Details

analyze2.0ms (0.1%)

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)

sample39.0ms (1.2%)

Algorithm

1×

intervals

Results

18.0ms	74×	body	1024	valid
8.0ms	128×	body	128	valid
4.0ms	29×	body	512	valid
2.0ms	21×	body	256	valid
2.0ms	4×	body	2048	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify96.0ms (3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

prune7.0ms (0.2%)

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

Error

31.6b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

3.0b	(log.f64 (+.f64 N 1))
3.4b	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))

rewrite14.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64_78`
11×	`log-prod_binary64_164`
8×	`add-sqr-sqrt_binary64_100` `pow1_binary64_139`
6×	`add-cube-cbrt_binary64_113` `log-pow_binary64_167`
4×	`distribute-lft-out--_binary64_30` `associate--l+_binary64_15` `log-div_binary64_165` `cancel-sign-sub-inv_binary64_44`
3×	`associate--r+_binary64_14` `add-exp-log_binary64_116`
2×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117` `flip-+_binary64_52` `distribute-lft-out_binary64_29` `associate--l-_binary64_16` `flip3-+_binary64_81`
1×	`flip3--_binary64_82` `diff-log_binary64_170` `flip--_binary64_53` `rem-log-exp_binary64_119` `difference-of-squares_binary64_47` `sub-neg_binary64_71`

Counts

2 → 44

Calls

2 calls:

8.0ms	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
3.0ms	(log.f64 (+.f64 N 1))

series42.0ms (1.3%)

Counts

2 → 6

Calls

2 calls:

29.0ms	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
12.0ms	(log.f64 (+.f64 N 1))

simplify93.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4935	668
1	4935	668

prune50.0ms (1.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	48	2	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	49	2	51

Error

0.0b

Counts

51 → 2

Compiler

Compiled 646 to 420 computations (35% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.2b	(/.f64 1/3 (pow.f64 N 3))
0.3b	(/.f64 1/2 (*.f64 N N))
13.6b	(-.f64 (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1 N)) (/.f64 1/2 (*.f64 N N)))

rewrite58.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`times-frac_binary64_84`
39×	`*-un-lft-identity_binary64_78`
36×	`add-sqr-sqrt_binary64_100`
32×	`add-cube-cbrt_binary64_113`
13×	`associate-/r*_binary64_22` `add-exp-log_binary64_116`
12×	`unpow-prod-down_binary64_157` `cube-prod_binary64_106`
10×	`add-cbrt-cube_binary64_114`
8×	`add-log-exp_binary64_117`
7×	`cancel-sign-sub-inv_binary64_44`
6×	`associate-/l*_binary64_23`
5×	`div-exp_binary64_129`
4×	`cube-mult_binary64_108` `sqr-pow_binary64_50` `div-inv_binary64_75` `unpow3_binary64_144`
3×	`cbrt-undiv_binary64_112` `frac-sub_binary64_87` `distribute-lft-out--_binary64_30` `pow1_binary64_139`
2×	`diff-log_binary64_170` `frac-2neg_binary64_89` `difference-of-squares_binary64_47` `clear-num_binary64_77` `distribute-lft-out_binary64_29`
1×	`pow-exp_binary64_146` `pow-to-exp_binary64_147` `frac-add_binary64_86` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `flip-+_binary64_52` `flip3--_binary64_82` `associate--l+_binary64_15` `flip--_binary64_53` `sub-neg_binary64_71` `sum-log_binary64_169` `flip3-+_binary64_81`

Counts

3 → 114

Calls

3 calls:

39.0ms	(-.f64 (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1 N)) (/.f64 1/2 (*.f64 N N)))
5.0ms	(/.f64 1/3 (pow.f64 N 3))
4.0ms	(/.f64 1/2 (*.f64 N N))

series53.0ms (1.7%)

Counts

3 → 9

Calls

3 calls:

22.0ms	(/.f64 1/3 (pow.f64 N 3))
17.0ms	(/.f64 1/2 (*.f64 N N))
14.0ms	(-.f64 (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1 N)) (/.f64 1/2 (*.f64 N N)))

simplify71.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4955	1941
1	4955	1941

prune141.0ms (4.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	122	3	125

Error

Counts

125 → 3

Compiler

Compiled 2579 to 1783 computations (30.9% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (sqrt.f64 1/2) N)
0.4b	(/.f64 (sqrt.f64 1/2) N)
9.9b	(sqrt.f64 (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1 N)))
9.9b	(sqrt.f64 (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1 N)))

rewrite82.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`*-un-lft-identity_binary64_78`
40×	`times-frac_binary64_84`
38×	`add-sqr-sqrt_binary64_100`
36×	`sqrt-prod_binary64_94` `add-cube-cbrt_binary64_113`
12×	`associate-/l*_binary64_23`
8×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
6×	`associate-/r*_binary64_22` `sqrt-div_binary64_95` `distribute-lft-out_binary64_29` `pow1_binary64_139`
4×	`add-log-exp_binary64_117` `div-inv_binary64_75`
2×	`frac-add_binary64_86` `sqrt-pow1_binary64_96` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `flip-+_binary64_52` `rem-sqrt-square_binary64_91` `frac-2neg_binary64_89` `clear-num_binary64_77` `pow1/2_binary64_158` `flip3-+_binary64_81`

