Details

analyze1.1s (11%)

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
25%	62.4%	12.6%	5
25%	56.2%	18.8%	6
28.1%	50%	22%	7
28.1%	46.8%	25.1%	8
29.7%	41.4%	29%	9
29.7%	39.4%	30.9%	10
31.1%	35.8%	33.1%	11
31.1%	34.4%	34.5%	12
31.5%	32.9%	35.6%	13
31.5%	32.1%	36.4%	14

sample199.0ms (2%)

Algorithm

1×

intervals

Results

68.0ms	122×	body	1280	valid
32.0ms	26×	body	1280	nan
19.0ms	43×	body	640	valid
17.0ms	26×	body	640	nan
14.0ms	81×	body	80	overflowed
8.0ms	24×	body	320	valid
7.0ms	17×	body	320	nan
5.0ms	56×	body	80	valid
4.0ms	4×	body	1280	invalid
3.0ms	5×	body	640	invalid
2.0ms	9×	body	160	nan
2.0ms	11×	body	160	valid
1.0ms	3×	body	320	invalid
1.0ms	20×	body	80	nan
1.0ms	3×	body	160	invalid
1.0ms	6×	body	80	invalid

simplify58.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4977	13
1	4977	13

prune5.0ms (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: 32.7b

Counts

2 → 1

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(pow.f64 (+.f64 x 1.0) (/.f64 1.0 n))
0.0b	(pow.f64 x (/.f64 1.0 n))
2.3b	(-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n)))

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64`
28×	`*-un-lft-identity_binary64`
26×	`pow-unpow_binary64`
19×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`
17×	`unpow-prod-down_binary64`
9×	`difference-of-squares_binary64`
8×	`sqr-pow_binary64`
5×	`add-log-exp_binary64` `pow1_binary64` `add-exp-log_binary64`
3×	`add-cbrt-cube_binary64` `distribute-lft-out--_binary64`
2×	`pow-to-exp_binary64` `distribute-lft-out_binary64` `pow-pow_binary64` `div-inv_binary64` `pow-exp_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `flip--_binary64`

Counts

3 → 78

Calls

3 calls:

10.0ms	(-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n)))
6.0ms	(pow.f64 (+.f64 x 1.0) (/.f64 1.0 n))
4.0ms	(pow.f64 x (/.f64 1.0 n))

series81.0ms (0.8%)

Counts

3 → 9

Calls

3 calls:

49.0ms	(-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n)))
19.0ms	(pow.f64 (+.f64 x 1.0) (/.f64 1.0 n))
12.0ms	(pow.f64 x (/.f64 1.0 n))

simplify44.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5141	1177

prune139.0ms (1.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	82	5	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	5	88

Merged error: 22.3b

Counts

88 → 5

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1.0))
0.0b	(pow.f64 x (/.f64 1.0 n))
0.0b	(*.f64 (pow.f64 (sqrt.f64 (+.f64 x 1.0)) (/.f64 1.0 n)) (pow.f64 (sqrt.f64 (+.f64 x 1.0)) (/.f64 1.0 n)))
4.4b	(-.f64 (*.f64 (pow.f64 (sqrt.f64 (+.f64 x 1.0)) (/.f64 1.0 n)) (pow.f64 (sqrt.f64 (+.f64 x 1.0)) (/.f64 1.0 n))) (pow.f64 x (/.f64 1.0 n)))

rewrite42.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`unpow-prod-down_binary64` `add-sqr-sqrt_binary64`
41×	`*-un-lft-identity_binary64`
34×	`sqrt-prod_binary64`
25×	`add-cube-cbrt_binary64`
17×	`add-exp-log_binary64`
16×	`unswap-sqr_binary64`
15×	`swap-sqr_binary64`
14×	`sqr-pow_binary64`
13×	`pow-unpow_binary64`
11×	`associate-r_binary64` `associate-l_binary64`
9×	`prod-exp_binary64` `times-frac_binary64`
7×	`pow-to-exp_binary64` `distribute-lft-out_binary64` `pow-exp_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `add-cbrt-cube_binary64`
3×	`difference-of-squares_binary64`
2×	`sqrt-div_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `sub-neg_binary64` `pow1/2_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `pow-prod-up_binary64` `pow-pow_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64` `pow-sqr_binary64` `flip--_binary64` `flip-+_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 132

Calls

4 calls:

16.0ms	(-.f64 (*.f64 (pow.f64 (sqrt.f64 (+.f64 x 1.0)) (/.f64 1.0 n)) (pow.f64 (sqrt.f64 (+.f64 x 1.0)) (/.f64 1.0 n))) (pow.f64 x (/.f64 1.0 n)))
15.0ms	(*.f64 (pow.f64 (sqrt.f64 (+.f64 x 1.0)) (/.f64 1.0 n)) (pow.f64 (sqrt.f64 (+.f64 x 1.0)) (/.f64 1.0 n)))
4.0ms	(pow.f64 x (/.f64 1.0 n))
3.0ms	(sqrt.f64 (+.f64 x 1.0))

series193.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

103.0ms	(-.f64 (*.f64 (pow.f64 (sqrt.f64 (+.f64 x 1.0)) (/.f64 1.0 n)) (pow.f64 (sqrt.f64 (+.f64 x 1.0)) (/.f64 1.0 n))) (pow.f64 x (/.f64 1.0 n)))
74.0ms	(*.f64 (pow.f64 (sqrt.f64 (+.f64 x 1.0)) (/.f64 1.0 n)) (pow.f64 (sqrt.f64 (+.f64 x 1.0)) (/.f64 1.0 n)))
12.0ms	(pow.f64 x (/.f64 1.0 n))
5.0ms	(sqrt.f64 (+.f64 x 1.0))

simplify69.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4960	2253
1	4960	2253

prune245.0ms (2.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	143	1	144
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	144	5	149

