Average Error: 0.2 → 0.2
Time: 13.2s
Precision: 64
Internal Precision: 128
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(m - m \cdot m\right) \cdot \frac{m}{v} - m\]

Error

Bits error versus m

Bits error versus v

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]

  2. Taylor expanded around 0 7.2

    \[\leadsto \color{blue}{\frac{{m}^{2}}{v} - \left(m + \frac{{m}^{3}}{v}\right)}\]

  3. Simplified0.2

    \[\leadsto \color{blue}{\frac{m}{v} \cdot \left(m - m \cdot m\right) - m}\]

  4. Final simplification0.2

    \[\leadsto \left(m - m \cdot m\right) \cdot \frac{m}{v} - m\]

Reproduce

herbie shell --seed 2019004 
(FPCore (m v)
  :name "a parameter of renormalized beta distribution"
  :pre (and (< 0 m) (< 0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) m))

Details

Time bar (total: 12.6s)Debug log

sample132.0ms

Algorithm
intervals

simplify395.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

394.0ms
(* (- (/ (* m (- 1 m)) v) 1) m)

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize26.0ms

Local error

Found 3 expressions with local error:

0.2b
(* (- (/ (* m (- 1 m)) v) 1) m)
0.1b
(/ (* m (- 1 m)) v)
0.0b
(* m (- 1 m))

rewrite36.0ms

Algorithm
rewrite-expression-head
Counts
3 → 44
Calls

3 calls. Slowest were:

27.0ms
(* (- (/ (* m (- 1 m)) v) 1) m)
6.0ms
(/ (* m (- 1 m)) v)
1.0ms
(* m (- 1 m))

series77.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

32.0ms
(* m (- 1 m))
25.0ms
(* (- (/ (* m (- 1 m)) v) 1) m)
20.0ms
(/ (* m (- 1 m)) v)

simplify1.0s

Counts
25 → 53
Calls

25 calls. Slowest were:

303.0ms
(* (- (pow (/ (* m (- 1 m)) v) 3) (pow 1 3)) m)
117.0ms
(- (/ (pow m 2) v) (+ m (/ (pow m 3) v)))
107.0ms
(- (/ (pow m 2) v) (+ m (/ (pow m 3) v)))

prune451.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 3 expressions with local error:

0.2b
(* (/ m v) (- m (* m m)))
0.0b
(- (* (/ m v) (- m (* m m))) m)
0.0b
(- m (* m m))

rewrite20.0ms

Algorithm
rewrite-expression-head
Counts
3 → 53
Calls

3 calls. Slowest were:

10.0ms
(- (* (/ m v) (- m (* m m))) m)
8.0ms
(* (/ m v) (- m (* m m)))
1.0ms
(- m (* m m))

series60.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

24.0ms
(* (/ m v) (- m (* m m)))
20.0ms
(- m (* m m))
16.0ms
(- (* (/ m v) (- m (* m m))) m)

simplify2.1s

Counts
32 → 62
Calls

32 calls. Slowest were:

663.0ms
(* v (+ (* m m) (+ (* (* m m) (* m m)) (* m (* m m)))))
188.0ms
(* m (- (* m m) (* (* m m) (* m m))))
157.0ms
(+ (* m m) (+ (* (* m m) (* m m)) (* m (* m m))))

prune575.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize21.0ms

Local error

Found 3 expressions with local error:

0.2b
(* (- (/ m (/ v (- 1 m))) 1) m)
0.0b
(/ m (/ v (- 1 m)))
0.0b
(/ v (- 1 m))

rewrite15.0ms

Algorithm
rewrite-expression-head
Counts
3 → 46
Calls

3 calls. Slowest were:

12.0ms
(* (- (/ m (/ v (- 1 m))) 1) m)
1.0ms
(/ m (/ v (- 1 m)))
1.0ms
(/ v (- 1 m))

series88.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

30.0ms
(/ v (- 1 m))
30.0ms
(/ m (/ v (- 1 m)))
28.0ms
(* (- (/ m (/ v (- 1 m))) 1) m)

simplify1.7s

Counts
26 → 55
Calls

26 calls. Slowest were:

488.0ms
(* (- (pow (/ m (/ v (- 1 m))) 3) (pow 1 3)) m)
151.0ms
(* (- (* (/ m (/ v (- 1 m))) (/ m (/ v (- 1 m)))) (* 1 1)) m)
147.0ms
(sqrt (- (/ m (/ v (- 1 m))) 1))

prune502.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (/ v (* m (- 1 m))))
0.2b
(* (- (/ 1 (/ v (* m (- 1 m)))) 1) m)
0.1b
(/ v (* m (- 1 m)))
0.0b
(* m (- 1 m))

rewrite10.0ms

Algorithm
rewrite-expression-head
Counts
4 → 64
Calls

4 calls. Slowest were:

6.0ms
(* (- (/ 1 (/ v (* m (- 1 m)))) 1) m)
1.0ms
(/ 1 (/ v (* m (- 1 m))))
1.0ms
(* m (- 1 m))

series133.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

39.0ms
(/ 1 (/ v (* m (- 1 m))))
36.0ms
(* (- (/ 1 (/ v (* m (- 1 m)))) 1) m)
29.0ms
(/ v (* m (- 1 m)))
28.0ms
(* m (- 1 m))

simplify2.5s

Counts
37 → 76
Calls

37 calls. Slowest were:

897.0ms
(* (- (* (/ 1 (/ v (* m (- 1 m)))) (/ 1 (/ v (* m (- 1 m))))) (* 1 1)) m)
359.0ms
(* (- (pow (/ 1 (/ v (* m (- 1 m)))) 3) (pow 1 3)) m)
184.0ms
(* (cbrt (- (/ 1 (/ v (* m (- 1 m)))) 1)) (cbrt (- (/ 1 (/ v (* m (- 1 m)))) 1)))

prune595.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes102.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch2.0ms

end0.0ms

sample2.0s

Algorithm
intervals