Rosa's TurbineBenchmark

Percentage Accurate: 84.3% → 99.1%

Time: 23.5s

Precision: binary64

Cost: 26564

• 52.8% of points produce a very large (infinite) output. You may want to add a precondition.

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;w \cdot w \leq 2 \cdot 10^{+298}:\\ \;\;\;\;\frac{2}{r \cdot r} + \left(-1.5 - \left(r \cdot \left(w \cdot \left(r \cdot w\right)\right)\right) \cdot \frac{0.375 + v \cdot -0.25}{1 - v}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(2, {r}^{-2}, 3\right) - \mathsf{fma}\left({\left(r \cdot w\right)}^{2}, 0.375, 4.5\right)\\ \end{array} \]

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
 (if (<= (* w w) 2e+298)
   (+
    (/ 2.0 (* r r))
    (- -1.5 (* (* r (* w (* r w))) (/ (+ 0.375 (* v -0.25)) (- 1.0 v)))))
   (- (fma 2.0 (pow r -2.0) 3.0) (fma (pow (* r w) 2.0) 0.375 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 tmp;
	if ((w * w) <= 2e+298) {
		tmp = (2.0 / (r * r)) + (-1.5 - ((r * (w * (r * w))) * ((0.375 + (v * -0.25)) / (1.0 - v))));
	} else {
		tmp = fma(2.0, pow(r, -2.0), 3.0) - fma(pow((r * w), 2.0), 0.375, 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)
	tmp = 0.0
	if (Float64(w * w) <= 2e+298)
		tmp = Float64(Float64(2.0 / Float64(r * r)) + Float64(-1.5 - Float64(Float64(r * Float64(w * Float64(r * w))) * Float64(Float64(0.375 + Float64(v * -0.25)) / Float64(1.0 - v)))));
	else
		tmp = Float64(fma(2.0, (r ^ -2.0), 3.0) - fma((Float64(r * w) ^ 2.0), 0.375, 4.5));
	end
	return 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_] := If[LessEqual[N[(w * w), $MachinePrecision], 2e+298], N[(N[(2.0 / N[(r * r), $MachinePrecision]), $MachinePrecision] + N[(-1.5 - N[(N[(r * N[(w * N[(r * w), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(0.375 + N[(v * -0.25), $MachinePrecision]), $MachinePrecision] / N[(1.0 - v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 * N[Power[r, -2.0], $MachinePrecision] + 3.0), $MachinePrecision] - N[(N[Power[N[(r * w), $MachinePrecision], 2.0], $MachinePrecision] * 0.375 + 4.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 w w) < 1.9999999999999999e298

   1. Initial program 91.8%

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

   2. Simplified 96.8%

      \[\leadsto \color{blue}{\frac{2}{r \cdot r} + \left(-1.5 - \left(r \cdot \left(r \cdot \left(w \cdot w\right)\right)\right) \cdot \frac{0.375 + v \cdot -0.25}{1 - v}\right)} \]
      Step-by-step derivation

      [Start] 91.8%	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5 \]
      associate--l- [=>] 91.8%	\[ \color{blue}{\left(3 + \frac{2}{r \cdot r}\right) - \left(\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v} + 4.5\right)} \]
      +-commutative [=>] 91.8%	\[ \color{blue}{\left(\frac{2}{r \cdot r} + 3\right)} - \left(\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v} + 4.5\right) \]
      associate--l+ [=>] 91.8%	\[ \color{blue}{\frac{2}{r \cdot r} + \left(3 - \left(\frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v} + 4.5\right)\right)} \]
      +-commutative [=>] 91.8%	\[ \frac{2}{r \cdot r} + \left(3 - \color{blue}{\left(4.5 + \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right)}\right) \]
      associate--r+ [=>] 91.8%	\[ \frac{2}{r \cdot r} + \color{blue}{\left(\left(3 - 4.5\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right)} \]
      metadata-eval [=>] 91.8%	\[ \frac{2}{r \cdot r} + \left(\color{blue}{-1.5} - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) \]
      associate-*l/ [<=] 96.8%	\[ \frac{2}{r \cdot r} + \left(-1.5 - \color{blue}{\frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v} \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}\right) \]
      *-commutative [=>] 96.8%	\[ \frac{2}{r \cdot r} + \left(-1.5 - \color{blue}{\left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right) \cdot \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v}}\right) \]
      *-commutative [=>] 96.8%	\[ \frac{2}{r \cdot r} + \left(-1.5 - \color{blue}{\left(r \cdot \left(\left(w \cdot w\right) \cdot r\right)\right)} \cdot \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v}\right) \]
      *-commutative [=>] 96.8%	\[ \frac{2}{r \cdot r} + \left(-1.5 - \left(r \cdot \color{blue}{\left(r \cdot \left(w \cdot w\right)\right)}\right) \cdot \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1 - v}\right) \]

