Average Error: 12.0 → 0.4
Time: 49.2s
Precision: 64
Internal Precision: 128
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{\frac{2}{r}}{r}\right) - 4.5\right) - \frac{\left(3 + v \cdot -2\right) \cdot 0.125}{\frac{1}{w \cdot r} \cdot \frac{1 - v}{w \cdot r}}\]

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 12.0

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

  2. Initial simplification0.4

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

  4. Applied associate-/r*0.4

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

  6. Applied *-un-lft-identity0.4

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

  7. Applied times-frac0.4

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

  8. Final simplification0.4

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

Reproduce

herbie shell --seed 2018360 
(FPCore (v w r)
  :name "Rosa's TurbineBenchmark"
  (- (- (+ 3 (/ 2 (* r r))) (/ (* (* 0.125 (- 3 (* 2 v))) (* (* (* w w) r) r)) (- 1 v))) 4.5))

Details

Time bar (total: 38.8s)Debug log

start378.0ms

Algorithm
intervals

setup599.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize42.0ms

Local error

Found 4 expressions with local error:

4.5b
(/ (* (+ (* -2 v) 3) 0.125) (/ (- 1 v) (* (* w r) (* w r))))
0.6b
(/ 2 (* r r))
0.3b
(* (* w r) (* w r))
0.2b
(/ (- 1 v) (* (* w r) (* w r)))

rewrite34.0ms

Algorithm
rewrite-expression-head
Counts
4 → 85
Calls

4 calls. Slowest were:

16.0ms
(/ (* (+ (* -2 v) 3) 0.125) (/ (- 1 v) (* (* w r) (* w r))))
11.0ms
(/ (- 1 v) (* (* w r) (* w r)))
3.0ms
(* (* w r) (* w r))

series144.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

62.0ms
(/ (* (+ (* -2 v) 3) 0.125) (/ (- 1 v) (* (* w r) (* w r))))
47.0ms
(/ (- 1 v) (* (* w r) (* w r)))
19.0ms
(/ 2 (* r r))
16.0ms
(* (* w r) (* w r))

simplify7.3s

Counts
65 → 97
Calls

65 calls. Slowest were:

645.0ms
(* (* (* (* w r) (* w r)) (* w r)) (* (* (* w r) (* w r)) (* w r)))
588.0ms
(- (log (* (+ (* -2 v) 3) 0.125)) (- (log (- 1 v)) (log (* (* w r) (* w r)))))
394.0ms
(+ (* 0.375 (* (pow r 2) (pow w 2))) (+ (* 0.125 (* (pow r 2) (* v (pow w 2)))) (* 0.125 (* (pow r 2) (* (pow v 2) (pow w 2))))))

prune1.9s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

4.5b
(/ (* (+ (* -2 v) 3) 0.125) (/ (- 1 v) (* (* w r) (* w r))))
0.3b
(* (* w r) (* w r))
0.2b
(/ (- 1 v) (* (* w r) (* w r)))
0.2b
(/ (/ 2 r) r)

rewrite32.0ms

Algorithm
rewrite-expression-head
Counts
4 → 89
Calls

4 calls. Slowest were:

11.0ms
(/ (* (+ (* -2 v) 3) 0.125) (/ (- 1 v) (* (* w r) (* w r))))
8.0ms
(/ (- 1 v) (* (* w r) (* w r)))
6.0ms
(* (* w r) (* w r))

series135.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

50.0ms
(/ (- 1 v) (* (* w r) (* w r)))
50.0ms
(/ (* (+ (* -2 v) 3) 0.125) (/ (- 1 v) (* (* w r) (* w r))))
18.0ms
(/ (/ 2 r) r)
16.0ms
(* (* w r) (* w r))

simplify7.2s

Counts
67 → 101
Calls

67 calls. Slowest were:

678.0ms
(* (* (* (* w r) (* w r)) (* w r)) (* (* (* w r) (* w r)) (* w r)))
523.0ms
(- (log (* (+ (* -2 v) 3) 0.125)) (- (log (- 1 v)) (log (* (* w r) (* w r)))))
453.0ms
(+ (* 0.375 (* (pow r 2) (pow w 2))) (+ (* 0.125 (* (pow r 2) (* v (pow w 2)))) (* 0.125 (* (pow r 2) (* (pow v 2) (pow w 2))))))

prune2.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

4.5b
(/ (* (+ (* -2 v) 3) 0.125) (* (/ 1 (* w r)) (/ (- 1 v) (* w r))))
0.3b
(/ 1 (* w r))
0.3b
(* (/ 1 (* w r)) (/ (- 1 v) (* w r)))
0.2b
(/ (- 1 v) (* w r))

rewrite18.0ms

Algorithm
rewrite-expression-head
Counts
4 → 91
Calls

4 calls. Slowest were:

9.0ms
(/ (* (+ (* -2 v) 3) 0.125) (* (/ 1 (* w r)) (/ (- 1 v) (* w r))))
5.0ms
(* (/ 1 (* w r)) (/ (- 1 v) (* w r)))
2.0ms
(/ (- 1 v) (* w r))

series137.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

61.0ms
(/ (* (+ (* -2 v) 3) 0.125) (* (/ 1 (* w r)) (/ (- 1 v) (* w r))))
48.0ms
(* (/ 1 (* w r)) (/ (- 1 v) (* w r)))
17.0ms
(/ (- 1 v) (* w r))
11.0ms
(/ 1 (* w r))

simplify8.0s

Counts
63 → 103
Calls

63 calls. Slowest were:

805.0ms
(/ (* (* (* (+ (* -2 v) 3) 0.125) (* (+ (* -2 v) 3) 0.125)) (* (+ (* -2 v) 3) 0.125)) (* (* (* (/ 1 (* w r)) (/ 1 (* w r))) (/ 1 (* w r))) (/ (* (* (- 1 v) (- 1 v)) (- 1 v)) (* (* (* w r) (* w r)) (* w r)))))
633.0ms
(/ (* (* (* (+ (* -2 v) 3) 0.125) (* (+ (* -2 v) 3) 0.125)) (* (+ (* -2 v) 3) 0.125)) (* (* (* (/ 1 (* w r)) (/ 1 (* w r))) (/ 1 (* w r))) (* (* (/ (- 1 v) (* w r)) (/ (- 1 v) (* w r))) (/ (- 1 v) (* w r)))))
518.0ms
(+ (log (/ 1 (* w r))) (- (log (- 1 v)) (log (* w r))))

prune2.5s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

11.3b
(sqrt (/ 2 (* r r)))
11.3b
(sqrt (/ 2 (* r r)))
4.5b
(/ (* (+ (* -2 v) 3) 0.125) (/ (- 1 v) (* (* w r) (* w r))))
0.6b
(/ 2 (* r r))

rewrite25.0ms

Algorithm
rewrite-expression-head
Counts
4 → 73
Calls

4 calls. Slowest were:

20.0ms
(/ (* (+ (* -2 v) 3) 0.125) (/ (- 1 v) (* (* w r) (* w r))))
1.0ms
(sqrt (/ 2 (* r r)))
1.0ms
(sqrt (/ 2 (* r r)))

series126.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

59.0ms
(/ (* (+ (* -2 v) 3) 0.125) (/ (- 1 v) (* (* w r) (* w r))))
29.0ms
(sqrt (/ 2 (* r r)))
20.0ms
(sqrt (/ 2 (* r r)))
18.0ms
(/ 2 (* r r))

simplify5.2s

Counts
55 → 85
Calls

55 calls. Slowest were:

520.0ms
(- (log (* (+ (* -2 v) 3) 0.125)) (- (log (- 1 v)) (log (* (* w r) (* w r)))))
395.0ms
(/ (* (* (* (+ (* -2 v) 3) 0.125) (* (+ (* -2 v) 3) 0.125)) (* (+ (* -2 v) 3) 0.125)) (* (* (/ (- 1 v) (* (* w r) (* w r))) (/ (- 1 v) (* (* w r) (* w r)))) (/ (- 1 v) (* (* w r) (* w r)))))
381.0ms
(/ (* (* (* (+ (* -2 v) 3) 0.125) (* (+ (* -2 v) 3) 0.125)) (* (+ (* -2 v) 3) 0.125)) (/ (* (* (- 1 v) (- 1 v)) (- 1 v)) (* (* (* (* w r) (* w r)) (* w r)) (* (* (* w r) (* w r)) (* w r)))))

prune2.0s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes511.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch3.0ms