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

Percentage Accurate: 99.8% → 99.8%

Time: 20.3s

Alternatives: 14

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. +-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. associate-+r+ 99.9%

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

   3. +-commutative 99.9%

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

   4. associate-+r+ 99.9%

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

   5. +-commutative 99.9%

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

   6. associate-+r+ 99.9%

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

   7. fma-def 99.9%

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

   8. associate-+l+ 99.9%

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

   9. +-commutative 99.9%

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

   10. associate-+r+ 99.9%

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

   11. +-commutative 99.9%

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

   12. associate-+l+ 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Final simplification 99.9%

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

Alternative 3: 81.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log c \cdot \left(b - 0.5\right)\\ t_2 := a + \left(z + t\right)\\ \mathbf{if}\;i \leq -6.8 \cdot 10^{+25}:\\ \;\;\;\;y \cdot i + \left(b \cdot \log c + t_2\right)\\ \mathbf{elif}\;i \leq 10^{-87}:\\ \;\;\;\;a + \left(z + \left(x \cdot \log y + t_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t_1 + t_2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (log c) (- b 0.5))) (t_2 (+ a (+ z t))))
   (if (<= i -6.8e+25)
     (+ (* y i) (+ (* b (log c)) t_2))
     (if (<= i 1e-87)
       (+ a (+ z (+ (* x (log y)) t_1)))
       (+ (* y i) (+ t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = log(c) * (b - 0.5);
	double t_2 = a + (z + t);
	double tmp;
	if (i <= -6.8e+25) {
		tmp = (y * i) + ((b * log(c)) + t_2);
	} else if (i <= 1e-87) {
		tmp = a + (z + ((x * log(y)) + t_1));
	} else {
		tmp = (y * i) + (t_1 + t_2);
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = log(c) * (b - 0.5d0)
    t_2 = a + (z + t)
    if (i <= (-6.8d+25)) then
        tmp = (y * i) + ((b * log(c)) + t_2)
    else if (i <= 1d-87) then
        tmp = a + (z + ((x * log(y)) + t_1))
    else
        tmp = (y * i) + (t_1 + t_2)
    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 = Math.log(c) * (b - 0.5);
	double t_2 = a + (z + t);
	double tmp;
	if (i <= -6.8e+25) {
		tmp = (y * i) + ((b * Math.log(c)) + t_2);
	} else if (i <= 1e-87) {
		tmp = a + (z + ((x * Math.log(y)) + t_1));
	} else {
		tmp = (y * i) + (t_1 + t_2);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = math.log(c) * (b - 0.5)
	t_2 = a + (z + t)
	tmp = 0
	if i <= -6.8e+25:
		tmp = (y * i) + ((b * math.log(c)) + t_2)
	elif i <= 1e-87:
		tmp = a + (z + ((x * math.log(y)) + t_1))
	else:
		tmp = (y * i) + (t_1 + t_2)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(log(c) * Float64(b - 0.5))
	t_2 = Float64(a + Float64(z + t))
	tmp = 0.0
	if (i <= -6.8e+25)
		tmp = Float64(Float64(y * i) + Float64(Float64(b * log(c)) + t_2));
	elseif (i <= 1e-87)
		tmp = Float64(a + Float64(z + Float64(Float64(x * log(y)) + t_1)));
	else
		tmp = Float64(Float64(y * i) + Float64(t_1 + t_2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = log(c) * (b - 0.5);
	t_2 = a + (z + t);
	tmp = 0.0;
	if (i <= -6.8e+25)
		tmp = (y * i) + ((b * log(c)) + t_2);
	elseif (i <= 1e-87)
		tmp = a + (z + ((x * log(y)) + t_1));
	else
		tmp = (y * i) + (t_1 + t_2);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -6.8e+25], N[(N[(y * i), $MachinePrecision] + N[(N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1e-87], N[(a + N[(z + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(t$95$1 + t$95$2), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if i < -6.79999999999999967e25

