Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	25.7%	74.3%	0
25.7%	0%	74.3%	1

Compiler

Compiled 26 to 19 computations (26.9% saved)

sample1.7s (72.3%)

Results

708.0ms	5415×	body	128	valid
461.0ms	1051×	body	1024	valid
376.0ms	1093×	body	512	valid
159.0ms	681×	body	256	valid
8.0ms	16×	body	2048	valid

Compiler

Compiled 52 to 38 computations (26.9% saved)

preprocess40.0ms (1.7%)

Algorithm

2×	egg-herbie

Rules

497×	`associate-l_binary64`
409×	`associate-r_binary64`
202×	`fma-neg_binary64`
186×	`cancel-sign-sub-inv_binary64`
176×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	26
1	32	26
2	76	26
3	262	26
4	1173	20
5	4317	20
0	2	2

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 11 to 8 computations (27.3% saved)

simplify21.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

517×	`cancel-sign-sub-inv_binary64`
510×	`fma-neg_binary64`
430×	`fma-def_binary64`
372×	`unswap-sqr_binary64`
269×	`associate-l_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	19	13
2	49	13
3	166	13
4	657	8
5	2742	8

Stop Event

1×	node limit

Counts

1 → 2

prune5.0ms (0.2%)

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

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(*.f64 eps (fma.f64 2 x eps))

Compiler

Compiled 33 to 21 computations (36.4% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 eps (fma.f64 2 x eps))

series6.0ms (0.2%)

Counts

1 → 24

Calls

6 calls:

1.0ms	(*.f64 eps (fma.f64 2 x eps))	eps	-inf
1.0ms	(*.f64 eps (fma.f64 2 x eps))	eps	inf
1.0ms	(*.f64 eps (fma.f64 2 x eps))	eps	0
1.0ms	(*.f64 eps (fma.f64 2 x eps))	x	-inf
1.0ms	(*.f64 eps (fma.f64 2 x eps))	x	inf

rewrite31.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

552×	`pow1_binary64`
507×	`add-log-exp_binary64`
507×	`log1p-expm1-u_binary64`
507×	`expm1-log1p-u_binary64`
497×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	120	8
2	1364	8

Stop Event

1×	node limit

Counts

1 → 15

simplify66.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

564×	`fma-def_binary64`
469×	`associate-l_binary64`
434×	`unswap-sqr_binary64`
370×	`sqr-pow_binary64`
292×	`*-commutative_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	8	231
1	19	231
2	37	213
3	75	177
4	168	177
5	464	177
6	1534	177
7	2777	177
8	3132	177
9	3354	177
10	3576	177
11	3880	177
12	4302	177
13	4812	177

Stop Event

1×	node limit

Counts

39 → 21

prune13.0ms (0.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	20	1	21
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	20	2	22

Error

0.0b

Counts

22 → 2

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 eps (fma.f64 2 x eps))
▶	0.0b	(+.f64 (.f64 2 (.f64 eps x)) (pow.f64 eps 2))

Compiler

Compiled 199 to 127 computations (36.2% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 2 (.f64 eps x))
✓	0.0b	(+.f64 (.f64 2 (.f64 eps x)) (pow.f64 eps 2))

series12.0ms (0.5%)

Counts

2 → 6

Calls

12 calls:

3.0ms	(.f64 2 (.f64 eps x))	eps	-inf
1.0ms	(+.f64 (.f64 2 (.f64 eps x)) (pow.f64 eps 2))	eps	-inf
1.0ms	(+.f64 (.f64 2 (.f64 eps x)) (pow.f64 eps 2))	eps	inf
1.0ms	(+.f64 (.f64 2 (.f64 eps x)) (pow.f64 eps 2))	eps	0
1.0ms	(+.f64 (.f64 2 (.f64 eps x)) (pow.f64 eps 2))	x	-inf

rewrite42.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

810×	`log1p-expm1-u_binary64`
810×	`expm1-log1p-u_binary64`
88×	`add-sqr-sqrt_binary64`
86×	`pow1_binary64`
85×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	176	18
2	2276	18

Stop Event

1×	node limit

Counts

2 → 51

simplify53.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

625×	`sqr-pow_binary64`
447×	`associate-l_binary64`
434×	`unswap-sqr_binary64`
285×	`cube-prod_binary64`
277×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	33
1	16	33
2	30	33
3	56	33
4	124	33
5	358	33
6	1252	33
7	2130	33
8	2294	33
9	2507	33
10	2727	33
11	3020	33
12	3420	33
13	3908	33
14	4469	33

Stop Event

1×	node limit

Counts

57 → 55

prune32.0ms (1.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	53	2	55
Fresh	0	0	0
Picked	1	0	1
Done	1	0	1
Total	55	2	57

Error

Counts

57 → 2

Alt Table

Status	Error	Program
	0.0b	(fma.f64 (.f64 2 eps) x (.f64 eps eps))
▶	0.0b	(fma.f64 eps eps (.f64 2 (.f64 eps x)))

