Details

analyze406.0ms (7.9%)

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

24.0ms	256×	body	128	valid
3.0ms	32×	body	128	nan

Compiler

Compiled 57 to 44 computations (22.8% saved)

simplify219.0ms (4.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (123.0ms)

Iter	Nodes	Cost
0	4968	9
1	4968	9

prune6.0ms (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 2 expressions with local error:

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

rewrite6.0ms (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

2 calls:

4.0ms	(/.f64 (atan2.f64 im re) (log.f64 base))
0.0ms	(/.f64 (atan2.f64 im re) (log.f64 base))

series226.0ms (4.4%)

Counts

1 → 9

Calls

1 calls:

226.0ms

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

Compiler

Compiled 126 to 126 computations (0% saved)

simplify73.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4804	572
1	4804	572

prune51.0ms (1%)

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

0.0b

Counts

42 → 13

Compiler

Compiled 616 to 195 computations (68.3% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite20.0ms (0.4%)

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

4 calls:

9.0ms	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
3.0ms	(/.f64 1 (log.f64 base))
0.0ms	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
0.0ms	(/.f64 1 (log.f64 base))

series312.0ms (6.1%)

Counts

2 → 12

Calls

2 calls:

224.0ms	(*.f64 (atan2.f64 im re) (/.f64 1 (log.f64 base)))
88.0ms	(/.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 (50.0ms)

Iter	Nodes	Cost
0	5058	929

prune69.0ms (1.4%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	82	4	86
Fresh	2	9	11
Picked	0	1	1
Done	0	1	1
Total	84	15	99

Error

0.0b

Counts

99 → 15

Compiler

Compiled 1173 to 494 computations (57.9% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
0.3b	(/.f64 (log.f64 base) (atan2.f64 im re))
0.3b	(/.f64 (log.f64 base) (atan2.f64 im re))
0.5b	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))

rewrite21.0ms (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

4 calls:

7.0ms	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
4.0ms	(/.f64 (log.f64 base) (atan2.f64 im re))
0.0ms	(/.f64 (log.f64 base) (atan2.f64 im re))
0.0ms	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))

series426.0ms (8.3%)

Counts

2 → 18

Calls

2 calls:

221.0ms	(/.f64 1 (/.f64 (log.f64 base) (atan2.f64 im re)))
205.0ms	(/.f64 (log.f64 base) (atan2.f64 im re))

Compiler

Compiled 288 to 288 computations (0% saved)

simplify82.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5084	2435

prune108.0ms (2.1%)

Pruning

15 alts after pruning (12 fresh and 3 done)

	Pruned	Kept	Total
New	134	3	137
Fresh	3	9	12
Picked	0	1	1
Done	0	2	2
Total	137	15	152

Error

Counts

152 → 15

Compiler

Compiled 2140 to 616 computations (71.2% saved)

localize10.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.5b	(cbrt.f64 (log.f64 base))
0.5b	(*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))
0.3b	(/.f64 (/.f64 (atan2.f64 im re) (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))) (cbrt.f64 (log.f64 base)))
0.3b	(/.f64 (atan2.f64 im re) (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base))))
0.5b	(*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))
0.5b	(cbrt.f64 (log.f64 base))
0.5b	(cbrt.f64 (log.f64 base))
0.5b	(cbrt.f64 (log.f64 base))

rewrite20.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`cbrt-prod_binary64_109`
23×	`add-sqr-sqrt_binary64_100`
20×	`pow1_binary64_139`
17×	`*-un-lft-identity_binary64_78`
15×	`add-cube-cbrt_binary64_113`
9×	`swap-sqr_binary64_45` `pow1/3_binary64_160` `log-pow_binary64_167`
7×	`associate-l_binary64_19` `associate-r_binary64_18`
6×	`add-exp-log_binary64_116`
4×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117` `unswap-sqr_binary64_46`
2×	`pow-sqr_binary64_51` `pow-prod-up_binary64_148` `pow-prod-down_binary64_149`
1×	`pow2_binary64_159` `*-commutative_binary64_9` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `pow-plus_binary64_141`

Counts

4 → 81

Calls

8 calls:

9.0ms	(*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))
1.0ms	(cbrt.f64 (log.f64 base))
1.0ms	(cbrt.f64 (log.f64 base))
1.0ms	(cbrt.f64 (log.f64 base))
0.0ms	(/.f64 (atan2.f64 im re) (*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base))))

series595.0ms (11.6%)

Counts

4 → 12

Calls

4 calls:

156.0ms	(cbrt.f64 (log.f64 base))
147.0ms	(*.f64 (cbrt.f64 (log.f64 base)) (cbrt.f64 (log.f64 base)))
147.0ms	(cbrt.f64 (log.f64 base))
144.0ms	(cbrt.f64 (log.f64 base))

Compiler

Compiled 440 to 354 computations (19.5% saved)

simplify59.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4995	799
1	4995	799

prune68.0ms (1.3%)

Pruning

14 alts after pruning (10 fresh and 4 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	2	9	11
Picked	0	1	1
Done	0	3	3
Total	94	14	108

Error

Counts

108 → 14

Compiler

Compiled 1616 to 391 computations (75.8% saved)

simplify14.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	174	840
1	174	840

regimes247.0ms (4.8%)

Compiler: Compiled 2118 to 1550 computations (26.8% saved)

bsearch0.0ms (0%)

regimes38.0ms (0.8%)

Accuracy

Total 0.3b remaining (97.2%)

Threshold costs 0.3b (97.2%)

Compiler

Compiled 15 to 54 computations (-260% saved)

bsearch44.0ms (0.9%)

Steps

Iters	Range		Point
8	1.3642132255460669e+80	1.397978154980093e+84	1.5180857450401232e+80

Compiler

Compiled 14 to 21 computations (-50% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	18
1	13	18

end0.0ms (0%)

sample1.9s (36.6%)

Algorithm

1×

intervals

Results

967.0ms	8000×	body	128	valid
89.0ms	995×	body	128	nan

Compiler

Compiled 569 to 423 computations (25.7% saved)

Pareto

0.03125377545999769

Details

analyze406.0ms (7.9%)

sample41.0ms (0.8%)

simplify219.0ms (4.3%)

prune6.0ms (0.1%)

localize6.0ms (0.1%)

rewrite6.0ms (0.1%)

series226.0ms (4.4%)

simplify73.0ms (1.4%)

prune51.0ms (1%)

localize7.0ms (0.1%)

rewrite20.0ms (0.4%)

series312.0ms (6.1%)

simplify65.0ms (1.3%)

prune69.0ms (1.4%)

localize7.0ms (0.1%)

rewrite21.0ms (0.4%)

series426.0ms (8.3%)

simplify82.0ms (1.6%)

prune108.0ms (2.1%)

localize10.0ms (0.2%)

rewrite20.0ms (0.4%)

series595.0ms (11.6%)

simplify59.0ms (1.1%)

prune68.0ms (1.3%)

simplify14.0ms (0.3%)

regimes247.0ms (4.8%)

bsearch0.0ms (0%)

regimes38.0ms (0.8%)

bsearch44.0ms (0.9%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.9s (36.6%)

Profiling