Details

analyze34.0ms (1.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	37.5%	62.5%	0
0%	37.5%	62.5%	1
0%	18.7%	81.3%	2
0%	9.4%	90.6%	3
0%	9.4%	90.6%	4
0%	7%	93%	5
1.2%	4.7%	94.1%	6
1.2%	3.5%	95.3%	7
1.8%	2.6%	95.6%	8
2%	1.9%	96%	9
2.4%	1.3%	96.3%	10
2.6%	1%	96.5%	11
2.7%	0.7%	96.6%	12
2.8%	0.5%	96.7%	13
2.9%	0.3%	96.7%	14

Compiler

Compiled 26 to 15 computations (42.3% saved)

sample1.1s (55%)

Results

1.0s	8256×	body	128	valid
46.0ms	372×	body	128	invalid

Compiler

Compiled 52 to 30 computations (42.3% saved)

preprocess29.0ms (1.5%)

Algorithm

2×	egg-herbie

Rules

303×	`associate-/l*_binary64`
282×	`associate-/r/_binary64`
258×	`times-frac_binary64`
232×	`fma-def_binary64`
190×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	40
1	47	34
2	137	30
3	394	30
4	1282	30
0	2	2

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 15 to 8 computations (46.7% saved)

simplify20.0ms (1%)

Algorithm

1×	egg-herbie

Rules

704×	`fma-def_binary64`
600×	`associate-/r*_binary64`
362×	`distribute-rgt-in_binary64`
331×	`distribute-lft-in_binary64`
206×	`div-sub_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	26	17
2	72	15
3	201	15
4	549	15
5	1979	15

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (0.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

13.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	13.3b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
▶	13.3b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))

Compiler

Compiled 79 to 45 computations (43% saved)

localize7.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))
✓	13.5b	(/.f64 b (*.f64 a a))

series36.0ms (1.8%)

Counts

2 → 48

Calls

12 calls:

8.0ms	(/.f64 b (*.f64 a a))	b	-inf
7.0ms	(/.f64 b (*.f64 a a))	b	0
6.0ms	(/.f64 b (*.f64 a a))	b	inf
2.0ms	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))	a	0
2.0ms	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))	b	inf

rewrite42.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

772×	`log1p-expm1-u_binary64`
772×	`expm1-log1p-u_binary64`
92×	`add-sqr-sqrt_binary64`
89×	`*-un-lft-identity_binary64`
89×	`pow1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	22
1	183	20
2	2344	20

Stop Event

1×	node limit

Counts

2 → 57

simplify55.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

693×	`associate-/r/_binary64`
497×	`fma-def_binary64`
434×	`unswap-sqr_binary64`
232×	`associate-/r*_binary64`
211×	`times-frac_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	528
1	17	528
2	30	528
3	55	528
4	136	528
5	444	528
6	1879	528
7	3242	528
8	3964	528
9	4573	528

Stop Event

1×	node limit

Counts

105 → 61

prune40.0ms (2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	60	1	61
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	61	2	63

Error

0.0b

Counts

63 → 2

Alt Table

Status	Error	Program
	13.3b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
▶	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (pow.f64 (/.f64 (sqrt.f64 b) a) 2) -1)))

Compiler

Compiled 895 to 615 computations (31.3% saved)

localize8.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (pow.f64 (/.f64 (sqrt.f64 b) a) 2) -1)))
✓	0.3b	(/.f64 (sqrt.f64 b) a)
✓	0.5b	(pow.f64 (/.f64 (sqrt.f64 b) a) 2)

series43.0ms (2.2%)

Counts

3 → 48

Calls

18 calls:

6.0ms	(sqrt.f64 (fabs.f64 (fma.f64 b (pow.f64 (/.f64 (sqrt.f64 b) a) 2) -1)))	a	0
4.0ms	(pow.f64 (/.f64 (sqrt.f64 b) a) 2)	b	-inf
4.0ms	(/.f64 (sqrt.f64 b) a)	b	-inf
3.0ms	(pow.f64 (/.f64 (sqrt.f64 b) a) 2)	b	0
3.0ms	(pow.f64 (/.f64 (sqrt.f64 b) a) 2)	b	inf

rewrite56.0ms (2.8%)

Algorithm

1×	batch-egg-rewrite

Rules

855×	`log1p-expm1-u_binary64`
855×	`expm1-log1p-u_binary64`
107×	`add-sqr-sqrt_binary64`
104×	`pow1_binary64`
103×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	32
1	224	26
2	2605	26

