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

Percentage Accurate: 99.8% → 99.8%

Time: 17.9s

Alternatives: 17

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.4× speedup

Math

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

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 99.9%

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

   1. associate-+l+ 99.9%

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

   2. associate-+l+ 99.9%

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

   3. +-commutative 99.9%

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

   4. +-commutative 99.9%

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

   5. associate-+r+ 99.9%

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

   6. associate-+l+ 99.9%

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

   7. +-commutative 99.9%

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

   8. associate-+l+ 99.9%

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

   9. +-commutative 99.9%

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

   10. fma-def 99.9%

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

   11. +-commutative 99.9%

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

   12. fma-def 99.9%

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

   13. sub-neg 99.9%

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

   14. metadata-eval 99.9%

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

   15. +-commutative 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

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 + (t + (z + (x * log(y))))) + (log(c) * (b - 0.5d0))) + (y * i)
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 + (t + (z + (x * Math.log(y))))) + (Math.log(c) * (b - 0.5))) + (y * i);
}

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 + (t + (z + (x * math.log(y))))) + (math.log(c) * (b - 0.5))) + (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)
	return Float64(Float64(Float64(a + Float64(t + Float64(z + Float64(x * log(y))))) + Float64(log(c) * Float64(b - 0.5))) + Float64(y * i))
end

MATLAB

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 + (t + (z + (x * log(y))))) + (log(c) * (b - 0.5))) + (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_] := N[(N[(N[(a + N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

2. Final simplification 99.9%

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

Alternative 3: 92.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+80}:\\ \;\;\;\;y \cdot i + \left(\left(t + a\right) + \mathsf{fma}\left(x, \log y, z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(x \cdot \log y + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \end{array} \end{array} \]

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 (<= z -3.5e+80)
   (+ (* y i) (+ (+ t a) (fma x (log y) z)))
   (+ (* y i) (+ a (+ (* x (log y)) (* (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 <= -3.5e+80) {
		tmp = (y * i) + ((t + a) + fma(x, log(y), z));
	} else {
		tmp = (y * i) + (a + ((x * log(y)) + (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 <= -3.5e+80)
		tmp = Float64(Float64(y * i) + Float64(Float64(t + a) + fma(x, log(y), z)));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(Float64(x * log(y)) + Float64(log(c) * Float64(b - 0.5)))));
	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[LessEqual[z, -3.5e+80], N[(N[(y * i), $MachinePrecision] + N[(N[(t + a), $MachinePrecision] + N[(x * N[Log[y], $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.49999999999999994e80

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. fma-def 99.9%

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

      4. sub-neg 99.9%

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

      5. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 90.7%

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

      1. *-commutative 90.7%

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

   6. Simplified 90.7%

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

   if -3.49999999999999994e80 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 86.5%

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

   3. Taylor expanded in z around 0 80.3%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+80}:\\ \;\;\;\;y \cdot i + \left(\left(t + a\right) + \mathsf{fma}\left(x, \log y, z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(x \cdot \log y + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \end{array} \]

Alternative 4: 99.0% accurate, 1.0× speedup

Math

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

FPCore

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

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 = (y * i) + (a + (z + ((x * log(y)) + (log(c) * (b - 0.5d0)))))
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 (y * i) + (a + (z + ((x * Math.log(y)) + (Math.log(c) * (b - 0.5)))));
}

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 (y * i) + (a + (z + ((x * math.log(y)) + (math.log(c) * (b - 0.5)))))

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(y * i) + Float64(a + Float64(z + Float64(Float64(x * log(y)) + Float64(log(c) * Float64(b - 0.5))))))
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 = (y * i) + (a + (z + ((x * log(y)) + (log(c) * (b - 0.5)))));
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[(y * i), $MachinePrecision] + N[(a + N[(z + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in t around 0 86.0%

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

3. Final simplification 86.0%

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

Alternative 5: 93.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1460 \lor \neg \left(x \leq 9.8 \cdot 10^{+35}\right):\\ \;\;\;\;y \cdot i + \left(\left(t + a\right) + \mathsf{fma}\left(x, \log y, z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

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 -1460.0) (not (<= x 9.8e+35)))
   (+ (* y i) (+ (+ t a) (fma x (log y) z)))
   (+ (* y i) (+ (* (log c) (- b 0.5)) (+ a (+ z t))))))

