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

Percentage Accurate: 99.8% → 99.5%

Time: 21.6s

Alternatives: 17

Speedup: 0.4×

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: 99.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := \sqrt[3]{b + -0.5} \cdot \sqrt[3]{\log c}\\ \left(\left(x \cdot \log y + z\right) + \left(t + a\right)\right) + \mathsf{fma}\left({t\_1}^{2}, t\_1, y \cdot i\right) \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (cbrt (+ b -0.5)) (cbrt (log c)))))
   (+ (+ (+ (* x (log y)) z) (+ t a)) (fma (pow t_1 2.0) t_1 (* y i)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = cbrt((b + -0.5)) * cbrt(log(c));
	return (((x * log(y)) + z) + (t + a)) + fma(pow(t_1, 2.0), t_1, (y * i));
}

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(cbrt(Float64(b + -0.5)) * cbrt(log(c)))
	return Float64(Float64(Float64(Float64(x * log(y)) + z) + Float64(t + a)) + fma((t_1 ^ 2.0), t_1, Float64(y * i)))
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[Power[N[(b + -0.5), $MachinePrecision], 1/3], $MachinePrecision] * N[Power[N[Log[c], $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]}, N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + N[(t + a), $MachinePrecision]), $MachinePrecision] + N[(N[Power[t$95$1, 2.0], $MachinePrecision] * t$95$1 + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 99.5%

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

   1. associate-+l+ 99.5%

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

   2. +-commutative 99.5%

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

   3. +-commutative 99.5%

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

   4. associate-+l+ 99.5%

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

   5. fma-define 99.5%

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

   6. sub-neg 99.5%

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

   7. metadata-eval 99.5%

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

3. Simplified 99.5%

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

   1. fma-define 99.5%

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

6. Applied egg-rr 99.5%

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

   1. add-cube-cbrt 99.2%

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

   2. fma-define 99.2%

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

   3. pow2 99.2%

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

   4. *-commutative 99.2%

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

   5. *-commutative 99.2%

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

8. Applied egg-rr 99.2%

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

   1. metadata-eval 99.2%

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

   2. sub-neg 99.2%

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

   3. *-commutative 99.2%

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

   4. cbrt-prod 99.2%

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

   5. sub-neg 99.2%

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

   6. metadata-eval 99.2%

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

10. Applied egg-rr 99.2%

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

    1. metadata-eval 99.2%

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

    2. sub-neg 99.2%

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

    3. *-commutative 99.2%

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

    4. cbrt-prod 99.2%

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

    5. sub-neg 99.2%

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

    6. metadata-eval 99.2%

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

12. Applied egg-rr 99.6%

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

13. Final simplification 99.6%

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

Alternative 2: 99.8% accurate, 0.4× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(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

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
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

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
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

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
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 99.5%

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

   1. associate-+l+ 99.5%

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

   2. associate-+l+ 99.5%

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

   3. +-commutative 99.5%

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

   4. +-commutative 99.5%

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

   5. associate-+r+ 99.5%

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

   6. associate-+l+ 99.5%

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

   7. +-commutative 99.5%

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

   8. associate-+l+ 99.5%

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

   9. +-commutative 99.5%

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

   10. fma-define 99.5%

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

   11. +-commutative 99.5%

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

   12. fma-define 99.5%

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

   13. sub-neg 99.5%

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

   14. metadata-eval 99.5%

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

   15. +-commutative 99.5%

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

3. Simplified 99.5%

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

5. Final simplification 99.5%

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

Alternative 3: 94.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+147} \lor \neg \left(x \leq 1.35 \cdot 10^{+172}\right):\\ \;\;\;\;\left(\left(x \cdot \log y + z\right) + \left(t + a\right)\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;z + \left(a + \mathsf{fma}\left(\log c, b + -0.5, y \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -2.8e+147) (not (<= x 1.35e+172)))
   (+ (+ (+ (* x (log y)) z) (+ t a)) (* y i))
   (+ z (+ a (fma (log c) (+ b -0.5) (* y i))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -2.8e+147) || !(x <= 1.35e+172)) {
		tmp = (((x * log(y)) + z) + (t + a)) + (y * i);
	} else {
		tmp = z + (a + fma(log(c), (b + -0.5), (y * i)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -2.8e+147) || !(x <= 1.35e+172))
		tmp = Float64(Float64(Float64(Float64(x * log(y)) + z) + Float64(t + a)) + Float64(y * i));
	else
		tmp = Float64(z + Float64(a + fma(log(c), Float64(b + -0.5), Float64(y * i))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -2.8e+147], N[Not[LessEqual[x, 1.35e+172]], $MachinePrecision]], N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + N[(t + a), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(z + N[(a + N[(N[Log[c], $MachinePrecision] * N[(b + -0.5), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.8000000000000001e147 or 1.35e172 < x

