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

Percentage Accurate: 99.8% → 99.8%

Time: 22.0s

Alternatives: 20

Speedup: 0.7×

• could not determine a ground truth

  1. x = 3.920973997838638e-291
  2. y = 2.1291108985480764e+128
  3. z = 2.0549442932623114e+217
  4. t = -1.0215135169729659e-206
  5. a = -1.2860058420900018e+218
  6. b = 2.0319235215764726e+164
  7. c = 3.2600208043384713e+305
  8. i = -5.755181543193286e-36

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 99.8%

   \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
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 99.9%

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

5. Final simplification 99.9%

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

Alternative 2: 99.8% accurate, 0.7× speedup

Math

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

FPCore

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. associate-+l+ 99.8%

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

   2. associate-+l+ 99.8%

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

   3. fma-define 99.8%

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

   4. sub-neg 99.8%

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

   5. metadata-eval 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 3: 89.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \log c\\ \mathbf{if}\;x \leq -5.3 \cdot 10^{+162} \lor \neg \left(x \leq 4.6 \cdot 10^{+158}\right):\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t\_1 + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* b (log c))))
   (if (or (<= x -5.3e+162) (not (<= x 4.6e+158)))
     (+ (* y i) (+ (* x (log y)) t_1))
     (+ (* y i) (+ t_1 (+ a (+ z t)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = b * log(c);
	double tmp;
	if ((x <= -5.3e+162) || !(x <= 4.6e+158)) {
		tmp = (y * i) + ((x * log(y)) + t_1);
	} else {
		tmp = (y * i) + (t_1 + (a + (z + t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * log(c)
    if ((x <= (-5.3d+162)) .or. (.not. (x <= 4.6d+158))) then
        tmp = (y * i) + ((x * log(y)) + t_1)
    else
        tmp = (y * i) + (t_1 + (a + (z + t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = b * Math.log(c);
	double tmp;
	if ((x <= -5.3e+162) || !(x <= 4.6e+158)) {
		tmp = (y * i) + ((x * Math.log(y)) + t_1);
	} else {
		tmp = (y * i) + (t_1 + (a + (z + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = b * math.log(c)
	tmp = 0
	if (x <= -5.3e+162) or not (x <= 4.6e+158):
		tmp = (y * i) + ((x * math.log(y)) + t_1)
	else:
		tmp = (y * i) + (t_1 + (a + (z + t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(b * log(c))
	tmp = 0.0
	if ((x <= -5.3e+162) || !(x <= 4.6e+158))
		tmp = Float64(Float64(y * i) + Float64(Float64(x * log(y)) + t_1));
	else
		tmp = Float64(Float64(y * i) + Float64(t_1 + Float64(a + Float64(z + t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = b * log(c);
	tmp = 0.0;
	if ((x <= -5.3e+162) || ~((x <= 4.6e+158)))
		tmp = (y * i) + ((x * log(y)) + t_1);
	else
		tmp = (y * i) + (t_1 + (a + (z + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -5.3e+162], N[Not[LessEqual[x, 4.6e+158]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(t$95$1 + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.3000000000000002e162 or 4.59999999999999971e158 < x

   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. Taylor expanded in b around inf 99.6%

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

      1. *-commutative 99.6%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in a around inf 72.0%

      \[\leadsto \left(\color{blue}{a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \frac{x \cdot \log y}{a}\right)\right)\right)} + \log c \cdot b\right) + y \cdot i \]
   7. Step-by-step derivation

      1. associate-/l* 71.9%

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

   8. Simplified 71.9%

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

   9. Taylor expanded in z around 0 71.4%

      \[\leadsto \left(\color{blue}{a \cdot \left(1 + \left(\frac{t}{a} + \frac{x \cdot \log y}{a}\right)\right)} + \log c \cdot b\right) + y \cdot i \]
   10. Step-by-step derivation

       1. associate-+r+ 71.4%

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

       2. associate-*r/ 71.3%

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

   11. Simplified 71.3%

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

   12. Taylor expanded in x around inf 76.2%

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

   if -5.3000000000000002e162 < x < 4.59999999999999971e158

   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 x around 0 95.8%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.3 \cdot 10^{+162} \lor \neg \left(x \leq 4.6 \cdot 10^{+158}\right):\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + b \cdot \log c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(b \cdot \log c + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 91.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := \log c \cdot \left(b - 0.5\right)\\ \mathbf{if}\;x \leq -1.6 \cdot 10^{+93}:\\ \;\;\;\;a + \left(t + \left(z + \left(t\_1 + t\_2\right)\right)\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+158}:\\ \;\;\;\;y \cdot i + \left(\left(a + \left(z + t\right)\right) + t\_2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t\_1 + b \cdot \log c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (* (log c) (- b 0.5))))
   (if (<= x -1.6e+93)
     (+ a (+ t (+ z (+ t_1 t_2))))
     (if (<= x 4.6e+158)
       (+ (* y i) (+ (+ a (+ z t)) t_2))
       (+ (* y i) (+ t_1 (* b (log c))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * log(y);
	double t_2 = log(c) * (b - 0.5);
	double tmp;
	if (x <= -1.6e+93) {
		tmp = a + (t + (z + (t_1 + t_2)));
	} else if (x <= 4.6e+158) {
		tmp = (y * i) + ((a + (z + t)) + t_2);
	} else {
		tmp = (y * i) + (t_1 + (b * log(c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * log(y)
    t_2 = log(c) * (b - 0.5d0)
    if (x <= (-1.6d+93)) then
        tmp = a + (t + (z + (t_1 + t_2)))
    else if (x <= 4.6d+158) then
        tmp = (y * i) + ((a + (z + t)) + t_2)
    else
        tmp = (y * i) + (t_1 + (b * log(c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x * Math.log(y);
	double t_2 = Math.log(c) * (b - 0.5);
	double tmp;
	if (x <= -1.6e+93) {
		tmp = a + (t + (z + (t_1 + t_2)));
	} else if (x <= 4.6e+158) {
		tmp = (y * i) + ((a + (z + t)) + t_2);
	} else {
		tmp = (y * i) + (t_1 + (b * Math.log(c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x * math.log(y)
	t_2 = math.log(c) * (b - 0.5)
	tmp = 0
	if x <= -1.6e+93:
		tmp = a + (t + (z + (t_1 + t_2)))
	elif x <= 4.6e+158:
		tmp = (y * i) + ((a + (z + t)) + t_2)
	else:
		tmp = (y * i) + (t_1 + (b * math.log(c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x * log(y))
	t_2 = Float64(log(c) * Float64(b - 0.5))
	tmp = 0.0
	if (x <= -1.6e+93)
		tmp = Float64(a + Float64(t + Float64(z + Float64(t_1 + t_2))));
	elseif (x <= 4.6e+158)
		tmp = Float64(Float64(y * i) + Float64(Float64(a + Float64(z + t)) + t_2));
	else
		tmp = Float64(Float64(y * i) + Float64(t_1 + Float64(b * log(c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x * log(y);
	t_2 = log(c) * (b - 0.5);
	tmp = 0.0;
	if (x <= -1.6e+93)
		tmp = a + (t + (z + (t_1 + t_2)));
	elseif (x <= 4.6e+158)
		tmp = (y * i) + ((a + (z + t)) + t_2);
	else
		tmp = (y * i) + (t_1 + (b * log(c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.6e+93], N[(a + N[(t + N[(z + N[(t$95$1 + t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.6e+158], N[(N[(y * i), $MachinePrecision] + N[(N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(t$95$1 + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.6000000000000001e93

