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

Percentage Accurate: 99.8% → 99.8%

Time: 18.3s

Alternatives: 16

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. associate-+l+ 99.8%

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

   2. associate-+l+ 99.8%

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

   3. +-commutative 99.8%

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

   4. +-commutative 99.8%

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

   5. associate-+r+ 99.8%

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

   6. associate-+l+ 99.8%

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

   7. +-commutative 99.8%

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

   8. associate-+l+ 99.8%

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

   9. +-commutative 99.8%

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

   10. fma-define 99.8%

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

   11. +-commutative 99.8%

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

   12. fma-define 99.8%

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

   13. sub-neg 99.8%

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

   14. metadata-eval 99.8%

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

   15. +-commutative 99.8%

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

   16. associate-+l+ 99.8%

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

   17. fma-define 99.8%

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

   18. +-commutative 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 2: 90.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+198} \lor \neg \left(x \leq 1.9 \cdot 10^{+181}\right):\\ \;\;\;\;y \cdot i + \left(z + \left(x \cdot \log y + -0.5 \cdot \log c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(t + a\right) + \left(z + \left(b + -0.5\right) \cdot \log c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -8.8e+198) (not (<= x 1.9e+181)))
   (+ (* y i) (+ z (+ (* x (log y)) (* -0.5 (log c)))))
   (+ (* y i) (+ (+ t a) (+ z (* (+ b -0.5) (log c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -8.8e+198) || !(x <= 1.9e+181)) {
		tmp = (y * i) + (z + ((x * log(y)) + (-0.5 * log(c))));
	} else {
		tmp = (y * i) + ((t + a) + (z + ((b + -0.5) * log(c))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-8.8d+198)) .or. (.not. (x <= 1.9d+181))) then
        tmp = (y * i) + (z + ((x * log(y)) + ((-0.5d0) * log(c))))
    else
        tmp = (y * i) + ((t + a) + (z + ((b + (-0.5d0)) * log(c))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -8.8e+198) || !(x <= 1.9e+181)) {
		tmp = (y * i) + (z + ((x * Math.log(y)) + (-0.5 * Math.log(c))));
	} else {
		tmp = (y * i) + ((t + a) + (z + ((b + -0.5) * Math.log(c))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -8.8e+198) or not (x <= 1.9e+181):
		tmp = (y * i) + (z + ((x * math.log(y)) + (-0.5 * math.log(c))))
	else:
		tmp = (y * i) + ((t + a) + (z + ((b + -0.5) * math.log(c))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -8.8e+198) || !(x <= 1.9e+181))
		tmp = Float64(Float64(y * i) + Float64(z + Float64(Float64(x * log(y)) + Float64(-0.5 * log(c)))));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(t + a) + Float64(z + Float64(Float64(b + -0.5) * log(c)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -8.8e+198) || ~((x <= 1.9e+181)))
		tmp = (y * i) + (z + ((x * log(y)) + (-0.5 * log(c))));
	else
		tmp = (y * i) + ((t + a) + (z + ((b + -0.5) * log(c))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -8.8e+198], N[Not[LessEqual[x, 1.9e+181]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(z + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(-0.5 * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(t + a), $MachinePrecision] + N[(z + N[(N[(b + -0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.7999999999999998e198 or 1.9000000000000001e181 < 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 a around 0 94.0%

