Details

analyze521.0ms (6.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
6.2%	93.6%	0.2%	8
25%	74.9%	0.2%	9
28.1%	71.7%	0.2%	10
29.6%	70.2%	0.2%	11
53%	46.8%	0.2%	12
71.3%	28.5%	0.2%	13
71.7%	28.1%	0.2%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample22.0ms (0.3%)

Algorithm

1×

intervals

Results

12.0ms	256×	body	128	valid
1.0ms	15×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify95.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	18	30
1	18	30

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

Error

29.0b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))
1.4b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
28.5b	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite26.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795` `add-sqr-sqrt_binary64_782`
9×	`times-frac_binary64_766`
7×	`add-log-exp_binary64_799`
5×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
4×	`flip3-+_binary64_763` `flip-+_binary64_734`
3×	`associate-/r_binary64_704` `associate-/l_binary64_705` `pow1_binary64_821`
2×	`associate-/r/_binary64_706` `associate-/l/_binary64_707` `+-commutative_binary64_690` `sum-log_binary64_851`
1×	`frac-2neg_binary64_771` `cbrt-undiv_binary64_794` `div-inv_binary64_757` `div-exp_binary64_811` `clear-num_binary64_759`

Counts

3 → 53

Calls

3 calls:

9.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
4.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))
4.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))

series479.0ms (6.2%)

Counts

3 → 60

Calls

3 calls:

271.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
124.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
83.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))

Compiler

Compiled 1290 to 1074 computations (16.7% saved)

simplify103.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	5051	2576

prune124.0ms (1.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	106	7	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	107	7	114

Error

6.6b

Counts

114 → 7

Compiler

Compiled 2213 to 787 computations (64.4% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.4b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
15.4b	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
31.1b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
31.1b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite41.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64_760`
28×	`sqrt-prod_binary64_776`
25×	`add-sqr-sqrt_binary64_782`
24×	`times-frac_binary64_766`
23×	`add-cube-cbrt_binary64_795`
10×	`distribute-lft-out_binary64_711` `unpow-prod-down_binary64_839`
8×	`associate-/r*_binary64_704`
6×	`add-exp-log_binary64_798` `add-log-exp_binary64_799` `sqrt-div_binary64_777` `add-cbrt-cube_binary64_796` `pow1_binary64_821`
5×	`flip3-+_binary64_763` `flip-+_binary64_734`
3×	`associate-/l*_binary64_705`
2×	`rem-sqrt-square_binary64_773` `associate-/r/_binary64_706` `associate-/l/_binary64_707` `sqrt-pow1_binary64_778` `pow1/2_binary64_840`
1×	`frac-2neg_binary64_771` `cbrt-undiv_binary64_794` `div-inv_binary64_757` `+-commutative_binary64_690` `sum-log_binary64_851` `div-exp_binary64_811` `clear-num_binary64_759`

Counts

4 → 94

Calls

4 calls:

16.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
4.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
4.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

series797.0ms (10.3%)

Counts

4 → 89

Calls

4 calls:

402.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
161.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
118.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
116.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

Compiler

Compiled 3448 to 2688 computations (22% saved)

simplify118.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4969	4640
1	4969	4640

prune219.0ms (2.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	180	3	183
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	182	8	190

Error

6.5b

Counts

190 → 8

Compiler

Compiled 5510 to 2218 computations (59.7% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.4b	(+.f64 (.f64 y.re x.re) (.f64 y.im x.im))
15.5b	(/.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) (+.f64 (.f64 y.re x.re) (.f64 y.im x.im)))
31.1b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
31.1b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite40.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64_760`
28×	`sqrt-prod_binary64_776`
25×	`add-sqr-sqrt_binary64_782`
24×	`times-frac_binary64_766`
23×	`add-cube-cbrt_binary64_795`
10×	`distribute-lft-out_binary64_711` `unpow-prod-down_binary64_839`
8×	`associate-/l*_binary64_705`
6×	`add-exp-log_binary64_798` `add-log-exp_binary64_799` `sqrt-div_binary64_777` `add-cbrt-cube_binary64_796` `pow1_binary64_821`
5×	`flip3-+_binary64_763` `flip-+_binary64_734`
3×	`associate-/r*_binary64_704`
2×	`rem-sqrt-square_binary64_773` `associate-/r/_binary64_706` `associate-/l/_binary64_707` `sqrt-pow1_binary64_778` `pow1/2_binary64_840`
1×	`frac-2neg_binary64_771` `cbrt-undiv_binary64_794` `div-inv_binary64_757` `+-commutative_binary64_690` `sum-log_binary64_851` `div-exp_binary64_811` `clear-num_binary64_759`

Counts

4 → 94

Calls

4 calls:

13.0ms	(/.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) (+.f64 (.f64 y.re x.re) (.f64 y.im x.im)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
4.0ms	(+.f64 (.f64 y.re x.re) (.f64 y.im x.im))

series743.0ms (9.6%)

