Details

analyze714.0ms (18%)

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	81.1%	18.9%	7
6.2%	74.9%	18.9%	8
9.4%	65.5%	25.1%	9
15.6%	48.4%	36%	10
20.3%	43.1%	36.6%	11
22.6%	36%	41.4%	12
27.1%	25.1%	47.8%	13
29.5%	22.5%	48%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample29.0ms (0.7%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
2.0ms	50×	body	128	nan
1.0ms	21×	body	128	invalid

Compiler

Compiled 30 to 20 computations (33.3% saved)

simplify330.0ms (8.3%)

Algorithm

1×	egg-herbie

Rules

3990×	`distribute-rgt-in_binary64`
2232×	`associate--r-_binary64`
1285×	`sub-neg_binary64`
783×	`unsub-neg_binary64`
741×	`*-commutative_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	15
1	18	15
2	28	15
3	53	15
4	103	15
5	229	15
6	354	15
7	732	15
8	1115	15
9	1919	15
10	2168	15
11	2475	15
12	2705	15
13	2819	15
14	2819	15
15	3778	15
16	3618	15
17	3938	15
18	3938	15
19	3858	15
20	4018	15
21	4098	15
22	4098	15
23	4098	15
24	4863	15
25	4880	15
26	10529	15

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

24.2b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	24.2b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))

Compiler

Compiled 26 to 16 computations (38.5% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
2.0b	(-.f64 (.f64 y y) (.f64 z z))
23.6b	(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))

rewrite42.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

11.8b

Rules

12×	`add-sqr-sqrt_binary64`
9×	`sqrt-prod_binary64`
7×	`associate-r_binary64`
7×	`*-un-lft-identity_binary64`
7×	`add-cube-cbrt_binary64`

Counts

3 → 54

Calls

3 calls:

5.0ms	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
3.0ms	(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))
3.0ms	(-.f64 (.f64 y y) (.f64 z z))

Compiler

Compiled 955 to 190 computations (80.1% saved)

series77.0ms (1.9%)

Error

0.4b

Counts

3 → 39

Calls

3 calls:

33.0ms	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
18.0ms	(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))
14.0ms	(-.f64 (.f64 y y) (.f64 z z))

Compiler

Compiled 1101 to 814 computations (26.1% saved)

simplify94.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

495×	`times-frac_binary64`
399×	`distribute-neg-frac_binary64`
312×	`associate-/l*_binary64`
225×	`div-sub_binary64`
210×	`unswap-sqr_binary64`

Counts

93 → 66

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	132	1560
1	308	1476
2	1033	1476
3	3480	1476
4	4903	1476
5	5179	1476

prune26.0ms (0.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	62	4	66
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	62	5	67

Error

0.4b

Counts

67 → 5

Alt Table

Status	Error	Program
✓	24.2b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
	41.7b	(/.f64 (.f64 x (sqrt.f64 (-.f64 (pow.f64 y 4) (pow.f64 z 4)))) (sqrt.f64 (+.f64 (.f64 y y) (*.f64 z z))))
	30.3b	(.f64 x (.f64 (sqrt.f64 (+.f64 z y)) (sqrt.f64 (-.f64 y z))))
	32.8b	(*.f64 x (neg.f64 y))
▶	28.0b	(.f64 x (-.f64 y (.f64 1/2 (/.f64 (*.f64 z z) y))))

Compiler

Compiled 801 to 330 computations (58.8% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(.f64 x (-.f64 y (.f64 1/2 (/.f64 (*.f64 z z) y))))
0.0b	(.f64 1/2 (/.f64 (.f64 z z) y))
8.1b	(/.f64 (*.f64 z z) y)

rewrite57.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

0.4b

Rules

19×	`add-cbrt-cube_binary64`
19×	`add-exp-log_binary64`
16×	`add-sqr-sqrt_binary64`
10×	`associate-r_binary64`
10×	`*-un-lft-identity_binary64`

Counts

3 → 73

Calls

3 calls:

5.0ms	(.f64 1/2 (/.f64 (.f64 z z) y))
4.0ms	(.f64 x (-.f64 y (.f64 1/2 (/.f64 (*.f64 z z) y))))
3.0ms	(/.f64 (*.f64 z z) y)

Compiler

Compiled 1291 to 541 computations (58.1% saved)

series69.0ms (1.7%)