   3. Taylor expanded in r around 0 96.8%

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

   4. Simplified 99.8%

      \[\leadsto \frac{2}{r \cdot r} + \left(-1.5 - \left(r \cdot \color{blue}{\left(w \cdot \left(w \cdot r\right)\right)}\right) \cdot \frac{0.375 + v \cdot -0.25}{1 - v}\right) \]
      Step-by-step derivation

      [Start] 96.8%	\[ \frac{2}{r \cdot r} + \left(-1.5 - \left(r \cdot \left({w}^{2} \cdot r\right)\right) \cdot \frac{0.375 + v \cdot -0.25}{1 - v}\right) \]
      unpow2 [=>] 96.8%	\[ \frac{2}{r \cdot r} + \left(-1.5 - \left(r \cdot \left(\color{blue}{\left(w \cdot w\right)} \cdot r\right)\right) \cdot \frac{0.375 + v \cdot -0.25}{1 - v}\right) \]
      associate-*l* [=>] 99.8%	\[ \frac{2}{r \cdot r} + \left(-1.5 - \left(r \cdot \color{blue}{\left(w \cdot \left(w \cdot r\right)\right)}\right) \cdot \frac{0.375 + v \cdot -0.25}{1 - v}\right) \]

   if 1.9999999999999999e298 < (*.f64 w w)

   1. Initial program 66.0%

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

   2. Simplified 66.0%

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

      [Start] 66.0%	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5 \]
      sub-neg [=>] 66.0%	\[ \color{blue}{\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) + \left(-4.5\right)} \]
      associate-/l* [=>] 66.0%	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \color{blue}{\frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{\frac{1 - v}{\left(\left(w \cdot w\right) \cdot r\right) \cdot r}}}\right) + \left(-4.5\right) \]
      cancel-sign-sub-inv [=>] 66.0%	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \color{blue}{\left(3 + \left(-2\right) \cdot v\right)}}{\frac{1 - v}{\left(\left(w \cdot w\right) \cdot r\right) \cdot r}}\right) + \left(-4.5\right) \]
      metadata-eval [=>] 66.0%	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 + \color{blue}{-2} \cdot v\right)}{\frac{1 - v}{\left(\left(w \cdot w\right) \cdot r\right) \cdot r}}\right) + \left(-4.5\right) \]
      *-commutative [=>] 66.0%	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 + -2 \cdot v\right)}{\frac{1 - v}{\color{blue}{r \cdot \left(\left(w \cdot w\right) \cdot r\right)}}}\right) + \left(-4.5\right) \]
      *-commutative [=>] 66.0%	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 + -2 \cdot v\right)}{\frac{1 - v}{r \cdot \color{blue}{\left(r \cdot \left(w \cdot w\right)\right)}}}\right) + \left(-4.5\right) \]
      metadata-eval [=>] 66.0%	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 + -2 \cdot v\right)}{\frac{1 - v}{r \cdot \left(r \cdot \left(w \cdot w\right)\right)}}\right) + \color{blue}{-4.5} \]

   3. Taylor expanded in v around 0 66.0%

      \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \color{blue}{0.375 \cdot \left({w}^{2} \cdot {r}^{2}\right)}\right) + -4.5 \]

   4. Simplified 66.0%

      \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \color{blue}{\left(w \cdot w\right) \cdot \left(\left(r \cdot r\right) \cdot 0.375\right)}\right) + -4.5 \]
      Step-by-step derivation

      [Start] 66.0%	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - 0.375 \cdot \left({w}^{2} \cdot {r}^{2}\right)\right) + -4.5 \]
      *-commutative [=>] 66.0%	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \color{blue}{\left({w}^{2} \cdot {r}^{2}\right) \cdot 0.375}\right) + -4.5 \]
      associate-*l* [=>] 66.0%	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \color{blue}{{w}^{2} \cdot \left({r}^{2} \cdot 0.375\right)}\right) + -4.5 \]
      unpow2 [=>] 66.0%	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \color{blue}{\left(w \cdot w\right)} \cdot \left({r}^{2} \cdot 0.375\right)\right) + -4.5 \]
      unpow2 [=>] 66.0%	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \left(w \cdot w\right) \cdot \left(\color{blue}{\left(r \cdot r\right)} \cdot 0.375\right)\right) + -4.5 \]

   5. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(2, {r}^{-2}, 3\right) - \mathsf{fma}\left({\left(r \cdot w\right)}^{2}, 0.375, 4.5\right)} \]
      Step-by-step derivation