Counts

4 → 92

Calls

4 calls:

356.0ms	(/.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) (+.f64 (.f64 y.re x.re) (.f64 y.im x.im)))
155.0ms	(+.f64 (.f64 y.re x.re) (.f64 y.im x.im))
119.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
112.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

Compiler

Compiled 4464 to 3522 computations (21.1% saved)

simplify80.0ms (1%)

Algorithm

1×	egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5431	5307

prune265.0ms (3.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	186	0	186
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	186	8	194

Error

6.5b

Counts

194 → 8

Compiler

Compiled 6259 to 2882 computations (54% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))
0.3b	(/.f64 1 (/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (+.f64 (.f64 x.re y.re) (.f64 x.im y.im))))
1.4b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
28.3b	(/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)))

rewrite63.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

140×	`*-un-lft-identity_binary64_760`
138×	`times-frac_binary64_766`
72×	`add-cube-cbrt_binary64_795` `add-sqr-sqrt_binary64_782`
34×	`distribute-lft-out_binary64_711` `unpow-prod-down_binary64_839`
24×	`associate-/r*_binary64_704`
17×	`add-exp-log_binary64_798`
11×	`associate-/r/_binary64_706` `add-cbrt-cube_binary64_796`
8×	`flip3-+_binary64_763` `add-log-exp_binary64_799` `flip-+_binary64_734` `associate-/l*_binary64_705` `div-exp_binary64_811`
6×	`div-inv_binary64_757`
5×	`pow1_binary64_821`
4×	`cbrt-undiv_binary64_794`
2×	`frac-2neg_binary64_771` `associate-/l/_binary64_707` `+-commutative_binary64_690` `sum-log_binary64_851` `rec-exp_binary64_810` `clear-num_binary64_759` `1-exp_binary64_804`
1×	`inv-pow_binary64_845` `pow-flip_binary64_834`

Counts

4 → 171

Calls

4 calls:

16.0ms	(/.f64 1 (/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (+.f64 (.f64 x.re y.re) (.f64 x.im y.im))))
15.0ms	(/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
8.0ms	(+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))
4.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))

series826.0ms (10.7%)

Counts

4 → 96

Calls

4 calls:

326.0ms	(/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
273.0ms	(/.f64 1 (/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (+.f64 (.f64 x.re y.re) (.f64 x.im y.im))))
140.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
88.0ms	(+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))

Compiler

Compiled 3075 to 2577 computations (16.2% saved)

simplify141.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

267 → 267

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4973	9609
1	4973	9609

prune320.0ms (4.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	265	2	267
Fresh	3	2	5
Picked	0	1	1
Done	1	1	2
Total	269	6	275

Error

3.9b

Counts

275 → 6

Compiler

Compiled 6698 to 3232 computations (51.7% saved)

regimes968.0ms (12.6%)

Accuracy

Total 12.8b remaining (82%)

Threshold costs 0b (0%)

Compiler

Compiled 5173 to 3869 computations (25.2% saved)

bsearch134.0ms (1.7%)

Steps

Iters	Range		Point
7	7.823978455161784e+137	9.062783192871607e+139	1.5502634880996575e+138
8	3.5930668303625946e-101	1.0966230988704298e-97	1.3036553766139397e-100
7	2.1332595376670005e-250	2.130180205607659e-248	7.394456512723899e-250
10	-1.920318587397419e-156	-1.660375354011322e-173	-6.9928432867369925e-158
10	-2.9043760302608785e-99	-7.440277825091289e-110	-2.8729525879036938e-99
7	-1.5525050159358997e-62	-6.691285575431222e-65	-9.738484663641292e-65
7	-6.678150942900368e+132	-4.010819567973752e+131	-1.1580744504135465e+132

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	57	221
1	57	221

end0.0ms (0%)

sample1.5s (19.7%)

Algorithm

1×

intervals

Results

334.0ms	8000×	body	128	valid
19.0ms	480×	body	128	invalid

Compiler

Compiled 1161 to 841 computations (27.6% saved)

Details

analyze521.0ms (6.8%)

sample22.0ms (0.3%)

simplify95.0ms (1.2%)

prune3.0ms (0%)

localize10.0ms (0.1%)

rewrite26.0ms (0.3%)

series479.0ms (6.2%)

simplify103.0ms (1.3%)

prune124.0ms (1.6%)

localize16.0ms (0.2%)

rewrite41.0ms (0.5%)

series797.0ms (10.3%)

simplify118.0ms (1.5%)

prune219.0ms (2.8%)

localize17.0ms (0.2%)

rewrite40.0ms (0.5%)

series743.0ms (9.6%)

simplify80.0ms (1%)

prune265.0ms (3.4%)

localize11.0ms (0.1%)

rewrite63.0ms (0.8%)

series826.0ms (10.7%)

simplify141.0ms (1.8%)

prune320.0ms (4.2%)

regimes968.0ms (12.6%)

bsearch134.0ms (1.7%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.5s (19.7%)

Profiling