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

Percentage Accurate: 99.8% → 99.8%

Time: 14.5s

Alternatives: 15

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. associate-+l+ 99.9%

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

   2. associate-+l+ 99.9%

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

   3. +-commutative 99.9%

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

   4. associate-+l+ 99.9%

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

   5. +-commutative 99.9%

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

   6. associate-+l+ 99.9%

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

   7. +-commutative 99.9%

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

   8. associate-+l+ 99.9%

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

   9. +-commutative 99.9%

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

   10. fma-define 99.9%

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

   11. +-commutative 99.9%

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

   12. fma-define 99.9%

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

3. Simplified 99.9%

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

Alternative 2: 84.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log c \cdot \left(b - 0.5\right)\\ t_2 := z + t\_1\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+49}:\\ \;\;\;\;a + t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+215}:\\ \;\;\;\;a + \left(t + \left(z + \left(x \cdot \log y + y \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* (log c) (- b 0.5))) (t_2 (+ z t_1)))
   (if (<= t_1 -1e+49)
     (+ a t_2)
     (if (<= t_1 2e+215)
       (+ a (+ t (+ z (+ (* x (log y)) (* y i)))))
       (+ (* y i) 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 = z + t_1;
	double tmp;
	if (t_1 <= -1e+49) {
		tmp = a + t_2;
	} else if (t_1 <= 2e+215) {
		tmp = a + (t + (z + ((x * log(y)) + (y * i))));
	} else {
		tmp = (y * i) + 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 = z + t_1
    if (t_1 <= (-1d+49)) then
        tmp = a + t_2
    else if (t_1 <= 2d+215) then
        tmp = a + (t + (z + ((x * log(y)) + (y * i))))
    else
        tmp = (y * i) + 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 = z + t_1;
	double tmp;
	if (t_1 <= -1e+49) {
		tmp = a + t_2;
	} else if (t_1 <= 2e+215) {
		tmp = a + (t + (z + ((x * Math.log(y)) + (y * i))));
	} else {
		tmp = (y * i) + 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 = z + t_1
	tmp = 0
	if t_1 <= -1e+49:
		tmp = a + t_2
	elif t_1 <= 2e+215:
		tmp = a + (t + (z + ((x * math.log(y)) + (y * i))))
	else:
		tmp = (y * i) + 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(z + t_1)
	tmp = 0.0
	if (t_1 <= -1e+49)
		tmp = Float64(a + t_2);
	elseif (t_1 <= 2e+215)
		tmp = Float64(a + Float64(t + Float64(z + Float64(Float64(x * log(y)) + Float64(y * i)))));
	else
		tmp = Float64(Float64(y * i) + 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 = z + t_1;
	tmp = 0.0;
	if (t_1 <= -1e+49)
		tmp = a + t_2;
	elseif (t_1 <= 2e+215)
		tmp = a + (t + (z + ((x * log(y)) + (y * i))));
	else
		tmp = (y * i) + 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[(z + t$95$1), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+49], N[(a + t$95$2), $MachinePrecision], If[LessEqual[t$95$1, 2e+215], N[(a + N[(t + N[(z + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c)) < -9.99999999999999946e48

   1. Initial program 99.8%

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

      1. associate-+l+ 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. associate-+l+ 99.8%

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

      5. +-commutative 99.8%

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

      6. associate-+l+ 99.8%

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

      7. +-commutative 99.8%

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

      8. associate-+l+ 99.8%

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

      9. +-commutative 99.8%

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

      10. fma-define 99.8%

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

      11. +-commutative 99.8%

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

      12. fma-define 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in i around inf 60.5%

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

      1. associate-+r+ 60.5%

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

      2. associate-+r+ 60.5%

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

      3. associate-/l* 60.5%

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

      4. sub-neg 60.5%

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

      5. metadata-eval 60.5%

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

      6. associate-/l* 60.4%

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

      7. +-commutative 60.4%

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

   7. Simplified 60.4%

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

   8. Taylor expanded in t around 0 54.3%

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

   9. Taylor expanded in i around 0 75.7%

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

   10. Taylor expanded in x around 0 65.9%

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

   if -9.99999999999999946e48 < (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c)) < 1.99999999999999981e215

