Average Error: 0.2 → 0.2
Time: 18.1s
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 2019022 
(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: 17.1s)Debug log

sample295.0ms

Algorithm
intervals
Results
188.0ms432×body80valid
21.0ms432×pre80true

simplify315.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
313.0ms
(* (- (/ (* m (- 1 m)) v) 1) m)

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×add-cube-cbrt
6×*-un-lft-identity
4×add-log-exp
4×flip--
4×add-exp-log
4×associate-*r/
4×associate-*l*
4×add-cbrt-cube
4×flip3--
4×pow1
3×associate-*r*
3×sub-neg
2×associate-/l/
2×*-commutative
2×associate-*l/
2×difference-of-sqr-1
2×distribute-lft-in
2×distribute-rgt-in
1×associate-/l*
1×div-inv
1×frac-2neg
1×clear-num
Counts
4 → 56
Calls
4 calls:
Slowest
16.0ms
(* (- (/ (* m (- 1 m)) v) 1) m)
6.0ms
(- (/ (* m (- 1 m)) v) 1)
5.0ms
(/ (* m (- 1 m)) v)
2.0ms
(* m (- 1 m))

series93.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
36.0ms
(* (- (/ (* m (- 1 m)) v) 1) m)
20.0ms
(* m (- 1 m))
18.0ms
(/ (* m (- 1 m)) v)
13.0ms
(- (/ (* m (- 1 m)) v) 1)

simplify1.7s

Counts
29 → 68
Calls
29 calls:
Slowest
676.0ms
(* (- (pow (/ (* m (- 1 m)) v) 3) (pow 1 3)) m)
127.0ms
(- (/ (pow m 2) v) (+ m (/ (pow m 3) v)))
117.0ms
(* (cbrt (- (/ (* m (- 1 m)) v) 1)) (cbrt (- (/ (* m (- 1 m)) v) 1)))
98.0ms
(sqrt (- (/ (* m (- 1 m)) v) 1))
96.0ms
(* (- (* (/ (* m (- 1 m)) v) (/ (* m (- 1 m)) v)) (* 1 1)) m)

prune562.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

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))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
6×sub-neg
5×add-cube-cbrt
5×add-exp-log
5×add-cbrt-cube
5×*-un-lft-identity
5×pow1
5×add-sqr-sqrt
4×flip--
4×associate--l+
4×associate-*l*
4×flip3--
4×distribute-lft-in
4×distribute-rgt-in
3×add-log-exp
3×associate-*r*
2×associate-*r/
2×frac-times
1×div-inv
1×cbrt-unprod
1×*-commutative
1×prod-exp
1×associate-*l/
1×pow-prod-down
Counts
3 → 53
Calls
3 calls:
Slowest
14.0ms
(- (* (/ m v) (- m (* m m))) m)
7.0ms
(* (/ m v) (- m (* m m)))
1.0ms
(- m (* m m))

series97.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
39.0ms
(* (/ m v) (- m (* m m)))
32.0ms
(- m (* m m))
26.0ms
(- (* (/ m v) (- m (* m m))) m)

simplify1.7s

Counts
32 → 62
Calls
32 calls:
Slowest
298.0ms
(* v (+ (* m m) (+ (* (* m m) (* m m)) (* m (* m m)))))
188.0ms
(* m (- (* m m) (* (* m m) (* m m))))
179.0ms
(+ (* m m) (+ (* (* m m) (* m m)) (* m (* m m))))
166.0ms
(* m (- (pow m 3) (pow (* m m) 3)))
123.0ms
(* (/ m v) (- m (* m m)))

prune563.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt (/ m v)) (* (sqrt (/ m v)) (- m (* m m))))
0.3b
(* (sqrt (/ m v)) (- m (* m m)))
0.1b
(sqrt (/ m v))
0.1b
(sqrt (/ m v))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
17×sqrt-div
16×sqrt-prod
14×associate-*l*
13×add-sqr-sqrt
11×add-cube-cbrt
11×add-exp-log
11×associate-*r/
11×add-cbrt-cube
11×*-un-lft-identity
11×pow1
11×frac-times
10×distribute-lft-in
10×distribute-rgt-in
6×flip--
6×flip3--
6×sub-neg
4×add-log-exp
4×div-inv
4×cbrt-unprod
4×prod-exp
4×associate-*l/
4×pow-prod-down
4×associate-*r*
2×*-commutative
2×pow1/2
2×rem-sqrt-square
Counts
4 → 99
Calls
4 calls:
Slowest
23.0ms
(* (sqrt (/ m v)) (* (sqrt (/ m v)) (- m (* m m))))
8.0ms
(* (sqrt (/ m v)) (- m (* m m)))
1.0ms
(sqrt (/ m v))
1.0ms
(sqrt (/ m v))

series189.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
71.0ms
(* (sqrt (/ m v)) (- m (* m m)))
45.0ms
(* (sqrt (/ m v)) (* (sqrt (/ m v)) (- m (* m m))))
37.0ms
(sqrt (/ m v))
37.0ms
(sqrt (/ m v))

simplify6.1s

Counts
84 → 111
Calls
84 calls:
Slowest
552.0ms
(* (* (* (sqrt (/ m v)) (sqrt (/ m v))) (sqrt (/ m v))) (* (* (- m (* m m)) (- m (* m m))) (- m (* m m))))
442.0ms
(* (sqrt m) (* (sqrt m) (- (pow m 3) (pow (* m m) 3))))
367.0ms
(* (sqrt v) (+ (* m m) (+ (* (* m m) (* m m)) (* m (* m m)))))
360.0ms
(* (sqrt v) (+ (* m m) (+ (* (* m m) (* m m)) (* m (* m m)))))
313.0ms
(* (sqrt m) (- (* m m) (* (* m m) (* m m))))

prune905.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize1.0ms

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))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
6×sub-neg
5×add-cube-cbrt
5×add-exp-log
5×add-cbrt-cube
5×*-un-lft-identity
5×pow1
5×add-sqr-sqrt
4×flip--
4×associate--l+
4×associate-*l*
4×flip3--
4×distribute-lft-in
4×distribute-rgt-in
3×add-log-exp
3×associate-*r*
2×associate-*r/
2×frac-times
1×div-inv
1×cbrt-unprod
1×*-commutative
1×prod-exp
1×associate-*l/
1×pow-prod-down
Counts
3 → 53
Calls
3 calls:
Slowest
9.0ms
(- (* (/ m v) (- m (* m m))) m)
4.0ms
(* (/ m v) (- m (* m m)))
1.0ms
(- m (* m m))

series73.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
30.0ms
(* (/ m v) (- m (* m m)))
26.0ms
(- m (* m m))
17.0ms
(- (* (/ m v) (- m (* m m))) m)

simplify1.7s

Counts
32 → 62
Calls
32 calls:
Slowest
307.0ms
(* v (+ (* m m) (+ (* (* m m) (* m m)) (* m (* m m)))))
191.0ms
(+ (* m m) (+ (* (* m m) (* m m)) (* m (* m m))))
172.0ms
(* m (- (* m m) (* (* m m) (* m m))))
141.0ms
(* m (- (pow m 3) (pow (* m m) 3)))
121.0ms
(- (/ (pow m 2) v) (+ m (/ (pow m 3) v)))

prune411.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes147.0ms

Accuracy

0% (0.2b remaining)

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

bsearch2.0ms

end0.0ms

sample2.1s

Algorithm
intervals
Results
1.3s13704×body80valid
507.0ms13704×pre80true