Average Error: 12.6 → 0.6

Time: 16.3s

Precision: binary64

Cost: 21312

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

↓

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

\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

↓

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

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

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 ((2.0 / (r * r)) + -1.5) - ((0.375 + (v * -0.25)) * (((r * w) / (cbrt(1.0 - v) * cbrt(1.0 - v))) * (r / (cbrt(1.0 - v) / w))));
}

Error

The X axis uses an exponential scale — Bits error versus `v`

Try it out

In
Out

Enter valid numbers for all inputs

Alternatives

Alternative 1
Error	13.1
Cost	40768

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

Alternative 2
Error	1.2
Cost	40768

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

Alternative 3
Error	36.0
Cost	34176

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

Alternative 4
Error	26.4
Cost	34112

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

Alternative 5
Error	17.0
Cost	34112

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

Alternative 6
Error	43.1
Cost	27520

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

Alternative 7
Error	8.9
Cost	23104

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

Alternative 8
Error	8.9
Cost	22336

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

Alternative 9
Error	8.9
Cost	22208

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

Alternative 10
Error	4.1
Cost	22208

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

Alternative 11
Error	4.2
Cost	21568

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

Alternative 12
Error	2.9
Cost	21568

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

Alternative 13
Error	2.9
Cost	21312

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

Alternative 14
Error	8.9
Cost	21056

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

Alternative 15
Error	8.5
Cost	21056

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

Alternative 16
Error	15.3
Cost	21056

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

Alternative 17
Error	2.9
Cost	21056

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

Alternative 18
Error	3.3
Cost	21056

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

Alternative 19
Error	8.7
Cost	15552

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

Alternative 20
Error	36.5
Cost	15168

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

Alternative 21
Error	14.6
Cost	15168

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

Alternative 22
Error	36.5
Cost	15040

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

Alternative 23
Error	2.6
Cost	14784

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

Alternative 24
Error	3.9
Cost	14784

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

Alternative 25
Error	36.3
Cost	14656

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

Alternative 26
Error	28.3
Cost	14656

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

Alternative 27
Error	16.4
Cost	14656

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

Alternative 28
Error	22.1
Cost	14656

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

Alternative 29
Error	32.0
Cost	14656

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

Alternative 30
Error	35.0
Cost	14528

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

Alternative 31
Error	34.2
Cost	14528

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

Alternative 32
Error	4.0
Cost	14528

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

Alternative 33
Error	2.7
Cost	14528

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

Alternative 34
Error	16.5
Cost	14464

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

Alternative 35
Error	41.2
Cost	14464

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

Alternative 36
Error	38.3
Cost	14464

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

Alternative 37
Error	23.3
Cost	14464

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

Alternative 38
Error	36.5
Cost	14464

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

Alternative 39
Error	39.0
Cost	14464

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

Alternative 40
Error	36.6
Cost	14464

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

Alternative 41
Error	14.7
Cost	14464

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

Alternative 42
Error	36.4
Cost	14464

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

Alternative 43
Error	25.3
Cost	14400

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

Alternative 44
Error	22.6
Cost	14336

\[\left(-1.5 + \sqrt[3]{\frac{8}{{r}^{6}}}\right) - \left(0.375 + v \cdot -0.25\right) \cdot \frac{r}{\frac{1 - v}{w \cdot \left(r \cdot w\right)}}\]

Alternative 45
Error	27.4
Cost	9088

\[\left(\frac{2}{r \cdot r} + -1.5\right) - \frac{\left(0.052734375 + {\left(v \cdot -0.25\right)}^{3}\right) \cdot \frac{r}{\frac{1 - v}{r \cdot \left(w \cdot w\right)}}}{0.140625 + \left(\left(v \cdot -0.25\right) \cdot \left(v \cdot -0.25\right) - 0.375 \cdot \left(v \cdot -0.25\right)\right)}\]

