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)

sample39.0ms (0.8%)

Algorithm

1×

intervals

Results

14.0ms	57×	body	1024	valid
9.0ms	142×	body	128	valid
6.0ms	36×	body	512	valid
3.0ms	6×	body	2048	valid
1.0ms	15×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify258.0ms (5.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

prune4.0ms (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: 28.4b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize11.0ms (0.2%)

Local error

Found 2 expressions with local error:

2.6b	(log.f64 (+.f64 N 1))
2.9b	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))

rewrite27.0ms (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:

15.0ms	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
6.0ms	(log.f64 (+.f64 N 1))

series136.0ms (2.9%)

Counts

2 → 6

Calls

2 calls:

96.0ms	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
40.0ms	(log.f64 (+.f64 N 1))

simplify90.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	5011	673

prune75.0ms (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

Merged error: 0.0b

Counts

51 → 2

Compiler

Compiled 649 to 422 computations (35% saved)

localize22.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(log.f64 (log.f64 (+.f64 N 1)))
0.7b	(exp.f64 (log.f64 (log.f64 (+.f64 N 1))))
2.6b	(log.f64 (+.f64 N 1))
25.0b	(-.f64 (exp.f64 (log.f64 (log.f64 (+.f64 N 1)))) (log.f64 N))

rewrite39.0ms (0.8%)

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:

16.0ms	(-.f64 (exp.f64 (log.f64 (log.f64 (+.f64 N 1)))) (log.f64 N))
7.0ms	(log.f64 (+.f64 N 1))
5.0ms	(exp.f64 (log.f64 (log.f64 (+.f64 N 1))))
3.0ms	(log.f64 (log.f64 (+.f64 N 1)))

series272.0ms (5.8%)

Counts

4 → 12

Calls

4 calls:

115.0ms	(-.f64 (exp.f64 (log.f64 (log.f64 (+.f64 N 1)))) (log.f64 N))
80.0ms	(exp.f64 (log.f64 (log.f64 (+.f64 N 1))))
54.0ms	(log.f64 (log.f64 (+.f64 N 1)))
22.0ms	(log.f64 (+.f64 N 1))

simplify112.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	5418	1064

prune106.0ms (2.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	78	2	80

Merged error: 0.0b

Counts

80 → 2

Compiler

Compiled 1096 to 741 computations (32.4% saved)

localize20.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1 N))
0.3b	(/.f64 1/3 (pow.f64 N 3))
0.4b	(/.f64 1/2 (*.f64 N N))
13.0b	(-.f64 (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1 N)) (/.f64 1/2 (*.f64 N N)))

rewrite133.0ms (2.8%)

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:

70.0ms	(-.f64 (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1 N)) (/.f64 1/2 (*.f64 N N)))
39.0ms	(+.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))

series222.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

89.0ms	(+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1 N))
51.0ms	(/.f64 1/3 (pow.f64 N 3))
44.0ms	(-.f64 (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1 N)) (/.f64 1/2 (*.f64 N N)))
37.0ms	(/.f64 1/2 (*.f64 N N))

simplify73.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	4967	2226
1	4967	2226

prune221.0ms (4.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	140	1	141
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	140	3	143

Merged error: 0b

Counts

143 → 3

Compiler

Compiled 2910 to 2017 computations (30.7% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 N N) (+.f64 (pow.f64 N 3) (*.f64 1/3 N)))
0.4b	(*.f64 1/3 N)
17.4b	(-.f64 (.f64 (.f64 N N) (+.f64 (pow.f64 N 3) (.f64 1/3 N))) (.f64 1/2 (pow.f64 N 4)))
47.9b	(/.f64 (-.f64 (.f64 (.f64 N N) (+.f64 (pow.f64 N 3) (.f64 1/3 N))) (.f64 1/2 (pow.f64 N 4))) (pow.f64 N 6))

