Details

analyze1.1s (9.1%)

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)

sample214.0ms (1.7%)

Algorithm

1×

intervals

Results

50.0ms	87×	body	1024	valid
48.0ms	54×	body	1024	nan
43.0ms	60×	body	2048	valid
14.0ms	71×	body	128	overflowed
12.0ms	30×	body	512	valid
8.0ms	5×	body	1024	invalid
7.0ms	13×	body	512	nan
6.0ms	63×	body	128	valid
3.0ms	16×	body	256	valid
3.0ms	10×	body	256	nan
2.0ms	5×	body	512	invalid
2.0ms	27×	body	128	nan
2.0ms	6×	body	256	invalid
1.0ms	7×	body	128	invalid

Compiler

Compiled 27 to 25 computations (7.4% saved)

simplify225.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (59.0ms)

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: 31.2b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(pow.f64 x (/.f64 1 n))
0.1b	(pow.f64 (+.f64 x 1) (/.f64 1 n))
2.7b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

rewrite28.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64_98`
28×	`*-un-lft-identity_binary64_77`
26×	`pow-unpow_binary64_151`
19×	`add-cube-cbrt_binary64_109`
18×	`times-frac_binary64_83`
17×	`unpow-prod-down_binary64_153`
9×	`difference-of-squares_binary64_46`
8×	`sqr-pow_binary64_49`
5×	`add-exp-log_binary64_112` `add-log-exp_binary64_113` `pow1_binary64_135`
3×	`add-cbrt-cube_binary64_110` `distribute-lft-out--_binary64_31`
2×	`pow-to-exp_binary64_143` `pow-exp_binary64_142` `pow-pow_binary64_146` `distribute-lft-out_binary64_30` `div-inv_binary64_74`
1×	`sub-neg_binary64_70` `flip--_binary64_52` `flip3--_binary64_81` `diff-log_binary64_166`

Counts

3 → 78

Calls

3 calls:

11.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
6.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
4.0ms	(pow.f64 x (/.f64 1 n))

series455.0ms (3.7%)

Counts

3 → 9

Calls

3 calls:

263.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
103.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
89.0ms	(pow.f64 x (/.f64 1 n))

simplify85.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4925	1618
1	4925	1618

prune116.0ms (0.9%)

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: 22.5b

Counts

88 → 5

Compiler

Compiled 1873 to 1294 computations (30.9% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(exp.f64 (/.f64 (log.f64 x) n))
0.1b	(pow.f64 (+.f64 x 1) (/.f64 1 n))
0.3b	(/.f64 (log.f64 x) n)
2.7b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (exp.f64 (/.f64 (log.f64 x) n)))

rewrite36.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-sqr-sqrt_binary64_98`
33×	`times-frac_binary64_83` `*-un-lft-identity_binary64_77`
29×	`add-cube-cbrt_binary64_109`
16×	`exp-prod_binary64_126`
13×	`pow-unpow_binary64_151`
12×	`pow1_binary64_135`
7×	`add-exp-log_binary64_112` `add-log-exp_binary64_113` `log-pow_binary64_163`
6×	`add-cbrt-cube_binary64_110`
5×	`unpow-prod-down_binary64_153`
4×	`associate-/l*_binary64_24` `div-inv_binary64_74`
3×	`associate-/r*_binary64_23` `difference-of-squares_binary64_46`
2×	`sqr-pow_binary64_49`
1×	`pow-to-exp_binary64_143` `cbrt-undiv_binary64_108` `distribute-lft-out--_binary64_31` `sub-neg_binary64_70` `pow-exp_binary64_142` `flip--_binary64_52` `div-exp_binary64_125` `clear-num_binary64_76` `flip3--_binary64_81` `diff-log_binary64_166` `rem-exp-log_binary64_114` `frac-2neg_binary64_88` `pow-pow_binary64_146` `distribute-lft-out_binary64_30` `exp-to-pow_binary64_136`

Counts

4 → 99

Calls

4 calls:

13.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (exp.f64 (/.f64 (log.f64 x) n)))
6.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
5.0ms	(exp.f64 (/.f64 (log.f64 x) n))
4.0ms	(/.f64 (log.f64 x) n)

series529.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

276.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (exp.f64 (/.f64 (log.f64 x) n)))
104.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
90.0ms	(exp.f64 (/.f64 (log.f64 x) n))
59.0ms	(/.f64 (log.f64 x) n)

simplify77.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5905	1705

prune108.0ms (0.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	110	1	111
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	111	5	116

Merged error: 22.5b

Counts

116 → 5

Compiler

Compiled 2250 to 1158 computations (48.5% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(cbrt.f64 (pow.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (exp.f64 (/.f64 (log.f64 x) n))) 3))
0.1b	(pow.f64 (+.f64 x 1) (/.f64 1 n))
0.3b	(/.f64 (log.f64 x) n)
2.7b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (exp.f64 (/.f64 (log.f64 x) n)))

rewrite44.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64_98`
32×	`*-un-lft-identity_binary64_77`
24×	`add-cube-cbrt_binary64_109`
21×	`times-frac_binary64_83`
20×	`cbrt-prod_binary64_105`
14×	`unpow-prod-down_binary64_153`
13×	`pow-unpow_binary64_151`
9×	`pow1_binary64_135` `difference-of-squares_binary64_46`
7×	`add-exp-log_binary64_112` `cube-prod_binary64_102`
6×	`add-cbrt-cube_binary64_110` `add-log-exp_binary64_113`
5×	`sqr-pow_binary64_49`
4×	`associate-/l*_binary64_24` `log-pow_binary64_163`
3×	`associate-/r*_binary64_23` `distribute-lft-out--_binary64_31`
2×	`cube-div_binary64_103` `cbrt-div_binary64_106` `flip--_binary64_52` `flip3--_binary64_81` `div-inv_binary64_74`
1×	`pow-to-exp_binary64_143` `rem-cbrt-cube_binary64_100` `cbrt-undiv_binary64_108` `sub-neg_binary64_70` `pow-exp_binary64_142` `cube-mult_binary64_104` `div-exp_binary64_125` `clear-num_binary64_76` `diff-log_binary64_166` `pow1/3_binary64_156` `frac-2neg_binary64_88` `pow-pow_binary64_146` `distribute-lft-out_binary64_30` `unpow3_binary64_140`

Counts

4 → 105

Calls

4 calls:

13.0ms	(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)))
6.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
4.0ms	(/.f64 (log.f64 x) n)

series668.0ms (5.4%)

Counts

4 → 12

Calls

4 calls:

263.0ms	(cbrt.f64 (pow.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (exp.f64 (/.f64 (log.f64 x) n))) 3))
258.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (exp.f64 (/.f64 (log.f64 x) n)))
90.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
56.0ms	(/.f64 (log.f64 x) n)

simplify104.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4897	2519
1	4897	2519

prune136.0ms (1.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	116	1	117
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	116	6	122

Merged error: 22.5b

Counts

122 → 6

Compiler

Compiled 2780 to 1585 computations (43% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (+.f64 (pow.f64 x (/.f64 1/2 n)) (pow.f64 (+.f64 x 1) (/.f64 1/2 n))) (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1/2 n)) (pow.f64 x (/.f64 1/2 n))))
0.1b	(pow.f64 (+.f64 x 1) (/.f64 1/2 n))
0.1b	(pow.f64 (+.f64 x 1) (/.f64 1/2 n))
2.7b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1/2 n)) (pow.f64 x (/.f64 1/2 n)))

rewrite70.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`add-sqr-sqrt_binary64_98`
47×	`*-un-lft-identity_binary64_77`
32×	`unpow-prod-down_binary64_153`
26×	`pow-unpow_binary64_151`
22×	`add-cube-cbrt_binary64_109`
18×	`times-frac_binary64_83` `difference-of-squares_binary64_46`
15×	`associate-r_binary64_19`
14×	`sqr-pow_binary64_49`
8×	`add-exp-log_binary64_112` `pow1_binary64_135` `distribute-lft-out_binary64_30`
6×	`associate-l_binary64_20` `add-cbrt-cube_binary64_110` `add-log-exp_binary64_113` `distribute-lft-out--_binary64_31`
4×	`frac-times_binary64_87` `flip--_binary64_52` `flip3--_binary64_81`
3×	`flip-+_binary64_51` `flip3-+_binary64_80` `sub-neg_binary64_70`
2×	`pow-to-exp_binary64_143` `pow-exp_binary64_142` `associate-l/_binary64_22` `associate-r/_binary64_21` `pow-pow_binary64_146` `div-inv_binary64_74`
1×	`pow-prod-down_binary64_145` `cbrt-unprod_binary64_107` `distribute-lft-in_binary64_28` `unswap-sqr_binary64_45` `prod-exp_binary64_123` `*-commutative_binary64_10` `diff-log_binary64_166` `distribute-rgt-in_binary64_29`

