Details

analyze1.1s (8.3%)

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

Compiler

Compiled 14 to 12 computations (14.3% saved)

sample199.0ms (1.5%)

Algorithm

1×

intervals

Results

38.0ms	45×	body	1024	nan
35.0ms	72×	body	1024	valid
34.0ms	52×	body	2048	valid
18.0ms	94×	body	128	overflowed
17.0ms	27×	body	512	nan
14.0ms	39×	body	512	valid
7.0ms	75×	body	128	valid
6.0ms	6×	body	1024	invalid
4.0ms	14×	body	256	nan
4.0ms	18×	body	256	valid
2.0ms	5×	body	512	invalid
2.0ms	8×	body	256	invalid
2.0ms	33×	body	128	nan
1.0ms	6×	body	128	invalid

Compiler

Compiled 27 to 25 computations (7.4% saved)

simplify228.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5176	19

prune3.0ms (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: 29.0b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b	(pow.f64 x (/.f64 1 n))
0.1b	(pow.f64 (+.f64 x 1) (/.f64 1 n))
2.4b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

rewrite34.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64_435`
28×	`*-un-lft-identity_binary64_414`
26×	`pow-unpow_binary64_488`
19×	`add-cube-cbrt_binary64_446`
18×	`times-frac_binary64_420`
17×	`unpow-prod-down_binary64_490`
9×	`difference-of-squares_binary64_383`
8×	`sqr-pow_binary64_386`
5×	`pow1_binary64_472` `add-exp-log_binary64_449` `add-log-exp_binary64_450`
3×	`distribute-lft-out--_binary64_368` `add-cbrt-cube_binary64_447`
2×	`div-inv_binary64_411` `pow-pow_binary64_483` `pow-exp_binary64_479` `pow-to-exp_binary64_480` `distribute-lft-out_binary64_367`
1×	`flip3--_binary64_418` `diff-log_binary64_503` `sub-neg_binary64_407` `flip--_binary64_389`

Counts

3 → 78

Calls

3 calls:

15.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
7.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
4.0ms	(pow.f64 x (/.f64 1 n))

series448.0ms (3.4%)

Counts

3 → 9

Calls

3 calls:

265.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
95.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
87.0ms	(pow.f64 x (/.f64 1 n))

simplify85.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4925	1618
1	4925	1618

prune120.0ms (0.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	80	7	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	7	88

Merged error: 20.4b

Counts

88 → 7

Compiler

Compiled 1922 to 1335 computations (30.5% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))) 3)
0.1b	(pow.f64 x (/.f64 1 n))
0.1b	(pow.f64 (+.f64 x 1) (/.f64 1 n))
2.4b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

rewrite54.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`add-sqr-sqrt_binary64_435`
52×	`unpow-prod-down_binary64_490`
46×	`*-un-lft-identity_binary64_414`
29×	`pow-unpow_binary64_488`
27×	`difference-of-squares_binary64_383`
23×	`add-cube-cbrt_binary64_446`
21×	`sqr-pow_binary64_386`
18×	`times-frac_binary64_420`
15×	`cube-prod_binary64_439`
9×	`distribute-lft-out--_binary64_368`
7×	`pow1_binary64_472` `add-exp-log_binary64_449`
6×	`add-log-exp_binary64_450`
5×	`add-cbrt-cube_binary64_447`
4×	`distribute-lft-out_binary64_367`
3×	`pow-pow_binary64_483` `pow-exp_binary64_479` `pow-to-exp_binary64_480`
2×	`flip3--_binary64_418` `div-inv_binary64_411` `flip--_binary64_389` `cube-div_binary64_440`
1×	`diff-log_binary64_503` `cube-mult_binary64_441` `sub-neg_binary64_407` `unpow3_binary64_477` `rem-cube-cbrt_binary64_436`

Counts

4 → 127

Calls

4 calls:

17.0ms	(pow.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))) 3)
12.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
7.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
4.0ms	(pow.f64 x (/.f64 1 n))

series816.0ms (6.2%)

