Details

analyze5.0ms (0.3%)

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)

sample1.2s (55.1%)

Results

953.0ms	8256×	body	128	valid
1.0ms	6×	body	128	invalid

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify199.0ms (9.4%)

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)

localize8.0ms (0.4%)

Local error

Found 2 expressions with local error:

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

series7.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

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

rewrite70.0ms (3.3%)

Algorithm

2×	batch-egg-rewrite

Rules

481×	`log-prod_binary64`
394×	`fma-def_binary64`
192×	`fma-neg_binary64`
183×	`log-div_binary64`
175×	`expm1-udef_binary64`

Counts

2 → 113

Calls

2 calls:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	27
1	207	27
2	2760	27
3	5276	27
0	0	0
1	0	0

simplify146.0ms (6.8%)

Algorithm

1×	egg-herbie

Rules

668×	`cancel-sign-sub-inv_binary64`
494×	`fma-neg_binary64`
326×	`times-frac_binary64`
320×	`div-sub_binary64`
284×	`neg-mul-1_binary64`

Counts

137 → 157

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	74	475
1	233	459
2	681	445
3	2154	439
4	4226	439
5	4883	439
6	5144	439

prune208.0ms (9.8%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	156	1	157
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	157	1	158

Error

Counts

158 → 1

Alt Table

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

Compiler

Compiled 3091 to 2079 computations (32.7% saved)

localize8.0ms (0.4%)

Local error

Found 2 expressions with local error:

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

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))

rewrite72.0ms (3.4%)

Algorithm

2×	batch-egg-rewrite

Rules

727×	`log1p-expm1-u_binary64`
727×	`expm1-log1p-u_binary64`
522×	`prod-diff_binary64`
74×	`add-sqr-sqrt_binary64`
71×	`add-log-exp_binary64`

Counts

1 → 33

Calls

1 calls:

71.0ms

(+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	153	12
2	1823	12
3	5353	12
0	0	0
1	0	0

simplify48.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

787×	`fma-neg_binary64`
686×	`associate-/r*_binary64`
667×	`associate-l_binary64`
537×	`fma-def_binary64`
416×	`cancel-sign-sub-inv_binary64`

Counts

45 → 56

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	41	198
1	131	185
2	355	180
3	1165	176
4	4576	176
5	5117	176

prune86.0ms (4%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	109	1	110

Error

Counts

110 → 1

Alt Table

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

Compiler

Compiled 2121 to 1622 computations (23.5% saved)

regimes36.0ms (1.7%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0.0b (0%)

Counts

10 → 1

Compiler

Compiled 364 to 283 computations (22.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	19	20
2	25	20
3	29	20
4	31	20
5	30	20

end56.0ms (2.6%)

Compiler: Compiled 42 to 33 computations (21.4% saved)

Details

analyze5.0ms (0.3%)

sample1.2s (55.1%)

simplify199.0ms (9.4%)

prune2.0ms (0.1%)

localize8.0ms (0.4%)

series7.0ms (0.3%)

rewrite70.0ms (3.3%)

simplify146.0ms (6.8%)

prune208.0ms (9.8%)

localize8.0ms (0.4%)

series3.0ms (0.1%)

rewrite72.0ms (3.4%)

simplify48.0ms (2.2%)

prune86.0ms (4%)

regimes36.0ms (1.7%)

simplify2.0ms (0.1%)

end56.0ms (2.6%)

Profiling