * i) + ((math.log(c) * (b - 0.5)) + (a + (z + t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -2.6e+55) || !(x <= 8.6e+139))
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + Float64(x * log(y)))));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(log(c) * Float64(b - 0.5)) + Float64(a + Float64(z + t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -2.6e+55) || ~((x <= 8.6e+139)))
		tmp = (y * i) + (a + (z + (x * log(y))));
	else
		tmp = (y * i) + ((log(c) * (b - 0.5)) + (a + (z + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -2.6e+55], N[Not[LessEqual[x, 8.6e+139]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.6e55 or 8.5999999999999996e139 < x

   1. Initial program 99.7%

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

      1. associate-+l+ 99.7%

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

      2. +-commutative 99.7%

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

      3. +-commutative 99.7%

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

      4. associate-+l+ 99.7%

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

      5. fma-def 99.8%

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

      6. sub-neg 99.8%

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

      7. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 94.0%

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

      1. *-commutative 94.0%

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

   7. Simplified 94.0%

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

   8. Taylor expanded in t around 0 80.5%

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

   if -2.6e55 < x < 8.5999999999999996e139

   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 99.6%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+55} \lor \neg \left(x \leq 8.6 \cdot 10^{+139}\right):\\ \;\;\;\;y \cdot i + \left(a + \left(z + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -2 \cdot 10^{+58}:\\ \;\;\;\;a + \left(y \cdot i + t_1\right)\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-267}:\\ \;\;\;\;\left(t + a\right) + \left(z + \left(b + -0.5\right) \cdot \log c\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+142}:\\ \;\;\;\;y \cdot i + \left(z + \left(t + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + t_1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -2e+58)
     (+ a (+ (* y i) t_1))
     (if (<= x 1.65e-267)
       (+ (+ t a) (+ z (* (+ b -0.5) (log c))))
       (if (<= x 2.8e+142) (+ (* y i) (+ z (+ t a))) (+ a (+ t (+ z t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * log(y);
	double tmp;
	if (x <= -2e+58) {
		tmp = a + ((y * i) + t_1);
	} else if (x <= 1.65e-267) {
		tmp = (t + a) + (z + ((b + -0.5) * log(c)));
	} else if (x <= 2.8e+142) {
		tmp = (y * i) + (z + (t + a));
	} else {
		tmp = a + (t + (z + t_1));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * log(y)
    if (x <= (-2d+58)) then
        tmp = a + ((y * i) + t_1)
    else if (x <= 1.65d-267) then
        tmp = (t + a) + (z + ((b + (-0.5d0)) * log(c)))
    else if (x <= 2.8d+142) then
        tmp = (y * i) + (z + (t + a))
    else
        tmp = a + (t + (z + t_1))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * Math.log(y);
	double tmp;
	if (x <= -2e+58) {
		tmp = a + ((y * i) + t_1);
	} else if (x <= 1.65e-267) {
		tmp = (t + a) + (z + ((b + -0.5) * Math.log(c)));
	} else if (x <= 2.8e+142) {
		tmp = (y * i) + (z + (t + a));
	} else {
		tmp = a + (t + (z + t_1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x * math.log(y)
	tmp = 0
	if x <= -2e+58:
		tmp = a + ((y * i) + t_1)
	elif x <= 1.65e-267:
		tmp = (t + a) + (z + ((b + -0.5) * math.log(c)))
	elif x <= 2.8e+142:
		tmp = (y * i) + (z + (t + a))
	else:
		tmp = a + (t + (z + t_1))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -2e+58)
		tmp = Float64(a + Float64(Float64(y * i) + t_1));
	elseif (x <= 1.65e-267)
		tmp = Float64(Float64(t + a) + Float64(z + Float64(Float64(b + -0.5) * log(c))));
	elseif (x <= 2.8e+142)
		tmp = Float64(Float64(y * i) + Float64(z + Float64(t + a)));
	else
		tmp = Float64(a + Float64(t + Float64(z + t_1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x * log(y);
	tmp = 0.0;
	if (x <= -2e+58)
		tmp = a + ((y * i) + t_1);
	elseif (x <= 1.65e-267)
		tmp = (t + a) + (z + ((b + -0.5) * log(c)));
	elseif (x <= 2.8e+142)
		tmp = (y * i) + (z + (t + a));
	else
		tmp = a + (t + (z + t_1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2e+58], N[(a + N[(N[(y * i), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.65e-267], N[(N[(t + a), $MachinePrecision] + N[(z + N[(N[(b + -0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.8e+142], N[(N[(y * i), $MachinePrecision] + N[(z + N[(t + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(t + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.99999999999999989e58