Counts

4 → 116

Calls

4 calls:

31.0ms	(sqrt.f64 (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1 N)))
29.0ms	(sqrt.f64 (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1 N)))
4.0ms	(/.f64 (sqrt.f64 1/2) N)
4.0ms	(/.f64 (sqrt.f64 1/2) N)

series86.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

28.0ms	(/.f64 (sqrt.f64 1/2) N)
23.0ms	(/.f64 (sqrt.f64 1/2) N)
17.0ms	(sqrt.f64 (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1 N)))
17.0ms	(sqrt.f64 (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1 N)))

simplify71.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5178	2018

prune286.0ms (8.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	128	3	131

Error

Counts

131 → 3

Compiler

Compiled 4779 to 3794 computations (20.6% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(log.f64 (log.f64 (+.f64 N 1)))
0.8b	(exp.f64 (log.f64 (log.f64 (+.f64 N 1))))
3.0b	(log.f64 (+.f64 N 1))
28.8b	(-.f64 (exp.f64 (log.f64 (log.f64 (+.f64 N 1)))) (log.f64 N))

rewrite18.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`log-prod_binary64_164`
15×	`*-un-lft-identity_binary64_78`
14×	`add-sqr-sqrt_binary64_100`
11×	`pow1_binary64_139`
10×	`add-cube-cbrt_binary64_113`
7×	`log-pow_binary64_167`
6×	`add-exp-log_binary64_116`
5×	`add-log-exp_binary64_117` `exp-sum_binary64_124`
4×	`add-cbrt-cube_binary64_114` `exp-prod_binary64_130` `cancel-sign-sub-inv_binary64_44`
3×	`associate--r+_binary64_14`
2×	`distribute-lft-out--_binary64_30` `rem-log-exp_binary64_119` `log-div_binary64_165` `difference-of-squares_binary64_47`
1×	`flip-+_binary64_52` `flip3--_binary64_82` `diff-log_binary64_170` `rem-exp-log_binary64_118` `flip--_binary64_53` `distribute-lft-out_binary64_29` `sub-neg_binary64_71` `flip3-+_binary64_81`

Counts

4 → 66

Calls

4 calls:

7.0ms	(-.f64 (exp.f64 (log.f64 (log.f64 (+.f64 N 1)))) (log.f64 N))
3.0ms	(log.f64 (+.f64 N 1))
2.0ms	(exp.f64 (log.f64 (log.f64 (+.f64 N 1))))
1.0ms	(log.f64 (log.f64 (+.f64 N 1)))

series133.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

55.0ms	(-.f64 (exp.f64 (log.f64 (log.f64 (+.f64 N 1)))) (log.f64 N))
37.0ms	(exp.f64 (log.f64 (log.f64 (+.f64 N 1))))
27.0ms	(log.f64 (log.f64 (+.f64 N 1)))
15.0ms	(log.f64 (+.f64 N 1))

simplify63.0ms (2%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5883	1056

prune63.0ms (2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	78	3	81

Error

Counts

81 → 3

Compiler

Compiled 1076 to 724 computations (32.7% saved)

regimes91.0ms (2.8%)

Accuracy

Total 0.1b remaining (74.3%)

Threshold costs 0.1b (74.3%)

Compiler

Compiled 814 to 650 computations (20.1% saved)

bsearch1.0ms (0%)

Compiler: Compiled 7 to 6 computations (14.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	48	49
1	48	49

end0.0ms (0%)

sample1.6s (50%)

Algorithm

1×

intervals

Results

468.0ms	1932×	body	1024	valid
260.0ms	4333×	body	128	valid
157.0ms	1016×	body	512	valid
88.0ms	233×	body	2048	valid
49.0ms	486×	body	256	valid

Compiler

Compiled 439 to 350 computations (20.3% saved)

Details

analyze2.0ms (0.1%)

sample39.0ms (1.2%)

simplify96.0ms (3%)

prune7.0ms (0.2%)

localize7.0ms (0.2%)

rewrite14.0ms (0.4%)

series42.0ms (1.3%)

simplify93.0ms (2.9%)

prune50.0ms (1.6%)

localize9.0ms (0.3%)

rewrite58.0ms (1.8%)

series53.0ms (1.7%)

simplify71.0ms (2.2%)

prune141.0ms (4.4%)

localize13.0ms (0.4%)

rewrite82.0ms (2.6%)

series86.0ms (2.7%)

simplify71.0ms (2.2%)

prune286.0ms (8.9%)

localize9.0ms (0.3%)

rewrite18.0ms (0.6%)

series133.0ms (4.2%)

simplify63.0ms (2%)

prune63.0ms (2%)

regimes91.0ms (2.8%)

bsearch1.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.6s (50%)

Profiling