Average Error: 0.2 → 0.2
Time: 16.6s
Precision: 64
Internal Precision: 128
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\frac{m - m \cdot m}{v} \cdot m - m\]

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. Initial simplification0.2

    \[\leadsto \frac{m - m \cdot m}{\frac{v}{m}} - m\]
  3. Using strategy rm

  4. Applied associate-/r/0.2

    \[\leadsto \color{blue}{\frac{m - m \cdot m}{v} \cdot m} - m\]

  5. Final simplification0.2

    \[\leadsto \frac{m - m \cdot m}{v} \cdot m - m\]

Reproduce

herbie shell --seed 2018362 
(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: 12.3s)Debug log

start154.0ms

Algorithm
intervals

setup487.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 3 expressions with local error:

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

rewrite21.0ms

Algorithm
rewrite-expression-head
Counts
3 → 58
Calls

3 calls. Slowest were:

11.0ms
(- (/ (- m (* m m)) (/ v m)) m)
7.0ms
(/ (- m (* m m)) (/ v m))
1.0ms
(- m (* m m))

series108.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

46.0ms
(/ (- m (* m m)) (/ v m))
35.0ms
(- m (* m m))
27.0ms
(- (/ (- m (* m m)) (/ v m)) m)

simplify2.2s

Counts
45 → 67
Calls

45 calls. Slowest were:

514.0ms
(- (* m m) (* (* m m) (* m m)))
387.0ms
(/ (* (* (- m (* m m)) (- m (* m m))) (- m (* m m))) (* (* (/ v m) (/ v m)) (/ v m)))
114.0ms
(/ (- m (* m m)) (/ 1 m))

prune548.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite13.0ms

Algorithm
rewrite-expression-head
Counts
3 → 70
Calls

3 calls. Slowest were:

8.0ms
(- (/ (+ m (- (* m m))) (/ v m)) m)
4.0ms
(/ (+ m (- (* m m))) (/ v m))
1.0ms
(+ m (- (* m m)))

series71.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

33.0ms
(/ (+ m (- (* m m))) (/ v m))
22.0ms
(+ m (- (* m m)))
16.0ms
(- (/ (+ m (- (* m m))) (/ v m)) m)

simplify1.9s

Counts
61 → 79
Calls

61 calls. Slowest were:

263.0ms
(+ (pow m 3) (pow (- (* m m)) 3))
191.0ms
(- (* m m) (* (- (* m m)) (- (* m m))))
119.0ms
(- (/ (pow m 2) v) (+ m (/ (pow m 3) v)))

prune703.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite10.0ms

Algorithm
rewrite-expression-head
Counts
4 → 51
Calls

4 calls. Slowest were:

4.0ms
(- (* (/ (- m (* m m)) v) m) m)
3.0ms
(* (/ (- m (* m m)) v) m)
2.0ms
(/ (- m (* m m)) v)

series97.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

33.0ms
(* (/ (- m (* m m)) v) m)
24.0ms
(- (* (/ (- m (* m m)) v) m) m)
22.0ms
(- m (* m m))
18.0ms
(/ (- m (* m m)) v)

simplify1.2s

Counts
21 → 63
Calls

21 calls. Slowest were:

516.0ms
(- (* m m) (* (* m m) (* m m)))
110.0ms
(- (/ (pow m 2) v) (+ m (/ (pow m 3) v)))
88.0ms
(- (/ (pow m 2) v) (+ m (/ (pow m 3) v)))

prune515.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite17.0ms

Algorithm
rewrite-expression-head
Counts
4 → 78
Calls

4 calls. Slowest were:

8.0ms
(- (/ (/ (- m (* m m)) v) (/ 1 m)) m)
6.0ms
(/ (/ (- m (* m m)) v) (/ 1 m))
2.0ms
(/ (- m (* m m)) v)

series112.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

36.0ms
(/ (/ (- m (* m m)) v) (/ 1 m))
27.0ms
(- m (* m m))
26.0ms
(- (/ (/ (- m (* m m)) v) (/ 1 m)) m)
22.0ms
(/ (- m (* m m)) v)

simplify3.3s

Counts
61 → 90
Calls

61 calls. Slowest were:

516.0ms
(- (* m m) (* (* m m) (* m m)))
368.0ms
(/ (/ (- m (* m m)) v) (/ 1 m))
288.0ms
(/ (/ (- m (* m m)) v) (/ 1 m))

prune737.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes162.0ms

Accuracy

0% (0.2b remaining)

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

bsearch3.0ms