Rosa's TurbineBenchmark

Average Error: 12.8 → 1.0

Time: 16.9s

Precision: binary64

Cost: 7688

Math

\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5 \]

↓

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -2100000:\\ \;\;\;\;t_0 + \left(-1.5 - \frac{r \cdot w}{\frac{4}{r \cdot w}}\right)\\ \mathbf{elif}\;v \leq 6.2 \cdot 10^{-34}:\\ \;\;\;\;2 \cdot {r}^{-2} + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{2.6666666666666665}{r}}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(t_0 + 3\right) + \left(r \cdot \left(w \cdot \left(r \cdot w\right)\right)\right) \cdot \frac{\left(3 + v \cdot -2\right) \cdot -0.125}{1 - v}\right) + -4.5\\ \end{array} \]

FPCore

(FPCore (v w r)
 :precision binary64
 (-
  (-
   (+ 3.0 (/ 2.0 (* r r)))
   (/ (* (* 0.125 (- 3.0 (* 2.0 v))) (* (* (* w w) r) r)) (- 1.0 v)))
  4.5))

↓

(FPCore (v w r)
 :precision binary64
 (let* ((t_0 (/ 2.0 (* r r))))
   (if (<= v -2100000.0)
     (+ t_0 (- -1.5 (/ (* r w) (/ 4.0 (* r w)))))
     (if (<= v 6.2e-34)
       (+
        (* 2.0 (pow r -2.0))
        (- -1.5 (* (* r w) (/ w (/ 2.6666666666666665 r)))))
       (+
        (+
         (+ t_0 3.0)
         (* (* r (* w (* r w))) (/ (* (+ 3.0 (* v -2.0)) -0.125) (- 1.0 v))))
        -4.5)))))

C

double code(double v, double w, double r) {
	return ((3.0 + (2.0 / (r * r))) - (((0.125 * (3.0 - (2.0 * v))) * (((w * w) * r) * r)) / (1.0 - v))) - 4.5;
}

↓

double code(double v, double w, double r) {
	double t_0 = 2.0 / (r * r);
	double tmp;
	if (v <= -2100000.0) {
		tmp = t_0 + (-1.5 - ((r * w) / (4.0 / (r * w))));
	} else if (v <= 6.2e-34) {
		tmp = (2.0 * pow(r, -2.0)) + (-1.5 - ((r * w) * (w / (2.6666666666666665 / r))));
	} else {
		tmp = ((t_0 + 3.0) + ((r * (w * (r * w))) * (((3.0 + (v * -2.0)) * -0.125) / (1.0 - v)))) + -4.5;
	}
	return tmp;
}

Fortran

real(8) function code(v, w, r)
    real(8), intent (in) :: v
    real(8), intent (in) :: w
    real(8), intent (in) :: r
    code = ((3.0d0 + (2.0d0 / (r * r))) - (((0.125d0 * (3.0d0 - (2.0d0 * v))) * (((w * w) * r) * r)) / (1.0d0 - v))) - 4.5d0
end function

↓

real(8) function code(v, w, r)
    real(8), intent (in) :: v
    real(8), intent (in) :: w
    real(8), intent (in) :: r
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 2.0d0 / (r * r)
    if (v <= (-2100000.0d0)) then
        tmp = t_0 + ((-1.5d0) - ((r * w) / (4.0d0 / (r * w))))
    else if (v <= 6.2d-34) then
        tmp = (2.0d0 * (r ** (-2.0d0))) + ((-1.5d0) - ((r * w) * (w / (2.6666666666666665d0 / r))))
    else
        tmp = ((t_0 + 3.0d0) + ((r * (w * (r * w))) * (((3.0d0 + (v * (-2.0d0))) * (-0.125d0)) / (1.0d0 - v)))) + (-4.5d0)
    end if
    code = tmp
end function

Java

public static double code(double v, double w, double r) {
	return ((3.0 + (2.0 / (r * r))) - (((0.125 * (3.0 - (2.0 * v))) * (((w * w) * r) * r)) / (1.0 - v))) - 4.5;
}

↓

public static double code(double v, double w, double r) {
	double t_0 = 2.0 / (r * r);
	double tmp;
	if (v <= -2100000.0) {
		tmp = t_0 + (-1.5 - ((r * w) / (4.0 / (r * w))));
	} else if (v <= 6.2e-34) {
		tmp = (2.0 * Math.pow(r, -2.0)) + (-1.5 - ((r * w) * (w / (2.6666666666666665 / r))));
	} else {
		tmp = ((t_0 + 3.0) + ((r * (w * (r * w))) * (((3.0 + (v * -2.0)) * -0.125) / (1.0 - v)))) + -4.5;
	}
	return tmp;
}

