Details

analyze108.0ms (6%)

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
25%	74.9%	0.1%	4
25%	74.9%	0.1%	5
43.7%	50%	6.3%	6
43.7%	43.7%	12.6%	7
59.3%	26.5%	14.1%	8
59.3%	22.6%	18%	9
67.1%	13.7%	19.2%	10
67.1%	11.5%	21.4%	11
71%	6.9%	22%	12
71%	5.8%	23.2%	13
73%	3.5%	23.5%	14

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample15.0ms (0.8%)

Algorithm

1×

intervals

Results

8.0ms	256×	body	128	valid
0.0ms	9×	body	128	nan

Compiler

Compiled 19 to 13 computations (31.6% saved)

simplify8.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	7	9
2	7	9

prune1.0ms (0.1%)

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

19.8b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	19.8b	(sqrt.f64 (+.f64 (*.f64 x x) y))

Compiler

Compiled 16 to 10 computations (37.5% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (*.f64 x x) y)
18.4b	(sqrt.f64 (+.f64 (*.f64 x x) y))

rewrite17.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

19.8b

Rules

4×	`add-sqr-sqrt_binary64`
4×	`add-log-exp_binary64`
3×	`*-un-lft-identity_binary64`
3×	`sqrt-prod_binary64`
3×	`add-cube-cbrt_binary64`

Counts

2 → 26

Calls

2 calls:

3.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
3.0ms	(+.f64 (*.f64 x x) y)

Compiler

Compiled 342 to 89 computations (74% saved)

series37.0ms (2%)

Error

0.0b

Counts

2 → 28

Calls

2 calls:

19.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
11.0ms	(+.f64 (*.f64 x x) y)

Compiler

Compiled 530 to 388 computations (26.8% saved)

simplify73.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

607×	`associate-/l*_binary64`
496×	`associate-/r*_binary64`
381×	`cancel-sign-sub-inv_binary64`
266×	`unswap-sqr_binary64`
207×	`distribute-rgt-in_binary64`

Counts

54 → 39

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	75	679
1	186	638
2	468	638
3	1555	620
4	4938	620
5	4971	620

prune16.0ms (0.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	35	4	39
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	35	5	40

Error

Counts

40 → 5

Alt Table

Status	Error	Program
▶	23.1b	(exp.f64 (log.f64 (sqrt.f64 (+.f64 y (*.f64 x x)))))
	44.5b	(neg.f64 x)
	40.0b	(+.f64 x (*.f64 1/2 (/.f64 y x)))
	41.5b	(+.f64 (sqrt.f64 y) (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) (*.f64 x x))))
✓	19.8b	(sqrt.f64 (+.f64 (*.f64 x x) y))

Compiler

Compiled 428 to 197 computations (54% saved)

localize8.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 y (*.f64 x x))
0.0b	(log.f64 (sqrt.f64 (+.f64 y (*.f64 x x))))
5.4b	(exp.f64 (log.f64 (sqrt.f64 (+.f64 y (*.f64 x x)))))
18.4b	(sqrt.f64 (+.f64 y (*.f64 x x)))

rewrite30.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

12×	`log-prod_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`
9×	`sqrt-prod_binary64`

Counts

4 → 67

Calls

4 calls:

3.0ms	(exp.f64 (log.f64 (sqrt.f64 (+.f64 y (*.f64 x x)))))
2.0ms	(log.f64 (sqrt.f64 (+.f64 y (*.f64 x x))))
2.0ms	(sqrt.f64 (+.f64 y (*.f64 x x)))
2.0ms	(+.f64 y (*.f64 x x))

Compiler

Compiled 1005 to 260 computations (74.1% saved)

series96.0ms (5.4%)

Error

Counts

4 → 53

Calls

4 calls:

30.0ms	(exp.f64 (log.f64 (sqrt.f64 (+.f64 y (*.f64 x x)))))
22.0ms	(log.f64 (sqrt.f64 (+.f64 y (*.f64 x x))))
17.0ms	(sqrt.f64 (+.f64 y (*.f64 x x)))
13.0ms	(+.f64 y (*.f64 x x))

Compiler

Compiled 1775 to 1361 computations (23.3% saved)

simplify94.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

509×	`associate-/r*_binary64`
464×	`associate-/l*_binary64`
331×	`associate-r_binary64`
314×	`associate-l_binary64`
256×	`associate-*l/_binary64`

Counts

120 → 76

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	185	1773
1	411	1666
2	1144	1608
3	4629	1608
4	5001	1608

prune25.0ms (1.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	76	5	81

Error

Counts

81 → 5

Alt Table

Status	Error	Program
✓	23.1b	(exp.f64 (log.f64 (sqrt.f64 (+.f64 y (*.f64 x x)))))
	44.5b	(neg.f64 x)
▶	40.0b	(+.f64 x (*.f64 1/2 (/.f64 y x)))
	41.5b	(+.f64 (sqrt.f64 y) (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) (*.f64 x x))))
✓	19.8b	(sqrt.f64 (+.f64 (*.f64 x x) y))

Compiler

Compiled 814 to 392 computations (51.8% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(*.f64 1/2 (/.f64 y x))
0.0b	(+.f64 x (*.f64 1/2 (/.f64 y x)))

rewrite26.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

15×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
10×	`times-frac_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`

Counts

2 → 43

Calls

2 calls:

5.0ms	(*.f64 1/2 (/.f64 y x))
2.0ms	(+.f64 x (*.f64 1/2 (/.f64 y x)))

Compiler

Compiled 599 to 308 computations (48.6% saved)

series26.0ms (1.5%)