Counts

4 → 12

Calls

4 calls:

400.0ms	(pow.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))) 3)
247.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
95.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
74.0ms	(pow.f64 x (/.f64 1 n))

simplify60.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5330	3500

prune355.0ms (2.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	133	6	139
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	135	11	146

Merged error: 20.3b

Counts

146 → 11

Compiler

Compiled 3795 to 2827 computations (25.5% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(pow.f64 (+.f64 x 1) (/.f64 1 n))
0.3b	(/.f64 (log.f64 x) n)
0.3b	(cbrt.f64 (pow.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (exp.f64 (/.f64 (log.f64 x) n))) 3))
2.7b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (exp.f64 (/.f64 (log.f64 x) n)))

rewrite50.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64_435`
32×	`*-un-lft-identity_binary64_414`
24×	`add-cube-cbrt_binary64_446`
21×	`times-frac_binary64_420`
20×	`cbrt-prod_binary64_442`
14×	`unpow-prod-down_binary64_490`
13×	`pow-unpow_binary64_488`
9×	`pow1_binary64_472` `difference-of-squares_binary64_383`
7×	`cube-prod_binary64_439` `add-exp-log_binary64_449`
6×	`add-cbrt-cube_binary64_447` `add-log-exp_binary64_450`
5×	`sqr-pow_binary64_386`
4×	`log-pow_binary64_500` `associate-/l*_binary64_361`
3×	`distribute-lft-out--_binary64_368` `associate-/r*_binary64_360`
2×	`flip3--_binary64_418` `cbrt-div_binary64_443` `div-inv_binary64_411` `flip--_binary64_389` `cube-div_binary64_440`
1×	`clear-num_binary64_413` `diff-log_binary64_503` `cube-mult_binary64_441` `cbrt-undiv_binary64_445` `pow-pow_binary64_483` `pow-exp_binary64_479` `rem-cbrt-cube_binary64_437` `pow-to-exp_binary64_480` `sub-neg_binary64_407` `unpow3_binary64_477` `frac-2neg_binary64_425` `distribute-lft-out_binary64_367` `pow1/3_binary64_493` `div-exp_binary64_462`

Counts

4 → 105

Calls

4 calls:

14.0ms	(cbrt.f64 (pow.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (exp.f64 (/.f64 (log.f64 x) n))) 3))
11.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (exp.f64 (/.f64 (log.f64 x) n)))
9.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
4.0ms	(/.f64 (log.f64 x) n)

series666.0ms (5.1%)

Counts

4 → 12

Calls

4 calls:

263.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (exp.f64 (/.f64 (log.f64 x) n)))
258.0ms	(cbrt.f64 (pow.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (exp.f64 (/.f64 (log.f64 x) n))) 3))
90.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
55.0ms	(/.f64 (log.f64 x) n)

simplify98.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4897	2519
1	4897	2519

prune146.0ms (1.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	116	1	117
Fresh	0	10	10
Picked	1	0	1
Done	0	0	0
Total	117	11	128

Merged error: 20.3b

Counts

128 → 11

Compiler

Compiled 2957 to 1730 computations (41.5% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (log.f64 x) n)
0.3b	(cbrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (exp.f64 (/.f64 (log.f64 x) n))) 3)) 3))
0.3b	(cbrt.f64 (pow.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (exp.f64 (/.f64 (log.f64 x) n))) 3))
2.7b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (exp.f64 (/.f64 (log.f64 x) n)))

