Rosa's TurbineBenchmark

Average Error: 12.7 → 0.2

Time: 19.4s

Precision: binary64

Cost: 14208

Math

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

↓

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

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
 (+
  (* (pow r -2.0) 2.0)
  (- -1.5 (* (/ w (/ (/ (- 1.0 v) (fma v -0.25 0.375)) r)) (* r w)))))

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) {
	return (pow(r, -2.0) * 2.0) + (-1.5 - ((w / (((1.0 - v) / fma(v, -0.25, 0.375)) / r)) * (r * w)));
}

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)
	return Float64(Float64((r ^ -2.0) * 2.0) + Float64(-1.5 - Float64(Float64(w / Float64(Float64(Float64(1.0 - v) / fma(v, -0.25, 0.375)) / r)) * Float64(r * w))))
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_] := N[(N[(N[Power[r, -2.0], $MachinePrecision] * 2.0), $MachinePrecision] + N[(-1.5 - N[(N[(w / N[(N[(N[(1.0 - v), $MachinePrecision] / N[(v * -0.25 + 0.375), $MachinePrecision]), $MachinePrecision] / r), $MachinePrecision]), $MachinePrecision] * N[(r * w), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 12.7

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

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
   (+.f64 (/.f64 2 (*.f64 r r)) (-.f64 -3/2 (*.f64 (/.f64 w (/.f64 (/.f64 (-.f64 1 v) (fma.f64 v -1/4 3/8)) r)) (*.f64 r w)))): 0 points increase in error, 0 points decrease in error
   (+.f64 (/.f64 2 (*.f64 r r)) (-.f64 (Rewrite<= metadata-eval (+.f64 -9/2 3)) (*.f64 (/.f64 w (/.f64 (/.f64 (-.f64 1 v) (fma.f64 v -1/4 3/8)) r)) (*.f64 r w)))): 0 points increase in error, 0 points decrease in error
   (+.f64 (/.f64 2 (*.f64 r r)) (-.f64 (+.f64 (Rewrite<= metadata-eval (neg.f64 9/2)) 3) (*.f64 (/.f64 w (/.f64 (/.f64 (-.f64 1 v) (fma.f64 v -1/4 3/8)) r)) (*.f64 r w)))): 0 points increase in error, 0 points decrease in error
   (+.f64 (/.f64 2 (*.f64 r r)) (-.f64 (+.f64 (neg.f64 9/2) 3) (*.f64 (/.f64 w (/.f64 (/.f64 (-.f64 1 v) (fma.f64 v (Rewrite<= metadata-eval (*.f64 1/8 -2)) 3/8)) r)) (*.f64 r w)))): 0 points increase in error, 0 points decrease in error
   (+.f64 (/.f64 2 (*.f64 r r)) (-.f64 (+.f64 (neg.f64 9/2) 3) (*.f64 (/.f64 w (/.f64 (/.f64 (-.f64 1 v) (fma.f64 v (*.f64 1/8 (Rewrite<= metadata-eval (neg.f64 2))) 3/8)) r)) (*.f64 r w)))): 19 points increase in error, 0 points decrease in error
   (+.f64 (/.f64 2 (*.f64 r r)) (-.f64 (+.f64 (neg.f64 9/2) 3) (*.f64 (/.f64 w (/.f64 (/.f64 (-.f64 1 v) (fma.f64 v (*.f64 1/8 (neg.f64 2)) (Rewrite<= metadata-eval (*.f64 1/8 3)))) r)) (*.f64 r w)))): 0 points increase in error, 19 points decrease in error
   (+.f64 (/.f64 2 (*.f64 r r)) (-.f64 (+.f64 (neg.f64 9/2) 3) (*.f64 (/.f64 w (/.f64 (/.f64 (-.f64 1 v) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 v (*.f64 1/8 (neg.f64 2))) (*.f64 1/8 3)))) r)) (*.f64 r w)))): 19 points increase in error, 0 points decrease in error
   (+.f64 (/.f64 2 (*.f64 r r)) (-.f64 (+.f64 (neg.f64 9/2) 3) (*.f64 (/.f64 w (/.f64 (/.f64 (-.f64 1 v) (+.f64 (Rewrite=> *-commutative_binary64 (*.f64 (*.f64 1/8 (neg.f64 2)) v)) (*.f64 1/8 3))) r)) (*.f64 r w)))): 0 points increase in error, 19 points decrease in error
