Rosa's TurbineBenchmark

Average Error: 12.6 → 0.8

Time: 20.9s

Precision: binary64

Cost: 8392

Math

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

↓

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r} + 3\\ t_1 := \frac{1 - v}{r}\\ \mathbf{if}\;r \leq -2 \cdot 10^{+197}:\\ \;\;\;\;\left(t_0 - \frac{w \cdot \left(\left(r \cdot w\right) \cdot \mathsf{fma}\left(0.125, v \cdot -2, 0.375\right)\right)}{t_1}\right) + -4.5\\ \mathbf{elif}\;r \leq 10^{+165}:\\ \;\;\;\;\left(t_0 - \frac{\mathsf{fma}\left(v, -0.25, 0.375\right)}{1 - v} \cdot \left(w \cdot \left(r \cdot \left(r \cdot w\right)\right)\right)\right) + -4.5\\ \mathbf{else}:\\ \;\;\;\;\left(t_0 - \frac{\mathsf{fma}\left(-0.25, v, 0.375\right)}{t_1 \cdot \frac{1}{w \cdot \left(r \cdot w\right)}}\right) + -4.5\\ \end{array} \]

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)) 3.0)) (t_1 (/ (- 1.0 v) r)))
   (if (<= r -2e+197)
     (+ (- t_0 (/ (* w (* (* r w) (fma 0.125 (* v -2.0) 0.375))) t_1)) -4.5)
     (if (<= r 1e+165)
       (+
        (- t_0 (* (/ (fma v -0.25 0.375) (- 1.0 v)) (* w (* r (* r w)))))
        -4.5)
       (+
        (- t_0 (/ (fma -0.25 v 0.375) (* t_1 (/ 1.0 (* w (* r w))))))
        -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)) + 3.0;
	double t_1 = (1.0 - v) / r;
	double tmp;
	if (r <= -2e+197) {
		tmp = (t_0 - ((w * ((r * w) * fma(0.125, (v * -2.0), 0.375))) / t_1)) + -4.5;
	} else if (r <= 1e+165) {
		tmp = (t_0 - ((fma(v, -0.25, 0.375) / (1.0 - v)) * (w * (r * (r * w))))) + -4.5;
	} else {
		tmp = (t_0 - (fma(-0.25, v, 0.375) / (t_1 * (1.0 / (w * (r * w)))))) + -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(Float64(2.0 / Float64(r * r)) + 3.0)
	t_1 = Float64(Float64(1.0 - v) / r)
	tmp = 0.0
	if (r <= -2e+197)
		tmp = Float64(Float64(t_0 - Float64(Float64(w * Float64(Float64(r * w) * fma(0.125, Float64(v * -2.0), 0.375))) / t_1)) + -4.5);
	elseif (r <= 1e+165)
		tmp = Float64(Float64(t_0 - Float64(Float64(fma(v, -0.25, 0.375) / Float64(1.0 - v)) * Float64(w * Float64(r * Float64(r * w))))) + -4.5);
	else
		tmp = Float64(Float64(t_0 - Float64(fma(-0.25, v, 0.375) / Float64(t_1 * Float64(1.0 / Float64(w * Float64(r * w)))))) + -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_] := Block[{t$95$0 = N[(N[(2.0 / N[(r * r), $MachinePrecision]), $MachinePrecision] + 3.0), $MachinePrecision]}, Block[{t$95$1 = N[(N[(1.0 - v), $MachinePrecision] / r), $MachinePrecision]}, If[LessEqual[r, -2e+197], N[(N[(t$95$0 - N[(N[(w * N[(N[(r * w), $MachinePrecision] * N[(0.125 * N[(v * -2.0), $MachinePrecision] + 0.375), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + -4.5), $MachinePrecision], If[LessEqual[r, 1e+165], N[(N[(t$95$0 - N[(N[(N[(v * -0.25 + 0.375), $MachinePrecision] / N[(1.0 - v), $MachinePrecision]), $MachinePrecision] * N[(w * N[(r * N[(r * w), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -4.5), $MachinePrecision], N[(N[(t$95$0 - N[(N[(-0.25 * v + 0.375), $MachinePrecision] / N[(t$95$1 * N[(1.0 / N[(w * N[(r * w), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -4.5), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if r < -1.9999999999999999e197