   1. Initial program 99.7%

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

      1. associate-+l+ 99.7%

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

      2. associate-+l+ 99.7%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 89.5%

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

   if -1.6000000000000001e93 < x < 4.59999999999999971e158

   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 x around 0 97.5%

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

   if 4.59999999999999971e158 < x

   1. Initial program 99.5%

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

   3. Taylor expanded in b around inf 99.5%

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

      1. *-commutative 99.5%

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

   5. Simplified 99.5%

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

   6. Taylor expanded in a around inf 64.5%

      \[\leadsto \left(\color{blue}{a \cdot \left(1 + \left(\frac{t}{a} + \left(\frac{z}{a} + \frac{x \cdot \log y}{a}\right)\right)\right)} + \log c \cdot b\right) + y \cdot i \]
   7. Step-by-step derivation

      1. associate-/l* 64.5%

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

   8. Simplified 64.5%

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

   9. Taylor expanded in z around 0 64.5%

      \[\leadsto \left(\color{blue}{a \cdot \left(1 + \left(\frac{t}{a} + \frac{x \cdot \log y}{a}\right)\right)} + \log c \cdot b\right) + y \cdot i \]
   10. Step-by-step derivation

       1. associate-+r+ 64.5%

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

       2. associate-*r/ 64.5%

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

   11. Simplified 64.5%

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

   12. Taylor expanded in x around inf 87.4%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+93}:\\ \;\;\;\;a + \left(t + \left(z + \left(x \cdot \log y + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+158}:\\ \;\;\;\;y \cdot i + \left(\left(a + \left(z + t\right)\right) + \log c \cdot \left(b - 0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(x \cdot \log y + b \cdot \log c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \log c\\ \mathbf{if}\;z \leq -5 \cdot 10^{+146}:\\ \;\;\;\;y \cdot i + \left(t\_1 + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(t\_1 + \left(a + \left(t + x \cdot \log y\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* b (log c))))
   (if (<= z -5e+146)
     (+ (* y i) (+ t_1 (+ a (+ z t))))
     (+ (* y i) (+ t_1 (+ a (+ t (* x (log y)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = b * log(c);
	double tmp;
	if (z <= -5e+146) {
		tmp = (y * i) + (t_1 + (a + (z + t)));
	} else {
		tmp = (y * i) + (t_1 + (a + (t + (x * log(y)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * log(c)
    if (z <= (-5d+146)) then
        tmp = (y * i) + (t_1 + (a + (z + t)))
    else
        tmp = (y * i) + (t_1 + (a + (t + (x * log(y)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = b * Math.log(c);
	double tmp;
	if (z <= -5e+146) {
		tmp = (y * i) + (t_1 + (a + (z + t)));
	} else {
		tmp = (y * i) + (t_1 + (a + (t + (x * Math.log(y)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = b * math.log(c)
	tmp = 0
	if z <= -5e+146:
		tmp = (y * i) + (t_1 + (a + (z + t)))
	else:
		tmp = (y * i) + (t_1 + (a + (t + (x * math.log(y)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(b * log(c))
	tmp = 0.0
	if (z <= -5e+146)
		tmp = Float64(Float64(y * i) + Float64(t_1 + Float64(a + Float64(z + t))));
	else
		tmp = Float64(Float64(y * i) + Float64(t_1 + Float64(a + Float64(t + Float64(x * log(y))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = b * log(c);
	tmp = 0.0;
	if (z <= -5e+146)
		tmp = (y * i) + (t_1 + (a + (z + t)));
	else
		tmp = (y * i) + (t_1 + (a + (t + (x * log(y)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5e+146], N[(N[(y * i), $MachinePrecision] + N[(t$95$1 + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(t$95$1 + N[(a + N[(t + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.9999999999999999e146

   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 x around 0 95.8%

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

   if -4.9999999999999999e146 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf 99.8%

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

      1. *-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in x around inf 92.7%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+146}:\\ \;\;\;\;y \cdot i + \left(b \cdot \log c + \left(a + \left(z + t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(b \cdot \log c + \left(a + \left(t + x \cdot \log y\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in b around inf 99.8%

