Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 55.8% → 82.5%

Time: 21.7s

Alternatives: 15

Speedup: 1.7×

Specification

Math

\[\begin{array}{l} \\ \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (/
  (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t)
  (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + 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 * y) + z) * y) + 27464.7644705d0) * y) + 230661.510616d0) * y) + t) / (((((((y + a) * y) + b) * y) + 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 * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
}

Python

def code(x, y, z, t, a, b, c, i):
	return ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(y + a) * y) + b) * y) + c) * y) + i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision] * y), $MachinePrecision] + 27464.7644705), $MachinePrecision] * y), $MachinePrecision] + 230661.510616), $MachinePrecision] * y), $MachinePrecision] + t), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(y + a), $MachinePrecision] * y), $MachinePrecision] + b), $MachinePrecision] * y), $MachinePrecision] + c), $MachinePrecision] * y), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]

Initial Program: 55.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (/
  (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t)
  (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + 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 * y) + z) * y) + 27464.7644705d0) * y) + 230661.510616d0) * y) + t) / (((((((y + a) * y) + b) * y) + 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 * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
}

Python

def code(x, y, z, t, a, b, c, i):
	return ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(y + a) * y) + b) * y) + c) * y) + i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision] * y), $MachinePrecision] + 27464.7644705), $MachinePrecision] * y), $MachinePrecision] + 230661.510616), $MachinePrecision] * y), $MachinePrecision] + t), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(y + a), $MachinePrecision] * y), $MachinePrecision] + b), $MachinePrecision] * y), $MachinePrecision] + c), $MachinePrecision] * y), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]

Alternative 1: 82.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)\right)\\ t_2 := c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\\ \mathbf{if}\;\frac{t\_1}{y \cdot t\_2 + i} \leq \infty:\\ \;\;\;\;\frac{t\_1}{i + \frac{y}{\frac{1}{t\_2}}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (+
          t
          (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ (* x y) z))))))))
        (t_2 (+ c (* y (+ (* y (+ y a)) b)))))
   (if (<= (/ t_1 (+ (* y t_2) i)) INFINITY)
     (/ t_1 (+ i (/ y (/ 1.0 t_2))))
     (+ x (/ (- z (* x a)) y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = t + (y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))));
	double t_2 = c + (y * ((y * (y + a)) + b));
	double tmp;
	if ((t_1 / ((y * t_2) + i)) <= ((double) INFINITY)) {
		tmp = t_1 / (i + (y / (1.0 / t_2)));
	} else {
		tmp = x + ((z - (x * a)) / y);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = t + (y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))));
	double t_2 = c + (y * ((y * (y + a)) + b));
	double tmp;
	if ((t_1 / ((y * t_2) + i)) <= Double.POSITIVE_INFINITY) {
		tmp = t_1 / (i + (y / (1.0 / t_2)));
	} else {
		tmp = x + ((z - (x * a)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = t + (y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))))
	t_2 = c + (y * ((y * (y + a)) + b))
	tmp = 0
	if (t_1 / ((y * t_2) + i)) <= math.inf:
		tmp = t_1 / (i + (y / (1.0 / t_2)))
	else:
		tmp = x + ((z - (x * a)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(Float64(x * y) + z)))))))
	t_2 = Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b)))
	tmp = 0.0
	if (Float64(t_1 / Float64(Float64(y * t_2) + i)) <= Inf)
		tmp = Float64(t_1 / Float64(i + Float64(y / Float64(1.0 / t_2))));
	else
		tmp = Float64(x + Float64(Float64(z - Float64(x * a)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = t + (y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))));
	t_2 = c + (y * ((y * (y + a)) + b));
	tmp = 0.0;
	if ((t_1 / ((y * t_2) + i)) <= Inf)
		tmp = t_1 / (i + (y / (1.0 / t_2)));
	else
		tmp = x + ((z - (x * a)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$1 / N[(N[(y * t$95$2), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], Infinity], N[(t$95$1 / N[(i + N[(y / N[(1.0 / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i)) < +inf.0

   1. Initial program 92.4%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right), y\right), \frac{54929528941}{2000000}\right), y\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\left(y \cdot \left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right)\right), i\right)\right) \]

      2. flip-+ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right), y\right), \frac{54929528941}{2000000}\right), y\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\left(y \cdot \frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y\right) \cdot \left(\left(\left(y + a\right) \cdot y + b\right) \cdot y\right) - c \cdot c}{\left(\left(y + a\right) \cdot y + b\right) \cdot y - c}\right), i\right)\right) \]

      3. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right), y\right), \frac{54929528941}{2000000}\right), y\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\left(y \cdot \frac{1}{\frac{\left(\left(y + a\right) \cdot y + b\right) \cdot y - c}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y\right) \cdot \left(\left(\left(y + a\right) \cdot y + b\right) \cdot y\right) - c \cdot c}}\right), i\right)\right) \]

      4. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right), y\right), \frac{54929528941}{2000000}\right), y\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\left(\frac{y}{\frac{\left(\left(y + a\right) \cdot y + b\right) \cdot y - c}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y\right) \cdot \left(\left(\left(y + a\right) \cdot y + b\right) \cdot y\right) - c \cdot c}}\right), i\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right), y\right), \frac{54929528941}{2000000}\right), y\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(y, \left(\frac{\left(\left(y + a\right) \cdot y + b\right) \cdot y - c}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y\right) \cdot \left(\left(\left(y + a\right) \cdot y + b\right) \cdot y\right) - c \cdot c}\right)\right), i\right)\right) \]

      6. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right), y\right), \frac{54929528941}{2000000}\right), y\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(y, \left(\frac{1}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y\right) \cdot \left(\left(\left(y + a\right) \cdot y + b\right) \cdot y\right) - c \cdot c}{\left(\left(y + a\right) \cdot y + b\right) \cdot y - c}}\right)\right), i\right)\right) \]

      7. flip-+ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right), y\right), \frac{54929528941}{2000000}\right), y\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(y, \left(\frac{1}{\left(\left(y + a\right) \cdot y + b\right) \cdot y + c}\right)\right), i\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right), y\right), \frac{54929528941}{2000000}\right), y\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(y, \mathsf{/.f64}\left(1, \left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right)\right)\right), i\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right), y\right), \frac{54929528941}{2000000}\right), y\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(y, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y\right), c\right)\right)\right), i\right)\right) \]

   4. Applied egg-rr 92.4%

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\color{blue}{\frac{y}{\frac{1}{y \cdot \left(y \cdot \left(y + a\right) + b\right) + c}}} + i} \]

   if +inf.0 < (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))

   1. Initial program 0.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(-1 \cdot \frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}\right)}\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1 \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)}{\color{blue}{y}}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(-1 \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right), \color{blue}{y}\right)\right) \]

      4. distribute-lft-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(-1 \cdot \left(-1 \cdot \left(z - a \cdot x\right)\right)\right), y\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(\left(-1 \cdot -1\right) \cdot \left(z - a \cdot x\right)\right), y\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(1 \cdot \left(z - a \cdot x\right)\right), y\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(1, \left(z - a \cdot x\right)\right), y\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(1, \mathsf{\_.f64}\left(z, \left(a \cdot x\right)\right)\right), y\right)\right) \]

      9. *-lowering-*.f64 71.2%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(1, \mathsf{\_.f64}\left(z, \mathsf{*.f64}\left(a, x\right)\right)\right), y\right)\right) \]

