Details

analyze529.0ms (10.1%)

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)

sample20.0ms (0.4%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
1.0ms	13×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify169.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	18	30
1	18	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

Merged error: 27.2b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.4b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
26.7b	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite18.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_1477` `add-cube-cbrt_binary64_1490` `*-un-lft-identity_binary64_1455`
9×	`times-frac_binary64_1461`
4×	`add-log-exp_binary64_1494` `add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
3×	`flip-+_binary64_1429` `associate-/r_binary64_1399` `associate-/l_binary64_1400` `flip3-+_binary64_1458`
2×	`associate-/r/_binary64_1401` `pow1_binary64_1516` `associate-/l/_binary64_1402`
1×	`div-exp_binary64_1506` `clear-num_binary64_1454` `cbrt-undiv_binary64_1489` `frac-2neg_binary64_1466` `div-inv_binary64_1452` `sum-log_binary64_1546` `+-commutative_binary64_1385`

Counts

2 → 42

Calls

2 calls:

10.0ms	(/.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 x.re y.re) (.f64 x.im y.im))

series244.0ms (4.6%)

Counts

2 → 6

Calls

2 calls:

175.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
68.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))

simplify70.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5449	1541

prune401.0ms (7.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	40	8	48
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	40	9	49

Merged error: 26.4b

Counts

49 → 9

Compiler

Compiled 8221 to 5233 computations (36.3% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
17.5b	(/.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))))
28.4b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
28.4b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite43.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64_1455`
28×	`sqrt-prod_binary64_1471`
25×	`add-sqr-sqrt_binary64_1477`
24×	`times-frac_binary64_1461`
23×	`add-cube-cbrt_binary64_1490`
10×	`distribute-lft-out_binary64_1406` `unpow-prod-down_binary64_1534`
8×	`associate-/r*_binary64_1399`
6×	`sqrt-div_binary64_1472` `pow1_binary64_1516` `add-log-exp_binary64_1494` `add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
5×	`flip-+_binary64_1429` `flip3-+_binary64_1458`
3×	`associate-/l*_binary64_1400`
2×	`sqrt-pow1_binary64_1473` `associate-/r/_binary64_1401` `rem-sqrt-square_binary64_1468` `associate-/l/_binary64_1402` `pow1/2_binary64_1535`
1×	`div-exp_binary64_1506` `clear-num_binary64_1454` `cbrt-undiv_binary64_1489` `frac-2neg_binary64_1466` `div-inv_binary64_1452` `sum-log_binary64_1546` `+-commutative_binary64_1385`

Counts

4 → 94

Calls

4 calls:

15.0ms	(/.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)))
5.0ms	(+.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)))

series413.0ms (7.9%)

Counts

4 → 12

Calls

4 calls:

242.0ms	(/.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))))
77.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
49.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
44.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

simplify67.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4963	3187
1	4963	3187

prune263.0ms (5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	101	5	106
Fresh	4	3	7
Picked	0	1	1
Done	0	1	1
Total	105	10	115

Merged error: 25.5b

Counts

115 → 10

Compiler

Compiled 5919 to 3259 computations (44.9% saved)

localize19.0ms (0.4%)

Local error

Found 4 expressions with local error:

17.5b	(/.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))))
28.4b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
28.4b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
28.4b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite57.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64_1455`
35×	`sqrt-prod_binary64_1471`
27×	`add-sqr-sqrt_binary64_1477`
24×	`add-cube-cbrt_binary64_1490` `times-frac_binary64_1461`
14×	`distribute-lft-out_binary64_1406` `unpow-prod-down_binary64_1534`
8×	`sqrt-div_binary64_1472` `associate-/r*_binary64_1399`
7×	`pow1_binary64_1516`
6×	`add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
5×	`flip-+_binary64_1429` `flip3-+_binary64_1458`
4×	`add-log-exp_binary64_1494`
3×	`sqrt-pow1_binary64_1473` `rem-sqrt-square_binary64_1468` `associate-/l*_binary64_1400` `pow1/2_binary64_1535`
2×	`associate-/r/_binary64_1401` `associate-/l/_binary64_1402`
1×	`div-exp_binary64_1506` `clear-num_binary64_1454` `cbrt-undiv_binary64_1489` `frac-2neg_binary64_1466` `div-inv_binary64_1452`