Stop Event

1×	node limit

Counts

3 → 95

simplify49.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

618×	`unswap-sqr_binary64`
568×	`fma-def_binary64`
391×	`associate-/l*_binary64`
289×	`*-commutative_binary64`
286×	`associate-/l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	672
1	29	564
2	61	516
3	199	516
4	929	516
5	2526	516
6	3079	516
7	4239	516

Stop Event

1×	node limit

Counts

143 → 100

prune63.0ms (3.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	100	2	102

Error

0.0b

Counts

102 → 2

Alt Table

Status	Error	Program
✓	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (pow.f64 (/.f64 (sqrt.f64 b) a) 2) -1)))
▶	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (pow.f64 (exp.f64 (log.f64 (/.f64 (sqrt.f64 b) a))) 2) -1)))

Compiler

Compiled 1523 to 800 computations (47.5% saved)

localize12.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (pow.f64 (exp.f64 (log.f64 (/.f64 (sqrt.f64 b) a))) 2) -1)))
	0.3b	(/.f64 (sqrt.f64 b) a)
✓	0.5b	(pow.f64 (exp.f64 (log.f64 (/.f64 (sqrt.f64 b) a))) 2)
✓	4.1b	(exp.f64 (log.f64 (/.f64 (sqrt.f64 b) a)))

series42.0ms (2.1%)

Counts

3 → 48

Calls

18 calls:

6.0ms	(pow.f64 (exp.f64 (log.f64 (/.f64 (sqrt.f64 b) a))) 2)	b	inf
5.0ms	(sqrt.f64 (fabs.f64 (fma.f64 b (pow.f64 (exp.f64 (log.f64 (/.f64 (sqrt.f64 b) a))) 2) -1)))	a	0
3.0ms	(pow.f64 (exp.f64 (log.f64 (/.f64 (sqrt.f64 b) a))) 2)	b	0
3.0ms	(pow.f64 (exp.f64 (log.f64 (/.f64 (sqrt.f64 b) a))) 2)	b	-inf
2.0ms	(sqrt.f64 (fabs.f64 (fma.f64 b (pow.f64 (exp.f64 (log.f64 (/.f64 (sqrt.f64 b) a))) 2) -1)))	b	inf

rewrite53.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

474×	`log-prod_binary64`
262×	`pow2_binary64`
182×	`pow1/3_binary64`
180×	`expm1-udef_binary64`
180×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	32
1	249	26
2	2805	26

Stop Event

1×	node limit

Counts

3 → 117

simplify51.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

618×	`unswap-sqr_binary64`
568×	`fma-def_binary64`
391×	`associate-/l*_binary64`
292×	`*-commutative_binary64`
290×	`associate-/l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	672
1	29	564
2	61	516
3	203	516
4	937	516
5	2541	516
6	3094	516
7	4254	516

Stop Event

1×	node limit

Counts

165 → 121

prune95.0ms (4.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	158	0	158
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	158	2	160

Error

0.0b

Counts

160 → 2

Alt Table

Status	Error	Program
✓	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (pow.f64 (/.f64 (sqrt.f64 b) a) 2) -1)))
✓	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (pow.f64 (exp.f64 (log.f64 (/.f64 (sqrt.f64 b) a))) 2) -1)))

Compiler

Compiled 2518 to 1380 computations (45.2% saved)

regimes101.0ms (5.1%)

Accuracy

Total -0.0b remaining (-2.2%)

Threshold costs -0.0b (-2.2%)

Counts

15 → 1

Compiler

Compiled 1623 to 1126 computations (30.6% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	15

Stop Event

1×

saturated

end55.0ms (2.8%)

Stop Event

1×

done

Compiler

Compiled 52 to 38 computations (26.9% saved)

Details

analyze34.0ms (1.7%)

sample1.1s (55%)

preprocess29.0ms (1.5%)

simplify20.0ms (1%)

prune3.0ms (0.2%)

localize7.0ms (0.4%)

series36.0ms (1.8%)

rewrite42.0ms (2.1%)

simplify55.0ms (2.8%)

prune40.0ms (2%)

localize8.0ms (0.4%)

series43.0ms (2.2%)

rewrite56.0ms (2.8%)

simplify49.0ms (2.5%)

prune63.0ms (3.1%)

localize12.0ms (0.6%)

series42.0ms (2.1%)

rewrite53.0ms (2.6%)

simplify51.0ms (2.6%)

prune95.0ms (4.8%)

regimes101.0ms (5.1%)

simplify2.0ms (0.1%)

end55.0ms (2.8%)

Profiling