      [Start] 66.0%	\[ \left(\left(3 + \frac{2}{r \cdot r}\right) - \left(w \cdot w\right) \cdot \left(\left(r \cdot r\right) \cdot 0.375\right)\right) + -4.5 \]
      associate-+l- [=>] 66.0%	\[ \color{blue}{\left(3 + \frac{2}{r \cdot r}\right) - \left(\left(w \cdot w\right) \cdot \left(\left(r \cdot r\right) \cdot 0.375\right) - -4.5\right)} \]
      +-commutative [=>] 66.0%	\[ \color{blue}{\left(\frac{2}{r \cdot r} + 3\right)} - \left(\left(w \cdot w\right) \cdot \left(\left(r \cdot r\right) \cdot 0.375\right) - -4.5\right) \]
      div-inv [=>] 66.0%	\[ \left(\color{blue}{2 \cdot \frac{1}{r \cdot r}} + 3\right) - \left(\left(w \cdot w\right) \cdot \left(\left(r \cdot r\right) \cdot 0.375\right) - -4.5\right) \]
      fma-def [=>] 66.0%	\[ \color{blue}{\mathsf{fma}\left(2, \frac{1}{r \cdot r}, 3\right)} - \left(\left(w \cdot w\right) \cdot \left(\left(r \cdot r\right) \cdot 0.375\right) - -4.5\right) \]
      pow2 [=>] 66.0%	\[ \mathsf{fma}\left(2, \frac{1}{\color{blue}{{r}^{2}}}, 3\right) - \left(\left(w \cdot w\right) \cdot \left(\left(r \cdot r\right) \cdot 0.375\right) - -4.5\right) \]
      pow-flip [=>] 66.0%	\[ \mathsf{fma}\left(2, \color{blue}{{r}^{\left(-2\right)}}, 3\right) - \left(\left(w \cdot w\right) \cdot \left(\left(r \cdot r\right) \cdot 0.375\right) - -4.5\right) \]
      metadata-eval [=>] 66.0%	\[ \mathsf{fma}\left(2, {r}^{\color{blue}{-2}}, 3\right) - \left(\left(w \cdot w\right) \cdot \left(\left(r \cdot r\right) \cdot 0.375\right) - -4.5\right) \]
      associate-*r* [=>] 66.0%	\[ \mathsf{fma}\left(2, {r}^{-2}, 3\right) - \left(\color{blue}{\left(\left(w \cdot w\right) \cdot \left(r \cdot r\right)\right) \cdot 0.375} - -4.5\right) \]
      fma-neg [=>] 66.0%	\[ \mathsf{fma}\left(2, {r}^{-2}, 3\right) - \color{blue}{\mathsf{fma}\left(\left(w \cdot w\right) \cdot \left(r \cdot r\right), 0.375, --4.5\right)} \]
      pow2 [=>] 66.0%	\[ \mathsf{fma}\left(2, {r}^{-2}, 3\right) - \mathsf{fma}\left(\color{blue}{{w}^{2}} \cdot \left(r \cdot r\right), 0.375, --4.5\right) \]
      pow2 [=>] 66.0%	\[ \mathsf{fma}\left(2, {r}^{-2}, 3\right) - \mathsf{fma}\left({w}^{2} \cdot \color{blue}{{r}^{2}}, 0.375, --4.5\right) \]
      pow-prod-down [=>] 99.9%	\[ \mathsf{fma}\left(2, {r}^{-2}, 3\right) - \mathsf{fma}\left(\color{blue}{{\left(w \cdot r\right)}^{2}}, 0.375, --4.5\right) \]
      *-commutative [=>] 99.9%	\[ \mathsf{fma}\left(2, {r}^{-2}, 3\right) - \mathsf{fma}\left({\color{blue}{\left(r \cdot w\right)}}^{2}, 0.375, --4.5\right) \]
      metadata-eval [=>] 99.9%	\[ \mathsf{fma}\left(2, {r}^{-2}, 3\right) - \mathsf{fma}\left({\left(r \cdot w\right)}^{2}, 0.375, \color{blue}{4.5}\right) \]

   6. Simplified 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(2, {r}^{-2}, 3\right) - \mathsf{fma}\left({\left(w \cdot r\right)}^{2}, 0.375, 4.5\right)} \]
      Step-by-step derivation

      [Start] 99.9%	\[ \mathsf{fma}\left(2, {r}^{-2}, 3\right) - \mathsf{fma}\left({\left(r \cdot w\right)}^{2}, 0.375, 4.5\right) \]
      *-commutative [=>] 99.9%	\[ \mathsf{fma}\left(2, {r}^{-2}, 3\right) - \mathsf{fma}\left({\color{blue}{\left(w \cdot r\right)}}^{2}, 0.375, 4.5\right) \]