Counts

4 → 102

Calls

4 calls:

15.0ms	(/.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))))
9.0ms	(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)))
9.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

series359.0ms (6.8%)

Counts

4 → 12

Calls

4 calls:

231.0ms	(/.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))))
46.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
41.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
41.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

simplify78.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4965	3261
1	4965	3261

prune277.0ms (5.3%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	112	2	114
Fresh	1	6	7
Picked	0	1	1
Done	0	2	2
Total	113	11	124

Merged error: 25.5b

Counts

124 → 11

Compiler

Compiled 5579 to 3635 computations (34.8% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

13.3b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) (cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))) (/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
29.3b	(cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
29.3b	(cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
29.3b	(cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite101.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`*-un-lft-identity_binary64_1455`
49×	`add-exp-log_binary64_1493`
45×	`add-sqr-sqrt_binary64_1477`
39×	`times-frac_binary64_1461`
33×	`cbrt-prod_binary64_1486`
30×	`associate-r_binary64_1395`
24×	`add-cube-cbrt_binary64_1490`
20×	`prod-exp_binary64_1504` `cbrt-div_binary64_1487`
18×	`add-cbrt-cube_binary64_1491`
15×	`div-exp_binary64_1506` `associate-l_binary64_1396`
12×	`distribute-lft-out_binary64_1406` `unpow-prod-down_binary64_1534`
10×	`associate-/r/_binary64_1401` `flip-+_binary64_1429` `flip3-+_binary64_1458`
9×	`unswap-sqr_binary64_1423`
8×	`cbrt-unprod_binary64_1488`
7×	`cbrt-undiv_binary64_1489`
6×	`pow1_binary64_1516`
5×	`frac-times_binary64_1465`
4×	`1-exp_binary64_1499` `add-log-exp_binary64_1494` `rec-exp_binary64_1505`
3×	`associate-r/_binary64_1397` `pow1/3_binary64_1537` `associate-l/_binary64_1398`
2×	`div-inv_binary64_1452`
1×	`*-commutative_binary64_1386` `pow-prod-down_binary64_1526`

Counts

4 → 131

Calls

4 calls:

54.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) (cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))) (/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
9.0ms	(cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
8.0ms	(cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
8.0ms	(cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

series664.0ms (12.6%)

Counts

4 → 12

Calls

4 calls:

272.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) (cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))) (/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
138.0ms	(cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
128.0ms	(cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
126.0ms	(cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

simplify116.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4940	5235
1	4940	5235

prune292.0ms (5.6%)

Pruning

11 alts after pruning (7 fresh and 4 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	7	7
Picked	0	1	1
Done	0	3	3
Total	143	11	154

Merged error: 25.5b

Counts

154 → 11

Compiler

Compiled 5840 to 3668 computations (37.2% saved)

regimes138.0ms (2.6%)

Compiler: Compiled 1284 to 1067 computations (16.9% saved)

bsearch1.0ms (0%)

Compiler: Compiled 15 to 11 computations (26.7% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	103
1	32	103

end0.0ms (0%)

sample859.0ms (16.4%)

Algorithm

1×

intervals

Results

341.0ms	8000×	body	128	valid
20.0ms	425×	body	128	invalid

Compiler

Compiled 309 to 235 computations (23.9% saved)

Details

analyze529.0ms (10.1%)

sample20.0ms (0.4%)

simplify169.0ms (3.2%)

prune2.0ms (0%)

localize10.0ms (0.2%)

rewrite18.0ms (0.3%)

series244.0ms (4.6%)

simplify70.0ms (1.3%)

prune401.0ms (7.6%)

localize18.0ms (0.3%)

rewrite43.0ms (0.8%)

series413.0ms (7.9%)

simplify67.0ms (1.3%)

prune263.0ms (5%)

localize19.0ms (0.4%)

rewrite57.0ms (1.1%)

series359.0ms (6.8%)

simplify78.0ms (1.5%)

prune277.0ms (5.3%)

localize17.0ms (0.3%)

rewrite101.0ms (1.9%)

series664.0ms (12.6%)

simplify116.0ms (2.2%)

prune292.0ms (5.6%)

regimes138.0ms (2.6%)

bsearch1.0ms (0%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample859.0ms (16.4%)

Profiling