Details

analyze2.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	0%	50%	4

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample38.0ms (0.9%)

Algorithm

1×

intervals

Results

14.0ms	60×	body	1024	valid
8.0ms	142×	body	128	valid
4.0ms	11×	body	2048	valid
4.0ms	28×	body	512	valid
1.0ms	15×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify168.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

prune2.0ms (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: 28.1b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

2.8b	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
3.4b	(log.f64 (+.f64 N 1))

rewrite15.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64_77`
11×	`log-prod_binary64_160`
7×	`pow1_binary64_135` `add-sqr-sqrt_binary64_98`
5×	`add-cube-cbrt_binary64_109` `log-pow_binary64_163`
4×	`associate--l+_binary64_16` `distribute-lft-out--_binary64_31` `log-div_binary64_161`
3×	`add-exp-log_binary64_112` `associate--r+_binary64_15`
2×	`add-cbrt-cube_binary64_110` `associate--l-_binary64_17` `add-log-exp_binary64_113` `flip-+_binary64_51` `flip3-+_binary64_80` `distribute-lft-out_binary64_30`
1×	`rem-log-exp_binary64_115` `sub-neg_binary64_70` `flip--_binary64_52` `difference-of-squares_binary64_46` `flip3--_binary64_81` `diff-log_binary64_166`

Counts

2 → 40

Calls

2 calls:

8.0ms	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
4.0ms	(log.f64 (+.f64 N 1))

series75.0ms (1.8%)

Counts

2 → 6

Calls

2 calls:

50.0ms	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
25.0ms	(log.f64 (+.f64 N 1))

simplify107.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 0 (93.0ms)

Iter	Nodes	Cost
0	4866	648
1	4866	648

prune56.0ms (1.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	42	4	46
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	4	47

Merged error: 0.0b

Counts

47 → 4

Compiler

Compiled 639 to 423 computations (33.8% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (+.f64 N 1) N)
2.8b	(log.f64 (/.f64 (+.f64 N 1) N))

rewrite16.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`*-un-lft-identity_binary64_77`
24×	`times-frac_binary64_83`
19×	`add-cube-cbrt_binary64_109` `add-sqr-sqrt_binary64_98`
16×	`log-prod_binary64_160`
7×	`add-exp-log_binary64_112` `distribute-lft-out_binary64_30`
4×	`add-cbrt-cube_binary64_110` `associate-/l*_binary64_24`
3×	`associate-/r*_binary64_23` `pow1_binary64_135`
2×	`rem-log-exp_binary64_115` `add-log-exp_binary64_113` `div-exp_binary64_125` `associate-/l/_binary64_26` `div-inv_binary64_74`
1×	`flip-+_binary64_51` `cbrt-undiv_binary64_108` `flip3-+_binary64_80` `log-div_binary64_161` `clear-num_binary64_76` `log-pow_binary64_163` `frac-2neg_binary64_88`

Counts

2 → 60

Calls

2 calls:

6.0ms	(/.f64 (+.f64 N 1) N)
5.0ms	(log.f64 (/.f64 (+.f64 N 1) N))

series103.0ms (2.5%)

Counts

2 → 6

Calls

2 calls:

60.0ms	(/.f64 (+.f64 N 1) N)
43.0ms	(log.f64 (/.f64 (+.f64 N 1) N))

simplify76.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5305	940

prune56.0ms (1.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	64	2	66
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	66	4	70

Merged error: 0.0b

Counts

70 → 4

Compiler

Compiled 833 to 563 computations (32.4% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 N)
0.6b	(cbrt.f64 N)
0.6b	(cbrt.f64 N)
3.4b	(+.f64 (log.f64 (/.f64 (sqrt.f64 (+.f64 N 1)) (*.f64 (cbrt.f64 N) (cbrt.f64 N)))) (log.f64 (/.f64 (sqrt.f64 (+.f64 N 1)) (cbrt.f64 N))))

rewrite39.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`log-prod_binary64_160`
55×	`*-un-lft-identity_binary64_77`
49×	`times-frac_binary64_83`
46×	`associate-+r+_binary64_11`
37×	`add-cube-cbrt_binary64_109` `add-sqr-sqrt_binary64_98`
30×	`cbrt-prod_binary64_105`
28×	`sqrt-prod_binary64_92`
11×	`associate-+l+_binary64_12` `distribute-lft-out_binary64_30`
8×	`pow1_binary64_135`
4×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110` `add-log-exp_binary64_113` `log-pow_binary64_163`
3×	`pow1/3_binary64_156`
2×	`log-div_binary64_161` `div-inv_binary64_74`
1×	`flip-+_binary64_51` `flip3-+_binary64_80` `associate-+l-_binary64_14` `+-commutative_binary64_9` `associate-+r-_binary64_13` `sum-log_binary64_165`

Counts

4 → 107

Calls

4 calls:

22.0ms	(+.f64 (log.f64 (/.f64 (sqrt.f64 (+.f64 N 1)) (*.f64 (cbrt.f64 N) (cbrt.f64 N)))) (log.f64 (/.f64 (sqrt.f64 (+.f64 N 1)) (cbrt.f64 N))))
1.0ms	(cbrt.f64 N)
1.0ms	(cbrt.f64 N)
1.0ms	(cbrt.f64 N)

series769.0ms (19%)

Counts

4 → 12

Calls

4 calls:

293.0ms	(+.f64 (log.f64 (/.f64 (sqrt.f64 (+.f64 N 1)) (*.f64 (cbrt.f64 N) (cbrt.f64 N)))) (log.f64 (/.f64 (sqrt.f64 (+.f64 N 1)) (cbrt.f64 N))))
173.0ms	(cbrt.f64 N)
152.0ms	(cbrt.f64 N)
151.0ms	(cbrt.f64 N)

simplify65.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4950	2559
1	4950	2559

prune165.0ms (4.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	119	4	123

Merged error: 0.0b

Counts

123 → 4

Compiler

Compiled 3086 to 2023 computations (34.4% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (+.f64 N 1) (cbrt.f64 N))
0.6b	(cbrt.f64 N)
0.6b	(cbrt.f64 N)
3.2b	(+.f64 (*.f64 (log.f64 (cbrt.f64 N)) -2) (log.f64 (/.f64 (+.f64 N 1) (cbrt.f64 N))))

rewrite32.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

64×	`*-un-lft-identity_binary64_77`
48×	`times-frac_binary64_83`
38×	`add-cube-cbrt_binary64_109` `add-sqr-sqrt_binary64_98`
33×	`cbrt-prod_binary64_105`
28×	`log-prod_binary64_160` `associate-+r+_binary64_11`
13×	`distribute-lft-out_binary64_30`
6×	`add-exp-log_binary64_112` `associate-/r*_binary64_23`
5×	`add-cbrt-cube_binary64_110` `add-log-exp_binary64_113`
4×	`pow1_binary64_135` `associate-/l*_binary64_24`
2×	`flip-+_binary64_51` `flip3-+_binary64_80` `pow1/3_binary64_156` `associate-/l/_binary64_26` `div-inv_binary64_74`
1×	`cbrt-undiv_binary64_108` `+-commutative_binary64_9` `associate-+r-_binary64_13` `div-exp_binary64_125` `log-div_binary64_161` `clear-num_binary64_76` `frac-2neg_binary64_88` `sum-log_binary64_165`

Counts

4 → 110

Calls

4 calls:

12.0ms	(+.f64 (*.f64 (log.f64 (cbrt.f64 N)) -2) (log.f64 (/.f64 (+.f64 N 1) (cbrt.f64 N))))
7.0ms	(/.f64 (+.f64 N 1) (cbrt.f64 N))
1.0ms	(cbrt.f64 N)
1.0ms	(cbrt.f64 N)

series754.0ms (18.6%)

Counts

4 → 12

Calls

4 calls:

292.0ms	(/.f64 (+.f64 N 1) (cbrt.f64 N))
166.0ms	(cbrt.f64 N)
159.0ms	(cbrt.f64 N)
135.0ms	(+.f64 (*.f64 (log.f64 (cbrt.f64 N)) -2) (log.f64 (/.f64 (+.f64 N 1) (cbrt.f64 N))))

simplify85.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4911	1927
1	4911	1927

prune117.0ms (2.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	122	4	126

Merged error: 0.0b

Counts

126 → 4

Compiler

Compiled 2333 to 1391 computations (40.4% saved)

regimes18.0ms (0.5%)

Compiler: Compiled 56 to 43 computations (23.2% saved)

bsearch18.0ms (0.4%)

Steps

Iters	Range		Point
9	247.75516650173577	543114540.1748827	7259.645207967956

Compiler

Compiled 1 to 1 computations (0% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	37
1	39	37

end0.0ms (0%)

sample1.2s (30.6%)

Algorithm

1×

intervals

Results

469.0ms	1947×	body	1024	valid
250.0ms	4291×	body	128	valid
149.0ms	1002×	body	512	valid
105.0ms	269×	body	2048	valid
47.0ms	491×	body	256	valid

Compiler

Compiled 87 to 68 computations (21.8% saved)

Details

analyze2.0ms (0%)

sample38.0ms (0.9%)

simplify168.0ms (4.1%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

rewrite15.0ms (0.4%)

series75.0ms (1.8%)

simplify107.0ms (2.6%)

prune56.0ms (1.4%)

localize5.0ms (0.1%)

rewrite16.0ms (0.4%)

series103.0ms (2.5%)

simplify76.0ms (1.9%)

prune56.0ms (1.4%)

localize13.0ms (0.3%)

rewrite39.0ms (1%)

series769.0ms (19%)

simplify65.0ms (1.6%)

prune165.0ms (4.1%)

localize11.0ms (0.3%)

rewrite32.0ms (0.8%)

series754.0ms (18.6%)

simplify85.0ms (2.1%)

prune117.0ms (2.9%)

regimes18.0ms (0.5%)

bsearch18.0ms (0.4%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.2s (30.6%)

Profiling