   1. Initial program 99.9%

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

   3. Taylor expanded in b around inf 97.3%

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

      1. *-commutative 97.3%

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

   5. Simplified 97.3%

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

   6. Taylor expanded in b around 0 94.1%

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

   if 1.99999999999999981e215 < (*.f64 (-.f64 b #s(literal 1/2 binary64)) (log.f64 c))

   1. Initial program 99.6%

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

      1. add-cube-cbrt 99.5%

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

      2. pow3 99.5%

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

   4. Applied egg-rr 99.5%

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

   5. Taylor expanded in z around inf 74.1%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\log c \cdot \left(b - 0.5\right) \leq -1 \cdot 10^{+49}:\\ \;\;\;\;a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{elif}\;\log c \cdot \left(b - 0.5\right) \leq 2 \cdot 10^{+215}:\\ \;\;\;\;a + \left(t + \left(z + \left(x \cdot \log y + y \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+95} \lor \neg \left(x \leq 3.6 \cdot 10^{+174}\right):\\ \;\;\;\;a + \left(t + \left(z + \left(x \cdot \log y + y \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -3.6e+95) (not (<= x 3.6e+174)))
   (+ a (+ t (+ z (+ (* x (log y)) (* y i)))))
   (fma y i (+ a (+ t (+ z (* (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 <= -3.6e+95) || !(x <= 3.6e+174)) {
		tmp = a + (t + (z + ((x * log(y)) + (y * i))));
	} else {
		tmp = fma(y, i, (a + (t + (z + (log(c) * (b - 0.5))))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -3.6e+95) || !(x <= 3.6e+174))
		tmp = Float64(a + Float64(t + Float64(z + Float64(Float64(x * log(y)) + Float64(y * i)))));
	else
		tmp = fma(y, i, Float64(a + Float64(t + Float64(z + Float64(log(c) * Float64(b - 0.5))))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -3.6e+95], N[Not[LessEqual[x, 3.6e+174]], $MachinePrecision]], N[(a + N[(t + N[(z + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * i + N[(a + N[(t + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.59999999999999978e95 or 3.6000000000000002e174 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in b around inf 99.9%

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

      1. *-commutative 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in b around 0 94.8%

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

   if -3.59999999999999978e95 < x < 3.6000000000000002e174

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. associate-+l+ 99.9%

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

      7. +-commutative 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 99.4%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+95} \lor \neg \left(x \leq 3.6 \cdot 10^{+174}\right):\\ \;\;\;\;a + \left(t + \left(z + \left(x \cdot \log y + y \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, i, a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 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. Add Preprocessing

3. Final simplification 99.9%

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

Alternative 5: 97.8% accurate, 1.0× speedup

Math

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

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. Add Preprocessing

3. Taylor expanded in b around inf 98.0%

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

   1. *-commutative 98.0%

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

5. Simplified 98.0%

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

6. Final simplification 98.0%

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

Alternative 6: 94.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+96} \lor \neg \left(x \leq 1.45 \cdot 10^{+174}\right):\\ \;\;\;\;a + \left(t + \left(z + \left(x \cdot \log y + y \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + \left(\log c \cdot \left(b - 0.5\right) + y \cdot i\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -2.3e+96) (not (<= x 1.45e+174)))
   (+ a (+ t (+ z (+ (* x (log y)) (* y i)))))
   (+ a (+ t (+ z (+ (* (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) {
	double tmp;
	if ((x <= -2.3e+96) || !(x <= 1.45e+174)) {
		tmp = a + (t + (z + ((x * log(y)) + (y * i))));
	} else {
		tmp = a + (t + (z + ((log(c) * (b - 0.5)) + (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 ((x <= (-2.3d+96)) .or. (.not. (x <= 1.45d+174))) then
        tmp = a + (t + (z + ((x * log(y)) + (y * i))))
    else
        tmp = a + (t + (z + ((log(c) * (b - 0.5d0)) + (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 ((x <= -2.3e+96) || !(x <= 1.45e+174)) {
		tmp = a + (t + (z + ((x * Math.log(y)) + (y * i))));
	} else {
		tmp = a + (t + (z + ((Math.log(c) * (b - 0.5)) + (y * i))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -2.3e+96) or not (x <= 1.45e+174):
		tmp = a + (t + (z + ((x * math.log(y)) + (y * i))))
	else:
		tmp = a + (t + (z + ((math.log(c) * (b - 0.5)) + (y * i))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -2.3e+96) || !(x <= 1.45e+174))
		tmp = Float64(a + Float64(t + Float64(z + Float64(Float64(x * log(y)) + Float64(y * i)))));
	else
		tmp = Float64(a + Float64(t + Float64(z + Float64(Float64(log(c) * Float64(b - 0.5)) + Float64(y * i)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -2.3e+96) || ~((x <= 1.45e+174)))
		tmp = a + (t + (z + ((x * log(y)) + (y * i))));
	else
		tmp = a + (t + (z + ((log(c) * (b - 0.5)) + (y * i))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -2.3e+96], N[Not[LessEqual[x, 1.45e+174]], $MachinePrecision]], N[(a + N[(t + N[(z + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(t + N[(z + N[(N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.30000000000000015e96 or 1.45e174 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in b around inf 99.9%