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

   1. *-commutative 99.8%

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

5. Simplified 99.8%

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

6. Final simplification 99.8%

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

Alternative 7: 42.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot i + b \cdot \log c\\ t_2 := z + y \cdot i\\ \mathbf{if}\;a \leq -5.6 \cdot 10^{-263}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 4.45 \cdot 10^{-156}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+143}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+185}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y i) (* b (log c)))) (t_2 (+ z (* y i))))
   (if (<= a -5.6e-263)
     t_2
     (if (<= a 4.45e-156)
       t_1
       (if (<= a 1.55e+143) t_2 (if (<= a 8.5e+185) t_1 (+ a (* y i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * i) + (b * log(c));
	double t_2 = z + (y * i);
	double tmp;
	if (a <= -5.6e-263) {
		tmp = t_2;
	} else if (a <= 4.45e-156) {
		tmp = t_1;
	} else if (a <= 1.55e+143) {
		tmp = t_2;
	} else if (a <= 8.5e+185) {
		tmp = t_1;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * i) + (b * log(c))
    t_2 = z + (y * i)
    if (a <= (-5.6d-263)) then
        tmp = t_2
    else if (a <= 4.45d-156) then
        tmp = t_1
    else if (a <= 1.55d+143) then
        tmp = t_2
    else if (a <= 8.5d+185) then
        tmp = t_1
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * i) + (b * Math.log(c));
	double t_2 = z + (y * i);
	double tmp;
	if (a <= -5.6e-263) {
		tmp = t_2;
	} else if (a <= 4.45e-156) {
		tmp = t_1;
	} else if (a <= 1.55e+143) {
		tmp = t_2;
	} else if (a <= 8.5e+185) {
		tmp = t_1;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y * i) + (b * math.log(c))
	t_2 = z + (y * i)
	tmp = 0
	if a <= -5.6e-263:
		tmp = t_2
	elif a <= 4.45e-156:
		tmp = t_1
	elif a <= 1.55e+143:
		tmp = t_2
	elif a <= 8.5e+185:
		tmp = t_1
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * i) + Float64(b * log(c)))
	t_2 = Float64(z + Float64(y * i))
	tmp = 0.0
	if (a <= -5.6e-263)
		tmp = t_2;
	elseif (a <= 4.45e-156)
		tmp = t_1;
	elseif (a <= 1.55e+143)
		tmp = t_2;
	elseif (a <= 8.5e+185)
		tmp = t_1;
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y * i) + (b * log(c));
	t_2 = z + (y * i);
	tmp = 0.0;
	if (a <= -5.6e-263)
		tmp = t_2;
	elseif (a <= 4.45e-156)
		tmp = t_1;
	elseif (a <= 1.55e+143)
		tmp = t_2;
	elseif (a <= 8.5e+185)
		tmp = t_1;
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(y * i), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.6e-263], t$95$2, If[LessEqual[a, 4.45e-156], t$95$1, If[LessEqual[a, 1.55e+143], t$95$2, If[LessEqual[a, 8.5e+185], t$95$1, N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.6000000000000001e-263 or 4.4500000000000001e-156 < a < 1.54999999999999995e143

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf 99.8%

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

      1. *-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in x around 0 83.6%

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

   7. Taylor expanded in z around inf 36.1%

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

   if -5.6000000000000001e-263 < a < 4.4500000000000001e-156 or 1.54999999999999995e143 < a < 8.50000000000000013e185

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf 99.8%

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

      1. *-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in x around 0 79.6%

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

   7. Taylor expanded in b around inf 47.3%

      \[\leadsto \color{blue}{b \cdot \log c} + y \cdot i \]

   if 8.50000000000000013e185 < a

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf 99.8%

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

      1. *-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in x around 0 83.8%

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

   7. Taylor expanded in a around inf 71.3%

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

4. Final simplification 42.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{-263}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;a \leq 4.45 \cdot 10^{-156}:\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+143}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+185}:\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 43.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z + y \cdot i\\ \mathbf{if}\;a \leq -8 \cdot 10^{-262}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-155}:\\ \;\;\;\;y \cdot i + \log c \cdot \left(b - 0.5\right)\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+143}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{+186}:\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ z (* y i))))
   (if (<= a -8e-262)
     t_1
     (if (<= a 2.1e-155)
       (+ (* y i) (* (log c) (- b 0.5)))
       (if (<= a 3.3e+143)
         t_1
         (if (<= a 4.3e+186) (+ (* y i) (* b (log c))) (+ a (* y i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = z + (y * i);
	double tmp;
	if (a <= -8e-262) {
		tmp = t_1;
	} else if (a <= 2.1e-155) {
		tmp = (y * i) + (log(c) * (b - 0.5));
	} else if (a <= 3.3e+143) {
		tmp = t_1;
	} else if (a <= 4.3e+186) {
		tmp = (y * i) + (b * log(c));
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z + (y * i)
    if (a <= (-8d-262)) then
        tmp = t_1
    else if (a <= 2.1d-155) then
        tmp = (y * i) + (log(c) * (b - 0.5d0))
    else if (a <= 3.3d+143) then
        tmp = t_1
    else if (a <= 4.3d+186) then
        tmp = (y * i) + (b * log(c))
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = z + (y * i);
	double tmp;
	if (a <= -8e-262) {
		tmp = t_1;
	} else if (a <= 2.1e-155) {
		tmp = (y * i) + (Math.log(c) * (b - 0.5));
	} else if (a <= 3.3e+143) {
		tmp = t_1;
	} else if (a <= 4.3e+186) {
		tmp = (y * i) + (b * Math.log(c));
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = z + (y * i)
	tmp = 0
	if a <= -8e-262:
		tmp = t_1
	elif a <= 2.1e-155:
		tmp = (y * i) + (math.log(c) * (b - 0.5))
	elif a <= 3.3e+143:
		tmp = t_1
	elif a <= 4.3e+186:
		tmp = (y * i) + (b * math.log(c))
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(z + Float64(y * i))
	tmp = 0.0
	if (a <= -8e-262)
		tmp = t_1;
	elseif (a <= 2.1e-155)
		tmp = Float64(Float64(y * i) + Float64(log(c) * Float64(b - 0.5)));
	elseif (a <= 3.3e+143)
		tmp = t_1;
	elseif (a <= 4.3e+186)
		tmp = Float64(Float64(y * i) + Float64(b * log(c)));
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = z + (y * i);
	tmp = 0.0;
	if (a <= -8e-262)
		tmp = t_1;
	elseif (a <= 2.1e-155)
		tmp = (y * i) + (log(c) * (b - 0.5));
	elseif (a <= 3.3e+143)
		tmp = t_1;
	elseif (a <= 4.3e+186)
		tmp = (y * i) + (b * log(c));
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8e-262], t$95$1, If[LessEqual[a, 2.1e-155], N[(N[(y * i), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.3e+143], t$95$1, If[LessEqual[a, 4.3e+186], N[(N[(y * i), $MachinePrecision] + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -8.0000000000000001e-262 or 2.1000000000000002e-155 < a < 3.3e143