   1. Initial program 99.7%

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

      1. associate-+l+ 99.7%

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

      2. +-commutative 99.7%

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

      3. +-commutative 99.7%

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

      4. associate-+l+ 99.7%

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

      5. fma-define 99.8%

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

      6. sub-neg 99.8%

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

      7. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

      1. fma-define 99.7%

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

   6. Applied egg-rr 99.7%

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

      1. add-cube-cbrt 99.7%

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

      2. fma-define 99.7%

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

      3. pow2 99.7%

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

      4. *-commutative 99.7%

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

      5. *-commutative 99.7%

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

   8. Applied egg-rr 99.7%

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

   9. Taylor expanded in y around inf 94.2%

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

   if -2.8000000000000001e147 < x < 1.35e172

   1. Initial program 99.4%

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

   3. Taylor expanded in x around 0 96.4%

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

   4. Taylor expanded in t around 0 81.7%

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

      1. associate-+r+ 81.7%

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

      2. *-commutative 81.7%

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

      3. sub-neg 81.7%

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

      4. metadata-eval 81.7%

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

      5. distribute-rgt-in 81.7%

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

      6. distribute-rgt-in 81.7%

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

      7. fma-define 81.7%

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

      8. associate-+r+ 81.7%

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

      9. +-commutative 81.7%

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

      10. +-commutative 81.7%

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

      11. +-commutative 81.7%

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

      12. associate-+l+ 81.7%

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

      13. fma-define 81.7%

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

      14. +-commutative 81.7%

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

      15. fma-define 82.2%

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

      16. *-commutative 82.2%

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

   6. Simplified 82.2%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+147} \lor \neg \left(x \leq 1.35 \cdot 10^{+172}\right):\\ \;\;\;\;\left(\left(x \cdot \log y + z\right) + \left(t + a\right)\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;z + \left(a + \mathsf{fma}\left(\log c, b + -0.5, y \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.8% accurate, 1.0× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (+ (+ (+ (* x (log y)) z) (+ t a)) (+ (* y i) (* (+ b -0.5) (log c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
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)) + ((y * i) + ((b + -0.5) * log(c)));
}

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
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)) + ((y * i) + ((b + (-0.5d0)) * log(c)))
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
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)) + ((y * i) + ((b + -0.5) * Math.log(c)));
}

Python

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

Julia

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

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp = code(x, y, z, t, a, b, c, i)
	tmp = (((x * log(y)) + z) + (t + a)) + ((y * i) + ((b + -0.5) * log(c)));
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + N[(t + a), $MachinePrecision]), $MachinePrecision] + N[(N[(y * i), $MachinePrecision] + N[(N[(b + -0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.5%

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

   1. associate-+l+ 99.5%

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

   2. +-commutative 99.5%

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

   3. +-commutative 99.5%

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

   4. associate-+l+ 99.5%

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

   5. fma-define 99.5%

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

   6. sub-neg 99.5%

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

   7. metadata-eval 99.5%

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

3. Simplified 99.5%

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

   1. fma-define 99.5%

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

6. Applied egg-rr 99.5%

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

7. Final simplification 99.5%

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

Alternative 5: 97.8% accurate, 1.0× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (+ (+ (+ (* x (log y)) z) (+ t a)) (+ (* y i) (* b (log c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
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)) + ((y * i) + (b * log(c)));
}

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
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)) + ((y * i) + (b * log(c)))
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
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)) + ((y * i) + (b * Math.log(c)));
}

Python

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

Julia

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

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp = code(x, y, z, t, a, b, c, i)
	tmp = (((x * log(y)) + z) + (t + a)) + ((y * i) + (b * log(c)));
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + N[(t + a), $MachinePrecision]), $MachinePrecision] + N[(N[(y * i), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.5%

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

   1. associate-+l+ 99.5%

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

   2. +-commutative 99.5%

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

   3. +-commutative 99.5%

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

   4. associate-+l+ 99.5%

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

   5. fma-define 99.5%

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

   6. sub-neg 99.5%

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

   7. metadata-eval 99.5%

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

3. Simplified 99.5%

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

   1. fma-define 99.5%

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

6. Applied egg-rr 99.5%

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

7. Taylor expanded in b around inf 97.8%

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

   1. *-commutative 97.8%

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

9. Simplified 97.8%

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

10. Final simplification 97.8%

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

Alternative 6: 94.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+144} \lor \neg \left(x \leq 7.2 \cdot 10^{+171}\right):\\ \;\;\;\;\left(\left(x \cdot \log y + z\right) + \left(t + a\right)\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + \left(y \cdot i + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -4.5e+144) (not (<= x 7.2e+171)))
   (+ (+ (+ (* x (log y)) z) (+ t a)) (* y i))
   (+ a (+ t (+ z (+ (* y i) (* (log c) (- b 0.5))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -4.5e+144) || !(x <= 7.2e+171)) {
		tmp = (((x * log(y)) + z) + (t + a)) + (y * i);
	} else {
		tmp = a + (t + (z + ((y * i) + (log(c) * (b - 0.5)))));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-4.5d+144)) .or. (.not. (x <= 7.2d+171))) then
        tmp = (((x * log(y)) + z) + (t + a)) + (y * i)
    else
        tmp = a + (t + (z + ((y * i) + (log(c) * (b - 0.5d0)))))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -4.5e+144) || !(x <= 7.2e+171)) {
		tmp = (((x * Math.log(y)) + z) + (t + a)) + (y * i);
	} else {
		tmp = a + (t + (z + ((y * i) + (Math.log(c) * (b - 0.5)))));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -4.5e+144) or not (x <= 7.2e+171):
		tmp = (((x * math.log(y)) + z) + (t + a)) + (y * i)
	else:
		tmp = a + (t + (z + ((y * i) + (math.log(c) * (b - 0.5)))))
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -4.5e+144) || !(x <= 7.2e+171))
		tmp = Float64(Float64(Float64(Float64(x * log(y)) + z) + Float64(t + a)) + Float64(y * i));
	else
		tmp = Float64(a + Float64(t + Float64(z + Float64(Float64(y * i) + Float64(log(c) * Float64(b - 0.5))))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -4.5e+144) || ~((x <= 7.2e+171)))
		tmp = (((x * log(y)) + z) + (t + a)) + (y * i);
	else
		tmp = a + (t + (z + ((y * i) + (log(c) * (b - 0.5)))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -4.5e+144], N[Not[LessEqual[x, 7.2e+171]], $MachinePrecision]], N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + N[(t + a), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(a + N[(t + N[(z + N[(N[(y * i), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.49999999999999967e144 or 7.20000000000000036e171 < x

