Details

sample331.0ms

Algorithm

intervals

Results

10.0ms	39×	body	2560	valid
10.0ms	175×	body	80	valid
6.0ms	27×	body	1280	valid
4.0ms	100×	body	80	nan
3.0ms	15×	body	640	valid
1.0ms	8×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	1×	body	160	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	7
1	22	7
2	25	7
3	27	7
4	29	7
5	29	7

prune23.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 35.9b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.2b	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
25.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `times-frac`
10×	`distribute-lft-out` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in` `associate-/l*`
3×	`associate-/r*` `sqrt-prod`
2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 80

Calls

4 calls:

11.0ms	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series268.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
72.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
33.0ms	(- (* b_2 b_2) (* a c))
74.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify42.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	358	790
1	1261	727
2	5001	705

prune222.0ms

Filtered

92 candidates to 69 candidates (75.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	81	11	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	11	93

Merged error: 7.4b

Counts

93 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
1.0b	(- (* b_2 b_2) (* a c))
25.3b	(sqrt (- (* b_2 b_2) (* a c)))
25.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite16.0ms

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:

4.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(- (* b_2 b_2) (* a c))
3.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series187.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (* b_2 b_2) (* a c))
36.0ms	(- (* b_2 b_2) (* a c))
57.0ms	(sqrt (- (* b_2 b_2) (* a c)))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify52.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (46.0ms)

Iter	Nodes	Cost
0	140	390
1	455	366
2	1490	364
3	5002	360

prune196.0ms

Filtered

66 candidates to 50 candidates (75.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	66	11	77

Merged error: 7.4b

Counts

77 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
25.3b	(sqrt (- (* b_2 b_2) (* a c)))
25.3b	(sqrt (- (* b_2 b_2) (* a c)))
25.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div` `add-log-exp`
4×	`add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `diff-log`

Counts

4 → 57

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series216.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (* b_2 b_2) (* a c))
57.0ms	(sqrt (- (* b_2 b_2) (* a c)))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify53.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 3 (47.0ms)

Iter	Nodes	Cost
0	140	423
1	455	403
2	1490	400
3	5002	394

prune215.0ms

Filtered

69 candidates to 55 candidates (79.7%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	69	11	80

Merged error: 7.4b

Counts

80 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
25.3b	(sqrt (- (* b_2 b_2) (* a c)))
25.3b	(sqrt (- (* b_2 b_2) (* a c)))
25.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div` `add-log-exp`
4×	`add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `diff-log`

Counts

4 → 57

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series215.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* b_2 b_2) (* a c))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))
59.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify51.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 3 (46.0ms)

Iter	Nodes	Cost
0	140	423
1	455	403
2	1490	400
3	5002	394

prune204.0ms

Filtered

69 candidates to 55 candidates (79.7%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	69	11	80

Merged error: 7.4b

Counts

80 → 11

Details

sample331.0ms

simplify15.0ms

prune23.0ms

localize12.0ms

rewrite31.0ms

series268.0ms

simplify42.0ms

prune222.0ms

localize12.0ms

rewrite16.0ms

series187.0ms

simplify52.0ms

prune196.0ms

localize14.0ms

rewrite16.0ms

series216.0ms

simplify53.0ms

prune215.0ms

localize14.0ms

rewrite19.0ms

series215.0ms

simplify51.0ms

prune204.0ms

regimes360.0ms

bsearch4.0ms

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