Average Error: 0.2 → 0.2
Time: 31.1s
Precision: 64
Internal Precision: 128
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[m \cdot \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right)\]

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. Final simplification0.2

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

Reproduce

herbie shell --seed 2018360 +o rules:numerics
(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: 27.6s)Debug log

start340.0ms

Algorithm
intervals

setup817.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize35.0ms

Local error

Found 2 expressions with local error:

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

rewrite30.0ms

Algorithm
rewrite-expression-head
Counts
2 → 31
Calls

2 calls. Slowest were:

20.0ms
(* (- (/ (* m (- 1 m)) v) 1) m)
7.0ms
(/ (* m (- 1 m)) v)

series51.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

33.0ms
(* (- (/ (* m (- 1 m)) v) 1) m)
17.0ms
(/ (* m (- 1 m)) v)

simplify1.9s

Counts
13 → 37
Calls

13 calls. Slowest were:

811.0ms
(* (- (* (/ (* m (- 1 m)) v) (/ (* m (- 1 m)) v)) (* 1 1)) m)
195.0ms
(* (- (pow (/ (* m (- 1 m)) v) 3) (pow 1 3)) m)
191.0ms
(- (/ (pow m 2) v) (+ m (/ (pow m 3) v)))

prune393.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite8.0ms

Algorithm
rewrite-expression-head
Counts
3 → 53
Calls

3 calls. Slowest were:

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

series77.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

31.0ms
(/ v (* m (- 1 m)))
25.0ms
(/ 1 (/ v (* m (- 1 m))))
21.0ms
(* (- (/ 1 (/ v (* m (- 1 m)))) 1) m)

simplify2.1s

Counts
25 → 62
Calls

25 calls. Slowest were:

363.0ms
(- (/ m v) (/ (pow m 2) v))
297.0ms
(* (- (pow (/ 1 (/ v (* m (- 1 m)))) 3) (pow 1 3)) m)
183.0ms
(- (/ (pow m 2) v) (+ m (/ (pow m 3) v)))

prune594.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize21.0ms

Local error

Found 3 expressions with local error:

0.4b
(/ (/ 1 v) (/ 1 (* m (- 1 m))))
0.2b
(* (- (/ (/ 1 v) (/ 1 (* m (- 1 m)))) 1) m)
0.0b
(/ 1 (* m (- 1 m)))

rewrite61.0ms

Algorithm
rewrite-expression-head
Counts
3 → 86
Calls

3 calls. Slowest were:

47.0ms
(* (- (/ (/ 1 v) (/ 1 (* m (- 1 m)))) 1) m)
8.0ms
(/ (/ 1 v) (/ 1 (* m (- 1 m))))
3.0ms
(/ 1 (* m (- 1 m)))

series87.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

41.0ms
(/ (/ 1 v) (/ 1 (* m (- 1 m))))
35.0ms
(* (- (/ (/ 1 v) (/ 1 (* m (- 1 m)))) 1) m)
11.0ms
(/ 1 (* m (- 1 m)))

simplify8.5s

Counts
79 → 95
Calls

79 calls. Slowest were:

639.0ms
(* (- (pow (/ (/ 1 v) (/ 1 (* m (- 1 m)))) 3) (pow 1 3)) m)
482.0ms
(* (cbrt (- (/ (/ 1 v) (/ 1 (* m (- 1 m)))) 1)) (cbrt (- (/ (/ 1 v) (/ 1 (* m (- 1 m)))) 1)))
430.0ms
(* (- (* (/ (/ 1 v) (/ 1 (* m (- 1 m)))) (/ (/ 1 v) (/ 1 (* m (- 1 m))))) (* 1 1)) m)

prune926.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (/ 1 v) (/ 1 (* m (- 1 m))))
0.4b
(cbrt (fma (- 1 m) (/ m v) -1))
0.4b
(cbrt (fma (- 1 m) (/ m v) -1))
0.4b
(cbrt (- (/ (/ 1 v) (/ 1 (* m (- 1 m)))) 1))

rewrite17.0ms

Algorithm
rewrite-expression-head
Counts
4 → 94
Calls

4 calls. Slowest were:

10.0ms
(cbrt (- (/ (/ 1 v) (/ 1 (* m (- 1 m)))) 1))
4.0ms
(/ (/ 1 v) (/ 1 (* m (- 1 m))))
1.0ms
(cbrt (fma (- 1 m) (/ m v) -1))

series792.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

508.0ms
(cbrt (- (/ (/ 1 v) (/ 1 (* m (- 1 m)))) 1))
129.0ms
(cbrt (fma (- 1 m) (/ m v) -1))
126.0ms
(cbrt (fma (- 1 m) (/ m v) -1))
28.0ms
(/ (/ 1 v) (/ 1 (* m (- 1 m))))

simplify9.2s

Counts
85 → 106
Calls

85 calls. Slowest were:

644.0ms
(cbrt (- (pow (/ (/ 1 v) (/ 1 (* m (- 1 m)))) 3) (pow 1 3)))
505.0ms
(cbrt (sqrt (- (/ (/ 1 v) (/ 1 (* m (- 1 m)))) 1)))
475.0ms
(cbrt (* (cbrt (- (/ (/ 1 v) (/ 1 (* m (- 1 m)))) 1)) (cbrt (- (/ (/ 1 v) (/ 1 (* m (- 1 m)))) 1))))

prune1.4s

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 0b

regimes135.0ms

Accuracy

0% (0.2b remaining)

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

bsearch1.0ms