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 <= -1460.0) || !(x <= 9.8e+35)) {
		tmp = (y * i) + ((t + a) + fma(x, log(y), z));
	} else {
		tmp = (y * i) + ((log(c) * (b - 0.5)) + (a + (z + t)));
	}
	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 <= -1460.0) || !(x <= 9.8e+35))
		tmp = Float64(Float64(y * i) + Float64(Float64(t + a) + fma(x, log(y), z)));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(log(c) * Float64(b - 0.5)) + Float64(a + Float64(z + t))));
	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, -1460.0], N[Not[LessEqual[x, 9.8e+35]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(N[(t + a), $MachinePrecision] + N[(x * N[Log[y], $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1460 or 9.8000000000000005e35 < x

   1. Initial program 99.8%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. 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. fma-def 99.8%

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

      4. sub-neg 99.8%

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

      5. 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. Taylor expanded in y around inf 93.6%

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

      1. *-commutative 93.6%

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

   6. Simplified 93.6%

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

   if -1460 < x < 9.8000000000000005e35

   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. Taylor expanded in x around 0 99.1%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1460 \lor \neg \left(x \leq 9.8 \cdot 10^{+35}\right):\\ \;\;\;\;y \cdot i + \left(\left(t + a\right) + \mathsf{fma}\left(x, \log y, z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \]

Alternative 6: 90.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+103} \lor \neg \left(x \leq 2.35 \cdot 10^{+191}\right):\\ \;\;\;\;y \cdot i + \left(a + x \cdot \log y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

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+103) (not (<= x 2.35e+191)))
   (+ (* y i) (+ a (* x (log y))))
   (+ (* y i) (+ (* (log c) (- b 0.5)) (+ a (+ z t))))))

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+103) || !(x <= 2.35e+191)) {
		tmp = (y * i) + (a + (x * log(y)));
	} else {
		tmp = (y * i) + ((log(c) * (b - 0.5)) + (a + (z + t)));
	}
	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+103)) .or. (.not. (x <= 2.35d+191))) then
        tmp = (y * i) + (a + (x * log(y)))
    else
        tmp = (y * i) + ((log(c) * (b - 0.5d0)) + (a + (z + t)))
    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+103) || !(x <= 2.35e+191)) {
		tmp = (y * i) + (a + (x * Math.log(y)));
	} else {
		tmp = (y * i) + ((Math.log(c) * (b - 0.5)) + (a + (z + t)));
	}
	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+103) or not (x <= 2.35e+191):
		tmp = (y * i) + (a + (x * math.log(y)))
	else:
		tmp = (y * i) + ((math.log(c) * (b - 0.5)) + (a + (z + t)))
	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+103) || !(x <= 2.35e+191))
		tmp = Float64(Float64(y * i) + Float64(a + Float64(x * log(y))));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(log(c) * Float64(b - 0.5)) + Float64(a + Float64(z + t))));
	end
	return tmp
end

MATLAB

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+103) || ~((x <= 2.35e+191)))
		tmp = (y * i) + (a + (x * log(y)));
	else
		tmp = (y * i) + ((log(c) * (b - 0.5)) + (a + (z + t)));
	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+103], N[Not[LessEqual[x, 2.35e+191]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(a + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.50000000000000001e103 or 2.35000000000000005e191 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 94.1%

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

   3. Taylor expanded in x around inf 81.8%

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

   if -4.50000000000000001e103 < x < 2.35000000000000005e191

   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. Taylor expanded in x around 0 93.3%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+103} \lor \neg \left(x \leq 2.35 \cdot 10^{+191}\right):\\ \;\;\;\;y \cdot i + \left(a + x \cdot \log y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \]

Alternative 7: 74.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := \left(t + a\right) + \left(z + y \cdot i\right)\\ t_2 := y \cdot i + \left(a + x \cdot \log y\right)\\ \mathbf{if}\;x \leq -3.3 \cdot 10^{+103}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.15 \cdot 10^{-111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-34}:\\ \;\;\;\;a + \left(b \cdot \log c + \left(z + t\right)\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+126}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

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 (+ (+ t a) (+ z (* y i)))) (t_2 (+ (* y i) (+ a (* x (log y))))))
   (if (<= x -3.3e+103)
     t_2
     (if (<= x -2.15e-111)
       t_1
       (if (<= x 7.6e-34)
         (+ a (+ (* b (log c)) (+ z t)))
         (if (<= x 9e+126) t_1 t_2))))))