   1. Initial program 99.7%

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

      1. associate-+l+ 99.7%

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

      2. +-commutative 99.7%

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

      3. +-commutative 99.7%

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

      4. associate-+l+ 99.7%

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

      5. fma-define 99.8%

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

      6. sub-neg 99.8%

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

      7. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

      1. fma-define 99.7%

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

   6. Applied egg-rr 99.7%

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

      1. add-cube-cbrt 99.7%

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

      2. fma-define 99.7%

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

      3. pow2 99.7%

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

      4. *-commutative 99.7%

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

      5. *-commutative 99.7%

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

   8. Applied egg-rr 99.7%

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

   9. Taylor expanded in y around inf 94.2%

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

   if -4.49999999999999967e144 < x < 7.20000000000000036e171

   1. Initial program 99.4%

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

   3. Taylor expanded in x around 0 96.4%

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

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+144} \lor \neg \left(x \leq 7.2 \cdot 10^{+171}\right):\\ \;\;\;\;\left(\left(x \cdot \log y + z\right) + \left(t + a\right)\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + \left(y \cdot i + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 3.6 \cdot 10^{+92} \lor \neg \left(y \leq 1.55 \cdot 10^{+109}\right) \land y \leq 4.3 \cdot 10^{+176}:\\ \;\;\;\;\left(z + a\right) + \left(b + -0.5\right) \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y 3.6e+92) (and (not (<= y 1.55e+109)) (<= y 4.3e+176)))
   (+ (+ z a) (* (+ b -0.5) (log c)))
   (* y i)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= 3.6e+92) || (!(y <= 1.55e+109) && (y <= 4.3e+176))) {
		tmp = (z + a) + ((b + -0.5) * log(c));
	} else {
		tmp = y * i;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= 3.6d+92) .or. (.not. (y <= 1.55d+109)) .and. (y <= 4.3d+176)) then
        tmp = (z + a) + ((b + (-0.5d0)) * log(c))
    else
        tmp = y * i
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= 3.6e+92) || (!(y <= 1.55e+109) && (y <= 4.3e+176))) {
		tmp = (z + a) + ((b + -0.5) * Math.log(c));
	} else {
		tmp = y * i;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= 3.6e+92) or (not (y <= 1.55e+109) and (y <= 4.3e+176)):
		tmp = (z + a) + ((b + -0.5) * math.log(c))
	else:
		tmp = y * i
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= 3.6e+92) || (!(y <= 1.55e+109) && (y <= 4.3e+176)))
		tmp = Float64(Float64(z + a) + Float64(Float64(b + -0.5) * log(c)));
	else
		tmp = Float64(y * i);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= 3.6e+92) || (~((y <= 1.55e+109)) && (y <= 4.3e+176)))
		tmp = (z + a) + ((b + -0.5) * log(c));
	else
		tmp = y * i;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, 3.6e+92], And[N[Not[LessEqual[y, 1.55e+109]], $MachinePrecision], LessEqual[y, 4.3e+176]]], N[(N[(z + a), $MachinePrecision] + N[(N[(b + -0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.6e92 or 1.54999999999999996e109 < y < 4.30000000000000026e176