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

   4. Taylor expanded in b around 0 94.0%

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

      1. +-commutative 94.0%

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

      2. fma-define 94.0%

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

      3. *-commutative 94.0%

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

   6. Simplified 94.0%

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

   7. Taylor expanded in t around 0 93.8%

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

   if -8.7999999999999998e198 < x < 1.9000000000000001e181

   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 93.8%

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

      1. associate-+r+ 93.8%

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

      2. sub-neg 93.8%

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

      3. metadata-eval 93.8%

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

      4. +-commutative 93.8%

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

   5. Simplified 93.8%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+198} \lor \neg \left(x \leq 1.9 \cdot 10^{+181}\right):\\ \;\;\;\;y \cdot i + \left(z + \left(x \cdot \log y + -0.5 \cdot \log c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(t + a\right) + \left(z + \left(b + -0.5\right) \cdot \log c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+200} \lor \neg \left(x \leq 1.5 \cdot 10^{+180}\right):\\ \;\;\;\;y \cdot i + \left(z + \left(x \cdot \log y + -0.5 \cdot \log c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\mathsf{fma}\left(\log c, b + -0.5, z\right) + \left(t + a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -2.7e+200) (not (<= x 1.5e+180)))
   (+ (* y i) (+ z (+ (* x (log y)) (* -0.5 (log c)))))
   (+ (* y i) (+ (fma (log c) (+ b -0.5) 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 <= -2.7e+200) || !(x <= 1.5e+180)) {
		tmp = (y * i) + (z + ((x * log(y)) + (-0.5 * log(c))));
	} else {
		tmp = (y * i) + (fma(log(c), (b + -0.5), z) + (t + a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -2.7e+200) || !(x <= 1.5e+180))
		tmp = Float64(Float64(y * i) + Float64(z + Float64(Float64(x * log(y)) + Float64(-0.5 * log(c)))));
	else
		tmp = Float64(Float64(y * i) + Float64(fma(log(c), Float64(b + -0.5), z) + Float64(t + a)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -2.7e+200], N[Not[LessEqual[x, 1.5e+180]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(z + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(-0.5 * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision] + z), $MachinePrecision] + N[(t + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.70000000000000016e200 or 1.50000000000000001e180 < 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 a around 0 94.0%

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

   4. Taylor expanded in b around 0 94.0%

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

      1. +-commutative 94.0%

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

      2. fma-define 94.0%

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

      3. *-commutative 94.0%

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

   6. Simplified 94.0%

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

   7. Taylor expanded in t around 0 93.8%

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

   if -2.70000000000000016e200 < x < 1.50000000000000001e180

   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 93.8%

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

      1. associate-+r+ 93.8%

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

      2. +-commutative 93.8%

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

      3. +-commutative 93.8%

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

      4. +-commutative 93.8%

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

      5. sub-neg 93.8%

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

      6. metadata-eval 93.8%

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

      7. fma-define 93.8%

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

      8. +-commutative 93.8%

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

      9. +-commutative 93.8%

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

   5. Simplified 93.8%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+200} \lor \neg \left(x \leq 1.5 \cdot 10^{+180}\right):\\ \;\;\;\;y \cdot i + \left(z + \left(x \cdot \log y + -0.5 \cdot \log c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\mathsf{fma}\left(\log c, b + -0.5, z\right) + \left(t + a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 92.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -6.6 \cdot 10^{+104}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + \left(t\_1 + b \cdot \log c\right)\right)\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+179}:\\ \;\;\;\;y \cdot i + \left(\mathsf{fma}\left(\log c, b + -0.5, z\right) + \left(t + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + \left(t\_1 + -0.5 \cdot \log c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -6.6e+104)
     (+ (* y i) (+ t (+ z (+ t_1 (* b (log c))))))
     (if (<= x 2.8e+179)
       (+ (* y i) (+ (fma (log c) (+ b -0.5) z) (+ t a)))
       (+ (* y i) (+ z (+ t_1 (* -0.5 (log c)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * log(y);
	double tmp;
	if (x <= -6.6e+104) {
		tmp = (y * i) + (t + (z + (t_1 + (b * log(c)))));
	} else if (x <= 2.8e+179) {
		tmp = (y * i) + (fma(log(c), (b + -0.5), z) + (t + a));
	} else {
		tmp = (y * i) + (z + (t_1 + (-0.5 * log(c))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -6.6e+104)
		tmp = Float64(Float64(y * i) + Float64(t + Float64(z + Float64(t_1 + Float64(b * log(c))))));
	elseif (x <= 2.8e+179)
		tmp = Float64(Float64(y * i) + Float64(fma(log(c), Float64(b + -0.5), z) + Float64(t + a)));
	else
		tmp = Float64(Float64(y * i) + Float64(z + Float64(t_1 + Float64(-0.5 * log(c)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.6e+104], N[(N[(y * i), $MachinePrecision] + N[(t + N[(z + N[(t$95$1 + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.8e+179], N[(N[(y * i), $MachinePrecision] + N[(N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision] + z), $MachinePrecision] + N[(t + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(z + N[(t$95$1 + N[(-0.5 * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.59999999999999969e104