   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 0 91.5%

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

      1. associate-+r+ 91.5%

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

      2. fma-def 91.5%

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

      3. sub-neg 91.5%

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

      4. metadata-eval 91.5%

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

      5. +-commutative 91.5%

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

   5. Simplified 91.5%

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

   6. Taylor expanded in b around inf 91.5%

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

      1. *-commutative 91.5%

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

   8. Simplified 91.5%

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

   9. Taylor expanded in b around 0 85.4%

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

       1. associate-+r+ 85.4%

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

       2. *-commutative 85.4%

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

   11. Simplified 85.4%

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

   12. Taylor expanded in t around 0 77.6%

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

   if -1.99999999999999989e58 < x < 1.65000000000000002e-267

   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 99.9%

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

   4. Taylor expanded in y around 0 78.6%

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

      1. associate-+r+ 78.6%

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

      2. sub-neg 78.6%

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

      3. metadata-eval 78.6%

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

   6. Simplified 78.6%

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

   if 1.65000000000000002e-267 < x < 2.8e142

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+l+ 99.9%

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

      5. fma-def 99.9%

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

      6. sub-neg 99.9%

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

      7. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 84.4%

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

      1. *-commutative 84.4%

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

   7. Simplified 84.4%

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

   8. Taylor expanded in x around 0 84.1%

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

      1. +-commutative 84.1%

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

      2. +-commutative 84.1%

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

      3. associate-+l+ 84.1%

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

      4. +-commutative 84.1%

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

   10. Simplified 84.1%

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

   if 2.8e142 < x

   1. Initial program 99.7%

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

      1. associate-+l+ 99.7%

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

      2. +-commutative 99.7%

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

      3. +-commutative 99.7%

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

      4. associate-+l+ 99.7%

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

      5. fma-def 99.7%

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

      6. sub-neg 99.7%

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

      7. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 94.1%

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

      1. *-commutative 94.1%

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

   7. Simplified 94.1%

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

   8. Taylor expanded in y around 0 89.0%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+58}:\\ \;\;\;\;a + \left(y \cdot i + x \cdot \log y\right)\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-267}:\\ \;\;\;\;\left(t + a\right) + \left(z + \left(b + -0.5\right) \cdot \log c\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+142}:\\ \;\;\;\;y \cdot i + \left(z + \left(t + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+135} \lor \neg \left(x \leq 8.2 \cdot 10^{+142}\right):\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + \left(t + a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -6.5e+135) (not (<= x 8.2e+142)))
   (+ a (+ t (+ z (* x (log y)))))
   (+ (* y i) (+ z (+ t a)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -6.5e+135) || !(x <= 8.2e+142)) {
		tmp = a + (t + (z + (x * log(y))));
	} else {
		tmp = (y * i) + (z + (t + a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-6.5d+135)) .or. (.not. (x <= 8.2d+142))) then
        tmp = a + (t + (z + (x * log(y))))
    else
        tmp = (y * i) + (z + (t + a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -6.5e+135) || !(x <= 8.2e+142)) {
		tmp = a + (t + (z + (x * Math.log(y))));
	} else {
		tmp = (y * i) + (z + (t + a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -6.5e+135) or not (x <= 8.2e+142):
		tmp = a + (t + (z + (x * math.log(y))))
	else:
		tmp = (y * i) + (z + (t + a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -6.5e+135) || !(x <= 8.2e+142))
		tmp = Float64(a + Float64(t + Float64(z + Float64(x * log(y)))));
	else
		tmp = Float64(Float64(y * i) + Float64(z + Float64(t + a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -6.5e+135) || ~((x <= 8.2e+142)))
		tmp = a + (t + (z + (x * log(y))));
	else
		tmp = (y * i) + (z + (t + a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -6.5e+135], N[Not[LessEqual[x, 8.2e+142]], $MachinePrecision]], N[(a + N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(z + N[(t + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.5000000000000003e135 or 8.19999999999999963e142 < x

