Details

analyze5.0ms (0.1%)

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
74.9%	25%	0.1%	3
87.4%	12.5%	0.1%	4
93.7%	6.2%	0.1%	5
96.8%	3.1%	0.1%	6
98.3%	1.6%	0.1%	7
99.1%	0.8%	0.1%	8
99.5%	0.4%	0.1%	9
99.7%	0.2%	0.1%	10
99.8%	0.1%	0.1%	11
99.9%	0%	0.1%	12
99.9%	0%	0.1%	13
99.9%	0%	0.1%	14

Compiler

Compiled 13 to 11 computations (15.4% saved)

sample22.0ms (0.4%)

Algorithm

1×

intervals

Results

15.0ms

256×

body

128

valid

Compiler

Compiled 25 to 23 computations (8% saved)

simplify166.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	12	19
1	12	19

prune3.0ms (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

Merged error: 29.9b

Counts

2 → 1

Compiler

Compiled 24 to 20 computations (16.7% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.6b	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 10))
27.6b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite19.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`times-frac_binary64_85`
22×	`log-pow_binary64_168`
20×	`pow1_binary64_140`
16×	`add-sqr-sqrt_binary64_101`
15×	`add-cube-cbrt_binary64_114` `*-un-lft-identity_binary64_79`
6×	`associate-/l*_binary64_24` `sqrt-pow1_binary64_97` `pow1/2_binary64_159`
4×	`associate-/r*_binary64_23` `add-exp-log_binary64_117` `add-cbrt-cube_binary64_115` `sqrt-div_binary64_96`
3×	`sqrt-prod_binary64_95`
2×	`flip-+_binary64_53` `div-sub_binary64_84` `log-div_binary64_166` `add-log-exp_binary64_118` `flip3-+_binary64_82`
1×	`cbrt-undiv_binary64_113` `div-exp_binary64_130` `div-inv_binary64_76` `rem-sqrt-square_binary64_92` `clear-num_binary64_78` `frac-2neg_binary64_90`

Counts

2 → 63

Calls

2 calls:

9.0ms	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 10))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series183.0ms (3.2%)

Counts

2 → 6

Calls

2 calls:

139.0ms	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 10))
44.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify80.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5073	1640

prune309.0ms (5.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	56	13	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	57	13	70

Merged error: 5.4b

Counts

70 → 13

Compiler

Compiled 5993 to 3083 computations (48.6% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(/.f64 (log.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))))) (log.f64 10))
27.6b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
27.6b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
27.6b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite76.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

126×	`pow1_binary64_140`
94×	`log-pow_binary64_168`
72×	`times-frac_binary64_85`
60×	`sqrt-div_binary64_96`
54×	`cbrt-div_binary64_111`
45×	`pow-prod-up_binary64_149` `pow1/3_binary64_161`
34×	`add-sqr-sqrt_binary64_101`
31×	`add-cube-cbrt_binary64_114` `*-un-lft-identity_binary64_79`
30×	`flip-+_binary64_53` `pow-plus_binary64_142` `flip3-+_binary64_82`
28×	`frac-times_binary64_89`
26×	`div-sub_binary64_84` `log-div_binary64_166`
25×	`pow-prod-down_binary64_150`
18×	`associate-/l*_binary64_24`
15×	`pow-sqr_binary64_52`
14×	`associate-*l/_binary64_22`
10×	`pow2_binary64_160`
9×	`sqrt-prod_binary64_95`
8×	`associate-*r/_binary64_21`
6×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115`
5×	`pow3_binary64_162`
4×	`associate-/r*_binary64_23` `add-log-exp_binary64_118`
3×	`rem-sqrt-square_binary64_92` `sqrt-pow1_binary64_97` `pow1/2_binary64_159`
1×	`cbrt-undiv_binary64_113` `div-exp_binary64_130` `div-inv_binary64_76` `clear-num_binary64_78` `frac-2neg_binary64_90`

Counts

4 → 177

Calls

4 calls:

31.0ms	(/.f64 (log.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))))) (log.f64 10))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series280.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

149.0ms	(/.f64 (log.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))))) (log.f64 10))
49.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
43.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
39.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify158.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 0 (102.0ms)

Iter	Nodes	Cost
0	4898	5691
1	4898	5691

prune304.0ms (5.4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	186	3	189
Fresh	3	9	12
Picked	0	1	1
Done	0	0	0
Total	189	13	202

Merged error: 5.4b

Counts

202 → 13

Compiler

Compiled 7055 to 3003 computations (57.4% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 3 (/.f64 (log.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) (log.f64 10)))
0.6b	(/.f64 (log.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) (log.f64 10))
0.6b	(cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
27.6b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite43.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`times-frac_binary64_85`
35×	`add-sqr-sqrt_binary64_101`
29×	`add-cube-cbrt_binary64_114` `log-pow_binary64_168` `*-un-lft-identity_binary64_79`
27×	`pow1_binary64_140`
24×	`associate-r_binary64_19`
11×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115`
10×	`pow1/3_binary64_161`
6×	`sqrt-prod_binary64_95` `sqrt-div_binary64_96` `cbrt-prod_binary64_110`
5×	`associate-/l*_binary64_24`
4×	`associate-/r*_binary64_23` `cbrt-div_binary64_111` `add-log-exp_binary64_118`
3×	`associate-l_binary64_20` `flip-+_binary64_53` `flip3-+_binary64_82`
2×	`cbrt-undiv_binary64_113` `div-exp_binary64_130` `div-sub_binary64_84` `div-inv_binary64_76` `unswap-sqr_binary64_47` `cbrt-unprod_binary64_112` `prod-exp_binary64_128` `log-div_binary64_166`
1×	`associate-r/_binary64_21` `rem-sqrt-square_binary64_92` `-commutative_binary64_10` `pow-prod-down_binary64_150` `sqrt-pow1_binary64_97` `clear-num_binary64_78` `pow1/2_binary64_159` `frac-2neg_binary64_90`