Merged error: 22.3b

Counts

149 → 5

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 x (/.f64 1.0 n))
0.0b	(pow.f64 (+.f64 x 1.0) (/.f64 1.0 n))
2.2b	(log.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n)))))
2.3b	(-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n)))

rewrite37.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-sqr-sqrt_binary64`
38×	`*-un-lft-identity_binary64`
27×	`unpow-prod-down_binary64`
26×	`pow-unpow_binary64`
22×	`add-cube-cbrt_binary64`
18×	`difference-of-squares_binary64` `times-frac_binary64`
16×	`log-pow_binary64`
15×	`exp-prod_binary64`
14×	`sqr-pow_binary64`
7×	`pow1_binary64`
6×	`add-log-exp_binary64` `add-exp-log_binary64` `distribute-lft-out--_binary64`
4×	`log-prod_binary64` `add-cbrt-cube_binary64`
3×	`distribute-lft-out_binary64`
2×	`pow-to-exp_binary64` `sub-neg_binary64` `pow-pow_binary64` `div-inv_binary64` `pow-exp_binary64`
1×	`flip3--_binary64` `diff-log_binary64` `rem-log-exp_binary64` `exp-diff_binary64` `exp-sum_binary64` `log-div_binary64` `flip--_binary64`

Counts

4 → 107

Calls

4 calls:

13.0ms	(log.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n)))))
10.0ms	(-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n)))
6.0ms	(pow.f64 (+.f64 x 1.0) (/.f64 1.0 n))
4.0ms	(pow.f64 x (/.f64 1.0 n))

series118.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

44.0ms	(log.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n)))))
42.0ms	(-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n)))
19.0ms	(pow.f64 (+.f64 x 1.0) (/.f64 1.0 n))
12.0ms	(pow.f64 x (/.f64 1.0 n))

simplify48.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5298	1665

prune176.0ms (1.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	118	1	119
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	118	6	124

Merged error: 22.3b

Counts

124 → 6

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.3b	(-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n)))
2.3b	(-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n)))
2.3b	(log.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n))))))
2.3b	(log.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n))))))

rewrite45.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64`
20×	`unpow-prod-down_binary64`
18×	`difference-of-squares_binary64`
14×	`log-prod_binary64`
12×	`sqr-pow_binary64`
8×	`add-log-exp_binary64` `add-cube-cbrt_binary64` `cbrt-prod_binary64`
6×	`pow1_binary64` `add-exp-log_binary64` `distribute-lft-out--_binary64`
4×	`sub-neg_binary64` `log-pow_binary64` `add-cbrt-cube_binary64`
2×	`cbrt-div_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `rem-log-exp_binary64` `pow1/3_binary64` `exp-diff_binary64` `exp-sum_binary64` `log-div_binary64` `flip--_binary64`

Counts

4 → 82

Calls

4 calls:

11.0ms	(log.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n))))))
11.0ms	(log.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n))))))
10.0ms	(-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n)))
10.0ms	(-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n)))

series319.0ms (3.2%)

Counts

4 → 12

Calls

4 calls:

118.0ms	(log.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n))))))
115.0ms	(log.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n))))))
44.0ms	(-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n)))
42.0ms	(-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n)))

simplify55.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4958	2100
1	4958	2100

prune214.0ms (2.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	91	3	94
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	92	8	100

Merged error: 22.1b

Counts

100 → 8

regimes314.0ms (3.1%)

Accuracy

Total 1.7b remaining (7.1%)

Threshold costs 0b (0%)

bsearch1.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	184	80
1	184	80

end0.0ms (0%)

sample6.5s (64.3%)

Algorithm

1×

intervals

Results

2.1s	3774×	body	1280	valid
1.2s	1069×	body	1280	nan
677.0ms	956×	body	640	nan
651.0ms	1488×	body	640	valid
455.0ms	2654×	body	80	overflowed
226.0ms	753×	body	320	valid
180.0ms	259×	body	640	invalid
176.0ms	423×	body	320	nan
148.0ms	1635×	body	80	valid
125.0ms	95×	body	1280	invalid
74.0ms	350×	body	160	valid
61.0ms	153×	body	320	invalid
47.0ms	212×	body	160	nan
30.0ms	513×	body	80	nan
27.0ms	219×	body	80	invalid
18.0ms	74×	body	160	invalid

Details

analyze1.1s (11%)

sample199.0ms (2%)

simplify58.0ms (0.6%)

prune5.0ms (0%)

localize8.0ms (0.1%)

rewrite22.0ms (0.2%)

series81.0ms (0.8%)

simplify44.0ms (0.4%)

prune139.0ms (1.4%)

localize10.0ms (0.1%)

rewrite42.0ms (0.4%)

series193.0ms (1.9%)

simplify69.0ms (0.7%)

prune245.0ms (2.4%)

localize10.0ms (0.1%)

rewrite37.0ms (0.4%)

series118.0ms (1.2%)

simplify48.0ms (0.5%)

prune176.0ms (1.8%)

localize14.0ms (0.1%)

rewrite45.0ms (0.4%)

series319.0ms (3.2%)

simplify55.0ms (0.6%)

prune214.0ms (2.1%)

regimes314.0ms (3.1%)

bsearch1.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample6.5s (64.3%)

Profiling