Python

def code(v, w, r):
	return ((3.0 + (2.0 / (r * r))) - (((0.125 * (3.0 - (2.0 * v))) * (((w * w) * r) * r)) / (1.0 - v))) - 4.5

↓

def code(v, w, r):
	t_0 = 2.0 / (r * r)
	tmp = 0
	if v <= -2100000.0:
		tmp = t_0 + (-1.5 - ((r * w) / (4.0 / (r * w))))
	elif v <= 6.2e-34:
		tmp = (2.0 * math.pow(r, -2.0)) + (-1.5 - ((r * w) * (w / (2.6666666666666665 / r))))
	else:
		tmp = ((t_0 + 3.0) + ((r * (w * (r * w))) * (((3.0 + (v * -2.0)) * -0.125) / (1.0 - v)))) + -4.5
	return tmp

Julia

function code(v, w, r)
	return Float64(Float64(Float64(3.0 + Float64(2.0 / Float64(r * r))) - Float64(Float64(Float64(0.125 * Float64(3.0 - Float64(2.0 * v))) * Float64(Float64(Float64(w * w) * r) * r)) / Float64(1.0 - v))) - 4.5)
end

↓

function code(v, w, r)
	t_0 = Float64(2.0 / Float64(r * r))
	tmp = 0.0
	if (v <= -2100000.0)
		tmp = Float64(t_0 + Float64(-1.5 - Float64(Float64(r * w) / Float64(4.0 / Float64(r * w)))));
	elseif (v <= 6.2e-34)
		tmp = Float64(Float64(2.0 * (r ^ -2.0)) + Float64(-1.5 - Float64(Float64(r * w) * Float64(w / Float64(2.6666666666666665 / r)))));
	else
		tmp = Float64(Float64(Float64(t_0 + 3.0) + Float64(Float64(r * Float64(w * Float64(r * w))) * Float64(Float64(Float64(3.0 + Float64(v * -2.0)) * -0.125) / Float64(1.0 - v)))) + -4.5);
	end
	return tmp
end

MATLAB

function tmp = code(v, w, r)
	tmp = ((3.0 + (2.0 / (r * r))) - (((0.125 * (3.0 - (2.0 * v))) * (((w * w) * r) * r)) / (1.0 - v))) - 4.5;
end

↓

function tmp_2 = code(v, w, r)
	t_0 = 2.0 / (r * r);
	tmp = 0.0;
	if (v <= -2100000.0)
		tmp = t_0 + (-1.5 - ((r * w) / (4.0 / (r * w))));
	elseif (v <= 6.2e-34)
		tmp = (2.0 * (r ^ -2.0)) + (-1.5 - ((r * w) * (w / (2.6666666666666665 / r))));
	else
		tmp = ((t_0 + 3.0) + ((r * (w * (r * w))) * (((3.0 + (v * -2.0)) * -0.125) / (1.0 - v)))) + -4.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[v_, w_, r_] := N[(N[(N[(3.0 + N[(2.0 / N[(r * r), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(0.125 * N[(3.0 - N[(2.0 * v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(w * w), $MachinePrecision] * r), $MachinePrecision] * r), $MachinePrecision]), $MachinePrecision] / N[(1.0 - v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 4.5), $MachinePrecision]

↓

code[v_, w_, r_] := Block[{t$95$0 = N[(2.0 / N[(r * r), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[v, -2100000.0], N[(t$95$0 + N[(-1.5 - N[(N[(r * w), $MachinePrecision] / N[(4.0 / N[(r * w), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[v, 6.2e-34], N[(N[(2.0 * N[Power[r, -2.0], $MachinePrecision]), $MachinePrecision] + N[(-1.5 - N[(N[(r * w), $MachinePrecision] * N[(w / N[(2.6666666666666665 / r), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t$95$0 + 3.0), $MachinePrecision] + N[(N[(r * N[(w * N[(r * w), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(3.0 + N[(v * -2.0), $MachinePrecision]), $MachinePrecision] * -0.125), $MachinePrecision] / N[(1.0 - v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -4.5), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if v < -2.1e6

   1. Initial program 17.1

      \[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5 \]