   5. Simplified 71.2%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)\right)}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i} \leq \infty:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)\right)}{i + \frac{y}{\frac{1}{c + y \cdot \left(y \cdot \left(y + a\right) + b\right)}}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 82.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)\right)}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i}\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (/
          (+
           t
           (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ (* x y) z)))))))
          (+ (* y (+ c (* y (+ (* y (+ y a)) b)))) i))))
   (if (<= t_1 INFINITY) t_1 (+ x (/ (- z (* x a)) y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = x + ((z - (x * a)) / y);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i);
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = x + ((z - (x * a)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i)
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = x + ((z - (x * a)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(Float64(x * y) + z))))))) / Float64(Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b)))) + i))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(z - Float64(x * a)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z))))))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i);
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = x + ((z - (x * a)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i)) < +inf.0

   1. Initial program 92.4%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   if +inf.0 < (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))

   1. Initial program 0.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(-1 \cdot \frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}\right)}\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1 \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)}{\color{blue}{y}}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(-1 \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right), \color{blue}{y}\right)\right) \]

      4. distribute-lft-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(-1 \cdot \left(-1 \cdot \left(z - a \cdot x\right)\right)\right), y\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(\left(-1 \cdot -1\right) \cdot \left(z - a \cdot x\right)\right), y\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(1 \cdot \left(z - a \cdot x\right)\right), y\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(1, \left(z - a \cdot x\right)\right), y\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(1, \mathsf{\_.f64}\left(z, \left(a \cdot x\right)\right)\right), y\right)\right) \]

      9. *-lowering-*.f64 71.2%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(1, \mathsf{\_.f64}\left(z, \mathsf{*.f64}\left(a, x\right)\right)\right), y\right)\right) \]

   5. Simplified 71.2%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)\right)}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i} \leq \infty:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)\right)}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 78.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\\ t_2 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -1.18 \cdot 10^{+57}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 10^{-24}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + x \cdot \left(y \cdot y\right)\right)\right)}{y \cdot t\_1 + i}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+48}:\\ \;\;\;\;\frac{\frac{1}{y}}{t\_1} \cdot \left(t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ c (* y (+ (* y (+ y a)) b)))) (t_2 (+ x (/ (- z (* x a)) y))))
   (if (<= y -1.18e+57)
     t_2
     (if (<= y 1e-24)
       (/
        (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* x (* y y)))))))
        (+ (* y t_1) i))
       (if (<= y 6.5e+48)
         (*
          (/ (/ 1.0 y) t_1)
          (+
           t
           (*
            y
            (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ (* x y) z))))))))
         t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c + (y * ((y * (y + a)) + b));
	double t_2 = x + ((z - (x * a)) / y);
	double tmp;
	if (y <= -1.18e+57) {
		tmp = t_2;
	} else if (y <= 1e-24) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (x * (y * y))))))) / ((y * t_1) + i);
	} else if (y <= 6.5e+48) {
		tmp = ((1.0 / y) / t_1) * (t + (y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z)))))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c + (y * ((y * (y + a)) + b))
    t_2 = x + ((z - (x * a)) / y)
    if (y <= (-1.18d+57)) then
        tmp = t_2
    else if (y <= 1d-24) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (x * (y * y))))))) / ((y * t_1) + i)
    else if (y <= 6.5d+48) then
        tmp = ((1.0d0 / y) / t_1) * (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * ((x * y) + z)))))))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = c + (y * ((y * (y + a)) + b));
	double t_2 = x + ((z - (x * a)) / y);
	double tmp;
	if (y <= -1.18e+57) {
		tmp = t_2;
	} else if (y <= 1e-24) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (x * (y * y))))))) / ((y * t_1) + i);
	} else if (y <= 6.5e+48) {
		tmp = ((1.0 / y) / t_1) * (t + (y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z)))))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = c + (y * ((y * (y + a)) + b))
	t_2 = x + ((z - (x * a)) / y)
	tmp = 0
	if y <= -1.18e+57:
		tmp = t_2
	elif y <= 1e-24:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (x * (y * y))))))) / ((y * t_1) + i)
	elif y <= 6.5e+48:
		tmp = ((1.0 / y) / t_1) * (t + (y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z)))))))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b)))
	t_2 = Float64(x + Float64(Float64(z - Float64(x * a)) / y))
	tmp = 0.0
	if (y <= -1.18e+57)
		tmp = t_2;
	elseif (y <= 1e-24)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(x * Float64(y * y))))))) / Float64(Float64(y * t_1) + i));
	elseif (y <= 6.5e+48)
		tmp = Float64(Float64(Float64(1.0 / y) / t_1) * Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(Float64(x * y) + z))))))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = c + (y * ((y * (y + a)) + b));
	t_2 = x + ((z - (x * a)) / y);
	tmp = 0.0;
	if (y <= -1.18e+57)
		tmp = t_2;
	elseif (y <= 1e-24)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (x * (y * y))))))) / ((y * t_1) + i);
	elseif (y <= 6.5e+48)
		tmp = ((1.0 / y) / t_1) * (t + (y * (230661.510616 + (y * (27464.7644705 + (y * ((x * y) + z)))))));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.18e+57], t$95$2, If[LessEqual[y, 1e-24], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * t$95$1), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e+48], N[(N[(N[(1.0 / y), $MachinePrecision] / t$95$1), $MachinePrecision] * N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.18e57 or 6.49999999999999972e48 < y

   1. Initial program 2.4%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(-1 \cdot \frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}\right)}\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1 \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)}{\color{blue}{y}}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(-1 \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right), \color{blue}{y}\right)\right) \]

      4. distribute-lft-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(-1 \cdot \left(-1 \cdot \left(z - a \cdot x\right)\right)\right), y\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(\left(-1 \cdot -1\right) \cdot \left(z - a \cdot x\right)\right), y\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(1 \cdot \left(z - a \cdot x\right)\right), y\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(1, \left(z - a \cdot x\right)\right), y\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(1, \mathsf{\_.f64}\left(z, \left(a \cdot x\right)\right)\right), y\right)\right) \]

      9. *-lowering-*.f64 70.5%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(1, \mathsf{\_.f64}\left(z, \mathsf{*.f64}\left(a, x\right)\right)\right), y\right)\right) \]

   5. Simplified 70.5%

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

   if -1.18e57 < y < 9.99999999999999924e-25

   1. Initial program 96.5%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(y \cdot \left(\frac{54929528941}{2000000} + x \cdot {y}^{2}\right)\right)}, \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{54929528941}{2000000} + x \cdot {y}^{2}\right)\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right)}, y\right), c\right), y\right), i\right)\right) \]

      2. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{54929528941}{2000000} + x \cdot \left(y \cdot y\right)\right)\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{54929528941}{2000000} + \left(x \cdot y\right) \cdot y\right)\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{54929528941}{2000000}, \left(\left(x \cdot y\right) \cdot y\right)\right)\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), \color{blue}{b}\right), y\right), c\right), y\right), i\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{54929528941}{2000000}, \left(x \cdot \left(y \cdot y\right)\right)\right)\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

      6. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{54929528941}{2000000}, \left(x \cdot {y}^{2}\right)\right)\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{54929528941}{2000000}, \mathsf{*.f64}\left(x, \left({y}^{2}\right)\right)\right)\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

      8. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{54929528941}{2000000}, \mathsf{*.f64}\left(x, \left(y \cdot y\right)\right)\right)\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

      9. *-lowering-*.f64 90.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{54929528941}{2000000}, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, y\right)\right)\right)\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

   5. Simplified 90.7%

      \[\leadsto \frac{\left(\color{blue}{y \cdot \left(27464.7644705 + x \cdot \left(y \cdot y\right)\right)} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   if 9.99999999999999924e-25 < y < 6.49999999999999972e48