   1. Initial program 99.7%

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

      1. associate-+l+ 99.7%

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

      2. +-commutative 99.7%

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

      3. +-commutative 99.7%

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

      4. associate-+l+ 99.7%

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

      5. fma-def 99.7%

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

      6. sub-neg 99.7%

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

      7. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 92.3%

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

      1. *-commutative 92.3%

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

   7. Simplified 92.3%

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

   8. Taylor expanded in y around 0 83.9%

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

   if -6.5000000000000003e135 < x < 8.19999999999999963e142

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+l+ 99.9%

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

      5. fma-def 99.9%

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

      6. sub-neg 99.9%

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

      7. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 79.3%

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

      1. *-commutative 79.3%

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

   7. Simplified 79.3%

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

   8. Taylor expanded in x around 0 77.8%

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

      1. +-commutative 77.8%

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

      2. +-commutative 77.8%

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

      3. associate-+l+ 77.8%

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

      4. +-commutative 77.8%

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

   10. Simplified 77.8%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+135} \lor \neg \left(x \leq 8.2 \cdot 10^{+142}\right):\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + \left(t + a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -5 \cdot 10^{+84}:\\ \;\;\;\;a + \left(y \cdot i + t_1\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+142}:\\ \;\;\;\;y \cdot i + \left(z + \left(t + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + t_1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -5e+84)
     (+ a (+ (* y i) t_1))
     (if (<= x 6.5e+142) (+ (* y i) (+ z (+ t a))) (+ a (+ t (+ z t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * log(y);
	double tmp;
	if (x <= -5e+84) {
		tmp = a + ((y * i) + t_1);
	} else if (x <= 6.5e+142) {
		tmp = (y * i) + (z + (t + a));
	} else {
		tmp = a + (t + (z + t_1));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * log(y)
    if (x <= (-5d+84)) then
        tmp = a + ((y * i) + t_1)
    else if (x <= 6.5d+142) then
        tmp = (y * i) + (z + (t + a))
    else
        tmp = a + (t + (z + t_1))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * Math.log(y);
	double tmp;
	if (x <= -5e+84) {
		tmp = a + ((y * i) + t_1);
	} else if (x <= 6.5e+142) {
		tmp = (y * i) + (z + (t + a));
	} else {
		tmp = a + (t + (z + t_1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x * math.log(y)
	tmp = 0
	if x <= -5e+84:
		tmp = a + ((y * i) + t_1)
	elif x <= 6.5e+142:
		tmp = (y * i) + (z + (t + a))
	else:
		tmp = a + (t + (z + t_1))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -5e+84)
		tmp = Float64(a + Float64(Float64(y * i) + t_1));
	elseif (x <= 6.5e+142)
		tmp = Float64(Float64(y * i) + Float64(z + Float64(t + a)));
	else
		tmp = Float64(a + Float64(t + Float64(z + t_1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x * log(y);
	tmp = 0.0;
	if (x <= -5e+84)
		tmp = a + ((y * i) + t_1);
	elseif (x <= 6.5e+142)
		tmp = (y * i) + (z + (t + a));
	else
		tmp = a + (t + (z + t_1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5e+84], N[(a + N[(N[(y * i), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.5e+142], N[(N[(y * i), $MachinePrecision] + N[(z + N[(t + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(t + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.0000000000000001e84

