Details

analyze395.0ms (12.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	50%	25%	4
25%	37.5%	37.5%	5
25%	31.2%	43.8%	6
25%	28.1%	46.9%	7
25%	26.5%	48.5%	8
25%	25.8%	49.2%	9
25%	25.4%	49.6%	10
25%	25.2%	49.8%	11
25%	25.1%	49.9%	12
25%	25%	50%	13
25%	25%	50%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample1.9s (60.5%)

Results

868.0ms	8256×	body	128	valid
812.0ms	8253×	body	128	invalid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify151.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

871×	`fma-neg_binary64`
804×	`unsub-neg_binary64`
461×	`distribute-neg-in_binary64`
434×	`sub-neg_binary64`
338×	`distribute-rgt-out_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	18	12
2	22	12
3	37	12
4	64	12
5	113	12
6	247	12
7	500	12
8	1560	12
9	2513	12
10	3218	12
11	3602	12
12	3803	12
13	3974	12
14	4075	12
15	4392	12
16	4836	12
17	4898	12
18	4901	12

prune3.0ms (0.1%)

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

29.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	29.3b	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))

Compiler

Compiled 36 to 24 computations (33.3% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
✓	27.3b	(sqrt.f64 (fma.f64 x x -1))

series11.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

6.0ms	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
5.0ms	(sqrt.f64 (fma.f64 x x -1))

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
4×	`log-prod_binary64`
4×	`add-cube-cbrt_binary64`
4×	`pow1_binary64`

Counts

2 → 32

Calls

2 calls:

3.0ms	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
1.0ms	(sqrt.f64 (fma.f64 x x -1))

simplify69.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

549×	`fma-neg_binary64`
294×	`associate-/l/_binary64`
291×	`sub-neg_binary64`
254×	`distribute-neg-frac_binary64`
221×	`fma-def_binary64`

Counts

56 → 79

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	136	988
1	330	928
2	885	889
3	3023	888
4	4940	888
5	4940	888

prune48.0ms (1.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	77	2	79
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	2	80

Error

Counts

80 → 2

Alt Table

Status	Error	Program
▶	0.5b	(log.f64 (+.f64 x x))
	29.3b	(log.f64 (+.f64 x (*.f64 (fabs.f64 (cbrt.f64 (fma.f64 x x -1))) (sqrt.f64 (cbrt.f64 (fma.f64 x x -1))))))

Compiler

Compiled 1319 to 989 computations (25% saved)

localize4.0ms (0.1%)

prune2.0ms (0.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

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

Error

Counts

2 → 2

Alt Table

Status	Error	Program
✓	0.5b	(log.f64 (+.f64 x x))
▶	29.3b	(log.f64 (+.f64 x (*.f64 (fabs.f64 (cbrt.f64 (fma.f64 x x -1))) (sqrt.f64 (cbrt.f64 (fma.f64 x x -1))))))

Compiler

Compiled 39 to 27 computations (30.8% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (+.f64 x (*.f64 (fabs.f64 (cbrt.f64 (fma.f64 x x -1))) (sqrt.f64 (cbrt.f64 (fma.f64 x x -1))))))
✓	0.1b	(sqrt.f64 (cbrt.f64 (fma.f64 x x -1)))
✓	0.3b	(*.f64 (fabs.f64 (cbrt.f64 (fma.f64 x x -1))) (sqrt.f64 (cbrt.f64 (fma.f64 x x -1))))
✓	28.2b	(cbrt.f64 (fma.f64 x x -1))

series49.0ms (1.6%)

Counts

4 → 48

Calls

4 calls:

18.0ms	(log.f64 (+.f64 x (*.f64 (fabs.f64 (cbrt.f64 (fma.f64 x x -1))) (sqrt.f64 (cbrt.f64 (fma.f64 x x -1))))))
16.0ms	(*.f64 (fabs.f64 (cbrt.f64 (fma.f64 x x -1))) (sqrt.f64 (cbrt.f64 (fma.f64 x x -1))))
8.0ms	(cbrt.f64 (fma.f64 x x -1))
7.0ms	(sqrt.f64 (cbrt.f64 (fma.f64 x x -1)))

rewrite19.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`add-sqr-sqrt_binary64`
26×	`cbrt-prod_binary64`
22×	`sqrt-prod_binary64`
15×	`unswap-sqr_binary64`
14×	`*-un-lft-identity_binary64`

Counts

4 → 100

Calls

4 calls:

7.0ms	(*.f64 (fabs.f64 (cbrt.f64 (fma.f64 x x -1))) (sqrt.f64 (cbrt.f64 (fma.f64 x x -1))))
2.0ms	(log.f64 (+.f64 x (*.f64 (fabs.f64 (cbrt.f64 (fma.f64 x x -1))) (sqrt.f64 (cbrt.f64 (fma.f64 x x -1))))))
1.0ms	(cbrt.f64 (fma.f64 x x -1))
1.0ms	(sqrt.f64 (cbrt.f64 (fma.f64 x x -1)))

simplify122.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

884×	`times-frac_binary64`
597×	`fma-neg_binary64`
318×	`sub-neg_binary64`
268×	`associate-r_binary64`
253×	`unswap-sqr_binary64`

Counts

148 → 230

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	318	4156
1	831	3520
2	2659	3219
3	4308	3141
4	5076	3141

prune194.0ms (6.3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	262	0	262
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	262	2	264

Error

Counts

264 → 2

Alt Table

Status	Error	Program
✓	0.5b	(log.f64 (+.f64 x x))
✓	29.3b	(log.f64 (+.f64 x (*.f64 (fabs.f64 (cbrt.f64 (fma.f64 x x -1))) (sqrt.f64 (cbrt.f64 (fma.f64 x x -1))))))

Compiler

Compiled 6915 to 5137 computations (25.7% saved)

regimes90.0ms (2.9%)

Accuracy

Total 0.5b remaining (91.9%)

Threshold costs 0.5b (91.9%)

Counts

31 → 1

Compiler

Compiled 1158 to 832 computations (28.2% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	6
1	4	6

end39.0ms (1.3%)

Compiler: Compiled 32 to 21 computations (34.4% saved)

Details

analyze395.0ms (12.8%)

sample1.9s (60.5%)

simplify151.0ms (4.9%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series11.0ms (0.4%)

rewrite5.0ms (0.2%)

simplify69.0ms (2.2%)

prune48.0ms (1.6%)

localize4.0ms (0.1%)

prune2.0ms (0.1%)

localize9.0ms (0.3%)

series49.0ms (1.6%)

rewrite19.0ms (0.6%)

simplify122.0ms (3.9%)

prune194.0ms (6.3%)

regimes90.0ms (2.9%)

simplify3.0ms (0.1%)

end39.0ms (1.3%)

Profiling