   1. Initial program 100.0%

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

   2. Taylor expanded in b around inf 100.0%

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

      1. *-commutative 73.9%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in x around 0 96.8%

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

   if -6.79999999999999967e25 < i < 1.00000000000000002e-87

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 78.3%

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

      1. +-commutative 78.3%

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

      2. log-pow 38.2%

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

      3. associate-+r+ 38.2%

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

      4. log-pow 78.3%

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

      5. fma-udef 78.3%

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

   4. Simplified 78.3%

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

   5. Taylor expanded in y around 0 73.8%

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

   if 1.00000000000000002e-87 < i

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 95.0%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -6.8 \cdot 10^{+25}:\\ \;\;\;\;y \cdot i + \left(b \cdot \log c + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{elif}\;i \leq 10^{-87}:\\ \;\;\;\;a + \left(z + \left(x \cdot \log y + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \]

Alternative 4: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

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))))) + (b * log(c)));
}

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))))) + (b * log(c)))
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))))) + (b * Math.log(c)));
}

Python

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

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(b * log(c))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = (y * i) + ((a + (t + (z + (x * log(y))))) + (b * log(c)));
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[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in 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 57.4%

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

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. Final simplification 98.3%

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

Alternative 5: 43.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+135}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-60}:\\ \;\;\;\;y \cdot i + \left(a + -0.5 \cdot \log c\right)\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-141} \lor \neg \left(z \leq -7.5 \cdot 10^{-182}\right) \land z \leq 6.9 \cdot 10^{-292}:\\ \;\;\;\;\log c \cdot \left(b - 0.5\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -5.5e+135)
   (+ z (* y i))
   (if (<= z -2.2e-60)
     (+ (* y i) (+ a (* -0.5 (log c))))
     (if (or (<= z -2.7e-141) (and (not (<= z -7.5e-182)) (<= z 6.9e-292)))
       (+ (* (log c) (- b 0.5)) (* y i))
       (+ a (* y i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -5.5e+135) {
		tmp = z + (y * i);
	} else if (z <= -2.2e-60) {
		tmp = (y * i) + (a + (-0.5 * log(c)));
	} else if ((z <= -2.7e-141) || (!(z <= -7.5e-182) && (z <= 6.9e-292))) {
		tmp = (log(c) * (b - 0.5)) + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-5.5d+135)) then
        tmp = z + (y * i)
    else if (z <= (-2.2d-60)) then
        tmp = (y * i) + (a + ((-0.5d0) * log(c)))
    else if ((z <= (-2.7d-141)) .or. (.not. (z <= (-7.5d-182))) .and. (z <= 6.9d-292)) then
        tmp = (log(c) * (b - 0.5d0)) + (y * i)
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -5.5e+135) {
		tmp = z + (y * i);
	} else if (z <= -2.2e-60) {
		tmp = (y * i) + (a + (-0.5 * Math.log(c)));
	} else if ((z <= -2.7e-141) || (!(z <= -7.5e-182) && (z <= 6.9e-292))) {
		tmp = (Math.log(c) * (b - 0.5)) + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -5.5e+135:
		tmp = z + (y * i)
	elif z <= -2.2e-60:
		tmp = (y * i) + (a + (-0.5 * math.log(c)))
	elif (z <= -2.7e-141) or (not (z <= -7.5e-182) and (z <= 6.9e-292)):
		tmp = (math.log(c) * (b - 0.5)) + (y * i)
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -5.5e+135)
		tmp = Float64(z + Float64(y * i));
	elseif (z <= -2.2e-60)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(-0.5 * log(c))));
	elseif ((z <= -2.7e-141) || (!(z <= -7.5e-182) && (z <= 6.9e-292)))
		tmp = Float64(Float64(log(c) * Float64(b - 0.5)) + Float64(y * i));
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -5.5e+135)
		tmp = z + (y * i);
	elseif (z <= -2.2e-60)
		tmp = (y * i) + (a + (-0.5 * log(c)));
	elseif ((z <= -2.7e-141) || (~((z <= -7.5e-182)) && (z <= 6.9e-292)))
		tmp = (log(c) * (b - 0.5)) + (y * i);
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -5.5e+135], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.2e-60], N[(N[(y * i), $MachinePrecision] + N[(a + N[(-0.5 * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -2.7e-141], And[N[Not[LessEqual[z, -7.5e-182]], $MachinePrecision], LessEqual[z, 6.9e-292]]], N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.4999999999999999e135