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 = (t + a) + (z + (y * i));
	double t_2 = (y * i) + (a + (x * log(y)));
	double tmp;
	if (x <= -3.3e+103) {
		tmp = t_2;
	} else if (x <= -2.15e-111) {
		tmp = t_1;
	} else if (x <= 7.6e-34) {
		tmp = a + ((b * log(c)) + (z + t));
	} else if (x <= 9e+126) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t + a) + (z + (y * i))
    t_2 = (y * i) + (a + (x * log(y)))
    if (x <= (-3.3d+103)) then
        tmp = t_2
    else if (x <= (-2.15d-111)) then
        tmp = t_1
    else if (x <= 7.6d-34) then
        tmp = a + ((b * log(c)) + (z + t))
    else if (x <= 9d+126) then
        tmp = t_1
    else
        tmp = t_2
    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 t_1 = (t + a) + (z + (y * i));
	double t_2 = (y * i) + (a + (x * Math.log(y)));
	double tmp;
	if (x <= -3.3e+103) {
		tmp = t_2;
	} else if (x <= -2.15e-111) {
		tmp = t_1;
	} else if (x <= 7.6e-34) {
		tmp = a + ((b * Math.log(c)) + (z + t));
	} else if (x <= 9e+126) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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):
	t_1 = (t + a) + (z + (y * i))
	t_2 = (y * i) + (a + (x * math.log(y)))
	tmp = 0
	if x <= -3.3e+103:
		tmp = t_2
	elif x <= -2.15e-111:
		tmp = t_1
	elif x <= 7.6e-34:
		tmp = a + ((b * math.log(c)) + (z + t))
	elif x <= 9e+126:
		tmp = t_1
	else:
		tmp = t_2
	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)
	t_1 = Float64(Float64(t + a) + Float64(z + Float64(y * i)))
	t_2 = Float64(Float64(y * i) + Float64(a + Float64(x * log(y))))
	tmp = 0.0
	if (x <= -3.3e+103)
		tmp = t_2;
	elseif (x <= -2.15e-111)
		tmp = t_1;
	elseif (x <= 7.6e-34)
		tmp = Float64(a + Float64(Float64(b * log(c)) + Float64(z + t)));
	elseif (x <= 9e+126)
		tmp = t_1;
	else
		tmp = t_2;
	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)
	t_1 = (t + a) + (z + (y * i));
	t_2 = (y * i) + (a + (x * log(y)));
	tmp = 0.0;
	if (x <= -3.3e+103)
		tmp = t_2;
	elseif (x <= -2.15e-111)
		tmp = t_1;
	elseif (x <= 7.6e-34)
		tmp = a + ((b * log(c)) + (z + t));
	elseif (x <= 9e+126)
		tmp = t_1;
	else
		tmp = t_2;
	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_] := Block[{t$95$1 = N[(N[(t + a), $MachinePrecision] + N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * i), $MachinePrecision] + N[(a + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.3e+103], t$95$2, If[LessEqual[x, -2.15e-111], t$95$1, If[LessEqual[x, 7.6e-34], N[(a + N[(N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision] + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9e+126], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.30000000000000009e103 or 8.99999999999999947e126 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 92.6%

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

   3. Taylor expanded in x around inf 79.7%

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

   if -3.30000000000000009e103 < x < -2.1499999999999999e-111 or 7.6000000000000002e-34 < x < 8.99999999999999947e126

   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. Taylor expanded in x around 0 89.1%

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

   3. Taylor expanded in b around inf 88.2%

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

      1. *-commutative 88.2%

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

   5. Simplified 88.2%

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

   6. Taylor expanded in b around 0 79.7%

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

      1. associate-+r+ 79.7%

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

      2. *-commutative 79.7%

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

   8. Simplified 79.7%

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

   if -2.1499999999999999e-111 < x < 7.6000000000000002e-34

   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. Taylor expanded in x around 0 99.9%

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

   3. Taylor expanded in b around inf 97.9%

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

      1. *-commutative 97.9%

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

   5. Simplified 97.9%

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

   6. Taylor expanded in y around 0 80.4%

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

      1. associate-+r+ 80.4%

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

   8. Simplified 80.4%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{+103}:\\ \;\;\;\;y \cdot i + \left(a + x \cdot \log y\right)\\ \mathbf{elif}\;x \leq -2.15 \cdot 10^{-111}:\\ \;\;\;\;\left(t + a\right) + \left(z + y \cdot i\right)\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-34}:\\ \;\;\;\;a + \left(b \cdot \log c + \left(z + t\right)\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+126}:\\ \;\;\;\;\left(t + a\right) + \left(z + y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + x \cdot \log y\right)\\ \end{array} \]