   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 79.3%

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

   4. Taylor expanded in t around 0 65.9%

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

   5. Taylor expanded in i around 0 54.4%

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

      1. associate-+r+ 54.4%

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

      2. +-commutative 54.4%

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

      3. sub-neg 54.4%

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

      4. metadata-eval 54.4%

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

      5. +-commutative 54.4%

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

   7. Simplified 54.4%

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

   if 3.6e92 < y < 1.54999999999999996e109 or 4.30000000000000026e176 < y

   1. Initial program 98.6%

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

   3. Taylor expanded in y around inf 65.0%

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

      1. *-commutative 65.0%

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

   5. Simplified 65.0%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.6 \cdot 10^{+92} \lor \neg \left(y \leq 1.55 \cdot 10^{+109}\right) \land y \leq 4.3 \cdot 10^{+176}:\\ \;\;\;\;\left(z + a\right) + \left(b + -0.5\right) \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 88.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+237} \lor \neg \left(x \leq 5 \cdot 10^{+231}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;a + \left(z + \left(y \cdot i + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -5e+237) (not (<= x 5e+231)))
   (* x (log y))
   (+ a (+ z (+ (* y i) (* (log c) (- b 0.5)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -5e+237) || !(x <= 5e+231)) {
		tmp = x * log(y);
	} else {
		tmp = a + (z + ((y * i) + (log(c) * (b - 0.5))));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
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 <= (-5d+237)) .or. (.not. (x <= 5d+231))) then
        tmp = x * log(y)
    else
        tmp = a + (z + ((y * i) + (log(c) * (b - 0.5d0))))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -5e+237) || !(x <= 5e+231)) {
		tmp = x * Math.log(y);
	} else {
		tmp = a + (z + ((y * i) + (Math.log(c) * (b - 0.5))));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -5e+237) or not (x <= 5e+231):
		tmp = x * math.log(y)
	else:
		tmp = a + (z + ((y * i) + (math.log(c) * (b - 0.5))))
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -5e+237) || !(x <= 5e+231))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(a + Float64(z + Float64(Float64(y * i) + Float64(log(c) * Float64(b - 0.5)))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -5e+237) || ~((x <= 5e+231)))
		tmp = x * log(y);
	else
		tmp = a + (z + ((y * i) + (log(c) * (b - 0.5))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -5e+237], N[Not[LessEqual[x, 5e+231]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(a + N[(z + N[(N[(y * i), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.0000000000000002e237 or 5.00000000000000028e231 < 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 x around inf 63.3%

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

   if -5.0000000000000002e237 < x < 5.00000000000000028e231

   1. Initial program 99.4%

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

   3. Taylor expanded in x around 0 91.4%

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

   4. Taylor expanded in t around 0 78.4%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+237} \lor \neg \left(x \leq 5 \cdot 10^{+231}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;a + \left(z + \left(y \cdot i + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 94.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+147} \lor \neg \left(x \leq 7.2 \cdot 10^{+171}\right):\\ \;\;\;\;\left(\left(x \cdot \log y + z\right) + \left(t + a\right)\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + \left(z + \left(y \cdot i + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -6.2e+147) (not (<= x 7.2e+171)))
   (+ (+ (+ (* x (log y)) z) (+ t a)) (* y i))
   (+ a (+ z (+ (* y i) (* (log c) (- b 0.5)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -6.2e+147) || !(x <= 7.2e+171)) {
		tmp = (((x * log(y)) + z) + (t + a)) + (y * i);
	} else {
		tmp = a + (z + ((y * i) + (log(c) * (b - 0.5))));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-6.2d+147)) .or. (.not. (x <= 7.2d+171))) then
        tmp = (((x * log(y)) + z) + (t + a)) + (y * i)
    else
        tmp = a + (z + ((y * i) + (log(c) * (b - 0.5d0))))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -6.2e+147) || !(x <= 7.2e+171)) {
		tmp = (((x * Math.log(y)) + z) + (t + a)) + (y * i);
	} else {
		tmp = a + (z + ((y * i) + (Math.log(c) * (b - 0.5))));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -6.2e+147) or not (x <= 7.2e+171):
		tmp = (((x * math.log(y)) + z) + (t + a)) + (y * i)
	else:
		tmp = a + (z + ((y * i) + (math.log(c) * (b - 0.5))))
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -6.2e+147) || !(x <= 7.2e+171))
		tmp = Float64(Float64(Float64(Float64(x * log(y)) + z) + Float64(t + a)) + Float64(y * i));
	else
		tmp = Float64(a + Float64(z + Float64(Float64(y * i) + Float64(log(c) * Float64(b - 0.5)))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -6.2e+147) || ~((x <= 7.2e+171)))
		tmp = (((x * log(y)) + z) + (t + a)) + (y * i);
	else
		tmp = a + (z + ((y * i) + (log(c) * (b - 0.5))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -6.2e+147], N[Not[LessEqual[x, 7.2e+171]], $MachinePrecision]], N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + N[(t + a), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(a + N[(z + N[(N[(y * i), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.2000000000000001e147 or 7.20000000000000036e171 < x