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf 99.8%

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

      1. *-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in x around 0 83.6%

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

   7. Taylor expanded in z around inf 36.1%

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

   if -8.0000000000000001e-262 < a < 2.1000000000000002e-155

   1. Initial program 99.8%

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

   3. Taylor expanded in t around inf 76.1%

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

   4. Taylor expanded in t around 0 63.6%

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

   if 3.3e143 < a < 4.3e186

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf 99.8%

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

      1. *-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in x around 0 54.6%

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

   7. Taylor expanded in b around inf 11.2%

      \[\leadsto \color{blue}{b \cdot \log c} + y \cdot i \]

   if 4.3e186 < a

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf 99.8%

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

      1. *-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in x around 0 83.8%

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

   7. Taylor expanded in a around inf 71.3%

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

4. Final simplification 42.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{-262}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-155}:\\ \;\;\;\;y \cdot i + \log c \cdot \left(b - 0.5\right)\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+143}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{+186}:\\ \;\;\;\;y \cdot i + b \cdot \log c\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 83.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.25 \cdot 10^{+187} \lor \neg \left(x \leq 1.32 \cdot 10^{+246}\right):\\ \;\;\;\;z \cdot \left(1 + \frac{x \cdot \log y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(b \cdot \log c + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -3.25e+187) (not (<= x 1.32e+246)))
   (* z (+ 1.0 (/ (* x (log y)) z)))
   (+ (* y i) (+ (* b (log c)) (+ a (+ z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -3.25e+187) || !(x <= 1.32e+246)) {
		tmp = z * (1.0 + ((x * log(y)) / z));
	} else {
		tmp = (y * i) + ((b * log(c)) + (a + (z + t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-3.25d+187)) .or. (.not. (x <= 1.32d+246))) then
        tmp = z * (1.0d0 + ((x * log(y)) / z))
    else
        tmp = (y * i) + ((b * log(c)) + (a + (z + t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -3.25e+187) || !(x <= 1.32e+246)) {
		tmp = z * (1.0 + ((x * Math.log(y)) / z));
	} else {
		tmp = (y * i) + ((b * Math.log(c)) + (a + (z + t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -3.25e+187) or not (x <= 1.32e+246):
		tmp = z * (1.0 + ((x * math.log(y)) / z))
	else:
		tmp = (y * i) + ((b * math.log(c)) + (a + (z + t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -3.25e+187) || !(x <= 1.32e+246))
		tmp = Float64(z * Float64(1.0 + Float64(Float64(x * log(y)) / z)));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(b * log(c)) + Float64(a + Float64(z + t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -3.25e+187) || ~((x <= 1.32e+246)))
		tmp = z * (1.0 + ((x * log(y)) / z));
	else
		tmp = (y * i) + ((b * log(c)) + (a + (z + t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -3.25e+187], N[Not[LessEqual[x, 1.32e+246]], $MachinePrecision]], N[(z * N[(1.0 + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.24999999999999984e187 or 1.32000000000000004e246 < x

   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. Step-by-step derivation

      1. associate-+l+ 99.6%

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

      2. associate-+l+ 99.6%

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

      3. fma-define 99.6%

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

      4. sub-neg 99.6%

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

      5. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around inf 48.3%

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

      1. associate-/l* 48.3%

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

      2. associate-/l* 48.4%

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

      3. sub-neg 48.4%

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

      4. metadata-eval 48.4%

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

      5. associate-/l* 48.4%

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

      6. +-commutative 48.4%

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

   7. Simplified 48.4%

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

   8. Taylor expanded in x around inf 25.8%

      \[\leadsto z \cdot \left(1 + \color{blue}{\frac{x \cdot \log y}{z}}\right) \]

