Details

analyze1.1s (7.4%)

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)

sample179.0ms (1.2%)

Algorithm

1×

intervals

Results

42.0ms	84×	body	1024	valid
37.0ms	56×	body	2048	valid
35.0ms	39×	body	1024	nan
15.0ms	41×	body	512	valid
14.0ms	77×	body	128	overflowed
6.0ms	12×	body	512	nan
5.0ms	58×	body	128	valid
3.0ms	17×	body	256	valid
2.0ms	5×	body	512	invalid
2.0ms	10×	body	256	nan
2.0ms	2×	body	1024	invalid
1.0ms	4×	body	256	invalid
1.0ms	16×	body	128	nan
0.0ms	2×	body	128	invalid

Compiler

Compiled 27 to 25 computations (7.4% saved)

simplify65.0ms (0.5%)

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: 30.9b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(pow.f64 x (/.f64 1 n))
0.1b	(pow.f64 (+.f64 x 1) (/.f64 1 n))
1.8b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

rewrite31.0ms (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:

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 (3.1%)

Counts

3 → 9

Calls

3 calls:

257.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
105.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
83.0ms	(pow.f64 x (/.f64 1 n))

simplify82.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4925	1618
1	4925	1618

prune113.0ms (0.8%)

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: 21.2b

Counts

88 → 5

Compiler

Compiled 1893 to 1310 computations (30.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 x (/.f64 1 n))
0.1b	(pow.f64 (+.f64 x 1) (/.f64 1 n))
1.8b	(log.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))))
1.8b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

rewrite46.0ms (0.3%)

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:

12.0ms	(log.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)))
6.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
4.0ms	(pow.f64 x (/.f64 1 n))

series867.0ms (6%)

Counts

4 → 12

Calls

4 calls:

448.0ms	(log.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))))
255.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
93.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
71.0ms	(pow.f64 x (/.f64 1 n))

simplify77.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4949	2309
1	4949	2309

prune153.0ms (1.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	117	2	119
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	117	7	124

Merged error: 21.2b

Counts

124 → 7

Compiler

Compiled 2862 to 2047 computations (28.5% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.8b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
1.8b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
1.8b	(log.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))))
1.8b	(log.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))))

rewrite59.0ms (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:

14.0ms	(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))))))
11.0ms	(-.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)))

series1.9s (13.2%)

Counts

4 → 12

Calls

4 calls:

798.0ms	(log.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))))
645.0ms	(log.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))))
231.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
227.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

simplify107.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4894	3034
1	4894	3034

prune229.0ms (1.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	91	3	94
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	93	8	101

Merged error: 21.1b

Counts

101 → 8

Compiler

Compiled 4437 to 3358 computations (24.3% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))))
1.8b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
1.8b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
1.8b	(log.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))))

rewrite58.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

13.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
12.0ms	(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 (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)))

series1.7s (12%)

Counts

4 → 12

Calls

4 calls:

663.0ms	(log.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))))
603.0ms	(cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))))
241.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
221.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

simplify88.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4896	2787
1	4896	2787

prune205.0ms (1.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	84	5	89
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	87	10	97

Merged error: 21.1b

Counts

97 → 10

Compiler

Compiled 3867 to 2900 computations (25% saved)

regimes197.0ms (1.4%)

Compiler: Compiled 1919 to 1555 computations (19% 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	71	157
1	71	157

end0.0ms (0%)

sample6.6s (46.2%)

Algorithm

1×

intervals

Results

1.4s	2637×	body	1024	valid
1.2s	1451×	body	1024	nan
1.2s	1844×	body	2048	valid
479.0ms	2656×	body	128	overflowed
407.0ms	1194×	body	512	valid
326.0ms	681×	body	512	nan
175.0ms	1780×	body	128	valid
174.0ms	183×	body	1024	invalid
114.0ms	213×	body	512	invalid
112.0ms	545×	body	256	valid
86.0ms	356×	body	256	nan
60.0ms	774×	body	128	nan
43.0ms	158×	body	256	invalid
36.0ms	261×	body	128	invalid
7.0ms	6×	body	2048	nan

Compiler

Compiled 518 to 412 computations (20.5% saved)

Details

analyze1.1s (7.4%)

sample179.0ms (1.2%)

simplify65.0ms (0.5%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite31.0ms (0.2%)

series445.0ms (3.1%)

simplify82.0ms (0.6%)

prune113.0ms (0.8%)

localize10.0ms (0.1%)

rewrite46.0ms (0.3%)

series867.0ms (6%)

simplify77.0ms (0.5%)

prune153.0ms (1.1%)

localize14.0ms (0.1%)

rewrite59.0ms (0.4%)

series1.9s (13.2%)

simplify107.0ms (0.7%)

prune229.0ms (1.6%)

localize15.0ms (0.1%)

rewrite58.0ms (0.4%)

series1.7s (12%)

simplify88.0ms (0.6%)

prune205.0ms (1.4%)

regimes197.0ms (1.4%)

bsearch2.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample6.6s (46.2%)

Profiling