Details

analyze6.0ms (0.2%)

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)

sample40.0ms (1.3%)

Algorithm

1×

intervals

Results

15.0ms	65×	body	1024	valid
9.0ms	139×	body	128	valid
6.0ms	14×	body	2048	valid
4.0ms	26×	body	512	valid
1.0ms	12×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify159.0ms (5.1%)

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: 28.6b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

2.3b	(log.f64 (+.f64 N 1))
2.6b	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))

rewrite17.0ms (0.5%)

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:

11.0ms	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
3.0ms	(log.f64 (+.f64 N 1))

series70.0ms (2.3%)

Counts

2 → 6

Calls

2 calls:

48.0ms	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
23.0ms	(log.f64 (+.f64 N 1))

simplify105.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 0 (94.0ms)

Iter	Nodes	Cost
0	4866	648
1	4866	648

prune55.0ms (1.8%)

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: 0.1b

Counts

47 → 4

Compiler

Compiled 660 to 436 computations (33.9% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (+.f64 N 1) N)
2.7b	(log.f64 (/.f64 (+.f64 N 1) N))

rewrite15.0ms (0.5%)

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))

series105.0ms (3.4%)

Counts

2 → 6

Calls

2 calls:

62.0ms	(/.f64 (+.f64 N 1) N)
43.0ms	(log.f64 (/.f64 (+.f64 N 1) N))

simplify71.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5305	940

prune50.0ms (1.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

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

Merged error: 0.1b

Counts

70 → 4

Compiler

Compiled 849 to 574 computations (32.4% saved)

localize16.0ms (0.5%)

Local error

Found 4 expressions with local error:

2.3b	(log.f64 (+.f64 N 1))
2.3b	(log.f64 (+.f64 N 1))
2.3b	(log.f64 (+.f64 N 1))
2.5b	(-.f64 (pow.f64 (log.f64 (+.f64 N 1)) 3) (pow.f64 (log.f64 N) 3))

rewrite36.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`*-un-lft-identity_binary64_77` `add-sqr-sqrt_binary64_98`
24×	`unpow-prod-down_binary64_153` `cube-prod_binary64_102`
23×	`pow1_binary64_135`
19×	`log-pow_binary64_163`
17×	`distribute-lft-out--_binary64_31`
16×	`difference-of-squares_binary64_46`
12×	`log-prod_binary64_160`
8×	`sqr-pow_binary64_49`
7×	`add-exp-log_binary64_112` `add-cube-cbrt_binary64_109`
6×	`add-log-exp_binary64_113` `log-div_binary64_161`
4×	`add-cbrt-cube_binary64_110`
3×	`rem-log-exp_binary64_115` `flip-+_binary64_51` `flip3-+_binary64_80` `distribute-lft-out_binary64_30`
1×	`difference-cubes_binary64_79` `sub-neg_binary64_70` `flip--_binary64_52` `flip3--_binary64_81` `diff-log_binary64_166`

Counts

4 → 90

Calls

4 calls:

15.0ms	(-.f64 (pow.f64 (log.f64 (+.f64 N 1)) 3) (pow.f64 (log.f64 N) 3))
3.0ms	(log.f64 (+.f64 N 1))
3.0ms	(log.f64 (+.f64 N 1))
3.0ms	(log.f64 (+.f64 N 1))

series287.0ms (9.2%)

Counts

4 → 12

Calls

4 calls:

213.0ms	(-.f64 (pow.f64 (log.f64 (+.f64 N 1)) 3) (pow.f64 (log.f64 N) 3))
27.0ms	(log.f64 (+.f64 N 1))
25.0ms	(log.f64 (+.f64 N 1))
22.0ms	(log.f64 (+.f64 N 1))

simplify44.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5289	2220

prune197.0ms (6.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	102	4	106

Merged error: 0.0b

Counts

106 → 4

Compiler

Compiled 4054 to 2572 computations (36.6% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1 N))
0.1b	(/.f64 1/3 (pow.f64 N 3))
0.6b	(/.f64 1/2 (*.f64 N N))
11.4b	(-.f64 (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1 N)) (/.f64 1/2 (*.f64 N N)))

