Details

Time bar (total: 11.2s)

sample22.0ms

Algorithm
intervals
Results
7.0ms58×body1280valid
4.0ms38×body640valid
3.0ms133×body80valid
1.0ms20×body320valid
0.0ms7×body160valid

simplify20.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0126
1166
2196
3216
4276
5396
6586
7796
81076
91606
102776
113036
123036

prune1.0ms

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: 28.9b

Counts
2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ x (+ x 1.0))
0.0b
(/ (+ x 1.0) (- x 1.0))
1.9b
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
99×*-un-lft-identity
52×times-frac
45×add-sqr-sqrt
23×add-cube-cbrt
18×distribute-lft-out distribute-lft-out--
9×associate-/r* difference-of-squares
7×add-exp-log add-cbrt-cube associate-/l*
5×add-log-exp
4×associate-/r/
3×pow1
2×cbrt-undiv flip3-- frac-2neg flip3-+ div-exp clear-num flip-- flip-+ div-inv associate-/l/
1×sub-neg diff-log frac-sub
Counts
3 → 104
Calls
3 calls:
5.0ms
(/ x (+ x 1.0))
7.0ms
(/ (+ x 1.0) (- x 1.0))
31.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series203.0ms

Counts
3 → 9
Calls
3 calls:
33.0ms
(/ x (+ x 1.0))
42.0ms
(/ (+ x 1.0) (- x 1.0))
128.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify44.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0392760
11379726
25001716

prune196.0ms

Filtered
113 candidates to 76 candidates (67.3%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New1085113
Fresh000
Picked101
Done000
Total1095114

Merged error: 0.0b

Counts
114 → 5

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (- x 1.0))
0.0b
(/ x (+ x 1.0))
0.1b
(* (+ x 1.0) (/ 1 (- x 1.0)))
6.5b
(- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
58×*-un-lft-identity
54×add-sqr-sqrt
44×times-frac
33×add-cube-cbrt
21×associate-*r*
19×add-exp-log
13×add-cbrt-cube
9×associate-/r*
7×pow1 distribute-lft-out-- difference-of-squares
6×associate-/r/ frac-sub associate-/l* add-log-exp
5×flip3-+ div-exp flip-+ distribute-lft-out
4×frac-times associate-*l* associate-*l/ prod-exp
3×cbrt-undiv flip3-- flip-- div-inv unswap-sqr
2×rec-exp frac-2neg 1-exp associate-*r/ clear-num un-div-inv cbrt-unprod
1×sub-neg pow-flip diff-log pow-prod-down *-commutative inv-pow
Counts
4 → 141
Calls
4 calls:
5.0ms
(/ 1 (- x 1.0))
5.0ms
(/ x (+ x 1.0))
12.0ms
(* (+ x 1.0) (/ 1 (- x 1.0)))
9.0ms
(- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

series238.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(/ 1 (- x 1.0))
38.0ms
(/ x (+ x 1.0))
37.0ms
(* (+ x 1.0) (/ 1 (- x 1.0)))
138.0ms
(- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

simplify74.0ms

Algorithm
egg-herbie
Counts
153 → 153
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
0576948
12837860
25001818

prune188.0ms

Filtered
153 candidates to 98 candidates (64.1%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New1530153
Fresh044
Picked011
Done000
Total1535158

Merged error: 0.0b

Counts
158 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (+ x 1.0))
0.3b
(cbrt (+ x 1.0))
0.3b
(cbrt (+ x 1.0))
18.8b
(- (/ x (+ x 1.0)) (* (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ (cbrt (+ x 1.0)) (- x 1.0))))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
30×cbrt-div
17×frac-sub
16×frac-times
15×flip3-+ flip-+
13×*-un-lft-identity
12×cbrt-prod associate-*l/
7×add-sqr-sqrt add-cube-cbrt
6×add-log-exp
5×associate-*r/
4×pow1 add-exp-log add-cbrt-cube
3×pow1/3 distribute-lft-out
1×sub-neg flip3-- diff-log flip--
Counts
4 → 71
Calls
4 calls:
3.0ms
(cbrt (+ x 1.0))
3.0ms
(cbrt (+ x 1.0))
3.0ms
(cbrt (+ x 1.0))
12.0ms
(- (/ x (+ x 1.0)) (* (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ (cbrt (+ x 1.0)) (- x 1.0))))