Alternative 8: 75.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} t_1 := \left(t + a\right) + \left(z + y \cdot i\right)\\ t_2 := y \cdot i + \left(a + x \cdot \log y\right)\\ \mathbf{if}\;x \leq -4.5 \cdot 10^{+103}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-112}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-34}:\\ \;\;\;\;a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+128}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

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 (+ (+ t a) (+ z (* y i)))) (t_2 (+ (* y i) (+ a (* x (log y))))))
   (if (<= x -4.5e+103)
     t_2
     (if (<= x -7e-112)
       t_1
       (if (<= x 2.1e-34)
         (+ a (+ t (+ z (* (log c) (- b 0.5)))))
         (if (<= x 2.2e+128) t_1 t_2))))))

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 = (t + a) + (z + (y * i));
	double t_2 = (y * i) + (a + (x * log(y)));
	double tmp;
	if (x <= -4.5e+103) {
		tmp = t_2;
	} else if (x <= -7e-112) {
		tmp = t_1;
	} else if (x <= 2.1e-34) {
		tmp = a + (t + (z + (log(c) * (b - 0.5))));
	} else if (x <= 2.2e+128) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t + a) + (z + (y * i))
    t_2 = (y * i) + (a + (x * log(y)))
    if (x <= (-4.5d+103)) then
        tmp = t_2
    else if (x <= (-7d-112)) then
        tmp = t_1
    else if (x <= 2.1d-34) then
        tmp = a + (t + (z + (log(c) * (b - 0.5d0))))
    else if (x <= 2.2d+128) then
        tmp = t_1
    else
        tmp = t_2
    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 t_1 = (t + a) + (z + (y * i));
	double t_2 = (y * i) + (a + (x * Math.log(y)));
	double tmp;
	if (x <= -4.5e+103) {
		tmp = t_2;
	} else if (x <= -7e-112) {
		tmp = t_1;
	} else if (x <= 2.1e-34) {
		tmp = a + (t + (z + (Math.log(c) * (b - 0.5))));
	} else if (x <= 2.2e+128) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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):
	t_1 = (t + a) + (z + (y * i))
	t_2 = (y * i) + (a + (x * math.log(y)))
	tmp = 0
	if x <= -4.5e+103:
		tmp = t_2
	elif x <= -7e-112:
		tmp = t_1
	elif x <= 2.1e-34:
		tmp = a + (t + (z + (math.log(c) * (b - 0.5))))
	elif x <= 2.2e+128:
		tmp = t_1
	else:
		tmp = t_2
	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)
	t_1 = Float64(Float64(t + a) + Float64(z + Float64(y * i)))
	t_2 = Float64(Float64(y * i) + Float64(a + Float64(x * log(y))))
	tmp = 0.0
	if (x <= -4.5e+103)
		tmp = t_2;
	elseif (x <= -7e-112)
		tmp = t_1;
	elseif (x <= 2.1e-34)
		tmp = Float64(a + Float64(t + Float64(z + Float64(log(c) * Float64(b - 0.5)))));
	elseif (x <= 2.2e+128)
		tmp = t_1;
	else
		tmp = t_2;
	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)
	t_1 = (t + a) + (z + (y * i));
	t_2 = (y * i) + (a + (x * log(y)));
	tmp = 0.0;
	if (x <= -4.5e+103)
		tmp = t_2;
	elseif (x <= -7e-112)
		tmp = t_1;
	elseif (x <= 2.1e-34)
		tmp = a + (t + (z + (log(c) * (b - 0.5))));
	elseif (x <= 2.2e+128)
		tmp = t_1;
	else
		tmp = t_2;
	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_] := Block[{t$95$1 = N[(N[(t + a), $MachinePrecision] + N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * i), $MachinePrecision] + N[(a + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.5e+103], t$95$2, If[LessEqual[x, -7e-112], t$95$1, If[LessEqual[x, 2.1e-34], N[(a + N[(t + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.2e+128], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.50000000000000001e103 or 2.20000000000000017e128 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 92.6%

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

   3. Taylor expanded in x around inf 79.7%

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

   if -4.50000000000000001e103 < x < -6.99999999999999988e-112 or 2.1000000000000001e-34 < x < 2.20000000000000017e128

   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. Taylor expanded in x around 0 89.1%