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 89.5%

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

      1. associate-+r+ 89.5%

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

      2. fma-def 89.5%

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

      3. sub-neg 89.5%

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

      4. metadata-eval 89.5%

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

      5. +-commutative 89.5%

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

   5. Simplified 89.5%

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

   6. Taylor expanded in b around inf 89.5%

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

      1. *-commutative 89.5%

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

   8. Simplified 89.5%

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

   9. Taylor expanded in b around 0 82.1%

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

       1. associate-+r+ 82.1%

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

       2. *-commutative 82.1%

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

   11. Simplified 82.1%

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

   12. Taylor expanded in t around 0 74.9%

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

   if -5.0000000000000001e84 < x < 6.4999999999999997e142

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+l+ 99.9%

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

      5. fma-def 99.9%

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

      6. sub-neg 99.9%

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

      7. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 78.2%

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

      1. *-commutative 78.2%

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

   7. Simplified 78.2%

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

   8. Taylor expanded in x around 0 77.8%

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

      1. +-commutative 77.8%

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

      2. +-commutative 77.8%

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

      3. associate-+l+ 77.8%

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

      4. +-commutative 77.8%

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

   10. Simplified 77.8%

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

   if 6.4999999999999997e142 < x

   1. Initial program 99.7%

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

      1. associate-+l+ 99.7%

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

      2. +-commutative 99.7%

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

      3. +-commutative 99.7%

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

      4. associate-+l+ 99.7%

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

      5. fma-def 99.7%

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

      6. sub-neg 99.7%

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

      7. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 94.1%

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

      1. *-commutative 94.1%

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

   7. Simplified 94.1%

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

   8. Taylor expanded in y around 0 89.0%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+84}:\\ \;\;\;\;a + \left(y \cdot i + x \cdot \log y\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+142}:\\ \;\;\;\;y \cdot i + \left(z + \left(t + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 73.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-6}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(y \cdot i + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -1.3e-6)
   (+ (* y i) (+ a (+ z (* x (log y)))))
   (+ a (+ t (+ (* y i) (* (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-6) {
		tmp = (y * i) + (a + (z + (x * log(y))));
	} else {
		tmp = a + (t + ((y * i) + (log(c) * (b - 0.5))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-1.3d-6)) then
        tmp = (y * i) + (a + (z + (x * log(y))))
    else
        tmp = a + (t + ((y * i) + (log(c) * (b - 0.5d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -1.3e-6) {
		tmp = (y * i) + (a + (z + (x * Math.log(y))));
	} else {
		tmp = a + (t + ((y * i) + (Math.log(c) * (b - 0.5))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -1.3e-6:
		tmp = (y * i) + (a + (z + (x * math.log(y))))
	else:
		tmp = a + (t + ((y * i) + (math.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-6)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + Float64(x * log(y)))));
	else
		tmp = Float64(a + Float64(t + Float64(Float64(y * i) + Float64(log(c) * Float64(b - 0.5)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -1.3e-6)
		tmp = (y * i) + (a + (z + (x * log(y))));
	else
		tmp = a + (t + ((y * i) + (log(c) * (b - 0.5))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -1.3e-6], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(t + N[(N[(y * i), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.30000000000000005e-6