Alternative 46
Error	24.8
Cost	8832

\[\left(\frac{2}{r \cdot r} + -1.5\right) - \frac{r \cdot \left(0.052734375 + {\left(v \cdot -0.25\right)}^{3}\right)}{\frac{1 - v}{w \cdot \left(r \cdot w\right)} \cdot \left(0.140625 + \left(v \cdot \left(v \cdot 0.0625\right) - v \cdot -0.09375\right)\right)}\]

Alternative 47
Error	28.2
Cost	8704

\[\left(\frac{2}{r \cdot r} + -1.5\right) - \frac{r \cdot \left(0.052734375 + {\left(v \cdot -0.25\right)}^{3}\right)}{\frac{1 - v}{r \cdot \left(w \cdot w\right)} \cdot \left(0.140625 + v \cdot \left(v \cdot 0.0625 - -0.09375\right)\right)}\]

Alternative 48
Error	22.8
Cost	2112

\[\left(\frac{2}{r \cdot r} + -1.5\right) - \frac{\frac{r}{\frac{1 - v}{r \cdot \left(w \cdot w\right)}} \cdot \left(0.140625 - v \cdot \left(v \cdot 0.0625\right)\right)}{0.375 - v \cdot -0.25}\]

Alternative 49
Error	24.3
Cost	2112

\[\left(\frac{2}{r \cdot r} + -1.5\right) - \frac{r \cdot \left(0.140625 - v \cdot \left(v \cdot 0.0625\right)\right)}{\frac{1 - v}{r \cdot \left(w \cdot w\right)} \cdot \left(0.375 - v \cdot -0.25\right)}\]

Alternative 50
Error	12.6
Cost	1856

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

Alternative 51
Error	8.3
Cost	1728

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

Alternative 52
Error	2.6
Cost	1728

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

Alternative 53
Error	2.5
Cost	1728

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

Alternative 54
Error	3.9
Cost	1728

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

Alternative 55
Error	3.8
Cost	1728

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

Alternative 56
Error	8.3
Cost	1728

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

Alternative 57
Error	8.3
Cost	1728

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

Alternative 58
Error	13.9
Cost	1600

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

Alternative 59
Error	2.6
Cost	1600

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

Alternative 60
Error	8.4
Cost	1600

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

Alternative 61
Error	3.8
Cost	1600

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

Alternative 62
Error	9.1
Cost	1600

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

Alternative 63
Error	3.8
Cost	1600

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

Alternative 64
Error	17.8
Cost	1600

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

Alternative 65
Error	2.7
Cost	1600

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

Alternative 66
Error	3.7
Cost	1600

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

Alternative 67
Error	2.5
Cost	1600

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

Alternative 68
Error	2.5
Cost	1600

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

Alternative 69
Error	8.4
Cost	1600

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

Alternative 70
Error	8.8
Cost	1600

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

Alternative 71
Error	8.7
Cost	1600

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

Alternative 72
Error	13.4
Cost	1600

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

Alternative 73
Error	8.3
Cost	1600

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

Alternative 74
Error	27.1
Cost	1600

\[\left(\frac{2}{r \cdot r} + -1.5\right) - \left(w \cdot w\right) \cdot \left(\left(r \cdot r\right) \cdot 0.375 + 0.125 \cdot \left(\left(r \cdot r\right) \cdot v\right)\right)\]

Alternative 75
Error	10.6
Cost	1600

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

Alternative 76
Error	19.2
Cost	1472

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

Alternative 77
Error	16.7
Cost	1472

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

Alternative 78
Error	19.0
Cost	1472

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

Alternative 79
Error	18.7
Cost	1472

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

Alternative 80
Error	18.6
Cost	1344

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

Alternative 81
Error	16.9
Cost	1344

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

Alternative 82
Error	19.1
Cost	1344

\[\left(\frac{2}{r \cdot r} + -1.5\right) - \left(r \cdot \left(r \cdot \left(w \cdot w\right)\right)\right) \cdot \left(0.25 - \frac{0.125}{v}\right)\]