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 90.5%

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

      1. +-commutative 90.5%

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

      2. log-pow 45.2%

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

      3. associate-+r+ 45.2%

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

      4. log-pow 90.5%

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

      5. fma-udef 90.5%

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

   4. Simplified 90.5%

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

   5. Taylor expanded in z around inf 76.7%

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

   6. Taylor expanded in z around inf 67.0%

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

   if -5.4999999999999999e135 < z < -2.1999999999999999e-60

   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 a around inf 52.7%

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

   3. Taylor expanded in b around 0 42.7%

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

      1. *-commutative 42.7%

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

   5. Simplified 42.7%

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

   if -2.1999999999999999e-60 < z < -2.7000000000000003e-141 or -7.49999999999999935e-182 < z < 6.89999999999999969e-292

   1. Initial program 100.0%

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

   2. Taylor expanded in a around inf 74.9%

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

   3. Taylor expanded in a around 0 51.8%

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

   if -2.7000000000000003e-141 < z < -7.49999999999999935e-182 or 6.89999999999999969e-292 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in a around inf 58.7%

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

      1. sub-neg 58.7%

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

      2. metadata-eval 58.7%

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

      3. *-commutative 58.7%

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

      4. flip-+ 45.5%

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

      5. associate-*r/ 45.5%

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

      6. fma-neg 45.5%

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

      7. metadata-eval 45.5%

         \[\leadsto \left(a + \frac{\log c \cdot \mathsf{fma}\left(b, b, -\color{blue}{0.25}\right)}{b - -0.5}\right) + y \cdot i \]

      8. metadata-eval 45.5%

         \[\leadsto \left(a + \frac{\log c \cdot \mathsf{fma}\left(b, b, \color{blue}{-0.25}\right)}{b - -0.5}\right) + y \cdot i \]

      9. sub-neg 45.5%

         \[\leadsto \left(a + \frac{\log c \cdot \mathsf{fma}\left(b, b, -0.25\right)}{\color{blue}{b + \left(--0.5\right)}}\right) + y \cdot i \]

      10. metadata-eval 45.5%

          \[\leadsto \left(a + \frac{\log c \cdot \mathsf{fma}\left(b, b, -0.25\right)}{b + \color{blue}{0.5}}\right) + y \cdot i \]

   4. Applied egg-rr 45.5%

      \[\leadsto \left(a + \color{blue}{\frac{\log c \cdot \mathsf{fma}\left(b, b, -0.25\right)}{b + 0.5}}\right) + y \cdot i \]
   5. Step-by-step derivation

      1. associate-/l* 45.5%

         \[\leadsto \left(a + \color{blue}{\frac{\log c}{\frac{b + 0.5}{\mathsf{fma}\left(b, b, -0.25\right)}}}\right) + y \cdot i \]

   6. Simplified 45.5%

      \[\leadsto \left(a + \color{blue}{\frac{\log c}{\frac{b + 0.5}{\mathsf{fma}\left(b, b, -0.25\right)}}}\right) + y \cdot i \]

   7. Taylor expanded in a around inf 44.9%

      \[\leadsto \color{blue}{a} + y \cdot i \]
3. Recombined 4 regimes into one program.

