Details

analyze419.0ms (8.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
23.4%	51.5%	25.1%	7
24.2%	50.7%	25.1%	8
24.6%	50.3%	25.1%	9
36.9%	25.5%	37.6%	10
37.2%	25.3%	37.6%	11
37.3%	25.1%	37.6%	12
43.5%	12.7%	43.8%	13
43.6%	12.6%	43.8%	14

Compiler

Compiled 29 to 21 computations (27.6% saved)

sample41.0ms (0.8%)

Algorithm

1×

intervals

Results

27.0ms	256×	body	128	valid
3.0ms	34×	body	128	nan

Compiler

Compiled 57 to 44 computations (22.8% saved)

simplify213.0ms (4.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (116.0ms)

Iter	Nodes	Cost
0	4968	9
1	4968	9

prune5.0ms (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

Error

0.3b

Counts

2 → 2

Compiler

Compiled 40 to 32 computations (20% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.3b	(/.f64 (atan2.f64 im re) (log.f64 base))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`times-frac_binary64_84`
10×	`add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
5×	`pow1_binary64_139`
4×	`associate-/r*_binary64_22` `log-pow_binary64_167`
3×	`add-cbrt-cube_binary64_114` `associate-/l*_binary64_23` `add-exp-log_binary64_116`
1×	`add-log-exp_binary64_117` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `frac-2neg_binary64_89` `div-inv_binary64_75` `clear-num_binary64_77`

Counts

1 → 31

Calls

1 calls:

4.0ms

(/.f64 (atan2.f64 im re) (log.f64 base))

series224.0ms (4.4%)

Counts

1 → 9

Calls

1 calls:

224.0ms

(/.f64 (atan2.f64 im re) (log.f64 base))

Compiler

Compiled 126 to 126 computations (0% saved)

simplify81.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4804	572
1	4804	572

prune40.0ms (0.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	29	11	40
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	29	13	42

Error

0.1b

Counts

42 → 13

Compiler

Compiled 621 to 196 computations (68.4% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.3b	(/.f64 1 (log.f64 base))
0.3b	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))

rewrite17.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64_100`
26×	`times-frac_binary64_84`
21×	`*-un-lft-identity_binary64_78`
20×	`add-cube-cbrt_binary64_113`
16×	`associate-r_binary64_18`
15×	`add-exp-log_binary64_116`
12×	`pow1_binary64_139`
9×	`add-cbrt-cube_binary64_114`
7×	`log-pow_binary64_167`
4×	`prod-exp_binary64_127` `div-exp_binary64_129` `associate-/r*_binary64_22`
3×	`associate-l_binary64_19` `associate-/l*_binary64_23` `unswap-sqr_binary64_46`
2×	`add-log-exp_binary64_117` `cbrt-unprod_binary64_111` `cbrt-undiv_binary64_112` `1-exp_binary64_122` `div-inv_binary64_75` `rec-exp_binary64_128`
1×	`-commutative_binary64_9` `inv-pow_binary64_163` `un-div-inv_binary64_76` `frac-2neg_binary64_89` `pow-flip_binary64_152` `pow-prod-down_binary64_149` `associate-r/_binary64_20` `clear-num_binary64_77`

Counts

2 → 74

Calls

2 calls:

9.0ms	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
3.0ms	(/.f64 1 (log.f64 base))

series307.0ms (6%)

Counts

2 → 12

Calls

2 calls:

220.0ms	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
86.0ms	(/.f64 1 (log.f64 base))

Compiler

Compiled 188 to 188 computations (0% saved)

simplify65.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5058	929

prune63.0ms (1.2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	84	2	86
Fresh	3	8	11
Picked	0	1	1
Done	0	1	1
Total	87	12	99

Error

0.0b

Counts

99 → 12

Compiler

Compiled 1114 to 451 computations (59.5% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.2b	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
0.3b	(/.f64 (log.f64 base) (atan2.f64 im re))

rewrite20.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

108×	`times-frac_binary64_84`
60×	`add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
19×	`associate-/r*_binary64_22` `pow1_binary64_139`
16×	`log-pow_binary64_167`
15×	`add-exp-log_binary64_116`
9×	`add-cbrt-cube_binary64_114`
8×	`div-exp_binary64_129`
7×	`associate-/l*_binary64_23`
6×	`div-inv_binary64_75`
4×	`cbrt-undiv_binary64_112`
2×	`add-log-exp_binary64_117` `frac-2neg_binary64_89` `1-exp_binary64_122` `rec-exp_binary64_128` `clear-num_binary64_77`
1×	`inv-pow_binary64_163` `pow-flip_binary64_152` `associate-/r/_binary64_24`

Counts

2 → 119

Calls

2 calls:

6.0ms	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
4.0ms	(/.f64 (log.f64 base) (atan2.f64 im re))

series408.0ms (8%)

