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

Percentage Accurate: 99.8% → 99.8%

Time: 16.2s

Alternatives: 20

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. +-commutative 99.8%

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

   2. fma-def 99.9%

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

   3. associate-+l+ 99.9%

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

   4. +-commutative 99.9%

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

   5. associate-+r+ 99.9%

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

   6. +-commutative 99.9%

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

   7. associate-+l+ 99.9%

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

   8. +-commutative 99.9%

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

   9. fma-def 99.9%

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

   10. associate-+l+ 99.9%

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

   11. fma-def 99.9%

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

   12. +-commutative 99.9%

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

3. Simplified 99.9%

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

   1. fma-udef 99.8%

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

   2. fma-udef 99.8%

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

   3. fma-udef 99.8%

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

   4. associate-+l+ 99.8%

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

   5. +-commutative 99.8%

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

   6. associate-+l+ 99.8%

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

   7. associate-+r+ 99.9%

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

   8. associate-+l+ 99.9%

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

   9. fma-udef 99.9%

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

   10. sub-neg 99.9%

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

   11. metadata-eval 99.9%

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

5. Applied egg-rr 99.9%

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

6. Final simplification 99.9%

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

Alternative 2: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Final simplification 99.8%

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

Alternative 3: 87.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;a \leq 2.16 \cdot 10^{+77}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + \left(t_1 + b \cdot \log c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + t_1\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= a 2.16e+77)
     (+ (* y i) (+ t (+ z (+ t_1 (* b (log c))))))
     (+ (* y i) (+ a (+ t (+ z t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * log(y);
	double tmp;
	if (a <= 2.16e+77) {
		tmp = (y * i) + (t + (z + (t_1 + (b * log(c)))));
	} else {
		tmp = (y * i) + (a + (t + (z + t_1)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * log(y)
    if (a <= 2.16d+77) then
        tmp = (y * i) + (t + (z + (t_1 + (b * log(c)))))
    else
        tmp = (y * i) + (a + (t + (z + t_1)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * Math.log(y);
	double tmp;
	if (a <= 2.16e+77) {
		tmp = (y * i) + (t + (z + (t_1 + (b * Math.log(c)))));
	} else {
		tmp = (y * i) + (a + (t + (z + t_1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x * math.log(y)
	tmp = 0
	if a <= 2.16e+77:
		tmp = (y * i) + (t + (z + (t_1 + (b * math.log(c)))))
	else:
		tmp = (y * i) + (a + (t + (z + t_1)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (a <= 2.16e+77)
		tmp = Float64(Float64(y * i) + Float64(t + Float64(z + Float64(t_1 + Float64(b * log(c))))));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(t + Float64(z + t_1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x * log(y);
	tmp = 0.0;
	if (a <= 2.16e+77)
		tmp = (y * i) + (t + (z + (t_1 + (b * log(c)))));
	else
		tmp = (y * i) + (a + (t + (z + t_1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, 2.16e+77], N[(N[(y * i), $MachinePrecision] + N[(t + N[(z + N[(t$95$1 + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(t + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < 2.15999999999999992e77

   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 b around inf 97.8%

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

      1. *-commutative 97.8%

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

   4. Simplified 97.8%

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

   5. Taylor expanded in a around 0 86.2%

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

   if 2.15999999999999992e77 < 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 b around inf 99.9%

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

      1. *-commutative 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in b around 0 96.9%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 2.16 \cdot 10^{+77}:\\ \;\;\;\;y \cdot i + \left(t + \left(z + \left(x \cdot \log y + b \cdot \log c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right)\\ \end{array} \]

Alternative 4: 98.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in b around inf 98.2%

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

   1. *-commutative 98.2%

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

4. Simplified 98.2%

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

5. Final simplification 98.2%

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

Alternative 5: 95.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+55} \lor \neg \left(x \leq 7 \cdot 10^{+84}\right):\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a + \left(b + -0.5\right) \cdot \log c\right) + \left(y \cdot i + \left(z + t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -4.2e+55) (not (<= x 7e+84)))
   (+ (* y i) (+ a (+ t (+ z (* x (log y))))))
   (+ (+ a (* (+ b -0.5) (log c))) (+ (* y i) (+ z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -4.2e+55) || !(x <= 7e+84)) {
		tmp = (y * i) + (a + (t + (z + (x * log(y)))));
	} else {
		tmp = (a + ((b + -0.5) * log(c))) + ((y * i) + (z + t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-4.2d+55)) .or. (.not. (x <= 7d+84))) then
        tmp = (y * i) + (a + (t + (z + (x * log(y)))))
    else
        tmp = (a + ((b + (-0.5d0)) * log(c))) + ((y * i) + (z + t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -4.2e+55) || !(x <= 7e+84)) {
		tmp = (y * i) + (a + (t + (z + (x * Math.log(y)))));
	} else {
		tmp = (a + ((b + -0.5) * Math.log(c))) + ((y * i) + (z + t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -4.2e+55) or not (x <= 7e+84):
		tmp = (y * i) + (a + (t + (z + (x * math.log(y)))))
	else:
		tmp = (a + ((b + -0.5) * math.log(c))) + ((y * i) + (z + t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -4.2e+55) || !(x <= 7e+84))
		tmp = Float64(Float64(y * i) + Float64(a + Float64(t + Float64(z + Float64(x * log(y))))));
	else
		tmp = Float64(Float64(a + Float64(Float64(b + -0.5) * log(c))) + Float64(Float64(y * i) + Float64(z + t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -4.2e+55) || ~((x <= 7e+84)))
		tmp = (y * i) + (a + (t + (z + (x * log(y)))));
	else
		tmp = (a + ((b + -0.5) * log(c))) + ((y * i) + (z + t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -4.2e+55], N[Not[LessEqual[x, 7e+84]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(a + N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a + N[(N[(b + -0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y * i), $MachinePrecision] + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.2000000000000001e55 or 6.9999999999999998e84 < 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. Taylor expanded in b around inf 99.7%

