Details

analyze446.0ms (8.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	37.5%	0.1%	6
68.7%	31.2%	0.1%	7
68.7%	31.2%	0.1%	8
71.8%	28.1%	0.1%	9
71.8%	28.1%	0.1%	10
73.4%	26.5%	0.1%	11
73.4%	26.5%	0.1%	12
74.1%	25.8%	0.1%	13
74.1%	25.8%	0.1%	14

Compiler

Compiled 18 to 13 computations (27.8% saved)

sample44.0ms (0.8%)

Algorithm

1×

intervals

Results

11.0ms	26×	body	2048	valid
11.0ms	185×	body	128	valid
10.0ms	25×	body	4096	valid
2.0ms	8×	body	1024	valid
1.0ms	8×	body	512	valid
0.0ms	4×	body	256	valid

Compiler

Compiled 37 to 27 computations (27% saved)

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`distribute-lft-in_binary64`
2×	`distribute-rgt-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	23
1	23	23
2	23	23
3	23	23

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

41.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	41.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))

Compiler

Compiled 51 to 36 computations (29.4% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.0b	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
1.4b	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
33.0b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite102.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

41.1b

Rules

8×	`add-log-exp_binary64`
8×	`pow1_binary64`
7×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`

Counts

4 → 51

Calls

4 calls:

9.0ms	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
6.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
3.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
3.0ms	(+.f64 (.f64 re re) (.f64 im im))

Compiler

Compiled 1237 to 435 computations (64.8% saved)

series130.0ms (2.5%)

Error

8.4b

Counts

4 → 57

Calls

4 calls:

35.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
28.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
21.0ms	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
19.0ms	(+.f64 (.f64 re re) (.f64 im im))

Compiler

Compiled 2157 to 1753 computations (18.7% saved)

simplify115.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

464×	`associate-r_binary64`
416×	`associate-l_binary64`
344×	`times-frac_binary64`
259×	`associate-/l*_binary64`
218×	`sub-neg_binary64`

Counts

108 → 78

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	160	1820
1	415	1731
2	1130	1711
3	4417	1708
4	4830	1708
5	5202	1708

prune47.0ms (0.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	71	7	78
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	71	8	79

Error

8.4b

Counts

79 → 8

Alt Table

Status	Error	Program
	59.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (neg.f64 re) re))))
✓	41.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
	51.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im))) re))))
▶	44.4b	(.f64 1/2 (/.f64 (sqrt.f64 (.f64 2 (.f64 im im))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))))
	48.2b	(.f64 1/2 (.f64 2 (sqrt.f64 re)))
	51.1b	(.f64 1/2 (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 im) (.f64 1/2 (.f64 re (sqrt.f64 (/.f64 1 im)))))))
	44.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	53.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (/.f64 (.f64 im im) re) -1/2))))

Compiler

Compiled 1370 to 784 computations (42.8% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (sqrt.f64 (.f64 2 (.f64 im im))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
0.8b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
29.7b	(sqrt.f64 (.f64 2 (.f64 im im)))
33.0b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite91.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

8.4b

Rules

51×	`add-sqr-sqrt_binary64`
50×	`sqrt-prod_binary64`
38×	`*-un-lft-identity_binary64`
36×	`times-frac_binary64`
26×	`add-cube-cbrt_binary64`

Counts

4 → 108

Calls

4 calls:

14.0ms	(/.f64 (sqrt.f64 (.f64 2 (.f64 im im))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
6.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
3.0ms	(sqrt.f64 (.f64 2 (.f64 im im)))
3.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 2950 to 960 computations (67.5% saved)

series128.0ms (2.4%)

Error

3.1b

Counts

4 → 46

Calls

4 calls:

35.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
32.0ms	(/.f64 (sqrt.f64 (.f64 2 (.f64 im im))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
30.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
6.0ms	(sqrt.f64 (.f64 2 (.f64 im im)))

Compiler

Compiled 2236 to 1688 computations (24.5% saved)

simplify238.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

477×	`times-frac_binary64`
441×	`associate-r_binary64`
401×	`associate-l_binary64`
372×	`associate-/l*_binary64`
246×	`associate-/r*_binary64`

Counts

154 → 95

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	226	4334
1	493	4162
2	1305	4116
3	4983	4116
4	5000	4116
5	4936	4116

prune64.0ms (1.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	89	6	95
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	91	12	103