Counts

4 → 122

Calls

4 calls:

27.0ms	(*.f64 (+.f64 (pow.f64 x (/.f64 1/2 n)) (pow.f64 (+.f64 x 1) (/.f64 1/2 n))) (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1/2 n)) (pow.f64 x (/.f64 1/2 n))))
11.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1/2 n)) (pow.f64 x (/.f64 1/2 n)))
6.0ms	(pow.f64 (+.f64 x 1) (/.f64 1/2 n))
6.0ms	(pow.f64 (+.f64 x 1) (/.f64 1/2 n))

series993.0ms (8%)

Counts

4 → 12

Calls

4 calls:

531.0ms	(*.f64 (+.f64 (pow.f64 x (/.f64 1/2 n)) (pow.f64 (+.f64 x 1) (/.f64 1/2 n))) (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1/2 n)) (pow.f64 x (/.f64 1/2 n))))
254.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1/2 n)) (pow.f64 x (/.f64 1/2 n)))
110.0ms	(pow.f64 (+.f64 x 1) (/.f64 1/2 n))
98.0ms	(pow.f64 (+.f64 x 1) (/.f64 1/2 n))

simplify90.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4983	3579
1	4983	3579

prune248.0ms (2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	134	6	140

Merged error: 22.5b

Counts

140 → 6

Compiler

Compiled 4769 to 3374 computations (29.3% saved)

regimes57.0ms (0.5%)

Compiler: Compiled 266 to 206 computations (22.6% saved)

bsearch120.0ms (1%)

Steps

Iters	Range		Point
8	1269801087.5628436	7249083317945.832	1871075736.4773417
9	-45330148694.10113	-17861.081965927067	-190663400.55017483

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	64	72
1	64	72

end0.0ms (0%)

sample6.8s (54.8%)

Algorithm

1×

intervals

Results

1.5s	2670×	body	1024	valid
1.3s	1457×	body	1024	nan
1.2s	1696×	body	2048	valid
497.0ms	2554×	body	128	overflowed
448.0ms	1225×	body	512	valid
418.0ms	797×	body	512	nan
195.0ms	191×	body	1024	invalid
184.0ms	1824×	body	128	valid
130.0ms	585×	body	256	valid
114.0ms	214×	body	512	invalid
93.0ms	362×	body	256	nan
61.0ms	796×	body	128	nan
42.0ms	144×	body	256	invalid
37.0ms	250×	body	128	invalid
4.0ms	3×	body	2048	nan

Compiler

Compiled 192 to 145 computations (24.5% saved)

Details

analyze1.1s (9.1%)

sample214.0ms (1.7%)

simplify225.0ms (1.8%)

prune3.0ms (0%)

localize9.0ms (0.1%)

rewrite28.0ms (0.2%)

series455.0ms (3.7%)

simplify85.0ms (0.7%)

prune116.0ms (0.9%)

localize11.0ms (0.1%)

rewrite36.0ms (0.3%)

series529.0ms (4.3%)

simplify77.0ms (0.6%)

prune108.0ms (0.9%)

localize13.0ms (0.1%)

rewrite44.0ms (0.4%)

series668.0ms (5.4%)

simplify104.0ms (0.8%)

prune136.0ms (1.1%)

localize11.0ms (0.1%)

rewrite70.0ms (0.6%)

series993.0ms (8%)

simplify90.0ms (0.7%)

prune248.0ms (2%)

regimes57.0ms (0.5%)

bsearch120.0ms (1%)

simplify3.0ms (0%)

end0.0ms (0%)

sample6.8s (54.8%)

Profiling