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

   3. Taylor expanded in b around inf 88.2%

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

      1. *-commutative 88.2%

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

   5. Simplified 88.2%

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

   6. Taylor expanded in b around 0 79.7%

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

      1. associate-+r+ 79.7%

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

      2. *-commutative 79.7%

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

   8. Simplified 79.7%

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

   if -6.99999999999999988e-112 < x < 2.1000000000000001e-34

   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. Taylor expanded in x around 0 99.9%

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

   3. Taylor expanded in y around 0 82.5%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+103}:\\ \;\;\;\;y \cdot i + \left(a + x \cdot \log y\right)\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-112}:\\ \;\;\;\;\left(t + a\right) + \left(z + y \cdot i\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-34}:\\ \;\;\;\;a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+128}:\\ \;\;\;\;\left(t + a\right) + \left(z + y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + x \cdot \log y\right)\\ \end{array} \]

Alternative 9: 89.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+103} \lor \neg \left(x \leq 1.12 \cdot 10^{+177}\right):\\ \;\;\;\;y \cdot i + \left(a + x \cdot \log y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(a + \left(z + t\right)\right) + b \cdot \log c\right)\\ \end{array} \end{array} \]

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 -2.5e+103) (not (<= x 1.12e+177)))
   (+ (* y i) (+ a (* x (log y))))
   (+ (* y i) (+ (+ a (+ z t)) (* 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) {
	double tmp;
	if ((x <= -2.5e+103) || !(x <= 1.12e+177)) {
		tmp = (y * i) + (a + (x * log(y)));
	} else {
		tmp = (y * i) + ((a + (z + t)) + (b * log(c)));
	}
	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 <= (-2.5d+103)) .or. (.not. (x <= 1.12d+177))) then
        tmp = (y * i) + (a + (x * log(y)))
    else
        tmp = (y * i) + ((a + (z + t)) + (b * log(c)))
    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 <= -2.5e+103) || !(x <= 1.12e+177)) {
		tmp = (y * i) + (a + (x * Math.log(y)));
	} else {
		tmp = (y * i) + ((a + (z + t)) + (b * Math.log(c)));
	}
	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 <= -2.5e+103) or not (x <= 1.12e+177):
		tmp = (y * i) + (a + (x * math.log(y)))
	else:
		tmp = (y * i) + ((a + (z + t)) + (b * math.log(c)))
	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 <= -2.5e+103) || !(x <= 1.12e+177))
		tmp = Float64(Float64(y * i) + Float64(a + Float64(x * log(y))));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(a + Float64(z + t)) + Float64(b * log(c))));
	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 <= -2.5e+103) || ~((x <= 1.12e+177)))
		tmp = (y * i) + (a + (x * log(y)));
	else
		tmp = (y * i) + ((a + (z + t)) + (b * log(c)));
	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, -2.5e+103], N[Not[LessEqual[x, 1.12e+177]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(a + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.5e103 or 1.1200000000000001e177 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 94.1%

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

   3. Taylor expanded in x around inf 81.8%

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

   if -2.5e103 < x < 1.1200000000000001e177

   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. Taylor expanded in x around 0 93.3%

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

   3. Taylor expanded in b around inf 91.9%

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

      1. *-commutative 91.9%

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

   5. Simplified 91.9%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+103} \lor \neg \left(x \leq 1.12 \cdot 10^{+177}\right):\\ \;\;\;\;y \cdot i + \left(a + x \cdot \log y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(a + \left(z + t\right)\right) + b \cdot \log c\right)\\ \end{array} \]

Alternative 10: 75.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.36 \cdot 10^{+191} \lor \neg \left(b \leq 9.2 \cdot 10^{+83}\right):\\ \;\;\;\;a + \left(b \cdot \log c + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t + a\right) + \left(z + y \cdot i\right)\\ \end{array} \end{array} \]

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
 (if (or (<= b -1.36e+191) (not (<= b 9.2e+83)))
   (+ a (+ (* b (log c)) (+ z t)))
   (+ (+ t a) (+ z (* 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 ((b <= -1.36e+191) || !(b <= 9.2e+83)) {
		tmp = a + ((b * log(c)) + (z + t));
	} else {
		tmp = (t + a) + (z + (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 ((b <= (-1.36d+191)) .or. (.not. (b <= 9.2d+83))) then
        tmp = a + ((b * log(c)) + (z + t))
    else
        tmp = (t + a) + (z + (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 ((b <= -1.36e+191) || !(b <= 9.2e+83)) {
		tmp = a + ((b * Math.log(c)) + (z + t));
	} else {
		tmp = (t + a) + (z + (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 (b <= -1.36e+191) or not (b <= 9.2e+83):
		tmp = a + ((b * math.log(c)) + (z + t))
	else:
		tmp = (t + a) + (z + (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 ((b <= -1.36e+191) || !(b <= 9.2e+83))
		tmp = Float64(a + Float64(Float64(b * log(c)) + Float64(z + t)));
	else
		tmp = Float64(Float64(t + a) + Float64(z + 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 ((b <= -1.36e+191) || ~((b <= 9.2e+83)))
		tmp = a + ((b * log(c)) + (z + t));
	else
		tmp = (t + a) + (z + (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[b, -1.36e+191], N[Not[LessEqual[b, 9.2e+83]], $MachinePrecision]], N[(a + N[(N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision] + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + a), $MachinePrecision] + N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.36e191 or 9.1999999999999998e83 < b