   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. Add Preprocessing

   3. Taylor expanded in a around 0 90.5%

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

   4. Taylor expanded in b around inf 90.5%

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

   if -6.59999999999999969e104 < x < 2.8e179

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 96.2%

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

      1. associate-+r+ 96.2%

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

      2. +-commutative 96.2%

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

      3. +-commutative 96.2%

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

      4. +-commutative 96.2%

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

      5. sub-neg 96.2%

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

      6. metadata-eval 96.2%

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

      7. fma-define 96.2%

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

      8. +-commutative 96.2%

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

      9. +-commutative 96.2%

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

   5. Simplified 96.2%

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

   if 2.8e179 < 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 a around 0 89.0%

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

   4. Taylor expanded in b around 0 89.0%

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

      1. +-commutative 89.0%

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

      2. fma-define 89.0%

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

      3. *-commutative 89.0%

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

   6. Simplified 89.0%

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

   7. Taylor expanded in t around 0 88.6%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{+104}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + \left(x \cdot \log y + b \cdot \log c\right)\right)\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+179}:\\ \;\;\;\;y \cdot i + \left(\mathsf{fma}\left(\log c, b + -0.5, z\right) + \left(t + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + \left(x \cdot \log y + -0.5 \cdot \log c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 91.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;a \leq 4 \cdot 10^{-29}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + \left(t\_1 + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(a + \left(t + \left(z + t\_1\right)\right)\right) + b \cdot \log c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= a 4e-29)
     (+ (* y i) (+ t (+ z (+ t_1 (* (log c) (- b 0.5))))))
     (+ (* y i) (+ (+ a (+ t (+ z t_1))) (* b (log c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * log(y);
	double tmp;
	if (a <= 4e-29) {
		tmp = (y * i) + (t + (z + (t_1 + (log(c) * (b - 0.5)))));
	} else {
		tmp = (y * i) + ((a + (t + (z + t_1))) + (b * log(c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * log(y)
    if (a <= 4d-29) then
        tmp = (y * i) + (t + (z + (t_1 + (log(c) * (b - 0.5d0)))))
    else
        tmp = (y * i) + ((a + (t + (z + t_1))) + (b * log(c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * Math.log(y);
	double tmp;
	if (a <= 4e-29) {
		tmp = (y * i) + (t + (z + (t_1 + (Math.log(c) * (b - 0.5)))));
	} else {
		tmp = (y * i) + ((a + (t + (z + t_1))) + (b * Math.log(c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x * math.log(y)
	tmp = 0
	if a <= 4e-29:
		tmp = (y * i) + (t + (z + (t_1 + (math.log(c) * (b - 0.5)))))
	else:
		tmp = (y * i) + ((a + (t + (z + t_1))) + (b * math.log(c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (a <= 4e-29)
		tmp = Float64(Float64(y * i) + Float64(t + Float64(z + Float64(t_1 + Float64(log(c) * Float64(b - 0.5))))));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(a + Float64(t + Float64(z + t_1))) + Float64(b * log(c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x * log(y);
	tmp = 0.0;
	if (a <= 4e-29)
		tmp = (y * i) + (t + (z + (t_1 + (log(c) * (b - 0.5)))));
	else
		tmp = (y * i) + ((a + (t + (z + t_1))) + (b * log(c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, 4e-29], N[(N[(y * i), $MachinePrecision] + N[(t + N[(z + N[(t$95$1 + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(a + N[(t + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < 3.99999999999999977e-29