Counts

2 → 18

Calls

2 calls:

218.0ms	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
189.0ms	(/.f64 (log.f64 base) (atan2.f64 im re))

Compiler

Compiled 288 to 288 computations (0% saved)

simplify76.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5084	2435

prune101.0ms (2%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	132	5	137
Fresh	2	7	9
Picked	1	0	1
Done	0	2	2
Total	135	14	149

Error

0.0b

Counts

149 → 14

Compiler

Compiled 2128 to 596 computations (72% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 1 (log.f64 base))
0.3b	(*.f64 (atan2.f64 im re) (cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3)))
0.6b	(cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3))
0.6b	(pow.f64 (/.f64 1 (log.f64 base)) 3)

rewrite52.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

88×	`times-frac_binary64_84`
85×	`add-sqr-sqrt_binary64_100`
84×	`cbrt-prod_binary64_109`
68×	`*-un-lft-identity_binary64_78`
66×	`add-cube-cbrt_binary64_113`
51×	`unpow-prod-down_binary64_157` `cube-prod_binary64_106`
41×	`associate-r_binary64_18`
31×	`pow1_binary64_139`
22×	`log-pow_binary64_167`
15×	`add-exp-log_binary64_116`
10×	`add-cbrt-cube_binary64_114`
9×	`unswap-sqr_binary64_46`
7×	`div-inv_binary64_75`
4×	`pow-exp_binary64_146` `add-log-exp_binary64_117` `div-exp_binary64_129` `sqr-pow_binary64_50` `associate-/r*_binary64_22`
3×	`cube-mult_binary64_108` `associate-l_binary64_19` `cube-div_binary64_107` `pow-pow_binary64_150` `associate-/l*_binary64_23` `pow-unpow_binary64_155` `unpow3_binary64_144`
2×	`rem-cube-cbrt_binary64_101` `cbrt-div_binary64_110` `cbrt-undiv_binary64_112` `inv-pow_binary64_163` `1-exp_binary64_122` `pow-flip_binary64_152` `rec-exp_binary64_128`
1×	`-commutative_binary64_9` `rem-cbrt-cube_binary64_102` `pow-to-exp_binary64_147` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `pow1/3_binary64_160` `frac-2neg_binary64_89` `pow-prod-down_binary64_149` `associate-r/_binary64_20` `clear-num_binary64_77`

Counts

4 → 204

Calls

4 calls:

19.0ms	(*.f64 (atan2.f64 im re) (cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3)))
6.0ms	(pow.f64 (/.f64 1 (log.f64 base)) 3)
6.0ms	(cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3))
4.0ms	(/.f64 1 (log.f64 base))

series532.0ms (10.4%)

Counts

4 → 18

Calls

4 calls:

229.0ms	(*.f64 (atan2.f64 im re) (cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3)))
138.0ms	(pow.f64 (/.f64 1 (log.f64 base)) 3)
87.0ms	(/.f64 1 (log.f64 base))
78.0ms	(cbrt.f64 (pow.f64 (/.f64 1 (log.f64 base)) 3))

Compiler

Compiled 348 to 348 computations (0% saved)

simplify81.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

222 → 222

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4943	2477
1	4943	2477

prune171.0ms (3.3%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	219	3	222
Fresh	3	8	11
Picked	1	0	1
Done	0	2	2
Total	223	13	236

Error

Counts

236 → 13

Compiler

Compiled 3086 to 1612 computations (47.8% saved)

regimes348.0ms (6.8%)

Accuracy

Total 0.3b remaining (95.7%)

Threshold costs 0.3b (95.7%)

Compiler

Compiled 3066 to 2341 computations (23.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	9
1	7	9

end0.0ms (0%)

sample1.8s (35.5%)

Algorithm

1×

intervals

Results

800.0ms	8000×	body	128	valid
90.0ms	996×	body	128	nan

Compiler

Compiled 635 to 485 computations (23.6% saved)

Details

analyze419.0ms (8.2%)

sample41.0ms (0.8%)

simplify213.0ms (4.2%)

prune5.0ms (0.1%)

localize6.0ms (0.1%)

rewrite5.0ms (0.1%)

series224.0ms (4.4%)

simplify81.0ms (1.6%)

prune40.0ms (0.8%)

localize7.0ms (0.1%)

rewrite17.0ms (0.3%)

series307.0ms (6%)

simplify65.0ms (1.3%)

prune63.0ms (1.2%)

localize7.0ms (0.1%)

rewrite20.0ms (0.4%)

series408.0ms (8%)

simplify76.0ms (1.5%)

prune101.0ms (2%)

localize10.0ms (0.2%)

rewrite52.0ms (1%)

series532.0ms (10.4%)

simplify81.0ms (1.6%)

prune171.0ms (3.3%)

regimes348.0ms (6.8%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.8s (35.5%)

Profiling