Details

analyze1.1s (9.2%)

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)

sample207.0ms (1.7%)

Algorithm

1×

intervals

Results

48.0ms	56×	body	1024	nan
46.0ms	91×	body	1024	valid
36.0ms	52×	body	2048	valid
15.0ms	79×	body	128	overflowed
14.0ms	40×	body	512	valid
8.0ms	17×	body	512	nan
6.0ms	14×	body	256	valid
6.0ms	59×	body	128	valid
5.0ms	6×	body	1024	invalid
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)

simplify218.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4814	19
1	4814	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)

localize8.0ms (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)))

rewrite30.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64_445`
30×	`*-un-lft-identity_binary64_423`
26×	`pow-unpow_binary64_500`
21×	`add-cube-cbrt_binary64_458`
20×	`unpow-prod-down_binary64_502`
18×	`times-frac_binary64_429`
9×	`difference-of-squares_binary64_392` `sqr-pow_binary64_395`
7×	`cancel-sign-sub-inv_binary64_389`
5×	`pow1_binary64_484` `add-exp-log_binary64_461` `add-log-exp_binary64_462`
3×	`distribute-lft-out--_binary64_375` `add-cbrt-cube_binary64_459`
2×	`pow-to-exp_binary64_492` `distribute-lft-out_binary64_374` `pow-exp_binary64_491` `pow-pow_binary64_495` `div-inv_binary64_420`
1×	`sub-neg_binary64_416` `diff-log_binary64_515` `flip3--_binary64_427` `flip--_binary64_398`

Counts

3 → 85

Calls

3 calls:

12.0ms	(-.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))

series457.0ms (3.7%)

Counts

3 → 9

Calls

3 calls:

265.0ms	(-.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))
86.0ms	(pow.f64 x (/.f64 1 n))

simplify93.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4899	1701
1	4899	1701

prune416.0ms (3.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	86	8	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	87	8	95

Merged error: 24.1b

Counts

95 → 8

Compiler

Compiled 4838 to 3649 computations (24.6% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(cbrt.f64 (+.f64 x 1))
0.3b	(cbrt.f64 (+.f64 x 1))
0.3b	(cbrt.f64 (+.f64 x 1))
3.6b	(-.f64 (.f64 (pow.f64 (.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1))) (/.f64 1 n)) (pow.f64 (cbrt.f64 (+.f64 x 1)) (/.f64 1 n))) (pow.f64 x (/.f64 1 n)))

rewrite31.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64_423`
12×	`cbrt-prod_binary64_454`
9×	`add-cube-cbrt_binary64_458` `add-sqr-sqrt_binary64_445`
7×	`cancel-sign-sub-inv_binary64_389`
6×	`cbrt-div_binary64_455` `add-log-exp_binary64_462`
4×	`pow1_binary64_484` `add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
3×	`flip-+_binary64_397` `distribute-lft-out_binary64_374` `pow1/3_binary64_505` `flip3-+_binary64_426` `unpow-prod-down_binary64_502`
1×	`sub-neg_binary64_416` `diff-log_binary64_515` `flip3--_binary64_427` `flip--_binary64_398` `sqr-pow_binary64_395`

Counts

4 → 60

Calls

4 calls:

14.0ms	(-.f64 (.f64 (pow.f64 (.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1))) (/.f64 1 n)) (pow.f64 (cbrt.f64 (+.f64 x 1)) (/.f64 1 n))) (pow.f64 x (/.f64 1 n)))
4.0ms	(cbrt.f64 (+.f64 x 1))
3.0ms	(cbrt.f64 (+.f64 x 1))
3.0ms	(cbrt.f64 (+.f64 x 1))

series700.0ms (5.6%)

Counts

4 → 12

Calls

4 calls:

573.0ms	(-.f64 (.f64 (pow.f64 (.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1))) (/.f64 1 n)) (pow.f64 (cbrt.f64 (+.f64 x 1)) (/.f64 1 n))) (pow.f64 x (/.f64 1 n)))
44.0ms	(cbrt.f64 (+.f64 x 1))
42.0ms	(cbrt.f64 (+.f64 x 1))
40.0ms	(cbrt.f64 (+.f64 x 1))

simplify44.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	4948	1712
1	4948	1712

prune212.0ms (1.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	69	3	72
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	69	11	80

Merged error: 23.9b

Counts

80 → 11

Compiler

Compiled 4125 to 3071 computations (25.6% 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)))

rewrite41.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`add-sqr-sqrt_binary64_445`
39×	`*-un-lft-identity_binary64_423` `pow-unpow_binary64_500`
30×	`add-cube-cbrt_binary64_458`
27×	`times-frac_binary64_429`
23×	`unpow-prod-down_binary64_502`
10×	`sqr-pow_binary64_395`
9×	`difference-of-squares_binary64_392`
7×	`cancel-sign-sub-inv_binary64_389` `pow1_binary64_484` `add-exp-log_binary64_461`
6×	`add-log-exp_binary64_462`
4×	`add-cbrt-cube_binary64_459`
3×	`pow-to-exp_binary64_492` `pow-exp_binary64_491` `distribute-lft-out--_binary64_375` `pow-pow_binary64_495` `div-inv_binary64_420`
2×	`distribute-lft-out_binary64_374`
1×	`sub-neg_binary64_416` `diff-log_binary64_515` `flip3--_binary64_427` `flip--_binary64_398`