   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. Taylor expanded in x around 0 90.0%

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

   3. Taylor expanded in b around inf 90.0%

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

      1. *-commutative 90.0%

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

   5. Simplified 90.0%

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

   6. Taylor expanded in y around 0 78.2%

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

      1. associate-+r+ 78.2%

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

   8. Simplified 78.2%

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

   if -1.36e191 < b < 9.1999999999999998e83

   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. Taylor expanded in x around 0 78.9%

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

   3. Taylor expanded in b around inf 77.5%

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

      1. *-commutative 77.5%

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

   5. Simplified 77.5%

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

   6. Taylor expanded in b around 0 74.9%

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

      1. associate-+r+ 74.9%

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

      2. *-commutative 74.9%

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

   8. Simplified 74.9%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.36 \cdot 10^{+191} \lor \neg \left(b \leq 9.2 \cdot 10^{+83}\right):\\ \;\;\;\;a + \left(b \cdot \log c + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t + a\right) + \left(z + y \cdot i\right)\\ \end{array} \]

Alternative 11: 73.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{+191} \lor \neg \left(b \leq 3 \cdot 10^{+218}\right):\\ \;\;\;\;a + \left(t + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t + a\right) + \left(z + y \cdot i\right)\\ \end{array} \end{array} \]

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
 (if (or (<= b -9.5e+191) (not (<= b 3e+218)))
   (+ a (+ t (* b (log c))))
   (+ (+ t a) (+ z (* 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 ((b <= -9.5e+191) || !(b <= 3e+218)) {
		tmp = a + (t + (b * log(c)));
	} else {
		tmp = (t + a) + (z + (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 ((b <= (-9.5d+191)) .or. (.not. (b <= 3d+218))) then
        tmp = a + (t + (b * log(c)))
    else
        tmp = (t + a) + (z + (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 ((b <= -9.5e+191) || !(b <= 3e+218)) {
		tmp = a + (t + (b * Math.log(c)));
	} else {
		tmp = (t + a) + (z + (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 (b <= -9.5e+191) or not (b <= 3e+218):
		tmp = a + (t + (b * math.log(c)))
	else:
		tmp = (t + a) + (z + (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 ((b <= -9.5e+191) || !(b <= 3e+218))
		tmp = Float64(a + Float64(t + Float64(b * log(c))));
	else
		tmp = Float64(Float64(t + a) + Float64(z + 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 ((b <= -9.5e+191) || ~((b <= 3e+218)))
		tmp = a + (t + (b * log(c)));
	else
		tmp = (t + a) + (z + (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[b, -9.5e+191], N[Not[LessEqual[b, 3e+218]], $MachinePrecision]], N[(a + N[(t + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t + a), $MachinePrecision] + N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -9.4999999999999998e191 or 3.0000000000000001e218 < b

   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. Taylor expanded in x around 0 98.3%

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

   3. Taylor expanded in y around 0 88.9%

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

   4. Taylor expanded in b around inf 86.1%

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

      1. *-commutative 86.1%

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

   6. Simplified 86.1%

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

   if -9.4999999999999998e191 < b < 3.0000000000000001e218

   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. Taylor expanded in x around 0 79.0%

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

   3. Taylor expanded in b around inf 77.8%

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

      1. *-commutative 77.8%

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

   5. Simplified 77.8%

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

   6. Taylor expanded in b around 0 71.3%

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

      1. associate-+r+ 71.3%

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

      2. *-commutative 71.3%

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

   8. Simplified 71.3%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{+191} \lor \neg \left(b \leq 3 \cdot 10^{+218}\right):\\ \;\;\;\;a + \left(t + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t + a\right) + \left(z + y \cdot i\right)\\ \end{array} \]