   (+.f64 (/.f64 2 (*.f64 r r)) (-.f64 (+.f64 (neg.f64 9/2) 3) (*.f64 (/.f64 w (/.f64 (/.f64 (-.f64 1 v) (+.f64 (Rewrite<= associate-*r*_binary64 (*.f64 1/8 (*.f64 (neg.f64 2) v))) (*.f64 1/8 3))) r)) (*.f64 r w)))): 16 points increase in error, 0 points decrease in error
   (+.f64 (/.f64 2 (*.f64 r r)) (-.f64 (+.f64 (neg.f64 9/2) 3) (*.f64 (/.f64 w (/.f64 (/.f64 (-.f64 1 v) (+.f64 (*.f64 1/8 (Rewrite<= distribute-lft-neg-in_binary64 (neg.f64 (*.f64 2 v)))) (*.f64 1/8 3))) r)) (*.f64 r w)))): 16 points increase in error, 16 points decrease in error
   (+.f64 (/.f64 2 (*.f64 r r)) (-.f64 (+.f64 (neg.f64 9/2) 3) (*.f64 (/.f64 w (/.f64 (/.f64 (-.f64 1 v) (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 1/8 3) (*.f64 1/8 (neg.f64 (*.f64 2 v)))))) r)) (*.f64 r w)))): 0 points increase in error, 32 points decrease in error
   (+.f64 (/.f64 2 (*.f64 r r)) (-.f64 (+.f64 (neg.f64 9/2) 3) (*.f64 (/.f64 w (/.f64 (/.f64 (-.f64 1 v) (Rewrite<= distribute-lft-in_binary64 (*.f64 1/8 (+.f64 3 (neg.f64 (*.f64 2 v)))))) r)) (*.f64 r w)))): 0 points increase in error, 0 points decrease in error
   (+.f64 (/.f64 2 (*.f64 r r)) (-.f64 (+.f64 (neg.f64 9/2) 3) (*.f64 (/.f64 w (/.f64 (/.f64 (-.f64 1 v) (*.f64 1/8 (Rewrite<= sub-neg_binary64 (-.f64 3 (*.f64 2 v))))) r)) (*.f64 r w)))): 0 points increase in error, 0 points decrease in error
   (+.f64 (/.f64 2 (*.f64 r r)) (-.f64 (+.f64 (neg.f64 9/2) 3) (*.f64 (/.f64 w (Rewrite<= associate-/r*_binary64 (/.f64 (-.f64 1 v) (*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) r)))) (*.f64 r w)))): 31 points increase in error, 0 points decrease in error
   (+.f64 (/.f64 2 (*.f64 r r)) (-.f64 (+.f64 (neg.f64 9/2) 3) (*.f64 (/.f64 w (/.f64 (-.f64 1 v) (*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) r))) (Rewrite<= *-commutative_binary64 (*.f64 w r))))): 1 points increase in error, 30 points decrease in error
   (+.f64 (/.f64 2 (*.f64 r r)) (-.f64 (+.f64 (neg.f64 9/2) 3) (Rewrite<= associate-/r/_binary64 (/.f64 w (/.f64 (/.f64 (-.f64 1 v) (*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) r)) (*.f64 w r)))))): 0 points increase in error, 16 points decrease in error
   (+.f64 (/.f64 2 (*.f64 r r)) (-.f64 (+.f64 (neg.f64 9/2) 3) (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 w (*.f64 w r)) (/.f64 (-.f64 1 v) (*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) r)))))): 0 points increase in error, 0 points decrease in error
   (+.f64 (/.f64 2 (*.f64 r r)) (-.f64 (+.f64 (neg.f64 9/2) 3) (/.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 w w) r)) (/.f64 (-.f64 1 v) (*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) r))))): 14 points increase in error, 0 points decrease in error
   (+.f64 (/.f64 2 (*.f64 r r)) (-.f64 (+.f64 (neg.f64 9/2) 3) (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (*.f64 (*.f64 w w) r) (*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) r)) (-.f64 1 v))))): 0 points increase in error, 14 points decrease in error
   (+.f64 (/.f64 2 (*.f64 r r)) (-.f64 (+.f64 (neg.f64 9/2) 3) (/.f64 (Rewrite=> *-commutative_binary64 (*.f64 (*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) r) (*.f64 (*.f64 w w) r))) (-.f64 1 v)))): 29 points increase in error, 0 points decrease in error