Alternative 83
Error	14.6
Cost	1088

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

Alternative 84
Error	9.1
Cost	1088

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

Alternative 85
Error	11.0
Cost	1088

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

Alternative 86
Error	9.5
Cost	1088

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

Alternative 87
Error	10.7
Cost	1088

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

Alternative 88
Error	9.1
Cost	1088

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

Alternative 89
Error	14.8
Cost	1088

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

Alternative 90
Error	62.2
Cost	64

\[1\]

Alternative 91
Error	62.4
Cost	64

\[0\]

Alternative 92
Error	59.2
Cost	64

\[-1\]

Error

Derivation

Initial program 12.6
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
Simplified8.7
\[\leadsto \color{blue}{\left(\frac{2}{r \cdot r} + -1.5\right) - \left(0.375 + v \cdot -0.25\right) \cdot \frac{r}{\frac{1 - v}{r \cdot \left(w \cdot w\right)}}}\]
Using strategy rm
Applied associate-*r*_binary643.8
\[\leadsto \left(\frac{2}{r \cdot r} + -1.5\right) - \left(0.375 + v \cdot -0.25\right) \cdot \frac{r}{\frac{1 - v}{\color{blue}{\left(r \cdot w\right) \cdot w}}}\]
Using strategy rm
Applied add-cube-cbrt_binary643.9
\[\leadsto \left(\frac{2}{r \cdot r} + -1.5\right) - \left(0.375 + v \cdot -0.25\right) \cdot \frac{r}{\frac{\color{blue}{\left(\sqrt[3]{1 - v} \cdot \sqrt[3]{1 - v}\right) \cdot \sqrt[3]{1 - v}}}{\left(r \cdot w\right) \cdot w}}\]
Applied times-frac_binary642.8
\[\leadsto \left(\frac{2}{r \cdot r} + -1.5\right) - \left(0.375 + v \cdot -0.25\right) \cdot \frac{r}{\color{blue}{\frac{\sqrt[3]{1 - v} \cdot \sqrt[3]{1 - v}}{r \cdot w} \cdot \frac{\sqrt[3]{1 - v}}{w}}}\]
Applied *-un-lft-identity_binary642.8
\[\leadsto \left(\frac{2}{r \cdot r} + -1.5\right) - \left(0.375 + v \cdot -0.25\right) \cdot \frac{\color{blue}{1 \cdot r}}{\frac{\sqrt[3]{1 - v} \cdot \sqrt[3]{1 - v}}{r \cdot w} \cdot \frac{\sqrt[3]{1 - v}}{w}}\]
Applied times-frac_binary640.7
\[\leadsto \left(\frac{2}{r \cdot r} + -1.5\right) - \left(0.375 + v \cdot -0.25\right) \cdot \color{blue}{\left(\frac{1}{\frac{\sqrt[3]{1 - v} \cdot \sqrt[3]{1 - v}}{r \cdot w}} \cdot \frac{r}{\frac{\sqrt[3]{1 - v}}{w}}\right)}\]
Simplified0.6
\[\leadsto \left(\frac{2}{r \cdot r} + -1.5\right) - \left(0.375 + v \cdot -0.25\right) \cdot \left(\color{blue}{\frac{r \cdot w}{\sqrt[3]{1 - v} \cdot \sqrt[3]{1 - v}}} \cdot \frac{r}{\frac{\sqrt[3]{1 - v}}{w}}\right)\]
Simplified0.6
\[\leadsto \color{blue}{\left(\frac{2}{r \cdot r} + -1.5\right) - \left(0.375 + v \cdot -0.25\right) \cdot \left(\frac{r \cdot w}{\sqrt[3]{1 - v} \cdot \sqrt[3]{1 - v}} \cdot \frac{r}{\frac{\sqrt[3]{1 - v}}{w}}\right)}\]
Final simplification0.6
\[\leadsto \left(\frac{2}{r \cdot r} + -1.5\right) - \left(0.375 + v \cdot -0.25\right) \cdot \left(\frac{r \cdot w}{\sqrt[3]{1 - v} \cdot \sqrt[3]{1 - v}} \cdot \frac{r}{\frac{\sqrt[3]{1 - v}}{w}}\right)\]

Reproduce

herbie shell --seed 2021042 
(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))