   1. Initial program 68.9%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}}} \]

      2. associate-/r/ N/A

         \[\leadsto \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \cdot \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\right), \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t\right)}\right) \]

   4. Applied egg-rr 68.8%

      \[\leadsto \color{blue}{\frac{1}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i} \cdot \left(y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t\right)} \]

   5. Taylor expanded in i around 0

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(\frac{1}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right)\right), \frac{54929528941}{2000000}\right)\right), \frac{28832688827}{125000}\right)\right), t\right)\right) \]
   6. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{\frac{1}{y}}{c + y \cdot \left(b + y \cdot \left(a + y\right)\right)}\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right)\right), \frac{54929528941}{2000000}\right)\right), \frac{28832688827}{125000}\right)\right)}, t\right)\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{1}{y}\right), \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right)\right), \frac{54929528941}{2000000}\right)\right), \frac{28832688827}{125000}\right)\right)}, t\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(1, y\right), \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{y}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right)\right), \frac{54929528941}{2000000}\right)\right), \frac{28832688827}{125000}\right)\right), t\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(1, y\right), \mathsf{+.f64}\left(c, \left(y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \color{blue}{\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right)\right), \frac{54929528941}{2000000}\right)\right), \frac{28832688827}{125000}\right)}\right), t\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(1, y\right), \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(y, \left(b + y \cdot \left(a + y\right)\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right)\right), \frac{54929528941}{2000000}\right)\right), \color{blue}{\frac{28832688827}{125000}}\right)\right), t\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(1, y\right), \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \left(y \cdot \left(a + y\right)\right)\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right)\right), \frac{54929528941}{2000000}\right)\right), \frac{28832688827}{125000}\right)\right), t\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(1, y\right), \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(y, \left(a + y\right)\right)\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right)\right), \frac{54929528941}{2000000}\right)\right), \frac{28832688827}{125000}\right)\right), t\right)\right) \]

      8. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(1, y\right), \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(y, \left(y + a\right)\right)\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right)\right), \frac{54929528941}{2000000}\right)\right), \frac{28832688827}{125000}\right)\right), t\right)\right) \]

      9. +-lowering-+.f64 72.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(1, y\right), \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(y, a\right)\right)\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right)\right), \frac{54929528941}{2000000}\right)\right), \frac{28832688827}{125000}\right)\right), t\right)\right) \]

   7. Simplified 72.5%

      \[\leadsto \color{blue}{\frac{\frac{1}{y}}{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)}} \cdot \left(y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.18 \cdot 10^{+57}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 10^{-24}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + x \cdot \left(y \cdot y\right)\right)\right)}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+48}:\\ \;\;\;\;\frac{\frac{1}{y}}{c + y \cdot \left(y \cdot \left(y + a\right) + b\right)} \cdot \left(t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(x \cdot y + z\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ t_2 := y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-33}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{t\_2}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+47}:\\ \;\;\;\;\frac{t + y \cdot \left(x \cdot \left(y \cdot \left(y \cdot y\right)\right)\right)}{t\_2}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ (- z (* x a)) y)))
        (t_2 (+ (* y (+ c (* y (+ (* y (+ y a)) b)))) i)))
   (if (<= y -4.2e+59)
     t_1
     (if (<= y 4.3e-33)
       (/ (+ t (* y (+ 230661.510616 (* y 27464.7644705)))) t_2)
       (if (<= y 7.5e+47) (/ (+ t (* y (* x (* y (* y y))))) t_2) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z - (x * a)) / y);
	double t_2 = (y * (c + (y * ((y * (y + a)) + b)))) + i;
	double tmp;
	if (y <= -4.2e+59) {
		tmp = t_1;
	} else if (y <= 4.3e-33) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / t_2;
	} else if (y <= 7.5e+47) {
		tmp = (t + (y * (x * (y * (y * y))))) / t_2;
	} else {
		tmp = 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) :: t_2
    real(8) :: tmp
    t_1 = x + ((z - (x * a)) / y)
    t_2 = (y * (c + (y * ((y * (y + a)) + b)))) + i
    if (y <= (-4.2d+59)) then
        tmp = t_1
    else if (y <= 4.3d-33) then
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / t_2
    else if (y <= 7.5d+47) then
        tmp = (t + (y * (x * (y * (y * y))))) / t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z - (x * a)) / y);
	double t_2 = (y * (c + (y * ((y * (y + a)) + b)))) + i;
	double tmp;
	if (y <= -4.2e+59) {
		tmp = t_1;
	} else if (y <= 4.3e-33) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / t_2;
	} else if (y <= 7.5e+47) {
		tmp = (t + (y * (x * (y * (y * y))))) / t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z - (x * a)) / y)
	t_2 = (y * (c + (y * ((y * (y + a)) + b)))) + i
	tmp = 0
	if y <= -4.2e+59:
		tmp = t_1
	elif y <= 4.3e-33:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / t_2
	elif y <= 7.5e+47:
		tmp = (t + (y * (x * (y * (y * y))))) / t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z - Float64(x * a)) / y))
	t_2 = Float64(Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b)))) + i)
	tmp = 0.0
	if (y <= -4.2e+59)
		tmp = t_1;
	elseif (y <= 4.3e-33)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / t_2);
	elseif (y <= 7.5e+47)
		tmp = Float64(Float64(t + Float64(y * Float64(x * Float64(y * Float64(y * y))))) / t_2);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + ((z - (x * a)) / y);
	t_2 = (y * (c + (y * ((y * (y + a)) + b)))) + i;
	tmp = 0.0;
	if (y <= -4.2e+59)
		tmp = t_1;
	elseif (y <= 4.3e-33)
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / t_2;
	elseif (y <= 7.5e+47)
		tmp = (t + (y * (x * (y * (y * y))))) / t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]}, If[LessEqual[y, -4.2e+59], t$95$1, If[LessEqual[y, 4.3e-33], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[y, 7.5e+47], N[(N[(t + N[(y * N[(x * N[(y * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.19999999999999968e59 or 7.4999999999999999e47 < y

   1. Initial program 2.4%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(-1 \cdot \frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}\right)}\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1 \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)}{\color{blue}{y}}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(-1 \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right), \color{blue}{y}\right)\right) \]

      4. distribute-lft-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(-1 \cdot \left(-1 \cdot \left(z - a \cdot x\right)\right)\right), y\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(\left(-1 \cdot -1\right) \cdot \left(z - a \cdot x\right)\right), y\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(1 \cdot \left(z - a \cdot x\right)\right), y\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(1, \left(z - a \cdot x\right)\right), y\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(1, \mathsf{\_.f64}\left(z, \left(a \cdot x\right)\right)\right), y\right)\right) \]

      9. *-lowering-*.f64 71.3%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(1, \mathsf{\_.f64}\left(z, \mathsf{*.f64}\left(a, x\right)\right)\right), y\right)\right) \]

   5. Simplified 71.3%

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

   if -4.19999999999999968e59 < y < 4.30000000000000031e-33

   1. Initial program 95.8%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(\frac{54929528941}{2000000} \cdot y\right)}, \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(y \cdot \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right)}, y\right), c\right), y\right), i\right)\right) \]

      2. *-lowering-*.f64 88.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right)}, y\right), c\right), y\right), i\right)\right) \]

   5. Simplified 88.0%

      \[\leadsto \frac{\left(\color{blue}{y \cdot 27464.7644705} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   if 4.30000000000000031e-33 < y < 7.4999999999999999e47