   1. Initial program 99.8%

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

      1. associate-+l+ 99.8%

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

      2. +-commutative 99.8%

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

      3. +-commutative 99.8%

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

      4. associate-+l+ 99.8%

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

      5. fma-def 99.9%

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

      6. sub-neg 99.9%

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

      7. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 87.4%

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

      1. *-commutative 87.4%

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

   7. Simplified 87.4%

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

   8. Taylor expanded in t around 0 75.0%

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

   if -1.30000000000000005e-6 < z

   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 0 88.8%

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

      1. associate-+r+ 88.8%

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

      2. fma-def 88.9%

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

      3. sub-neg 88.9%

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

      4. metadata-eval 88.9%

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

      5. +-commutative 88.9%

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

   5. Simplified 88.9%

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

   6. Taylor expanded in x around 0 73.3%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-6}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(y \cdot i + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 73.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+158} \lor \neg \left(x \leq 1.15 \cdot 10^{+218}\right):\\ \;\;\;\;a + \left(t + x \cdot \log y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + \left(t + a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -1.05e+158) (not (<= x 1.15e+218)))
   (+ a (+ t (* x (log y))))
   (+ (* y i) (+ z (+ t a)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1.05e+158) || !(x <= 1.15e+218)) {
		tmp = a + (t + (x * log(y)));
	} else {
		tmp = (y * i) + (z + (t + a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-1.05d+158)) .or. (.not. (x <= 1.15d+218))) then
        tmp = a + (t + (x * log(y)))
    else
        tmp = (y * i) + (z + (t + a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1.05e+158) || !(x <= 1.15e+218)) {
		tmp = a + (t + (x * Math.log(y)));
	} else {
		tmp = (y * i) + (z + (t + a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -1.05e+158) or not (x <= 1.15e+218):
		tmp = a + (t + (x * math.log(y)))
	else:
		tmp = (y * i) + (z + (t + a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -1.05e+158) || !(x <= 1.15e+218))
		tmp = Float64(a + Float64(t + Float64(x * log(y))));
	else
		tmp = Float64(Float64(y * i) + Float64(z + Float64(t + a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -1.05e+158) || ~((x <= 1.15e+218)))
		tmp = a + (t + (x * log(y)));
	else
		tmp = (y * i) + (z + (t + a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -1.05e+158], N[Not[LessEqual[x, 1.15e+218]], $MachinePrecision]], N[(a + N[(t + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(z + N[(t + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.0499999999999999e158 or 1.15e218 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 87.5%

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

      1. associate-+r+ 87.5%

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

      2. fma-def 87.5%

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

      3. sub-neg 87.5%

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

      4. metadata-eval 87.5%

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

      5. +-commutative 87.5%

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

   5. Simplified 87.5%

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

   6. Taylor expanded in b around inf 87.5%

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

      1. *-commutative 87.5%

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

   8. Simplified 87.5%

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

   9. Taylor expanded in b around 0 82.9%

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

       1. associate-+r+ 82.9%

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

       2. *-commutative 82.9%

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

   11. Simplified 82.9%

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

   12. Taylor expanded in y around 0 75.8%

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

       1. *-commutative 75.8%

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

   14. Simplified 75.8%

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

   if -1.0499999999999999e158 < x < 1.15e218

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+l+ 99.9%

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

      5. fma-def 99.9%

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

      6. sub-neg 99.9%

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

      7. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 80.4%

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

      1. *-commutative 80.4%

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

   7. Simplified 80.4%

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

   8. Taylor expanded in x around 0 75.3%

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

      1. +-commutative 75.3%

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

      2. +-commutative 75.3%

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

      3. associate-+l+ 75.3%

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

      4. +-commutative 75.3%

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

   10. Simplified 75.3%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+158} \lor \neg \left(x \leq 1.15 \cdot 10^{+218}\right):\\ \;\;\;\;a + \left(t + x \cdot \log y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + \left(t + a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 75.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.85 \cdot 10^{-44}:\\ \;\;\;\;\left(t + a\right) + \left(z + \left(b + -0.5\right) \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + x \cdot \log y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 1.85e-44)
   (+ (+ t a) (+ z (* (+ b -0.5) (log c))))
   (+ (* y i) (+ a (+ z (* x (log y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 1.85e-44) {
		tmp = (t + a) + (z + ((b + -0.5) * log(c)));
	} else {
		tmp = (y * i) + (a + (z + (x * log(y))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= 1.85d-44) then
        tmp = (t + a) + (z + ((b + (-0.5d0)) * log(c)))
    else
        tmp = (y * i) + (a + (z + (x * log(y))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 1.85e-44) {
		tmp = (t + a) + (z + ((b + -0.5) * Math.log(c)));
	} else {
		tmp = (y * i) + (a + (z + (x * Math.log(y))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 1.85e-44:
		tmp = (t + a) + (z + ((b + -0.5) * math.log(c)))
	else:
		tmp = (y * i) + (a + (z + (x * math.log(y))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 1.85e-44)
		tmp = Float64(Float64(t + a) + Float64(z + Float64(Float64(b + -0.5) * log(c))));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + Float64(x * log(y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= 1.85e-44)
		tmp = (t + a) + (z + ((b + -0.5) * log(c)));
	else
		tmp = (y * i) + (a + (z + (x * log(y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 1.85e-44], N[(N[(t + a), $MachinePrecision] + N[(z + N[(N[(b + -0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.85e-44