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

      1. *-commutative 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in b around 0 92.0%

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

   if -4.2000000000000001e55 < x < 6.9999999999999998e84

   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. +-commutative 99.9%

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

      2. fma-def 99.9%

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

      3. associate-+l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+r+ 99.9%

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

      6. +-commutative 99.9%

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

      7. associate-+l+ 99.9%

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

      8. +-commutative 99.9%

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

      9. fma-def 99.9%

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

      10. associate-+l+ 99.9%

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

      11. fma-def 99.9%

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

      12. +-commutative 99.9%

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

   3. Simplified 99.9%

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

      1. fma-udef 99.9%

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

      2. fma-udef 99.9%

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

      3. fma-udef 99.9%

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

      4. associate-+l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. associate-+l+ 99.9%

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

      7. associate-+r+ 99.9%

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

      8. associate-+l+ 99.9%

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

      9. fma-udef 99.9%

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

      10. sub-neg 99.9%

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

      11. metadata-eval 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in x around 0 99.3%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+55} \lor \neg \left(x \leq 7 \cdot 10^{+84}\right):\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a + \left(b + -0.5\right) \cdot \log c\right) + \left(y \cdot i + \left(z + t\right)\right)\\ \end{array} \]

Alternative 6: 84.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -11500000 \lor \neg \left(x \leq 5.5 \cdot 10^{+84}\right):\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(z + \left(y \cdot i + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -11500000.0) (not (<= x 5.5e+84)))
   (+ (* y i) (+ a (+ t (+ z (* x (log y))))))
   (+ a (+ z (+ (* y i) (* (log c) (- b 0.5)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -11500000.0) || !(x <= 5.5e+84)) {
		tmp = (y * i) + (a + (t + (z + (x * log(y)))));
	} else {
		tmp = a + (z + ((y * i) + (log(c) * (b - 0.5))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-11500000.0d0)) .or. (.not. (x <= 5.5d+84))) then
        tmp = (y * i) + (a + (t + (z + (x * log(y)))))
    else
        tmp = a + (z + ((y * i) + (log(c) * (b - 0.5d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -11500000.0) || !(x <= 5.5e+84)) {
		tmp = (y * i) + (a + (t + (z + (x * Math.log(y)))));
	} else {
		tmp = a + (z + ((y * i) + (Math.log(c) * (b - 0.5))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -11500000.0) or not (x <= 5.5e+84):
		tmp = (y * i) + (a + (t + (z + (x * math.log(y)))))
	else:
		tmp = a + (z + ((y * i) + (math.log(c) * (b - 0.5))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -11500000.0) || !(x <= 5.5e+84))
		tmp = Float64(Float64(y * i) + Float64(a + Float64(t + Float64(z + 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

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -11500000.0) || ~((x <= 5.5e+84)))
		tmp = (y * i) + (a + (t + (z + (x * log(y)))));
	else
		tmp = a + (z + ((y * i) + (log(c) * (b - 0.5))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -11500000.0], N[Not[LessEqual[x, 5.5e+84]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(a + N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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 < -1.15e7 or 5.5000000000000004e84 < 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 b around inf 99.8%

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

      1. *-commutative 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in b around 0 92.8%

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

   if -1.15e7 < x < 5.5000000000000004e84

   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. +-commutative 99.9%

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

      2. fma-def 99.9%

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

      3. associate-+l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+r+ 99.9%

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

      6. +-commutative 99.9%

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

      7. associate-+l+ 99.9%

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

      8. +-commutative 99.9%

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

      9. fma-def 99.9%

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

      10. associate-+l+ 99.9%

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

      11. fma-def 99.9%

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

      12. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 99.3%

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

   5. Taylor expanded in t around 0 80.7%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -11500000 \lor \neg \left(x \leq 5.5 \cdot 10^{+84}\right):\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(z + \left(y \cdot i + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \end{array} \]

Alternative 7: 77.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -8.2 \cdot 10^{+167}:\\ \;\;\;\;a + \left(t + \left(z + t_1\right)\right)\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+204}:\\ \;\;\;\;a + \left(z + \left(y \cdot i + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t + \left(z + \left(y \cdot i + t_1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -8.2e+167)
     (+ a (+ t (+ z t_1)))
     (if (<= x 7.8e+204)
       (+ a (+ z (+ (* y i) (* (log c) (- b 0.5)))))
       (+ t (+ z (+ (* y i) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * log(y);
	double tmp;
	if (x <= -8.2e+167) {
		tmp = a + (t + (z + t_1));
	} else if (x <= 7.8e+204) {
		tmp = a + (z + ((y * i) + (log(c) * (b - 0.5))));
	} else {
		tmp = t + (z + ((y * i) + t_1));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * log(y)
    if (x <= (-8.2d+167)) then
        tmp = a + (t + (z + t_1))
    else if (x <= 7.8d+204) then
        tmp = a + (z + ((y * i) + (log(c) * (b - 0.5d0))))
    else
        tmp = t + (z + ((y * i) + t_1))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * Math.log(y);
	double tmp;
	if (x <= -8.2e+167) {
		tmp = a + (t + (z + t_1));
	} else if (x <= 7.8e+204) {
		tmp = a + (z + ((y * i) + (Math.log(c) * (b - 0.5))));
	} else {
		tmp = t + (z + ((y * i) + t_1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x * math.log(y)
	tmp = 0
	if x <= -8.2e+167:
		tmp = a + (t + (z + t_1))
	elif x <= 7.8e+204:
		tmp = a + (z + ((y * i) + (math.log(c) * (b - 0.5))))
	else:
		tmp = t + (z + ((y * i) + t_1))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -8.2e+167)
		tmp = Float64(a + Float64(t + Float64(z + t_1)));
	elseif (x <= 7.8e+204)
		tmp = Float64(a + Float64(z + Float64(Float64(y * i) + Float64(log(c) * Float64(b - 0.5)))));
	else
		tmp = Float64(t + Float64(z + Float64(Float64(y * i) + t_1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x * log(y);
	tmp = 0.0;
	if (x <= -8.2e+167)
		tmp = a + (t + (z + t_1));
	elseif (x <= 7.8e+204)
		tmp = a + (z + ((y * i) + (log(c) * (b - 0.5))));
	else
		tmp = t + (z + ((y * i) + t_1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8.2e+167], N[(a + N[(t + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.8e+204], N[(a + N[(z + N[(N[(y * i), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(z + N[(N[(y * i), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.2e167