   1. Initial program 71.8%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\left(x \cdot {y}^{3}\right)}, y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \left({y}^{3}\right)\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right)}, c\right), y\right), i\right)\right) \]

      2. cube-mult N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \left(y \cdot \left(y \cdot y\right)\right)\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), \color{blue}{y}\right), c\right), y\right), i\right)\right) \]

      3. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \left(y \cdot {y}^{2}\right)\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \left({y}^{2}\right)\right)\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), \color{blue}{y}\right), c\right), y\right), i\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \left(y \cdot y\right)\right)\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

      6. *-lowering-*.f64 49.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, y\right)\right)\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

   5. Simplified 49.5%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+59}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-33}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+47}:\\ \;\;\;\;\frac{t + y \cdot \left(x \cdot \left(y \cdot \left(y \cdot y\right)\right)\right)}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 78.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -2.55 \cdot 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+49}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + x \cdot \left(y \cdot y\right)\right)\right)}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ (- z (* x a)) y))))
   (if (<= y -2.55e+59)
     t_1
     (if (<= y 1.9e+49)
       (/
        (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* x (* y y)))))))
        (+ (* y (+ c (* y (+ (* y (+ y a)) b)))) i))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z - (x * a)) / y);
	double tmp;
	if (y <= -2.55e+59) {
		tmp = t_1;
	} else if (y <= 1.9e+49) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (x * (y * y))))))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((z - (x * a)) / y)
    if (y <= (-2.55d+59)) then
        tmp = t_1
    else if (y <= 1.9d+49) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (x * (y * y))))))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z - (x * a)) / y);
	double tmp;
	if (y <= -2.55e+59) {
		tmp = t_1;
	} else if (y <= 1.9e+49) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (x * (y * y))))))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z - (x * a)) / y)
	tmp = 0
	if y <= -2.55e+59:
		tmp = t_1
	elif y <= 1.9e+49:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (x * (y * y))))))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z - Float64(x * a)) / y))
	tmp = 0.0
	if (y <= -2.55e+59)
		tmp = t_1;
	elseif (y <= 1.9e+49)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(x * Float64(y * y))))))) / Float64(Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b)))) + i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + ((z - (x * a)) / y);
	tmp = 0.0;
	if (y <= -2.55e+59)
		tmp = t_1;
	elseif (y <= 1.9e+49)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (x * (y * y))))))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.55e+59], t$95$1, If[LessEqual[y, 1.9e+49], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.5500000000000002e59 or 1.8999999999999999e49 < y

   1. Initial program 2.4%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(-1 \cdot \frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}\right)}\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1 \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)}{\color{blue}{y}}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(-1 \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right), \color{blue}{y}\right)\right) \]

      4. distribute-lft-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(-1 \cdot \left(-1 \cdot \left(z - a \cdot x\right)\right)\right), y\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(\left(-1 \cdot -1\right) \cdot \left(z - a \cdot x\right)\right), y\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(1 \cdot \left(z - a \cdot x\right)\right), y\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(1, \left(z - a \cdot x\right)\right), y\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(1, \mathsf{\_.f64}\left(z, \left(a \cdot x\right)\right)\right), y\right)\right) \]

      9. *-lowering-*.f64 70.5%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(1, \mathsf{\_.f64}\left(z, \mathsf{*.f64}\left(a, x\right)\right)\right), y\right)\right) \]

   5. Simplified 70.5%

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

   if -2.5500000000000002e59 < y < 1.8999999999999999e49

   1. Initial program 93.3%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(y \cdot \left(\frac{54929528941}{2000000} + x \cdot {y}^{2}\right)\right)}, \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{54929528941}{2000000} + x \cdot {y}^{2}\right)\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right)}, y\right), c\right), y\right), i\right)\right) \]

      2. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{54929528941}{2000000} + x \cdot \left(y \cdot y\right)\right)\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{54929528941}{2000000} + \left(x \cdot y\right) \cdot y\right)\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{54929528941}{2000000}, \left(\left(x \cdot y\right) \cdot y\right)\right)\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), \color{blue}{b}\right), y\right), c\right), y\right), i\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{54929528941}{2000000}, \left(x \cdot \left(y \cdot y\right)\right)\right)\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

      6. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{54929528941}{2000000}, \left(x \cdot {y}^{2}\right)\right)\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{54929528941}{2000000}, \mathsf{*.f64}\left(x, \left({y}^{2}\right)\right)\right)\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

      8. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{54929528941}{2000000}, \mathsf{*.f64}\left(x, \left(y \cdot y\right)\right)\right)\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

      9. *-lowering-*.f64 85.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{54929528941}{2000000}, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(y, y\right)\right)\right)\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

   5. Simplified 85.9%

      \[\leadsto \frac{\left(\color{blue}{y \cdot \left(27464.7644705 + x \cdot \left(y \cdot y\right)\right)} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{+59}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+49}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + x \cdot \left(y \cdot y\right)\right)\right)}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -4.6 \cdot 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+45}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ (- z (* x a)) y))))
   (if (<= y -4.6e+59)
     t_1
     (if (<= y 2.5e+45)
       (/
        (+ t (* y (+ 230661.510616 (* y 27464.7644705))))
        (+ (* y (+ c (* y (+ (* y (+ y a)) b)))) i))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z - (x * a)) / y);
	double tmp;
	if (y <= -4.6e+59) {
		tmp = t_1;
	} else if (y <= 2.5e+45) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((z - (x * a)) / y)
    if (y <= (-4.6d+59)) then
        tmp = t_1
    else if (y <= 2.5d+45) then
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z - (x * a)) / y);
	double tmp;
	if (y <= -4.6e+59) {
		tmp = t_1;
	} else if (y <= 2.5e+45) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z - (x * a)) / y)
	tmp = 0
	if y <= -4.6e+59:
		tmp = t_1
	elif y <= 2.5e+45:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z - Float64(x * a)) / y))
	tmp = 0.0
	if (y <= -4.6e+59)
		tmp = t_1;
	elseif (y <= 2.5e+45)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / Float64(Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b)))) + i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + ((z - (x * a)) / y);
	tmp = 0.0;
	if (y <= -4.6e+59)
		tmp = t_1;
	elseif (y <= 2.5e+45)
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * (c + (y * ((y * (y + a)) + b)))) + i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.6e+59], t$95$1, If[LessEqual[y, 2.5e+45], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.60000000000000016e59 or 2.5e45 < y

   1. Initial program 2.4%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(-1 \cdot \frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}\right)}\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1 \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)}{\color{blue}{y}}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(-1 \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right), \color{blue}{y}\right)\right) \]

      4. distribute-lft-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(-1 \cdot \left(-1 \cdot \left(z - a \cdot x\right)\right)\right), y\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(\left(-1 \cdot -1\right) \cdot \left(z - a \cdot x\right)\right), y\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(1 \cdot \left(z - a \cdot x\right)\right), y\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(1, \left(z - a \cdot x\right)\right), y\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(1, \mathsf{\_.f64}\left(z, \left(a \cdot x\right)\right)\right), y\right)\right) \]

      9. *-lowering-*.f64 71.3%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(1, \mathsf{\_.f64}\left(z, \mathsf{*.f64}\left(a, x\right)\right)\right), y\right)\right) \]

   5. Simplified 71.3%

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

   if -4.60000000000000016e59 < y < 2.5e45

   1. Initial program 92.8%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(\frac{54929528941}{2000000} \cdot y\right)}, \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(y \cdot \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right)}, y\right), c\right), y\right), i\right)\right) \]

      2. *-lowering-*.f64 80.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right)}, y\right), c\right), y\right), i\right)\right) \]

   5. Simplified 80.2%

      \[\leadsto \frac{\left(\color{blue}{y \cdot 27464.7644705} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
3. Recombined 2 regimes into one program.