Error

3.1b

Counts

103 → 12

Alt Table

Status	Error	Program
✓	41.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
	50.1b	(.f64 1/2 (/.f64 (.f64 im (sqrt.f64 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
	48.2b	(.f64 1/2 (.f64 2 (sqrt.f64 re)))
	50.1b	(.f64 1/2 (/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)) im)))
	44.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	50.2b	(.f64 1/2 (.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))) (/.f64 im (sqrt.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))))
	50.6b	(.f64 1/2 (/.f64 (.f64 (neg.f64 im) (sqrt.f64 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
	51.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im))) re))))
	51.1b	(.f64 1/2 (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 im) (.f64 1/2 (.f64 re (sqrt.f64 (/.f64 1 im)))))))
	53.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (/.f64 (.f64 im im) re) -1/2))))
▶	44.3b	(.f64 1/2 (/.f64 (sqrt.f64 (.f64 2 (.f64 im im))) (sqrt.f64 (-.f64 (.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) re))))
	51.7b	(.f64 1/2 (/.f64 (sqrt.f64 (.f64 2 (.f64 im im))) (sqrt.f64 (.f64 re -2))))

Compiler

Compiled 2112 to 1038 computations (50.9% saved)

localize20.0ms (0.4%)

Local error

Found 4 expressions with local error:

5.9b	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) re)
29.7b	(sqrt.f64 (.f64 2 (.f64 im im)))
34.1b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
34.1b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite69.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

3.1b

Rules

10×	`pow1_binary64`
7×	`*-un-lft-identity_binary64`
7×	`add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`
6×	`cbrt-prod_binary64`

Counts

4 → 52

Calls

4 calls:

17.0ms	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) re)
3.0ms	(sqrt.f64 (.f64 2 (.f64 im im)))
3.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
3.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 2144 to 574 computations (73.2% saved)

series237.0ms (4.5%)

Error

3.1b

Counts

4 → 54

Calls

4 calls:

74.0ms	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) re)
70.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
56.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
6.0ms	(sqrt.f64 (.f64 2 (.f64 im im)))

Compiler

Compiled 4226 to 3138 computations (25.7% saved)

simplify191.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

492×	`cancel-sign-sub-inv_binary64`
410×	`*-commutative_binary64`
288×	`distribute-rgt-in_binary64`
250×	`distribute-lft-in_binary64`
247×	`neg-mul-1_binary64`

Counts

106 → 90

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	179	2882
1	460	2477
2	1215	2379
3	2530	2302
4	4528	2246
5	4897	2246
6	5000	2246
7	4862	2246

prune49.0ms (0.9%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	90	12	102

Error

3.1b

Counts

102 → 12

Alt Table

Status	Error	Program
✓	41.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
	50.1b	(.f64 1/2 (/.f64 (.f64 im (sqrt.f64 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
	48.2b	(.f64 1/2 (.f64 2 (sqrt.f64 re)))
	50.1b	(.f64 1/2 (/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)) im)))
▶	44.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	50.2b	(.f64 1/2 (.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))) (/.f64 im (sqrt.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))))
	50.6b	(.f64 1/2 (/.f64 (.f64 (neg.f64 im) (sqrt.f64 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
	51.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im))) re))))
	51.1b	(.f64 1/2 (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 im) (.f64 1/2 (.f64 re (sqrt.f64 (/.f64 1 im)))))))
	53.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (/.f64 (.f64 im im) re) -1/2))))
✓	44.3b	(.f64 1/2 (/.f64 (sqrt.f64 (.f64 2 (.f64 im im))) (sqrt.f64 (-.f64 (.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) re))))
	51.7b	(.f64 1/2 (/.f64 (sqrt.f64 (.f64 2 (.f64 im im))) (sqrt.f64 (.f64 re -2))))

Compiler

Compiled 2335 to 1095 computations (53.1% saved)

localize4.0ms (0.1%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Error

3.1b

Counts

0 → 0

Compiler

Compiled 0 to 0 computations (0% saved)

series0.0ms (0%)

Error: 3.1b
Counts: 0 → 0
Compiler: Compiled 0 to 0 computations (0% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune8.0ms (0.1%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	9	9
Picked	1	1
Done	2	2
Total	12	12