   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 b around inf 99.7%

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

      1. *-commutative 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in b around 0 99.7%

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

   6. Taylor expanded in y around 0 89.9%

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

   if -8.2e167 < x < 7.80000000000000033e204

   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. +-commutative 99.9%

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

      2. fma-def 99.9%

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

      3. associate-+l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+r+ 99.9%

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

      6. +-commutative 99.9%

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

      7. associate-+l+ 99.9%

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

      8. +-commutative 99.9%

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

      9. fma-def 99.9%

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

      10. associate-+l+ 99.9%

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

      11. fma-def 99.9%

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

      12. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 94.1%

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

   5. Taylor expanded in t around 0 77.9%

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

   if 7.80000000000000033e204 < 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 b around inf 99.8%

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

      1. *-commutative 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in b around 0 97.4%

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

   6. Taylor expanded in a around 0 86.3%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+167}:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+204}:\\ \;\;\;\;a + \left(z + \left(y \cdot i + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t + \left(z + \left(y \cdot i + x \cdot \log y\right)\right)\\ \end{array} \]

Alternative 8: 73.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{if}\;y \leq 3.9 \cdot 10^{-290}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-257}:\\ \;\;\;\;a + \left(z + b \cdot \log c\right)\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (+ t (+ z (* x (log y)))))))
   (if (<= y 3.9e-290)
     t_1
     (if (<= y 2.3e-257)
       (+ a (+ z (* b (log c))))
       (if (<= y 4.6e-8) t_1 (+ (* y i) (+ a (+ z t))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (t + (z + (x * log(y))));
	double tmp;
	if (y <= 3.9e-290) {
		tmp = t_1;
	} else if (y <= 2.3e-257) {
		tmp = a + (z + (b * log(c)));
	} else if (y <= 4.6e-8) {
		tmp = t_1;
	} else {
		tmp = (y * i) + (a + (z + t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a + (t + (z + (x * log(y))))
    if (y <= 3.9d-290) then
        tmp = t_1
    else if (y <= 2.3d-257) then
        tmp = a + (z + (b * log(c)))
    else if (y <= 4.6d-8) then
        tmp = t_1
    else
        tmp = (y * i) + (a + (z + t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (t + (z + (x * Math.log(y))));
	double tmp;
	if (y <= 3.9e-290) {
		tmp = t_1;
	} else if (y <= 2.3e-257) {
		tmp = a + (z + (b * Math.log(c)));
	} else if (y <= 4.6e-8) {
		tmp = t_1;
	} else {
		tmp = (y * i) + (a + (z + t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (t + (z + (x * math.log(y))))
	tmp = 0
	if y <= 3.9e-290:
		tmp = t_1
	elif y <= 2.3e-257:
		tmp = a + (z + (b * math.log(c)))
	elif y <= 4.6e-8:
		tmp = t_1
	else:
		tmp = (y * i) + (a + (z + t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(t + Float64(z + Float64(x * log(y)))))
	tmp = 0.0
	if (y <= 3.9e-290)
		tmp = t_1;
	elseif (y <= 2.3e-257)
		tmp = Float64(a + Float64(z + Float64(b * log(c))));
	elseif (y <= 4.6e-8)
		tmp = t_1;
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (t + (z + (x * log(y))));
	tmp = 0.0;
	if (y <= 3.9e-290)
		tmp = t_1;
	elseif (y <= 2.3e-257)
		tmp = a + (z + (b * log(c)));
	elseif (y <= 4.6e-8)
		tmp = t_1;
	else
		tmp = (y * i) + (a + (z + t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, 3.9e-290], t$95$1, If[LessEqual[y, 2.3e-257], N[(a + N[(z + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.6e-8], t$95$1, N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < 3.89999999999999973e-290 or 2.3e-257 < y < 4.6000000000000002e-8

   1. Initial program 99.8%

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

   2. Taylor expanded in b around inf 98.8%

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

      1. *-commutative 98.8%

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

   4. Simplified 98.8%

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

   5. Taylor expanded in b around 0 86.9%

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

   6. Taylor expanded in y around 0 84.1%

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

   if 3.89999999999999973e-290 < y < 2.3e-257

   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. +-commutative 99.7%

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

      2. fma-def 99.7%

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

      3. associate-+l+ 99.7%

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

      4. +-commutative 99.7%

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

      5. associate-+r+ 99.7%

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

      6. +-commutative 99.7%

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

      7. associate-+l+ 99.7%

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

      8. +-commutative 99.7%

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

      9. fma-def 99.7%

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

      10. associate-+l+ 99.7%

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

      11. fma-def 99.7%

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

      12. +-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 87.8%

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

   5. Taylor expanded in t around 0 57.6%

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

   6. Taylor expanded in i around 0 57.6%

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

   7. Taylor expanded in b around inf 51.7%

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

      1. *-commutative 51.7%

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

   9. Simplified 51.7%

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

   if 4.6000000000000002e-8 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in b around inf 98.3%

