Details

analyze752.0ms (14.4%)

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
3.1%	90.5%	6.3%	6
4.7%	85.9%	9.5%	7
21.1%	64%	14.9%	8
23.4%	58.9%	17.7%	9
27.7%	51.3%	21%	10
28.9%	48.5%	22.6%	11
31.1%	44.4%	24.5%	12
31.7%	42.9%	25.4%	13
32.7%	41%	26.3%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample2.8s (53.2%)

Results

1.1s	1828×	body	1024	valid
615.0ms	4668×	body	128	valid
414.0ms	1047×	body	512	valid
159.0ms	168×	body	2048	valid
140.0ms	545×	body	256	valid
111.0ms	200×	body	1024	invalid
89.0ms	236×	body	512	invalid
54.0ms	445×	body	128	invalid
44.0ms	177×	body	256	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify33.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

522×	`unswap-sqr_binary64`
255×	`fma-def_binary64`
248×	`associate-l_binary64`
206×	`div-sub_binary64`
200×	`times-frac_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	16	13
2	25	13
3	54	13
4	133	13
5	326	13
6	874	13
7	3245	13

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

14.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	14.5b	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)

Compiler

Compiled 44 to 22 computations (50% saved)

localize5.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (+.f64 x y))
✓	0.0b	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
✓	7.8b	(pow.f64 (/.f64 x (+.f64 x y)) x)

series72.0ms (1.4%)

Counts

3 → 72

Calls

3 calls:

38.0ms	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
26.0ms	(pow.f64 (/.f64 x (+.f64 x y)) x)
7.0ms	(/.f64 x (+.f64 x y))

rewrite53.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

521×	`prod-diff_binary64`
458×	`log-prod_binary64`
195×	`fma-def_binary64`
157×	`expm1-udef_binary64`
157×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	30
1	165	30
2	2522	30

Stop Event

1×	node limit

Counts

3 → 95

Calls

3 calls:

51.0ms	(/.f64 x (+.f64 x y))
51.0ms	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
51.0ms	(pow.f64 (/.f64 x (+.f64 x y)) x)

simplify78.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

309×	`fma-def_binary64`
293×	`sub-neg_binary64`
255×	`+-commutative_binary64`
230×	`associate-+r+_binary64`
211×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	331	3601
1	1091	3493
2	4274	3191

Stop Event

1×	node limit

Counts

167 → 177

prune186.0ms (3.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	174	3	177
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	175	3	178

Error

0.0b

Counts

178 → 3

Alt Table

Status	Error	Program
	16.7b	(/.f64 (fma.f64 1/2 (*.f64 (/.f64 y (/.f64 x y)) (exp.f64 (neg.f64 y))) (exp.f64 (neg.f64 y))) x)
	14.5b	(pow.f64 (/.f64 x (pow.f64 (/.f64 x (+.f64 x y)) x)) -1)
▶	11.5b	(/.f64 1 x)

Compiler

Compiled 5230 to 2657 computations (49.2% saved)

localize2.0ms (0%)

prune3.0ms (0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	2	2
Picked	1	1
Done	0	0
Total	3	3

Error

0.0b

Counts

3 → 3

Alt Table

Status	Error	Program
	16.7b	(/.f64 (fma.f64 1/2 (*.f64 (/.f64 y (/.f64 x y)) (exp.f64 (neg.f64 y))) (exp.f64 (neg.f64 y))) x)
▶	14.5b	(pow.f64 (/.f64 x (pow.f64 (/.f64 x (+.f64 x y)) x)) -1)
✓	11.5b	(/.f64 1 x)

Compiler

Compiled 67 to 40 computations (40.3% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (/.f64 x (pow.f64 (/.f64 x (+.f64 x y)) x)) -1)
	0.0b	(/.f64 x (+.f64 x y))
✓	0.0b	(/.f64 x (pow.f64 (/.f64 x (+.f64 x y)) x))
	7.8b	(pow.f64 (/.f64 x (+.f64 x y)) x)

series99.0ms (1.9%)

Counts

2 → 48

Calls

2 calls:

52.0ms	(pow.f64 (/.f64 x (pow.f64 (/.f64 x (+.f64 x y)) x)) -1)
47.0ms	(/.f64 x (pow.f64 (/.f64 x (+.f64 x y)) x))

rewrite48.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

521×	`prod-diff_binary64`
195×	`fma-def_binary64`
183×	`expm1-udef_binary64`
183×	`log1p-udef_binary64`
112×	`fma-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	29
1	206	26
2	2967	26

Stop Event

1×	node limit

Counts

2 → 75

Calls

2 calls:

47.0ms	(pow.f64 (/.f64 x (pow.f64 (/.f64 x (+.f64 x y)) x)) -1)
47.0ms	(/.f64 x (pow.f64 (/.f64 x (+.f64 x y)) x))

simplify65.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

313×	`fma-def_binary64`
239×	`+-commutative_binary64`
231×	`associate-+r+_binary64`
215×	`times-frac_binary64`
215×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	335	3192
1	1098	3092
2	4504	2814

Stop Event

1×	node limit

Counts

123 → 146

prune223.0ms (4.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	251	1	252
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	251	4	255

