Details

analyze704.0ms (6.9%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4985	210
1	4985	210
0	4	4
1	4	4

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)

sample26.0ms (0.3%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
1.0ms	18×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify128.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (122.0ms)

Iter	Nodes	Cost
0	5232	30

prune2.0ms (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

23.6b

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))
0.5b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
23.2b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite83.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

23.4b

Rules

11×	`add-cube-cbrt_binary64_1477` `add-sqr-sqrt_binary64_1464` `*-un-lft-identity_binary64_1442`
9×	`times-frac_binary64_1448`
7×	`add-log-exp_binary64_1481`
5×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
3×	`pow1_binary64_1503` `associate-/l_binary64_1387` `associate-/r_binary64_1386`
2×	`flip3--_binary64_1446` `associate-/l/_binary64_1389` `flip--_binary64_1417` `flip3-+_binary64_1445` `associate-/r/_binary64_1388` `flip-+_binary64_1416`
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` `sum-log_binary64_1533` `+-commutative_binary64_1372`

Counts

3 → 55

Calls

3 calls:

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

Compiler

Compiled 1509 to 201 computations (86.7% saved)

series607.0ms (5.9%)

Error

5.1b

Counts

3 → 63

Calls

3 calls:

338.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
144.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
84.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))

Compiler

Compiled 2250 to 1442 computations (35.9% saved)

simplify92.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	6104	2684

prune108.0ms (1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	110	8	118
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	111	8	119

Error

5.1b

Counts

119 → 8

Compiler

Compiled 2273 to 821 computations (63.9% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b	(-.f64 (.f64 y.re x.im) (.f64 y.im x.re))
14.0b	(/.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))))
28.8b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
28.8b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite214.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

5.1b

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:

13.0ms	(/.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)))
7.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
4.0ms	(-.f64 (.f64 y.re x.im) (.f64 y.im x.re))

Compiler

Compiled 3878 to 2286 computations (41.1% saved)

series987.0ms (9.6%)

Error

5.1b

Counts

4 → 93

Calls

4 calls:

428.0ms	(/.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))))
165.0ms	(-.f64 (.f64 y.re x.im) (.f64 y.im x.re))
140.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
130.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

Compiler

Compiled 6354 to 4849 computations (23.7% saved)

simplify91.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5000	4915

prune307.0ms (3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	187	4	191
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	190	9	199

Error

5.1b

Counts

199 → 9

Compiler

Compiled 6158 to 3714 computations (39.7% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(-.f64 (.f64 y.re x.im) (.f64 y.im x.re))
14.0b	(/.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)))
28.8b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
28.8b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite230.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

5.1b

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-/l*_binary64_1387`
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-/r*_binary64_1386`
2×	`pow1/2_binary64_1522` `sqrt-pow1_binary64_1460` `rem-sqrt-square_binary64_1455` `associate-/l/_binary64_1389` `flip3--_binary64_1446` `associate-/r/_binary64_1388` `flip--_binary64_1417`
1×	`div-exp_binary64_1493` `cbrt-undiv_binary64_1476` `frac-2neg_binary64_1453` `clear-num_binary64_1441` `div-inv_binary64_1439` `diff-log_binary64_1534` `sub-neg_binary64_1435` `cancel-sign-sub-inv_binary64_1408`

Counts

4 → 97

Calls

4 calls:

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

Compiler

Compiled 4036 to 2456 computations (39.1% saved)

series877.0ms (8.6%)

Error

5.1b

Counts

4 → 85

Calls

4 calls:

306.0ms	(/.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)))
170.0ms	(-.f64 (.f64 y.re x.im) (.f64 y.im x.re))
141.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
133.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

Compiler

Compiled 6899 to 5394 computations (21.8% saved)

simplify100.0ms (1%)

Algorithm

1×	egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4966	4795
1	4966	4795

prune318.0ms (3.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	180	2	182
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	181	10	191

Error

5.1b

Counts

191 → 10

Compiler

Compiled 6379 to 4042 computations (36.6% 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))
0.5b	(-.f64 (.f64 y.re x.im) (.f64 y.im x.re))
0.6b	(/.f64 1 (/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (-.f64 (.f64 y.re x.im) (.f64 y.im x.re))))
22.9b	(/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)))

rewrite303.0ms (3%)