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+59}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+45}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -1 \cdot 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-24}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+119}:\\ \;\;\;\;z \cdot \frac{y \cdot y}{c + y \cdot \left(y \cdot \left(y + a\right) + b\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ (- z (* x a)) y))))
   (if (<= y -1e+30)
     t_1
     (if (<= y 4.2e-24)
       (/
        (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
        (+ i (* y c)))
       (if (<= y 6e+119)
         (* z (/ (* y y) (+ c (* y (+ (* y (+ y a)) b)))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z - (x * a)) / y);
	double tmp;
	if (y <= -1e+30) {
		tmp = t_1;
	} else if (y <= 4.2e-24) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * c));
	} else if (y <= 6e+119) {
		tmp = z * ((y * y) / (c + (y * ((y * (y + a)) + b))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((z - (x * a)) / y)
    if (y <= (-1d+30)) then
        tmp = t_1
    else if (y <= 4.2d-24) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / (i + (y * c))
    else if (y <= 6d+119) then
        tmp = z * ((y * y) / (c + (y * ((y * (y + a)) + b))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z - (x * a)) / y);
	double tmp;
	if (y <= -1e+30) {
		tmp = t_1;
	} else if (y <= 4.2e-24) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * c));
	} else if (y <= 6e+119) {
		tmp = z * ((y * y) / (c + (y * ((y * (y + a)) + b))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z - (x * a)) / y)
	tmp = 0
	if y <= -1e+30:
		tmp = t_1
	elif y <= 4.2e-24:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * c))
	elif y <= 6e+119:
		tmp = z * ((y * y) / (c + (y * ((y * (y + a)) + b))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z - Float64(x * a)) / y))
	tmp = 0.0
	if (y <= -1e+30)
		tmp = t_1;
	elseif (y <= 4.2e-24)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / Float64(i + Float64(y * c)));
	elseif (y <= 6e+119)
		tmp = Float64(z * Float64(Float64(y * y) / Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + ((z - (x * a)) / y);
	tmp = 0.0;
	if (y <= -1e+30)
		tmp = t_1;
	elseif (y <= 4.2e-24)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * c));
	elseif (y <= 6e+119)
		tmp = z * ((y * y) / (c + (y * ((y * (y + a)) + b))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1e+30], t$95$1, If[LessEqual[y, 4.2e-24], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e+119], N[(z * N[(N[(y * y), $MachinePrecision] / N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1e30 or 6.00000000000000002e119 < y

   1. Initial program 2.5%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(-1 \cdot \frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}\right)}\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1 \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)}{\color{blue}{y}}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(-1 \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right), \color{blue}{y}\right)\right) \]

      4. distribute-lft-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(-1 \cdot \left(-1 \cdot \left(z - a \cdot x\right)\right)\right), y\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(\left(-1 \cdot -1\right) \cdot \left(z - a \cdot x\right)\right), y\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(1 \cdot \left(z - a \cdot x\right)\right), y\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(1, \left(z - a \cdot x\right)\right), y\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(1, \mathsf{\_.f64}\left(z, \left(a \cdot x\right)\right)\right), y\right)\right) \]

      9. *-lowering-*.f64 70.9%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(1, \mathsf{\_.f64}\left(z, \mathsf{*.f64}\left(a, x\right)\right)\right), y\right)\right) \]

   5. Simplified 70.9%

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

   if -1e30 < y < 4.1999999999999999e-24

   1. Initial program 99.1%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right), y\right), \frac{54929528941}{2000000}\right), y\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\color{blue}{\left(c \cdot y\right)}, i\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right), y\right), \frac{54929528941}{2000000}\right), y\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\left(y \cdot c\right), i\right)\right) \]

      2. *-lowering-*.f64 87.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right), y\right), \frac{54929528941}{2000000}\right), y\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, c\right), i\right)\right) \]

   5. Simplified 87.2%

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\color{blue}{y \cdot c} + i} \]

   6. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(y \cdot z\right)}, \frac{54929528941}{2000000}\right), y\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, c\right), i\right)\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 85.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, z\right), \frac{54929528941}{2000000}\right), y\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, c\right), i\right)\right) \]

   8. Simplified 85.8%

      \[\leadsto \frac{\left(\left(\color{blue}{y \cdot z} + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{y \cdot c + i} \]

   if 4.1999999999999999e-24 < y < 6.00000000000000002e119

   1. Initial program 54.6%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left({y}^{3} \cdot z\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(z \cdot {y}^{3}\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right)}, i\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left({y}^{3}\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right)}, i\right)\right) \]

      3. cube-mult N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(y \cdot \left(y \cdot y\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), \color{blue}{y}\right), i\right)\right) \]

      4. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(y \cdot {y}^{2}\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \left({y}^{2}\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), \color{blue}{y}\right), i\right)\right) \]

      6. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \left(y \cdot y\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

      7. *-lowering-*.f64 21.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, y\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

   5. Simplified 21.5%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{y \cdot \left(y \cdot y\right)}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\right), \color{blue}{z}\right) \]

   7. Applied egg-rr 25.4%

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

   8. Taylor expanded in i around 0

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(\frac{{y}^{2}}{c + y \cdot \left(b + y \cdot \left(a + y\right)\right)}\right)}, z\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left({y}^{2}\right), \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right), z\right) \]

      2. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y \cdot y\right), \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right), z\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right), z\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{+.f64}\left(c, \left(y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right)\right), z\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(y, \left(b + y \cdot \left(a + y\right)\right)\right)\right)\right), z\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \left(y \cdot \left(a + y\right)\right)\right)\right)\right)\right), z\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(y, \left(a + y\right)\right)\right)\right)\right)\right), z\right) \]

      8. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(y, \left(y + a\right)\right)\right)\right)\right)\right), z\right) \]

      9. +-lowering-+.f64 29.3%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(y, a\right)\right)\right)\right)\right)\right), z\right) \]

   10. Simplified 29.3%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+30}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-24}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot c}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+119}:\\ \;\;\;\;z \cdot \frac{y \cdot y}{c + y \cdot \left(y \cdot \left(y + a\right) + b\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 71.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -5.7 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-24}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+119}:\\ \;\;\;\;z \cdot \frac{y \cdot y}{c + y \cdot \left(y \cdot \left(y + a\right) + b\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ (- z (* x a)) y))))
   (if (<= y -5.7e+35)
     t_1
     (if (<= y 4.2e-24)
       (/ (+ t (* y 230661.510616)) (+ i (* y (+ c (* y b)))))
       (if (<= y 6e+119)
         (* z (/ (* y y) (+ c (* y (+ (* y (+ y a)) b)))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z - (x * a)) / y);
	double tmp;
	if (y <= -5.7e+35) {
		tmp = t_1;
	} else if (y <= 4.2e-24) {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	} else if (y <= 6e+119) {
		tmp = z * ((y * y) / (c + (y * ((y * (y + a)) + b))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((z - (x * a)) / y)
    if (y <= (-5.7d+35)) then
        tmp = t_1
    else if (y <= 4.2d-24) then
        tmp = (t + (y * 230661.510616d0)) / (i + (y * (c + (y * b))))
    else if (y <= 6d+119) then
        tmp = z * ((y * y) / (c + (y * ((y * (y + a)) + b))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z - (x * a)) / y);
	double tmp;
	if (y <= -5.7e+35) {
		tmp = t_1;
	} else if (y <= 4.2e-24) {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	} else if (y <= 6e+119) {
		tmp = z * ((y * y) / (c + (y * ((y * (y + a)) + b))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z - (x * a)) / y)
	tmp = 0
	if y <= -5.7e+35:
		tmp = t_1
	elif y <= 4.2e-24:
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))))
	elif y <= 6e+119:
		tmp = z * ((y * y) / (c + (y * ((y * (y + a)) + b))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z - Float64(x * a)) / y))
	tmp = 0.0
	if (y <= -5.7e+35)
		tmp = t_1;
	elseif (y <= 4.2e-24)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	elseif (y <= 6e+119)
		tmp = Float64(z * Float64(Float64(y * y) / Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + ((z - (x * a)) / y);
	tmp = 0.0;
	if (y <= -5.7e+35)
		tmp = t_1;
	elseif (y <= 4.2e-24)
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	elseif (y <= 6e+119)
		tmp = z * ((y * y) / (c + (y * ((y * (y + a)) + b))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.7e+35], t$95$1, If[LessEqual[y, 4.2e-24], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e+119], N[(z * N[(N[(y * y), $MachinePrecision] / N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.69999999999999993e35 or 6.00000000000000002e119 < y