   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 0 90.5%

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

   if 3.99999999999999977e-29 < a

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf 99.8%

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

      1. *-commutative 99.8%

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

   5. Simplified 99.8%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 4 \cdot 10^{-29}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + \left(x \cdot \log y + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right) + b \cdot \log c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Final simplification 99.8%

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

Alternative 7: 43.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t + a\right) + \left(b + -0.5\right) \cdot \log c\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+107}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+81}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-75}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (+ t a) (* (+ b -0.5) (log c)))))
   (if (<= z -1.35e+107)
     (+ z (* y i))
     (if (<= z -1.5e+81)
       t_1
       (if (<= z -1.35e-8)
         (+ (* x (log y)) (* y i))
         (if (<= z -1.5e-75) t_1 (fma y i a)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (t + a) + ((b + -0.5) * log(c));
	double tmp;
	if (z <= -1.35e+107) {
		tmp = z + (y * i);
	} else if (z <= -1.5e+81) {
		tmp = t_1;
	} else if (z <= -1.35e-8) {
		tmp = (x * log(y)) + (y * i);
	} else if (z <= -1.5e-75) {
		tmp = t_1;
	} else {
		tmp = fma(y, i, a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(t + a) + Float64(Float64(b + -0.5) * log(c)))
	tmp = 0.0
	if (z <= -1.35e+107)
		tmp = Float64(z + Float64(y * i));
	elseif (z <= -1.5e+81)
		tmp = t_1;
	elseif (z <= -1.35e-8)
		tmp = Float64(Float64(x * log(y)) + Float64(y * i));
	elseif (z <= -1.5e-75)
		tmp = t_1;
	else
		tmp = fma(y, i, a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(t + a), $MachinePrecision] + N[(N[(b + -0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35e+107], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.5e+81], t$95$1, If[LessEqual[z, -1.35e-8], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.5e-75], t$95$1, N[(y * i + a), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.3500000000000001e107

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 70.2%

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

   if -1.3500000000000001e107 < z < -1.49999999999999999e81 or -1.35000000000000001e-8 < z < -1.4999999999999999e-75

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 82.1%

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

      1. associate-+r+ 82.1%

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

      2. sub-neg 82.1%

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

      3. metadata-eval 82.1%

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

      4. +-commutative 82.1%

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

   5. Simplified 82.1%

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

   6. Taylor expanded in z around 0 82.1%

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

      1. associate-+r+ 82.1%

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

      2. sub-neg 82.1%

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

      3. metadata-eval 82.1%

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

      4. +-commutative 82.1%

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

   8. Simplified 82.1%

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

   9. Taylor expanded in y around 0 52.5%

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

       1. associate-+r+ 52.5%

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

       2. +-commutative 52.5%

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

       3. sub-neg 52.5%

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

       4. metadata-eval 52.5%

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

   11. Simplified 52.5%

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

   if -1.49999999999999999e81 < z < -1.35000000000000001e-8

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 41.3%

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

   if -1.4999999999999999e-75 < 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. Step-by-step derivation

