Details

analyze217.0ms (9.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
12.5%	25%	62.5%	4
18.7%	12.5%	68.8%	5
21.9%	6.2%	71.9%	6
23.4%	3.1%	73.5%	7
24.2%	1.6%	74.2%	8
24.6%	0.8%	74.6%	9
24.8%	0.4%	74.8%	10
24.9%	0.2%	74.9%	11
24.9%	0.1%	75%	12
25%	0%	75%	13
25%	0%	75%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample24.0ms (1.1%)

Algorithm

1×

intervals

Results

17.0ms

256×

body

128

valid

Compiler

Compiled 30 to 22 computations (26.7% saved)

simplify200.0ms (9.2%)

Algorithm

1×	egg-herbie

Rules

1115×	`distribute-rgt-neg-in_binary64`
788×	`distribute-rgt-out--_binary64`
692×	`unsub-neg_binary64`
492×	`fma-neg_binary64`
461×	`distribute-neg-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	18	20
2	24	20
3	34	20
4	50	20
5	73	20
6	113	20
7	247	20
8	452	20
9	742	20
10	1560	20
11	2338	20
12	2392	20
13	2628	20
14	2776	20
15	2774	20
16	2851	20
17	3110	20
18	3673	20
19	4665	20
20	4910	20
21	4952	20
22	4963	20
23	4960	20
24	6208	20

prune2.0ms (0.1%)

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

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

Compiler

Compiled 42 to 30 computations (28.6% saved)

localize8.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 1 (*.f64 x x))
✓	0.0b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
✓	0.0b	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
✓	0.0b	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)

series25.0ms (1.1%)

Counts

4 → 48

Calls

4 calls:

10.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
7.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
5.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
2.0ms	(-.f64 1 (*.f64 x x))

rewrite54.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

74×	`*-un-lft-identity_binary64`
59×	`times-frac_binary64`
50×	`add-sqr-sqrt_binary64`
39×	`add-cube-cbrt_binary64`
26×	`sqrt-prod_binary64`

Counts

4 → 141

Calls

4 calls:

20.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
18.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
5.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
2.0ms	(-.f64 1 (*.f64 x x))

simplify128.0ms (5.9%)

Algorithm

1×	egg-herbie

Rules

528×	`fma-def_binary64`
513×	`associate-/r*_binary64`
364×	`fma-neg_binary64`
289×	`cancel-sign-sub-inv_binary64`
279×	`times-frac_binary64`

Counts

189 → 236

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	256	3550
1	587	3366
2	1638	3325
3	4360	3290
4	4888	3290

prune176.0ms (8%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	235	1	236
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	236	1	237

Error

Counts

237 → 1

Alt Table

Status	Error	Program
▶	0b	(log.f64 (.f64 (+.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) 1) (/.f64 1 x)))

Compiler

Compiled 4905 to 3309 computations (32.5% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))
	0.0b	(-.f64 1 (*.f64 x x))
✓	0.0b	(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1)
✓	0.0b	(.f64 (+.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) 1) (/.f64 1 x))

series13.0ms (0.6%)

Counts

3 → 36

Calls

3 calls:

5.0ms	(.f64 (+.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) 1) (/.f64 1 x))
4.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))
3.0ms	(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1)

rewrite25.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
23×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`
13×	`associate-r_binary64`
12×	`sqrt-prod_binary64`

Counts

3 → 86

Calls

3 calls:

11.0ms	(.f64 (+.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) 1) (/.f64 1 x))
7.0ms	(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1)
3.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))

simplify82.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

678×	`fma-neg_binary64`
515×	`fma-def_binary64`
334×	`associate-/r*_binary64`
319×	`sub-neg_binary64`
254×	`times-frac_binary64`

Counts

122 → 189

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	189	2103
1	495	1919
2	1412	1888
3	4068	1888
4	5052	1888

prune135.0ms (6.2%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	221	0	221
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	221	1	222

Error

Counts

222 → 1

Alt Table

Status	Error	Program
✓	0b	(log.f64 (.f64 (+.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) 1) (/.f64 1 x)))

Compiler

Compiled 4409 to 3231 computations (26.7% saved)

regimes306.0ms (14%)

Accuracy

Total -0.0b remaining (-1.5%)

Threshold costs -0.0b (-1.5%)

Counts

87 → 1

Compiler

Compiled 5275 to 3791 computations (28.1% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	17	17
2	23	17
3	27	17
4	29	17
5	28	17

end0.0ms (0%)

Compiler: Compiled 12 to 9 computations (25% saved)

sample777.0ms (35.6%)

Algorithm

1×

intervals

Results

547.0ms	8000×	body	128	valid
0.0ms	5×	body	128	nan

Compiler

Compiled 42 to 32 computations (23.8% saved)

Details

analyze217.0ms (9.9%)

sample24.0ms (1.1%)

simplify200.0ms (9.2%)

prune2.0ms (0.1%)

localize8.0ms (0.4%)

series25.0ms (1.1%)

rewrite54.0ms (2.5%)

simplify128.0ms (5.9%)

prune176.0ms (8%)

localize10.0ms (0.4%)

series13.0ms (0.6%)

rewrite25.0ms (1.1%)

simplify82.0ms (3.8%)

prune135.0ms (6.2%)

regimes306.0ms (14%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample777.0ms (35.6%)

Profiling