series398.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(cbrt (+ x 1.0))
88.0ms
(cbrt (+ x 1.0))
89.0ms
(cbrt (+ x 1.0))
132.0ms
(- (/ x (+ x 1.0)) (* (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ (cbrt (+ x 1.0)) (- x 1.0))))

simplify55.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
05511195
117111125
250021113

prune205.0ms

Filtered
83 candidates to 67 candidates (80.7%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New82183
Fresh123
Picked011
Done011
Total83588

Merged error: 0.0b

Counts
88 → 5

localize26.0ms

Local error

Found 4 expressions with local error:

6.4b
(/ (- (* x (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (* (+ x 1.0) (* (* (cbrt (- (* x x) (* 1.0 1.0))) (cbrt (- (* x x) (* 1.0 1.0)))) (/ (cbrt (+ x 1.0)) (- x 1.0))))) (* (+ x 1.0) (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))))
16.2b
(cbrt (- (* x x) (* 1.0 1.0)))
16.2b
(cbrt (- (* x x) (* 1.0 1.0)))
22.5b
(- (* x (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (* (+ x 1.0) (* (* (cbrt (- (* x x) (* 1.0 1.0))) (cbrt (- (* x x) (* 1.0 1.0)))) (/ (cbrt (+ x 1.0)) (- x 1.0)))))

rewrite344.0ms

Algorithm
rewrite-expression-head
Rules
2464×cbrt-div
1764×frac-times
1586×associate-*r/
1234×flip3-- flip--
848×frac-sub
828×associate-*l/
426×associate-/l/
297×flip3-+ flip-+
26×associate-/r/
13×add-exp-log
11×add-cbrt-cube
8×cbrt-prod add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×add-log-exp
4×pow1
3×cbrt-undiv times-frac div-exp prod-exp cbrt-unprod associate-/l*
2×pow1/3 difference-of-squares
1×sub-neg frac-2neg diff-log div-sub clear-num associate-/r* div-inv
Counts
4 → 940
Calls
4 calls:
87.0ms
(/ (- (* x (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (* (+ x 1.0) (* (* (cbrt (- (* x x) (* 1.0 1.0))) (cbrt (- (* x x) (* 1.0 1.0)))) (/ (cbrt (+ x 1.0)) (- x 1.0))))) (* (+ x 1.0) (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))))
4.0ms
(cbrt (- (* x x) (* 1.0 1.0)))
4.0ms
(cbrt (- (* x x) (* 1.0 1.0)))
37.0ms
(- (* x (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (* (+ x 1.0) (* (* (cbrt (- (* x x) (* 1.0 1.0))) (cbrt (- (* x x) (* 1.0 1.0)))) (/ (cbrt (+ x 1.0)) (- x 1.0)))))

series1.1s

Counts
4 → 12
Calls
4 calls:
468.0ms
(/ (- (* x (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (* (+ x 1.0) (* (* (cbrt (- (* x x) (* 1.0 1.0))) (cbrt (- (* x x) (* 1.0 1.0)))) (/ (cbrt (+ x 1.0)) (- x 1.0))))) (* (+ x 1.0) (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))))
189.0ms
(cbrt (- (* x x) (* 1.0 1.0)))
193.0ms
(cbrt (- (* x x) (* 1.0 1.0)))
260.0ms
(- (* x (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (* (+ x 1.0) (* (* (cbrt (- (* x x) (* 1.0 1.0))) (cbrt (- (* x x) (* 1.0 1.0)))) (/ (cbrt (+ x 1.0)) (- x 1.0)))))

simplify433.0ms

Algorithm
egg-herbie
Counts
952 → 952
Iterations

Useful iterations: 0 (31.0ms)

IterNodesCost
0500248256

prune7.5s

Filtered
952 candidates to 946 candidates (99.4%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New9511952
Fresh022
Picked101
Done202
Total9543957

Merged error: 0.0b

Counts
957 → 3

regimes30.0ms

bsearch3.0ms

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