   1. Initial program 34.2

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

   2. Applied egg-rr 0.7

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

   3. Applied egg-rr 5.9

      \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \color{blue}{\frac{w \cdot \left(\left(w \cdot r\right) \cdot \mathsf{fma}\left(0.125, v \cdot -2, 0.375\right)\right)}{\frac{1 - v}{r}}}\right) - 4.5 \]

   if -1.9999999999999999e197 < r < 9.99999999999999899e164

   1. Initial program 9.1

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

   2. Taylor expanded in w around 0 11.9

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

   3. Simplified 0.5

      \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \color{blue}{\frac{\mathsf{fma}\left(v, -0.25, 0.375\right)}{1 - v} \cdot \left(w \cdot \left(\left(w \cdot r\right) \cdot r\right)\right)}\right) - 4.5 \]
      Proof
      (*.f64 (/.f64 (fma.f64 v -1/4 3/8) (-.f64 1 v)) (*.f64 w (*.f64 (*.f64 w r) r))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 v -1/4) 3/8)) (-.f64 1 v)) (*.f64 w (*.f64 (*.f64 w r) r))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 -1/4 v)) 3/8) (-.f64 1 v)) (*.f64 w (*.f64 (*.f64 w r) r))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (+.f64 (*.f64 (Rewrite<= metadata-eval (*.f64 1/8 -2)) v) 3/8) (-.f64 1 v)) (*.f64 w (*.f64 (*.f64 w r) r))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (+.f64 (Rewrite<= associate-*r*_binary64 (*.f64 1/8 (*.f64 -2 v))) 3/8) (-.f64 1 v)) (*.f64 w (*.f64 (*.f64 w r) r))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (+.f64 (*.f64 1/8 (*.f64 (Rewrite<= metadata-eval (neg.f64 2)) v)) 3/8) (-.f64 1 v)) (*.f64 w (*.f64 (*.f64 w r) r))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (+.f64 (*.f64 1/8 (Rewrite<= distribute-lft-neg-in_binary64 (neg.f64 (*.f64 2 v)))) 3/8) (-.f64 1 v)) (*.f64 w (*.f64 (*.f64 w r) r))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (+.f64 (*.f64 1/8 (neg.f64 (*.f64 2 v))) (Rewrite<= metadata-eval (*.f64 1/8 3))) (-.f64 1 v)) (*.f64 w (*.f64 (*.f64 w r) r))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (Rewrite<= distribute-lft-in_binary64 (*.f64 1/8 (+.f64 (neg.f64 (*.f64 2 v)) 3))) (-.f64 1 v)) (*.f64 w (*.f64 (*.f64 w r) r))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (*.f64 1/8 (Rewrite<= +-commutative_binary64 (+.f64 3 (neg.f64 (*.f64 2 v))))) (-.f64 1 v)) (*.f64 w (*.f64 (*.f64 w r) r))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (*.f64 1/8 (Rewrite<= sub-neg_binary64 (-.f64 3 (*.f64 2 v)))) (-.f64 1 v)) (*.f64 w (*.f64 (*.f64 w r) r))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (-.f64 1 v)) (*.f64 w (Rewrite<= associate-*r*_binary64 (*.f64 w (*.f64 r r))))): 62 points increase in error, 23 points decrease in error
      (*.f64 (/.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (-.f64 1 v)) (*.f64 w (*.f64 w (Rewrite<= unpow2_binary64 (pow.f64 r 2))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (-.f64 1 v)) (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 w w) (pow.f64 r 2)))): 30 points increase in error, 33 points decrease in error
      (*.f64 (/.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (-.f64 1 v)) (*.f64 (Rewrite<= unpow2_binary64 (pow.f64 w 2)) (pow.f64 r 2))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-/r/_binary64 (/.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (/.f64 (-.f64 1 v) (*.f64 (pow.f64 w 2) (pow.f64 r 2))))): 13 points increase in error, 12 points decrease in error
      (Rewrite<= associate-*r/_binary64 (*.f64 1/8 (/.f64 (-.f64 3 (*.f64 2 v)) (/.f64 (-.f64 1 v) (*.f64 (pow.f64 w 2) (pow.f64 r 2)))))): 0 points increase in error, 0 points decrease in error
      (*.f64 1/8 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (-.f64 3 (*.f64 2 v)) (*.f64 (pow.f64 w 2) (pow.f64 r 2))) (-.f64 1 v)))): 21 points increase in error, 14 points decrease in error

   if 9.99999999999999899e164 < r

   1. Initial program 29.8

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

   2. Applied egg-rr 1.3

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

   3. Applied egg-rr 1.3

      \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\color{blue}{\frac{\mathsf{fma}\left(0.125, v \cdot -2, 0.375\right)}{\frac{1}{w \cdot \left(w \cdot r\right)}}}}{1} \cdot \frac{r}{1 - v}\right) - 4.5 \]