   1. Initial program 2.5%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(-1 \cdot \frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}\right)}\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1 \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)}{\color{blue}{y}}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(-1 \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right), \color{blue}{y}\right)\right) \]

      4. distribute-lft-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(-1 \cdot \left(-1 \cdot \left(z - a \cdot x\right)\right)\right), y\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(\left(-1 \cdot -1\right) \cdot \left(z - a \cdot x\right)\right), y\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(1 \cdot \left(z - a \cdot x\right)\right), y\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(1, \left(z - a \cdot x\right)\right), y\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(1, \mathsf{\_.f64}\left(z, \left(a \cdot x\right)\right)\right), y\right)\right) \]

      9. *-lowering-*.f64 71.7%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(1, \mathsf{\_.f64}\left(z, \mathsf{*.f64}\left(a, x\right)\right)\right), y\right)\right) \]

   5. Simplified 71.7%

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

   if -5.69999999999999993e35 < y < 4.1999999999999999e-24

   1. Initial program 98.4%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(\frac{28832688827}{125000} \cdot y\right)}, t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(y \cdot \frac{28832688827}{125000}\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right)}, y\right), i\right)\right) \]

      2. *-lowering-*.f64 89.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{28832688827}{125000}\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right)}, y\right), i\right)\right) \]

   5. Simplified 89.4%

      \[\leadsto \frac{\color{blue}{y \cdot 230661.510616} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{28832688827}{125000}\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(b \cdot y\right)}, c\right), y\right), i\right)\right) \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{28832688827}{125000}\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(y \cdot b\right), c\right), y\right), i\right)\right) \]

      2. *-lowering-*.f64 84.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{28832688827}{125000}\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, b\right), c\right), y\right), i\right)\right) \]

   8. Simplified 84.9%

      \[\leadsto \frac{y \cdot 230661.510616 + t}{\left(\color{blue}{y \cdot b} + c\right) \cdot y + i} \]

   if 4.1999999999999999e-24 < y < 6.00000000000000002e119

   1. Initial program 54.6%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left({y}^{3} \cdot z\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(z \cdot {y}^{3}\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right)}, i\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left({y}^{3}\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right)}, i\right)\right) \]

      3. cube-mult N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(y \cdot \left(y \cdot y\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), \color{blue}{y}\right), i\right)\right) \]

      4. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(y \cdot {y}^{2}\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \left({y}^{2}\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), \color{blue}{y}\right), i\right)\right) \]

      6. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \left(y \cdot y\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

      7. *-lowering-*.f64 21.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, y\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

   5. Simplified 21.5%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{y \cdot \left(y \cdot y\right)}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\right), \color{blue}{z}\right) \]

   7. Applied egg-rr 25.4%

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

   8. Taylor expanded in i around 0

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(\frac{{y}^{2}}{c + y \cdot \left(b + y \cdot \left(a + y\right)\right)}\right)}, z\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left({y}^{2}\right), \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right), z\right) \]

      2. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y \cdot y\right), \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right), z\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right), z\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{+.f64}\left(c, \left(y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right)\right), z\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(y, \left(b + y \cdot \left(a + y\right)\right)\right)\right)\right), z\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \left(y \cdot \left(a + y\right)\right)\right)\right)\right)\right), z\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(y, \left(a + y\right)\right)\right)\right)\right)\right), z\right) \]

      8. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(y, \left(y + a\right)\right)\right)\right)\right)\right), z\right) \]

      9. +-lowering-+.f64 29.3%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(y, a\right)\right)\right)\right)\right)\right), z\right) \]

   10. Simplified 29.3%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.7 \cdot 10^{+35}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-24}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+119}:\\ \;\;\;\;z \cdot \frac{y \cdot y}{c + y \cdot \left(y \cdot \left(y + a\right) + b\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+46}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ (- z (* x a)) y))))
   (if (<= y -4.8e+60)
     t_1
     (if (<= y 1.2e+46)
       (/
        (+ t (* y 230661.510616))
        (+ (* y (+ c (* y (+ (* y (+ y a)) b)))) i))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z - (x * a)) / y);
	double tmp;
	if (y <= -4.8e+60) {
		tmp = t_1;
	} else if (y <= 1.2e+46) {
		tmp = (t + (y * 230661.510616)) / ((y * (c + (y * ((y * (y + a)) + b)))) + i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((z - (x * a)) / y)
    if (y <= (-4.8d+60)) then
        tmp = t_1
    else if (y <= 1.2d+46) then
        tmp = (t + (y * 230661.510616d0)) / ((y * (c + (y * ((y * (y + a)) + b)))) + i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z - (x * a)) / y);
	double tmp;
	if (y <= -4.8e+60) {
		tmp = t_1;
	} else if (y <= 1.2e+46) {
		tmp = (t + (y * 230661.510616)) / ((y * (c + (y * ((y * (y + a)) + b)))) + i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z - (x * a)) / y)
	tmp = 0
	if y <= -4.8e+60:
		tmp = t_1
	elif y <= 1.2e+46:
		tmp = (t + (y * 230661.510616)) / ((y * (c + (y * ((y * (y + a)) + b)))) + i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z - Float64(x * a)) / y))
	tmp = 0.0
	if (y <= -4.8e+60)
		tmp = t_1;
	elseif (y <= 1.2e+46)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(Float64(y * Float64(c + Float64(y * Float64(Float64(y * Float64(y + a)) + b)))) + i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + ((z - (x * a)) / y);
	tmp = 0.0;
	if (y <= -4.8e+60)
		tmp = t_1;
	elseif (y <= 1.2e+46)
		tmp = (t + (y * 230661.510616)) / ((y * (c + (y * ((y * (y + a)) + b)))) + i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.8e+60], t$95$1, If[LessEqual[y, 1.2e+46], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(c + N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.8e60 or 1.20000000000000004e46 < y

   1. Initial program 2.4%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(-1 \cdot \frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}\right)}\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1 \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)}{\color{blue}{y}}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(-1 \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right), \color{blue}{y}\right)\right) \]