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

      1. *-commutative 98.3%

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

   4. Simplified 98.3%

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

   5. Taylor expanded in b around 0 87.2%

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

   6. Taylor expanded in z around inf 77.1%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.9 \cdot 10^{-290}:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-257}:\\ \;\;\;\;a + \left(z + b \cdot \log c\right)\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-8}:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \end{array} \]

Alternative 9: 73.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{if}\;y \leq 6.2 \cdot 10^{-289}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-256}:\\ \;\;\;\;a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (+ t (+ z (* x (log y)))))))
   (if (<= y 6.2e-289)
     t_1
     (if (<= y 1.35e-256)
       (+ a (+ z (* (log c) (- b 0.5))))
       (if (<= y 1.25e-8) t_1 (+ (* y i) (+ a (+ z t))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (t + (z + (x * log(y))));
	double tmp;
	if (y <= 6.2e-289) {
		tmp = t_1;
	} else if (y <= 1.35e-256) {
		tmp = a + (z + (log(c) * (b - 0.5)));
	} else if (y <= 1.25e-8) {
		tmp = t_1;
	} else {
		tmp = (y * i) + (a + (z + t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a + (t + (z + (x * log(y))))
    if (y <= 6.2d-289) then
        tmp = t_1
    else if (y <= 1.35d-256) then
        tmp = a + (z + (log(c) * (b - 0.5d0)))
    else if (y <= 1.25d-8) then
        tmp = t_1
    else
        tmp = (y * i) + (a + (z + t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (t + (z + (x * Math.log(y))));
	double tmp;
	if (y <= 6.2e-289) {
		tmp = t_1;
	} else if (y <= 1.35e-256) {
		tmp = a + (z + (Math.log(c) * (b - 0.5)));
	} else if (y <= 1.25e-8) {
		tmp = t_1;
	} else {
		tmp = (y * i) + (a + (z + t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (t + (z + (x * math.log(y))))
	tmp = 0
	if y <= 6.2e-289:
		tmp = t_1
	elif y <= 1.35e-256:
		tmp = a + (z + (math.log(c) * (b - 0.5)))
	elif y <= 1.25e-8:
		tmp = t_1
	else:
		tmp = (y * i) + (a + (z + t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(t + Float64(z + Float64(x * log(y)))))
	tmp = 0.0
	if (y <= 6.2e-289)
		tmp = t_1;
	elseif (y <= 1.35e-256)
		tmp = Float64(a + Float64(z + Float64(log(c) * Float64(b - 0.5))));
	elseif (y <= 1.25e-8)
		tmp = t_1;
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (t + (z + (x * log(y))));
	tmp = 0.0;
	if (y <= 6.2e-289)
		tmp = t_1;
	elseif (y <= 1.35e-256)
		tmp = a + (z + (log(c) * (b - 0.5)));
	elseif (y <= 1.25e-8)
		tmp = t_1;
	else
		tmp = (y * i) + (a + (z + t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, 6.2e-289], t$95$1, If[LessEqual[y, 1.35e-256], N[(a + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.25e-8], t$95$1, N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < 6.2e-289 or 1.3500000000000001e-256 < y < 1.2499999999999999e-8

   1. Initial program 99.8%

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

   2. Taylor expanded in b around inf 98.8%

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

      1. *-commutative 98.8%

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

   4. Simplified 98.8%

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

   5. Taylor expanded in b around 0 86.9%

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

   6. Taylor expanded in y around 0 84.1%

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

   if 6.2e-289 < y < 1.3500000000000001e-256

   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. +-commutative 99.7%

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

      2. fma-def 99.7%

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

      3. associate-+l+ 99.7%

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

      4. +-commutative 99.7%

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

      5. associate-+r+ 99.7%

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

      6. +-commutative 99.7%

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

      7. associate-+l+ 99.7%

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

      8. +-commutative 99.7%

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

      9. fma-def 99.7%

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

      10. associate-+l+ 99.7%

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

      11. fma-def 99.7%

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

      12. +-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 87.8%

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

   5. Taylor expanded in t around 0 57.6%

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

   6. Taylor expanded in i around 0 57.6%

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

   if 1.2499999999999999e-8 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in b around inf 98.3%

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

      1. *-commutative 98.3%

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

   4. Simplified 98.3%

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

   5. Taylor expanded in b around 0 87.2%

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

   6. Taylor expanded in z around inf 77.1%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 6.2 \cdot 10^{-289}:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-256}:\\ \;\;\;\;a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-8}:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \end{array} \]

