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)

sample40.0ms (1%)

Algorithm

1×

intervals

Results

18.0ms	82×	body	1024	valid
7.0ms	123×	body	128	valid
4.0ms	30×	body	512	valid
4.0ms	10×	body	2048	valid
1.0ms	11×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify96.0ms (2.3%)

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: 32.8b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

2.6b	(log.f64 (+.f64 N 1))
3.5b	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))

rewrite14.0ms (0.3%)

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))

series44.0ms (1.1%)

Counts

2 → 6

Calls

2 calls:

31.0ms	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
13.0ms	(log.f64 (+.f64 N 1))

simplify90.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4943	668
1	4943	668

prune52.0ms (1.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	47	3	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	3	51

Merged error: 0.1b

Counts

51 → 3

Compiler

Compiled 657 to 427 computations (35% saved)

localize9.0ms (0.2%)

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))
0.5b	(/.f64 1/2 (*.f64 N N))
14.6b	(-.f64 (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1 N)) (/.f64 1/2 (*.f64 N N)))

rewrite94.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`*-un-lft-identity_binary64_78`
45×	`times-frac_binary64_84`
37×	`add-sqr-sqrt_binary64_100`
33×	`add-cube-cbrt_binary64_113`
14×	`add-exp-log_binary64_116`
13×	`associate-/r*_binary64_22`
12×	`unpow-prod-down_binary64_157` `cube-prod_binary64_106`
11×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117`
7×	`cancel-sign-sub-inv_binary64_44`
6×	`associate-/l*_binary64_23`
5×	`div-exp_binary64_129` `div-inv_binary64_75` `distribute-lft-out_binary64_29`
4×	`cube-mult_binary64_108` `sqr-pow_binary64_50` `unpow3_binary64_144` `pow1_binary64_139`
3×	`cbrt-undiv_binary64_112` `frac-sub_binary64_87` `distribute-lft-out--_binary64_30`
2×	`frac-add_binary64_86` `flip-+_binary64_52` `diff-log_binary64_170` `frac-2neg_binary64_89` `difference-of-squares_binary64_47` `clear-num_binary64_77` `sum-log_binary64_169` `flip3-+_binary64_81`
1×	`+-commutative_binary64_8` `pow-exp_binary64_146` `pow-to-exp_binary64_147` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `flip3--_binary64_82` `associate--l+_binary64_15` `flip--_binary64_53` `sub-neg_binary64_71`

Counts

4 → 129

Calls

4 calls:

41.0ms	(-.f64 (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1 N)) (/.f64 1/2 (*.f64 N N)))
32.0ms	(+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1 N))
6.0ms	(/.f64 1/3 (pow.f64 N 3))
4.0ms	(/.f64 1/2 (*.f64 N N))

series94.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

36.0ms	(+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1 N))
27.0ms	(/.f64 1/3 (pow.f64 N 3))
16.0ms	(/.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)))

simplify51.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	4952	2250
1	4952	2250

prune163.0ms (3.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	139	2	141
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	139	5	144

Merged error: 0.1b

Counts

144 → 5

Compiler

Compiled 3008 to 2087 computations (30.6% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

8.7b	(sqrt.f64 (-.f64 (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1 N)) (/.f64 1/2 (*.f64 N N))))
8.7b	(sqrt.f64 (-.f64 (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1 N)) (/.f64 1/2 (*.f64 N N))))
14.6b	(-.f64 (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1 N)) (/.f64 1/2 (*.f64 N N)))
14.6b	(-.f64 (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1 N)) (/.f64 1/2 (*.f64 N N)))

rewrite176.0ms (4.3%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64_78`
28×	`add-sqr-sqrt_binary64_100`
16×	`sqrt-prod_binary64_94`
14×	`add-log-exp_binary64_117` `cancel-sign-sub-inv_binary64_44`
12×	`frac-sub_binary64_87` `distribute-lft-out--_binary64_30`
10×	`add-cube-cbrt_binary64_113` `times-frac_binary64_84` `sqrt-div_binary64_95`
8×	`difference-of-squares_binary64_47` `distribute-lft-out_binary64_29`
6×	`div-inv_binary64_75` `pow1_binary64_139`
4×	`add-cbrt-cube_binary64_114` `frac-add_binary64_86` `flip-+_binary64_52` `flip3--_binary64_82` `diff-log_binary64_170` `flip--_binary64_53` `add-exp-log_binary64_116` `flip3-+_binary64_81`
2×	`sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `associate--l+_binary64_15` `pow1/2_binary64_158` `sub-neg_binary64_71` `sum-log_binary64_169`

Counts

4 → 102

Calls

4 calls:

43.0ms	(sqrt.f64 (-.f64 (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1 N)) (/.f64 1/2 (*.f64 N N))))
42.0ms	(-.f64 (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1 N)) (/.f64 1/2 (*.f64 N N)))
39.0ms	(-.f64 (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1 N)) (/.f64 1/2 (*.f64 N N)))
38.0ms	(sqrt.f64 (-.f64 (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1 N)) (/.f64 1/2 (*.f64 N N))))

series84.0ms (2%)