   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 85.4%

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

   4. Taylor expanded in y around 0 82.1%

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

      1. associate-+r+ 82.1%

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

      2. sub-neg 82.1%

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

      3. metadata-eval 82.1%

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

   6. Simplified 82.1%

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

   if 1.85e-44 < y

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+l+ 99.9%

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

      5. fma-def 99.9%

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

      6. sub-neg 99.9%

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

      7. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 91.3%

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

      1. *-commutative 91.3%

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

   7. Simplified 91.3%

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

   8. Taylor expanded in t around 0 77.8%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.85 \cdot 10^{-44}:\\ \;\;\;\;\left(t + a\right) + \left(z + \left(b + -0.5\right) \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + x \cdot \log y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 71.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+241} \lor \neg \left(x \leq 7.5 \cdot 10^{+221}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + \left(t + a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -4e+241) (not (<= x 7.5e+221)))
   (* x (log y))
   (+ (* y i) (+ z (+ t a)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -4e+241) || !(x <= 7.5e+221)) {
		tmp = x * log(y);
	} else {
		tmp = (y * i) + (z + (t + a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-4d+241)) .or. (.not. (x <= 7.5d+221))) then
        tmp = x * log(y)
    else
        tmp = (y * i) + (z + (t + a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -4e+241) || !(x <= 7.5e+221)) {
		tmp = x * Math.log(y);
	} else {
		tmp = (y * i) + (z + (t + a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -4e+241) or not (x <= 7.5e+221):
		tmp = x * math.log(y)
	else:
		tmp = (y * i) + (z + (t + a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -4e+241) || !(x <= 7.5e+221))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(Float64(y * i) + Float64(z + Float64(t + a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -4e+241) || ~((x <= 7.5e+221)))
		tmp = x * log(y);
	else
		tmp = (y * i) + (z + (t + a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -4e+241], N[Not[LessEqual[x, 7.5e+221]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(z + N[(t + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.0000000000000002e241 or 7.50000000000000035e221 < x

   1. Initial program 99.6%

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

      1. associate-+l+ 99.6%

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

      2. +-commutative 99.6%

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

      3. +-commutative 99.6%

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

      4. associate-+l+ 99.6%

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

      5. fma-def 99.6%

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

      6. sub-neg 99.6%

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

      7. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf 96.4%

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

      1. *-commutative 96.4%

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

   7. Simplified 96.4%

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

   8. Taylor expanded in x around inf 69.9%

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

   if -4.0000000000000002e241 < x < 7.50000000000000035e221

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+l+ 99.9%

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

      5. fma-def 99.9%

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

      6. sub-neg 99.9%

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

      7. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 81.0%

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

      1. *-commutative 81.0%

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

   7. Simplified 81.0%

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

   8. Taylor expanded in x around 0 74.4%

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

      1. +-commutative 74.4%

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

      2. +-commutative 74.4%

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

      3. associate-+l+ 74.4%

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

      4. +-commutative 74.4%

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

   10. Simplified 74.4%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+241} \lor \neg \left(x \leq 7.5 \cdot 10^{+221}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + \left(t + a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 22.6% accurate, 16.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+146}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-103}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -3.2e+146) z (if (<= z -4.3e-103) (* 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 (z <= -3.2e+146) {
		tmp = z;
	} else if (z <= -4.3e-103) {
		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 (z <= (-3.2d+146)) then
        tmp = z
    else if (z <= (-4.3d-103)) 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 (z <= -3.2e+146) {
		tmp = z;
	} else if (z <= -4.3e-103) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -3.2e+146:
		tmp = z
	elif z <= -4.3e-103:
		tmp = y * i
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -3.2e+146)
		tmp = z;
	elseif (z <= -4.3e-103)
		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 (z <= -3.2e+146)
		tmp = z;
	elseif (z <= -4.3e-103)
		tmp = y * i;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -3.2e+146], z, If[LessEqual[z, -4.3e-103], N[(y * i), $MachinePrecision], a]]