   1. Initial program 99.7%

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

      1. associate-+l+ 99.7%

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

      2. +-commutative 99.7%

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

      3. +-commutative 99.7%

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

      4. associate-+l+ 99.7%

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

      5. fma-define 99.8%

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

      6. sub-neg 99.8%

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

      7. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

      1. fma-define 99.7%

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

   6. Applied egg-rr 99.7%

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

      1. add-cube-cbrt 99.7%

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

      2. fma-define 99.7%

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

      3. pow2 99.7%

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

      4. *-commutative 99.7%

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

      5. *-commutative 99.7%

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

   8. Applied egg-rr 99.7%

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

   9. Taylor expanded in y around inf 94.2%

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

   if -6.2000000000000001e147 < x < 7.20000000000000036e171

   1. Initial program 99.4%

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

   3. Taylor expanded in x around 0 96.4%

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

   4. Taylor expanded in t around 0 81.7%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+147} \lor \neg \left(x \leq 7.2 \cdot 10^{+171}\right):\\ \;\;\;\;\left(\left(x \cdot \log y + z\right) + \left(t + a\right)\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + \left(z + \left(y \cdot i + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 77.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -5.7 \cdot 10^{+206}:\\ \;\;\;\;\left(z + a\right) + \left(b + -0.5\right) \cdot \log c\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{+129}:\\ \;\;\;\;a + \left(t + \left(z + \left(y \cdot i + -0.5 \cdot \log c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(y \cdot i + \log c \cdot \left(b - 0.5\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= b -5.7e+206)
   (+ (+ z a) (* (+ b -0.5) (log c)))
   (if (<= b 1.6e+129)
     (+ a (+ t (+ z (+ (* y i) (* -0.5 (log c))))))
     (+ a (+ (* y i) (* (log c) (- b 0.5)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (b <= -5.7e+206) {
		tmp = (z + a) + ((b + -0.5) * log(c));
	} else if (b <= 1.6e+129) {
		tmp = a + (t + (z + ((y * i) + (-0.5 * log(c)))));
	} else {
		tmp = a + ((y * i) + (log(c) * (b - 0.5)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (b <= (-5.7d+206)) then
        tmp = (z + a) + ((b + (-0.5d0)) * log(c))
    else if (b <= 1.6d+129) then
        tmp = a + (t + (z + ((y * i) + ((-0.5d0) * log(c)))))
    else
        tmp = a + ((y * i) + (log(c) * (b - 0.5d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (b <= -5.7e+206) {
		tmp = (z + a) + ((b + -0.5) * Math.log(c));
	} else if (b <= 1.6e+129) {
		tmp = a + (t + (z + ((y * i) + (-0.5 * Math.log(c)))));
	} else {
		tmp = a + ((y * i) + (Math.log(c) * (b - 0.5)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if b <= -5.7e+206:
		tmp = (z + a) + ((b + -0.5) * math.log(c))
	elif b <= 1.6e+129:
		tmp = a + (t + (z + ((y * i) + (-0.5 * math.log(c)))))
	else:
		tmp = a + ((y * i) + (math.log(c) * (b - 0.5)))
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (b <= -5.7e+206)
		tmp = Float64(Float64(z + a) + Float64(Float64(b + -0.5) * log(c)));
	elseif (b <= 1.6e+129)
		tmp = Float64(a + Float64(t + Float64(z + Float64(Float64(y * i) + Float64(-0.5 * log(c))))));
	else
		tmp = Float64(a + Float64(Float64(y * i) + Float64(log(c) * Float64(b - 0.5))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (b <= -5.7e+206)
		tmp = (z + a) + ((b + -0.5) * log(c));
	elseif (b <= 1.6e+129)
		tmp = a + (t + (z + ((y * i) + (-0.5 * log(c)))));
	else
		tmp = a + ((y * i) + (log(c) * (b - 0.5)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[b, -5.7e+206], N[(N[(z + a), $MachinePrecision] + N[(N[(b + -0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.6e+129], N[(a + N[(t + N[(z + N[(N[(y * i), $MachinePrecision] + N[(-0.5 * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(N[(y * i), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.6999999999999998e206