      4. distribute-lft-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(-1 \cdot \left(-1 \cdot \left(z - a \cdot x\right)\right)\right), y\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(\left(-1 \cdot -1\right) \cdot \left(z - a \cdot x\right)\right), y\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(1 \cdot \left(z - a \cdot x\right)\right), y\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(1, \left(z - a \cdot x\right)\right), y\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(1, \mathsf{\_.f64}\left(z, \left(a \cdot x\right)\right)\right), y\right)\right) \]

      9. *-lowering-*.f64 71.3%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(1, \mathsf{\_.f64}\left(z, \mathsf{*.f64}\left(a, x\right)\right)\right), y\right)\right) \]

   5. Simplified 71.3%

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

   if -4.8e60 < y < 1.20000000000000004e46

   1. Initial program 92.8%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(\frac{28832688827}{125000} \cdot y\right)}, t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(y \cdot \frac{28832688827}{125000}\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right)}, y\right), i\right)\right) \]

      2. *-lowering-*.f64 79.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{28832688827}{125000}\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right)}, y\right), i\right)\right) \]

   5. Simplified 79.4%

      \[\leadsto \frac{\color{blue}{y \cdot 230661.510616} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+60}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+46}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(c + y \cdot \left(y \cdot \left(y + a\right) + b\right)\right) + i}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 72.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -1.24 \cdot 10^{+36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+43}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ (- z (* x a)) y))))
   (if (<= y -1.24e+36)
     t_1
     (if (<= y 7.2e+43)
       (/ (+ t (* y 230661.510616)) (+ i (* y (+ c (* y b)))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z - (x * a)) / y);
	double tmp;
	if (y <= -1.24e+36) {
		tmp = t_1;
	} else if (y <= 7.2e+43) {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((z - (x * a)) / y)
    if (y <= (-1.24d+36)) then
        tmp = t_1
    else if (y <= 7.2d+43) then
        tmp = (t + (y * 230661.510616d0)) / (i + (y * (c + (y * b))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z - (x * a)) / y);
	double tmp;
	if (y <= -1.24e+36) {
		tmp = t_1;
	} else if (y <= 7.2e+43) {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z - (x * a)) / y)
	tmp = 0
	if y <= -1.24e+36:
		tmp = t_1
	elif y <= 7.2e+43:
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z - Float64(x * a)) / y))
	tmp = 0.0
	if (y <= -1.24e+36)
		tmp = t_1;
	elseif (y <= 7.2e+43)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + ((z - (x * a)) / y);
	tmp = 0.0;
	if (y <= -1.24e+36)
		tmp = t_1;
	elseif (y <= 7.2e+43)
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.24e+36], t$95$1, If[LessEqual[y, 7.2e+43], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.23999999999999995e36 or 7.2000000000000002e43 < y

   1. Initial program 4.5%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(-1 \cdot \frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}\right)}\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1 \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)}{\color{blue}{y}}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(-1 \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right), \color{blue}{y}\right)\right) \]

      4. distribute-lft-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(-1 \cdot \left(-1 \cdot \left(z - a \cdot x\right)\right)\right), y\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(\left(-1 \cdot -1\right) \cdot \left(z - a \cdot x\right)\right), y\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(1 \cdot \left(z - a \cdot x\right)\right), y\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(1, \left(z - a \cdot x\right)\right), y\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(1, \mathsf{\_.f64}\left(z, \left(a \cdot x\right)\right)\right), y\right)\right) \]

      9. *-lowering-*.f64 67.1%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(1, \mathsf{\_.f64}\left(z, \mathsf{*.f64}\left(a, x\right)\right)\right), y\right)\right) \]

   5. Simplified 67.1%

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

   if -1.23999999999999995e36 < y < 7.2000000000000002e43

   1. Initial program 94.9%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(\frac{28832688827}{125000} \cdot y\right)}, t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(y \cdot \frac{28832688827}{125000}\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right)}, y\right), i\right)\right) \]

      2. *-lowering-*.f64 81.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{28832688827}{125000}\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right)}, y\right), i\right)\right) \]

   5. Simplified 81.7%

      \[\leadsto \frac{\color{blue}{y \cdot 230661.510616} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{28832688827}{125000}\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(b \cdot y\right)}, c\right), y\right), i\right)\right) \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{28832688827}{125000}\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(y \cdot b\right), c\right), y\right), i\right)\right) \]

      2. *-lowering-*.f64 75.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{28832688827}{125000}\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, b\right), c\right), y\right), i\right)\right) \]

   8. Simplified 75.8%

      \[\leadsto \frac{y \cdot 230661.510616 + t}{\left(\color{blue}{y \cdot b} + c\right) \cdot y + i} \]
3. Recombined 2 regimes into one program.

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.24 \cdot 10^{+36}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+43}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 69.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -1.4 \cdot 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+43}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ (- z (* x a)) y))))
   (if (<= y -1.4e+30)
     t_1
     (if (<= y 7.5e+43) (/ (+ t (* y 230661.510616)) (+ i (* y c))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z - (x * a)) / y);
	double tmp;
	if (y <= -1.4e+30) {
		tmp = t_1;
	} else if (y <= 7.5e+43) {
		tmp = (t + (y * 230661.510616)) / (i + (y * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((z - (x * a)) / y)
    if (y <= (-1.4d+30)) then
        tmp = t_1
    else if (y <= 7.5d+43) then
        tmp = (t + (y * 230661.510616d0)) / (i + (y * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z - (x * a)) / y);
	double tmp;
	if (y <= -1.4e+30) {
		tmp = t_1;
	} else if (y <= 7.5e+43) {
		tmp = (t + (y * 230661.510616)) / (i + (y * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z - (x * a)) / y)
	tmp = 0
	if y <= -1.4e+30:
		tmp = t_1
	elif y <= 7.5e+43:
		tmp = (t + (y * 230661.510616)) / (i + (y * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z - Float64(x * a)) / y))
	tmp = 0.0
	if (y <= -1.4e+30)
		tmp = t_1;
	elseif (y <= 7.5e+43)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + ((z - (x * a)) / y);
	tmp = 0.0;
	if (y <= -1.4e+30)
		tmp = t_1;
	elseif (y <= 7.5e+43)
		tmp = (t + (y * 230661.510616)) / (i + (y * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.4e+30], t$95$1, If[LessEqual[y, 7.5e+43], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.39999999999999992e30 or 7.49999999999999967e43 < y

   1. Initial program 4.5%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(-1 \cdot \frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}\right)}\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1 \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)}{\color{blue}{y}}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(-1 \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right), \color{blue}{y}\right)\right) \]

      4. distribute-lft-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(-1 \cdot \left(-1 \cdot \left(z - a \cdot x\right)\right)\right), y\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(\left(-1 \cdot -1\right) \cdot \left(z - a \cdot x\right)\right), y\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(1 \cdot \left(z - a \cdot x\right)\right), y\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(1, \left(z - a \cdot x\right)\right), y\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(1, \mathsf{\_.f64}\left(z, \left(a \cdot x\right)\right)\right), y\right)\right) \]

      9. *-lowering-*.f64 67.1%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(1, \mathsf{\_.f64}\left(z, \mathsf{*.f64}\left(a, x\right)\right)\right), y\right)\right) \]

   5. Simplified 67.1%

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

   if -1.39999999999999992e30 < y < 7.49999999999999967e43

   1. Initial program 94.9%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right), y\right), \frac{54929528941}{2000000}\right), y\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\color{blue}{\left(c \cdot y\right)}, i\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right), y\right), \frac{54929528941}{2000000}\right), y\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\left(y \cdot c\right), i\right)\right) \]

      2. *-lowering-*.f64 79.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right), y\right), \frac{54929528941}{2000000}\right), y\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, c\right), i\right)\right) \]

   5. Simplified 79.0%

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\color{blue}{y \cdot c} + i} \]

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(t + \frac{28832688827}{125000} \cdot y\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, c\right), i\right)\right) \]
   7. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{28832688827}{125000} \cdot y + t\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(y, c\right)}, i\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{28832688827}{125000} \cdot y\right), t\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(y, c\right)}, i\right)\right) \]

      3. *-lowering-*.f64 73.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{28832688827}{125000}, y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{y}, c\right), i\right)\right) \]

   8. Simplified 73.2%

      \[\leadsto \frac{\color{blue}{230661.510616 \cdot y + t}}{y \cdot c + i} \]
3. Recombined 2 regimes into one program.

