Details

analyze1.1s (20.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
6.2%	93.6%	0.1%	7
9.4%	90.5%	0.1%	8
14%	85.8%	0.1%	9
19.5%	80.4%	0.1%	10
20.7%	79.2%	0.1%	11
22%	77.8%	0.1%	12
23.5%	76.4%	0.1%	13
23.8%	76%	0.1%	14

sample89.0ms (1.7%)

Algorithm

1×

intervals

Results

50.0ms	98×	body	1280	valid
15.0ms	51×	body	640	valid
6.0ms	33×	body	320	valid
4.0ms	67×	body	80	valid
1.0ms	7×	body	160	valid

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	9
1	20	9

prune12.0ms (0.2%)

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: 17.8b

Counts

2 → 2

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
3.2b	(cos (+ a b))

rewrite14.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
5×	`pow1`
3×	`times-frac` `associate-r` `associate-l` `associate-/r*` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
1×	`cos-sum` `frac-2neg` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l` `unswap-sqr`

Counts

3 → 47

Calls

3 calls:

5.0ms	(/ (* r (sin b)) (cos (+ a b)))
4.0ms	(cos (+ a b))
4.0ms	(* r (sin b))

series42.0ms (0.8%)

Counts

3 → 9

Calls

3 calls:

25.0ms	(/ (* r (sin b)) (cos (+ a b)))
11.0ms	(* r (sin b))
6.0ms	(cos (+ a b))

simplify55.0ms (1%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5357	439

prune96.0ms (1.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	51	5	56
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	52	6	58

Merged error: 0.2b

Counts

58 → 6

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(* (cos a) (cos b))
0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.2b	(* (sin a) (sin b))

rewrite25.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`add-exp-log` `add-cbrt-cube`
12×	`add-cube-cbrt` `*-un-lft-identity`
10×	`pow1`
9×	`associate-r` `associate-l`
4×	`prod-exp` `associate-/r/` `cbrt-unprod` `add-log-exp`
3×	`times-frac` `pow-prod-down` `associate-/r` `cos-mult` `-commutative` `sin-mult` `unswap-sqr`
2×	`cbrt-undiv` `div-exp`
1×	`flip3--` `frac-2neg` `clear-num` `frac-sub` `flip--` `div-inv` `associate-/l*` `sub-div`

Counts

4 → 81

Calls

4 calls:

10.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
4.0ms	(* (sin a) (sin b))
4.0ms	(* (cos a) (cos b))
4.0ms	(* r (sin b))

series77.0ms (1.5%)

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
10.0ms	(* (sin a) (sin b))
8.0ms	(* (cos a) (cos b))
7.0ms	(* r (sin b))

simplify39.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4976	875
1	4976	875

prune178.0ms (3.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	82	11	93
Fresh	5	0	5
Picked	1	0	1
Done	0	0	0
Total	88	11	99

Merged error: 0.0b

Counts

99 → 11

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(- (* (/ (cos a) (sin b)) (cos b)) (sin a))
0.2b	(* (/ (cos a) (sin b)) (cos b))
0.2b	(/ (cos a) (sin b))
0.2b	(/ r (- (* (/ (cos a) (sin b)) (cos b)) (sin a)))

rewrite28.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
28×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
13×	`add-exp-log` `associate-l` `add-cbrt-cube`
6×	`pow1` `associate-/r` `associate-/l` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-r` `div-inv`
2×	`flip3--` `frac-2neg` `prod-exp` `clear-num` `associate-/r/` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `diff-log` `pow-prod-down` `associate-l/` `-commutative`

Counts

4 → 99

Calls

4 calls:

8.0ms	(/ r (- (* (/ (cos a) (sin b)) (cos b)) (sin a)))
6.0ms	(* (/ (cos a) (sin b)) (cos b))
6.0ms	(- (* (/ (cos a) (sin b)) (cos b)) (sin a))
4.0ms	(/ (cos a) (sin b))

series96.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

49.0ms	(/ r (- (* (/ (cos a) (sin b)) (cos b)) (sin a)))
20.0ms	(- (* (/ (cos a) (sin b)) (cos b)) (sin a))
17.0ms	(* (/ (cos a) (sin b)) (cos b))
10.0ms	(/ (cos a) (sin b))

simplify48.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4937	1443
1	4937	1443

prune171.0ms (3.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	108	3	111
Fresh	4	6	10
Picked	0	1	1
Done	0	0	0
Total	112	10	122

Merged error: 0b

Counts

122 → 10

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(/ (cos b) (sin b))
0.2b	(* (cos a) (/ (cos b) (sin b)))
0.2b	(* r (/ 1 (- (* (cos a) (/ (cos b) (sin b))) (sin a))))
0.3b	(/ 1 (- (* (cos a) (/ (cos b) (sin b))) (sin a)))

rewrite40.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
39×	`times-frac`
37×	`*-un-lft-identity`
36×	`add-cube-cbrt`
28×	`associate-r`
24×	`add-exp-log`
18×	`add-cbrt-cube`
9×	`pow1`
6×	`div-exp` `associate-l` `prod-exp` `associate-/r` `associate-/l`
5×	`unswap-sqr`
4×	`cbrt-undiv` `associate-/r/` `cbrt-unprod` `div-inv` `add-log-exp`
2×	`rec-exp` `flip3--` `frac-2neg` `1-exp` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `flip--`
1×	`pow-flip` `un-div-inv` `inv-pow`

Counts

4 → 130

Calls

4 calls:

13.0ms	(* r (/ 1 (- (* (cos a) (/ (cos b) (sin b))) (sin a))))
9.0ms	(* (cos a) (/ (cos b) (sin b)))
9.0ms	(/ 1 (- (* (cos a) (/ (cos b) (sin b))) (sin a)))
4.0ms	(/ (cos b) (sin b))

series100.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

46.0ms	(* r (/ 1 (- (* (cos a) (/ (cos b) (sin b))) (sin a))))
28.0ms	(/ 1 (- (* (cos a) (/ (cos b) (sin b))) (sin a)))
19.0ms	(* (cos a) (/ (cos b) (sin b)))
6.0ms	(/ (cos b) (sin b))

simplify65.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	6001	1856

prune166.0ms (3.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	142	10	152

Merged error: 0b

Counts

152 → 10

regimes255.0ms (4.8%)

Accuracy

Total 0.3b remaining (86.2%)

Threshold costs 0.3b (86.2%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	13
1	22	13

end0.0ms (0%)

sample2.5s (48%)

Algorithm

1×

intervals

Results

1.4s	2883×	body	1280	valid
534.0ms	1859×	body	640	valid
159.0ms	792×	body	320	valid
145.0ms	2096×	body	80	valid
59.0ms	370×	body	160	valid
0.0ms	1×	body	80	invalid

Details

analyze1.1s (20.6%)

sample89.0ms (1.7%)

simplify3.0ms (0%)

prune12.0ms (0.2%)

localize11.0ms (0.2%)

rewrite14.0ms (0.3%)

series42.0ms (0.8%)

simplify55.0ms (1%)

prune96.0ms (1.8%)

localize17.0ms (0.3%)

rewrite25.0ms (0.5%)

series77.0ms (1.5%)

simplify39.0ms (0.7%)

prune178.0ms (3.4%)

localize15.0ms (0.3%)

rewrite28.0ms (0.5%)

series96.0ms (1.8%)

simplify48.0ms (0.9%)

prune171.0ms (3.2%)

localize17.0ms (0.3%)

rewrite40.0ms (0.8%)

series100.0ms (1.9%)

simplify65.0ms (1.2%)

prune166.0ms (3.1%)

regimes255.0ms (4.8%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample2.5s (48%)

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