   if -3.24999999999999984e187 < x < 1.32000000000000004e246

   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 x around 0 92.6%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.25 \cdot 10^{+187} \lor \neg \left(x \leq 1.32 \cdot 10^{+246}\right):\\ \;\;\;\;z \cdot \left(1 + \frac{x \cdot \log y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(b \cdot \log c + \left(a + \left(z + t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 42.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 7.8 \cdot 10^{+149}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{+184}:\\ \;\;\;\;t + \log c \cdot \left(b - 0.5\right)\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+189} \lor \neg \left(a \leq 3.6 \cdot 10^{+252}\right):\\ \;\;\;\;a + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 + \frac{z}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 7.8e+149)
   (+ z (* y i))
   (if (<= a 6.4e+184)
     (+ t (* (log c) (- b 0.5)))
     (if (or (<= a 3.4e+189) (not (<= a 3.6e+252)))
       (+ a (* 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 <= 7.8e+149) {
		tmp = z + (y * i);
	} else if (a <= 6.4e+184) {
		tmp = t + (log(c) * (b - 0.5));
	} else if ((a <= 3.4e+189) || !(a <= 3.6e+252)) {
		tmp = a + (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 <= 7.8d+149) then
        tmp = z + (y * i)
    else if (a <= 6.4d+184) then
        tmp = t + (log(c) * (b - 0.5d0))
    else if ((a <= 3.4d+189) .or. (.not. (a <= 3.6d+252))) then
        tmp = a + (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 <= 7.8e+149) {
		tmp = z + (y * i);
	} else if (a <= 6.4e+184) {
		tmp = t + (Math.log(c) * (b - 0.5));
	} else if ((a <= 3.4e+189) || !(a <= 3.6e+252)) {
		tmp = a + (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 <= 7.8e+149:
		tmp = z + (y * i)
	elif a <= 6.4e+184:
		tmp = t + (math.log(c) * (b - 0.5))
	elif (a <= 3.4e+189) or not (a <= 3.6e+252):
		tmp = a + (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 <= 7.8e+149)
		tmp = Float64(z + Float64(y * i));
	elseif (a <= 6.4e+184)
		tmp = Float64(t + Float64(log(c) * Float64(b - 0.5)));
	elseif ((a <= 3.4e+189) || !(a <= 3.6e+252))
		tmp = Float64(a + 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 <= 7.8e+149)
		tmp = z + (y * i);
	elseif (a <= 6.4e+184)
		tmp = t + (log(c) * (b - 0.5));
	elseif ((a <= 3.4e+189) || ~((a <= 3.6e+252)))
		tmp = a + (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, 7.8e+149], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.4e+184], N[(t + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, 3.4e+189], N[Not[LessEqual[a, 3.6e+252]], $MachinePrecision]], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(1.0 + N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < 7.7999999999999998e149

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf 99.8%

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

      1. *-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in x around 0 84.9%

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

   7. Taylor expanded in z around inf 41.0%

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

   if 7.7999999999999998e149 < a < 6.39999999999999966e184

   1. Initial program 99.8%

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

   3. Taylor expanded in t around inf 32.0%

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

   4. Taylor expanded in y around 0 31.5%

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

   if 6.39999999999999966e184 < a < 3.39999999999999983e189 or 3.5999999999999999e252 < a

   1. Initial program 99.7%

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

   3. Taylor expanded in b around inf 99.7%

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

      1. *-commutative 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in x around 0 80.9%

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

   7. Taylor expanded in a around inf 80.9%

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

   if 3.39999999999999983e189 < a < 3.5999999999999999e252

   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. fma-define 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 54.8%

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

      1. associate-/l* 54.8%

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

      2. associate-/l* 54.8%

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

      3. sub-neg 54.8%

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

      4. metadata-eval 54.8%

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

      5. associate-/l* 54.8%

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

      6. +-commutative 54.8%

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

   7. Simplified 54.8%

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

   8. Taylor expanded in a around inf 34.8%

      \[\leadsto z \cdot \left(1 + \color{blue}{\frac{a}{z}}\right) \]

   9. Taylor expanded in a around inf 50.3%

      \[\leadsto \color{blue}{a \cdot \left(1 + \frac{z}{a}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 43.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 7.8 \cdot 10^{+149}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{+184}:\\ \;\;\;\;t + \log c \cdot \left(b - 0.5\right)\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+189} \lor \neg \left(a \leq 3.6 \cdot 10^{+252}\right):\\ \;\;\;\;a + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 + \frac{z}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+156}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \log c \cdot \left(b - 0.5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -3.3e+156) (+ z (* y i)) (+ (* y i) (+ a (* (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 (z <= -3.3e+156) {
		tmp = z + (y * i);
	} else {
		tmp = (y * i) + (a + (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 (z <= (-3.3d+156)) then
        tmp = z + (y * i)
    else
        tmp = (y * i) + (a + (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 (z <= -3.3e+156) {
		tmp = z + (y * i);
	} else {
		tmp = (y * i) + (a + (Math.log(c) * (b - 0.5)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -3.3e+156:
		tmp = z + (y * i)
	else:
		tmp = (y * i) + (a + (math.log(c) * (b - 0.5)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -3.3e+156)
		tmp = Float64(z + Float64(y * i));
	else
		tmp = Float64(Float64(y * i) + Float64(a + 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 (z <= -3.3e+156)
		tmp = z + (y * i);
	else
		tmp = (y * i) + (a + (log(c) * (b - 0.5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -3.3e+156], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.2999999999999999e156

   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 x around 0 95.7%

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

   7. Taylor expanded in z around inf 66.9%

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

   if -3.2999999999999999e156 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in a around inf 54.0%

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

4. Final simplification 55.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+156}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \log c \cdot \left(b - 0.5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 71.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \log c\\ \mathbf{if}\;a \leq 2.1 \cdot 10^{+175}:\\ \;\;\;\;y \cdot i + \left(t\_1 + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* b (log c))))
   (if (<= a 2.1e+175) (+ (* y i) (+ t_1 (+ z t))) (+ (* y i) (+ a t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = b * log(c);
	double tmp;
	if (a <= 2.1e+175) {
		tmp = (y * i) + (t_1 + (z + t));
	} else {
		tmp = (y * i) + (a + t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * log(c)
    if (a <= 2.1d+175) then
        tmp = (y * i) + (t_1 + (z + t))
    else
        tmp = (y * i) + (a + t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = b * Math.log(c);
	double tmp;
	if (a <= 2.1e+175) {
		tmp = (y * i) + (t_1 + (z + t));
	} else {
		tmp = (y * i) + (a + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = b * math.log(c)
	tmp = 0
	if a <= 2.1e+175:
		tmp = (y * i) + (t_1 + (z + t))
	else:
		tmp = (y * i) + (a + t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(b * log(c))
	tmp = 0.0
	if (a <= 2.1e+175)
		tmp = Float64(Float64(y * i) + Float64(t_1 + Float64(z + t)));
	else
		tmp = Float64(Float64(y * i) + Float64(a + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = b * log(c);
	tmp = 0.0;
	if (a <= 2.1e+175)
		tmp = (y * i) + (t_1 + (z + t));
	else
		tmp = (y * i) + (a + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, 2.1e+175], N[(N[(y * i), $MachinePrecision] + N[(t$95$1 + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < 2.0999999999999999e175

