Details

Time bar (total: 3.3s)

sample48.0ms

Algorithm
intervals
Results
10.0ms39×body2560valid
8.0ms175×body80valid
6.0ms27×body1280valid
4.0ms100×body80nan
3.0ms15×body640valid
1.0ms8×body320valid
1.0ms2×body5120valid
0.0ms1×body160valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0219
1429
2769
3949
41029
51029

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 35.9b

Counts
2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 3.0 a) c)
0.2b
(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.0b
(- (* b b) (* (* 3.0 a) c))
25.3b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1 *-un-lft-identity add-log-exp
9×add-exp-log add-cbrt-cube
7×add-sqr-sqrt
6×add-cube-cbrt
3×associate-*r* pow-prod-down prod-exp sqrt-prod cbrt-unprod
2×flip3-- sqrt-div sum-log flip-- distribute-lft-out
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 flip3-+ pow1/2 diff-log associate-*l* neg-log *-commutative flip-+
Counts
4 → 60
Calls
4 calls:
5.0ms
(* (* 3.0 a) c)
8.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.0ms
(- (* b b) (* (* 3.0 a) c))
3.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series214.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(* (* 3.0 a) c)
79.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
44.0ms
(- (* b b) (* (* 3.0 a) c))
72.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify41.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0307469
11303428
25001417

prune166.0ms

Filtered
72 candidates to 52 candidates (72.2%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New64872
Fresh000
Picked011
Done000
Total64973

Merged error: 14.4b

Counts
73 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* (* 3.0 a) c))
1.0b
(- (* b b) (* (* 3.0 a) c))
25.3b
(sqrt (- (* b b) (* (* 3.0 a) c)))
25.3b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log flip3-- sqrt-div add-cbrt-cube flip--
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
Counts
4 → 54
Calls
4 calls:
3.0ms
(- (* b b) (* (* 3.0 a) c))
3.0ms
(- (* b b) (* (* 3.0 a) c))
3.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series221.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(- (* b b) (* (* 3.0 a) c))
45.0ms
(- (* b b) (* (* 3.0 a) c))
67.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
66.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify77.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 3 (71.0ms)

IterNodesCost
0149476
1576446
22486444
35001440

prune265.0ms

Filtered
66 candidates to 50 candidates (75.8%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New66066
Fresh077
Picked011
Done011
Total66975

Merged error: 14.4b

Counts
75 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* (* 3.0 a) c))
12.7b
(+ (neg b) (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c))))))
25.3b
(sqrt (- (* b b) (* (* 3.0 a) c)))
25.3b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
10×add-log-exp
8×add-sqr-sqrt
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log sqrt-div add-cbrt-cube
3×flip3-- flip--
2×rem-sqrt-square sqrt-pow1 pow1/2 sum-log
1×+-commutative neg-sub0 associate-+l- sub-neg flip3-+ diff-log neg-log flip-+
Counts
4 → 55
Calls
4 calls:
4.0ms
(- (* b b) (* (* 3.0 a) c))
4.0ms
(+ (neg b) (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c))))))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series269.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(- (* b b) (* (* 3.0 a) c))
77.0ms
(+ (neg b) (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c))))))
66.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
79.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify134.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 3 (127.0ms)

IterNodesCost
0251648
11020537
24512523
35002521

prune203.0ms

Filtered
67 candidates to 51 candidates (76.1%)
Pruning

11 alts after pruning (8 fresh and 3 done)

PrunedKeptTotal
New64367
Fresh156
Picked011
Done022
Total651176

Merged error: 14.4b

Counts
76 → 11

localize25.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* (* 3.0 a) c))
3.3b
(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
14.5b
(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
25.3b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
80×add-sqr-sqrt
79×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
20×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
13×sqrt-prod
10×distribute-rgt-neg-in
8×associate-/r*
7×cbrt-undiv div-exp
6×associate-/r/ add-log-exp
5×pow1 flip3-- flip--
4×div-inv
3×associate-/l/
2×frac-2neg sqrt-div prod-exp clear-num cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 148
Calls
4 calls:
3.0ms
(- (* b b) (* (* 3.0 a) c))
20.0ms
(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
14.0ms
(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
6.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series435.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(- (* b b) (* (* 3.0 a) c))
141.0ms
(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
181.0ms
(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
66.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify112.0ms

Algorithm
egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 2 (91.0ms)

IterNodesCost
06352579
130872333
250012320

prune361.0ms

Filtered
160 candidates to 106 candidates (66.3%)
Pruning

18 alts after pruning (15 fresh and 3 done)

PrunedKeptTotal
New1528160
Fresh077
Picked101
Done033
Total15318171

Merged error: 13.6b

Counts
171 → 18

regimes566.0ms

bsearch4.0ms

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