rewrite72.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

112×	`cbrt-prod_binary64_442`
60×	`add-sqr-sqrt_binary64_435`
51×	`unpow-prod-down_binary64_490`
44×	`cube-prod_binary64_439`
39×	`*-un-lft-identity_binary64_414`
25×	`add-cube-cbrt_binary64_446`
21×	`difference-of-squares_binary64_383`
12×	`times-frac_binary64_420`
11×	`sqr-pow_binary64_386`
8×	`pow1_binary64_472`
7×	`distribute-lft-out--_binary64_368`
6×	`cbrt-div_binary64_443` `add-exp-log_binary64_449` `add-cbrt-cube_binary64_447` `add-log-exp_binary64_450` `cube-div_binary64_440`
4×	`log-pow_binary64_500` `cube-mult_binary64_441` `unpow3_binary64_477` `associate-/l*_binary64_361`
3×	`flip3--_binary64_418` `flip--_binary64_389` `associate-/r*_binary64_360`
2×	`rem-cbrt-cube_binary64_437` `pow1/3_binary64_493`
1×	`clear-num_binary64_413` `diff-log_binary64_503` `div-inv_binary64_411` `cbrt-undiv_binary64_445` `sub-neg_binary64_407` `frac-2neg_binary64_425` `div-exp_binary64_462`

Counts

4 → 140

Calls

4 calls:

20.0ms	(cbrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (exp.f64 (/.f64 (log.f64 x) n))) 3)) 3))
14.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (exp.f64 (/.f64 (log.f64 x) n)))
14.0ms	(cbrt.f64 (pow.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (exp.f64 (/.f64 (log.f64 x) n))) 3))
4.0ms	(/.f64 (log.f64 x) n)

series833.0ms (6.3%)

Counts

4 → 12

Calls

4 calls:

265.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (exp.f64 (/.f64 (log.f64 x) n)))
257.0ms	(cbrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (exp.f64 (/.f64 (log.f64 x) n))) 3)) 3))
251.0ms	(cbrt.f64 (pow.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (exp.f64 (/.f64 (log.f64 x) n))) 3))
61.0ms	(/.f64 (log.f64 x) n)

simplify81.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5408	4635

prune202.0ms (1.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	151	1	152
Fresh	0	10	10
Picked	1	0	1
Done	0	0	0
Total	152	11	163

Merged error: 20.3b

Counts

163 → 11

Compiler

Compiled 4013 to 2306 computations (42.5% saved)

regimes363.0ms (2.8%)

Compiler: Compiled 2608 to 2118 computations (18.8% saved)

bsearch3.0ms (0%)

Compiler: Compiled 3 to 4 computations (-33.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	82	126
1	82	126

end0.0ms (0%)

sample7.1s (53.9%)

Algorithm

1×

intervals

Results

1.4s	2709×	body	1024	valid
1.3s	1471×	body	1024	nan
1.2s	1692×	body	2048	valid
510.0ms	2688×	body	128	overflowed
449.0ms	1258×	body	512	valid
405.0ms	778×	body	512	nan
184.0ms	179×	body	1024	invalid
173.0ms	1774×	body	128	valid
125.0ms	567×	body	256	valid
120.0ms	231×	body	512	invalid
96.0ms	388×	body	256	nan
63.0ms	847×	body	128	nan
49.0ms	174×	body	256	invalid
42.0ms	289×	body	128	invalid
8.0ms	6×	body	2048	nan

Compiler

Compiled 651 to 519 computations (20.3% saved)

Details

analyze1.1s (8.3%)

sample199.0ms (1.5%)

simplify228.0ms (1.7%)

prune3.0ms (0%)

localize8.0ms (0.1%)

rewrite34.0ms (0.3%)

series448.0ms (3.4%)

simplify85.0ms (0.6%)

prune120.0ms (0.9%)

localize11.0ms (0.1%)

rewrite54.0ms (0.4%)

series816.0ms (6.2%)

simplify60.0ms (0.5%)

prune355.0ms (2.7%)

localize13.0ms (0.1%)

rewrite50.0ms (0.4%)

series666.0ms (5.1%)

simplify98.0ms (0.7%)

prune146.0ms (1.1%)

localize15.0ms (0.1%)

rewrite72.0ms (0.5%)

series833.0ms (6.3%)

simplify81.0ms (0.6%)

prune202.0ms (1.5%)

regimes363.0ms (2.8%)

bsearch3.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample7.1s (53.9%)

Profiling