Details

analyze889.0ms (5.3%)

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)

sample40.0ms (0.2%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
1.0ms	18×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify259.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (154.0ms)

Iter	Nodes	Cost
0	5232	30

prune4.0ms (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

27.9b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize27.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.9b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
27.4b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite85.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

27.8b

Rules

10×	`add-cube-cbrt_binary64_1477` `add-sqr-sqrt_binary64_1464` `*-un-lft-identity_binary64_1442`
9×	`times-frac_binary64_1448`
4×	`add-exp-log_binary64_1480` `add-log-exp_binary64_1481` `add-cbrt-cube_binary64_1478`
3×	`associate-/l_binary64_1387` `associate-/r_binary64_1386`
2×	`pow1_binary64_1503` `flip3--_binary64_1446` `associate-/l/_binary64_1389` `flip--_binary64_1417` `associate-/r/_binary64_1388`
1×	`div-exp_binary64_1493` `cbrt-undiv_binary64_1476` `frac-2neg_binary64_1453` `div-sub_binary64_1447` `clear-num_binary64_1441` `div-inv_binary64_1439` `flip3-+_binary64_1445` `flip-+_binary64_1416` `diff-log_binary64_1534` `sub-neg_binary64_1435` `cancel-sign-sub-inv_binary64_1408`

Counts

2 → 44

Calls

2 calls:

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

Compiler

Compiled 1243 to 168 computations (86.5% saved)

series600.0ms (3.6%)

Error

3.6b

Counts

2 → 48

Calls

2 calls:

378.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
181.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))

Compiler

Compiled 1692 to 1064 computations (37.1% saved)

simplify88.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4934	2277
1	4934	2277

prune120.0ms (0.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	84	8	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	8	93

Error

3.5b

Counts

93 → 8

Compiler

Compiled 1876 to 657 computations (65% saved)

localize34.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.9b	(-.f64 (.f64 y.re x.im) (.f64 y.im x.re))
18.0b	(/.f64 (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
30.3b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
30.3b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite204.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

3.5b

Rules

43×	`*-un-lft-identity_binary64_1442`
28×	`sqrt-prod_binary64_1458`
25×	`add-sqr-sqrt_binary64_1464`
24×	`times-frac_binary64_1448`
23×	`add-cube-cbrt_binary64_1477`
10×	`unpow-prod-down_binary64_1521` `distribute-lft-out_binary64_1393`
8×	`associate-/r*_binary64_1386`
6×	`pow1_binary64_1503` `add-log-exp_binary64_1481` `add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478` `sqrt-div_binary64_1459`
3×	`flip3-+_binary64_1445` `flip-+_binary64_1416` `associate-/l*_binary64_1387`
2×	`pow1/2_binary64_1522` `sqrt-pow1_binary64_1460` `rem-sqrt-square_binary64_1455` `flip3--_binary64_1446` `associate-/l/_binary64_1389` `flip--_binary64_1417` `associate-/r/_binary64_1388`
1×	`div-exp_binary64_1493` `cbrt-undiv_binary64_1476` `frac-2neg_binary64_1453` `div-sub_binary64_1447` `clear-num_binary64_1441` `div-inv_binary64_1439` `diff-log_binary64_1534` `sub-neg_binary64_1435` `cancel-sign-sub-inv_binary64_1408`

Counts

4 → 96

Calls

4 calls:

14.0ms	(/.f64 (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)) (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)))
8.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
4.0ms	(-.f64 (.f64 y.re x.im) (.f64 y.im x.re))

Compiler

Compiled 3624 to 1413 computations (61% saved)

series1.2s (6.9%)

Error

3.5b

Counts

4 → 94

Calls

4 calls:

530.0ms	(/.f64 (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
185.0ms	(-.f64 (.f64 y.re x.im) (.f64 y.im x.re))
168.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
165.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

Compiler

Compiled 5956 to 3776 computations (36.6% saved)

simplify113.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5066	4932

prune276.0ms (1.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	187	3	190
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	189	9	198

Error

3.5b

Counts

198 → 9

Compiler

Compiled 5790 to 2365 computations (59.2% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.9b	(-.f64 (.f64 y.re x.im) (.f64 y.im x.re))
18.0b	(/.f64 (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
30.3b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
30.3b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite271.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

3.5b

Rules

47×	`*-un-lft-identity_binary64_1442`
30×	`sqrt-prod_binary64_1458`
25×	`add-sqr-sqrt_binary64_1464`
24×	`times-frac_binary64_1448`
23×	`add-cube-cbrt_binary64_1477`
12×	`unpow-prod-down_binary64_1521` `distribute-lft-out_binary64_1393`
8×	`associate-/r*_binary64_1386`
6×	`pow1_binary64_1503` `add-log-exp_binary64_1481` `add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478` `sqrt-div_binary64_1459`
3×	`flip3-+_binary64_1445` `flip-+_binary64_1416` `associate-/l*_binary64_1387`
2×	`pow1/2_binary64_1522` `sqrt-pow1_binary64_1460` `rem-sqrt-square_binary64_1455` `flip3--_binary64_1446` `associate-/l/_binary64_1389` `flip--_binary64_1417` `associate-/r/_binary64_1388`
1×	`div-exp_binary64_1493` `cbrt-undiv_binary64_1476` `frac-2neg_binary64_1453` `div-sub_binary64_1447` `clear-num_binary64_1441` `div-inv_binary64_1439` `diff-log_binary64_1534` `sub-neg_binary64_1435` `cancel-sign-sub-inv_binary64_1408`

