Details

analyze8.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	25%	75%	0
0%	25%	75%	1
0%	12.5%	87.5%	2
0%	6.3%	93.7%	3
0%	3.1%	96.9%	4
0%	1.6%	98.4%	5
0%	0.8%	99.2%	6
0%	0.4%	99.6%	7
0%	0.2%	99.8%	8
0.1%	0.1%	99.8%	9
0.1%	0%	99.9%	10
0.1%	0%	99.9%	11
0.1%	0%	99.9%	12
0.1%	0%	99.9%	13
0.1%	0%	99.9%	14

sample66.0ms (1.4%)

Algorithm

1×

intervals

Results

51.0ms	256×	body	80	valid
3.0ms	265×	pre	80	true
2.0ms	9×	body	80	invalid

simplify21.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5216	49

prune17.0ms (0.3%)

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: 2.9b

Counts

2 → 2

localize29.0ms (0.6%)

Local error

Found 4 expressions with local error:

1.0b	(sqrt PI)
1.1b	(pow (/ 1.0 (fabs x)) 5)
1.4b	(pow (/ 1.0 (fabs x)) 7)
2.6b	(exp (* (fabs x) (fabs x)))

rewrite14.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`unpow-prod-down`
22×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
10×	`add-exp-log`
7×	`pow1`
6×	`pow-unpow` `add-log-exp`
4×	`pow-exp` `add-cbrt-cube`
3×	`sqrt-prod`
2×	`pow-to-exp` `pow-pow` `div-exp` `div-inv` `sqr-pow`
1×	`rem-sqrt-square` `exp-prod` `exp-to-pow` `sqrt-pow1` `pow1/2` `rem-exp-log`

Counts

4 → 79

Calls

4 calls:

4.0ms	(pow (/ 1.0 (fabs x)) 5)
4.0ms	(pow (/ 1.0 (fabs x)) 7)
2.0ms	(exp (* (fabs x) (fabs x)))
1.0ms	(sqrt PI)

series40.0ms (0.8%)

Counts

4 → 10

Calls

4 calls:

15.0ms	(pow (/ 1.0 (fabs x)) 5)
14.0ms	(pow (/ 1.0 (fabs x)) 7)
10.0ms	(exp (* (fabs x) (fabs x)))
0.0ms	(sqrt PI)

simplify37.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5430	802

prune400.0ms (8.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	76	13	89
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	78	13	91

Merged error: 1.0b

Counts

91 → 13

localize37.0ms (0.8%)

Local error

Found 4 expressions with local error:

1.0b	(sqrt PI)
1.1b	(pow (/ 1.0 (fabs x)) 5)
1.1b	(pow (exp (fabs x)) (fabs x))
1.4b	(pow (/ 1.0 (fabs x)) 7)

rewrite16.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`unpow-prod-down`
25×	`add-sqr-sqrt`
24×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
10×	`add-exp-log`
9×	`pow-unpow`
8×	`pow1`
6×	`pow-pow`
5×	`pow-exp`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow-to-exp` `exp-prod` `sqrt-prod` `sqr-pow`
2×	`div-exp` `div-inv`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 89

Calls

4 calls:

4.0ms	(pow (/ 1.0 (fabs x)) 7)
4.0ms	(pow (/ 1.0 (fabs x)) 5)
3.0ms	(pow (exp (fabs x)) (fabs x))
1.0ms	(sqrt PI)

series55.0ms (1.1%)

Counts

4 → 10

Calls

4 calls:

28.0ms	(pow (exp (fabs x)) (fabs x))
14.0ms	(pow (/ 1.0 (fabs x)) 7)
12.0ms	(pow (/ 1.0 (fabs x)) 5)
0.0ms	(sqrt PI)

simplify42.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5007	843

prune448.0ms (9.3%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	91	8	99
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	94	18	112

Merged error: 0.6b

Counts

112 → 18

localize44.0ms (0.9%)

Local error

Found 4 expressions with local error:

1.0b	(cbrt 5)
1.1b	(pow (exp (fabs x)) (fabs x))
1.3b	(pow (pow (/ 1.0 (fabs x)) (* (cbrt 5) (cbrt 5))) (cbrt 5))
1.4b	(pow (/ 1.0 (fabs x)) 7)

rewrite18.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`unpow-prod-down`
26×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
12×	`pow-unpow`
11×	`add-exp-log`
9×	`pow-exp`
6×	`pow1` `cbrt-prod` `pow-pow`
4×	`pow-to-exp` `add-cbrt-cube` `add-log-exp` `sqr-pow`
3×	`exp-prod`
2×	`div-exp` `div-inv`
1×	`pow1/3`