Alternative 10: 75.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+100} \lor \neg \left(x \leq 2 \cdot 10^{+205}\right):\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(z + \left(y \cdot i + b \cdot \log c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -2.1e+100) (not (<= x 2e+205)))
   (+ a (+ t (+ z (* x (log y)))))
   (+ a (+ z (+ (* y i) (* b (log c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -2.1e+100) || !(x <= 2e+205)) {
		tmp = a + (t + (z + (x * log(y))));
	} else {
		tmp = a + (z + ((y * i) + (b * log(c))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-2.1d+100)) .or. (.not. (x <= 2d+205))) then
        tmp = a + (t + (z + (x * log(y))))
    else
        tmp = a + (z + ((y * i) + (b * log(c))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -2.1e+100) || !(x <= 2e+205)) {
		tmp = a + (t + (z + (x * Math.log(y))));
	} else {
		tmp = a + (z + ((y * i) + (b * Math.log(c))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -2.1e+100) or not (x <= 2e+205):
		tmp = a + (t + (z + (x * math.log(y))))
	else:
		tmp = a + (z + ((y * i) + (b * math.log(c))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -2.1e+100) || !(x <= 2e+205))
		tmp = Float64(a + Float64(t + Float64(z + Float64(x * log(y)))));
	else
		tmp = Float64(a + Float64(z + Float64(Float64(y * i) + Float64(b * log(c)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -2.1e+100) || ~((x <= 2e+205)))
		tmp = a + (t + (z + (x * log(y))));
	else
		tmp = a + (z + ((y * i) + (b * log(c))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -2.1e+100], N[Not[LessEqual[x, 2e+205]], $MachinePrecision]], N[(a + N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(z + N[(N[(y * i), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.0999999999999999e100 or 2.00000000000000003e205 < 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. Taylor expanded in b around inf 99.7%

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

      1. *-commutative 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in b around 0 95.1%

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

   6. Taylor expanded in y around 0 85.8%

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

   if -2.0999999999999999e100 < x < 2.00000000000000003e205

   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. +-commutative 99.9%

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

      2. fma-def 99.9%

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

      3. associate-+l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+r+ 99.9%

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

      6. +-commutative 99.9%

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

      7. associate-+l+ 99.9%

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

      8. +-commutative 99.9%

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

      9. fma-def 99.9%

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

      10. associate-+l+ 99.9%

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

      11. fma-def 99.9%

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

      12. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 95.4%

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

   5. Taylor expanded in t around 0 79.3%

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

   6. Taylor expanded in b around inf 77.1%

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

      1. *-commutative 53.8%

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

   8. Simplified 77.1%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+100} \lor \neg \left(x \leq 2 \cdot 10^{+205}\right):\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(z + \left(y \cdot i + b \cdot \log c\right)\right)\\ \end{array} \]

Alternative 11: 75.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -1.1 \cdot 10^{+100}:\\ \;\;\;\;a + \left(t + \left(z + t_1\right)\right)\\ \mathbf{elif}\;x \leq 8.4 \cdot 10^{+204}:\\ \;\;\;\;a + \left(z + \left(y \cdot i + b \cdot \log c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t + \left(z + \left(y \cdot i + t_1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -1.1e+100)
     (+ a (+ t (+ z t_1)))
     (if (<= x 8.4e+204)
       (+ a (+ z (+ (* y i) (* b (log c)))))
       (+ t (+ z (+ (* y i) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * log(y);
	double tmp;
	if (x <= -1.1e+100) {
		tmp = a + (t + (z + t_1));
	} else if (x <= 8.4e+204) {
		tmp = a + (z + ((y * i) + (b * log(c))));
	} else {
		tmp = t + (z + ((y * i) + t_1));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * log(y)
    if (x <= (-1.1d+100)) then
        tmp = a + (t + (z + t_1))
    else if (x <= 8.4d+204) then
        tmp = a + (z + ((y * i) + (b * log(c))))
    else
        tmp = t + (z + ((y * i) + t_1))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * Math.log(y);
	double tmp;
	if (x <= -1.1e+100) {
		tmp = a + (t + (z + t_1));
	} else if (x <= 8.4e+204) {
		tmp = a + (z + ((y * i) + (b * Math.log(c))));
	} else {
		tmp = t + (z + ((y * i) + t_1));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x * math.log(y)
	tmp = 0
	if x <= -1.1e+100:
		tmp = a + (t + (z + t_1))
	elif x <= 8.4e+204:
		tmp = a + (z + ((y * i) + (b * math.log(c))))
	else:
		tmp = t + (z + ((y * i) + t_1))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -1.1e+100)
		tmp = Float64(a + Float64(t + Float64(z + t_1)));
	elseif (x <= 8.4e+204)
		tmp = Float64(a + Float64(z + Float64(Float64(y * i) + Float64(b * log(c)))));
	else
		tmp = Float64(t + Float64(z + Float64(Float64(y * i) + t_1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x * log(y);
	tmp = 0.0;
	if (x <= -1.1e+100)
		tmp = a + (t + (z + t_1));
	elseif (x <= 8.4e+204)
		tmp = a + (z + ((y * i) + (b * log(c))));
	else
		tmp = t + (z + ((y * i) + t_1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.1e+100], N[(a + N[(t + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.4e+204], N[(a + N[(z + N[(N[(y * i), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(z + N[(N[(y * i), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.1e100

   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 b around inf 99.7%

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

      1. *-commutative 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in b around 0 93.9%

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

   6. Taylor expanded in y around 0 84.5%

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

   if -1.1e100 < x < 8.4000000000000002e204

   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. +-commutative 99.9%

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

      2. fma-def 99.9%

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

      3. associate-+l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+r+ 99.9%

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

      6. +-commutative 99.9%

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

      7. associate-+l+ 99.9%

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

      8. +-commutative 99.9%

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

      9. fma-def 99.9%

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

      10. associate-+l+ 99.9%

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

      11. fma-def 99.9%

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

      12. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 95.4%

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

   5. Taylor expanded in t around 0 79.3%

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

   6. Taylor expanded in b around inf 77.1%

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

      1. *-commutative 53.8%

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

   8. Simplified 77.1%

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

   if 8.4000000000000002e204 < 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 b around inf 99.8%

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

      1. *-commutative 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in b around 0 97.4%