Error

Counts

255 → 4

Alt Table

Status	Error	Program
	22.2b	(pow.f64 (fma.f64 (/.f64 x 1) (exp.f64 y) (/.f64 (.f64 (.f64 y y) -1/2) (exp.f64 (neg.f64 y)))) -1)
▶	16.7b	(/.f64 (fma.f64 1/2 (*.f64 (/.f64 y (/.f64 x y)) (exp.f64 (neg.f64 y))) (exp.f64 (neg.f64 y))) x)
✓	14.5b	(pow.f64 (/.f64 x (pow.f64 (/.f64 x (+.f64 x y)) x)) -1)
✓	11.5b	(/.f64 1 x)

Compiler

Compiled 7918 to 4206 computations (46.9% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (fma.f64 1/2 (*.f64 (/.f64 y (/.f64 x y)) (exp.f64 (neg.f64 y))) (exp.f64 (neg.f64 y))) x)
✓	0.1b	(/.f64 y (/.f64 x y))
✓	0.5b	(fma.f64 1/2 (*.f64 (/.f64 y (/.f64 x y)) (exp.f64 (neg.f64 y))) (exp.f64 (neg.f64 y)))
✓	6.4b	(*.f64 (/.f64 y (/.f64 x y)) (exp.f64 (neg.f64 y)))

series73.0ms (1.4%)

Counts

4 → 96

Calls

4 calls:

25.0ms	(/.f64 (fma.f64 1/2 (*.f64 (/.f64 y (/.f64 x y)) (exp.f64 (neg.f64 y))) (exp.f64 (neg.f64 y))) x)
18.0ms	(*.f64 (/.f64 y (/.f64 x y)) (exp.f64 (neg.f64 y)))
17.0ms	(fma.f64 1/2 (*.f64 (/.f64 y (/.f64 x y)) (exp.f64 (neg.f64 y))) (exp.f64 (neg.f64 y)))
14.0ms	(/.f64 y (/.f64 x y))

rewrite67.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

612×	`log-prod_binary64`
196×	`expm1-udef_binary64`
196×	`log1p-udef_binary64`
176×	`log-pow_binary64`
175×	`log-div_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	68
1	238	58
2	3416	58

Stop Event

1×	node limit

Counts

4 → 142

Calls

4 calls:

62.0ms	(/.f64 (fma.f64 1/2 (*.f64 (/.f64 y (/.f64 x y)) (exp.f64 (neg.f64 y))) (exp.f64 (neg.f64 y))) x)
62.0ms	(/.f64 y (/.f64 x y))
62.0ms	(fma.f64 1/2 (*.f64 (/.f64 y (/.f64 x y)) (exp.f64 (neg.f64 y))) (exp.f64 (neg.f64 y)))
62.0ms	(*.f64 (/.f64 y (/.f64 x y)) (exp.f64 (neg.f64 y)))

simplify51.0ms (1%)

Algorithm

1×	egg-herbie

Rules

493×	`associate-/r*_binary64`
401×	`fma-neg_binary64`
368×	`associate-/l/_binary64`
353×	`associate-/r/_binary64`
259×	`sub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	72	1601
1	203	1585
2	555	1454
3	2284	1338

Stop Event

1×	node limit

Counts

238 → 178

prune132.0ms (2.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	178	0	178
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	178	4	182

Error

Counts

182 → 4

Alt Table

Status	Error	Program
	22.2b	(pow.f64 (fma.f64 (/.f64 x 1) (exp.f64 y) (/.f64 (.f64 (.f64 y y) -1/2) (exp.f64 (neg.f64 y)))) -1)
✓	16.7b	(/.f64 (fma.f64 1/2 (*.f64 (/.f64 y (/.f64 x y)) (exp.f64 (neg.f64 y))) (exp.f64 (neg.f64 y))) x)
✓	14.5b	(pow.f64 (/.f64 x (pow.f64 (/.f64 x (+.f64 x y)) x)) -1)
✓	11.5b	(/.f64 1 x)

Compiler

Compiled 3707 to 1421 computations (61.7% saved)

regimes361.0ms (6.9%)

Accuracy

Total 0.9b remaining (99.2%)

Threshold costs 0.9b (99.2%)

Counts

66 → 3

Compiler

Compiled 2876 to 1872 computations (34.9% saved)

bsearch36.0ms (0.7%)

Steps

Iters	Range		Point
4	4.8031077022846414e-32	7.921997225875706e-32	7.8205546484089e-32
5	-18.76934416649638	-8.322816428101495e-5	-12.932303641541722

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`+-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	26	62
1	33	62
2	35	62
3	36	62

Stop Event

1×

saturated

end78.0ms (1.5%)

Compiler: Compiled 141 to 86 computations (39% saved)

Details

analyze752.0ms (14.4%)

sample2.8s (53.2%)

simplify33.0ms (0.6%)

prune3.0ms (0%)

localize5.0ms (0.1%)

series72.0ms (1.4%)

rewrite53.0ms (1%)

simplify78.0ms (1.5%)

prune186.0ms (3.6%)

localize2.0ms (0%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series99.0ms (1.9%)

rewrite48.0ms (0.9%)

simplify65.0ms (1.2%)

prune223.0ms (4.3%)

localize9.0ms (0.2%)

series73.0ms (1.4%)

rewrite67.0ms (1.3%)

simplify51.0ms (1%)

prune132.0ms (2.5%)

regimes361.0ms (6.9%)

bsearch36.0ms (0.7%)

simplify3.0ms (0.1%)

end78.0ms (1.5%)

Profiling