Counts

4 → 117

Calls

4 calls:

12.0ms	(.f64 3 (/.f64 (log.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) (log.f64 10)))
9.0ms	(/.f64 (log.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) (log.f64 10))
5.0ms	(cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series569.0ms (10%)

Counts

4 → 12

Calls

4 calls:

204.0ms	(.f64 3 (/.f64 (log.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) (log.f64 10)))
186.0ms	(/.f64 (log.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) (log.f64 10))
139.0ms	(cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
40.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify73.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4924	2982
1	4924	2982

prune326.0ms (5.8%)

Pruning

19 alts after pruning (17 fresh and 2 done)

	Pruned	Kept	Total
New	122	7	129
Fresh	1	10	11
Picked	0	1	1
Done	0	1	1
Total	123	19	142

Merged error: 5.3b

Counts

142 → 19

Compiler

Compiled 6260 to 3435 computations (45.1% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (pow.f64 (/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 10)) 3))
0.6b	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 10))
0.7b	(pow.f64 (/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 10)) 3)
27.6b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite57.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

120×	`times-frac_binary64_85`
94×	`log-pow_binary64_168`
79×	`pow1_binary64_140`
64×	`add-sqr-sqrt_binary64_101`
63×	`add-cube-cbrt_binary64_114` `*-un-lft-identity_binary64_79`
62×	`cbrt-prod_binary64_110`
56×	`unpow-prod-down_binary64_158` `cube-prod_binary64_107`
22×	`sqrt-pow1_binary64_97` `pow1/2_binary64_159`
9×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115`
6×	`associate-/l*_binary64_24`
5×	`div-inv_binary64_76`
4×	`associate-/r*_binary64_23` `sqrt-div_binary64_96` `add-log-exp_binary64_118`
3×	`sqrt-prod_binary64_95` `pow-unpow_binary64_156`
2×	`pow-exp_binary64_147` `cbrt-undiv_binary64_113` `div-exp_binary64_130` `cube-div_binary64_108` `flip-+_binary64_53` `sqr-pow_binary64_51` `div-sub_binary64_84` `rem-cube-cbrt_binary64_102` `cube-mult_binary64_109` `log-div_binary64_166` `flip3-+_binary64_82` `unpow3_binary64_145`
1×	`pow-to-exp_binary64_148` `pow-pow_binary64_151` `rem-cbrt-cube_binary64_103` `cbrt-div_binary64_111` `rem-sqrt-square_binary64_92` `clear-num_binary64_78` `pow1/3_binary64_161` `frac-2neg_binary64_90`

Counts

4 → 211

Calls

4 calls:

9.0ms	(cbrt.f64 (pow.f64 (/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 10)) 3))
9.0ms	(pow.f64 (/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 10)) 3)
9.0ms	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 10))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series558.0ms (9.8%)

Counts

4 → 12

Calls

4 calls:

249.0ms	(pow.f64 (/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 10)) 3)
134.0ms	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 10))
132.0ms	(cbrt.f64 (pow.f64 (/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 10)) 3))
43.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify86.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

223 → 223

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5483	6130

prune486.0ms (8.6%)

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	214	9	223
Fresh	4	12	16
Picked	1	0	1
Done	1	1	2
Total	220	22	242

Merged error: 5.3b

Counts

242 → 22

Compiler

Compiled 8668 to 5067 computations (41.5% saved)

regimes615.0ms (10.8%)

Compiler: Compiled 3961 to 2973 computations (24.9% saved)

bsearch92.0ms (1.6%)

Steps

Iters	Range		Point
9	2.0071015803147128e+32	5.218866978283333e+39	5.153255919931365e+39
10	-5.272324052581015e-219	-3.9423787400675606e-229	-3.735603583061054e-219
5	-1.8490931671190007e-175	-7.356869548807725e-176	-8.510846260708714e-176
9	-1.1896219103739998e+110	-6.33752334173124e+100	-6.504888998661915e+102

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	44	163
1	44	163

end0.0ms (0%)

sample1.1s (19.3%)

Algorithm

1×

intervals

Results

493.0ms

8000×

body

128

valid

Compiler

Compiled 441 to 312 computations (29.3% saved)

Details

analyze5.0ms (0.1%)

sample22.0ms (0.4%)

simplify166.0ms (2.9%)

prune3.0ms (0%)

localize10.0ms (0.2%)

rewrite19.0ms (0.3%)

series183.0ms (3.2%)

simplify80.0ms (1.4%)

prune309.0ms (5.5%)

localize17.0ms (0.3%)

rewrite76.0ms (1.3%)

series280.0ms (4.9%)

simplify158.0ms (2.8%)

prune304.0ms (5.4%)

localize13.0ms (0.2%)

rewrite43.0ms (0.8%)

series569.0ms (10%)

simplify73.0ms (1.3%)

prune326.0ms (5.8%)

localize16.0ms (0.3%)

rewrite57.0ms (1%)

series558.0ms (9.8%)

simplify86.0ms (1.5%)

prune486.0ms (8.6%)

regimes615.0ms (10.8%)

bsearch92.0ms (1.6%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample1.1s (19.3%)

Profiling