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+135}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-60}:\\ \;\;\;\;y \cdot i + \left(a + -0.5 \cdot \log c\right)\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-141} \lor \neg \left(z \leq -7.5 \cdot 10^{-182}\right) \land z \leq 6.9 \cdot 10^{-292}:\\ \;\;\;\;\log c \cdot \left(b - 0.5\right) + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]

Alternative 6: 42.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log c \cdot \left(b - 0.5\right) + y \cdot i\\ t_2 := z + y \cdot i\\ \mathbf{if}\;a \leq 8.5 \cdot 10^{-290}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.46 \cdot 10^{-182}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-84}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+84}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* (log c) (- b 0.5)) (* y i))) (t_2 (+ z (* y i))))
   (if (<= a 8.5e-290)
     t_2
     (if (<= a 1.46e-182)
       t_1
       (if (<= a 9e-84)
         t_2
         (if (<= a 1.9e-26) t_1 (if (<= a 1.6e+84) t_2 (+ a (* y i)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (log(c) * (b - 0.5)) + (y * i);
	double t_2 = z + (y * i);
	double tmp;
	if (a <= 8.5e-290) {
		tmp = t_2;
	} else if (a <= 1.46e-182) {
		tmp = t_1;
	} else if (a <= 9e-84) {
		tmp = t_2;
	} else if (a <= 1.9e-26) {
		tmp = t_1;
	} else if (a <= 1.6e+84) {
		tmp = t_2;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (log(c) * (b - 0.5d0)) + (y * i)
    t_2 = z + (y * i)
    if (a <= 8.5d-290) then
        tmp = t_2
    else if (a <= 1.46d-182) then
        tmp = t_1
    else if (a <= 9d-84) then
        tmp = t_2
    else if (a <= 1.9d-26) then
        tmp = t_1
    else if (a <= 1.6d+84) then
        tmp = t_2
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (Math.log(c) * (b - 0.5)) + (y * i);
	double t_2 = z + (y * i);
	double tmp;
	if (a <= 8.5e-290) {
		tmp = t_2;
	} else if (a <= 1.46e-182) {
		tmp = t_1;
	} else if (a <= 9e-84) {
		tmp = t_2;
	} else if (a <= 1.9e-26) {
		tmp = t_1;
	} else if (a <= 1.6e+84) {
		tmp = t_2;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (math.log(c) * (b - 0.5)) + (y * i)
	t_2 = z + (y * i)
	tmp = 0
	if a <= 8.5e-290:
		tmp = t_2
	elif a <= 1.46e-182:
		tmp = t_1
	elif a <= 9e-84:
		tmp = t_2
	elif a <= 1.9e-26:
		tmp = t_1
	elif a <= 1.6e+84:
		tmp = t_2
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(log(c) * Float64(b - 0.5)) + Float64(y * i))
	t_2 = Float64(z + Float64(y * i))
	tmp = 0.0
	if (a <= 8.5e-290)
		tmp = t_2;
	elseif (a <= 1.46e-182)
		tmp = t_1;
	elseif (a <= 9e-84)
		tmp = t_2;
	elseif (a <= 1.9e-26)
		tmp = t_1;
	elseif (a <= 1.6e+84)
		tmp = t_2;
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (log(c) * (b - 0.5)) + (y * i);
	t_2 = z + (y * i);
	tmp = 0.0;
	if (a <= 8.5e-290)
		tmp = t_2;
	elseif (a <= 1.46e-182)
		tmp = t_1;
	elseif (a <= 9e-84)
		tmp = t_2;
	elseif (a <= 1.9e-26)
		tmp = t_1;
	elseif (a <= 1.6e+84)
		tmp = t_2;
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, 8.5e-290], t$95$2, If[LessEqual[a, 1.46e-182], t$95$1, If[LessEqual[a, 9e-84], t$95$2, If[LessEqual[a, 1.9e-26], t$95$1, If[LessEqual[a, 1.6e+84], t$95$2, N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < 8.50000000000000045e-290 or 1.46e-182 < a < 9.00000000000000031e-84 or 1.90000000000000007e-26 < a < 1.60000000000000005e84