   4. Applied egg-rr 0.4

      \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \color{blue}{\frac{\mathsf{fma}\left(-0.25, v, 0.375\right)}{\frac{1 - v}{r} \cdot \frac{1}{w \cdot \left(w \cdot r\right)}}}\right) - 4.5 \]
3. Recombined 3 regimes into one program.

4. Final simplification 0.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;r \leq -2 \cdot 10^{+197}:\\ \;\;\;\;\left(\left(\frac{2}{r \cdot r} + 3\right) - \frac{w \cdot \left(\left(r \cdot w\right) \cdot \mathsf{fma}\left(0.125, v \cdot -2, 0.375\right)\right)}{\frac{1 - v}{r}}\right) + -4.5\\ \mathbf{elif}\;r \leq 10^{+165}:\\ \;\;\;\;\left(\left(\frac{2}{r \cdot r} + 3\right) - \frac{\mathsf{fma}\left(v, -0.25, 0.375\right)}{1 - v} \cdot \left(w \cdot \left(r \cdot \left(r \cdot w\right)\right)\right)\right) + -4.5\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\frac{2}{r \cdot r} + 3\right) - \frac{\mathsf{fma}\left(-0.25, v, 0.375\right)}{\frac{1 - v}{r} \cdot \frac{1}{w \cdot \left(r \cdot w\right)}}\right) + -4.5\\ \end{array} \]

Alternatives

Alternative 1
Error	2.8
Cost	14144

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

Alternative 2
Error	1.4
Cost	9540

\[\begin{array}{l} t_0 := 0.125 \cdot \left(2 \cdot v + -3\right)\\ t_1 := \frac{2}{r \cdot r}\\ t_2 := t_1 + 3\\ \mathbf{if}\;t_2 + \frac{\left(r \cdot \left(r \cdot \left(w \cdot w\right)\right)\right) \cdot t_0}{1 - v} \leq -\infty:\\ \;\;\;\;t_1 - \mathsf{fma}\left(v, -0.25, 0.375\right) \cdot \frac{w}{\frac{\frac{1 - v}{r}}{r \cdot w}}\\ \mathbf{else}:\\ \;\;\;\;\left(t_2 + \frac{\left(r \cdot \left(w \cdot \left(r \cdot w\right)\right)\right) \cdot t_0}{1 - v}\right) + -4.5\\ \end{array} \]

Alternative 3
Error	0.5
Cost	8392

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r} + 3\\ t_1 := \left(t_0 - \frac{\mathsf{fma}\left(-0.25, v, 0.375\right)}{\frac{1 - v}{r} \cdot \frac{1}{w \cdot \left(r \cdot w\right)}}\right) + -4.5\\ \mathbf{if}\;r \leq -1 \cdot 10^{+200}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;r \leq 10^{+165}:\\ \;\;\;\;\left(t_0 - \frac{\mathsf{fma}\left(v, -0.25, 0.375\right)}{1 - v} \cdot \left(w \cdot \left(r \cdot \left(r \cdot w\right)\right)\right)\right) + -4.5\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	2.1
Cost	7624

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ t_1 := r \cdot \left(w \cdot \left(r \cdot w\right)\right)\\ \mathbf{if}\;v \leq -1.2394302431365556 \cdot 10^{+57}:\\ \;\;\;\;t_0 - \left(1.5 + {\left(r \cdot w\right)}^{2} \cdot 0.25\right)\\ \mathbf{elif}\;v \leq 24459388.960660953:\\ \;\;\;\;\left(\left(t_0 + 3\right) + \frac{t_1 \cdot \left(0.125 \cdot \left(2 \cdot v + -3\right)\right)}{1 - v}\right) + -4.5\\ \mathbf{else}:\\ \;\;\;\;t_0 - \mathsf{fma}\left(t_1, 0.25, 1.5\right)\\ \end{array} \]