      1. associate-+l+ 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-+r+ 99.8%

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

      6. associate-+l+ 99.8%

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

      7. +-commutative 99.8%

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

      8. associate-+l+ 99.8%

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

      9. +-commutative 99.8%

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

      10. fma-define 99.8%

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

      11. +-commutative 99.8%

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

      12. fma-define 99.8%

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

      13. sub-neg 99.8%

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

      14. metadata-eval 99.8%

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

      15. +-commutative 99.8%

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

      16. associate-+l+ 99.8%

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

      17. fma-define 99.8%

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

      18. +-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 81.7%

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

   6. Taylor expanded in a around inf 35.3%

      \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{a}\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 42.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+107}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+81}:\\ \;\;\;\;\left(t + a\right) + \left(b + -0.5\right) \cdot \log c\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-75}:\\ \;\;\;\;\left(t + a\right) + \left(b + -0.5\right) \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 89.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+202} \lor \neg \left(x \leq 1.5 \cdot 10^{+214}\right):\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(t + a\right) + \left(z + \left(b + -0.5\right) \cdot \log c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -1.1e+202) (not (<= x 1.5e+214)))
   (+ (* x (log y)) (* y i))
   (+ (* y i) (+ (+ t a) (+ z (* (+ b -0.5) (log c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1.1e+202) || !(x <= 1.5e+214)) {
		tmp = (x * log(y)) + (y * i);
	} else {
		tmp = (y * i) + ((t + a) + (z + ((b + -0.5) * log(c))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-1.1d+202)) .or. (.not. (x <= 1.5d+214))) then
        tmp = (x * log(y)) + (y * i)
    else
        tmp = (y * i) + ((t + a) + (z + ((b + (-0.5d0)) * log(c))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1.1e+202) || !(x <= 1.5e+214)) {
		tmp = (x * Math.log(y)) + (y * i);
	} else {
		tmp = (y * i) + ((t + a) + (z + ((b + -0.5) * Math.log(c))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -1.1e+202) or not (x <= 1.5e+214):
		tmp = (x * math.log(y)) + (y * i)
	else:
		tmp = (y * i) + ((t + a) + (z + ((b + -0.5) * math.log(c))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -1.1e+202) || !(x <= 1.5e+214))
		tmp = Float64(Float64(x * log(y)) + Float64(y * i));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(t + a) + Float64(z + Float64(Float64(b + -0.5) * log(c)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -1.1e+202) || ~((x <= 1.5e+214)))
		tmp = (x * log(y)) + (y * i);
	else
		tmp = (y * i) + ((t + a) + (z + ((b + -0.5) * log(c))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -1.1e+202], N[Not[LessEqual[x, 1.5e+214]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(t + a), $MachinePrecision] + N[(z + N[(N[(b + -0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.09999999999999989e202 or 1.5000000000000001e214 < 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. Add Preprocessing

   3. Taylor expanded in x around inf 86.8%

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

   if -1.09999999999999989e202 < x < 1.5000000000000001e214

   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 93.1%

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

      1. associate-+r+ 93.1%

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

      2. sub-neg 93.1%

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

      3. metadata-eval 93.1%

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

      4. +-commutative 93.1%

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

   5. Simplified 93.1%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+202} \lor \neg \left(x \leq 1.5 \cdot 10^{+214}\right):\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(t + a\right) + \left(z + \left(b + -0.5\right) \cdot \log c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 73.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+274}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{+108}:\\ \;\;\;\;a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(t + a\right) + \left(b + -0.5\right) \cdot \log c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -6.2e+274)
   (+ z (* y i))
   (if (<= z -1.75e+108)
     (+ a (+ t (+ z (* (log c) (- b 0.5)))))
     (+ (* y i) (+ (+ t a) (* (+ b -0.5) (log c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -6.2e+274) {
		tmp = z + (y * i);
	} else if (z <= -1.75e+108) {
		tmp = a + (t + (z + (log(c) * (b - 0.5))));
	} else {
		tmp = (y * i) + ((t + a) + ((b + -0.5) * log(c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-6.2d+274)) then
        tmp = z + (y * i)
    else if (z <= (-1.75d+108)) then
        tmp = a + (t + (z + (log(c) * (b - 0.5d0))))
    else
        tmp = (y * i) + ((t + a) + ((b + (-0.5d0)) * log(c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -6.2e+274) {
		tmp = z + (y * i);
	} else if (z <= -1.75e+108) {
		tmp = a + (t + (z + (Math.log(c) * (b - 0.5))));
	} else {
		tmp = (y * i) + ((t + a) + ((b + -0.5) * Math.log(c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -6.2e+274:
		tmp = z + (y * i)
	elif z <= -1.75e+108:
		tmp = a + (t + (z + (math.log(c) * (b - 0.5))))
	else:
		tmp = (y * i) + ((t + a) + ((b + -0.5) * math.log(c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -6.2e+274)
		tmp = Float64(z + Float64(y * i));
	elseif (z <= -1.75e+108)
		tmp = Float64(a + Float64(t + Float64(z + Float64(log(c) * Float64(b - 0.5)))));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(t + a) + Float64(Float64(b + -0.5) * log(c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -6.2e+274)
		tmp = z + (y * i);
	elseif (z <= -1.75e+108)
		tmp = a + (t + (z + (log(c) * (b - 0.5))));
	else
		tmp = (y * i) + ((t + a) + ((b + -0.5) * log(c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -6.2e+274], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.75e+108], N[(a + N[(t + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(t + a), $MachinePrecision] + N[(N[(b + -0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.2e274