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

      1. *-commutative 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in b around 0 94.8%

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

   if -2.30000000000000015e96 < x < 1.45e174

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. associate-+l+ 99.9%

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

      7. +-commutative 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 99.4%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+96} \lor \neg \left(x \leq 1.45 \cdot 10^{+174}\right):\\ \;\;\;\;a + \left(t + \left(z + \left(x \cdot \log y + y \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + \left(\log c \cdot \left(b - 0.5\right) + y \cdot i\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -7.2 \cdot 10^{+167} \lor \neg \left(i \leq 4.4 \cdot 10^{+166}\right):\\ \;\;\;\;a \cdot \left(i \cdot \frac{y}{a} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= i -7.2e+167) (not (<= i 4.4e+166)))
   (* a (+ (* i (/ y a)) 1.0))
   (+ a (+ t (+ z (* (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 ((i <= -7.2e+167) || !(i <= 4.4e+166)) {
		tmp = a * ((i * (y / a)) + 1.0);
	} else {
		tmp = a + (t + (z + (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 ((i <= (-7.2d+167)) .or. (.not. (i <= 4.4d+166))) then
        tmp = a * ((i * (y / a)) + 1.0d0)
    else
        tmp = a + (t + (z + (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 ((i <= -7.2e+167) || !(i <= 4.4e+166)) {
		tmp = a * ((i * (y / a)) + 1.0);
	} else {
		tmp = a + (t + (z + (Math.log(c) * (b - 0.5))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (i <= -7.2e+167) or not (i <= 4.4e+166):
		tmp = a * ((i * (y / a)) + 1.0)
	else:
		tmp = a + (t + (z + (math.log(c) * (b - 0.5))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((i <= -7.2e+167) || !(i <= 4.4e+166))
		tmp = Float64(a * Float64(Float64(i * Float64(y / a)) + 1.0));
	else
		tmp = Float64(a + Float64(t + Float64(z + 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 ((i <= -7.2e+167) || ~((i <= 4.4e+166)))
		tmp = a * ((i * (y / a)) + 1.0);
	else
		tmp = a + (t + (z + (log(c) * (b - 0.5))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[i, -7.2e+167], N[Not[LessEqual[i, 4.4e+166]], $MachinePrecision]], N[(a * N[(N[(i * N[(y / a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(a + N[(t + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -7.20000000000000049e167 or 4.3999999999999998e166 < 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. Step-by-step derivation

      1. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. associate-+l+ 99.9%

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

      7. +-commutative 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 100.0%

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

      11. +-commutative 100.0%

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

      12. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in a around -inf 81.4%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(-1 \cdot \frac{t + \left(z + \left(i \cdot y + \left(x \cdot \log y + \log c \cdot \left(b - 0.5\right)\right)\right)\right)}{a} - 1\right)\right)} \]

   6. Taylor expanded in i around inf 66.4%

      \[\leadsto -1 \cdot \left(a \cdot \left(-1 \cdot \color{blue}{\frac{i \cdot y}{a}} - 1\right)\right) \]
   7. Step-by-step derivation

      1. associate-/l* 66.3%

         \[\leadsto -1 \cdot \left(a \cdot \left(-1 \cdot \color{blue}{\left(i \cdot \frac{y}{a}\right)} - 1\right)\right) \]

