Details

analyze634.0ms (6.7%)

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
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample2.4s (25.2%)

Results

661.0ms	5353×	body	128	valid
547.0ms	1182×	body	2048	valid
274.0ms	726×	body	1024	valid
212.0ms	385×	body	4096	valid
211.0ms	1036×	body	128	invalid
110.0ms	386×	body	512	valid
45.0ms	224×	body	256	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify86.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

518×	`div-sub_binary64`
428×	`fma-neg_binary64`
246×	`associate-/l*_binary64`
205×	`fma-def_binary64`
183×	`times-frac_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	27	20
2	54	20
3	115	20
4	179	20
5	291	20
6	417	20
7	528	20
8	602	20
9	854	20
10	1802	20
11	1043	20
12	1027	20
13	1035	20
14	1043	20
15	1043	20
16	1101	20
17	1137	20
18	1139	20
19	1151	20
20	1046	20

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

36.9b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	36.9b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)

Compiler

Compiled 48 to 30 computations (37.5% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
✓	1.4b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
✓	2.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
✓	27.7b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series531.0ms (5.6%)

Counts

4 → 96

Calls

4 calls:

331.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
110.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
81.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
8.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

rewrite42.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`add-sqr-sqrt_binary64`
80×	`*-un-lft-identity_binary64`
61×	`prod-diff_binary64`
60×	`add-cube-cbrt_binary64`
41×	`sqrt-prod_binary64`

Counts

4 → 176

Calls

4 calls:

10.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
9.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
3.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
3.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify273.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

819×	`fma-neg_binary64`
295×	`cancel-sign-sub-inv_binary64`
181×	`unswap-sqr_binary64`
169×	`sub-neg_binary64`
135×	`associate-r_binary64`

Counts

272 → 292

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	317	7693
1	779	6304
2	2682	5750
3	4584	5750
4	4974	5750

prune229.0ms (2.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	282	10	292
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	283	10	293

Error

6.9b

Counts

293 → 10

Alt Table

Status	Error	Program
	36.9b	(.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))
	45.8b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	45.6b	(/.f64 (*.f64 -2 b_2) a)
	55.3b	(/.f64 (-.f64 (neg.f64 b_2) (neg.f64 b_2)) a)
	47.2b	(.f64 (sqrt.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)) a)) (sqrt.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)))
	51.2b	(.f64 (+.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)) (sqrt.f64 (neg.f64 b_2))) (/.f64 (-.f64 (sqrt.f64 (neg.f64 b_2)) (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) a))
	37.2b	(/.f64 (/.f64 (.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) a)
	39.9b	(*.f64 -1/2 (/.f64 c b_2))
	37.9b	(/.f64 (-.f64 (neg.f64 b_2) (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 c a)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 c a)))))) a)
▶	33.2b	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)

Compiler

Compiled 9078 to 1990 computations (78.1% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)
✓	0.1b	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)
✓	0.5b	(-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))
✓	13.9b	(sqrt.f64 (neg.f64 (*.f64 c a)))

series564.0ms (6%)

Counts

4 → 42

Calls

4 calls:

280.0ms	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)
154.0ms	(-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))
112.0ms	(hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)
18.0ms	(sqrt.f64 (neg.f64 (*.f64 c a)))

rewrite26.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`*-un-lft-identity_binary64`
50×	`add-sqr-sqrt_binary64`
39×	`add-cube-cbrt_binary64`
30×	`prod-diff_binary64`
18×	`times-frac_binary64`

Counts

4 → 133

Calls

4 calls:

7.0ms	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)
6.0ms	(-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))
1.0ms	(sqrt.f64 (neg.f64 (*.f64 c a)))
0.0ms	(hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)

simplify152.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

659×	`fma-def_binary64`
455×	`fma-neg_binary64`
305×	`div-sub_binary64`
286×	`cancel-sign-sub-inv_binary64`
176×	`sub-neg_binary64`

Counts

175 → 206

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	282	5364
1	665	4289
2	2144	3828
3	4439	3824
4	5001	3824

prune116.0ms (1.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	202	4	206
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	205	11	216