Derivation

1. Split input into 3 regimes

2. if z < -3.2e146

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+l+ 99.9%

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

      5. fma-def 99.9%

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

      6. sub-neg 99.9%

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

      7. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 98.6%

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

      1. *-commutative 98.6%

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

   7. Simplified 98.6%

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

   8. Taylor expanded in z around inf 51.0%

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

   if -3.2e146 < z < -4.30000000000000023e-103

   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 a around inf 48.0%

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

   4. Taylor expanded in a around 0 28.0%

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

      1. *-commutative 28.0%

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

   6. Simplified 28.0%

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

   if -4.30000000000000023e-103 < 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 43.2%

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

   4. Taylor expanded in a around inf 18.2%

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

4. Final simplification 24.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+146}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-103}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 41.5% accurate, 21.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+175}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -2.8e+175) 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 <= -2.8e+175) {
		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 <= (-2.8d+175)) 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 <= -2.8e+175) {
		tmp = z;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -2.8e+175:
		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 <= -2.8e+175)
		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 <= -2.8e+175)
		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, -2.8e+175], z, N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.8000000000000001e175

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+l+ 99.9%

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

      5. fma-def 99.9%

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

      6. sub-neg 99.9%

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

      7. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 98.1%

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

      1. *-commutative 98.1%

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

   7. Simplified 98.1%

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

   8. Taylor expanded in z around inf 52.4%

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

   if -2.8000000000000001e175 < z

   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 a around inf 44.0%

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

4. Final simplification 44.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+175}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 67.5% accurate, 24.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. associate-+l+ 99.8%

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

   2. +-commutative 99.8%

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

   3. +-commutative 99.8%

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

   4. associate-+l+ 99.8%

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

   5. fma-def 99.8%

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

   6. sub-neg 99.8%

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

   7. metadata-eval 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in y around inf 82.8%

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

   1. *-commutative 82.8%

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

7. Simplified 82.8%

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

8. Taylor expanded in x around 0 67.8%

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

   1. +-commutative 67.8%

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

   2. +-commutative 67.8%

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

   3. associate-+l+ 67.8%

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

   4. +-commutative 67.8%

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

10. Simplified 67.8%

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

11. Final simplification 67.8%

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

Alternative 17: 52.7% accurate, 31.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in t around 0 86.9%

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

4. Taylor expanded in z around inf 55.8%

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

5. Final simplification 55.8%

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

Alternative 18: 21.4% accurate, 36.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+136}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (if (<= z -4.6e+136) 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 <= -4.6e+136) {
		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 <= (-4.6d+136)) 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 <= -4.6e+136) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -4.6e+136:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -4.6e+136)
		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 <= -4.6e+136)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -4.6e+136], z, a]

Derivation

1. Split input into 2 regimes

2. if z < -4.6e136

   1. Initial program 99.8%

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

      1. associate-+l+ 99.8%

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

      2. +-commutative 99.8%

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

      3. +-commutative 99.8%

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

      4. associate-+l+ 99.8%

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

      5. fma-def 99.8%

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

      6. sub-neg 99.8%

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

      7. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 98.6%

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

      1. *-commutative 98.6%

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

   7. Simplified 98.6%

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

   8. Taylor expanded in z around inf 48.7%

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

   if -4.6e136 < z

   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 a around inf 43.7%

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

   4. Taylor expanded in a around inf 18.9%

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

4. Final simplification 23.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+136}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 16.7% accurate, 219.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in a around inf 40.5%

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

4. Taylor expanded in a around inf 17.9%

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

5. Final simplification 17.9%

   \[\leadsto a \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024021 
(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)))