Error

3.1b

Counts

12 → 12

Alt Table

Status	Error	Program
	41.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
	50.1b	(.f64 1/2 (/.f64 (.f64 im (sqrt.f64 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
	48.2b	(.f64 1/2 (.f64 2 (sqrt.f64 re)))
	50.1b	(.f64 1/2 (/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)) im)))
	44.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (neg.f64 im))))
	50.2b	(.f64 1/2 (.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))) (/.f64 im (sqrt.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))))
	50.6b	(.f64 1/2 (/.f64 (.f64 (neg.f64 im) (sqrt.f64 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
	51.7b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im))) re))))
	51.1b	(.f64 1/2 (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 im) (.f64 1/2 (.f64 re (sqrt.f64 (/.f64 1 im)))))))
	53.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (.f64 (/.f64 (.f64 im im) re) -1/2))))
	44.3b	(.f64 1/2 (/.f64 (sqrt.f64 (.f64 2 (.f64 im im))) (sqrt.f64 (-.f64 (.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) re))))
	51.7b	(.f64 1/2 (/.f64 (sqrt.f64 (.f64 2 (.f64 im im))) (sqrt.f64 (.f64 re -2))))

Compiler

Compiled 227 to 154 computations (32.2% saved)

regimes1.5s (28.6%)

Accuracy

Total 21.9b remaining (90.4%)

Threshold costs 0b (0%)

Compiler

Compiled 12773 to 8404 computations (34.2% saved)

bsearch316.0ms (6%)

Steps

Iters	Range		Point
9	2.0429477675782238e+133	5.353051586065493e+140	1.6683128854529867e+136
9	2.0418958902591793e-162	4.215597237856784e-153	3.0826956855422842e-161
5	8.978652904049351e-203	2.112140482314802e-202	1.405562579947193e-202
5	6.951881549153793e-293	1.6613586815832723e-292	1.4425503680000377e-292
6	-2.7951787838812196e-280	-1.818871508806914e-281	-4.196486865911031e-281
10	-1.0247084781356295e-205	-3.2530036211115343e-221	-3.9551150572318455e-213
6	-8.529315826047455e-158	-5.402547336522317e-159	-6.2060713421920385e-158
6	-1.2483336201313033e-76	-8.000186216494982e-78	-8.698128566920095e-78
10	-2.455568708379274e-59	-4.487818416463052e-70	-1.8591419239134423e-59
8	-6.042803507981941e-51	-1.1227207407744281e-55	-4.892502961362615e-55
9	-25061852894526790.0	-2503488709.8803315	-24653266729299256.0
9	-1.1304540128272104e+32	-9.940178930244222e+26	-1.0041652957658585e+27

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify18.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

32×	`*-commutative_binary64`
13×	`+-commutative_binary64`
7×	`sub-neg_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	100	358
1	138	356
2	151	356
3	165	354
4	175	354
5	179	354
6	180	354
7	179	354

end3.0ms (0.1%)

Compiler: Compiled 233 to 131 computations (43.8% saved)

sample1.4s (26.4%)

Algorithm

1×

intervals

Results

382.0ms	6096×	body	128	valid
205.0ms	650×	body	2048	valid
192.0ms	525×	body	4096	valid
105.0ms	407×	body	1024	valid
37.0ms	201×	body	512	valid
17.0ms	121×	body	256	valid

Compiler

Compiled 480 to 300 computations (37.5% saved)

Details

analyze446.0ms (8.5%)

sample44.0ms (0.8%)

simplify10.0ms (0.2%)

prune2.0ms (0%)

localize10.0ms (0.2%)

rewrite102.0ms (1.9%)

series130.0ms (2.5%)

simplify115.0ms (2.2%)

prune47.0ms (0.9%)

localize15.0ms (0.3%)

rewrite91.0ms (1.7%)

series128.0ms (2.4%)

simplify238.0ms (4.5%)

prune64.0ms (1.2%)

localize20.0ms (0.4%)

rewrite69.0ms (1.3%)

series237.0ms (4.5%)

simplify191.0ms (3.6%)

prune49.0ms (0.9%)

localize4.0ms (0.1%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify9.0ms (0.2%)

prune8.0ms (0.1%)

regimes1.5s (28.6%)

bsearch316.0ms (6%)

simplify18.0ms (0.3%)

end3.0ms (0.1%)

sample1.4s (26.4%)

Profiling