Counts

4 → 96

Calls

4 calls:

6.0ms	(pow (pow (/ 1.0 (fabs x)) (* (cbrt 5) (cbrt 5))) (cbrt 5))
4.0ms	(pow (/ 1.0 (fabs x)) 7)
3.0ms	(pow (exp (fabs x)) (fabs x))
1.0ms	(cbrt 5)

series110.0ms (2.3%)

Counts

4 → 10

Calls

4 calls:

65.0ms	(pow (pow (/ 1.0 (fabs x)) (* (cbrt 5) (cbrt 5))) (cbrt 5))
29.0ms	(pow (exp (fabs x)) (fabs x))
15.0ms	(pow (/ 1.0 (fabs x)) 7)
0.0ms	(cbrt 5)

simplify58.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4950	1279
1	4950	1279

prune625.0ms (12.9%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	101	5	106
Fresh	5	12	17
Picked	1	0	1
Done	0	0	0
Total	107	17	124

Merged error: 0.6b

Counts

124 → 17

localize49.0ms (1%)

Local error

Found 4 expressions with local error:

1.0b	(cbrt 5)
1.0b	(cbrt 5)
1.1b	(pow (exp (fabs x)) (fabs x))
1.3b	(pow (pow (/ 1.0 (fabs x)) (* (cbrt 5) (cbrt 5))) (cbrt 5))

rewrite14.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`unpow-prod-down`
19×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`cbrt-prod` `pow-unpow` `times-frac`
8×	`add-exp-log`
7×	`pow-exp`
5×	`pow1` `pow-pow`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow-to-exp` `exp-prod` `sqr-pow`
2×	`pow1/3`
1×	`div-exp` `div-inv`

Counts

4 → 79

Calls

4 calls:

7.0ms	(pow (pow (/ 1.0 (fabs x)) (* (cbrt 5) (cbrt 5))) (cbrt 5))
3.0ms	(pow (exp (fabs x)) (fabs x))
1.0ms	(cbrt 5)
1.0ms	(cbrt 5)

series93.0ms (1.9%)

Counts

4 → 8

Calls

4 calls:

65.0ms	(pow (pow (/ 1.0 (fabs x)) (* (cbrt 5) (cbrt 5))) (cbrt 5))
27.0ms	(pow (exp (fabs x)) (fabs x))
0.0ms	(cbrt 5)
0.0ms	(cbrt 5)

simplify71.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4916	1000
1	4916	1000

prune422.0ms (8.7%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	83	4	87
Fresh	5	11	16
Picked	0	1	1
Done	0	0	0
Total	88	16	104

Merged error: 0.6b

Counts

104 → 16

regimes237.0ms (4.9%)

Accuracy

Total 0.7b remaining (53.1%)

Threshold costs 0.7b (53.1%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	56
1	43	56

end0.0ms (0%)

sample1.9s (38.5%)

Algorithm

1×

intervals

Results

1.6s	8000×	body	80	valid
93.0ms	8135×	pre	80	true
29.0ms	135×	body	80	invalid

Details

analyze8.0ms (0.2%)

sample66.0ms (1.4%)

simplify21.0ms (0.4%)

prune17.0ms (0.3%)

localize29.0ms (0.6%)

rewrite14.0ms (0.3%)

series40.0ms (0.8%)

simplify37.0ms (0.8%)

prune400.0ms (8.3%)

localize37.0ms (0.8%)

rewrite16.0ms (0.3%)

series55.0ms (1.1%)

simplify42.0ms (0.9%)

prune448.0ms (9.3%)

localize44.0ms (0.9%)

rewrite18.0ms (0.4%)

series110.0ms (2.3%)

simplify58.0ms (1.2%)

prune625.0ms (12.9%)

localize49.0ms (1%)

rewrite14.0ms (0.3%)

series93.0ms (1.9%)

simplify71.0ms (1.5%)

prune422.0ms (8.7%)

regimes237.0ms (4.9%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample1.9s (38.5%)

Profiling