   2. Simplified 0.3

      \[\leadsto \color{blue}{\frac{2}{r \cdot r} + \left(-1.5 - \frac{w}{\frac{\frac{1 - v}{\mathsf{fma}\left(v, -0.25, 0.375\right)}}{r}} \cdot \left(r \cdot w\right)\right)} \]
      Proof

      [Start] 17.1	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5 \]
      sub-neg [=>] 17.1	\[ \color{blue}{\left(\left(3 + \frac{2}{r \cdot r}\right) + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right)\right)} - 4.5 \]
      +-commutative [=>] 17.1	\[ \color{blue}{\left(\left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) + \left(3 + \frac{2}{r \cdot r}\right)\right)} - 4.5 \]
      associate--l+ [=>] 17.1	\[ \color{blue}{\left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) + \left(\left(3 + \frac{2}{r \cdot r}\right) - 4.5\right)} \]
      +-commutative [=>] 17.1	\[ \color{blue}{\left(\left(3 + \frac{2}{r \cdot r}\right) - 4.5\right) + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right)} \]
      sub-neg [=>] 17.1	\[ \color{blue}{\left(\left(3 + \frac{2}{r \cdot r}\right) + \left(-4.5\right)\right)} + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) \]
      +-commutative [=>] 17.1	\[ \color{blue}{\left(\left(-4.5\right) + \left(3 + \frac{2}{r \cdot r}\right)\right)} + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) \]
      associate-+r+ [=>] 17.1	\[ \color{blue}{\left(\left(\left(-4.5\right) + 3\right) + \frac{2}{r \cdot r}\right)} + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) \]
      +-commutative [<=] 17.1	\[ \color{blue}{\left(\frac{2}{r \cdot r} + \left(\left(-4.5\right) + 3\right)\right)} + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) \]
      associate-+r+ [<=] 17.1	\[ \color{blue}{\frac{2}{r \cdot r} + \left(\left(\left(-4.5\right) + 3\right) + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right)\right)} \]

   3. Applied egg-rr 0.3

      \[\leadsto \frac{2}{r \cdot r} + \left(-1.5 - \color{blue}{\frac{w \cdot r}{\frac{\frac{1 - v}{\mathsf{fma}\left(v, -0.25, 0.375\right)}}{w \cdot r}}}\right) \]

   4. Taylor expanded in v around inf 0.5

      \[\leadsto \frac{2}{r \cdot r} + \left(-1.5 - \frac{w \cdot r}{\color{blue}{\frac{4}{w \cdot r}}}\right) \]

   if -2.1e6 < v < 6.1999999999999996e-34

   1. Initial program 8.8

      \[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5 \]

   2. Simplified 0.3

      \[\leadsto \color{blue}{\frac{2}{r \cdot r} + \left(-1.5 - \frac{w}{\frac{\frac{1 - v}{\mathsf{fma}\left(v, -0.25, 0.375\right)}}{r}} \cdot \left(r \cdot w\right)\right)} \]
      Proof

      [Start] 8.8	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5 \]
      sub-neg [=>] 8.8	\[ \color{blue}{\left(\left(3 + \frac{2}{r \cdot r}\right) + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right)\right)} - 4.5 \]
      +-commutative [=>] 8.8	\[ \color{blue}{\left(\left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) + \left(3 + \frac{2}{r \cdot r}\right)\right)} - 4.5 \]
      associate--l+ [=>] 8.8	\[ \color{blue}{\left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) + \left(\left(3 + \frac{2}{r \cdot r}\right) - 4.5\right)} \]
      +-commutative [=>] 8.8	\[ \color{blue}{\left(\left(3 + \frac{2}{r \cdot r}\right) - 4.5\right) + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right)} \]
      sub-neg [=>] 8.8	\[ \color{blue}{\left(\left(3 + \frac{2}{r \cdot r}\right) + \left(-4.5\right)\right)} + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) \]
      +-commutative [=>] 8.8	\[ \color{blue}{\left(\left(-4.5\right) + \left(3 + \frac{2}{r \cdot r}\right)\right)} + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) \]
      associate-+r+ [=>] 8.8	\[ \color{blue}{\left(\left(\left(-4.5\right) + 3\right) + \frac{2}{r \cdot r}\right)} + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) \]
      +-commutative [<=] 8.8	\[ \color{blue}{\left(\frac{2}{r \cdot r} + \left(\left(-4.5\right) + 3\right)\right)} + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) \]
      associate-+r+ [<=] 8.8	\[ \color{blue}{\frac{2}{r \cdot r} + \left(\left(\left(-4.5\right) + 3\right) + \left(-\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right)\right)} \]

