Average Error: 0.2 → 0.2
Time: 25.8s
Precision: 64
Internal Precision: 128
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(\frac{1}{\frac{v}{m \cdot \left(1 - m\right)}} - 1\right) \cdot m\]

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 clear-num0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019007 +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: 25.2s)Debug log

sample201.0ms

Algorithm
intervals

simplify186.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

185.0ms
(* (- (/ (* m (- 1 m)) v) 1) m)

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 2 expressions with local error:

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

rewrite5.0ms

Algorithm
rewrite-expression-head
Counts
2 → 25
Calls

2 calls. Slowest were:

3.0ms
(* m (fma (- 1 m) (/ m v) -1))
0.0ms
(fma (- 1 m) (/ m v) -1)

series62.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

43.0ms
(* m (fma (- 1 m) (/ m v) -1))
18.0ms
(fma (- 1 m) (/ m v) -1)

simplify732.0ms

Counts
11 → 31
Calls

11 calls. Slowest were:

181.0ms
(- (/ (pow m 2) v) (+ m (/ (pow m 3) v)))
177.0ms
(- (/ (pow m 2) v) (+ m (/ (pow m 3) v)))
163.0ms
(- (/ (pow m 2) v) (+ m (/ (pow m 3) v)))

prune277.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite12.0ms

Algorithm
rewrite-expression-head
Counts
3 → 88
Calls

3 calls. Slowest were:

7.0ms
(* m (- (/ m v) (fma m (/ m v) 1)))
4.0ms
(- (/ m v) (fma m (/ m v) 1))
0.0ms
(fma m (/ m v) 1)

series68.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

25.0ms
(* m (- (/ m v) (fma m (/ m v) 1)))
22.0ms
(fma m (/ m v) 1)
21.0ms
(- (/ m v) (fma m (/ m v) 1))

simplify13.3s

Counts
74 → 97
Calls

74 calls. Slowest were:

561.0ms
(* (fma (- (fma m (/ m v) 1)) 1 (* (fma m (/ m v) 1) 1)) m)
547.0ms
(* m (fma (- (fma m (/ m v) 1)) 1 (* (fma m (/ m v) 1) 1)))
545.0ms
(* m (fma (- (fma m (/ m v) 1)) 1 (* (fma m (/ m v) 1) 1)))

prune857.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite38.0ms

Algorithm
rewrite-expression-head
Counts
4 → 69
Calls

4 calls. Slowest were:

17.0ms
(* (- (/ (* m (- 1 m)) v) 1) m)
9.0ms
(- (/ (* m (- 1 m)) v) 1)
7.0ms
(/ (* m (- 1 m)) v)

series108.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

36.0ms
(* m (- 1 m))
28.0ms
(* (- (/ (* m (- 1 m)) v) 1) m)
25.0ms
(/ (* m (- 1 m)) v)
19.0ms
(- (/ (* m (- 1 m)) v) 1)

simplify2.0s

Counts
33 → 81
Calls

33 calls. Slowest were:

328.0ms
(* (- (pow (/ (* m (- 1 m)) v) 3) (pow 1 3)) m)
198.0ms
(- (/ (pow m 2) v) (+ m (/ (pow m 3) v)))
166.0ms
(* (cbrt (- (/ (* m (- 1 m)) v) 1)) (cbrt (- (/ (* m (- 1 m)) v) 1)))

prune720.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

Algorithm
rewrite-expression-head
Counts
4 → 74
Calls

4 calls. Slowest were:

14.0ms
(* (- (/ 1 (/ v (* m (- 1 m)))) 1) m)
7.0ms
(- (/ 1 (/ v (* m (- 1 m)))) 1)
2.0ms
(/ 1 (/ v (* m (- 1 m))))

series114.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

43.0ms
(/ 1 (/ v (* m (- 1 m))))
39.0ms
(* (- (/ 1 (/ v (* m (- 1 m)))) 1) m)
18.0ms
(/ v (* m (- 1 m)))
14.0ms
(- (/ 1 (/ v (* m (- 1 m)))) 1)

simplify3.1s

Counts
34 → 86
Calls

34 calls. Slowest were:

397.0ms
(* (- (pow (/ 1 (/ v (* m (- 1 m)))) 3) (pow 1 3)) m)
283.0ms
(log (/ 1 (/ v (* m (- 1 m)))))
247.0ms
(* (cbrt (- (/ 1 (/ v (* m (- 1 m)))) 1)) (cbrt (- (/ 1 (/ v (* m (- 1 m)))) 1)))

prune645.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes118.0ms

Accuracy

0% (0.2b remaining)

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

bsearch3.0ms

end0.0ms

sample2.5s

Algorithm
intervals