Alternative 12: 39.0% accurate, 19.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 1.1 \cdot 10^{-247}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-155}:\\ \;\;\;\;y \cdot i\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+29}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+159}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

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 1.1e-247)
   z
   (if (<= a 2.7e-155)
     (* y i)
     (if (<= a 1.3e+29) z (if (<= a 6.5e+159) (* 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 <= 1.1e-247) {
		tmp = z;
	} else if (a <= 2.7e-155) {
		tmp = y * i;
	} else if (a <= 1.3e+29) {
		tmp = z;
	} else if (a <= 6.5e+159) {
		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 <= 1.1d-247) then
        tmp = z
    else if (a <= 2.7d-155) then
        tmp = y * i
    else if (a <= 1.3d+29) then
        tmp = z
    else if (a <= 6.5d+159) 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 <= 1.1e-247) {
		tmp = z;
	} else if (a <= 2.7e-155) {
		tmp = y * i;
	} else if (a <= 1.3e+29) {
		tmp = z;
	} else if (a <= 6.5e+159) {
		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 <= 1.1e-247:
		tmp = z
	elif a <= 2.7e-155:
		tmp = y * i
	elif a <= 1.3e+29:
		tmp = z
	elif a <= 6.5e+159:
		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 <= 1.1e-247)
		tmp = z;
	elseif (a <= 2.7e-155)
		tmp = Float64(y * i);
	elseif (a <= 1.3e+29)
		tmp = z;
	elseif (a <= 6.5e+159)
		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 <= 1.1e-247)
		tmp = z;
	elseif (a <= 2.7e-155)
		tmp = y * i;
	elseif (a <= 1.3e+29)
		tmp = z;
	elseif (a <= 6.5e+159)
		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, 1.1e-247], z, If[LessEqual[a, 2.7e-155], N[(y * i), $MachinePrecision], If[LessEqual[a, 1.3e+29], z, If[LessEqual[a, 6.5e+159], N[(y * i), $MachinePrecision], a]]]]

Derivation

1. Split input into 3 regimes

2. if a < 1.09999999999999996e-247 or 2.69999999999999981e-155 < a < 1.3e29

   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. Taylor expanded in x around 0 80.5%

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

   3. Taylor expanded in z around inf 10.6%

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

   if 1.09999999999999996e-247 < a < 2.69999999999999981e-155 or 1.3e29 < a < 6.5000000000000001e159

   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. Taylor expanded in a around inf 30.7%

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

   3. Taylor expanded in a around 0 28.5%

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

   if 6.5000000000000001e159 < 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. Taylor expanded in a around inf 73.3%

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

   3. Taylor expanded in a around inf 54.4%

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

4. Final simplification 20.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.1 \cdot 10^{-247}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-155}:\\ \;\;\;\;y \cdot i\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+29}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+159}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 13: 54.0% accurate, 19.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+205} \lor \neg \left(z \leq -4.6 \cdot 10^{+169}\right) \land z \leq -1 \cdot 10^{+155}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

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 (<= z -1.5e+205) (and (not (<= z -4.6e+169)) (<= z -1e+155)))
   z
   (+ a (* 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 ((z <= -1.5e+205) || (!(z <= -4.6e+169) && (z <= -1e+155))) {
		tmp = z;
	} else {
		tmp = a + (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 ((z <= (-1.5d+205)) .or. (.not. (z <= (-4.6d+169))) .and. (z <= (-1d+155))) then
        tmp = z
    else
        tmp = a + (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 ((z <= -1.5e+205) || (!(z <= -4.6e+169) && (z <= -1e+155))) {
		tmp = z;
	} else {
		tmp = a + (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 (z <= -1.5e+205) or (not (z <= -4.6e+169) and (z <= -1e+155)):
		tmp = z
	else:
		tmp = a + (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 ((z <= -1.5e+205) || (!(z <= -4.6e+169) && (z <= -1e+155)))
		tmp = z;
	else
		tmp = Float64(a + 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 ((z <= -1.5e+205) || (~((z <= -4.6e+169)) && (z <= -1e+155)))
		tmp = z;
	else
		tmp = a + (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[z, -1.5e+205], And[N[Not[LessEqual[z, -4.6e+169]], $MachinePrecision], LessEqual[z, -1e+155]]], z, N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.5e205 or -4.5999999999999999e169 < z < -1.00000000000000001e155

   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. Taylor expanded in x around 0 95.4%