Error

0.0b

Counts

216 → 11

Alt Table

Status	Error	Program
	37.2b	(/.f64 (/.f64 (.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) a)
	54.5b	(.f64 1/2 (/.f64 (pow.f64 (sqrt.f64 (neg.f64 (.f64 c a))) 2) (*.f64 a b_2)))
	36.9b	(.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))
	45.8b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	47.2b	(.f64 (sqrt.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)) a)) (sqrt.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)))
	51.2b	(.f64 (+.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)) (sqrt.f64 (neg.f64 b_2))) (/.f64 (-.f64 (sqrt.f64 (neg.f64 b_2)) (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) a))
	39.9b	(*.f64 -1/2 (/.f64 c b_2))
	44.9b	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2)) a)
	47.0b	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2)) a)
▶	33.4b	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (.f64 (fabs.f64 (cbrt.f64 (neg.f64 (.f64 c a)))) (sqrt.f64 (cbrt.f64 (neg.f64 (*.f64 c a))))) b_2)) a)
✓	33.2b	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)

Compiler

Compiled 6291 to 1617 computations (74.3% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (cbrt.f64 (neg.f64 (*.f64 c a))))
✓	0.2b	(.f64 (fabs.f64 (cbrt.f64 (neg.f64 (.f64 c a)))) (sqrt.f64 (cbrt.f64 (neg.f64 (*.f64 c a)))))
✓	0.5b	(-.f64 (neg.f64 b_2) (hypot.f64 (.f64 (fabs.f64 (cbrt.f64 (neg.f64 (.f64 c a)))) (sqrt.f64 (cbrt.f64 (neg.f64 (*.f64 c a))))) b_2))
✓	16.8b	(cbrt.f64 (neg.f64 (*.f64 c a)))

series1.9s (20.2%)

Counts

4 → 108

Calls

4 calls:

694.0ms	(-.f64 (neg.f64 b_2) (hypot.f64 (.f64 (fabs.f64 (cbrt.f64 (neg.f64 (.f64 c a)))) (sqrt.f64 (cbrt.f64 (neg.f64 (*.f64 c a))))) b_2))
434.0ms	(.f64 (fabs.f64 (cbrt.f64 (neg.f64 (.f64 c a)))) (sqrt.f64 (cbrt.f64 (neg.f64 (*.f64 c a)))))
394.0ms	(cbrt.f64 (neg.f64 (*.f64 c a)))
393.0ms	(sqrt.f64 (cbrt.f64 (neg.f64 (*.f64 c a))))

rewrite33.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`add-sqr-sqrt_binary64`
40×	`*-un-lft-identity_binary64`
38×	`cbrt-prod_binary64`
36×	`add-cube-cbrt_binary64`
30×	`prod-diff_binary64`

Counts

4 → 157

Calls

4 calls:

8.0ms	(.f64 (fabs.f64 (cbrt.f64 (neg.f64 (.f64 c a)))) (sqrt.f64 (cbrt.f64 (neg.f64 (*.f64 c a)))))
5.0ms	(-.f64 (neg.f64 b_2) (hypot.f64 (.f64 (fabs.f64 (cbrt.f64 (neg.f64 (.f64 c a)))) (sqrt.f64 (cbrt.f64 (neg.f64 (*.f64 c a))))) b_2))
2.0ms	(sqrt.f64 (cbrt.f64 (neg.f64 (*.f64 c a))))
1.0ms	(cbrt.f64 (neg.f64 (*.f64 c a)))

simplify200.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

934×	`times-frac_binary64`
615×	`fma-def_binary64`
450×	`fma-neg_binary64`
211×	`associate-l_binary64`
204×	`associate-r_binary64`

Counts

265 → 276

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	369	10035
1	826	7446
2	2167	6243
3	4792	6243
4	4970	6243

prune222.0ms (2.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	310	0	310
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	310	11	321