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf 99.8%

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

      1. *-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in x around 0 83.1%

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

   7. Taylor expanded in a around 0 75.7%

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

      1. associate-+r+ 75.7%

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

   9. Simplified 75.7%

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

   if 2.0999999999999999e175 < 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. 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 a around inf 71.9%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 2.1 \cdot 10^{+175}:\\ \;\;\;\;y \cdot i + \left(b \cdot \log c + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 41.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 7.8 \cdot 10^{+149}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+184}:\\ \;\;\;\;\log c \cdot \left(b - 0.5\right)\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+189} \lor \neg \left(a \leq 3.45 \cdot 10^{+252}\right):\\ \;\;\;\;a + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 + \frac{z}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 7.8e+149)
   (+ z (* y i))
   (if (<= a 2.3e+184)
     (* (log c) (- b 0.5))
     (if (or (<= a 2.3e+189) (not (<= a 3.45e+252)))
       (+ a (* 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 <= 7.8e+149) {
		tmp = z + (y * i);
	} else if (a <= 2.3e+184) {
		tmp = log(c) * (b - 0.5);
	} else if ((a <= 2.3e+189) || !(a <= 3.45e+252)) {
		tmp = a + (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 <= 7.8d+149) then
        tmp = z + (y * i)
    else if (a <= 2.3d+184) then
        tmp = log(c) * (b - 0.5d0)
    else if ((a <= 2.3d+189) .or. (.not. (a <= 3.45d+252))) then
        tmp = a + (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 <= 7.8e+149) {
		tmp = z + (y * i);
	} else if (a <= 2.3e+184) {
		tmp = Math.log(c) * (b - 0.5);
	} else if ((a <= 2.3e+189) || !(a <= 3.45e+252)) {
		tmp = a + (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 <= 7.8e+149:
		tmp = z + (y * i)
	elif a <= 2.3e+184:
		tmp = math.log(c) * (b - 0.5)
	elif (a <= 2.3e+189) or not (a <= 3.45e+252):
		tmp = a + (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 <= 7.8e+149)
		tmp = Float64(z + Float64(y * i));
	elseif (a <= 2.3e+184)
		tmp = Float64(log(c) * Float64(b - 0.5));
	elseif ((a <= 2.3e+189) || !(a <= 3.45e+252))
		tmp = Float64(a + 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 <= 7.8e+149)
		tmp = z + (y * i);
	elseif (a <= 2.3e+184)
		tmp = log(c) * (b - 0.5);
	elseif ((a <= 2.3e+189) || ~((a <= 3.45e+252)))
		tmp = a + (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, 7.8e+149], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.3e+184], N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, 2.3e+189], N[Not[LessEqual[a, 3.45e+252]], $MachinePrecision]], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(1.0 + N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < 7.7999999999999998e149

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf 99.8%

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

      1. *-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in x around 0 84.9%

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

   7. Taylor expanded in z around inf 41.0%

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

   if 7.7999999999999998e149 < a < 2.3e184

   1. Initial program 99.8%

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

   3. Taylor expanded in t around inf 34.2%

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

   4. Taylor expanded in y around 0 33.7%

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

   5. Taylor expanded in t around 0 11.9%

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

   if 2.3e184 < a < 2.3e189 or 3.45e252 < a

   1. Initial program 99.7%

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

   3. Taylor expanded in b around inf 99.7%

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

      1. *-commutative 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in x around 0 82.0%

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

   7. Taylor expanded in a around inf 76.5%

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

   if 2.3e189 < a < 3.45e252

   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. fma-define 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 54.8%

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

      1. associate-/l* 54.8%

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

      2. associate-/l* 54.8%

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

      3. sub-neg 54.8%

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

      4. metadata-eval 54.8%

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

      5. associate-/l* 54.8%

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

      6. +-commutative 54.8%

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

   7. Simplified 54.8%

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

   8. Taylor expanded in a around inf 34.8%

      \[\leadsto z \cdot \left(1 + \color{blue}{\frac{a}{z}}\right) \]

   9. Taylor expanded in a around inf 50.3%

      \[\leadsto \color{blue}{a \cdot \left(1 + \frac{z}{a}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 42.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 7.8 \cdot 10^{+149}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+184}:\\ \;\;\;\;\log c \cdot \left(b - 0.5\right)\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+189} \lor \neg \left(a \leq 3.45 \cdot 10^{+252}\right):\\ \;\;\;\;a + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 + \frac{z}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 56.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+156}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -2.05e+156) (+ z (* y i)) (+ (* y i) (+ a (* b (log c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -2.05e+156) {
		tmp = z + (y * i);
	} else {
		tmp = (y * i) + (a + (b * log(c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-2.05d+156)) then
        tmp = z + (y * i)
    else
        tmp = (y * i) + (a + (b * log(c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -2.05e+156) {
		tmp = z + (y * i);
	} else {
		tmp = (y * i) + (a + (b * Math.log(c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -2.05e+156:
		tmp = z + (y * i)
	else:
		tmp = (y * i) + (a + (b * math.log(c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -2.05e+156)
		tmp = Float64(z + Float64(y * i));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(b * log(c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -2.05e+156)
		tmp = z + (y * i);
	else
		tmp = (y * i) + (a + (b * log(c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -2.05e+156], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.0500000000000001e156

   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 x around 0 95.7%

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

   7. Taylor expanded in z around inf 66.9%

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

   if -2.0500000000000001e156 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf 99.8%