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 100.0%

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

   if -6.2e274 < z < -1.7500000000000001e108

   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 93.0%

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

      1. associate-+r+ 93.0%

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

      2. sub-neg 93.0%

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

      3. metadata-eval 93.0%

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

      4. +-commutative 93.0%

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

   5. Simplified 93.0%

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

   6. Taylor expanded in y around 0 79.3%

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

   if -1.7500000000000001e108 < 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 x around 0 82.9%

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

      1. associate-+r+ 82.9%

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

      2. sub-neg 82.9%

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

      3. metadata-eval 82.9%

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

      4. +-commutative 82.9%

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

   5. Simplified 82.9%

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

   6. Taylor expanded in z around 0 70.7%

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

      1. associate-+r+ 70.7%

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

      2. sub-neg 70.7%

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

      3. metadata-eval 70.7%

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

      4. +-commutative 70.7%

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

   8. Simplified 70.7%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+274}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{+108}:\\ \;\;\;\;a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(t + a\right) + \left(b + -0.5\right) \cdot \log c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z + y \cdot i\\ \mathbf{if}\;i \leq -9.4 \cdot 10^{+86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 8.5 \cdot 10^{+19}:\\ \;\;\;\;a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{elif}\;i \leq 1.4 \cdot 10^{+220}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ z (* y i))))
   (if (<= i -9.4e+86)
     t_1
     (if (<= i 8.5e+19)
       (+ a (+ t (+ z (* (log c) (- b 0.5)))))
       (if (<= i 1.4e+220) t_1 (+ a (* y i)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = z + (y * i);
	double tmp;
	if (i <= -9.4e+86) {
		tmp = t_1;
	} else if (i <= 8.5e+19) {
		tmp = a + (t + (z + (log(c) * (b - 0.5))));
	} else if (i <= 1.4e+220) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = z + (y * i)
    if (i <= (-9.4d+86)) then
        tmp = t_1
    else if (i <= 8.5d+19) then
        tmp = a + (t + (z + (log(c) * (b - 0.5d0))))
    else if (i <= 1.4d+220) then
        tmp = t_1
    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 t_1 = z + (y * i);
	double tmp;
	if (i <= -9.4e+86) {
		tmp = t_1;
	} else if (i <= 8.5e+19) {
		tmp = a + (t + (z + (Math.log(c) * (b - 0.5))));
	} else if (i <= 1.4e+220) {
		tmp = t_1;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = z + (y * i)
	tmp = 0
	if i <= -9.4e+86:
		tmp = t_1
	elif i <= 8.5e+19:
		tmp = a + (t + (z + (math.log(c) * (b - 0.5))))
	elif i <= 1.4e+220:
		tmp = t_1
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(z + Float64(y * i))
	tmp = 0.0
	if (i <= -9.4e+86)
		tmp = t_1;
	elseif (i <= 8.5e+19)
		tmp = Float64(a + Float64(t + Float64(z + Float64(log(c) * Float64(b - 0.5)))));
	elseif (i <= 1.4e+220)
		tmp = t_1;
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = z + (y * i);
	tmp = 0.0;
	if (i <= -9.4e+86)
		tmp = t_1;
	elseif (i <= 8.5e+19)
		tmp = a + (t + (z + (log(c) * (b - 0.5))));
	elseif (i <= 1.4e+220)
		tmp = t_1;
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -9.4e+86], t$95$1, If[LessEqual[i, 8.5e+19], N[(a + N[(t + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.4e+220], t$95$1, N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if i < -9.4000000000000004e86 or 8.5e19 < i < 1.4e220