Error

Counts

2 → 18

Calls

2 calls:

16.0ms	(+.f64 x (*.f64 1/2 (/.f64 y x)))
9.0ms	(*.f64 1/2 (/.f64 y x))

Compiler

Compiled 268 to 176 computations (34.3% saved)

simplify91.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

615×	`associate-/l*_binary64`
586×	`associate-*l/_binary64`
519×	`associate-*r/_binary64`
317×	`times-frac_binary64`
293×	`associate-/l/_binary64`

Counts

61 → 24

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	90	655
1	223	634
2	596	633
3	1550	633
4	4356	633
5	4501	633
6	4986	633
7	4926	633

prune10.0ms (0.6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	24	0	24
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	24	5	29

Error

Counts

29 → 5

Alt Table

Status	Error	Program
✓	23.1b	(exp.f64 (log.f64 (sqrt.f64 (+.f64 y (*.f64 x x)))))
	44.5b	(neg.f64 x)
✓	40.0b	(+.f64 x (*.f64 1/2 (/.f64 y x)))
▶	41.5b	(+.f64 (sqrt.f64 y) (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) (*.f64 x x))))
✓	19.8b	(sqrt.f64 (+.f64 (*.f64 x x) y))

Compiler

Compiled 245 to 145 computations (40.8% saved)

localize8.0ms (0.5%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (sqrt.f64 y) (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) (*.f64 x x))))
0.1b	(sqrt.f64 (/.f64 1 y))
1.8b	(.f64 (sqrt.f64 (/.f64 1 y)) (.f64 x x))

rewrite74.0ms (4.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

29×	`sqrt-prod_binary64`
27×	`add-sqr-sqrt_binary64`
22×	`times-frac_binary64`
20×	`*-un-lft-identity_binary64`
18×	`add-cube-cbrt_binary64`

Counts

3 → 75

Calls

3 calls:

8.0ms	(.f64 (sqrt.f64 (/.f64 1 y)) (.f64 x x))
3.0ms	(+.f64 (sqrt.f64 y) (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) (*.f64 x x))))
2.0ms	(sqrt.f64 (/.f64 1 y))

Compiler

Compiled 1437 to 869 computations (39.5% saved)

series42.0ms (2.3%)

Error

Counts

3 → 18

Calls

3 calls:

21.0ms	(+.f64 (sqrt.f64 y) (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) (*.f64 x x))))
15.0ms	(.f64 (sqrt.f64 (/.f64 1 y)) (.f64 x x))
4.0ms	(sqrt.f64 (/.f64 1 y))

Compiler

Compiled 533 to 415 computations (22.1% saved)

simplify85.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

418×	`unswap-sqr_binary64`
313×	`*-commutative_binary64`
305×	`associate-*l/_binary64`
260×	`associate-/l*_binary64`
243×	`distribute-rgt-neg-in_binary64`

Counts

93 → 69

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	100	1350
1	231	1247
2	692	1247
3	1562	1247
4	4206	1247
5	5141	1247

prune23.0ms (1.3%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	69	5	74

Error

Counts

74 → 5

Alt Table

Status	Error	Program
	23.1b	(exp.f64 (log.f64 (sqrt.f64 (+.f64 y (*.f64 x x)))))
	44.5b	(neg.f64 x)
	40.0b	(+.f64 x (*.f64 1/2 (/.f64 y x)))
	41.5b	(+.f64 (sqrt.f64 y) (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) (*.f64 x x))))
	19.8b	(sqrt.f64 (+.f64 (*.f64 x x) y))

Compiler

Compiled 883 to 538 computations (39.1% saved)

regimes141.0ms (7.9%)

Accuracy

Total 0.1b remaining (95.6%)

Threshold costs 0.1b (95.6%)

Compiler

Compiled 985 to 651 computations (33.9% saved)

bsearch18.0ms (1%)

Steps

Iters	Range		Point
8	4.7155801437998065e+110	2.3184334083997574e+115	2.2583755260511737e+115
4	-4.094729671818864e+166	-9.981390520726584e+147	-6.309494455453091e+153

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
2×	`*-commutative_binary64`
1×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	34
1	25	34
2	27	34
3	28	34
4	28	34

end1.0ms (0%)

Compiler: Compiled 25 to 16 computations (36% saved)

sample706.0ms (39.4%)

Algorithm

1×

intervals

Results

400.0ms	8000×	body	128	valid
5.0ms	187×	body	128	nan

Compiler

Compiled 82 to 56 computations (31.7% saved)

Details

analyze108.0ms (6%)

sample15.0ms (0.8%)

simplify8.0ms (0.5%)

prune1.0ms (0.1%)

localize6.0ms (0.3%)

rewrite17.0ms (0.9%)

series37.0ms (2%)

simplify73.0ms (4.1%)

prune16.0ms (0.9%)

localize8.0ms (0.4%)

rewrite30.0ms (1.7%)

series96.0ms (5.4%)

simplify94.0ms (5.2%)

prune25.0ms (1.4%)

localize4.0ms (0.2%)

rewrite26.0ms (1.4%)

series26.0ms (1.5%)

simplify91.0ms (5.1%)

prune10.0ms (0.6%)

localize8.0ms (0.5%)

rewrite74.0ms (4.1%)

series42.0ms (2.3%)

simplify85.0ms (4.7%)

prune23.0ms (1.3%)

regimes141.0ms (7.9%)

bsearch18.0ms (1%)

simplify4.0ms (0.2%)

end1.0ms (0%)

sample706.0ms (39.4%)

Profiling