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 79.2%

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

      1. +-commutative 79.2%

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

      2. log-pow 42.4%

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

      3. associate-+r+ 42.4%

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

      4. log-pow 79.2%

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

      5. fma-udef 79.2%

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

   4. Simplified 79.2%

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

   5. Taylor expanded in z around inf 54.5%

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

   6. Taylor expanded in z around inf 39.6%

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

   if 8.50000000000000045e-290 < a < 1.46e-182 or 9.00000000000000031e-84 < a < 1.90000000000000007e-26

   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 64.6%

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

   3. Taylor expanded in a around 0 64.6%

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

   if 1.60000000000000005e84 < 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 73.7%

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

      1. sub-neg 73.7%

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

      2. metadata-eval 73.7%

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

      3. *-commutative 73.7%

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

      4. flip-+ 54.0%

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

      5. associate-*r/ 54.0%

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

      6. fma-neg 54.0%

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

      7. metadata-eval 54.0%

         \[\leadsto \left(a + \frac{\log c \cdot \mathsf{fma}\left(b, b, -\color{blue}{0.25}\right)}{b - -0.5}\right) + y \cdot i \]

      8. metadata-eval 54.0%

         \[\leadsto \left(a + \frac{\log c \cdot \mathsf{fma}\left(b, b, \color{blue}{-0.25}\right)}{b - -0.5}\right) + y \cdot i \]

      9. sub-neg 54.0%

         \[\leadsto \left(a + \frac{\log c \cdot \mathsf{fma}\left(b, b, -0.25\right)}{\color{blue}{b + \left(--0.5\right)}}\right) + y \cdot i \]

      10. metadata-eval 54.0%

          \[\leadsto \left(a + \frac{\log c \cdot \mathsf{fma}\left(b, b, -0.25\right)}{b + \color{blue}{0.5}}\right) + y \cdot i \]

   4. Applied egg-rr 54.0%

      \[\leadsto \left(a + \color{blue}{\frac{\log c \cdot \mathsf{fma}\left(b, b, -0.25\right)}{b + 0.5}}\right) + y \cdot i \]
   5. Step-by-step derivation

      1. associate-/l* 54.0%

         \[\leadsto \left(a + \color{blue}{\frac{\log c}{\frac{b + 0.5}{\mathsf{fma}\left(b, b, -0.25\right)}}}\right) + y \cdot i \]

   6. Simplified 54.0%

      \[\leadsto \left(a + \color{blue}{\frac{\log c}{\frac{b + 0.5}{\mathsf{fma}\left(b, b, -0.25\right)}}}\right) + y \cdot i \]

   7. Taylor expanded in a around inf 62.9%

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

4. Final simplification 47.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 8.5 \cdot 10^{-290}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;a \leq 1.46 \cdot 10^{-182}:\\ \;\;\;\;\log c \cdot \left(b - 0.5\right) + y \cdot i\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-84}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-26}:\\ \;\;\;\;\log c \cdot \left(b - 0.5\right) + y \cdot i\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+84}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]

Alternative 7: 83.7% accurate, 1.9× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (y * i) + ((log(c) * (b - 0.5)) + (a + (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) + ((log(c) * (b - 0.5d0)) + (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) + ((Math.log(c) * (b - 0.5)) + (a + (z + t)));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in x around 0 87.2%