Error

0.4b

Counts

3 → 27

Calls

3 calls:

38.0ms	(.f64 x (-.f64 y (.f64 1/2 (/.f64 (*.f64 z z) y))))
16.0ms	(.f64 1/2 (/.f64 (.f64 z z) y))
11.0ms	(/.f64 (*.f64 z z) y)

Compiler

Compiled 716 to 502 computations (29.9% saved)

simplify101.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

493×	`associate-l_binary64`
460×	`associate-r_binary64`
441×	`associate-*r/_binary64`
413×	`associate-*l/_binary64`
319×	`associate-/l*_binary64`

Counts

100 → 75

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	133	1415
1	297	1298
2	982	1297
3	4447	1297
4	4919	1297
5	4980	1297

prune24.0ms (0.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	75	5	80

Error

0.4b

Counts

80 → 5

Alt Table

Status	Error	Program
✓	24.2b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
	41.7b	(/.f64 (.f64 x (sqrt.f64 (-.f64 (pow.f64 y 4) (pow.f64 z 4)))) (sqrt.f64 (+.f64 (.f64 y y) (*.f64 z z))))
▶	30.3b	(.f64 x (.f64 (sqrt.f64 (+.f64 z y)) (sqrt.f64 (-.f64 y z))))
	32.8b	(*.f64 x (neg.f64 y))
✓	28.0b	(.f64 x (-.f64 y (.f64 1/2 (/.f64 (*.f64 z z) y))))

Compiler

Compiled 784 to 381 computations (51.4% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (-.f64 y z))
0.0b	(.f64 x (.f64 (sqrt.f64 (+.f64 z y)) (sqrt.f64 (-.f64 y z))))
0.2b	(*.f64 (sqrt.f64 (+.f64 z y)) (sqrt.f64 (-.f64 y z)))

rewrite55.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

0.4b

Rules

26×	`sqrt-div_binary64`
24×	`add-sqr-sqrt_binary64`
18×	`sqrt-prod_binary64`
15×	`*-un-lft-identity_binary64`
13×	`pow1_binary64`

Counts

3 → 85

Calls

3 calls:

10.0ms	(*.f64 (sqrt.f64 (+.f64 z y)) (sqrt.f64 (-.f64 y z)))
9.0ms	(.f64 x (.f64 (sqrt.f64 (+.f64 z y)) (sqrt.f64 (-.f64 y z))))
2.0ms	(sqrt.f64 (-.f64 y z))

Compiler

Compiled 1517 to 352 computations (76.8% saved)

series74.0ms (1.9%)

Error

0.4b

Counts

3 → 36

Calls

3 calls:

30.0ms	(.f64 x (.f64 (sqrt.f64 (+.f64 z y)) (sqrt.f64 (-.f64 y z))))
19.0ms	(*.f64 (sqrt.f64 (+.f64 z y)) (sqrt.f64 (-.f64 y z)))
10.0ms	(sqrt.f64 (-.f64 y z))

Compiler

Compiled 1263 to 897 computations (29% saved)

simplify114.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

581×	`cancel-sign-sub-inv_binary64`
385×	`*-commutative_binary64`
264×	`distribute-neg-frac_binary64`
259×	`distribute-rgt-in_binary64`
236×	`distribute-lft-in_binary64`

Counts

121 → 89

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	193	2276
1	443	2210
2	1274	2128
3	3339	2128
4	4868	2128
5	5033	2128

prune38.0ms (0.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	88	1	89
Fresh	1	1	2
Picked	0	1	1
Done	1	1	2
Total	90	4	94

Error

0.4b

Counts

94 → 4

Alt Table

Status	Error	Program
▶	30.4b	(.f64 x (.f64 (sqrt.f64 (sqrt.f64 (+.f64 z y))) (*.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (sqrt.f64 (+.f64 y z))))))
✓	30.3b	(.f64 x (.f64 (sqrt.f64 (+.f64 z y)) (sqrt.f64 (-.f64 y z))))
	32.8b	(*.f64 x (neg.f64 y))
✓	28.0b	(.f64 x (-.f64 y (.f64 1/2 (/.f64 (*.f64 z z) y))))

