Details

analyze340.0ms (7.8%)

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
12.5%	87.4%	0.1%	4
18.7%	81.2%	0.1%	5
21.9%	78%	0.1%	6
50%	43.7%	6.3%	7
50%	43.7%	6.3%	8
56.2%	34.3%	9.5%	9
56.2%	34.3%	9.5%	10
59.3%	29.7%	11%	11
59.3%	29.7%	11%	12
60.9%	27.3%	11.8%	13
60.9%	27.3%	11.8%	14

sample80.0ms (1.8%)

Algorithm

1×

intervals

Results

16.0ms	53×	body	1280	invalid
12.0ms	34×	body	1280	valid
8.0ms	39×	body	640	valid
7.0ms	38×	body	640	invalid
7.0ms	147×	body	80	valid
5.0ms	17×	body	160	invalid
4.0ms	84×	body	80	invalid
3.0ms	24×	body	320	valid
2.0ms	17×	body	320	invalid
1.0ms	12×	body	160	valid

simplify46.0ms (1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4909	7
1	4909	7

prune6.0ms (0.1%)

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: 0.3b

Counts

2 → 1

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/ (sinh y) y)
0.0b	(sinh y)
0.2b	(* (sin x) (/ (sinh y) y))

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 68

Calls

3 calls:

7.0ms	(* (sin x) (/ (sinh y) y))
3.0ms	(/ (sinh y) y)
1.0ms	(sinh y)

series44.0ms (1%)

Counts

3 → 9

Calls

3 calls:

21.0ms	(* (sin x) (/ (sinh y) y))
11.0ms	(sinh y)
11.0ms	(/ (sinh y) y)

simplify46.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4972	621
1	4972	621

prune87.0ms (2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	75	2	77
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	75	3	78

Merged error: 0.2b

Counts

78 → 3

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/ (sinh y) y)
0.0b	(* (sin x) (sqrt (/ (sinh y) y)))
0.2b	(sqrt (/ (sinh y) y))
0.2b	(sqrt (/ (sinh y) y))

rewrite23.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
41×	`sqrt-prod`
39×	`times-frac`
35×	`add-cube-cbrt` `*-un-lft-identity`
16×	`associate-r`
8×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`rem-sqrt-square` `div-inv` `add-log-exp`
3×	`sqrt-div` `associate-l` `associate-/r` `associate-/l` `unswap-sqr`
2×	`sqrt-pow1` `pow1/2`
1×	`cbrt-undiv` `sinh-def` `frac-2neg` `associate-r/` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `-commutative` `cbrt-unprod` `associate-/l/`

Counts

4 → 112

Calls

4 calls:

8.0ms	(* (sin x) (sqrt (/ (sinh y) y)))
5.0ms	(sqrt (/ (sinh y) y))
3.0ms	(/ (sinh y) y)
3.0ms	(sqrt (/ (sinh y) y))

series96.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (sin x) (sqrt (/ (sinh y) y)))
19.0ms	(sqrt (/ (sinh y) y))
19.0ms	(sqrt (/ (sinh y) y))
11.0ms	(/ (sinh y) y)

simplify57.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4964	1714
1	4964	1714

prune161.0ms (3.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	124	3	127

Merged error: 0.2b

Counts

127 → 3

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (* (pow y 3) 1/6) (+ y (* 1/120 (pow y 5)))) y)
0.0b	(* (sin x) (/ (+ (* (pow y 3) 1/6) (+ y (* 1/120 (pow y 5)))) y))
0.1b	(* 1/120 (pow y 5))
0.1b	(* (pow y 3) 1/6)

rewrite37.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
27×	`add-cube-cbrt` `*-un-lft-identity`
23×	`associate-r`
21×	`add-exp-log`
19×	`times-frac`
18×	`associate-l`
15×	`add-cbrt-cube`
9×	`unswap-sqr`
8×	`unpow-prod-down` `prod-exp`
6×	`pow1`
4×	`cube-prod` `cbrt-unprod` `add-log-exp` `sqr-pow`
3×	`associate-/r` `-commutative` `associate-/l*`
2×	`cbrt-undiv` `pow-to-exp` `div-exp` `pow-exp` `div-inv` `associate-/l/`
1×	`cube-mult` `frac-2neg` `flip3-+` `unpow3` `associate-*r/` `pow-prod-down` `clear-num` `flip-+`

Counts

4 → 117

Calls

4 calls:

12.0ms	(/ (+ (* (pow y 3) 1/6) (+ y (* 1/120 (pow y 5)))) y)
11.0ms	(* (sin x) (/ (+ (* (pow y 3) 1/6) (+ y (* 1/120 (pow y 5)))) y))
6.0ms	(* (pow y 3) 1/6)
5.0ms	(* 1/120 (pow y 5))

series54.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (sin x) (/ (+ (* (pow y 3) 1/6) (+ y (* 1/120 (pow y 5)))) y))
7.0ms	(/ (+ (* (pow y 3) 1/6) (+ y (* 1/120 (pow y 5)))) y)
5.0ms	(* 1/120 (pow y 5))
4.0ms	(* (pow y 3) 1/6)

simplify33.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	4964	1795
1	4964	1795

prune293.0ms (6.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	128	1	129
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	129	3	132

Merged error: 0.2b

Counts

132 → 3

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(* 1/120 (pow y 5))
0.1b	(* 1/6 (pow y 3))
0.3b	(log (* (sin x) (/ (+ (* 1/6 (pow y 3)) (+ y (* 1/120 (pow y 5)))) y)))
1.7b	(exp (log (* (sin x) (/ (+ (* 1/6 (pow y 3)) (+ y (* 1/120 (pow y 5)))) y))))

rewrite32.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
20×	`add-exp-log`
19×	`associate-r`
12×	`add-cube-cbrt` `*-un-lft-identity`
10×	`pow1`
8×	`unpow-prod-down` `prod-exp` `add-cbrt-cube`
7×	`unswap-sqr`
6×	`associate-l`
5×	`exp-prod`
4×	`cube-prod` `log-pow` `add-log-exp` `sqr-pow`
3×	`rem-log-exp`
2×	`pow-to-exp` `log-div` `log-prod` `associate-r/` `pow-prod-down` `pow-exp` `-commutative` `cbrt-unprod`
1×	`cube-mult` `exp-diff` `unpow3` `div-exp` `exp-sum` `rem-exp-log`

Counts

4 → 85

Calls

4 calls:

10.0ms	(exp (log (* (sin x) (/ (+ (* 1/6 (pow y 3)) (+ y (* 1/120 (pow y 5)))) y))))
9.0ms	(log (* (sin x) (/ (+ (* 1/6 (pow y 3)) (+ y (* 1/120 (pow y 5)))) y)))
6.0ms	(* 1/6 (pow y 3))
5.0ms	(* 1/120 (pow y 5))

series95.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

47.0ms	(log (* (sin x) (/ (+ (* 1/6 (pow y 3)) (+ y (* 1/120 (pow y 5)))) y)))
40.0ms	(exp (log (* (sin x) (/ (+ (* 1/6 (pow y 3)) (+ y (* 1/120 (pow y 5)))) y))))
5.0ms	(* 1/120 (pow y 5))
4.0ms	(* 1/6 (pow y 3))

simplify46.0ms (1%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5124	976

prune224.0ms (5.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	97	3	100

Merged error: 0.2b

Counts

100 → 3

regimes191.0ms (4.4%)

Accuracy

Total 0.0b remaining (6.2%)

Threshold costs 0.0b (6.2%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	7
1	7	7

end0.0ms (0%)

sample2.3s (53.1%)

Algorithm

1×

intervals

Results

504.0ms	1513×	body	1280	valid
423.0ms	1423×	body	1280	invalid
262.0ms	1261×	body	640	valid
250.0ms	1276×	body	640	invalid
214.0ms	4303×	body	80	valid
120.0ms	2403×	body	80	invalid
87.0ms	610×	body	320	valid
87.0ms	632×	body	320	invalid
34.0ms	313×	body	160	valid
29.0ms	298×	body	160	invalid

Details

analyze340.0ms (7.8%)

sample80.0ms (1.8%)

simplify46.0ms (1%)

prune6.0ms (0.1%)

localize6.0ms (0.1%)

rewrite13.0ms (0.3%)

series44.0ms (1%)

simplify46.0ms (1.1%)

prune87.0ms (2%)

localize9.0ms (0.2%)

rewrite23.0ms (0.5%)

series96.0ms (2.2%)

simplify57.0ms (1.3%)

prune161.0ms (3.7%)

localize13.0ms (0.3%)

rewrite37.0ms (0.9%)

series54.0ms (1.2%)

simplify33.0ms (0.8%)

prune293.0ms (6.7%)

localize17.0ms (0.4%)

rewrite32.0ms (0.7%)

series95.0ms (2.2%)

simplify46.0ms (1%)

prune224.0ms (5.1%)

regimes191.0ms (4.4%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample2.3s (53.1%)

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