Compiler

Compiled 846 to 478 computations (43.5% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 eps eps (.f64 2 (.f64 eps x)))
	0.0b	(.f64 2 (.f64 eps x))

series6.0ms (0.3%)

Counts

1 → 24

Calls

6 calls:

1.0ms	(fma.f64 eps eps (.f64 2 (.f64 eps x)))	eps	inf
1.0ms	(fma.f64 eps eps (.f64 2 (.f64 eps x)))	eps	-inf
1.0ms	(fma.f64 eps eps (.f64 2 (.f64 eps x)))	eps	0
1.0ms	(fma.f64 eps eps (.f64 2 (.f64 eps x)))	x	-inf
1.0ms	(fma.f64 eps eps (.f64 2 (.f64 eps x)))	x	inf

rewrite37.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

656×	`pow1_binary64`
602×	`add-log-exp_binary64`
602×	`log1p-expm1-u_binary64`
602×	`expm1-log1p-u_binary64`
70×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	141	11
2	1633	11

Stop Event

1×	node limit

Counts

1 → 22

simplify68.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

564×	`fma-def_binary64`
469×	`associate-l_binary64`
434×	`unswap-sqr_binary64`
370×	`sqr-pow_binary64`
292×	`*-commutative_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	8	231
1	19	231
2	37	213
3	75	177
4	168	177
5	464	177
6	1534	177
7	2777	177
8	3132	177
9	3354	177
10	3576	177
11	3880	177
12	4302	177
13	4812	177

Stop Event

1×	node limit

Counts

46 → 28

prune20.0ms (0.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	41	0	41
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	41	2	43

Error

Counts

43 → 2

Alt Table

Status	Error	Program
▶	0.0b	(fma.f64 (.f64 2 eps) x (.f64 eps eps))
✓	0.0b	(fma.f64 eps eps (.f64 2 (.f64 eps x)))

Compiler

Compiled 506 to 290 computations (42.7% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (.f64 2 eps) x (.f64 eps eps))

series6.0ms (0.3%)

Counts

1 → 24

Calls

6 calls:

1.0ms	(fma.f64 (.f64 2 eps) x (.f64 eps eps))	x	-inf
1.0ms	(fma.f64 (.f64 2 eps) x (.f64 eps eps))	x	inf
1.0ms	(fma.f64 (.f64 2 eps) x (.f64 eps eps))	eps	-inf
1.0ms	(fma.f64 (.f64 2 eps) x (.f64 eps eps))	x	0
1.0ms	(fma.f64 (.f64 2 eps) x (.f64 eps eps))	eps	inf

rewrite35.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

617×	`pow1_binary64`
566×	`add-log-exp_binary64`
566×	`log1p-expm1-u_binary64`
566×	`expm1-log1p-u_binary64`
69×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	139	11
2	1578	11

Stop Event

1×	node limit

Counts

1 → 22

simplify63.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

564×	`fma-def_binary64`
469×	`associate-l_binary64`
434×	`unswap-sqr_binary64`
370×	`sqr-pow_binary64`
292×	`*-commutative_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	8	231
1	19	231
2	37	213
3	75	177
4	168	177
5	464	177
6	1534	177
7	2777	177
8	3132	177
9	3354	177
10	3576	177
11	3880	177
12	4302	177
13	4812	177

Stop Event

1×	node limit

Counts

46 → 28

prune13.0ms (0.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	28	0	28
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	28	2	30

Error

Counts

30 → 2

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 (.f64 2 eps) x (.f64 eps eps))
✓	0.0b	(fma.f64 eps eps (.f64 2 (.f64 eps x)))

Compiler

Compiled 357 to 195 computations (45.4% saved)

regimes34.0ms (1.4%)

Accuracy

Total 0.0b remaining (97.4%)

Threshold costs 0.0b (97.4%)

Counts

12 → 1

Compiler

Compiled 343 to 231 computations (32.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	7	8

Stop Event

1×

saturated

end36.0ms (1.5%)

Stop Event

1×

done

Compiler

Compiled 36 to 22 computations (38.9% saved)

Details

analyze3.0ms (0.1%)

sample1.7s (72.3%)

preprocess40.0ms (1.7%)

simplify21.0ms (0.9%)

prune5.0ms (0.2%)

localize4.0ms (0.2%)

series6.0ms (0.2%)

rewrite31.0ms (1.3%)

simplify66.0ms (2.8%)

prune13.0ms (0.5%)

localize5.0ms (0.2%)

series12.0ms (0.5%)

rewrite42.0ms (1.7%)

simplify53.0ms (2.2%)

prune32.0ms (1.4%)

localize5.0ms (0.2%)

series6.0ms (0.3%)

rewrite37.0ms (1.5%)

simplify68.0ms (2.8%)

prune20.0ms (0.8%)

localize6.0ms (0.2%)

series6.0ms (0.3%)

rewrite35.0ms (1.5%)

simplify63.0ms (2.6%)

prune13.0ms (0.5%)

regimes34.0ms (1.4%)

simplify2.0ms (0.1%)

end36.0ms (1.5%)

Profiling