   8. Simplified 66.3%

      \[\leadsto -1 \cdot \left(a \cdot \left(-1 \cdot \color{blue}{\left(i \cdot \frac{y}{a}\right)} - 1\right)\right) \]

   if -7.20000000000000049e167 < i < 4.3999999999999998e166

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. associate-+l+ 99.9%

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

      7. +-commutative 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 86.6%

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

   6. Taylor expanded in y around 0 75.7%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -7.2 \cdot 10^{+167} \lor \neg \left(i \leq 4.4 \cdot 10^{+166}\right):\\ \;\;\;\;a \cdot \left(i \cdot \frac{y}{a} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 54.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1.05 \cdot 10^{+168} \lor \neg \left(i \leq 6 \cdot 10^{+166}\right):\\ \;\;\;\;a \cdot \left(i \cdot \frac{y}{a} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= i -1.05e+168) (not (<= i 6e+166)))
   (* a (+ (* i (/ y a)) 1.0))
   (+ a (+ z (* (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 ((i <= -1.05e+168) || !(i <= 6e+166)) {
		tmp = a * ((i * (y / a)) + 1.0);
	} else {
		tmp = a + (z + (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 ((i <= (-1.05d+168)) .or. (.not. (i <= 6d+166))) then
        tmp = a * ((i * (y / a)) + 1.0d0)
    else
        tmp = a + (z + (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 ((i <= -1.05e+168) || !(i <= 6e+166)) {
		tmp = a * ((i * (y / a)) + 1.0);
	} else {
		tmp = a + (z + (Math.log(c) * (b - 0.5)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (i <= -1.05e+168) or not (i <= 6e+166):
		tmp = a * ((i * (y / a)) + 1.0)
	else:
		tmp = a + (z + (math.log(c) * (b - 0.5)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((i <= -1.05e+168) || !(i <= 6e+166))
		tmp = Float64(a * Float64(Float64(i * Float64(y / a)) + 1.0));
	else
		tmp = Float64(a + Float64(z + 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 ((i <= -1.05e+168) || ~((i <= 6e+166)))
		tmp = a * ((i * (y / a)) + 1.0);
	else
		tmp = a + (z + (log(c) * (b - 0.5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[i, -1.05e+168], N[Not[LessEqual[i, 6e+166]], $MachinePrecision]], N[(a * N[(N[(i * N[(y / a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(a + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -1.05000000000000001e168 or 5.99999999999999997e166 < 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. Step-by-step derivation

      1. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. associate-+l+ 99.9%

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

      7. +-commutative 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 100.0%

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

      11. +-commutative 100.0%

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

      12. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in a around -inf 81.4%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(-1 \cdot \frac{t + \left(z + \left(i \cdot y + \left(x \cdot \log y + \log c \cdot \left(b - 0.5\right)\right)\right)\right)}{a} - 1\right)\right)} \]

   6. Taylor expanded in i around inf 66.4%

      \[\leadsto -1 \cdot \left(a \cdot \left(-1 \cdot \color{blue}{\frac{i \cdot y}{a}} - 1\right)\right) \]
   7. Step-by-step derivation

      1. associate-/l* 66.3%

         \[\leadsto -1 \cdot \left(a \cdot \left(-1 \cdot \color{blue}{\left(i \cdot \frac{y}{a}\right)} - 1\right)\right) \]

   8. Simplified 66.3%

      \[\leadsto -1 \cdot \left(a \cdot \left(-1 \cdot \color{blue}{\left(i \cdot \frac{y}{a}\right)} - 1\right)\right) \]

   if -1.05000000000000001e168 < i < 5.99999999999999997e166

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. associate-+l+ 99.9%

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

      7. +-commutative 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in i around inf 55.7%