Error

0.0b

Counts

321 → 11

Alt Table

Status	Error	Program
	37.2b	(/.f64 (/.f64 (.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) a)
	54.5b	(.f64 1/2 (/.f64 (pow.f64 (sqrt.f64 (neg.f64 (.f64 c a))) 2) (*.f64 a b_2)))
▶	36.9b	(.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))
	45.8b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	47.2b	(.f64 (sqrt.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)) a)) (sqrt.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)))
	51.2b	(.f64 (+.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)) (sqrt.f64 (neg.f64 b_2))) (/.f64 (-.f64 (sqrt.f64 (neg.f64 b_2)) (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) a))
	39.9b	(*.f64 -1/2 (/.f64 c b_2))
	44.9b	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2)) a)
	47.0b	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2)) a)
✓	33.4b	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (.f64 (fabs.f64 (cbrt.f64 (neg.f64 (.f64 c a)))) (sqrt.f64 (cbrt.f64 (neg.f64 (*.f64 c a))))) b_2)) a)
✓	33.2b	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)

Compiler

Compiled 11274 to 3051 computations (72.9% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))
	1.4b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
	2.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
	27.7b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series86.0ms (0.9%)

Counts

1 → 20

Calls

1 calls:

85.0ms

(*.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64`
13×	`associate-r_binary64`
11×	`times-frac_binary64`
10×	`add-exp-log_binary64`

Counts

1 → 46

Calls

1 calls:

12.0ms

(*.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))

simplify76.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

740×	`times-frac_binary64`
400×	`fma-neg_binary64`
392×	`associate-/l*_binary64`
309×	`fma-def_binary64`
212×	`distribute-rgt-in_binary64`

Counts

66 → 94

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	148	1869
1	398	1694
2	1327	1613
3	4987	1613
4	5215	1613

prune141.0ms (1.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	298	1	299
Fresh	4	4	8
Picked	0	1	1
Done	2	0	2
Total	304	6	310

Error

0.0b

Counts

310 → 6

Alt Table

Status	Error	Program
✓	36.9b	(.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))
	45.8b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	33.2b	(/.f64 (/.f64 (.f64 c a) a) (+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
	39.9b	(*.f64 -1/2 (/.f64 c b_2))
	44.9b	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2)) a)
	47.0b	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2)) a)

Compiler

Compiled 9325 to 2488 computations (73.3% saved)

regimes1.5s (16%)

Accuracy

Total 10.5b remaining (99%)

Threshold costs 0b (0%)

Counts

111 → 3

Compiler

Compiled 9108 to 5314 computations (41.7% saved)

bsearch80.0ms (0.8%)

Steps

Iters	Range		Point
6	2.8151888881011815e+62	3.4279919876657144e+63	3.333556626530765e+63
10	-2.333067483298202e-14	-1.6891120434072655e-25	-1.707796379979102e-25

Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

11×	`+-commutative_binary64`
11×	`*-commutative_binary64`
10×	`sub-neg_binary64`
8×	`neg-sub0_binary64`
8×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	56
1	42	56
2	61	56
3	78	56
4	88	56
5	91	56
6	91	56

end88.0ms (0.9%)

Compiler: Compiled 173 to 111 computations (35.8% saved)

Details

analyze634.0ms (6.7%)

sample2.4s (25.2%)

simplify86.0ms (0.9%)

prune2.0ms (0%)

localize9.0ms (0.1%)

series531.0ms (5.6%)

rewrite42.0ms (0.4%)

simplify273.0ms (2.9%)

prune229.0ms (2.4%)

localize9.0ms (0.1%)

series564.0ms (6%)

rewrite26.0ms (0.3%)

simplify152.0ms (1.6%)

prune116.0ms (1.2%)

localize13.0ms (0.1%)

series1.9s (20.2%)

rewrite33.0ms (0.3%)

simplify200.0ms (2.1%)

prune222.0ms (2.3%)

localize19.0ms (0.2%)

series86.0ms (0.9%)

rewrite15.0ms (0.2%)

simplify76.0ms (0.8%)

prune141.0ms (1.5%)

regimes1.5s (16%)

bsearch80.0ms (0.8%)

simplify6.0ms (0.1%)

end88.0ms (0.9%)

Profiling