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+30}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+43}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 59.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z - x \cdot a}{y}\\ \mathbf{if}\;y \leq -4600000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+44}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ (- z (* x a)) y))))
   (if (<= y -4600000000.0)
     t_1
     (if (<= y 2.5e+44) (/ (+ t (* y 230661.510616)) i) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z - (x * a)) / y);
	double tmp;
	if (y <= -4600000000.0) {
		tmp = t_1;
	} else if (y <= 2.5e+44) {
		tmp = (t + (y * 230661.510616)) / i;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((z - (x * a)) / y)
    if (y <= (-4600000000.0d0)) then
        tmp = t_1
    else if (y <= 2.5d+44) then
        tmp = (t + (y * 230661.510616d0)) / i
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + ((z - (x * a)) / y);
	double tmp;
	if (y <= -4600000000.0) {
		tmp = t_1;
	} else if (y <= 2.5e+44) {
		tmp = (t + (y * 230661.510616)) / i;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + ((z - (x * a)) / y)
	tmp = 0
	if y <= -4600000000.0:
		tmp = t_1
	elif y <= 2.5e+44:
		tmp = (t + (y * 230661.510616)) / i
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(Float64(z - Float64(x * a)) / y))
	tmp = 0.0
	if (y <= -4600000000.0)
		tmp = t_1;
	elseif (y <= 2.5e+44)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / i);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + ((z - (x * a)) / y);
	tmp = 0.0;
	if (y <= -4600000000.0)
		tmp = t_1;
	elseif (y <= 2.5e+44)
		tmp = (t + (y * 230661.510616)) / i;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4600000000.0], t$95$1, If[LessEqual[y, 2.5e+44], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.6e9 or 2.4999999999999998e44 < y

   1. Initial program 7.3%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(-1 \cdot \frac{-1 \cdot z - -1 \cdot \left(a \cdot x\right)}{y}\right)}\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1 \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)}{\color{blue}{y}}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(-1 \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right), \color{blue}{y}\right)\right) \]

      4. distribute-lft-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(-1 \cdot \left(-1 \cdot \left(z - a \cdot x\right)\right)\right), y\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(\left(-1 \cdot -1\right) \cdot \left(z - a \cdot x\right)\right), y\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(1 \cdot \left(z - a \cdot x\right)\right), y\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(1, \left(z - a \cdot x\right)\right), y\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(1, \mathsf{\_.f64}\left(z, \left(a \cdot x\right)\right)\right), y\right)\right) \]

      9. *-lowering-*.f64 63.9%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(1, \mathsf{\_.f64}\left(z, \mathsf{*.f64}\left(a, x\right)\right)\right), y\right)\right) \]

   5. Simplified 63.9%

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

   if -4.6e9 < y < 2.4999999999999998e44

   1. Initial program 96.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(\frac{28832688827}{125000} \cdot y\right)}, t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(y \cdot \frac{28832688827}{125000}\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right)}, y\right), i\right)\right) \]

      2. *-lowering-*.f64 82.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{28832688827}{125000}\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right)}, y\right), i\right)\right) \]

   5. Simplified 82.3%

      \[\leadsto \frac{\color{blue}{y \cdot 230661.510616} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{28832688827}{125000}\right), t\right), \color{blue}{i}\right) \]
   7. Step-by-step derivation

   8. Simplified 56.9%

      \[\leadsto \frac{y \cdot 230661.510616 + t}{\color{blue}{i}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4600000000:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+44}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 55.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1450000000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+43}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -1450000000.0)
   x
   (if (<= y 7.2e+43) (/ (+ t (* y 230661.510616)) i) x)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -1450000000.0) {
		tmp = x;
	} else if (y <= 7.2e+43) {
		tmp = (t + (y * 230661.510616)) / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-1450000000.0d0)) then
        tmp = x
    else if (y <= 7.2d+43) then
        tmp = (t + (y * 230661.510616d0)) / i
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -1450000000.0) {
		tmp = x;
	} else if (y <= 7.2e+43) {
		tmp = (t + (y * 230661.510616)) / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -1450000000.0:
		tmp = x
	elif y <= 7.2e+43:
		tmp = (t + (y * 230661.510616)) / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -1450000000.0)
		tmp = x;
	elseif (y <= 7.2e+43)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / i);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -1450000000.0)
		tmp = x;
	elseif (y <= 7.2e+43)
		tmp = (t + (y * 230661.510616)) / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -1450000000.0], x, If[LessEqual[y, 7.2e+43], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1.45e9 or 7.2000000000000002e43 < y

   1. Initial program 7.3%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 52.5%

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

   if -1.45e9 < y < 7.2000000000000002e43

   1. Initial program 96.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(\frac{28832688827}{125000} \cdot y\right)}, t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(y \cdot \frac{28832688827}{125000}\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right)}, y\right), i\right)\right) \]

      2. *-lowering-*.f64 82.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{28832688827}{125000}\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right)}, y\right), i\right)\right) \]

   5. Simplified 82.3%

      \[\leadsto \frac{\color{blue}{y \cdot 230661.510616} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{28832688827}{125000}\right), t\right), \color{blue}{i}\right) \]
   7. Step-by-step derivation

   8. Simplified 56.9%

      \[\leadsto \frac{y \cdot 230661.510616 + t}{\color{blue}{i}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1450000000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+43}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 51.6% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+50}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -1.3e+18) x (if (<= y 2.2e+50) (/ t i) x)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -1.3e+18) {
		tmp = x;
	} else if (y <= 2.2e+50) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-1.3d+18)) then
        tmp = x
    else if (y <= 2.2d+50) then
        tmp = t / i
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -1.3e+18) {
		tmp = x;
	} else if (y <= 2.2e+50) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -1.3e+18:
		tmp = x
	elif y <= 2.2e+50:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -1.3e+18)
		tmp = x;
	elseif (y <= 2.2e+50)
		tmp = Float64(t / i);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -1.3e+18)
		tmp = x;
	elseif (y <= 2.2e+50)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -1.3e+18], x, If[LessEqual[y, 2.2e+50], N[(t / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1.3e18 or 2.20000000000000017e50 < y

   1. Initial program 5.5%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 54.0%

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

   if -1.3e18 < y < 2.20000000000000017e50

   1. Initial program 95.4%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{t}{i}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 47.7%

         \[\leadsto \mathsf{/.f64}\left(t, \color{blue}{i}\right) \]

   5. Simplified 47.7%

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

Alternative 15: 26.6% accurate, 33.0× speedup

Math

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

FPCore

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

C

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

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
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;
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 61.0%

   \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
2. Add Preprocessing

3. Taylor expanded in y around inf

   \[\leadsto \color{blue}{x} \]
4. Step-by-step derivation

5. Simplified 22.9%

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

Reproduce

herbie shell --seed 2024191 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2"
  :precision binary64
  (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))