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

3. Final simplification 87.2%

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

Alternative 8: 58.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 2.1 \cdot 10^{+84}:\\ \;\;\;\;y \cdot i + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 2.1e+84)
   (+ (* y i) (+ z (* (log c) (- b 0.5))))
   (+ (* y i) (+ a (* 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 (a <= 2.1e+84) {
		tmp = (y * i) + (z + (log(c) * (b - 0.5)));
	} else {
		tmp = (y * i) + (a + (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 (a <= 2.1d+84) then
        tmp = (y * i) + (z + (log(c) * (b - 0.5d0)))
    else
        tmp = (y * i) + (a + (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 (a <= 2.1e+84) {
		tmp = (y * i) + (z + (Math.log(c) * (b - 0.5)));
	} else {
		tmp = (y * i) + (a + (b * Math.log(c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 2.1e+84:
		tmp = (y * i) + (z + (math.log(c) * (b - 0.5)))
	else:
		tmp = (y * i) + (a + (b * math.log(c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 2.1e+84)
		tmp = Float64(Float64(y * i) + Float64(z + Float64(log(c) * Float64(b - 0.5))));
	else
		tmp = Float64(Float64(y * i) + Float64(a + 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 (a <= 2.1e+84)
		tmp = (y * i) + (z + (log(c) * (b - 0.5)));
	else
		tmp = (y * i) + (a + (b * log(c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 2.1e+84], N[(N[(y * i), $MachinePrecision] + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 2.10000000000000019e84

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 80.2%

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

      1. +-commutative 80.2%

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

      2. log-pow 42.2%

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

      3. associate-+r+ 42.2%

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

      4. log-pow 80.2%

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

      5. fma-udef 80.2%

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

   4. Simplified 80.2%

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

   5. Taylor expanded in z around inf 58.1%

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

   if 2.10000000000000019e84 < 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 73.7%

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

   3. Taylor expanded in b around inf 73.7%

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

      1. *-commutative 73.7%

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

   5. Simplified 73.7%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 2.1 \cdot 10^{+84}:\\ \;\;\;\;y \cdot i + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \end{array} \]

Alternative 9: 82.1% accurate, 1.9× speedup

Math

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

FPCore

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

Python

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

Julia

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

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = (y * i) + ((b * log(c)) + (a + (z + t)));
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[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in 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 57.4%

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

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 x around 0 85.7%

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

6. Final simplification 85.7%

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

Alternative 10: 56.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+190}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -2.4e+190) (+ z (* y i)) (+ (* y i) (+ a (* 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 (z <= -2.4e+190) {
		tmp = z + (y * i);
	} else {
		tmp = (y * i) + (a + (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 (z <= (-2.4d+190)) then
        tmp = z + (y * i)
    else
        tmp = (y * i) + (a + (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 (z <= -2.4e+190) {
		tmp = z + (y * i);
	} else {
		tmp = (y * i) + (a + (b * Math.log(c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -2.4e+190:
		tmp = z + (y * i)
	else:
		tmp = (y * i) + (a + (b * math.log(c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -2.4e+190)
		tmp = Float64(z + Float64(y * i));
	else
		tmp = Float64(Float64(y * i) + Float64(a + 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 (z <= -2.4e+190)
		tmp = z + (y * i);
	else
		tmp = (y * i) + (a + (b * log(c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -2.4e+190], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.3999999999999999e190

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 91.0%

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

      1. +-commutative 91.0%

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

      2. log-pow 47.4%

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

      3. associate-+r+ 47.4%

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

      4. log-pow 91.0%

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

      5. fma-udef 91.0%

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

   4. Simplified 91.0%

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

   5. Taylor expanded in z around inf 84.2%

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

   6. Taylor expanded in z around inf 76.9%

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

   if -2.3999999999999999e190 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in a around inf 60.9%

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

   3. Taylor expanded in b around inf 59.2%

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

      1. *-commutative 59.2%

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

   5. Simplified 59.2%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+190}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \end{array} \]