Alternative 5
Error	1.6
Cost	7560

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ t_1 := t_0 - \left(1.5 + {\left(r \cdot w\right)}^{2} \cdot 0.25\right)\\ \mathbf{if}\;v \leq -1.2394302431365556 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;v \leq 24459388.960660953:\\ \;\;\;\;\left(\left(t_0 + 3\right) + \frac{\left(r \cdot \left(w \cdot \left(r \cdot w\right)\right)\right) \cdot \left(0.125 \cdot \left(2 \cdot v + -3\right)\right)}{1 - v}\right) + -4.5\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	3.2
Cost	3652

\[\begin{array}{l} t_0 := w \cdot \left(r \cdot w\right)\\ t_1 := 0.125 \cdot \left(2 \cdot v + -3\right)\\ t_2 := \frac{2}{r \cdot r}\\ t_3 := t_2 + 3\\ \mathbf{if}\;t_3 + \frac{\left(r \cdot \left(r \cdot \left(w \cdot w\right)\right)\right) \cdot t_1}{1 - v} \leq -\infty:\\ \;\;\;\;t_2 + r \cdot \left(-0.25 \cdot t_0\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t_3 + \frac{\left(r \cdot t_0\right) \cdot t_1}{1 - v}\right) + -4.5\\ \end{array} \]

Alternative 7
Error	16.1
Cost	2260

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ t_1 := t_0 + r \cdot \left(-0.25 \cdot \left(w \cdot \left(r \cdot w\right)\right)\right)\\ \mathbf{if}\;w \cdot w \leq 5 \cdot 10^{-321}:\\ \;\;\;\;\frac{\frac{2}{r}}{r} + -1.5\\ \mathbf{elif}\;w \cdot w \leq 2 \cdot 10^{-182}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;w \cdot w \leq 10^{-140}:\\ \;\;\;\;t_0 + -1.5\\ \mathbf{elif}\;w \cdot w \leq 5 \cdot 10^{-50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;w \cdot w \leq 10^{-31}:\\ \;\;\;\;r \cdot \left(r \cdot \left(\left(w \cdot w\right) \cdot -0.375\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + -0.25 \cdot \left(w \cdot \left(\left(r \cdot r\right) \cdot w\right)\right)\\ \end{array} \]

Alternative 8
Error	16.7
Cost	2128

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ t_1 := w \cdot \left(r \cdot w\right)\\ t_2 := t_0 + r \cdot \left(-0.25 \cdot t_1\right)\\ \mathbf{if}\;w \cdot w \leq 5 \cdot 10^{-321}:\\ \;\;\;\;\frac{\frac{2}{r}}{r} + -1.5\\ \mathbf{elif}\;w \cdot w \leq 2 \cdot 10^{-182}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;w \cdot w \leq 10^{-140}:\\ \;\;\;\;t_0 + -1.5\\ \mathbf{elif}\;w \cdot w \leq 1.2 \cdot 10^{-63}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{r} \cdot \frac{1}{r} + r \cdot \left(t_1 \cdot -0.375\right)\\ \end{array} \]

Alternative 9
Error	16.7
Cost	2000

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ t_1 := w \cdot \left(r \cdot w\right)\\ t_2 := t_0 + r \cdot \left(-0.25 \cdot t_1\right)\\ \mathbf{if}\;w \cdot w \leq 5 \cdot 10^{-321}:\\ \;\;\;\;\frac{\frac{2}{r}}{r} + -1.5\\ \mathbf{elif}\;w \cdot w \leq 2 \cdot 10^{-182}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;w \cdot w \leq 10^{-140}:\\ \;\;\;\;t_0 + -1.5\\ \mathbf{elif}\;w \cdot w \leq 1.2 \cdot 10^{-63}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_0 + r \cdot \left(t_1 \cdot -0.375\right)\\ \end{array} \]