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

   6. Taylor expanded in a around 0 86.3%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+100}:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \mathbf{elif}\;x \leq 8.4 \cdot 10^{+204}:\\ \;\;\;\;a + \left(z + \left(y \cdot i + b \cdot \log c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t + \left(z + \left(y \cdot i + x \cdot \log y\right)\right)\\ \end{array} \]

Alternative 12: 67.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.7 \cdot 10^{-63}:\\ \;\;\;\;a + \left(z + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 4.7e-63) (+ a (+ z (* b (log c)))) (+ (* y i) (+ a (+ z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 4.7e-63) {
		tmp = a + (z + (b * log(c)));
	} else {
		tmp = (y * i) + (a + (z + t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= 4.7d-63) then
        tmp = a + (z + (b * log(c)))
    else
        tmp = (y * i) + (a + (z + t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 4.7e-63) {
		tmp = a + (z + (b * Math.log(c)));
	} else {
		tmp = (y * i) + (a + (z + t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 4.7e-63:
		tmp = a + (z + (b * math.log(c)))
	else:
		tmp = (y * i) + (a + (z + t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 4.7e-63)
		tmp = Float64(a + Float64(z + Float64(b * log(c))));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= 4.7e-63)
		tmp = a + (z + (b * log(c)));
	else
		tmp = (y * i) + (a + (z + t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 4.7e-63], N[(a + N[(z + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 4.7000000000000001e-63

   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. +-commutative 99.8%

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

      2. fma-def 99.8%

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

      3. associate-+l+ 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-+r+ 99.8%

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

      6. +-commutative 99.8%

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

      7. associate-+l+ 99.8%

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

      8. +-commutative 99.8%

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

      9. fma-def 99.8%

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

      10. associate-+l+ 99.8%

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

      11. fma-def 99.8%

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

      12. +-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 75.8%

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

   5. Taylor expanded in t around 0 56.6%

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

   6. Taylor expanded in i around 0 55.5%

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

   7. Taylor expanded in b around inf 53.4%

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

      1. *-commutative 53.4%

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

   9. Simplified 53.4%

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

   if 4.7000000000000001e-63 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in b around inf 98.6%

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

      1. *-commutative 98.6%

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

   4. Simplified 98.6%

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

   5. Taylor expanded in b around 0 88.8%

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

   6. Taylor expanded in z around inf 77.1%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.7 \cdot 10^{-63}:\\ \;\;\;\;a + \left(z + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \end{array} \]

Alternative 13: 71.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.12 \cdot 10^{+198} \lor \neg \left(x \leq 1.15 \cdot 10^{+278}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -1.12e+198) (not (<= x 1.15e+278)))
   (* x (log y))
   (+ (* y i) (+ a (+ z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1.12e+198) || !(x <= 1.15e+278)) {
		tmp = x * log(y);
	} else {
		tmp = (y * i) + (a + (z + t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-1.12d+198)) .or. (.not. (x <= 1.15d+278))) then
        tmp = x * log(y)
    else
        tmp = (y * i) + (a + (z + t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1.12e+198) || !(x <= 1.15e+278)) {
		tmp = x * Math.log(y);
	} else {
		tmp = (y * i) + (a + (z + t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -1.12e+198) or not (x <= 1.15e+278):
		tmp = x * math.log(y)
	else:
		tmp = (y * i) + (a + (z + t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -1.12e+198) || !(x <= 1.15e+278))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -1.12e+198) || ~((x <= 1.15e+278)))
		tmp = x * log(y);
	else
		tmp = (y * i) + (a + (z + t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -1.12e+198], N[Not[LessEqual[x, 1.15e+278]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.1199999999999999e198 or 1.1499999999999999e278 < 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. +-commutative 99.7%

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

      2. fma-def 99.7%

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

      3. associate-+l+ 99.7%

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

      4. +-commutative 99.7%

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

      5. associate-+r+ 99.7%

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

      6. +-commutative 99.7%

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

      7. associate-+l+ 99.7%

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

      8. +-commutative 99.7%

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

      9. fma-def 99.7%

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

      10. associate-+l+ 99.7%

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

      11. fma-def 99.7%

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

      12. +-commutative 99.7%

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

   3. Simplified 99.7%

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

      1. fma-udef 99.7%

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

      2. fma-udef 99.7%

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

      3. fma-udef 99.7%

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

      4. associate-+l+ 99.7%

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

      5. +-commutative 99.7%

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

      6. associate-+l+ 99.7%

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

      7. associate-+r+ 99.7%

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

      8. associate-+l+ 99.7%

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

      9. fma-udef 99.7%

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

      10. sub-neg 99.7%

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

      11. metadata-eval 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in x around inf 78.4%

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

   if -1.1199999999999999e198 < x < 1.1499999999999999e278

   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 b around inf 98.0%

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

      1. *-commutative 98.0%

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

   4. Simplified 98.0%

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

   5. Taylor expanded in b around 0 83.3%

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

   6. Taylor expanded in z around inf 74.7%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.12 \cdot 10^{+198} \lor \neg \left(x \leq 1.15 \cdot 10^{+278}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \end{array} \]

Alternative 14: 67.7% accurate, 24.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in b around inf 98.2%