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

      1. associate-+r+ 55.7%

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

      2. associate-+r+ 55.7%

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

      3. associate-/l* 55.7%

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

      4. sub-neg 55.7%

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

      5. metadata-eval 55.7%

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

      6. associate-/l* 55.7%

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

      7. +-commutative 55.7%

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

   7. Simplified 55.7%

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

   8. Taylor expanded in t around 0 50.4%

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

   9. Taylor expanded in i around 0 75.5%

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

   10. Taylor expanded in x around 0 62.7%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.05 \cdot 10^{+168} \lor \neg \left(i \leq 6 \cdot 10^{+166}\right):\\ \;\;\;\;a \cdot \left(i \cdot \frac{y}{a} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 2.9 \cdot 10^{+149}:\\ \;\;\;\;y \cdot i + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(i \cdot \frac{y}{a} + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 2.9e+149)
   (+ (* y i) (+ z (* (log c) (- b 0.5))))
   (* a (+ (* i (/ y a)) 1.0))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 2.9e+149) {
		tmp = (y * i) + (z + (log(c) * (b - 0.5)));
	} else {
		tmp = a * ((i * (y / a)) + 1.0);
	}
	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 <= 2.9d+149) then
        tmp = (y * i) + (z + (log(c) * (b - 0.5d0)))
    else
        tmp = a * ((i * (y / a)) + 1.0d0)
    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 <= 2.9e+149) {
		tmp = (y * i) + (z + (Math.log(c) * (b - 0.5)));
	} else {
		tmp = a * ((i * (y / a)) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 2.9e+149:
		tmp = (y * i) + (z + (math.log(c) * (b - 0.5)))
	else:
		tmp = a * ((i * (y / a)) + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 2.9e+149)
		tmp = Float64(Float64(y * i) + Float64(z + Float64(log(c) * Float64(b - 0.5))));
	else
		tmp = Float64(a * Float64(Float64(i * Float64(y / a)) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 2.9e+149)
		tmp = (y * i) + (z + (log(c) * (b - 0.5)));
	else
		tmp = a * ((i * (y / a)) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 2.9e+149], N[(N[(y * i), $MachinePrecision] + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(i * N[(y / a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 2.9000000000000002e149

   1. Initial program 99.9%

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

      1. add-cube-cbrt 99.6%

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

      2. pow3 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in z around inf 64.9%

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

   if 2.9000000000000002e149 < 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. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. associate-+l+ 99.9%

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

      7. +-commutative 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around -inf 99.9%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(-1 \cdot \frac{t + \left(z + \left(i \cdot y + \left(x \cdot \log y + \log c \cdot \left(b - 0.5\right)\right)\right)\right)}{a} - 1\right)\right)} \]

   6. Taylor expanded in i around inf 83.3%

      \[\leadsto -1 \cdot \left(a \cdot \left(-1 \cdot \color{blue}{\frac{i \cdot y}{a}} - 1\right)\right) \]
   7. Step-by-step derivation

      1. associate-/l* 83.3%

         \[\leadsto -1 \cdot \left(a \cdot \left(-1 \cdot \color{blue}{\left(i \cdot \frac{y}{a}\right)} - 1\right)\right) \]

   8. Simplified 83.3%

      \[\leadsto -1 \cdot \left(a \cdot \left(-1 \cdot \color{blue}{\left(i \cdot \frac{y}{a}\right)} - 1\right)\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 2.9 \cdot 10^{+149}:\\ \;\;\;\;y \cdot i + \left(z + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(i \cdot \frac{y}{a} + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 23.1% accurate, 12.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 34000000:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{+145}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 + \frac{z}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 34000000.0) z (if (<= a 2.25e+145) (* y i) (* a (+ 1.0 (/ 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 <= 34000000.0) {
		tmp = z;
	} else if (a <= 2.25e+145) {
		tmp = y * i;
	} else {
		tmp = a * (1.0 + (z / 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 <= 34000000.0d0) then
        tmp = z
    else if (a <= 2.25d+145) then
        tmp = y * i
    else
        tmp = a * (1.0d0 + (z / 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 <= 34000000.0) {
		tmp = z;
	} else if (a <= 2.25e+145) {
		tmp = y * i;
	} else {
		tmp = a * (1.0 + (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 34000000.0:
		tmp = z
	elif a <= 2.25e+145:
		tmp = y * i
	else:
		tmp = a * (1.0 + (z / a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 34000000.0)
		tmp = z;
	elseif (a <= 2.25e+145)
		tmp = Float64(y * i);
	else
		tmp = Float64(a * Float64(1.0 + Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 34000000.0)
		tmp = z;
	elseif (a <= 2.25e+145)
		tmp = y * i;
	else
		tmp = a * (1.0 + (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 34000000.0], z, If[LessEqual[a, 2.25e+145], N[(y * i), $MachinePrecision], N[(a * N[(1.0 + N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < 3.4e7