Counts

4 → 12

Calls

4 calls:

28.0ms	(sqrt.f64 (-.f64 (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1 N)) (/.f64 1/2 (*.f64 N N))))
26.0ms	(sqrt.f64 (-.f64 (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1 N)) (/.f64 1/2 (*.f64 N N))))
15.0ms	(-.f64 (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1 N)) (/.f64 1/2 (*.f64 N N)))
15.0ms	(-.f64 (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1 N)) (/.f64 1/2 (*.f64 N N)))

simplify93.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4876	3678
1	4876	3678

prune265.0ms (6.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	114	5	119

Merged error: 0.1b

Counts

119 → 5

Compiler

Compiled 4992 to 3559 computations (28.7% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

14.6b	(-.f64 (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1 N)) (/.f64 1/2 (*.f64 N N)))
20.6b	(cbrt.f64 (-.f64 (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1 N)) (/.f64 1/2 (*.f64 N N))))
20.6b	(cbrt.f64 (-.f64 (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1 N)) (/.f64 1/2 (*.f64 N N))))
20.6b	(cbrt.f64 (-.f64 (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1 N)) (/.f64 1/2 (*.f64 N N))))

rewrite178.0ms (4.3%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`*-un-lft-identity_binary64_78`
25×	`add-sqr-sqrt_binary64_100`
24×	`cbrt-prod_binary64_109`
15×	`cbrt-div_binary64_110`
12×	`frac-sub_binary64_87` `distribute-lft-out--_binary64_30`
9×	`add-log-exp_binary64_117` `add-cube-cbrt_binary64_113`
8×	`difference-of-squares_binary64_47` `distribute-lft-out_binary64_29`
7×	`times-frac_binary64_84` `cancel-sign-sub-inv_binary64_44`
5×	`div-inv_binary64_75`
4×	`add-cbrt-cube_binary64_114` `frac-add_binary64_86` `flip-+_binary64_52` `flip3--_binary64_82` `flip--_binary64_53` `add-exp-log_binary64_116` `pow1_binary64_139` `flip3-+_binary64_81`
3×	`pow1/3_binary64_160`
2×	`diff-log_binary64_170`
1×	`associate--l+_binary64_15` `sub-neg_binary64_71` `sum-log_binary64_169`

Counts

4 → 91

Calls

4 calls:

43.0ms	(cbrt.f64 (-.f64 (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1 N)) (/.f64 1/2 (*.f64 N N))))
42.0ms	(cbrt.f64 (-.f64 (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1 N)) (/.f64 1/2 (*.f64 N N))))
39.0ms	(-.f64 (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1 N)) (/.f64 1/2 (*.f64 N N)))
38.0ms	(cbrt.f64 (-.f64 (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1 N)) (/.f64 1/2 (*.f64 N N))))

series136.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

45.0ms	(cbrt.f64 (-.f64 (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1 N)) (/.f64 1/2 (*.f64 N N))))
39.0ms	(cbrt.f64 (-.f64 (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1 N)) (/.f64 1/2 (*.f64 N N))))
38.0ms	(cbrt.f64 (-.f64 (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1 N)) (/.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)))

simplify99.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4977	3738
1	4977	3738

prune361.0ms (8.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	103	5	108

Merged error: 0.1b

Counts

108 → 5

Compiler

Compiled 6361 to 4555 computations (28.4% saved)

regimes150.0ms (3.6%)

Compiler: Compiled 1593 to 1247 computations (21.7% saved)

bsearch2.0ms (0%)

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

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	53	61
1	53	61

end0.0ms (0%)

sample1.8s (43.7%)

Algorithm

1×

intervals

Results

460.0ms	2024×	body	1024	valid
238.0ms	4281×	body	128	valid
148.0ms	1004×	body	512	valid
86.0ms	240×	body	2048	valid
39.0ms	451×	body	256	valid

Compiler

Compiled 812 to 636 computations (21.7% saved)

Details

analyze2.0ms (0%)

sample40.0ms (1%)

simplify96.0ms (2.3%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

rewrite14.0ms (0.3%)

series44.0ms (1.1%)

simplify90.0ms (2.2%)

prune52.0ms (1.3%)

localize9.0ms (0.2%)

rewrite94.0ms (2.3%)

series94.0ms (2.3%)

simplify51.0ms (1.2%)

prune163.0ms (3.9%)

localize12.0ms (0.3%)

rewrite176.0ms (4.3%)

series84.0ms (2%)

simplify93.0ms (2.2%)

prune265.0ms (6.4%)

localize14.0ms (0.3%)

rewrite178.0ms (4.3%)

series136.0ms (3.3%)

simplify99.0ms (2.4%)

prune361.0ms (8.7%)

regimes150.0ms (3.6%)

bsearch2.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.8s (43.7%)

Profiling