   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 95.9%

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

   4. Taylor expanded in t around 0 92.1%

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

   5. Taylor expanded in i around 0 84.7%

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

      1. associate-+r+ 84.7%

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

      2. +-commutative 84.7%

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

      3. sub-neg 84.7%

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

      4. metadata-eval 84.7%

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

      5. +-commutative 84.7%

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

   7. Simplified 84.7%

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

   if -5.6999999999999998e206 < b < 1.6000000000000001e129

   1. Initial program 99.9%

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

   3. Taylor expanded in b around 0 97.9%

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

      1. *-commutative 97.9%

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

   5. Simplified 97.9%

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

   6. Taylor expanded in x around 0 78.6%

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

   if 1.6000000000000001e129 < b

   1. Initial program 96.8%

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

   3. Taylor expanded in x around 0 86.6%

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

   4. Taylor expanded in t around 0 82.6%

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

   5. Taylor expanded in z around 0 72.4%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.7 \cdot 10^{+206}:\\ \;\;\;\;\left(z + a\right) + \left(b + -0.5\right) \cdot \log c\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{+129}:\\ \;\;\;\;a + \left(t + \left(z + \left(y \cdot i + -0.5 \cdot \log c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(y \cdot i + \log c \cdot \left(b - 0.5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 74.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+222}:\\ \;\;\;\;t + \left(z + \left(y \cdot i + -0.5 \cdot \log c\right)\right)\\ \mathbf{elif}\;z \leq -5 \cdot 10^{+86}:\\ \;\;\;\;a + \left(\left(z + t\right) + \left(b + -0.5\right) \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(y \cdot i + \log c \cdot \left(b - 0.5\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -1.15e+222)
   (+ t (+ z (+ (* y i) (* -0.5 (log c)))))
   (if (<= z -5e+86)
     (+ a (+ (+ z t) (* (+ b -0.5) (log c))))
     (+ a (+ (* y i) (* (log c) (- b 0.5)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -1.15e+222) {
		tmp = t + (z + ((y * i) + (-0.5 * log(c))));
	} else if (z <= -5e+86) {
		tmp = a + ((z + t) + ((b + -0.5) * log(c)));
	} else {
		tmp = a + ((y * i) + (log(c) * (b - 0.5)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
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 <= (-1.15d+222)) then
        tmp = t + (z + ((y * i) + ((-0.5d0) * log(c))))
    else if (z <= (-5d+86)) then
        tmp = a + ((z + t) + ((b + (-0.5d0)) * log(c)))
    else
        tmp = a + ((y * i) + (log(c) * (b - 0.5d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -1.15e+222) {
		tmp = t + (z + ((y * i) + (-0.5 * Math.log(c))));
	} else if (z <= -5e+86) {
		tmp = a + ((z + t) + ((b + -0.5) * Math.log(c)));
	} else {
		tmp = a + ((y * i) + (Math.log(c) * (b - 0.5)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -1.15e+222:
		tmp = t + (z + ((y * i) + (-0.5 * math.log(c))))
	elif z <= -5e+86:
		tmp = a + ((z + t) + ((b + -0.5) * math.log(c)))
	else:
		tmp = a + ((y * i) + (math.log(c) * (b - 0.5)))
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -1.15e+222)
		tmp = Float64(t + Float64(z + Float64(Float64(y * i) + Float64(-0.5 * log(c)))));
	elseif (z <= -5e+86)
		tmp = Float64(a + Float64(Float64(z + t) + Float64(Float64(b + -0.5) * log(c))));
	else
		tmp = Float64(a + Float64(Float64(y * i) + Float64(log(c) * Float64(b - 0.5))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -1.15e+222)
		tmp = t + (z + ((y * i) + (-0.5 * log(c))));
	elseif (z <= -5e+86)
		tmp = a + ((z + t) + ((b + -0.5) * log(c)));
	else
		tmp = a + ((y * i) + (log(c) * (b - 0.5)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -1.15e+222], N[(t + N[(z + N[(N[(y * i), $MachinePrecision] + N[(-0.5 * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5e+86], N[(a + N[(N[(z + t), $MachinePrecision] + N[(N[(b + -0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(N[(y * i), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.15000000000000005e222

   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 b around 0 100.0%

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

      1. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in a around 0 99.3%

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

   7. Taylor expanded in x around 0 92.7%

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

   if -1.15000000000000005e222 < z < -4.9999999999999998e86

   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 86.4%

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

   4. Taylor expanded in i around 0 78.0%

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

      1. associate-+r+ 78.0%

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

      2. sub-neg 78.0%

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

      3. metadata-eval 78.0%

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

   6. Simplified 78.0%

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

   if -4.9999999999999998e86 < z

   1. Initial program 99.3%

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

   3. Taylor expanded in x around 0 80.5%

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

   4. Taylor expanded in t around 0 69.3%

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

   5. Taylor expanded in z around 0 61.1%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+222}:\\ \;\;\;\;t + \left(z + \left(y \cdot i + -0.5 \cdot \log c\right)\right)\\ \mathbf{elif}\;z \leq -5 \cdot 10^{+86}:\\ \;\;\;\;a + \left(\left(z + t\right) + \left(b + -0.5\right) \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(y \cdot i + \log c \cdot \left(b - 0.5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 47.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;i \leq -1.35 \cdot 10^{+110} \lor \neg \left(i \leq 1.7 \cdot 10^{+131}\right):\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \log c \cdot \left(b - 0.5\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= i -1.35e+110) (not (<= i 1.7e+131)))
   (* y i)
   (+ a (+ t (* (log c) (- b 0.5))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((i <= -1.35e+110) || !(i <= 1.7e+131)) {
		tmp = y * i;
	} else {
		tmp = a + (t + (log(c) * (b - 0.5)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((i <= (-1.35d+110)) .or. (.not. (i <= 1.7d+131))) then
        tmp = y * i
    else
        tmp = a + (t + (log(c) * (b - 0.5d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((i <= -1.35e+110) || !(i <= 1.7e+131)) {
		tmp = y * i;
	} else {
		tmp = a + (t + (Math.log(c) * (b - 0.5)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (i <= -1.35e+110) or not (i <= 1.7e+131):
		tmp = y * i
	else:
		tmp = a + (t + (math.log(c) * (b - 0.5)))
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((i <= -1.35e+110) || !(i <= 1.7e+131))
		tmp = Float64(y * i);
	else
		tmp = Float64(a + Float64(t + Float64(log(c) * Float64(b - 0.5))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((i <= -1.35e+110) || ~((i <= 1.7e+131)))
		tmp = y * i;
	else
		tmp = a + (t + (log(c) * (b - 0.5)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[i, -1.35e+110], N[Not[LessEqual[i, 1.7e+131]], $MachinePrecision]], N[(y * i), $MachinePrecision], N[(a + N[(t + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -1.35000000000000005e110 or 1.69999999999999993e131 < i

   1. Initial program 98.9%

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

   3. Taylor expanded in y around inf 53.2%

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

      1. *-commutative 53.2%

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

   5. Simplified 53.2%

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

   if -1.35000000000000005e110 < i < 1.69999999999999993e131

   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%

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

      4. +-commutative 99.8%

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

      5. associate-+r+ 99.8%

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

      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%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 79.9%