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. associate-+l+ 99.9%

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

      7. +-commutative 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 21.7%

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

   if 3.4e7 < a < 2.2499999999999999e145

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. associate-+l+ 99.9%

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

      7. +-commutative 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 39.0%

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

      1. *-commutative 39.0%

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

   7. Simplified 39.0%

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

   if 2.2499999999999999e145 < 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. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. associate-+l+ 99.9%

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

      7. +-commutative 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around -inf 99.9%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(-1 \cdot \frac{t + \left(z + \left(i \cdot y + \left(x \cdot \log y + \log c \cdot \left(b - 0.5\right)\right)\right)\right)}{a} - 1\right)\right)} \]

   6. Taylor expanded in z around inf 64.3%

      \[\leadsto -1 \cdot \left(a \cdot \left(-1 \cdot \color{blue}{\frac{z}{a}} - 1\right)\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 28.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 34000000:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{+145}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 + \frac{z}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 22.8% accurate, 12.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 25500000:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 9.4 \cdot 10^{+148}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 + \frac{t}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 25500000.0) z (if (<= a 9.4e+148) (* y i) (* a (+ 1.0 (/ t a))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 25500000.0) {
		tmp = z;
	} else if (a <= 9.4e+148) {
		tmp = y * i;
	} else {
		tmp = a * (1.0 + (t / 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 <= 25500000.0d0) then
        tmp = z
    else if (a <= 9.4d+148) then
        tmp = y * i
    else
        tmp = a * (1.0d0 + (t / 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 <= 25500000.0) {
		tmp = z;
	} else if (a <= 9.4e+148) {
		tmp = y * i;
	} else {
		tmp = a * (1.0 + (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 25500000.0:
		tmp = z
	elif a <= 9.4e+148:
		tmp = y * i
	else:
		tmp = a * (1.0 + (t / a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 25500000.0)
		tmp = z;
	elseif (a <= 9.4e+148)
		tmp = Float64(y * i);
	else
		tmp = Float64(a * Float64(1.0 + Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 25500000.0)
		tmp = z;
	elseif (a <= 9.4e+148)
		tmp = y * i;
	else
		tmp = a * (1.0 + (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 25500000.0], z, If[LessEqual[a, 9.4e+148], N[(y * i), $MachinePrecision], N[(a * N[(1.0 + N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < 2.55e7

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. associate-+l+ 99.9%

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

      7. +-commutative 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 21.7%

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

   if 2.55e7 < a < 9.3999999999999994e148

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. associate-+l+ 99.9%

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

      7. +-commutative 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 37.8%

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

      1. *-commutative 37.8%

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

   7. Simplified 37.8%

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

   if 9.3999999999999994e148 < 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. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. associate-+l+ 99.9%

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

      7. +-commutative 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around -inf 99.9%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(-1 \cdot \frac{t + \left(z + \left(i \cdot y + \left(x \cdot \log y + \log c \cdot \left(b - 0.5\right)\right)\right)\right)}{a} - 1\right)\right)} \]

   6. Taylor expanded in t around inf 61.2%

      \[\leadsto -1 \cdot \left(a \cdot \left(-1 \cdot \color{blue}{\frac{t}{a}} - 1\right)\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 27.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 25500000:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 9.4 \cdot 10^{+148}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 + \frac{t}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 25.0% accurate, 15.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 27500000:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(i \cdot \frac{y}{a} + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 27500000.0) z (* a (+ (* i (/ y a)) 1.0))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 27500000.0) {
		tmp = z;
	} else {
		tmp = a * ((i * (y / a)) + 1.0);
	}
	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 <= 27500000.0d0) then
        tmp = z
    else
        tmp = a * ((i * (y / a)) + 1.0d0)
    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 <= 27500000.0) {
		tmp = z;
	} else {
		tmp = a * ((i * (y / a)) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 27500000.0:
		tmp = z
	else:
		tmp = a * ((i * (y / a)) + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 27500000.0)
		tmp = z;
	else
		tmp = Float64(a * Float64(Float64(i * Float64(y / a)) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 27500000.0)
		tmp = z;
	else
		tmp = a * ((i * (y / a)) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 27500000.0], z, N[(a * N[(N[(i * N[(y / a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 2.75e7

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. associate-+l+ 99.9%

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

      7. +-commutative 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 21.7%

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

   if 2.75e7 < 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. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. associate-+l+ 99.9%