Alternative 10
Error	7.0
Cost	1864

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r} + 3\\ \mathbf{if}\;v \leq -3.107403765794593 \cdot 10^{+23}:\\ \;\;\;\;\left(t_0 - \left(r \cdot \left(w \cdot w\right)\right) \cdot \left(r \cdot 0.25\right)\right) + -4.5\\ \mathbf{elif}\;v \leq 0.000386:\\ \;\;\;\;\left(t_0 - \left(w \cdot \left(r \cdot \left(r \cdot w\right)\right)\right) \cdot \left(0.375 + v \cdot 0.125\right)\right) + -4.5\\ \mathbf{else}:\\ \;\;\;\;\left(t_0 + \frac{r}{1 - v} \cdot \left(v \cdot \left(0.25 \cdot \left(w \cdot \left(r \cdot w\right)\right)\right)\right)\right) + -4.5\\ \end{array} \]

Alternative 11
Error	6.8
Cost	1736

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r} + 3\\ t_1 := \left(t_0 - \left(r \cdot \left(w \cdot w\right)\right) \cdot \left(r \cdot 0.25\right)\right) + -4.5\\ \mathbf{if}\;v \leq -3.107403765794593 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;v \leq 0.000386:\\ \;\;\;\;\left(t_0 - \left(w \cdot \left(r \cdot \left(r \cdot w\right)\right)\right) \cdot \left(0.375 + v \cdot 0.125\right)\right) + -4.5\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	14.3
Cost	1616

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ t_1 := t_0 + r \cdot \left(-0.25 \cdot \left(w \cdot \left(r \cdot w\right)\right)\right)\\ t_2 := t_0 - \left(1.5 + w \cdot \left(\left(r \cdot r\right) \cdot \left(0.375 \cdot w\right)\right)\right)\\ \mathbf{if}\;w \leq -6.270601128539708 \cdot 10^{-98}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;w \leq -7.0243390508139966 \cdot 10^{-158}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;w \leq 1.4423605717940024 \cdot 10^{-138}:\\ \;\;\;\;\frac{\frac{2}{r}}{r} + -1.5\\ \mathbf{elif}\;w \leq 2.263748717364732 \cdot 10^{-98}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 13
Error	5.8
Cost	1608

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ t_1 := \left(\left(t_0 + 3\right) - \left(r \cdot \left(w \cdot w\right)\right) \cdot \left(r \cdot 0.25\right)\right) + -4.5\\ \mathbf{if}\;v \leq -3.107403765794593 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;v \leq 0.000386:\\ \;\;\;\;t_0 + \left(-1.5 - \left(r \cdot \left(w \cdot \left(r \cdot w\right)\right)\right) \cdot \left(0.375 + v \cdot 0.125\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	10.9
Cost	1480

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r}\\ t_1 := \left(\left(t_0 + 3\right) - \left(r \cdot \left(w \cdot w\right)\right) \cdot \left(r \cdot 0.25\right)\right) + -4.5\\ \mathbf{if}\;v \leq -0.04619609166797343:\\ \;\;\;\;t_1\\ \mathbf{elif}\;v \leq 7.203839455927979 \cdot 10^{-21}:\\ \;\;\;\;t_0 - \left(1.5 + w \cdot \left(\left(r \cdot r\right) \cdot \left(0.375 \cdot w\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Error	15.2
Cost	1224

\[\begin{array}{l} t_0 := \frac{2}{r \cdot r} + -0.25 \cdot \left(w \cdot \left(\left(r \cdot r\right) \cdot w\right)\right)\\ \mathbf{if}\;w \leq -9.8 \cdot 10^{-70}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;w \leq 6.2 \cdot 10^{-54}:\\ \;\;\;\;\frac{\frac{2}{r}}{r} + -1.5\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 16
Error	20.8
Cost	840

\[\begin{array}{l} t_0 := \frac{\frac{2}{r}}{r} + -1.5\\ \mathbf{if}\;w \leq -1750000000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;w \leq -7.8 \cdot 10^{-33}:\\ \;\;\;\;r \cdot \left(r \cdot \left(\left(w \cdot w\right) \cdot -0.375\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 17
Error	21.9
Cost	840

\[\begin{array}{l} t_0 := \frac{\frac{2}{r}}{r} + -1.5\\ \mathbf{if}\;v \leq -3.515526351100871 \cdot 10^{-233}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;v \leq 1.9979077256551003 \cdot 10^{-296}:\\ \;\;\;\;\left(r \cdot w\right) \cdot \left(w \cdot \left(r \cdot -0.375\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 18
Error	20.4
Cost	448

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

Alternative 19
Error	38.1
Cost	320

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

Reproduce

herbie shell --seed 2022295 
(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))