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

      1. *-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in a around inf 53.9%

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

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+156}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + b \cdot \log c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 41.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 7.8 \cdot 10^{+149}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+184}:\\ \;\;\;\;b \cdot \log c\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+189} \lor \neg \left(a \leq 3.3 \cdot 10^{+252}\right):\\ \;\;\;\;a + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 + \frac{z}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 7.8e+149)
   (+ z (* y i))
   (if (<= a 2.3e+184)
     (* b (log c))
     (if (or (<= a 2.8e+189) (not (<= a 3.3e+252)))
       (+ a (* 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 <= 7.8e+149) {
		tmp = z + (y * i);
	} else if (a <= 2.3e+184) {
		tmp = b * log(c);
	} else if ((a <= 2.8e+189) || !(a <= 3.3e+252)) {
		tmp = a + (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 <= 7.8d+149) then
        tmp = z + (y * i)
    else if (a <= 2.3d+184) then
        tmp = b * log(c)
    else if ((a <= 2.8d+189) .or. (.not. (a <= 3.3d+252))) then
        tmp = a + (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 <= 7.8e+149) {
		tmp = z + (y * i);
	} else if (a <= 2.3e+184) {
		tmp = b * Math.log(c);
	} else if ((a <= 2.8e+189) || !(a <= 3.3e+252)) {
		tmp = a + (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 <= 7.8e+149:
		tmp = z + (y * i)
	elif a <= 2.3e+184:
		tmp = b * math.log(c)
	elif (a <= 2.8e+189) or not (a <= 3.3e+252):
		tmp = a + (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 <= 7.8e+149)
		tmp = Float64(z + Float64(y * i));
	elseif (a <= 2.3e+184)
		tmp = Float64(b * log(c));
	elseif ((a <= 2.8e+189) || !(a <= 3.3e+252))
		tmp = Float64(a + 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 <= 7.8e+149)
		tmp = z + (y * i);
	elseif (a <= 2.3e+184)
		tmp = b * log(c);
	elseif ((a <= 2.8e+189) || ~((a <= 3.3e+252)))
		tmp = a + (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, 7.8e+149], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.3e+184], N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, 2.8e+189], N[Not[LessEqual[a, 3.3e+252]], $MachinePrecision]], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(1.0 + N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < 7.7999999999999998e149

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf 99.8%

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

      1. *-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in x around 0 84.9%

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

   7. Taylor expanded in z around inf 41.0%

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

   if 7.7999999999999998e149 < a < 2.3e184

   1. Initial program 99.8%

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

   3. Taylor expanded in t around inf 34.2%

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

   4. Taylor expanded in b around inf 11.9%

      \[\leadsto \color{blue}{b \cdot \log c} \]
   5. Step-by-step derivation

      1. *-commutative 11.9%

         \[\leadsto \color{blue}{\log c \cdot b} \]

   6. Simplified 11.9%

      \[\leadsto \color{blue}{\log c \cdot b} \]

   if 2.3e184 < a < 2.80000000000000006e189 or 3.3000000000000001e252 < a

   1. Initial program 99.7%

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

   3. Taylor expanded in b around inf 99.7%

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

      1. *-commutative 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in x around 0 82.0%

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

   7. Taylor expanded in a around inf 76.5%

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

   if 2.80000000000000006e189 < a < 3.3000000000000001e252

   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. fma-define 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 54.8%

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

      1. associate-/l* 54.8%

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

      2. associate-/l* 54.8%

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

      3. sub-neg 54.8%

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

      4. metadata-eval 54.8%

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

      5. associate-/l* 54.8%

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

      6. +-commutative 54.8%

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

   7. Simplified 54.8%

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

   8. Taylor expanded in a around inf 34.8%

      \[\leadsto z \cdot \left(1 + \color{blue}{\frac{a}{z}}\right) \]

   9. Taylor expanded in a around inf 50.3%

      \[\leadsto \color{blue}{a \cdot \left(1 + \frac{z}{a}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 42.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 7.8 \cdot 10^{+149}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+184}:\\ \;\;\;\;b \cdot \log c\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+189} \lor \neg \left(a \leq 3.3 \cdot 10^{+252}\right):\\ \;\;\;\;a + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 + \frac{z}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 44.0% accurate, 14.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -2 \cdot 10^{+32} \lor \neg \left(i \leq 1.5 \cdot 10^{+98}\right):\\ \;\;\;\;a + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= i -2e+32) (not (<= i 1.5e+98))) (+ a (* y i)) (+ z a)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((i <= -2e+32) || !(i <= 1.5e+98)) {
		tmp = a + (y * i);
	} else {
		tmp = 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 ((i <= (-2d+32)) .or. (.not. (i <= 1.5d+98))) then
        tmp = a + (y * i)
    else
        tmp = 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 ((i <= -2e+32) || !(i <= 1.5e+98)) {
		tmp = a + (y * i);
	} else {
		tmp = z + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (i <= -2e+32) or not (i <= 1.5e+98):
		tmp = a + (y * i)
	else:
		tmp = z + a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((i <= -2e+32) || !(i <= 1.5e+98))
		tmp = Float64(a + Float64(y * i));
	else
		tmp = Float64(z + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((i <= -2e+32) || ~((i <= 1.5e+98)))
		tmp = a + (y * i);
	else
		tmp = z + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[i, -2e+32], N[Not[LessEqual[i, 1.5e+98]], $MachinePrecision]], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(z + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -2.00000000000000011e32 or 1.5000000000000001e98 < 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. 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 x around 0 86.3%

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

   7. Taylor expanded in a around inf 63.4%

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

   if -2.00000000000000011e32 < i < 1.5000000000000001e98

   1. Initial program 99.8%

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

      1. associate-+l+ 99.8%

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

      2. associate-+l+ 99.8%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 64.2%

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

      1. associate-/l* 62.9%

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

      2. associate-/l* 62.9%

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

      3. sub-neg 62.9%

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

      4. metadata-eval 62.9%

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

      5. associate-/l* 62.8%

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

      6. +-commutative 62.8%

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

   7. Simplified 62.8%

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

   8. Taylor expanded in a around inf 26.1%

      \[\leadsto z \cdot \left(1 + \color{blue}{\frac{a}{z}}\right) \]