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

      7. +-commutative 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around -inf 99.9%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(-1 \cdot \frac{t + \left(z + \left(i \cdot y + \left(x \cdot \log y + \log c \cdot \left(b - 0.5\right)\right)\right)\right)}{a} - 1\right)\right)} \]

   6. Taylor expanded in i around inf 64.0%

      \[\leadsto -1 \cdot \left(a \cdot \left(-1 \cdot \color{blue}{\frac{i \cdot y}{a}} - 1\right)\right) \]
   7. Step-by-step derivation

      1. associate-/l* 64.0%

         \[\leadsto -1 \cdot \left(a \cdot \left(-1 \cdot \color{blue}{\left(i \cdot \frac{y}{a}\right)} - 1\right)\right) \]

   8. Simplified 64.0%

      \[\leadsto -1 \cdot \left(a \cdot \left(-1 \cdot \color{blue}{\left(i \cdot \frac{y}{a}\right)} - 1\right)\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 31.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 27500000:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(i \cdot \frac{y}{a} + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 21.8% accurate, 16.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 22000000:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+148}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 22000000.0) z (if (<= a 2.4e+148) (* 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 <= 22000000.0) {
		tmp = z;
	} else if (a <= 2.4e+148) {
		tmp = y * i;
	} 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 <= 22000000.0d0) then
        tmp = z
    else if (a <= 2.4d+148) then
        tmp = y * i
    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 <= 22000000.0) {
		tmp = z;
	} else if (a <= 2.4e+148) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 22000000.0:
		tmp = z
	elif a <= 2.4e+148:
		tmp = y * i
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 22000000.0)
		tmp = z;
	elseif (a <= 2.4e+148)
		tmp = Float64(y * i);
	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 <= 22000000.0)
		tmp = z;
	elseif (a <= 2.4e+148)
		tmp = y * i;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 22000000.0], z, If[LessEqual[a, 2.4e+148], N[(y * i), $MachinePrecision], a]]

Derivation

1. Split input into 3 regimes

2. if a < 2.2e7

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. associate-+l+ 99.9%

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

      7. +-commutative 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 21.7%

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

   if 2.2e7 < a < 2.39999999999999995e148

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. associate-+l+ 99.9%

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

      7. +-commutative 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 37.8%

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

      1. *-commutative 37.8%

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

   7. Simplified 37.8%

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

   if 2.39999999999999995e148 < 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. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. associate-+l+ 99.9%

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

      7. +-commutative 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around inf 61.2%

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

Alternative 14: 21.1% accurate, 36.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 3.3 \cdot 10^{+102}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (if (<= a 3.3e+102) 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 <= 3.3e+102) {
		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 <= 3.3d+102) 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 <= 3.3e+102) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 3.3e+102:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 3.3e+102)
		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 <= 3.3e+102)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 3.3e+102], z, a]

Derivation

1. Split input into 2 regimes

2. if a < 3.29999999999999999e102

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+l+ 99.9%

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

      5. +-commutative 99.9%

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

      6. associate-+l+ 99.9%

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

      7. +-commutative 99.9%

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

      8. associate-+l+ 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-define 99.9%

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

      11. +-commutative 99.9%

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

      12. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 20.8%

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

   if 3.29999999999999999e102 < a

   1. Initial program 100.0%

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

      1. associate-+l+ 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. associate-+l+ 100.0%

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

      5. +-commutative 100.0%

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

      6. associate-+l+ 100.0%

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

      7. +-commutative 100.0%

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

      8. associate-+l+ 100.0%

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

      9. +-commutative 100.0%

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

      10. fma-define 100.0%

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

      11. +-commutative 100.0%

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

      12. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in a around inf 50.6%

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

Alternative 15: 15.6% 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 99.9%

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

   1. associate-+l+ 99.9%

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

   2. associate-+l+ 99.9%

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

   3. +-commutative 99.9%

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

   4. associate-+l+ 99.9%

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

   5. +-commutative 99.9%

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

   6. associate-+l+ 99.9%

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

   7. +-commutative 99.9%

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

   8. associate-+l+ 99.9%

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

   9. +-commutative 99.9%

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

   10. fma-define 99.9%

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

   11. +-commutative 99.9%

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

   12. fma-define 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in a around inf 16.5%

   \[\leadsto \color{blue}{a} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024186 
(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)))