Details

analyze1.1s (9.5%)

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)

sample210.0ms (1.8%)

Algorithm

1×

intervals

Results

49.0ms	91×	body	1024	valid
48.0ms	56×	body	1024	nan
37.0ms	52×	body	2048	valid
16.0ms	79×	body	128	overflowed
15.0ms	40×	body	512	valid
8.0ms	17×	body	512	nan
6.0ms	59×	body	128	valid
5.0ms	6×	body	1024	invalid
3.0ms	14×	body	256	valid
3.0ms	5×	body	512	invalid
2.0ms	8×	body	256	nan
2.0ms	6×	body	256	invalid
1.0ms	17×	body	128	nan
1.0ms	8×	body	128	invalid

Compiler

Compiled 27 to 25 computations (7.4% saved)

simplify222.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5176	19

prune2.0ms (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: 35.2b

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 (+.f64 x 1) (/.f64 1 n))
0.0b	(pow.f64 x (/.f64 1 n))
3.1b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

rewrite31.0ms (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:

14.0ms	(-.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))

series445.0ms (3.7%)

Counts

3 → 9

Calls

3 calls:

252.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
106.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
87.0ms	(pow.f64 x (/.f64 1 n))

simplify88.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4925	1618
1	4925	1618

prune123.0ms (1%)

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: 24.1b

Counts

88 → 7

Compiler

Compiled 1933 to 1342 computations (30.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (+.f64 x 1) (/.f64 1/2 n))
0.0b	(pow.f64 x (/.f64 1/2 n))
0.0b	(pow.f64 x (/.f64 1/2 n))
3.1b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1/2 n)) (pow.f64 x (/.f64 1/2 n)))

rewrite40.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64_435`
39×	`pow-unpow_binary64_488`
37×	`*-un-lft-identity_binary64_414`
28×	`add-cube-cbrt_binary64_446`
27×	`times-frac_binary64_420`
20×	`unpow-prod-down_binary64_490`
9×	`difference-of-squares_binary64_383` `sqr-pow_binary64_386`
7×	`pow1_binary64_472` `add-exp-log_binary64_449`
6×	`add-log-exp_binary64_450`
4×	`add-cbrt-cube_binary64_447`
3×	`distribute-lft-out--_binary64_368` `div-inv_binary64_411` `pow-pow_binary64_483` `pow-exp_binary64_479` `pow-to-exp_binary64_480`
2×	`distribute-lft-out_binary64_367`
1×	`flip3--_binary64_418` `diff-log_binary64_503` `sub-neg_binary64_407` `flip--_binary64_389`

Counts

4 → 105

Calls

4 calls:

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 x (/.f64 1/2 n))
4.0ms	(pow.f64 x (/.f64 1/2 n))

series555.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

280.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1/2 n)) (pow.f64 x (/.f64 1/2 n)))
106.0ms	(pow.f64 (+.f64 x 1) (/.f64 1/2 n))
88.0ms	(pow.f64 x (/.f64 1/2 n))
81.0ms	(pow.f64 x (/.f64 1/2 n))

simplify111.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	4979	2124
1	4979	2124

prune372.0ms (3.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	114	3	117
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	116	8	124

Merged error: 24.1b

Counts

124 → 8

Compiler

Compiled 4315 to 3052 computations (29.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (+.f64 x 1) (/.f64 1 n))
0.1b	(exp.f64 (/.f64 (log.f64 x) n))
0.2b	(/.f64 (log.f64 x) n)
3.6b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (exp.f64 (/.f64 (log.f64 x) n)))

rewrite33.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-sqr-sqrt_binary64_435`
33×	`times-frac_binary64_420` `*-un-lft-identity_binary64_414`
29×	`add-cube-cbrt_binary64_446`
16×	`exp-prod_binary64_463`
13×	`pow-unpow_binary64_488`
12×	`pow1_binary64_472`
7×	`log-pow_binary64_500` `add-exp-log_binary64_449` `add-log-exp_binary64_450`
6×	`add-cbrt-cube_binary64_447`
5×	`unpow-prod-down_binary64_490`
4×	`div-inv_binary64_411` `associate-/l*_binary64_361`
3×	`difference-of-squares_binary64_383` `associate-/r*_binary64_360`
2×	`sqr-pow_binary64_386`
1×	`flip3--_binary64_418` `clear-num_binary64_413` `distribute-lft-out--_binary64_368` `exp-to-pow_binary64_473` `diff-log_binary64_503` `cbrt-undiv_binary64_445` `pow-pow_binary64_483` `rem-exp-log_binary64_451` `pow-exp_binary64_479` `pow-to-exp_binary64_480` `sub-neg_binary64_407` `frac-2neg_binary64_425` `distribute-lft-out_binary64_367` `flip--_binary64_389` `div-exp_binary64_462`

Counts

4 → 99

Calls

4 calls:

10.0ms	(-.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	(exp.f64 (/.f64 (log.f64 x) n))
4.0ms	(/.f64 (log.f64 x) n)

series505.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

267.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (exp.f64 (/.f64 (log.f64 x) n)))
103.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
73.0ms	(exp.f64 (/.f64 (log.f64 x) n))
62.0ms	(/.f64 (log.f64 x) n)

simplify76.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5905	1705

prune117.0ms (1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	110	1	111
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	111	8	119