Alternative 11: 57.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \log c\\ \mathbf{if}\;a \leq 2.1 \cdot 10^{+84}:\\ \;\;\;\;y \cdot i + \left(z + t_1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* b (log c))))
   (if (<= a 2.1e+84) (+ (* y i) (+ z t_1)) (+ (* y i) (+ a t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = b * log(c);
	double tmp;
	if (a <= 2.1e+84) {
		tmp = (y * i) + (z + t_1);
	} else {
		tmp = (y * i) + (a + 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 = b * log(c)
    if (a <= 2.1d+84) then
        tmp = (y * i) + (z + t_1)
    else
        tmp = (y * i) + (a + 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 = b * Math.log(c);
	double tmp;
	if (a <= 2.1e+84) {
		tmp = (y * i) + (z + t_1);
	} else {
		tmp = (y * i) + (a + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = b * math.log(c)
	tmp = 0
	if a <= 2.1e+84:
		tmp = (y * i) + (z + t_1)
	else:
		tmp = (y * i) + (a + t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(b * log(c))
	tmp = 0.0
	if (a <= 2.1e+84)
		tmp = Float64(Float64(y * i) + Float64(z + t_1));
	else
		tmp = Float64(Float64(y * i) + Float64(a + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = b * log(c);
	tmp = 0.0;
	if (a <= 2.1e+84)
		tmp = (y * i) + (z + t_1);
	else
		tmp = (y * i) + (a + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, 2.1e+84], N[(N[(y * i), $MachinePrecision] + N[(z + t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < 2.10000000000000019e84

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 80.2%

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

      1. +-commutative 80.2%

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

      2. log-pow 42.2%

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

      3. associate-+r+ 42.2%

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

      4. log-pow 80.2%

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

      5. fma-udef 80.2%

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

   4. Simplified 80.2%

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

   5. Taylor expanded in z around inf 58.1%

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

   6. Taylor expanded in b around inf 56.2%

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

      1. *-commutative 53.3%

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

   8. Simplified 56.2%

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

   if 2.10000000000000019e84 < 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 73.7%

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

   3. Taylor expanded in b around inf 73.7%

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

      1. *-commutative 73.7%

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

   5. Simplified 73.7%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 2.1 \cdot 10^{+84}:\\ \;\;\;\;y \cdot i + \left(z + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \end{array} \]

Alternative 12: 42.2% accurate, 31.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 2.1 \cdot 10^{+84}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 2.1e+84) (+ z (* y i)) (+ a (* y i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 2.1e+84) {
		tmp = z + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 2.1d+84) then
        tmp = z + (y * i)
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 2.1e+84) {
		tmp = z + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 2.1e+84:
		tmp = z + (y * i)
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 2.1e+84)
		tmp = Float64(z + Float64(y * i));
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 2.1e+84)
		tmp = z + (y * i);
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 2.1e+84], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 2.10000000000000019e84

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 80.2%

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

      1. +-commutative 80.2%

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

      2. log-pow 42.2%

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

      3. associate-+r+ 42.2%

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

      4. log-pow 80.2%

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

      5. fma-udef 80.2%

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

   4. Simplified 80.2%

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

   5. Taylor expanded in z around inf 58.1%

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

   6. Taylor expanded in z around inf 41.7%

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

   if 2.10000000000000019e84 < 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 73.7%

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

      1. sub-neg 73.7%

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

      2. metadata-eval 73.7%

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

      3. *-commutative 73.7%

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

      4. flip-+ 54.0%

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

      5. associate-*r/ 54.0%

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

      6. fma-neg 54.0%

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

      7. metadata-eval 54.0%

         \[\leadsto \left(a + \frac{\log c \cdot \mathsf{fma}\left(b, b, -\color{blue}{0.25}\right)}{b - -0.5}\right) + y \cdot i \]

      8. metadata-eval 54.0%

         \[\leadsto \left(a + \frac{\log c \cdot \mathsf{fma}\left(b, b, \color{blue}{-0.25}\right)}{b - -0.5}\right) + y \cdot i \]

      9. sub-neg 54.0%

         \[\leadsto \left(a + \frac{\log c \cdot \mathsf{fma}\left(b, b, -0.25\right)}{\color{blue}{b + \left(--0.5\right)}}\right) + y \cdot i \]

