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 (1.3%)

Algorithm

1×

intervals

Results

14.0ms	59×	body	1024	valid
12.0ms	147×	body	128	valid
5.0ms	33×	body	512	valid
2.0ms	4×	body	2048	valid
1.0ms	13×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify163.0ms (5.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

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: 26.2b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

2.2b	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
3.5b	(log.f64 (+.f64 N 1))

rewrite18.0ms (0.6%)

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:

11.0ms	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
4.0ms	(log.f64 (+.f64 N 1))

series78.0ms (2.5%)

Counts

2 → 6

Calls

2 calls:

53.0ms	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
24.0ms	(log.f64 (+.f64 N 1))

simplify68.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5011	673

prune55.0ms (1.8%)

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

Merged error: 0.0b

Counts

51 → 2

Compiler

Compiled 646 to 419 computations (35.1% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (+.f64 N 1) N)
2.1b	(log.f64 (/.f64 (+.f64 N 1) N))

rewrite16.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`*-un-lft-identity_binary64_78`
24×	`times-frac_binary64_84`
19×	`add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113`
16×	`log-prod_binary64_164`
7×	`add-exp-log_binary64_116` `distribute-lft-out_binary64_29`
4×	`add-cbrt-cube_binary64_114` `associate-/l*_binary64_23`
3×	`associate-/r*_binary64_22` `pow1_binary64_139`
2×	`add-log-exp_binary64_117` `div-exp_binary64_129` `div-inv_binary64_75` `rem-log-exp_binary64_119` `associate-/l/_binary64_25`
1×	`cbrt-undiv_binary64_112` `flip-+_binary64_52` `frac-2neg_binary64_89` `log-div_binary64_165` `clear-num_binary64_77` `log-pow_binary64_167` `flip3-+_binary64_81`

Counts

2 → 60

Calls

2 calls:

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

series102.0ms (3.3%)

Counts

2 → 6

Calls

2 calls:

60.0ms	(/.f64 (+.f64 N 1) N)
42.0ms	(log.f64 (/.f64 (+.f64 N 1) N))

simplify73.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5428	940

prune49.0ms (1.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	66	2	68

Merged error: 0.0b

Counts

68 → 2

Compiler

Compiled 800 to 539 computations (32.6% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.4b	(/.f64 1/3 (pow.f64 N 3))
0.5b	(/.f64 1/2 (*.f64 N N))
12.6b	(-.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3))) (/.f64 1/2 (*.f64 N N)))

rewrite65.0ms (2.1%)

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:

41.0ms	(-.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3))) (/.f64 1/2 (*.f64 N N)))
6.0ms	(/.f64 1/3 (pow.f64 N 3))
5.0ms	(/.f64 1/2 (*.f64 N N))

series108.0ms (3.5%)

Counts

3 → 9

Calls

3 calls:

46.0ms	(/.f64 1/3 (pow.f64 N 3))
34.0ms	(/.f64 1/2 (*.f64 N N))
27.0ms	(-.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3))) (/.f64 1/2 (*.f64 N N)))

simplify50.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5110	1919

prune132.0ms (4.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	123	2	125

Merged error: 0b

Counts

125 → 2

Compiler

Compiled 2537 to 1756 computations (30.8% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 1 N) (-.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1/2 (*.f64 N N))))
0.4b	(/.f64 1/3 (pow.f64 N 3))
0.5b	(/.f64 1/2 (*.f64 N N))
12.6b	(-.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1/2 (*.f64 N N)))

rewrite98.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Rules

61×	`add-sqr-sqrt_binary64_100`
60×	`times-frac_binary64_84`
47×	`*-un-lft-identity_binary64_78`
35×	`add-cube-cbrt_binary64_113`
14×	`unpow-prod-down_binary64_157` `add-exp-log_binary64_116` `cancel-sign-sub-inv_binary64_44` `cube-prod_binary64_106`
13×	`associate-/r*_binary64_22`
11×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117`
10×	`difference-of-squares_binary64_47`
8×	`associate-+r+_binary64_10`
6×	`sqr-pow_binary64_50` `div-inv_binary64_75` `associate-/l*_binary64_23`
5×	`cube-mult_binary64_108` `div-exp_binary64_129`
4×	`distribute-lft-out--_binary64_30` `distribute-lft-out_binary64_29` `unpow3_binary64_144` `pow1_binary64_139`
3×	`frac-add_binary64_86` `cbrt-undiv_binary64_112`
2×	`frac-sub_binary64_87` `flip3--_binary64_82` `diff-log_binary64_170` `frac-2neg_binary64_89` `flip--_binary64_53` `clear-num_binary64_77` `sub-neg_binary64_71` `sum-log_binary64_169`
1×	`+-commutative_binary64_8` `pow-exp_binary64_146` `pow-to-exp_binary64_147` `associate-+r-_binary64_12` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `flip-+_binary64_52` `flip3-+_binary64_81`

Counts

4 → 145

Calls

4 calls:

44.0ms	(+.f64 (/.f64 1 N) (-.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1/2 (*.f64 N N))))
28.0ms	(-.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1/2 (*.f64 N N)))
6.0ms	(/.f64 1/3 (pow.f64 N 3))
5.0ms	(/.f64 1/2 (*.f64 N N))

series233.0ms (7.6%)

Counts

4 → 12

Calls

4 calls:

119.0ms	(-.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1/2 (*.f64 N N)))
52.0ms	(/.f64 1/3 (pow.f64 N 3))
33.0ms	(/.f64 1/2 (*.f64 N N))
29.0ms	(+.f64 (/.f64 1 N) (-.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1/2 (*.f64 N N))))

simplify54.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	4959	2680
1	4959	2680

prune181.0ms (5.9%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	157	0	157
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	157	2	159

Merged error: 0b

Counts

159 → 2

Compiler

Compiled 3295 to 2278 computations (30.9% saved)

regimes67.0ms (2.2%)

Compiler: Compiled 412 to 340 computations (17.5% saved)

bsearch1.0ms (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	54	61
1	54	61

end0.0ms (0%)

sample1.4s (45%)

Algorithm

1×

intervals

Results

451.0ms	1974×	body	1024	valid
243.0ms	4296×	body	128	valid
147.0ms	1036×	body	512	valid
87.0ms	228×	body	2048	valid
40.0ms	466×	body	256	valid

Compiler

Compiled 245 to 201 computations (18% saved)

Details

analyze2.0ms (0.1%)

sample39.0ms (1.3%)

simplify163.0ms (5.3%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

rewrite18.0ms (0.6%)

series78.0ms (2.5%)

simplify68.0ms (2.2%)

prune55.0ms (1.8%)

localize5.0ms (0.1%)

rewrite16.0ms (0.5%)

series102.0ms (3.3%)

simplify73.0ms (2.4%)

prune49.0ms (1.6%)

localize10.0ms (0.3%)

rewrite65.0ms (2.1%)

series108.0ms (3.5%)

simplify50.0ms (1.6%)

prune132.0ms (4.3%)

localize12.0ms (0.4%)

rewrite98.0ms (3.2%)

series233.0ms (7.6%)

simplify54.0ms (1.8%)

prune181.0ms (5.9%)

regimes67.0ms (2.2%)

bsearch1.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.4s (45%)

Profiling