   (+.f64 (/.f64 2 (*.f64 r r)) (-.f64 (+.f64 (neg.f64 9/2) 3) (/.f64 (Rewrite<= associate-*r*_binary64 (*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (*.f64 r (*.f64 (*.f64 w w) r)))) (-.f64 1 v)))): 2 points increase in error, 29 points decrease in error
   (+.f64 (/.f64 2 (*.f64 r r)) (-.f64 (+.f64 (neg.f64 9/2) 3) (/.f64 (*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (Rewrite<= *-commutative_binary64 (*.f64 (*.f64 (*.f64 w w) r) r))) (-.f64 1 v)))): 0 points increase in error, 16 points decrease in error
   (+.f64 (/.f64 2 (*.f64 r r)) (Rewrite=> sub-neg_binary64 (+.f64 (+.f64 (neg.f64 9/2) 3) (neg.f64 (/.f64 (*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (*.f64 (*.f64 (*.f64 w w) r) r)) (-.f64 1 v)))))): 0 points increase in error, 0 points decrease in error
   (Rewrite=> associate-+r+_binary64 (+.f64 (+.f64 (/.f64 2 (*.f64 r r)) (+.f64 (neg.f64 9/2) 3)) (neg.f64 (/.f64 (*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (*.f64 (*.f64 (*.f64 w w) r) r)) (-.f64 1 v))))): 0 points increase in error, 0 points decrease in error
   (+.f64 (Rewrite=> +-commutative_binary64 (+.f64 (+.f64 (neg.f64 9/2) 3) (/.f64 2 (*.f64 r r)))) (neg.f64 (/.f64 (*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (*.f64 (*.f64 (*.f64 w w) r) r)) (-.f64 1 v)))): 14 points increase in error, 0 points decrease in error
   (+.f64 (Rewrite<= associate-+r+_binary64 (+.f64 (neg.f64 9/2) (+.f64 3 (/.f64 2 (*.f64 r r))))) (neg.f64 (/.f64 (*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (*.f64 (*.f64 (*.f64 w w) r) r)) (-.f64 1 v)))): 3 points increase in error, 1 points decrease in error
   (+.f64 (Rewrite<= +-commutative_binary64 (+.f64 (+.f64 3 (/.f64 2 (*.f64 r r))) (neg.f64 9/2))) (neg.f64 (/.f64 (*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (*.f64 (*.f64 (*.f64 w w) r) r)) (-.f64 1 v)))): 0 points increase in error, 16 points decrease in error
   (+.f64 (Rewrite<= sub-neg_binary64 (-.f64 (+.f64 3 (/.f64 2 (*.f64 r r))) 9/2)) (neg.f64 (/.f64 (*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (*.f64 (*.f64 (*.f64 w w) r) r)) (-.f64 1 v)))): 0 points increase in error, 0 points decrease in error
   (Rewrite<= +-commutative_binary64 (+.f64 (neg.f64 (/.f64 (*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (*.f64 (*.f64 (*.f64 w w) r) r)) (-.f64 1 v))) (-.f64 (+.f64 3 (/.f64 2 (*.f64 r r))) 9/2))): 7 points increase in error, 0 points decrease in error
   (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 (neg.f64 (/.f64 (*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (*.f64 (*.f64 (*.f64 w w) r) r)) (-.f64 1 v))) (+.f64 3 (/.f64 2 (*.f64 r r)))) 9/2)): 0 points increase in error, 7 points decrease in error
   (-.f64 (Rewrite<= +-commutative_binary64 (+.f64 (+.f64 3 (/.f64 2 (*.f64 r r))) (neg.f64 (/.f64 (*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (*.f64 (*.f64 (*.f64 w w) r) r)) (-.f64 1 v))))) 9/2): 7 points increase in error, 0 points decrease in error
   (-.f64 (Rewrite<= sub-neg_binary64 (-.f64 (+.f64 3 (/.f64 2 (*.f64 r r))) (/.f64 (*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (*.f64 (*.f64 (*.f64 w w) r) r)) (-.f64 1 v)))) 9/2): 0 points increase in error, 7 points decrease in error