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

   3. Taylor expanded in z around inf 60.6%

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

   if -1.5e205 < z < -4.5999999999999999e169 or -1.00000000000000001e155 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in a around inf 42.4%

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

4. Final simplification 44.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+205} \lor \neg \left(z \leq -4.6 \cdot 10^{+169}\right) \land z \leq -1 \cdot 10^{+155}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]

Alternative 14: 57.4% accurate, 24.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;i \leq -7.2 \cdot 10^{+93} \lor \neg \left(i \leq 2.3 \cdot 10^{+57}\right):\\ \;\;\;\;a + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + \left(z + t\right)\\ \end{array} \end{array} \]

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 -7.2e+93) (not (<= i 2.3e+57))) (+ a (* y i)) (+ a (+ z t))))

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 <= -7.2e+93) || !(i <= 2.3e+57)) {
		tmp = a + (y * i);
	} else {
		tmp = a + (z + t);
	}
	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 <= (-7.2d+93)) .or. (.not. (i <= 2.3d+57))) then
        tmp = a + (y * i)
    else
        tmp = a + (z + t)
    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 <= -7.2e+93) || !(i <= 2.3e+57)) {
		tmp = a + (y * i);
	} else {
		tmp = a + (z + t);
	}
	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 <= -7.2e+93) or not (i <= 2.3e+57):
		tmp = a + (y * i)
	else:
		tmp = a + (z + t)
	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 <= -7.2e+93) || !(i <= 2.3e+57))
		tmp = Float64(a + Float64(y * i));
	else
		tmp = Float64(a + Float64(z + t));
	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 <= -7.2e+93) || ~((i <= 2.3e+57)))
		tmp = a + (y * i);
	else
		tmp = a + (z + t);
	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, -7.2e+93], N[Not[LessEqual[i, 2.3e+57]], $MachinePrecision]], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -7.1999999999999998e93 or 2.2999999999999999e57 < i

   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. Taylor expanded in a around inf 60.1%

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

   if -7.1999999999999998e93 < i < 2.2999999999999999e57

   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. Taylor expanded in x around 0 77.2%

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

   3. Taylor expanded in y around 0 72.7%

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

   4. Taylor expanded in z around inf 49.8%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -7.2 \cdot 10^{+93} \lor \neg \left(i \leq 2.3 \cdot 10^{+57}\right):\\ \;\;\;\;a + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + \left(z + t\right)\\ \end{array} \]

Alternative 15: 68.2% accurate, 24.3× speedup

Math

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

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 (+ (+ t a) (+ z (* 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) {
	return (t + a) + (z + (y * i));
}

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 = (t + a) + (z + (y * i))
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 (t + a) + (z + (y * i));
}

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 (t + a) + (z + (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)
	return Float64(Float64(t + a) + Float64(z + Float64(y * i)))
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 = (t + a) + (z + (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_] := N[(N[(t + a), $MachinePrecision] + N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in x around 0 82.1%

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

3. Taylor expanded in b around inf 81.1%

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

   1. *-commutative 81.1%

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

5. Simplified 81.1%

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

6. Taylor expanded in b around 0 64.6%

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

   1. associate-+r+ 64.6%

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

   2. *-commutative 64.6%

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

8. Simplified 64.6%

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

9. Final simplification 64.6%

   \[\leadsto \left(t + a\right) + \left(z + y \cdot i\right) \]

Alternative 16: 38.6% accurate, 71.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c, i] = \mathsf{sort}([x, y, z, t, a, b, c, i])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 1.15 \cdot 10^{+116}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

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 1.15e+116) 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 <= 1.15e+116) {
		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 <= 1.15d+116) 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 <= 1.15e+116) {
		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 <= 1.15e+116:
		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 <= 1.15e+116)
		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 <= 1.15e+116)
		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, 1.15e+116], z, a]

Derivation

1. Split input into 2 regimes

2. if a < 1.14999999999999997e116

   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. Taylor expanded in x around 0 80.7%

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

   3. Taylor expanded in z around inf 13.3%

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

   if 1.14999999999999997e116 < a

   1. Initial program 99.9%

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

   2. Taylor expanded in a around inf 60.8%

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

   3. Taylor expanded in a around inf 44.4%

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

4. Final simplification 18.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.15 \cdot 10^{+116}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 17: 23.0% 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 99.9%

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

2. Taylor expanded in a around inf 40.5%

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

3. Taylor expanded in a around inf 16.9%

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

4. Final simplification 16.9%

   \[\leadsto a \]

Reproduce

herbie shell --seed 2023322 
(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)))