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

      1. fma-define 79.9%

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

      2. sub-neg 79.9%

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

      3. metadata-eval 79.9%

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

   7. Simplified 79.9%

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

   8. Taylor expanded in x around 0 61.4%

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

   9. Taylor expanded in y around 0 51.0%

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

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.35 \cdot 10^{+110} \lor \neg \left(i \leq 1.7 \cdot 10^{+131}\right):\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \log c \cdot \left(b - 0.5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 73.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 41:\\ \;\;\;\;\left(z + a\right) + \left(b + -0.5\right) \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;a + \left(y \cdot i + \log c \cdot \left(b - 0.5\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 41.0)
   (+ (+ z a) (* (+ b -0.5) (log c)))
   (+ a (+ (* y i) (* (log c) (- b 0.5))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 41.0) {
		tmp = (z + a) + ((b + -0.5) * log(c));
	} else {
		tmp = a + ((y * i) + (log(c) * (b - 0.5)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= 41.0d0) then
        tmp = (z + a) + ((b + (-0.5d0)) * log(c))
    else
        tmp = a + ((y * i) + (log(c) * (b - 0.5d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 41.0) {
		tmp = (z + a) + ((b + -0.5) * Math.log(c));
	} else {
		tmp = a + ((y * i) + (Math.log(c) * (b - 0.5)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 41.0:
		tmp = (z + a) + ((b + -0.5) * math.log(c))
	else:
		tmp = a + ((y * i) + (math.log(c) * (b - 0.5)))
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 41.0)
		tmp = Float64(Float64(z + a) + Float64(Float64(b + -0.5) * log(c)));
	else
		tmp = Float64(a + Float64(Float64(y * i) + Float64(log(c) * Float64(b - 0.5))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= 41.0)
		tmp = (z + a) + ((b + -0.5) * log(c));
	else
		tmp = a + ((y * i) + (log(c) * (b - 0.5)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 41.0], N[(N[(z + a), $MachinePrecision] + N[(N[(b + -0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(N[(y * i), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 41

   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 75.7%

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

   4. Taylor expanded in t around 0 59.4%

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

   5. Taylor expanded in i around 0 55.3%

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

      1. associate-+r+ 55.3%

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

      2. +-commutative 55.3%

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

      3. sub-neg 55.3%

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

      4. metadata-eval 55.3%

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

      5. +-commutative 55.3%

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

   7. Simplified 55.3%

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

   if 41 < y

   1. Initial program 99.1%

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

   3. Taylor expanded in x around 0 88.8%

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

   4. Taylor expanded in t around 0 82.0%

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

   5. Taylor expanded in z around 0 67.5%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 41:\\ \;\;\;\;\left(z + a\right) + \left(b + -0.5\right) \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;a + \left(y \cdot i + \log c \cdot \left(b - 0.5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 73.6% accurate, 1.9× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 6.0)
   (+ a (+ (+ z t) (* (+ b -0.5) (log c))))
   (+ a (+ (* y i) (* (log c) (- b 0.5))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 6.0) {
		tmp = a + ((z + t) + ((b + -0.5) * log(c)));
	} else {
		tmp = a + ((y * i) + (log(c) * (b - 0.5)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= 6.0d0) then
        tmp = a + ((z + t) + ((b + (-0.5d0)) * log(c)))
    else
        tmp = a + ((y * i) + (log(c) * (b - 0.5d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 6.0) {
		tmp = a + ((z + t) + ((b + -0.5) * Math.log(c)));
	} else {
		tmp = a + ((y * i) + (Math.log(c) * (b - 0.5)));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 6.0:
		tmp = a + ((z + t) + ((b + -0.5) * math.log(c)))
	else:
		tmp = a + ((y * i) + (math.log(c) * (b - 0.5)))
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 6.0)
		tmp = Float64(a + Float64(Float64(z + t) + Float64(Float64(b + -0.5) * log(c))));
	else
		tmp = Float64(a + Float64(Float64(y * i) + Float64(log(c) * Float64(b - 0.5))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= 6.0)
		tmp = a + ((z + t) + ((b + -0.5) * log(c)));
	else
		tmp = a + ((y * i) + (log(c) * (b - 0.5)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 6.0], N[(a + N[(N[(z + t), $MachinePrecision] + N[(N[(b + -0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(N[(y * i), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 6