3. Applied egg-rr 0.2

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

4. Final simplification 0.2

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

Alternatives

Alternative 1
Error	0.3
Cost	7872

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

Alternative 2
Error	0.5
Cost	1864

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -1.65:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{4}{r} + \frac{2}{r \cdot v}}\right)\\ \mathbf{elif}\;v \leq 1:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{2.6666666666666665 \cdot \frac{1}{r} + -0.8888888888888888 \cdot \frac{v}{r}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 - \frac{r \cdot w}{\frac{4}{r \cdot w}}\right)\\ \end{array} \]

Alternative 3
Error	0.3
Cost	1864

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -1.04 \cdot 10^{+15}:\\ \;\;\;\;t_0 + \left(-1.5 + \left(r \cdot w\right) \cdot \left(r \cdot \left(w \cdot -0.25\right)\right)\right)\\ \mathbf{elif}\;v \leq 230000000000:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{1 - v}{r \cdot \left(0.375 + v \cdot -0.25\right)}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 - \frac{r \cdot w}{\frac{4}{r \cdot w}}\right)\\ \end{array} \]

Alternative 4
Error	0.4
Cost	1856

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

Alternative 5
Error	0.6
Cost	1736

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -1.5:\\ \;\;\;\;t_0 + \left(-1.5 + \left(r \cdot w\right) \cdot \left(r \cdot \left(w \cdot -0.25\right)\right)\right)\\ \mathbf{elif}\;v \leq 1:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{-0.8888888888888888 \cdot \frac{v}{r} + \frac{2.6666666666666665}{r}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 - \frac{r \cdot w}{\frac{4}{r \cdot w}}\right)\\ \end{array} \]

Alternative 6
Error	0.5
Cost	1736

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -1.6:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{4}{r} + \frac{2}{r \cdot v}}\right)\\ \mathbf{elif}\;v \leq 1:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{-0.8888888888888888 \cdot \frac{v}{r} + \frac{2.6666666666666665}{r}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 - \frac{r \cdot w}{\frac{4}{r \cdot w}}\right)\\ \end{array} \]

Alternative 7
Error	0.6
Cost	1608

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -1.5:\\ \;\;\;\;t_0 + \left(-1.5 + \left(r \cdot w\right) \cdot \left(r \cdot \left(w \cdot -0.25\right)\right)\right)\\ \mathbf{elif}\;v \leq 1:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{r \cdot w}{2.6666666666666665 + v \cdot -0.8888888888888888}\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 - \frac{r \cdot w}{\frac{4}{r \cdot w}}\right)\\ \end{array} \]

Alternative 8
Error	2.8
Cost	1353

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -7.8 \lor \neg \left(v \leq 15\right):\\ \;\;\;\;t_0 + \left(-1.5 - w \cdot \left(r \cdot \frac{r \cdot w}{4}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 + \left(\left(r \cdot w\right) \cdot \left(r \cdot w\right)\right) \cdot -0.375\right)\\ \end{array} \]

Alternative 9
Error	2.7
Cost	1353

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -2.1 \lor \neg \left(v \leq 66\right):\\ \;\;\;\;t_0 + \left(-1.5 - w \cdot \left(r \cdot \frac{r \cdot w}{4}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \left(0.375 \cdot \left(r \cdot w\right)\right)\right)\\ \end{array} \]

Alternative 10
Error	0.7
Cost	1353

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -1.2 \lor \neg \left(v \leq 1\right):\\ \;\;\;\;t_0 + \left(-1.5 + \left(r \cdot w\right) \cdot \left(r \cdot \left(w \cdot -0.25\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \left(0.375 \cdot \left(r \cdot w\right)\right)\right)\\ \end{array} \]

Alternative 11
Error	0.7
Cost	1353

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -1.15 \lor \neg \left(v \leq 1\right):\\ \;\;\;\;t_0 + \left(-1.5 + \left(r \cdot w\right) \cdot \left(r \cdot \left(w \cdot -0.25\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \left(w \cdot \left(r \cdot 0.375\right)\right)\right)\\ \end{array} \]

Alternative 12
Error	0.7
Cost	1352

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -1.2:\\ \;\;\;\;t_0 + \left(-1.5 + \left(r \cdot w\right) \cdot \left(r \cdot \left(w \cdot -0.25\right)\right)\right)\\ \mathbf{elif}\;v \leq 1:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot w\right) \cdot \left(w \cdot \left(r \cdot 0.375\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 - \frac{r \cdot w}{\frac{4}{r \cdot w}}\right)\\ \end{array} \]

Alternative 13
Error	0.7
Cost	1352

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ \mathbf{if}\;v \leq -1.7:\\ \;\;\;\;t_0 + \left(-1.5 + \left(r \cdot w\right) \cdot \left(r \cdot \left(w \cdot -0.25\right)\right)\right)\\ \mathbf{elif}\;v \leq 0.82:\\ \;\;\;\;\frac{\frac{2}{r}}{r} + \left(-1.5 - \left(r \cdot w\right) \cdot \frac{w}{\frac{2.6666666666666665}{r}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(-1.5 - \frac{r \cdot w}{\frac{4}{r \cdot w}}\right)\\ \end{array} \]

Alternative 14
Error	10.6
Cost	1088

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

Alternative 15
Error	9.1
Cost	1088

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

Alternative 16
Error	22.1
Cost	840

\[\begin{array}{l} \mathbf{if}\;w \leq 4.4 \cdot 10^{+18}:\\ \;\;\;\;-1.5 + \frac{2}{r \cdot r}\\ \mathbf{elif}\;w \leq 6.2 \cdot 10^{+103}:\\ \;\;\;\;\left(r \cdot r\right) \cdot \left(-0.375 \cdot \left(w \cdot w\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{r} \cdot \frac{2}{r}\\ \end{array} \]

Alternative 17
Error	21.3
Cost	448

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

Alternative 18
Error	38.3
Cost	320

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

Reproduce

herbie shell --seed 2022343 
(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))