Details

analyze543.0ms (8.3%)

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)

sample21.0ms (0.3%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
1.0ms	17×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify223.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (123.0ms)

Iter	Nodes	Cost
0	5232	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

Merged error: 27.3b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize14.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))
0.4b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
26.8b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite21.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_1464` `add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
9×	`times-frac_binary64_1448`
7×	`add-log-exp_binary64_1481`
5×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
3×	`associate-/r_binary64_1386` `associate-/l_binary64_1387` `pow1_binary64_1503`
2×	`associate-/l/_binary64_1389` `associate-/r/_binary64_1388` `flip3--_binary64_1446` `flip--_binary64_1417` `flip3-+_binary64_1445` `flip-+_binary64_1416`
1×	`cbrt-undiv_binary64_1476` `cancel-sign-sub-inv_binary64_1408` `sum-log_binary64_1533` `div-inv_binary64_1439` `sub-neg_binary64_1435` `clear-num_binary64_1441` `+-commutative_binary64_1372` `frac-2neg_binary64_1453` `diff-log_binary64_1534` `div-sub_binary64_1447` `div-exp_binary64_1493`

Counts

3 → 55

Calls

3 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 y.re y.re) (.f64 y.im y.im))
4.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))

series577.0ms (8.8%)

Counts

3 → 65

Calls

3 calls:

339.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
141.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
96.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))

Compiler

Compiled 1469 to 1225 computations (16.6% saved)

simplify77.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5210	2857

prune138.0ms (2.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	111	9	120
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	111	10	121

Merged error: 5.1b

Counts

121 → 10

Compiler

Compiled 2377 to 933 computations (60.7% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
16.8b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
29.9b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
29.9b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite51.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

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

Counts

4 → 98

Calls

4 calls:

18.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (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)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
4.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))

series872.0ms (13.3%)

Counts

4 → 93

Calls

4 calls:

433.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
169.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
138.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
132.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

Compiler

Compiled 3869 to 3293 computations (14.9% saved)

simplify95.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5037	4984

prune336.0ms (5.1%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	189	2	191
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	189	12	201

Merged error: 5.1b

Counts

201 → 12

Compiler

Compiled 6225 to 3808 computations (38.8% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(-.f64 (.f64 y.re x.im) (.f64 y.im x.re))
16.9b	(/.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)))
29.9b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
29.9b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite46.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

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×	`distribute-lft-out_binary64_1393` `unpow-prod-down_binary64_1521`
8×	`associate-/l*_binary64_1387`
6×	`add-cbrt-cube_binary64_1478` `sqrt-div_binary64_1459` `add-log-exp_binary64_1481` `add-exp-log_binary64_1480` `pow1_binary64_1503`
3×	`associate-/r*_binary64_1386` `flip3-+_binary64_1445` `flip-+_binary64_1416`
2×	`sqrt-pow1_binary64_1460` `rem-sqrt-square_binary64_1455` `associate-/l/_binary64_1389` `associate-/r/_binary64_1388` `flip3--_binary64_1446` `flip--_binary64_1417` `pow1/2_binary64_1522`
1×	`cbrt-undiv_binary64_1476` `cancel-sign-sub-inv_binary64_1408` `div-inv_binary64_1439` `sub-neg_binary64_1435` `clear-num_binary64_1441` `frac-2neg_binary64_1453` `diff-log_binary64_1534` `div-exp_binary64_1493`

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)))
8.0ms	(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))

series767.0ms (11.7%)

Counts

4 → 86

Calls

4 calls:

315.0ms	(/.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)))
173.0ms	(-.f64 (.f64 y.re x.im) (.f64 y.im x.re))
143.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
136.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

Compiler

Compiled 4476 to 3798 computations (15.1% saved)

simplify76.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5267	4951

prune322.0ms (4.9%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	182	1	183
Fresh	1	8	9
Picked	1	0	1
Done	0	2	2
Total	184	11	195

Merged error: 4.8b

Counts

195 → 11

Compiler

Compiled 6486 to 4142 computations (36.1% saved)

localize2.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune1.0ms (0%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	8	8
Picked	1	1
Done	2	2
Total	11	11

Merged error: 4.8b

Counts

11 → 11

Compiler

Compiled 0 to 0 computations (0% saved)

regimes772.0ms (11.8%)

Compiler: Compiled 4523 to 3529 computations (22% saved)

bsearch76.0ms (1.2%)

Steps

Iters	Range		Point
4	5.473756808635552e+140	8.628528121025358e+140	6.219416782523323e+140
9	2.153185124342943e-126	5.44463872786771e-121	2.6776275404858526e-124
10	-1.6618940515417969e-128	-1.233818740205148e-138	-4.543194765813328e-138
7	-1.3000210288465644e+44	-7.665231850535463e+41	-6.473773710016467e+43

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	89	154
1	89	154

end0.0ms (0%)

sample1.5s (22.7%)

Algorithm

1×

intervals

Results

339.0ms	8000×	body	128	valid
18.0ms	461×	body	128	invalid

Compiler

Compiled 994 to 753 computations (24.2% saved)

Details

analyze543.0ms (8.3%)

sample21.0ms (0.3%)

simplify223.0ms (3.4%)

prune3.0ms (0%)

localize14.0ms (0.2%)

rewrite21.0ms (0.3%)

series577.0ms (8.8%)

simplify77.0ms (1.2%)

prune138.0ms (2.1%)

localize14.0ms (0.2%)

rewrite51.0ms (0.8%)

series872.0ms (13.3%)

simplify95.0ms (1.4%)

prune336.0ms (5.1%)

localize15.0ms (0.2%)

rewrite46.0ms (0.7%)

series767.0ms (11.7%)

simplify76.0ms (1.2%)

prune322.0ms (4.9%)

localize2.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify7.0ms (0.1%)

prune1.0ms (0%)

regimes772.0ms (11.8%)

bsearch76.0ms (1.2%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample1.5s (22.7%)

Profiling