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 75.7%

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

   4. Taylor expanded in i around 0 71.6%

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

      1. associate-+r+ 71.6%

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

      2. sub-neg 71.6%

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

      3. metadata-eval 71.6%

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

   6. Simplified 71.6%

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

   if 6 < y

   1. Initial program 99.1%

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

   3. Taylor expanded in x around 0 88.8%

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

   4. Taylor expanded in t around 0 82.0%

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

   5. Taylor expanded in z around 0 67.5%

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

4. Final simplification 69.5%

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

Alternative 15: 38.6% accurate, 6.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 9.5 \cdot 10^{-304}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-225}:\\ \;\;\;\;y \cdot i\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-158}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+140} \lor \neg \left(a \leq 1.72 \cdot 10^{+193}\right) \land a \leq 1.12 \cdot 10^{+204}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 9.5e-304)
   z
   (if (<= a 1.35e-225)
     (* y i)
     (if (<= a 3.6e-158)
       z
       (if (or (<= a 1.55e+140) (and (not (<= a 1.72e+193)) (<= a 1.12e+204)))
         (* y i)
         a)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 9.5e-304) {
		tmp = z;
	} else if (a <= 1.35e-225) {
		tmp = y * i;
	} else if (a <= 3.6e-158) {
		tmp = z;
	} else if ((a <= 1.55e+140) || (!(a <= 1.72e+193) && (a <= 1.12e+204))) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 9.5d-304) then
        tmp = z
    else if (a <= 1.35d-225) then
        tmp = y * i
    else if (a <= 3.6d-158) then
        tmp = z
    else if ((a <= 1.55d+140) .or. (.not. (a <= 1.72d+193)) .and. (a <= 1.12d+204)) then
        tmp = y * i
    else
        tmp = a
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 9.5e-304) {
		tmp = z;
	} else if (a <= 1.35e-225) {
		tmp = y * i;
	} else if (a <= 3.6e-158) {
		tmp = z;
	} else if ((a <= 1.55e+140) || (!(a <= 1.72e+193) && (a <= 1.12e+204))) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 9.5e-304:
		tmp = z
	elif a <= 1.35e-225:
		tmp = y * i
	elif a <= 3.6e-158:
		tmp = z
	elif (a <= 1.55e+140) or (not (a <= 1.72e+193) and (a <= 1.12e+204)):
		tmp = y * i
	else:
		tmp = a
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 9.5e-304)
		tmp = z;
	elseif (a <= 1.35e-225)
		tmp = Float64(y * i);
	elseif (a <= 3.6e-158)
		tmp = z;
	elseif ((a <= 1.55e+140) || (!(a <= 1.72e+193) && (a <= 1.12e+204)))
		tmp = Float64(y * i);
	else
		tmp = a;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 9.5e-304)
		tmp = z;
	elseif (a <= 1.35e-225)
		tmp = y * i;
	elseif (a <= 3.6e-158)
		tmp = z;
	elseif ((a <= 1.55e+140) || (~((a <= 1.72e+193)) && (a <= 1.12e+204)))
		tmp = y * i;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 9.5e-304], z, If[LessEqual[a, 1.35e-225], N[(y * i), $MachinePrecision], If[LessEqual[a, 3.6e-158], z, If[Or[LessEqual[a, 1.55e+140], And[N[Not[LessEqual[a, 1.72e+193]], $MachinePrecision], LessEqual[a, 1.12e+204]]], N[(y * i), $MachinePrecision], a]]]]

Derivation

1. Split input into 3 regimes

2. if a < 9.50000000000000023e-304 or 1.34999999999999996e-225 < a < 3.59999999999999991e-158

   1. Initial program 99.1%

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

   3. Taylor expanded in z around inf 18.2%

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

   if 9.50000000000000023e-304 < a < 1.34999999999999996e-225 or 3.59999999999999991e-158 < a < 1.55e140 or 1.7199999999999999e193 < a < 1.11999999999999996e204

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 27.3%

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

      1. *-commutative 27.3%

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

   5. Simplified 27.3%

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

   if 1.55e140 < a < 1.7199999999999999e193 or 1.11999999999999996e204 < a

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 54.4%

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

4. Final simplification 26.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 9.5 \cdot 10^{-304}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-225}:\\ \;\;\;\;y \cdot i\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-158}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+140} \lor \neg \left(a \leq 1.72 \cdot 10^{+193}\right) \land a \leq 1.12 \cdot 10^{+204}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 37.8% accurate, 36.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 2.9 \cdot 10^{+162}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i) :precision binary64 (if (<= a 2.9e+162) z a))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c && c < i);
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 2.9e+162) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 2.9d+162) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c && c < i;
public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 2.9e+162) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 2.9e+162:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 2.9e+162)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 2.9e+162)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 2.9e+162], z, a]

Derivation

1. Split input into 2 regimes

2. if a < 2.90000000000000006e162

   1. Initial program 99.4%

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

   3. Taylor expanded in z around inf 18.5%

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

   if 2.90000000000000006e162 < a

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 51.1%

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

4. Final simplification 23.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 2.9 \cdot 10^{+162}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 22.6% accurate, 219.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ a \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c i) :precision binary64 a)

C

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

Fortran

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
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

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

Python

[x, y, z, t, a, b, c, i] = sort([x, y, z, t, a, b, c, i])
def code(x, y, z, t, a, b, c, i):
	return a

Julia

x, y, z, t, a, b, c, i = sort([x, y, z, t, a, b, c, i])
function code(x, y, z, t, a, b, c, i)
	return a
end

MATLAB

x, y, z, t, a, b, c, i = num2cell(sort([x, y, z, t, a, b, c, i])){:}
function tmp = code(x, y, z, t, a, b, c, i)
	tmp = a;
end

Wolfram

NOTE: x, y, z, t, a, b, c, and i should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_, i_] := a

Derivation

1. Initial program 99.5%

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

3. Taylor expanded in a around inf 15.7%

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

4. Final simplification 15.7%

   \[\leadsto a \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024053 
(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)))