Average Error: 0.2 → 0.2
Time: 29.9s
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 6.8

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

  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 2019005 
(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: 29.4s)Debug log

sample196.0ms

Algorithm
intervals

simplify383.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

382.0ms
(* (- (/ (* m (- 1 m)) v) 1) m)

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

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))

rewrite16.0ms

Algorithm
rewrite-expression-head
Counts
3 → 44
Calls

3 calls. Slowest were:

10.0ms
(* (- (/ (* m (- 1 m)) v) 1) m)
3.0ms
(/ (* m (- 1 m)) v)
1.0ms
(* m (- 1 m))

series102.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

38.0ms
(* (- (/ (* m (- 1 m)) v) 1) m)
34.0ms
(* m (- 1 m))
29.0ms
(/ (* m (- 1 m)) v)

simplify981.0ms

Counts
25 → 53
Calls

25 calls. Slowest were:

235.0ms
(* (- (pow (/ (* m (- 1 m)) v) 3) (pow 1 3)) m)
113.0ms
(* (- (* (/ (* m (- 1 m)) v) (/ (* m (- 1 m)) v)) (* 1 1)) m)
94.0ms
(- (/ (pow m 2) v) (+ m (/ (pow m 3) v)))

prune526.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 3 expressions with local error:

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

rewrite12.0ms

Algorithm
rewrite-expression-head
Counts
3 → 53
Calls

3 calls. Slowest were:

7.0ms
(- (* (/ m v) (- m (* m m))) m)
4.0ms
(* (/ m v) (- m (* m m)))
0.0ms
(- m (* m m))

series74.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

35.0ms
(* (/ m v) (- m (* m m)))
23.0ms
(- m (* m m))
16.0ms
(- (* (/ m v) (- m (* m m))) m)

simplify1.9s

Counts
32 → 62
Calls

32 calls. Slowest were:

453.0ms
(* v (+ (* m m) (+ (* (* m m) (* m m)) (* m (* m m)))))
175.0ms
(+ (* m m) (+ (* (* m m) (* m m)) (* m (* m m))))
139.0ms
(* m (- (* m m) (* (* m m) (* m m))))

prune536.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

Algorithm
rewrite-expression-head
Counts
4 → 79
Calls

4 calls. Slowest were:

13.0ms
(- (* m (* (/ 1 v) (- m (* m m)))) m)
9.0ms
(* m (* (/ 1 v) (- m (* m m))))
8.0ms
(* (/ 1 v) (- m (* m m)))

series120.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

43.0ms
(* m (* (/ 1 v) (- m (* m m))))
38.0ms
(* (/ 1 v) (- m (* m m)))
20.0ms
(- (* m (* (/ 1 v) (- m (* m m)))) m)
19.0ms
(- m (* m m))

simplify7.1s

Counts
52 → 91
Calls

52 calls. Slowest were:

686.0ms
(* (* (* (/ 1 v) (/ 1 v)) (/ 1 v)) (* (* (- m (* m m)) (- m (* m m))) (- m (* m m))))
470.0ms
(* (* (/ 1 v) (- (* m m))) m)
469.0ms
(* (* (/ 1 v) (- (* m m))) m)

prune870.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite56.0ms

Algorithm
rewrite-expression-head
Counts
4 → 121
Calls

4 calls. Slowest were:

25.0ms
(* (sqrt (/ 1 v)) (* (sqrt (/ 1 v)) (- m (* m m))))
24.0ms
(* m (* (sqrt (/ 1 v)) (* (sqrt (/ 1 v)) (- m (* m m)))))
5.0ms
(* (sqrt (/ 1 v)) (- m (* m m)))

series124.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

45.0ms
(* (sqrt (/ 1 v)) (- m (* m m)))
42.0ms
(* (sqrt (/ 1 v)) (* (sqrt (/ 1 v)) (- m (* m m))))
25.0ms
(* m (* (sqrt (/ 1 v)) (* (sqrt (/ 1 v)) (- m (* m m)))))
12.0ms
(sqrt (/ 1 v))

simplify12.9s

Counts
106 → 133
Calls

106 calls. Slowest were:

625.0ms
(* (sqrt v) (+ (* m m) (+ (* (* m m) (* m m)) (* m (* m m)))))
611.0ms
(* (* (* (sqrt (/ 1 v)) (sqrt (/ 1 v))) (sqrt (/ 1 v))) (* (* (- m (* m m)) (- m (* m m))) (- m (* m m))))
452.0ms
(* (sqrt 1) (* (sqrt (/ 1 v)) (- (pow m 3) (pow (* m m) 3))))

prune1.2s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes140.0ms

Accuracy

0% (0.1b remaining)

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

bsearch2.0ms

end0.0ms

sample1.9s

Algorithm
intervals