Average Error: 12.8 → 0.7
Time: 6.6s
Precision: binary64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\frac{\frac{2}{r}}{r} + -1.5\right) - \left(\frac{r \cdot w}{\sqrt[3]{1 - v} \cdot \sqrt[3]{1 - v}} \cdot \left(0.375 + v \cdot -0.25\right)\right) \cdot \frac{r}{\frac{\sqrt[3]{1 - v}}{w}}\]
\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{\frac{2}{r}}{r} + -1.5\right) - \left(\frac{r \cdot w}{\sqrt[3]{1 - v} \cdot \sqrt[3]{1 - v}} \cdot \left(0.375 + v \cdot -0.25\right)\right) \cdot \frac{r}{\frac{\sqrt[3]{1 - v}}{w}}
(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)
  (*
   (* (/ (* r w) (* (cbrt (- 1.0 v)) (cbrt (- 1.0 v)))) (+ 0.375 (* v -0.25)))
   (/ 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) - ((((r * w) / (cbrt(1.0 - v) * cbrt(1.0 - v))) * (0.375 + (v * -0.25))) * (r / (cbrt(1.0 - v) / w)));
}

Error

Bits error versus v

Bits error versus w

Bits error versus r

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 12.8

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

  2. Simplified8.8

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

  4. Applied associate-*r*_binary643.7

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

  6. Applied add-cube-cbrt_binary643.8

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

  7. Applied times-frac_binary642.7

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

  8. Applied *-un-lft-identity_binary642.7

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

  9. Applied times-frac_binary640.8

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

  10. Applied associate-*r*_binary640.7

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

  11. Simplified0.7

    \[\leadsto \left(\frac{2}{r \cdot r} + -1.5\right) - \color{blue}{\left(\frac{r \cdot w}{\sqrt[3]{1 - v} \cdot \sqrt[3]{1 - v}} \cdot \left(0.375 + v \cdot -0.25\right)\right)} \cdot \frac{r}{\frac{\sqrt[3]{1 - v}}{w}}\]
  12. Using strategy rm

  13. Applied associate-/r*_binary640.7

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

  14. Final simplification0.7

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

Reproduce

herbie shell --seed 2020232 
(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))