Average Error: 0.2 → 0.2
Time: 14.8s
Precision: 64
Internal Precision: 128
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(\frac{m - {m}^{3}}{\left(1 + m\right) \cdot v} - 1\right) \cdot m\]

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. Using strategy rm

  3. Applied flip--0.2

    \[\leadsto \left(\frac{m \cdot \color{blue}{\frac{1 \cdot 1 - m \cdot m}{1 + m}}}{v} - 1\right) \cdot m\]

  4. Applied associate-*r/0.2

    \[\leadsto \left(\frac{\color{blue}{\frac{m \cdot \left(1 \cdot 1 - m \cdot m\right)}{1 + m}}}{v} - 1\right) \cdot m\]

  5. Applied associate-/l/0.2

    \[\leadsto \left(\color{blue}{\frac{m \cdot \left(1 \cdot 1 - m \cdot m\right)}{v \cdot \left(1 + m\right)}} - 1\right) \cdot m\]

  6. Simplified0.2

    \[\leadsto \left(\frac{\color{blue}{m - {m}^{3}}}{v \cdot \left(1 + m\right)} - 1\right) \cdot m\]

  7. Final simplification0.2

    \[\leadsto \left(\frac{m - {m}^{3}}{\left(1 + m\right) \cdot v} - 1\right) \cdot m\]

Reproduce

herbie shell --seed 2019002 
(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: 14.2s)Debug log

sample181.0ms

Algorithm
intervals

simplify356.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

356.0ms
(* (- (/ (* m (- 1 m)) v) 1) m)

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize27.0ms

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)) v) 1)

rewrite31.0ms

Algorithm
rewrite-expression-head
Counts
3 → 39
Calls

3 calls. Slowest were:

16.0ms
(* (- (/ (* m (- 1 m)) v) 1) m)
7.0ms
(- (/ (* m (- 1 m)) v) 1)
6.0ms
(/ (* m (- 1 m)) v)

series98.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

36.0ms
(* (- (/ (* m (- 1 m)) v) 1) m)
31.0ms
(/ (* m (- 1 m)) v)
20.0ms
(- (/ (* m (- 1 m)) v) 1)

simplify1.7s

Counts
17 → 48
Calls

17 calls. Slowest were:

398.0ms
(- (/ m v) (+ (/ (pow m 2) v) 1))
255.0ms
(* (- (pow (/ (* m (- 1 m)) v) 3) (pow 1 3)) m)
142.0ms
(* (- (* (/ (* m (- 1 m)) v) (/ (* m (- 1 m)) v)) (* 1 1)) m)

prune442.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (/ (- m (pow m 3)) (* v (+ 1 m))) 1) m)
0.1b
(/ (- m (pow m 3)) (* v (+ 1 m)))
0.0b
(- (/ (- m (pow m 3)) (* v (+ 1 m))) 1)
0.0b
(* v (+ 1 m))

rewrite44.0ms

Algorithm
rewrite-expression-head
Counts
4 → 66
Calls

4 calls. Slowest were:

21.0ms
(- (/ (- m (pow m 3)) (* v (+ 1 m))) 1)
17.0ms
(* (- (/ (- m (pow m 3)) (* v (+ 1 m))) 1) m)
3.0ms
(/ (- m (pow m 3)) (* v (+ 1 m)))

series137.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

47.0ms
(* (- (/ (- m (pow m 3)) (* v (+ 1 m))) 1) m)
41.0ms
(/ (- m (pow m 3)) (* v (+ 1 m)))
24.0ms
(* v (+ 1 m))
24.0ms
(- (/ (- m (pow m 3)) (* v (+ 1 m))) 1)

simplify3.2s

Counts
42 → 78
Calls

42 calls. Slowest were:

489.0ms
(* (- (pow (/ (- m (pow m 3)) (* v (+ 1 m))) 3) (pow 1 3)) m)
339.0ms
(* (cbrt (- (/ (- m (pow m 3)) (* v (+ 1 m))) 1)) (cbrt (- (/ (- m (pow m 3)) (* v (+ 1 m))) 1)))
319.0ms
(sqrt (- (/ (- m (pow m 3)) (* v (+ 1 m))) 1))

prune721.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.3b
(* (/ m v) (- m (* m m)))
0.0b
(- (* (/ m v) (- m (* m m))) m)
0.0b
(- m (* m m))

rewrite11.0ms

Algorithm
rewrite-expression-head
Counts
3 → 53
Calls

3 calls. Slowest were:

6.0ms
(- (* (/ m v) (- m (* m m))) m)
4.0ms
(* (/ m v) (- m (* m m)))
1.0ms
(- m (* m m))

series83.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

34.0ms
(* (/ m v) (- m (* m m)))
33.0ms
(- m (* m m))
16.0ms
(- (* (/ m v) (- m (* m m))) m)

simplify1.9s

Counts
32 → 62
Calls

32 calls. Slowest were:

376.0ms
(* v (+ (* m m) (+ (* (* m m) (* m m)) (* m (* m m)))))
226.0ms
(+ (* m m) (+ (* (* m m) (* m m)) (* m (* m m))))
216.0ms
(* m (- (* m m) (* (* m m) (* m m))))

prune484.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite20.0ms

Algorithm
rewrite-expression-head
Counts
4 → 58
Calls

4 calls. Slowest were:

9.0ms
(* (- (/ m (/ v (- 1 m))) 1) m)
8.0ms
(- (/ m (/ v (- 1 m))) 1)
1.0ms
(/ v (- 1 m))

series79.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

28.0ms
(* (- (/ m (/ v (- 1 m))) 1) m)
23.0ms
(/ m (/ v (- 1 m)))
17.0ms
(/ v (- 1 m))
11.0ms
(- (/ m (/ v (- 1 m))) 1)

simplify2.0s

Counts
30 → 70
Calls

30 calls. Slowest were:

486.0ms
(* (- (pow (/ m (/ v (- 1 m))) 3) (pow 1 3)) m)
184.0ms
(* (- (* (/ m (/ v (- 1 m))) (/ m (/ v (- 1 m)))) (* 1 1)) m)
162.0ms
(* (cbrt (- (/ m (/ v (- 1 m))) 1)) (cbrt (- (/ m (/ v (- 1 m))) 1)))

prune546.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

regimes103.0ms

Accuracy

0% (0.2b remaining)

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

bsearch3.0ms

end0.0ms

sample2.0s

Algorithm
intervals