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 56.9%

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

   if -9.4000000000000004e86 < i < 8.5e19

   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 85.1%

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

      1. associate-+r+ 85.1%

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

      2. sub-neg 85.1%

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

      3. metadata-eval 85.1%

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

      4. +-commutative 85.1%

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

   5. Simplified 85.1%

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

   6. Taylor expanded in y around 0 78.4%

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

   if 1.4e220 < i

   1. Initial program 99.8%

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

   3. Taylor expanded in a around inf 54.3%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -9.4 \cdot 10^{+86}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;i \leq 8.5 \cdot 10^{+19}:\\ \;\;\;\;a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{elif}\;i \leq 1.4 \cdot 10^{+220}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 43.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+89}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -9.8e+89)
   (+ z (* y i))
   (if (<= z -6.4e-8) (+ (* x (log y)) (* y i)) (fma y i a))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -9.8e+89) {
		tmp = z + (y * i);
	} else if (z <= -6.4e-8) {
		tmp = (x * log(y)) + (y * i);
	} else {
		tmp = fma(y, i, a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -9.8e+89)
		tmp = Float64(z + Float64(y * i));
	elseif (z <= -6.4e-8)
		tmp = Float64(Float64(x * log(y)) + Float64(y * i));
	else
		tmp = fma(y, i, a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -9.8e+89], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.4e-8], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(y * i + a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.79999999999999992e89

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 68.7%

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

   if -9.79999999999999992e89 < z < -6.4000000000000004e-8

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 40.5%

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

   if -6.4000000000000004e-8 < 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. Step-by-step derivation

      1. associate-+l+ 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-+r+ 99.8%

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

      6. associate-+l+ 99.8%

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

      7. +-commutative 99.8%

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

      8. associate-+l+ 99.8%

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

      9. +-commutative 99.8%

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

      10. fma-define 99.8%

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

      11. +-commutative 99.8%

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

      12. fma-define 99.8%

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

      13. sub-neg 99.8%

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

      14. metadata-eval 99.8%

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

      15. +-commutative 99.8%

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

      16. associate-+l+ 99.8%

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

      17. fma-define 99.8%

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

      18. +-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 81.8%

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

   6. Taylor expanded in a around inf 35.3%

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

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+89}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 42.9% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+100}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -8e+100) (+ z (* y i)) (fma y i a)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -8e+100) {
		tmp = z + (y * i);
	} else {
		tmp = fma(y, i, a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -8e+100)
		tmp = Float64(z + Float64(y * i));
	else
		tmp = fma(y, i, a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -8e+100], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(y * i + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.00000000000000013e100

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 68.7%

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

   if -8.00000000000000013e100 < 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. Step-by-step derivation