Compiler

Compiled 1434 to 501 computations (65.1% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (sqrt.f64 (+.f64 y z)))
0.1b	(sqrt.f64 (sqrt.f64 (+.f64 z y)))
0.1b	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 z y))) (.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (sqrt.f64 (+.f64 y z)))))
0.2b	(*.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (sqrt.f64 (+.f64 y z))))

rewrite100.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Error

0.4b

Rules

116×	`sqrt-div_binary64`
65×	`sqrt-prod_binary64`
50×	`add-sqr-sqrt_binary64`
32×	`frac-times_binary64`
26×	`*-un-lft-identity_binary64`

Counts

4 → 150

Calls

4 calls:

19.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 z y))) (.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (sqrt.f64 (+.f64 y z)))))
10.0ms	(*.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (sqrt.f64 (+.f64 y z))))
3.0ms	(sqrt.f64 (sqrt.f64 (+.f64 z y)))
3.0ms	(sqrt.f64 (sqrt.f64 (+.f64 y z)))

Compiler

Compiled 3744 to 820 computations (78.1% saved)

series114.0ms (2.9%)

Error

0.4b

Counts

4 → 44

Calls

4 calls:

29.0ms	(*.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (sqrt.f64 (+.f64 y z))))
27.0ms	(sqrt.f64 (sqrt.f64 (+.f64 y z)))
27.0ms	(sqrt.f64 (sqrt.f64 (+.f64 z y)))
16.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 z y))) (.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (sqrt.f64 (+.f64 y z)))))

Compiler

Compiled 2437 to 1773 computations (27.2% saved)

simplify182.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

409×	`*-commutative_binary64`
397×	`times-frac_binary64`
341×	`cancel-sign-sub-inv_binary64`
321×	`neg-mul-1_binary64`
221×	`distribute-rgt-neg-in_binary64`

Counts

194 → 151

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	275	4932
1	583	4543
2	1384	4369
3	2681	4369
4	4644	4308
5	5022	4308

prune59.0ms (1.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	151	0	151
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	151	4	155

Error

0.4b

Counts

155 → 4

Alt Table

Status	Error	Program
	30.4b	(.f64 x (.f64 (sqrt.f64 (sqrt.f64 (+.f64 z y))) (*.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (sqrt.f64 (+.f64 y z))))))
	30.3b	(.f64 x (.f64 (sqrt.f64 (+.f64 z y)) (sqrt.f64 (-.f64 y z))))
	32.8b	(*.f64 x (neg.f64 y))
	28.0b	(.f64 x (-.f64 y (.f64 1/2 (/.f64 (*.f64 z z) y))))

Compiler

Compiled 2976 to 908 computations (69.5% saved)

regimes623.0ms (15.7%)

Accuracy

Total 0.2b remaining (40.3%)

Threshold costs 0.2b (40.3%)

Compiler

Compiled 5542 to 3233 computations (41.7% saved)

bsearch53.0ms (1.3%)

Steps

Iters	Range		Point
2	-2.3325313640928883e-278	3.815834643915232e-186	9.474379742234504e-301

Compiler

Compiled 4 to 3 computations (25% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
6×	`+-commutative_binary64`
5×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	29
1	28	29
2	38	29
3	46	29
4	50	29
5	51	29
6	51	29

end1.0ms (0%)

Compiler: Compiled 22 to 14 computations (36.4% saved)

sample952.0ms (24%)

Algorithm

1×

intervals

Results

422.0ms	8000×	body	128	valid
89.0ms	1872×	body	128	nan
34.0ms	736×	body	128	invalid

Compiler

Compiled 95 to 63 computations (33.7% saved)

Details

analyze714.0ms (18%)

sample29.0ms (0.7%)

simplify330.0ms (8.3%)

prune1.0ms (0%)

localize7.0ms (0.2%)

rewrite42.0ms (1.1%)

series77.0ms (1.9%)

simplify94.0ms (2.4%)

prune26.0ms (0.6%)

localize7.0ms (0.2%)

rewrite57.0ms (1.4%)

series69.0ms (1.7%)

simplify101.0ms (2.5%)

prune24.0ms (0.6%)

localize8.0ms (0.2%)

rewrite55.0ms (1.4%)

series74.0ms (1.9%)

simplify114.0ms (2.9%)

prune38.0ms (0.9%)

localize16.0ms (0.4%)

rewrite100.0ms (2.5%)

series114.0ms (2.9%)

simplify182.0ms (4.6%)

prune59.0ms (1.5%)

regimes623.0ms (15.7%)

bsearch53.0ms (1.3%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample952.0ms (24%)

Profiling