      10. metadata-eval 54.0%

          \[\leadsto \left(a + \frac{\log c \cdot \mathsf{fma}\left(b, b, -0.25\right)}{b + \color{blue}{0.5}}\right) + y \cdot i \]

   4. Applied egg-rr 54.0%

      \[\leadsto \left(a + \color{blue}{\frac{\log c \cdot \mathsf{fma}\left(b, b, -0.25\right)}{b + 0.5}}\right) + y \cdot i \]
   5. Step-by-step derivation

      1. associate-/l* 54.0%

         \[\leadsto \left(a + \color{blue}{\frac{\log c}{\frac{b + 0.5}{\mathsf{fma}\left(b, b, -0.25\right)}}}\right) + y \cdot i \]

   6. Simplified 54.0%

      \[\leadsto \left(a + \color{blue}{\frac{\log c}{\frac{b + 0.5}{\mathsf{fma}\left(b, b, -0.25\right)}}}\right) + y \cdot i \]

   7. Taylor expanded in a around inf 62.9%

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

4. Final simplification 46.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 2.1 \cdot 10^{+84}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]

Alternative 13: 37.5% accurate, 43.8× speedup

Math

\[\begin{array}{l} \\ a + y \cdot i \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in a around inf 59.0%

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

   1. sub-neg 59.0%

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

   2. metadata-eval 59.0%

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

   3. *-commutative 59.0%

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

   4. flip-+ 46.0%

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

   5. associate-*r/ 45.7%

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

   6. fma-neg 45.7%

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

   7. metadata-eval 45.7%

      \[\leadsto \left(a + \frac{\log c \cdot \mathsf{fma}\left(b, b, -\color{blue}{0.25}\right)}{b - -0.5}\right) + y \cdot i \]

   8. metadata-eval 45.7%

      \[\leadsto \left(a + \frac{\log c \cdot \mathsf{fma}\left(b, b, \color{blue}{-0.25}\right)}{b - -0.5}\right) + y \cdot i \]

   9. sub-neg 45.7%

      \[\leadsto \left(a + \frac{\log c \cdot \mathsf{fma}\left(b, b, -0.25\right)}{\color{blue}{b + \left(--0.5\right)}}\right) + y \cdot i \]

   10. metadata-eval 45.7%

       \[\leadsto \left(a + \frac{\log c \cdot \mathsf{fma}\left(b, b, -0.25\right)}{b + \color{blue}{0.5}}\right) + y \cdot i \]

4. Applied egg-rr 45.7%

   \[\leadsto \left(a + \color{blue}{\frac{\log c \cdot \mathsf{fma}\left(b, b, -0.25\right)}{b + 0.5}}\right) + y \cdot i \]
5. Step-by-step derivation

   1. associate-/l* 46.0%

      \[\leadsto \left(a + \color{blue}{\frac{\log c}{\frac{b + 0.5}{\mathsf{fma}\left(b, b, -0.25\right)}}}\right) + y \cdot i \]

6. Simplified 46.0%

   \[\leadsto \left(a + \color{blue}{\frac{\log c}{\frac{b + 0.5}{\mathsf{fma}\left(b, b, -0.25\right)}}}\right) + y \cdot i \]

7. Taylor expanded in a around inf 43.8%

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

8. Final simplification 43.8%

   \[\leadsto a + y \cdot i \]

Alternative 14: 23.6% accurate, 73.0× speedup

Math

\[\begin{array}{l} \\ y \cdot i \end{array} \]

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in t around 0 81.7%

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

   1. +-commutative 81.7%

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

   2. log-pow 45.1%

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

   3. associate-+r+ 45.1%

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

   4. log-pow 81.7%

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

   5. fma-udef 81.7%

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

4. Simplified 81.7%

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

5. Taylor expanded in y around inf 27.2%

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

   1. *-commutative 27.2%

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

7. Simplified 27.2%

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

8. Final simplification 27.2%

   \[\leadsto y \cdot i \]

Reproduce

herbie shell --seed 2023310 
(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)))