   3. Taylor expanded in v around 0 0.6

      \[\leadsto \frac{2}{r \cdot r} + \left(-1.5 - \frac{w}{\color{blue}{\frac{2.6666666666666665}{r}}} \cdot \left(r \cdot w\right)\right) \]

   4. Applied egg-rr 0.5

      \[\leadsto \color{blue}{{r}^{-2} \cdot 2} + \left(-1.5 - \frac{w}{\frac{2.6666666666666665}{r}} \cdot \left(r \cdot w\right)\right) \]

   if 6.1999999999999996e-34 < v

   1. Initial program 15.8

      \[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5 \]

   2. Simplified 8.3

      \[\leadsto \color{blue}{\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \left(r \cdot \left(r \cdot \left(w \cdot w\right)\right)\right)\right) + -4.5} \]
      Proof

      [Start] 15.8	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5 \]
      sub-neg [=>] 15.8	\[ \color{blue}{\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) + \left(-4.5\right)} \]
      associate-*l/ [<=] 8.3	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \color{blue}{\frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}\right) + \left(-4.5\right) \]
      *-commutative [=>] 8.3	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \color{blue}{\left(r \cdot \left(\left(w \cdot w\right) \cdot r\right)\right)}\right) + \left(-4.5\right) \]
      *-commutative [=>] 8.3	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \left(r \cdot \color{blue}{\left(r \cdot \left(w \cdot w\right)\right)}\right)\right) + \left(-4.5\right) \]
      metadata-eval [=>] 8.3	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \left(r \cdot \left(r \cdot \left(w \cdot w\right)\right)\right)\right) + \color{blue}{-4.5} \]

   3. Taylor expanded in r around 0 8.3

      \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \left(r \cdot \color{blue}{\left({w}^{2} \cdot r\right)}\right)\right) + -4.5 \]

   4. Simplified 2.4

      \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \left(r \cdot \color{blue}{\left(w \cdot \left(w \cdot r\right)\right)}\right)\right) + -4.5 \]
      Proof

      [Start] 8.3	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \left(r \cdot \left({w}^{2} \cdot r\right)\right)\right) + -4.5 \]
      unpow2 [=>] 8.3	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \left(r \cdot \left(\color{blue}{\left(w \cdot w\right)} \cdot r\right)\right)\right) + -4.5 \]
      associate-*l* [=>] 2.4	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \left(r \cdot \color{blue}{\left(w \cdot \left(w \cdot r\right)\right)}\right)\right) + -4.5 \]

3. Recombined 3 regimes into one program.

4. Final simplification 1.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;v \leq -2100000:\\ \;\;\;\;\frac{2}{r \cdot r} + \left(-1.5 - \frac{r \cdot w}{\frac{4}{r \cdot w}}\right)\\ \mathbf{elif}\;v \leq 6.2 \cdot 10^{-34}:\\ \;\;\;\;2 \cdot {r}^{-2} + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{2.6666666666666665}{r}}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\frac{2}{r \cdot r} + 3\right) + \left(r \cdot \left(w \cdot \left(r \cdot w\right)\right)\right) \cdot \frac{\left(3 + v \cdot -2\right) \cdot -0.125}{1 - v}\right) + -4.5\\ \end{array} \]

Alternatives

Alternative 1
Error	0.3
Cost	7872

\[\frac{2}{r \cdot r} + \left(-1.5 - \frac{w}{\frac{\frac{1 - v}{\mathsf{fma}\left(v, -0.25, 0.375\right)}}{r}} \cdot \left(r \cdot w\right)\right) \]

Alternative 2
Error	1.0
Cost	2120

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -2100000:\\ \;\;\;\;t_0 + \left(-1.5 - \frac{r \cdot w}{\frac{4}{r \cdot w}}\right)\\ \mathbf{elif}\;v \leq 4 \cdot 10^{-33}:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{2.6666666666666665}{r} + \frac{v \cdot -0.8888888888888888}{r}}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(t_0 + 3\right) + \left(r \cdot \left(w \cdot \left(r \cdot w\right)\right)\right) \cdot \frac{\left(3 + v \cdot -2\right) \cdot -0.125}{1 - v}\right) + -4.5\\ \end{array} \]

