Details

analyze1.1s (10.2%)

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 (2%)

Algorithm

1×

intervals

Results

71.0ms	128×	body	1280	valid
38.0ms	36×	body	1280	nan
24.0ms	32×	body	640	nan
22.0ms	49×	body	640	valid
12.0ms	67×	body	80	overflowed
7.0ms	24×	body	320	valid
6.0ms	14×	body	320	nan
5.0ms	4×	body	1280	invalid
4.0ms	5×	body	640	invalid
4.0ms	47×	body	80	valid
3.0ms	7×	body	320	invalid
2.0ms	9×	body	160	nan
1.0ms	8×	body	160	valid
1.0ms	8×	body	80	invalid
1.0ms	17×	body	80	nan
0.0ms	1×	body	160	invalid

Compiler

Compiled 27 to 25 computations (7.4% saved)

simplify82.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4914	19
1	4914	19

prune6.0ms (0.1%)

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: 34.5b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(pow.f64 (+.f64 x 1) (/.f64 1 n))
2.0b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
14×	`unpow-prod-down_binary64`
13×	`pow-unpow_binary64`
10×	`add-cube-cbrt_binary64`
9×	`difference-of-squares_binary64` `times-frac_binary64`
7×	`sqr-pow_binary64`
4×	`add-log-exp_binary64`
3×	`pow1_binary64` `add-exp-log_binary64` `distribute-lft-out--_binary64`
2×	`distribute-lft-out_binary64` `add-cbrt-cube_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `pow-pow_binary64` `div-inv_binary64` `flip--_binary64` `pow-exp_binary64`

Counts

2 → 51

Calls

2 calls:

10.0ms	(-.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))

series44.0ms (0.4%)

Counts

2 → 6

Calls

2 calls:

31.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
13.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))

simplify103.0ms (1%)

Algorithm

1×	egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4959	1244
1	4959	1244

prune65.0ms (0.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	53	4	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	54	4	58

Merged error: 22.9b

Counts

58 → 4

Compiler

Compiled 1267 to 889 computations (29.8% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(pow.f64 (+.f64 x 1) (/.f64 1 n))
1.9b	(log.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))))
2.0b	(-.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

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

Counts

3 → 80

Calls

3 calls:

14.0ms	(log.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))))
10.0ms	(-.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))

series71.0ms (0.7%)

Counts

3 → 9

Calls

3 calls:

29.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
29.0ms	(log.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))))
13.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))

simplify63.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5020	1936

prune90.0ms (0.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	87	2	89
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	87	6	93

Merged error: 22.9b

Counts

93 → 6

Compiler

Compiled 2176 to 1563 computations (28.2% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.0b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
2.0b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
2.0b	(log.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))))
2.0b	(log.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 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) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))))
11.0ms	(log.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))))
10.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
10.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

series215.0ms (2%)

Counts

4 → 12

Calls

4 calls:

78.0ms	(log.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))))
77.0ms	(log.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))))
31.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
29.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

simplify66.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4975	3034
1	4975	3034

prune184.0ms (1.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	91	3	94
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	93	7	100

Merged error: 22.8b

Counts

100 → 7

Compiler

Compiled 4414 to 3337 computations (24.4% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.0b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
2.0b	(log.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))))
2.2b	(log.f64 (cbrt.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))))))
2.2b	(log.f64 (cbrt.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))))))

rewrite50.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`log-prod_binary64`
26×	`cbrt-prod_binary64`
24×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`
10×	`unpow-prod-down_binary64`
9×	`difference-of-squares_binary64`
7×	`pow1_binary64` `add-exp-log_binary64`
6×	`add-log-exp_binary64` `log-pow_binary64` `sqr-pow_binary64`
5×	`cbrt-div_binary64`
4×	`sub-neg_binary64` `add-cbrt-cube_binary64`
3×	`rem-log-exp_binary64` `pow1/3_binary64` `exp-diff_binary64` `exp-sum_binary64` `distribute-lft-out--_binary64` `log-div_binary64`
1×	`flip3--_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `flip--_binary64`

Counts

4 → 83

Calls

4 calls:

12.0ms	(log.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))))
12.0ms	(log.f64 (cbrt.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))))))
12.0ms	(log.f64 (cbrt.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))))))
11.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

series262.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

78.0ms	(log.f64 (cbrt.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))))))
77.0ms	(log.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))))
76.0ms	(log.f64 (cbrt.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))))))
31.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

simplify123.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4958	3305
1	4958	3305

prune279.0ms (2.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	93	2	95
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	95	7	102

Merged error: 22.7b

Counts

102 → 7

Compiler

Compiled 6226 to 4831 computations (22.4% saved)

regimes239.0ms (2.3%)

Compiler: Compiled 1358 to 1116 computations (17.8% saved)

bsearch1.0ms (0%)

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

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	97	190
1	97	190

end0.0ms (0%)

sample7.2s (67.9%)

Algorithm

1×

intervals

Results

2.0s	3734×	body	1280	valid
1.2s	1141×	body	1280	nan
724.0ms	1645×	body	640	valid
631.0ms	911×	body	640	nan
496.0ms	2841×	body	80	overflowed
234.0ms	757×	body	320	valid
185.0ms	450×	body	320	nan
155.0ms	226×	body	640	invalid
138.0ms	1536×	body	80	valid
115.0ms	89×	body	1280	invalid
78.0ms	180×	body	320	invalid
69.0ms	328×	body	160	valid
52.0ms	237×	body	160	nan
32.0ms	534×	body	80	nan
27.0ms	221×	body	80	invalid
24.0ms	102×	body	160	invalid

Compiler

Compiled 409 to 327 computations (20% saved)

Details

analyze1.1s (10.2%)

sample214.0ms (2%)

simplify82.0ms (0.8%)

prune6.0ms (0.1%)

localize8.0ms (0.1%)

rewrite18.0ms (0.2%)

series44.0ms (0.4%)

simplify103.0ms (1%)

prune65.0ms (0.6%)

localize10.0ms (0.1%)

rewrite34.0ms (0.3%)

series71.0ms (0.7%)

simplify63.0ms (0.6%)

prune90.0ms (0.8%)

localize14.0ms (0.1%)

rewrite45.0ms (0.4%)

series215.0ms (2%)

simplify66.0ms (0.6%)

prune184.0ms (1.7%)

localize19.0ms (0.2%)

rewrite50.0ms (0.5%)

series262.0ms (2.5%)

simplify123.0ms (1.2%)

prune279.0ms (2.6%)

regimes239.0ms (2.3%)

bsearch1.0ms (0%)

simplify8.0ms (0.1%)

end0.0ms (0%)

sample7.2s (67.9%)

Profiling