Merged error: 24.1b

Counts

119 → 8

Compiler

Compiled 2392 to 1268 computations (47% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (exp.f64 (/.f64 (log.f64 x) n)) 3)
0.1b	(exp.f64 (/.f64 (log.f64 x) n))
0.2b	(/.f64 (log.f64 x) n)
3.6b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (cbrt.f64 (pow.f64 (exp.f64 (/.f64 (log.f64 x) n)) 3)))

rewrite44.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`add-sqr-sqrt_binary64_435`
36×	`times-frac_binary64_420`
34×	`*-un-lft-identity_binary64_414`
32×	`add-cube-cbrt_binary64_446` `exp-prod_binary64_463`
18×	`pow-pow_binary64_483`
15×	`pow1_binary64_472` `difference-of-squares_binary64_383`
12×	`cbrt-prod_binary64_442`
11×	`unpow-prod-down_binary64_490`
10×	`log-pow_binary64_500`
9×	`sqr-pow_binary64_386`
7×	`add-cbrt-cube_binary64_447` `add-log-exp_binary64_450`
6×	`cube-prod_binary64_439` `add-exp-log_binary64_449`
5×	`div-inv_binary64_411`
4×	`associate-/l*_binary64_361`
3×	`pow-unpow_binary64_488` `associate-/r*_binary64_360`
2×	`exp-to-pow_binary64_473`
1×	`flip3--_binary64_418` `clear-num_binary64_413` `distribute-lft-out--_binary64_368` `diff-log_binary64_503` `cube-mult_binary64_441` `cbrt-undiv_binary64_445` `rem-exp-log_binary64_451` `pow-exp_binary64_479` `pow-to-exp_binary64_480` `sub-neg_binary64_407` `unpow3_binary64_477` `frac-2neg_binary64_425` `flip--_binary64_389` `rem-cube-cbrt_binary64_436` `div-exp_binary64_462`

Counts

4 → 123

Calls

4 calls:

16.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (cbrt.f64 (pow.f64 (exp.f64 (/.f64 (log.f64 x) n)) 3)))
7.0ms	(pow.f64 (exp.f64 (/.f64 (log.f64 x) n)) 3)
5.0ms	(exp.f64 (/.f64 (log.f64 x) n))
4.0ms	(/.f64 (log.f64 x) n)

series537.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

266.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (cbrt.f64 (pow.f64 (exp.f64 (/.f64 (log.f64 x) n)) 3)))
131.0ms	(pow.f64 (exp.f64 (/.f64 (log.f64 x) n)) 3)
70.0ms	(/.f64 (log.f64 x) n)
69.0ms	(exp.f64 (/.f64 (log.f64 x) n))

simplify76.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5345	2511

prune152.0ms (1.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	134	1	135
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	134	9	143

Merged error: 24.1b

Counts

143 → 9

Compiler

Compiled 3149 to 1708 computations (45.8% saved)

regimes149.0ms (1.2%)

Compiler: Compiled 1124 to 886 computations (21.2% saved)

bsearch2.0ms (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	90	147
1	90	147

end0.0ms (0%)

sample6.9s (57.5%)

Algorithm

1×

intervals

Results

1.4s	2645×	body	1024	valid
1.2s	1390×	body	1024	nan
1.2s	1743×	body	2048	valid
516.0ms	2580×	body	128	overflowed
449.0ms	1238×	body	512	valid
384.0ms	715×	body	512	nan
202.0ms	195×	body	1024	invalid
186.0ms	1806×	body	128	valid
127.0ms	568×	body	256	valid
124.0ms	229×	body	512	invalid
91.0ms	350×	body	256	nan
62.0ms	817×	body	128	nan
45.0ms	157×	body	256	invalid
39.0ms	264×	body	128	invalid
6.0ms	6×	body	2048	nan
1.0ms	1×	body	2048	invalid

Compiler

Compiled 383 to 296 computations (22.7% saved)

Details

analyze1.1s (9.5%)

sample210.0ms (1.8%)

simplify222.0ms (1.9%)

prune2.0ms (0%)

localize9.0ms (0.1%)

rewrite31.0ms (0.3%)

series445.0ms (3.7%)

simplify88.0ms (0.7%)

prune123.0ms (1%)

localize11.0ms (0.1%)

rewrite40.0ms (0.3%)

series555.0ms (4.7%)

simplify111.0ms (0.9%)

prune372.0ms (3.1%)

localize11.0ms (0.1%)

rewrite33.0ms (0.3%)

series505.0ms (4.2%)

simplify76.0ms (0.6%)

prune117.0ms (1%)

localize13.0ms (0.1%)

rewrite44.0ms (0.4%)

series537.0ms (4.5%)

simplify76.0ms (0.6%)

prune152.0ms (1.3%)

regimes149.0ms (1.2%)

bsearch2.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample6.9s (57.5%)

Profiling