Counts

4 → 98

Calls

4 calls:

14.0ms	(/.f64 (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
10.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
9.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
5.0ms	(-.f64 (.f64 y.re x.im) (.f64 y.im x.re))

Compiler

Compiled 3878 to 2286 computations (41.1% saved)

series1.2s (7.1%)

Error

3.5b

Counts

4 → 94

Calls

4 calls:

503.0ms	(/.f64 (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
234.0ms	(-.f64 (.f64 y.re x.im) (.f64 y.im x.re))
162.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
160.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

Compiler

Compiled 6396 to 4877 computations (23.7% saved)

simplify126.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4998	4974
1	4998	4974

prune372.0ms (2.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	192	0	192
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	192	9	201

Error

3.5b

Counts

201 → 9

Compiler

Compiled 6209 to 3740 computations (39.8% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

9.7b	(/.f64 (/.f64 (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
30.3b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
30.3b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
30.3b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite3.2s (19.3%)

Algorithm

1×	rewrite-expression-head

Error

3.5b

Rules

1001×	`sqrt-prod_binary64_1458`
825×	`times-frac_binary64_1448`
691×	`*-un-lft-identity_binary64_1442`
382×	`add-sqr-sqrt_binary64_1464`
379×	`add-cube-cbrt_binary64_1477`
156×	`unpow-prod-down_binary64_1521` `distribute-lft-out_binary64_1393`
58×	`sqrt-div_binary64_1459`
39×	`associate-/l*_binary64_1387`
26×	`associate-/r/_binary64_1388`
16×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
13×	`div-inv_binary64_1439`
11×	`associate-/r*_binary64_1386`
9×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
7×	`pow1_binary64_1503`
4×	`add-log-exp_binary64_1481`
3×	`pow1/2_binary64_1522` `sqrt-pow1_binary64_1460` `rem-sqrt-square_binary64_1455` `div-exp_binary64_1493` `cbrt-undiv_binary64_1476`
2×	`div-sub_binary64_1447`
1×	`frac-2neg_binary64_1453` `clear-num_binary64_1441` `associate-/l/_binary64_1389`

Counts

4 → 546

Calls

4 calls:

38.0ms	(/.f64 (/.f64 (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
17.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
15.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
8.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

Compiler

Compiled 35073 to 19078 computations (45.6% saved)

series1.2s (7.3%)

Error

3.5b

Counts

4 → 88

Calls

4 calls:

535.0ms	(/.f64 (/.f64 (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
201.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
182.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
169.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

Compiler

Compiled 7162 to 4762 computations (33.5% saved)

simplify490.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

634 → 634

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	5122	40847

prune2.4s (14.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	634	0	634
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	634	9	643

Error

3.5b

Counts

643 → 9

Compiler

Compiled 31257 to 15003 computations (52% saved)

regimes1.2s (7.3%)

Accuracy

Total 9.7b remaining (65.6%)

Threshold costs 0b (0%)

Compiler

Compiled 8159 to 5038 computations (38.3% saved)

bsearch112.0ms (0.7%)

Steps

Iters	Range		Point
9	1.585010678955201e+40	6.464176775332817e+45	5.943546987088161e+45
10	1.5317612403127707e-115	3.142734090316026e-99	4.0526762739374186e-107
8	-2.271203142594088e-161	-4.727330348033218e-164	-2.178304667980649e-161
8	-6.401469326770505e+102	-6.659753031856651e+99	-2.623594142603243e+102

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	85	178
1	85	178

end0.0ms (0%)

sample2.2s (13%)

Algorithm

1×

intervals

Results

380.0ms	8000×	body	128	valid
22.0ms	494×	body	128	invalid

Compiler

Compiled 1697 to 1034 computations (39.1% saved)

Details

analyze889.0ms (5.3%)

sample40.0ms (0.2%)

simplify259.0ms (1.6%)

prune4.0ms (0%)

localize27.0ms (0.2%)

rewrite85.0ms (0.5%)

series600.0ms (3.6%)

simplify88.0ms (0.5%)

prune120.0ms (0.7%)

localize34.0ms (0.2%)

rewrite204.0ms (1.2%)

series1.2s (6.9%)

simplify113.0ms (0.7%)

prune276.0ms (1.6%)

localize29.0ms (0.2%)

rewrite271.0ms (1.6%)

series1.2s (7.1%)

simplify126.0ms (0.8%)

prune372.0ms (2.2%)

localize22.0ms (0.1%)

rewrite3.2s (19.3%)

series1.2s (7.3%)

simplify490.0ms (2.9%)

prune2.4s (14.2%)

regimes1.2s (7.3%)

bsearch112.0ms (0.7%)

simplify4.0ms (0%)

end0.0ms (0%)

sample2.2s (13%)

Profiling