Details

analyze411.0ms (3.8%)

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)

sample40.0ms (0.4%)

Algorithm

1×

intervals

Results

24.0ms	256×	body	128	valid
3.0ms	33×	body	128	nan

Compiler

Compiled 57 to 44 computations (22.8% saved)

simplify194.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (99.0ms)

Iter	Nodes	Cost
0	5740	19

prune5.0ms (0%)

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

31.1b

Counts

2 → 2

Compiler

Compiled 52 to 40 computations (23.1% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.4b	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
28.9b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite97.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

31.0b

Rules

24×	`times-frac_binary64_84`
22×	`log-pow_binary64_167`
21×	`pow1_binary64_139`
17×	`add-sqr-sqrt_binary64_100`
16×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
6×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `associate-/l*_binary64_23`
5×	`add-log-exp_binary64_117` `add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
4×	`sqrt-div_binary64_95` `associate-/r*_binary64_22`
3×	`flip3-+_binary64_81` `flip-+_binary64_52` `sqrt-prod_binary64_94`
2×	`log-div_binary64_165` `div-sub_binary64_83`
1×	`rem-sqrt-square_binary64_91` `div-exp_binary64_129` `cbrt-undiv_binary64_112` `frac-2neg_binary64_89` `clear-num_binary64_77` `div-inv_binary64_75` `sum-log_binary64_169` `+-commutative_binary64_8`

Counts

3 → 74

Calls

3 calls:

7.0ms	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
4.0ms	(+.f64 (.f64 re re) (.f64 im im))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 1643 to 318 computations (80.6% saved)

series710.0ms (6.6%)

Error

0.4b

Counts

3 → 50

Calls

3 calls:

452.0ms	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
125.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
88.0ms	(+.f64 (.f64 re re) (.f64 im im))

Compiler

Compiled 1979 to 1581 computations (20.1% saved)

simplify77.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4946	2662
1	4946	2662

prune113.0ms (1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	110	14	124
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	111	15	126

Error

0.3b

Counts

126 → 15

Compiler

Compiled 2436 to 717 computations (70.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.3b	(/.f64 1/2 (/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
0.4b	(/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
30.0b	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite176.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Rules

140×	`times-frac_binary64_84`
72×	`add-cube-cbrt_binary64_113` `add-sqr-sqrt_binary64_100` `*-un-lft-identity_binary64_78`
47×	`pow1_binary64_139`
43×	`log-pow_binary64_167`
24×	`associate-/r*_binary64_22`
12×	`add-exp-log_binary64_116`
11×	`add-cbrt-cube_binary64_114`
7×	`associate-/l*_binary64_23`
6×	`add-log-exp_binary64_117` `div-inv_binary64_75`
4×	`div-exp_binary64_129` `cbrt-undiv_binary64_112`
3×	`log-prod_binary64_164`
2×	`flip3-+_binary64_81` `log-div_binary64_165` `flip-+_binary64_52` `frac-2neg_binary64_89` `clear-num_binary64_77`
1×	`rem-log-exp_binary64_119` `associate-/r/_binary64_24` `sum-log_binary64_169` `+-commutative_binary64_8`

Counts

4 → 159

Calls

4 calls:

7.0ms	(/.f64 1/2 (/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
4.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(+.f64 (.f64 re re) (.f64 im im))
4.0ms	(/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))

Compiler

Compiled 4159 to 1064 computations (74.4% saved)

series1.5s (13.5%)

Error

0.2b

Counts

4 → 71

Calls

4 calls:

677.0ms	(/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
459.0ms	(/.f64 1/2 (/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
141.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))
94.0ms	(+.f64 (.f64 re re) (.f64 im im))

Compiler

Compiled 4439 to 3588 computations (19.2% saved)

simplify113.0ms (1%)

Algorithm

1×	egg-herbie

Counts

230 → 230

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4963	7065
1	4963	7065

prune220.0ms (2%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	223	7	230
Fresh	6	8	14
Picked	1	0	1
Done	0	0	0
Total	230	15	245

Error

0.2b

Counts

245 → 15

Compiler

Compiled 5676 to 1852 computations (67.4% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.3b	(/.f64 1/2 (log.f64 base))
0.4b	(.f64 (/.f64 1/2 (log.f64 base)) (log.f64 (+.f64 (.f64 re re) (*.f64 im im))))
30.0b	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite110.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

30×	`add-sqr-sqrt_binary64_100`
25×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78` `times-frac_binary64_84`
16×	`associate-l_binary64_19`
15×	`pow1_binary64_139`
12×	`add-exp-log_binary64_116`
11×	`add-cbrt-cube_binary64_114`
9×	`log-pow_binary64_167` `log-prod_binary64_164`
6×	`add-log-exp_binary64_117`
4×	`associate-r_binary64_18` `associate-/r*_binary64_22`
3×	`distribute-rgt-in_binary64_28` `distribute-lft-in_binary64_27` `associate-/l*_binary64_23`
2×	`flip3-+_binary64_81` `log-div_binary64_165` `flip-+_binary64_52` `div-exp_binary64_129` `prod-exp_binary64_127` `cbrt-unprod_binary64_111` `cbrt-undiv_binary64_112` `unswap-sqr_binary64_46` `div-inv_binary64_75`
1×	`rem-log-exp_binary64_119` `pow-prod-down_binary64_149` `associate-l/_binary64_21` `-commutative_binary64_9` `frac-2neg_binary64_89` `clear-num_binary64_77` `sum-log_binary64_169` `+-commutative_binary64_8`

Counts

4 → 98

Calls

4 calls:

10.0ms	(.f64 (/.f64 1/2 (log.f64 base)) (log.f64 (+.f64 (.f64 re re) (*.f64 im im))))
4.0ms	(+.f64 (.f64 re re) (.f64 im im))
4.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))
3.0ms	(/.f64 1/2 (log.f64 base))

Compiler

Compiled 2165 to 705 computations (67.4% saved)

series857.0ms (7.9%)

Error

0.2b

Counts

4 → 52

Calls

4 calls:

465.0ms	(.f64 (/.f64 1/2 (log.f64 base)) (log.f64 (+.f64 (.f64 re re) (*.f64 im im))))
142.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))
99.0ms	(/.f64 1/2 (log.f64 base))
95.0ms	(+.f64 (.f64 re re) (.f64 im im))

Compiler

Compiled 2301 to 1893 computations (17.7% saved)

simplify85.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4956	2876
1	4956	2876

prune138.0ms (1.3%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	148	2	150
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	148	17	165

Error

0.2b

Counts

165 → 17

Compiler

Compiled 3023 to 1169 computations (61.3% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))
0.3b	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))
0.6b	(*.f64 (log.f64 base) (log.f64 base))
28.9b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite178.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

28×	`add-sqr-sqrt_binary64_100`
25×	`*-un-lft-identity_binary64_78`
23×	`pow1_binary64_139` `add-cube-cbrt_binary64_113`
12×	`log-prod_binary64_164`
10×	`add-exp-log_binary64_116` `add-cbrt-cube_binary64_114` `log-pow_binary64_167` `associate-l_binary64_19`
9×	`times-frac_binary64_84`
8×	`associate-r_binary64_18`
6×	`swap-sqr_binary64_45` `distribute-rgt-in_binary64_28` `distribute-lft-in_binary64_27`
4×	`add-log-exp_binary64_117`
3×	`flip3-+_binary64_81` `flip-+_binary64_52` `sqrt-prod_binary64_94` `associate-/l_binary64_23` `associate-/r_binary64_22`
2×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `sqrt-div_binary64_95` `pow-prod-down_binary64_149` `prod-exp_binary64_127` `cbrt-unprod_binary64_111` `unswap-sqr_binary64_46` `*-commutative_binary64_9` `associate-/l/_binary64_25` `associate-/r/_binary64_24`
1×	`rem-sqrt-square_binary64_91` `pow2_binary64_159` `pow-prod-up_binary64_148` `pow-plus_binary64_141` `pow-sqr_binary64_51` `div-exp_binary64_129` `cbrt-undiv_binary64_112` `frac-2neg_binary64_89` `clear-num_binary64_77` `div-inv_binary64_75`

Counts

4 → 110

Calls

4 calls:

10.0ms	(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))
6.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))
5.0ms	(*.f64 (log.f64 base) (log.f64 base))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 4493 to 1446 computations (67.8% saved)

series1.1s (10.5%)

Error

0.2b

Counts

4 → 60

Calls

4 calls:

444.0ms	(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))
412.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))
133.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
75.0ms	(*.f64 (log.f64 base) (log.f64 base))

Compiler

Compiled 4287 to 3033 computations (29.3% saved)

simplify103.0ms (1%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4928	3760
1	4928	3760

prune192.0ms (1.8%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	166	4	170
Fresh	2	13	15
Picked	1	0	1
Done	0	1	1
Total	169	18	187

Error

0.2b

Counts

187 → 18

Compiler

Compiled 5261 to 1817 computations (65.5% saved)

regimes1.4s (12.8%)

Accuracy

Total 18.5b remaining (98.6%)

Threshold costs 0b (0%)

Compiler

Compiled 8301 to 5901 computations (28.9% saved)

bsearch302.0ms (2.8%)

Steps

Iters	Range		Point
10	1.0134816276728828e+123	4.815803123037574e+133	2.148071380303255e+127
7	2.5929862117632706e-221	3.2556833789573564e-219	8.601619134334225e-221
9	6.636294047014928e-283	1.1026531945546414e-275	9.686995765174227e-282
7	-2.02588885016723e-216	-9.049579704811277e-218	-2.0009587246036498e-216
8	-1.9451638785071407e-137	-6.90127386601542e-140	-6.968239497015886e-140
9	-2.8977930858746226e+147	-1.7055676500209856e+141	-2.880171495702805e+142

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	60	134
1	60	134

end0.0ms (0%)

sample2.7s (24.7%)

Algorithm

1×

intervals

Results

787.0ms	8000×	body	128	valid
87.0ms	965×	body	128	nan

Compiler

Compiled 1762 to 1242 computations (29.5% saved)

Details

analyze411.0ms (3.8%)

sample40.0ms (0.4%)

simplify194.0ms (1.8%)

prune5.0ms (0%)

localize11.0ms (0.1%)

rewrite97.0ms (0.9%)

series710.0ms (6.6%)

simplify77.0ms (0.7%)

prune113.0ms (1%)

localize11.0ms (0.1%)

rewrite176.0ms (1.6%)

series1.5s (13.5%)

simplify113.0ms (1%)

prune220.0ms (2%)

localize11.0ms (0.1%)

rewrite110.0ms (1%)

series857.0ms (7.9%)

simplify85.0ms (0.8%)

prune138.0ms (1.3%)

localize19.0ms (0.2%)

rewrite178.0ms (1.6%)

series1.1s (10.5%)

simplify103.0ms (1%)

prune192.0ms (1.8%)

regimes1.4s (12.8%)

bsearch302.0ms (2.8%)

simplify4.0ms (0%)

end0.0ms (0%)

sample2.7s (24.7%)

Profiling