rewrite95.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64_100`
23×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
21×	`times-frac_binary64_84`
16×	`add-exp-log_binary64_116`
13×	`add-cbrt-cube_binary64_114`
12×	`unpow-prod-down_binary64_157`
11×	`pow1_binary64_139`
7×	`associate-r_binary64_18` `associate-/r*_binary64_22`
6×	`add-log-exp_binary64_117`
4×	`associate-l_binary64_19` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `sqr-pow_binary64_50` `pow-prod-down_binary64_149`
3×	`div-exp_binary64_129` `associate-/l*_binary64_23`
2×	`distribute-lft-in_binary64_27` `-commutative_binary64_9` `flip3--_binary64_82` `distribute-rgt-in_binary64_28` `associate--l+_binary64_15` `flip--_binary64_53` `unswap-sqr_binary64_46` `associate-r/_binary64_20` `associate-/l/_binary64_25`
1×	`pow-exp_binary64_146` `pow-to-exp_binary64_147` `cbrt-undiv_binary64_112` `flip-+_binary64_52` `diff-log_binary64_170` `distribute-rgt-out_binary64_31` `frac-2neg_binary64_89` `div-inv_binary64_75` `clear-num_binary64_77` `cancel-sign-sub-inv_binary64_44` `div-sub_binary64_83` `unpow3_binary64_144` `sub-neg_binary64_71` `flip3-+_binary64_81`

Counts

4 → 104

Calls

4 calls:

27.0ms	(.f64 (.f64 N N) (+.f64 (pow.f64 N 3) (*.f64 1/3 N)))
25.0ms	(-.f64 (.f64 (.f64 N N) (+.f64 (pow.f64 N 3) (.f64 1/3 N))) (.f64 1/2 (pow.f64 N 4)))
19.0ms	(/.f64 (-.f64 (.f64 (.f64 N N) (+.f64 (pow.f64 N 3) (.f64 1/3 N))) (.f64 1/2 (pow.f64 N 4))) (pow.f64 N 6))
8.0ms	(*.f64 1/3 N)

series396.0ms (8.5%)

Counts

4 → 12

Calls

4 calls:

270.0ms	(.f64 (.f64 N N) (+.f64 (pow.f64 N 3) (*.f64 1/3 N)))
56.0ms	(/.f64 (-.f64 (.f64 (.f64 N N) (+.f64 (pow.f64 N 3) (.f64 1/3 N))) (.f64 1/2 (pow.f64 N 4))) (pow.f64 N 6))
47.0ms	(-.f64 (.f64 (.f64 N N) (+.f64 (pow.f64 N 3) (.f64 1/3 N))) (.f64 1/2 (pow.f64 N 4)))
22.0ms	(*.f64 1/3 N)

simplify89.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5201	2849

prune200.0ms (4.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	116	3	119

Merged error: 0b

Counts

119 → 3

Compiler

Compiled 3127 to 2136 computations (31.7% saved)

regimes102.0ms (2.2%)

Compiler: Compiled 484 to 394 computations (18.6% 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	53	54
1	53	54

end0.0ms (0%)

sample1.9s (41%)

Algorithm

1×

intervals

Results

637.0ms	2004×	body	1024	valid
315.0ms	4262×	body	128	valid
203.0ms	1000×	body	512	valid
122.0ms	227×	body	2048	valid
62.0ms	507×	body	256	valid

Compiler

Compiled 277 to 225 computations (18.8% saved)

Details

analyze2.0ms (0%)

sample39.0ms (0.8%)

simplify258.0ms (5.5%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

rewrite27.0ms (0.6%)

series136.0ms (2.9%)

simplify90.0ms (1.9%)

prune75.0ms (1.6%)

localize22.0ms (0.5%)

rewrite39.0ms (0.8%)

series272.0ms (5.8%)

simplify112.0ms (2.4%)

prune106.0ms (2.3%)

localize20.0ms (0.4%)

rewrite133.0ms (2.8%)

series222.0ms (4.7%)

simplify73.0ms (1.6%)

prune221.0ms (4.7%)

localize16.0ms (0.3%)

rewrite95.0ms (2%)

series396.0ms (8.5%)

simplify89.0ms (1.9%)

prune200.0ms (4.3%)

regimes102.0ms (2.2%)

bsearch1.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.9s (41%)

Profiling