   9. Taylor expanded in z around 0 29.9%

      \[\leadsto \color{blue}{a + z} \]
   10. Step-by-step derivation

       1. +-commutative 29.9%

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

   11. Simplified 29.9%

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

4. Final simplification 43.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2 \cdot 10^{+32} \lor \neg \left(i \leq 1.5 \cdot 10^{+98}\right):\\ \;\;\;\;a + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 39.8% accurate, 16.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -7.5 \cdot 10^{+32} \lor \neg \left(i \leq 10^{+131}\right):\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= i -7.5e+32) (not (<= i 1e+131))) (* y i) (+ z a)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((i <= -7.5e+32) || !(i <= 1e+131)) {
		tmp = y * i;
	} else {
		tmp = 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 ((i <= (-7.5d+32)) .or. (.not. (i <= 1d+131))) then
        tmp = y * i
    else
        tmp = 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 ((i <= -7.5e+32) || !(i <= 1e+131)) {
		tmp = y * i;
	} else {
		tmp = z + a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (i <= -7.5e+32) or not (i <= 1e+131):
		tmp = y * i
	else:
		tmp = z + a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((i <= -7.5e+32) || !(i <= 1e+131))
		tmp = Float64(y * i);
	else
		tmp = Float64(z + a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((i <= -7.5e+32) || ~((i <= 1e+131)))
		tmp = y * i;
	else
		tmp = z + a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[i, -7.5e+32], N[Not[LessEqual[i, 1e+131]], $MachinePrecision]], N[(y * i), $MachinePrecision], N[(z + a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -7.49999999999999959e32 or 9.9999999999999991e130 < 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. fma-define 99.9%

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

      4. sub-neg 99.9%

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

      5. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 55.7%

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

      1. *-commutative 55.7%

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

   7. Simplified 55.7%

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

   if -7.49999999999999959e32 < i < 9.9999999999999991e130

   1. Initial program 99.8%

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

      1. associate-+l+ 99.8%

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

      2. associate-+l+ 99.8%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 65.4%

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

      1. associate-/l* 64.1%

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

      2. associate-/l* 64.1%

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

      3. sub-neg 64.1%

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

      4. metadata-eval 64.1%

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

      5. associate-/l* 64.1%

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

      6. +-commutative 64.1%

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

   7. Simplified 64.1%

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

   8. Taylor expanded in a around inf 26.9%

      \[\leadsto z \cdot \left(1 + \color{blue}{\frac{a}{z}}\right) \]

   9. Taylor expanded in z around 0 30.4%

      \[\leadsto \color{blue}{a + z} \]
   10. Step-by-step derivation

       1. +-commutative 30.4%

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

   11. Simplified 30.4%

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

4. Final simplification 39.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -7.5 \cdot 10^{+32} \lor \neg \left(i \leq 10^{+131}\right):\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 43.3% accurate, 21.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 7.5 \cdot 10^{+113}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 7.5e+113) (+ z (* y i)) (+ a (* y i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 7.5e+113) {
		tmp = z + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 7.5d+113) then
        tmp = z + (y * i)
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 7.5e+113) {
		tmp = z + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 7.5e+113:
		tmp = z + (y * i)
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 7.5e+113)
		tmp = Float64(z + Float64(y * i));
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 7.5e+113)
		tmp = z + (y * i);
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 7.5e+113], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 7.5000000000000001e113

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf 99.8%

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

      1. *-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in x around 0 85.1%

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

   7. Taylor expanded in z around inf 41.2%

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

   if 7.5000000000000001e113 < a

   1. Initial program 99.8%

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

   3. Taylor expanded in b around inf 99.8%

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

      1. *-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in x around 0 73.4%

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

   7. Taylor expanded in a around inf 48.8%

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

4. Final simplification 42.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 7.5 \cdot 10^{+113}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 27.2% accurate, 27.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 1.2 \cdot 10^{+188}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (if (<= a 1.2e+188) (* 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 <= 1.2e+188) {
		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 <= 1.2d+188) 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 <= 1.2e+188) {
		tmp = y * i;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 1.2e+188:
		tmp = y * i
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 1.2e+188)
		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 <= 1.2e+188)
		tmp = y * i;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 1.2e+188], N[(y * i), $MachinePrecision], a]

Derivation

1. Split input into 2 regimes

2. if a < 1.2e188

   1. Initial program 99.8%

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

      1. associate-+l+ 99.8%

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

      2. associate-+l+ 99.8%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 26.4%

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

      1. *-commutative 26.4%

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

   7. Simplified 26.4%

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

   if 1.2e188 < 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. fma-define 99.9%

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

      4. sub-neg 99.9%

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

      5. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 66.3%

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

      1. associate-/l* 66.3%

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

      2. associate-/l* 66.3%

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

      3. sub-neg 66.3%

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

      4. metadata-eval 66.3%

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

      5. associate-/l* 66.3%

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

      6. +-commutative 66.3%

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

   7. Simplified 66.3%

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

   8. Taylor expanded in a around inf 41.8%

      \[\leadsto z \cdot \left(1 + \color{blue}{\frac{a}{z}}\right) \]

   9. Taylor expanded in z around 0 55.8%

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

4. Final simplification 29.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.2 \cdot 10^{+188}:\\ \;\;\;\;y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 16.2% accurate, 219.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. associate-+l+ 99.8%

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

   2. associate-+l+ 99.8%

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

   3. fma-define 99.8%

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

   4. sub-neg 99.8%

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

   5. metadata-eval 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in z around inf 65.1%

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

   1. associate-/l* 64.2%

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

   2. associate-/l* 64.2%

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

   3. sub-neg 64.2%

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

   4. metadata-eval 64.2%

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

   5. associate-/l* 64.2%

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

   6. +-commutative 64.2%

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

7. Simplified 64.2%

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

8. Taylor expanded in a around inf 22.4%

   \[\leadsto z \cdot \left(1 + \color{blue}{\frac{a}{z}}\right) \]

9. Taylor expanded in z around 0 15.0%

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

10. Final simplification 15.0%

    \[\leadsto a \]
11. Add Preprocessing

Reproduce

herbie shell --seed 2024079 
(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)))