Algorithm

1×	rewrite-expression-head

Error

5.1b

Rules

140×	`*-un-lft-identity_binary64_1442`
138×	`times-frac_binary64_1448`
72×	`add-cube-cbrt_binary64_1477` `add-sqr-sqrt_binary64_1464`
34×	`unpow-prod-down_binary64_1521` `distribute-lft-out_binary64_1393`
24×	`associate-/r*_binary64_1386`
17×	`add-exp-log_binary64_1480`
11×	`add-cbrt-cube_binary64_1478` `associate-/r/_binary64_1388`
8×	`div-exp_binary64_1493` `add-log-exp_binary64_1481` `associate-/l*_binary64_1387`
6×	`div-inv_binary64_1439` `flip3--_binary64_1446` `flip--_binary64_1417`
5×	`pow1_binary64_1503`
4×	`cbrt-undiv_binary64_1476`
2×	`frac-2neg_binary64_1453` `clear-num_binary64_1441` `flip3-+_binary64_1445` `associate-/l/_binary64_1389` `flip-+_binary64_1416` `1-exp_binary64_1486` `rec-exp_binary64_1492`
1×	`inv-pow_binary64_1527` `pow-flip_binary64_1516` `diff-log_binary64_1534` `sub-neg_binary64_1435` `cancel-sign-sub-inv_binary64_1408` `sum-log_binary64_1533` `+-commutative_binary64_1372`

Counts

4 → 172

Calls

4 calls:

20.0ms	(/.f64 1 (/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (-.f64 (.f64 y.re x.im) (.f64 y.im x.re))))
13.0ms	(/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)))
7.0ms	(+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))
4.0ms	(-.f64 (.f64 y.re x.im) (.f64 y.im x.re))

Compiler

Compiled 5646 to 2768 computations (51% saved)

series955.0ms (9.3%)

Error

5.1b

Counts

4 → 93

Calls

4 calls:

337.0ms	(/.f64 1 (/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (-.f64 (.f64 y.re x.im) (.f64 y.im x.re))))
297.0ms	(/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)))
158.0ms	(-.f64 (.f64 y.re x.im) (.f64 y.im x.re))
84.0ms	(+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))

Compiler

Compiled 4470 to 3315 computations (25.8% saved)

simplify132.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

265 → 265

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5107	9145

prune291.0ms (2.8%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	261	4	265
Fresh	3	5	8
Picked	0	1	1
Done	0	1	1
Total	264	11	275

Error

2.9b

Counts

275 → 11

Compiler

Compiled 6441 to 3040 computations (52.8% saved)

regimes1.4s (13.9%)

Accuracy

Total 12.4b remaining (81.8%)

Threshold costs 0b (0%)

Compiler

Compiled 9211 to 6171 computations (33% saved)

bsearch94.0ms (0.9%)

Steps

Iters	Range		Point
8	3.818506499598949e+97	2.0633932676299287e+101	1.2844010281600191e+98
7	9.969763227567243e-65	4.805708286348249e-63	2.9287362350767606e-64
10	-4.98464034604884e-73	-2.327685270769025e-83	-8.576726686584933e-81
9	-9.214965594338194e+70	-6.851565655462375e+65	-9.123072789870653e+70

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	85	191
1	85	191

end0.0ms (0%)

sample2.1s (20.7%)

Algorithm

1×

intervals

Results

337.0ms	8000×	body	128	valid
25.0ms	463×	body	128	invalid

Compiler

Compiled 1911 to 1261 computations (34% saved)

Details

analyze704.0ms (6.9%)

sample26.0ms (0.3%)

simplify128.0ms (1.2%)

prune2.0ms (0%)

localize10.0ms (0.1%)

rewrite83.0ms (0.8%)

series607.0ms (5.9%)

simplify92.0ms (0.9%)

prune108.0ms (1%)

localize14.0ms (0.1%)

rewrite214.0ms (2.1%)

series987.0ms (9.6%)

simplify91.0ms (0.9%)

prune307.0ms (3%)

localize16.0ms (0.2%)

rewrite230.0ms (2.2%)

series877.0ms (8.6%)

simplify100.0ms (1%)

prune318.0ms (3.1%)

localize11.0ms (0.1%)

rewrite303.0ms (3%)

series955.0ms (9.3%)

simplify132.0ms (1.3%)

prune291.0ms (2.8%)

regimes1.4s (13.9%)

bsearch94.0ms (0.9%)

simplify5.0ms (0%)

end0.0ms (0%)

sample2.1s (20.7%)

Profiling