Counts

4 → 112

Calls

4 calls:

14.0ms	(-.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))
4.0ms	(pow.f64 x (/.f64 1/2 n))
4.0ms	(pow.f64 x (/.f64 1/2 n))

series523.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

253.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1/2 n)) (pow.f64 x (/.f64 1/2 n)))
105.0ms	(pow.f64 (+.f64 x 1) (/.f64 1/2 n))
83.0ms	(pow.f64 x (/.f64 1/2 n))
81.0ms	(pow.f64 x (/.f64 1/2 n))

simplify65.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5100	2207

prune343.0ms (2.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	121	3	124
Fresh	2	7	9
Picked	1	0	1
Done	0	1	1
Total	124	11	135

Merged error: 23.9b

Counts

135 → 11

Compiler

Compiled 6332 to 4522 computations (28.6% 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)))

rewrite34.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64_445`
34×	`*-un-lft-identity_binary64_423`
33×	`times-frac_binary64_429`
30×	`add-cube-cbrt_binary64_458`
16×	`exp-prod_binary64_475`
13×	`pow-unpow_binary64_500`
12×	`pow1_binary64_484`
7×	`log-pow_binary64_512` `add-exp-log_binary64_461` `add-log-exp_binary64_462`
6×	`add-cbrt-cube_binary64_459`
5×	`unpow-prod-down_binary64_502`
4×	`div-inv_binary64_420` `associate-/l*_binary64_368`
3×	`cancel-sign-sub-inv_binary64_389` `difference-of-squares_binary64_392` `associate-/r*_binary64_367`
2×	`sqr-pow_binary64_395`
1×	`sub-neg_binary64_416` `pow-to-exp_binary64_492` `diff-log_binary64_515` `exp-to-pow_binary64_485` `distribute-lft-out_binary64_374` `pow-exp_binary64_491` `rem-exp-log_binary64_463` `flip3--_binary64_427` `clear-num_binary64_422` `distribute-lft-out--_binary64_375` `pow-pow_binary64_495` `frac-2neg_binary64_434` `flip--_binary64_398` `cbrt-undiv_binary64_457` `div-exp_binary64_474`

Counts

4 → 102

Calls

4 calls:

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))
5.0ms	(exp.f64 (/.f64 (log.f64 x) n))
4.0ms	(/.f64 (log.f64 x) n)

series512.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

262.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (exp.f64 (/.f64 (log.f64 x) n)))
91.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
82.0ms	(/.f64 (log.f64 x) n)
77.0ms	(exp.f64 (/.f64 (log.f64 x) n))

simplify90.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4898	1754
1	4898	1754

prune169.0ms (1.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	0	9	9
Picked	1	0	1
Done	0	1	1
Total	114	11	125

Merged error: 23.9b

Counts

125 → 11

Compiler

Compiled 3501 to 2065 computations (41% saved)

regimes193.0ms (1.6%)

Compiler: Compiled 1869 to 1408 computations (24.7% saved)

bsearch2.0ms (0%)

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

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	89	158
1	89	158

end0.0ms (0%)

sample6.8s (55.2%)

Algorithm

1×

intervals

Results

1.4s	2645×	body	1024	valid
1.2s	1390×	body	1024	nan
1.2s	1743×	body	2048	valid
497.0ms	2580×	body	128	overflowed
440.0ms	1238×	body	512	valid
372.0ms	715×	body	512	nan
195.0ms	195×	body	1024	invalid
185.0ms	1806×	body	128	valid
126.0ms	568×	body	256	valid
123.0ms	229×	body	512	invalid
88.0ms	350×	body	256	nan
62.0ms	817×	body	128	nan
44.0ms	157×	body	256	invalid
38.0ms	264×	body	128	invalid
6.0ms	6×	body	2048	nan
1.0ms	1×	body	2048	invalid

Compiler

Compiled 542 to 403 computations (25.6% saved)

Details

analyze1.1s (9.2%)

sample207.0ms (1.7%)

simplify218.0ms (1.8%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite30.0ms (0.2%)

series457.0ms (3.7%)

simplify93.0ms (0.7%)

prune416.0ms (3.3%)

localize14.0ms (0.1%)

rewrite31.0ms (0.3%)

series700.0ms (5.6%)

simplify44.0ms (0.4%)

prune212.0ms (1.7%)

localize11.0ms (0.1%)

rewrite41.0ms (0.3%)

series523.0ms (4.2%)

simplify65.0ms (0.5%)

prune343.0ms (2.8%)

localize11.0ms (0.1%)

rewrite34.0ms (0.3%)

series512.0ms (4.1%)

simplify90.0ms (0.7%)

prune169.0ms (1.4%)

regimes193.0ms (1.6%)

bsearch2.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample6.8s (55.2%)

Profiling