Details

analyze6.0ms (0.2%)

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)

sample1.5s (56.4%)

Results

1.3s	8256×	body	128	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify226.0ms (8.4%)

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)

localize9.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	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))

series16.0ms (0.6%)

Counts

2 → 24

Calls

2 calls:

11.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
5.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))

rewrite136.0ms (5.1%)

Algorithm

2×	egg-rewrite

Rules

86×	`egg`
59×	`egg`

Counts

2 → 145

Calls

2 calls:

68.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
65.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	18
1	207	18
2	2760	18
3	5276	18
0	10	20
1	223	20
2	2931	18
3	5582	18

simplify70.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

854×	`fma-neg_binary64`
710×	`cancel-sign-sub-inv_binary64`
407×	`times-frac_binary64`
245×	`sub-neg_binary64`
223×	`distribute-neg-frac_binary64`

Counts

169 → 186

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	86	504
1	247	488
2	734	477
3	2418	474
4	4876	474
5	5244	474

prune120.0ms (4.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	185	1	186
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	185	2	187

Error

Counts

187 → 2

Alt Table

Status	Error	Program
✓	0.0b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
▶	33.2b	(log.f64 (.f64 (fma.f64 x (sqrt.f64 (-.f64 1 (.f64 x x))) x) (pow.f64 x -2)))

Compiler

Compiled 3745 to 2380 computations (36.4% saved)

localize10.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (.f64 (fma.f64 x (sqrt.f64 (-.f64 1 (.f64 x x))) x) (pow.f64 x -2)))
✓	0.0b	(fma.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
✓	31.1b	(.f64 (fma.f64 x (sqrt.f64 (-.f64 1 (.f64 x x))) x) (pow.f64 x -2))

series20.0ms (0.7%)

Counts

3 → 36

Calls

3 calls:

9.0ms	(log.f64 (.f64 (fma.f64 x (sqrt.f64 (-.f64 1 (.f64 x x))) x) (pow.f64 x -2)))
6.0ms	(.f64 (fma.f64 x (sqrt.f64 (-.f64 1 (.f64 x x))) x) (pow.f64 x -2))
4.0ms	(fma.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x))) x)

rewrite288.0ms (10.7%)

Algorithm

3×	egg-rewrite

Rules

47×	`egg`
38×	`egg`
31×	`egg`

Counts

3 → 116

Calls

3 calls:

142.0ms	(fma.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
88.0ms	(log.f64 (.f64 (fma.f64 x (sqrt.f64 (-.f64 1 (.f64 x x))) x) (pow.f64 x -2)))
56.0ms	(.f64 (fma.f64 x (sqrt.f64 (-.f64 1 (.f64 x x))) x) (pow.f64 x -2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	19
1	212	19
2	2336	19
3	5900	19
0	7	13
1	146	13
2	1653	13
3	4872	13
4	4970	13
5	4994	13
6	4918	13
0	11	21
1	229	21
2	2530	21
3	4934	21
4	4942	21

simplify58.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

646×	`fma-neg_binary64`
487×	`times-frac_binary64`
345×	`sub-neg_binary64`
326×	`fma-def_binary64`
266×	`unswap-sqr_binary64`

Counts

152 → 182

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	112	717
1	338	695
2	992	679
3	3164	676
4	4979	676

prune98.0ms (3.6%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	182	0	182
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	182	2	184

Error

Counts

184 → 2

Alt Table

Status	Error	Program
✓	0.0b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
✓	33.2b	(log.f64 (.f64 (fma.f64 x (sqrt.f64 (-.f64 1 (.f64 x x))) x) (pow.f64 x -2)))

Compiler

Compiled 3580 to 2439 computations (31.9% saved)

regimes61.0ms (2.3%)

Accuracy

Total 0.0b remaining (1%)

Threshold costs 0.0b (1%)

Counts

19 → 1

Compiler

Compiled 757 to 580 computations (23.4% saved)

simplify2.0ms (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	10	20
1	18	20
2	24	20
3	28	20
4	30	20
5	29	20

end51.0ms (1.9%)

Compiler: Compiled 57 to 40 computations (29.8% saved)

Details

analyze6.0ms (0.2%)

sample1.5s (56.4%)

simplify226.0ms (8.4%)

prune2.0ms (0.1%)

localize9.0ms (0.3%)

series16.0ms (0.6%)

rewrite136.0ms (5.1%)

simplify70.0ms (2.6%)

prune120.0ms (4.5%)

localize10.0ms (0.4%)

series20.0ms (0.7%)

rewrite288.0ms (10.7%)

simplify58.0ms (2.2%)

prune98.0ms (3.6%)

regimes61.0ms (2.3%)

simplify2.0ms (0.1%)

end51.0ms (1.9%)

Profiling