      1. associate-+l+ 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-+r+ 99.8%

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

      6. associate-+l+ 99.8%

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

      7. +-commutative 99.8%

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

      8. associate-+l+ 99.8%

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

      9. +-commutative 99.8%

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

      10. fma-define 99.8%

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

      11. +-commutative 99.8%

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

      12. fma-define 99.8%

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

      13. sub-neg 99.8%

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

      14. metadata-eval 99.8%

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

      15. +-commutative 99.8%

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

      16. associate-+l+ 99.8%

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

      17. fma-define 99.8%

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

      18. +-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 81.7%

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

   6. Taylor expanded in a around inf 34.5%

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

4. Final simplification 40.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+100}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 40.8% accurate, 21.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+234}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -9.8e+234) 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 <= -9.8e+234) {
		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 <= (-9.8d+234)) 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 <= -9.8e+234) {
		tmp = z;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -9.8e+234:
		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 <= -9.8e+234)
		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 <= -9.8e+234)
		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, -9.8e+234], z, N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.79999999999999979e234

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 97.3%

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

      1. associate-+r+ 97.3%

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

      2. sub-neg 97.3%

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

      3. metadata-eval 97.3%

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

      4. +-commutative 97.3%

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

   5. Simplified 97.3%

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

      1. add-sqr-sqrt 45.0%

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

      2. pow2 45.0%

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

      3. +-commutative 45.0%

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

      4. *-commutative 45.0%

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

   7. Applied egg-rr 45.0%

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

   8. Taylor expanded in z around inf 79.0%

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

   if -9.79999999999999979e234 < 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 33.9%

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

4. Final simplification 37.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+234}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 42.9% accurate, 21.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+105}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -4.3e+105) (+ z (* y i)) (+ a (* y i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -4.3e+105) {
		tmp = z + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-4.3d+105)) then
        tmp = z + (y * i)
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -4.3e+105) {
		tmp = z + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -4.3e+105:
		tmp = z + (y * i)
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -4.3e+105)
		tmp = Float64(z + Float64(y * i));
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -4.3e+105)
		tmp = z + (y * i);
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -4.3e+105], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.3000000000000002e105

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 68.7%

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

   if -4.3000000000000002e105 < 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 34.5%

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

4. Final simplification 40.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+105}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 21.6% accurate, 36.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+91}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (if (<= z -1.2e+91) z a))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -1.2e+91) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-1.2d+91)) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -1.2e+91) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -1.2e+91:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -1.2e+91)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -1.2e+91)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -1.2e+91], z, a]

Derivation

1. Split input into 2 regimes

2. if z < -1.19999999999999991e91

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 95.4%

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

      1. associate-+r+ 95.4%

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

      2. sub-neg 95.4%

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

      3. metadata-eval 95.4%

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

      4. +-commutative 95.4%

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

   5. Simplified 95.4%

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

      1. add-sqr-sqrt 46.4%

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

      2. pow2 46.4%

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

      3. +-commutative 46.4%

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

      4. *-commutative 46.4%

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

   7. Applied egg-rr 46.4%

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

   8. Taylor expanded in z around inf 51.1%

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

   if -1.19999999999999991e91 < 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 x around 0 82.7%

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

      1. associate-+r+ 82.7%

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

      2. sub-neg 82.7%

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

      3. metadata-eval 82.7%

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

      4. +-commutative 82.7%

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

   5. Simplified 82.7%

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

      1. add-sqr-sqrt 35.6%

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

      2. pow2 35.6%

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

      3. +-commutative 35.6%

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

      4. *-commutative 35.6%

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

   7. Applied egg-rr 35.6%

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

   8. Taylor expanded in a around inf 15.6%

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

4. Final simplification 21.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+91}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 16.8% 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 x around 0 84.9%

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

   1. associate-+r+ 84.9%

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

   2. sub-neg 84.9%

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

   3. metadata-eval 84.9%

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

   4. +-commutative 84.9%

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

5. Simplified 84.9%

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

   1. add-sqr-sqrt 37.4%

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

   2. pow2 37.4%

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

   3. +-commutative 37.4%

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

   4. *-commutative 37.4%

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

7. Applied egg-rr 37.4%

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

8. Taylor expanded in a around inf 14.2%

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

9. Final simplification 14.2%

   \[\leadsto a \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2024034 
(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)))