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

   1. *-commutative 98.2%

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

4. Simplified 98.2%

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

5. Taylor expanded in b around 0 84.9%

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

6. Taylor expanded in z around inf 68.5%

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

7. Final simplification 68.5%

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

Alternative 15: 22.3% accurate, 30.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 2.3 \cdot 10^{-103}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+85}:\\ \;\;\;\;y \cdot i\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{+144}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 2.3e-103) z (if (<= a 1.9e+85) (* y i) (if (<= a 8.6e+144) z a))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 2.3e-103) {
		tmp = z;
	} else if (a <= 1.9e+85) {
		tmp = y * i;
	} else if (a <= 8.6e+144) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 2.3d-103) then
        tmp = z
    else if (a <= 1.9d+85) then
        tmp = y * i
    else if (a <= 8.6d+144) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 2.3e-103) {
		tmp = z;
	} else if (a <= 1.9e+85) {
		tmp = y * i;
	} else if (a <= 8.6e+144) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 2.3e-103:
		tmp = z
	elif a <= 1.9e+85:
		tmp = y * i
	elif a <= 8.6e+144:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 2.3e-103)
		tmp = z;
	elseif (a <= 1.9e+85)
		tmp = Float64(y * i);
	elseif (a <= 8.6e+144)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 2.3e-103)
		tmp = z;
	elseif (a <= 1.9e+85)
		tmp = y * i;
	elseif (a <= 8.6e+144)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 2.3e-103], z, If[LessEqual[a, 1.9e+85], N[(y * i), $MachinePrecision], If[LessEqual[a, 8.6e+144], z, a]]]

Derivation

1. Split input into 3 regimes

2. if a < 2.3000000000000001e-103 or 1.89999999999999996e85 < a < 8.59999999999999968e144

   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. +-commutative 99.9%

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

      2. fma-def 99.9%

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

      3. associate-+l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+r+ 99.9%

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

      6. +-commutative 99.9%

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

      7. associate-+l+ 99.9%

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

      8. +-commutative 99.9%

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

      9. fma-def 99.9%

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

      10. associate-+l+ 99.9%

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

      11. fma-def 99.9%

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

      12. +-commutative 99.9%

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

   3. Simplified 99.9%

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

      1. fma-udef 99.9%

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

      2. fma-udef 99.9%

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

      3. fma-udef 99.9%

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

      4. associate-+l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. associate-+l+ 99.9%

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

      7. associate-+r+ 99.9%

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

      8. associate-+l+ 99.9%

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

      9. fma-udef 99.9%

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

      10. sub-neg 99.9%

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

      11. metadata-eval 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in z around inf 17.5%

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

   if 2.3000000000000001e-103 < a < 1.89999999999999996e85

   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 y around inf 26.2%

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

      1. *-commutative 26.2%

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

   4. Simplified 26.2%

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

   if 8.59999999999999968e144 < 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. Step-by-step derivation

      1. +-commutative 99.9%

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

      2. fma-def 99.9%

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

      3. associate-+l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+r+ 99.9%

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

      6. +-commutative 99.9%

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

      7. associate-+l+ 99.9%

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

      8. +-commutative 99.9%

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

      9. fma-def 99.9%

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

      10. associate-+l+ 99.9%

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

      11. fma-def 99.9%

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

      12. +-commutative 99.9%

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

   3. Simplified 99.9%

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

      1. fma-udef 99.9%

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

      2. fma-udef 99.9%

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

      3. fma-udef 99.9%

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

      4. associate-+l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. associate-+l+ 99.9%

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

      7. associate-+r+ 99.9%

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

      8. associate-+l+ 99.9%

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

      9. fma-udef 99.9%

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

      10. sub-neg 99.9%

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

      11. metadata-eval 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in a around inf 49.1%

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

4. Final simplification 23.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 2.3 \cdot 10^{-103}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+85}:\\ \;\;\;\;y \cdot i\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{+144}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 16: 45.5% accurate, 31.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 5.2 \cdot 10^{+43}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 5.2e+43) (+ z a) (+ (* y i) a)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 5.2e+43) {
		tmp = z + a;
	} else {
		tmp = (y * i) + a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= 5.2d+43) then
        tmp = z + a
    else
        tmp = (y * i) + a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 5.2e+43) {
		tmp = z + a;
	} else {
		tmp = (y * i) + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 5.2e+43:
		tmp = z + a
	else:
		tmp = (y * i) + a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 5.2e+43)
		tmp = Float64(z + a);
	else
		tmp = Float64(Float64(y * i) + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= 5.2e+43)
		tmp = z + a;
	else
		tmp = (y * i) + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 5.2e+43], N[(z + a), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 5.20000000000000042e43

   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. +-commutative 99.8%

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

      2. fma-def 99.8%

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

      3. associate-+l+ 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-+r+ 99.8%

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

      6. +-commutative 99.8%

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

      7. associate-+l+ 99.8%

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

      8. +-commutative 99.8%

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

      9. fma-def 99.8%

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

      10. associate-+l+ 99.8%

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

      11. fma-def 99.8%

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

      12. +-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 79.3%

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

   5. Taylor expanded in t around 0 62.0%

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

   6. Taylor expanded in z around inf 41.3%

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

   if 5.20000000000000042e43 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in a around inf 54.3%

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

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 5.2 \cdot 10^{+43}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + a\\ \end{array} \]

Alternative 17: 43.0% accurate, 31.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 9.5 \cdot 10^{+144}:\\ \;\;\;\;y \cdot i + z\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 9.5e+144) (+ (* y i) z) (+ (* y i) a)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 9.5e+144) {
		tmp = (y * i) + z;
	} else {
		tmp = (y * i) + a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 9.5d+144) then
        tmp = (y * i) + z
    else
        tmp = (y * i) + a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 9.5e+144) {
		tmp = (y * i) + z;
	} else {
		tmp = (y * i) + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 9.5e+144:
		tmp = (y * i) + z
	else:
		tmp = (y * i) + a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 9.5e+144)
		tmp = Float64(Float64(y * i) + z);
	else
		tmp = Float64(Float64(y * i) + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 9.5e+144)
		tmp = (y * i) + z;
	else
		tmp = (y * i) + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 9.5e+144], N[(N[(y * i), $MachinePrecision] + z), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 9.50000000000000031e144