Alternative 3
Error	0.3
Cost	1864

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -5 \cdot 10^{+22}:\\ \;\;\;\;t_0 + \left(-1.5 - \frac{r \cdot w}{\frac{4}{r \cdot w}}\right)\\ \mathbf{elif}\;v \leq 2.2 \cdot 10^{+53}:\\ \;\;\;\;t_0 + \left(-1.5 - \frac{r \cdot w}{\frac{1 - v}{\left(r \cdot w\right) \cdot \left(0.375 + v \cdot -0.25\right)}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{4}{r}}\right)\\ \end{array} \]

Alternative 4
Error	1.0
Cost	1736

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -2100000:\\ \;\;\;\;t_0 + \left(-1.5 - \frac{r \cdot w}{\frac{4}{r \cdot w}}\right)\\ \mathbf{elif}\;v \leq 1.05 \cdot 10^{-31}:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{2.6666666666666665}{r} + \frac{v \cdot -0.8888888888888888}{r}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{4 + \frac{2}{v}}{r}}\right)\\ \end{array} \]

Alternative 5
Error	1.0
Cost	1608

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -2100000:\\ \;\;\;\;t_0 + \left(-1.5 - \frac{r \cdot w}{\frac{4}{r \cdot w}}\right)\\ \mathbf{elif}\;v \leq 1.05 \cdot 10^{-31}:\\ \;\;\;\;t_0 + \left(-1.5 + \left(r \cdot w\right) \cdot \left(w \cdot \left(r \cdot -0.375\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{4 + \frac{2}{v}}{r}}\right)\\ \end{array} \]

Alternative 6
Error	4.2
Cost	1353

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -2300000 \lor \neg \left(v \leq 1.05 \cdot 10^{-31}\right):\\ \;\;\;\;t_0 + \left(-1.5 + -0.25 \cdot \left(w \cdot \left(r \cdot \left(r \cdot w\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 + \left(r \cdot \left(w \cdot \left(r \cdot w\right)\right)\right) \cdot -0.375\right)\\ \end{array} \]

Alternative 7
Error	3.1
Cost	1353

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -2100000 \lor \neg \left(v \leq 1.05 \cdot 10^{-31}\right):\\ \;\;\;\;t_0 + \left(-1.5 + -0.25 \cdot \left(w \cdot \left(r \cdot \left(r \cdot w\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 + \left(r \cdot w\right) \cdot \left(w \cdot \left(r \cdot -0.375\right)\right)\right)\\ \end{array} \]

Alternative 8
Error	1.0
Cost	1353

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -2100000 \lor \neg \left(v \leq 1.05 \cdot 10^{-31}\right):\\ \;\;\;\;t_0 + \left(-1.5 + \left(r \cdot w\right) \cdot \left(r \cdot \left(w \cdot -0.25\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 + \left(r \cdot w\right) \cdot \left(w \cdot \left(r \cdot -0.375\right)\right)\right)\\ \end{array} \]

Alternative 9
Error	1.0
Cost	1353

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -2100000 \lor \neg \left(v \leq 1.05 \cdot 10^{-31}\right):\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{4}{r}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 + \left(r \cdot w\right) \cdot \left(w \cdot \left(r \cdot -0.375\right)\right)\right)\\ \end{array} \]

Alternative 10
Error	1.0
Cost	1352

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -2100000:\\ \;\;\;\;t_0 + \left(-1.5 - \frac{r \cdot w}{\frac{4}{r \cdot w}}\right)\\ \mathbf{elif}\;v \leq 1.05 \cdot 10^{-31}:\\ \;\;\;\;t_0 + \left(-1.5 + \left(r \cdot w\right) \cdot \left(w \cdot \left(r \cdot -0.375\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{4}{r}}\right)\\ \end{array} \]

Alternative 11
Error	11.5
Cost	1088

\[\frac{2}{r \cdot r} + \left(-1.5 + -0.25 \cdot \left(w \cdot \left(r \cdot \left(r \cdot w\right)\right)\right)\right) \]

Alternative 12
Error	20.9
Cost	448

\[\frac{2}{r \cdot r} + -1.5 \]

Alternative 13
Error	37.9
Cost	320

\[\frac{2}{r \cdot r} \]

Alternative 14
Error	37.9
Cost	320

\[\frac{\frac{2}{r}}{r} \]

Reproduce

herbie shell --seed 2023041 
(FPCore (v w r)
  :name "Rosa's TurbineBenchmark"
  :precision binary64
  (- (- (+ 3.0 (/ 2.0 (* r r))) (/ (* (* 0.125 (- 3.0 (* 2.0 v))) (* (* (* w w) r) r)) (- 1.0 v))) 4.5))