Average Error: 0.2 → 0.2
Time: 13.7s
Precision: 64
Internal Precision: 128
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(\frac{1}{\frac{\frac{v}{m}}{1 - m}} - 1\right) \cdot m\]

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. Using strategy rm

  5. Applied associate-/r*0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019008 
(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: 13.0s)Debug log

sample192.0ms

Algorithm
intervals

simplify340.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

339.0ms
(* (- (/ (* m (- 1 m)) v) 1) m)

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite21.0ms

Algorithm
rewrite-expression-head
Counts
4 → 56
Calls

4 calls. Slowest were:

10.0ms
(* (- (/ (* m (- 1 m)) v) 1) m)
4.0ms
(- (/ (* m (- 1 m)) v) 1)
3.0ms
(/ (* m (- 1 m)) v)

series91.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

42.0ms
(* (- (/ (* m (- 1 m)) v) 1) m)
20.0ms
(* m (- 1 m))
18.0ms
(/ (* m (- 1 m)) v)
11.0ms
(- (/ (* m (- 1 m)) v) 1)

simplify1.2s

Counts
29 → 68
Calls

29 calls. Slowest were:

274.0ms
(* (- (pow (/ (* m (- 1 m)) v) 3) (pow 1 3)) m)
106.0ms
(- (/ (pow m 2) v) (+ m (/ (pow m 3) v)))
97.0ms
(* (- (* (/ (* m (- 1 m)) v) (/ (* m (- 1 m)) v)) (* 1 1)) m)

prune581.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite18.0ms

Algorithm
rewrite-expression-head
Counts
4 → 59
Calls

4 calls. Slowest were:

8.0ms
(* (- (/ 1 (/ v (* m (- 1 m)))) 1) m)
6.0ms
(- (/ 1 (/ v (* m (- 1 m)))) 1)
1.0ms
(/ v (* m (- 1 m)))

series131.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

41.0ms
(/ 1 (/ v (* m (- 1 m))))
39.0ms
(* (- (/ 1 (/ v (* m (- 1 m)))) 1) m)
29.0ms
(/ v (* m (- 1 m)))
21.0ms
(- (/ 1 (/ v (* m (- 1 m)))) 1)

simplify2.7s

Counts
29 → 71
Calls

29 calls. Slowest were:

851.0ms
(* (- (* (/ 1 (/ v (* m (- 1 m)))) (/ 1 (/ v (* m (- 1 m))))) (* 1 1)) m)
321.0ms
(* (- (pow (/ 1 (/ v (* m (- 1 m)))) 3) (pow 1 3)) m)
195.0ms
(+ (sqrt (/ 1 (/ v (* m (- 1 m))))) 1)

prune635.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.2b
(* (/ 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))

series87.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

36.0ms
(- m (* m m))
26.0ms
(* (/ m v) (- m (* m m)))
25.0ms
(- (* (/ m v) (- m (* m m))) m)

simplify1.9s

Counts
32 → 62
Calls

32 calls. Slowest were:

424.0ms
(* v (+ (* m m) (+ (* (* m m) (* m m)) (* m (* m m)))))
193.0ms
(* m (- (* m m) (* (* m m) (* m m))))
189.0ms
(+ (* m m) (+ (* (* m m) (* m m)) (* m (* m m))))

prune458.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

3.0b
(* (/ m v) (- (* m m)))
0.2b
(* (/ m v) m)
0.0b
(+ (* (/ m v) m) (* (/ m v) (- (* m m))))
0.0b
(- (+ (* (/ m v) m) (* (/ m v) (- (* m m)))) m)

rewrite43.0ms

Algorithm
rewrite-expression-head
Counts
4 → 65
Calls

4 calls. Slowest were:

26.0ms
(- (+ (* (/ m v) m) (* (/ m v) (- (* m m)))) m)
9.0ms
(+ (* (/ m v) m) (* (/ m v) (- (* m m))))
5.0ms
(* (/ m v) (- (* m m)))

series81.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

27.0ms
(- (+ (* (/ m v) m) (* (/ m v) (- (* m m)))) m)
24.0ms
(+ (* (/ m v) m) (* (/ m v) (- (* m m))))
21.0ms
(* (/ m v) (- (* m m)))
10.0ms
(* (/ m v) m)

simplify1.1s

Counts
36 → 77
Calls

36 calls. Slowest were:

158.0ms
(* (exp (* (/ m v) m)) (exp (* (/ m v) (- (* m m)))))
115.0ms
(- (/ (pow m 2) v) (+ m (/ (pow m 3) v)))
101.0ms
(+ (* (* m m) v) (* v (* m (- (* m m)))))

prune677.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes90.0ms

Accuracy

0% (0.2b remaining)

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

bsearch1.0ms

end0.0ms

sample2.6s

Algorithm
intervals