   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 z around inf 39.8%

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

   if 9.50000000000000031e144 < 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 54.8%

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

4. Final simplification 41.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 9.5 \cdot 10^{+144}:\\ \;\;\;\;y \cdot i + z\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + a\\ \end{array} \]

Alternative 18: 40.1% accurate, 43.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 7.5 \cdot 10^{+126}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y 7.5e+126) (+ z a) (* y i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 7.5e+126) {
		tmp = z + a;
	} else {
		tmp = y * i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= 7.5d+126) then
        tmp = z + a
    else
        tmp = y * i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= 7.5e+126) {
		tmp = z + a;
	} else {
		tmp = y * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= 7.5e+126:
		tmp = z + a
	else:
		tmp = y * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= 7.5e+126)
		tmp = Float64(z + a);
	else
		tmp = Float64(y * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= 7.5e+126)
		tmp = z + a;
	else
		tmp = y * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, 7.5e+126], N[(z + a), $MachinePrecision], N[(y * i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 7.5000000000000006e126

   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. +-commutative 99.8%

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

      2. fma-def 99.8%

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

      3. associate-+l+ 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-+r+ 99.8%

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

      6. +-commutative 99.8%

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

      7. associate-+l+ 99.8%

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

      8. +-commutative 99.8%

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

      9. fma-def 99.8%

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

      10. associate-+l+ 99.8%

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

      11. fma-def 99.8%

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

      12. +-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 81.2%

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

   5. Taylor expanded in t around 0 65.8%

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

   6. Taylor expanded in z around inf 40.6%

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

   if 7.5000000000000006e126 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 50.9%

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

      1. *-commutative 50.9%

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

   4. Simplified 50.9%

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

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 7.5 \cdot 10^{+126}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot i\\ \end{array} \]

Alternative 19: 21.1% accurate, 71.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 9 \cdot 10^{+145}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (if (<= a 9e+145) z a))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 9e+145) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 9d+145) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 9e+145) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 9e+145:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 9e+145)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 9e+145)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 9e+145], z, a]

Derivation

1. Split input into 2 regimes

2. if a < 8.9999999999999996e145

   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. +-commutative 99.8%

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

      2. fma-def 99.8%

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

      3. associate-+l+ 99.8%

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

      4. +-commutative 99.8%

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

      5. associate-+r+ 99.8%

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

      6. +-commutative 99.8%

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

      7. associate-+l+ 99.8%

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

      8. +-commutative 99.8%

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

      9. fma-def 99.8%

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

      10. associate-+l+ 99.8%

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

      11. fma-def 99.8%

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

      12. +-commutative 99.8%

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

   3. Simplified 99.8%

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

      1. fma-udef 99.8%

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

      2. fma-udef 99.8%

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

      3. fma-udef 99.8%

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

      4. associate-+l+ 99.8%

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

      5. +-commutative 99.8%

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

      6. associate-+l+ 99.8%

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

      7. associate-+r+ 99.8%

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

      8. associate-+l+ 99.8%

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

      9. fma-udef 99.8%

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

      10. sub-neg 99.8%

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

      11. metadata-eval 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in z around inf 18.0%

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

   if 8.9999999999999996e145 < 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. Step-by-step derivation

      1. +-commutative 99.9%

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

      2. fma-def 99.9%

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

      3. associate-+l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+r+ 99.9%

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

      6. +-commutative 99.9%

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

      7. associate-+l+ 99.9%

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

      8. +-commutative 99.9%

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

      9. fma-def 99.9%

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

      10. associate-+l+ 99.9%

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

      11. fma-def 99.9%

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

      12. +-commutative 99.9%

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

   3. Simplified 99.9%

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

      1. fma-udef 99.9%

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

      2. fma-udef 99.9%

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

      3. fma-udef 99.9%

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

      4. associate-+l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. associate-+l+ 99.9%

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

      7. associate-+r+ 99.9%

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

      8. associate-+l+ 99.9%

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

      9. fma-udef 99.9%

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

      10. sub-neg 99.9%

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

      11. metadata-eval 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in a around inf 49.1%

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

4. Final simplification 22.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 9 \cdot 10^{+145}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 20: 16.5% accurate, 219.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. +-commutative 99.8%

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

   2. fma-def 99.9%

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

   3. associate-+l+ 99.9%

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

   4. +-commutative 99.9%

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

   5. associate-+r+ 99.9%

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

   6. +-commutative 99.9%

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

   7. associate-+l+ 99.9%

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

   8. +-commutative 99.9%

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

   9. fma-def 99.9%

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

   10. associate-+l+ 99.9%

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

   11. fma-def 99.9%

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

   12. +-commutative 99.9%

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

3. Simplified 99.9%

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

   1. fma-udef 99.8%

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

   2. fma-udef 99.8%

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

   3. fma-udef 99.8%

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

   4. associate-+l+ 99.8%

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

   5. +-commutative 99.8%

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

   6. associate-+l+ 99.8%

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

   7. associate-+r+ 99.9%

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

   8. associate-+l+ 99.9%

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

   9. fma-udef 99.9%

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

   10. sub-neg 99.9%

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

   11. metadata-eval 99.9%

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

5. Applied egg-rr 99.9%

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

6. Taylor expanded in a around inf 18.4%

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

7. Final simplification 18.4%

   \[\leadsto a \]

Reproduce

herbie shell --seed 2023297 
(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)))