Details

analyze685.0ms (14.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.4%	24.3%	11
31.4%	44.3%	24.3%	12
31.4%	44.1%	24.5%	13
31.5%	43.8%	24.8%	14

Compiler

Compiled 14 to 12 computations (14.3% saved)

sample3.3s (69.7%)

Results

2.1s	2828×	body	1024	valid
427.0ms	1342×	body	512	valid
345.0ms	3102×	body	128	valid
184.0ms	313×	body	2048	valid
143.0ms	671×	body	256	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 41 to 35 computations (14.6% saved)

simplify43.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

667×	`div-sub_binary64`
601×	`associate-/l*_binary64`
488×	`associate-/r*_binary64`
380×	`fma-def_binary64`
279×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	11	13
1	25	13
2	34	13
3	59	13
4	123	11
5	318	8
6	1056	8
7	4350	8
8	4987	8

prune4.0ms (0.1%)

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
	41.6b	(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))

Compiler

Compiled 56 to 46 computations (17.9% saved)

localize4.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series9.0ms (0.2%)

Counts

3 → 12

Calls

3 calls:

5.0ms	(sqrt.f64 (+.f64 1 (exp.f64 x)))
2.0ms	(+.f64 1 (exp.f64 x))
2.0ms	(exp.f64 x)

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
6×	`add-log-exp_binary64`
6×	`add-cube-cbrt_binary64`
4×	`sqrt-prod_binary64`

Counts

3 → 51

Calls

3 calls:

4.0ms	(+.f64 1 (exp.f64 x))
3.0ms	(sqrt.f64 (+.f64 1 (exp.f64 x)))
1.0ms	(exp.f64 x)

simplify85.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

733×	`times-frac_binary64`
283×	`fma-neg_binary64`
258×	`fma-def_binary64`
228×	`distribute-rgt-in_binary64`
200×	`associate-+l+_binary64`

Counts

63 → 77

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	101	640
1	239	594
2	636	570
3	2350	554
4	4990	554
5	4947	554
6	4977	554

prune47.0ms (1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	76	1	77
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	77	2	79

Error

Counts

79 → 2

Alt Table

Status	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
▶	0.0b	(sqrt.f64 (/.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (neg.f64 (expm1.f64 x))))

Compiler

Compiled 883 to 630 computations (28.7% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (/.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (neg.f64 (expm1.f64 x))))
✓	0.0b	(/.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (neg.f64 (expm1.f64 x)))

series28.0ms (0.6%)

Counts

2 → 24

Calls

2 calls:

16.0ms	(sqrt.f64 (/.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (neg.f64 (expm1.f64 x))))
12.0ms	(/.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (neg.f64 (expm1.f64 x)))

rewrite41.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

201×	`times-frac_binary64`
132×	`add-sqr-sqrt_binary64`
129×	`*-un-lft-identity_binary64`
129×	`add-cube-cbrt_binary64`
126×	`distribute-lft-neg-in_binary64`

Counts

2 → 254

Calls

2 calls:

8.0ms	(sqrt.f64 (/.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (neg.f64 (expm1.f64 x))))
5.0ms	(/.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (neg.f64 (expm1.f64 x)))

simplify252.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

639×	`fma-def_binary64`
635×	`associate-/l*_binary64`
298×	`associate-/r/_binary64`
294×	`div-sub_binary64`
280×	`associate-/l/_binary64`

Counts

278 → 341

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	360	8231
1	635	7873
2	1908	7608
3	4461	7604
4	4951	7604

prune123.0ms (2.6%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	341	0	341
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	341	2	343

Error

Counts

343 → 2

Alt Table

Status	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
✓	0.0b	(sqrt.f64 (/.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (neg.f64 (expm1.f64 x))))

Compiler

Compiled 7236 to 1413 computations (80.5% saved)

regimes43.0ms (0.9%)

Accuracy

Total 0.0b remaining (6.7%)

Threshold costs 0.0b (6.7%)

Counts

10 → 1

Compiler

Compiled 365 to 304 computations (16.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	9	8
2	8	8

end45.0ms (1%)

Compiler: Compiled 29 to 23 computations (20.7% saved)

Details

analyze685.0ms (14.6%)

sample3.3s (69.7%)

simplify43.0ms (0.9%)

prune4.0ms (0.1%)

localize4.0ms (0.1%)

series9.0ms (0.2%)

rewrite9.0ms (0.2%)

simplify85.0ms (1.8%)

prune47.0ms (1%)

localize7.0ms (0.1%)

series28.0ms (0.6%)

rewrite41.0ms (0.9%)

simplify252.0ms (5.3%)

prune123.0ms (2.6%)

regimes43.0ms (0.9%)

simplify2.0ms (0%)

end45.0ms (1%)

Profiling