3. Recombined 2 regimes into one program.

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;w \cdot w \leq 2 \cdot 10^{+298}:\\ \;\;\;\;\frac{2}{r \cdot r} + \left(-1.5 - \left(r \cdot \left(w \cdot \left(r \cdot w\right)\right)\right) \cdot \frac{0.375 + v \cdot -0.25}{1 - v}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(2, {r}^{-2}, 3\right) - \mathsf{fma}\left({\left(r \cdot w\right)}^{2}, 0.375, 4.5\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	99.1%
Cost	26564

\[\begin{array}{l} \mathbf{if}\;w \cdot w \leq 2 \cdot 10^{+298}:\\ \;\;\;\;\frac{2}{r \cdot r} + \left(-1.5 - \left(r \cdot \left(w \cdot \left(r \cdot w\right)\right)\right) \cdot \frac{0.375 + v \cdot -0.25}{1 - v}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(2, {r}^{-2}, 3\right) - \mathsf{fma}\left({\left(r \cdot w\right)}^{2}, 0.375, 4.5\right)\\ \end{array} \]

Alternative 2
Accuracy	99.5%
Cost	26944

\[\frac{2}{r \cdot r} + \left(-1.5 - {\left(\sqrt[3]{{\left(r \cdot w\right)}^{2} \cdot \frac{\mathsf{fma}\left(v, -0.25, 0.375\right)}{1 - v}}\right)}^{3}\right) \]

Alternative 3
Accuracy	98.3%
Cost	8580

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;\left(t_0 + 3\right) + \frac{\left(r \cdot \left(r \cdot \left(w \cdot w\right)\right)\right) \cdot \left(0.125 \cdot \left(2 \cdot v - 3\right)\right)}{1 - v} \leq 3:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot \left(w \cdot \left(r \cdot w\right)\right)\right) \cdot \frac{0.375 + v \cdot -0.25}{1 - v}\right)\\ \mathbf{else}:\\ \;\;\;\;-1.5 + 2 \cdot {r}^{-2}\\ \end{array} \]

Alternative 4
Accuracy	98.3%
Cost	3396

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;\left(t_0 + 3\right) + \frac{\left(r \cdot \left(r \cdot \left(w \cdot w\right)\right)\right) \cdot \left(0.125 \cdot \left(2 \cdot v - 3\right)\right)}{1 - v} \leq 4 \cdot 10^{+274}:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot \left(w \cdot \left(r \cdot w\right)\right)\right) \cdot \frac{0.375 + v \cdot -0.25}{1 - v}\right)\\ \mathbf{else}:\\ \;\;\;\;-1.5 + \frac{\frac{2}{r}}{r}\\ \end{array} \]

Alternative 5
Accuracy	96.1%
Cost	1353

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -8.6 \cdot 10^{+24} \lor \neg \left(v \leq 5.5 \cdot 10^{-22}\right):\\ \;\;\;\;t_0 + \left(-1.5 - r \cdot \left(w \cdot \left(\left(r \cdot w\right) \cdot 0.25\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 - r \cdot \left(0.375 \cdot \left(w \cdot \left(r \cdot w\right)\right)\right)\right)\\ \end{array} \]

Alternative 6
Accuracy	90.7%
Cost	1088

\[\frac{2}{r \cdot r} + \left(-1.5 - r \cdot \left(0.375 \cdot \left(w \cdot \left(r \cdot w\right)\right)\right)\right) \]

Alternative 7
Accuracy	71.9%
Cost	841

\[\begin{array}{l} \mathbf{if}\;r \leq -2.4 \cdot 10^{+53} \lor \neg \left(r \leq 6.5 \cdot 10^{-39}\right):\\ \;\;\;\;\left(r \cdot r\right) \cdot \left(-0.25 \cdot \left(w \cdot w\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{r \cdot r} + -1.5\\ \end{array} \]

Alternative 8
Accuracy	71.9%
Cost	840

\[\begin{array}{l} \mathbf{if}\;r \leq -7.2 \cdot 10^{+53}:\\ \;\;\;\;\left(\left(r \cdot r\right) \cdot \left(w \cdot w\right)\right) \cdot -0.375\\ \mathbf{elif}\;r \leq 4.3 \cdot 10^{-39}:\\ \;\;\;\;\frac{2}{r \cdot r} + -1.5\\ \mathbf{else}:\\ \;\;\;\;\left(r \cdot r\right) \cdot \left(-0.25 \cdot \left(w \cdot w\right)\right)\\ \end{array} \]

Alternative 9
Accuracy	56.4%
Cost	448

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

Alternative 10
Accuracy	43.7%
Cost	320

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

Reproduce

herbie shell --seed 2023256 
(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))