rewrite90.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`*-un-lft-identity_binary64_77`
42×	`times-frac_binary64_83`
35×	`add-sqr-sqrt_binary64_98`
31×	`add-cube-cbrt_binary64_109`
14×	`add-exp-log_binary64_112`
13×	`associate-/r*_binary64_23`
12×	`unpow-prod-down_binary64_153` `cube-prod_binary64_102`
11×	`add-cbrt-cube_binary64_110` `add-log-exp_binary64_113`
6×	`associate-/l*_binary64_24`
5×	`div-exp_binary64_125` `distribute-lft-out_binary64_30`
4×	`sqr-pow_binary64_49` `pow1_binary64_135` `cube-mult_binary64_104` `div-inv_binary64_74` `unpow3_binary64_140`
3×	`cbrt-undiv_binary64_108` `distribute-lft-out--_binary64_31` `frac-sub_binary64_86`
2×	`frac-add_binary64_85` `flip-+_binary64_51` `flip3-+_binary64_80` `difference-of-squares_binary64_46` `clear-num_binary64_76` `diff-log_binary64_166` `frac-2neg_binary64_88` `sum-log_binary64_165`
1×	`pow-to-exp_binary64_143` `cbrt-unprod_binary64_107` `associate--l+_binary64_16` `sub-neg_binary64_70` `pow-exp_binary64_142` `flip--_binary64_52` `+-commutative_binary64_9` `prod-exp_binary64_123` `flip3--_binary64_81`

Counts

4 → 122

Calls

4 calls:

39.0ms	(-.f64 (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1 N)) (/.f64 1/2 (*.f64 N N)))
30.0ms	(+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1 N))
6.0ms	(/.f64 1/3 (pow.f64 N 3))
5.0ms	(/.f64 1/2 (*.f64 N N))

series206.0ms (6.6%)

Counts

4 → 12

Calls

4 calls:

89.0ms	(+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1 N))
47.0ms	(/.f64 1/3 (pow.f64 N 3))
40.0ms	(/.f64 1/2 (*.f64 N N))
29.0ms	(-.f64 (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1 N)) (/.f64 1/2 (*.f64 N N)))

simplify48.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5095	2154

prune144.0ms (4.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	132	2	134
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	132	6	138

Merged error: 0.0b

Counts

138 → 6

Compiler

Compiled 2771 to 1916 computations (30.9% saved)

regimes24.0ms (0.8%)

Compiler: Compiled 149 to 98 computations (34.2% saved)

bsearch18.0ms (0.6%)

Steps

Iters	Range		Point
8	15.591766883003832	7979.45918561764	7619.493613923111

Compiler

Compiled 1 to 1 computations (0% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	37
1	39	37

end0.0ms (0%)

sample1.3s (41.3%)

Algorithm

1×

intervals

Results

481.0ms	2033×	body	1024	valid
248.0ms	4301×	body	128	valid
141.0ms	941×	body	512	valid
101.0ms	258×	body	2048	valid
42.0ms	467×	body	256	valid

Compiler

Compiled 180 to 123 computations (31.7% saved)

Details

analyze6.0ms (0.2%)

sample40.0ms (1.3%)

simplify159.0ms (5.1%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

rewrite17.0ms (0.5%)

series70.0ms (2.3%)

simplify105.0ms (3.4%)

prune55.0ms (1.8%)

localize5.0ms (0.1%)

rewrite15.0ms (0.5%)

series105.0ms (3.4%)

simplify71.0ms (2.3%)

prune50.0ms (1.6%)

localize16.0ms (0.5%)

rewrite36.0ms (1.2%)

series287.0ms (9.2%)

simplify44.0ms (1.4%)

prune197.0ms (6.3%)

localize10.0ms (0.3%)

rewrite90.0ms (2.9%)

series206.0ms (6.6%)

simplify48.0ms (1.5%)

prune144.0ms (4.6%)

regimes24.0ms (0.8%)

bsearch18.0ms (0.6%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.3s (41.3%)

Profiling