Details

analyze957.0ms (22.3%)

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)

sample533.0ms (12.4%)

Algorithm

1×

intervals

Results

475.0ms	256×	body	128	valid
24.0ms	130×	body	2048	nan
11.0ms	72×	body	1024	nan
4.0ms	35×	body	512	nan
4.0ms	16×	body	128	nan
1.0ms	19×	body	256	nan

Compiler

Compiled 22 to 16 computations (27.3% saved)

simplify162.0ms (3.8%)

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 → 1

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

2 alts after pruning (2 fresh and 0 done)

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

Error

33.4b

Counts

2 → 2

Alt Table

Status	Error	Program
	33.4b	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
▶	33.4b	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))

Compiler

Compiled 47 to 32 computations (31.9% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 x (sqrt.f64 (fma.f64 x x -1)))
31.1b	(sqrt.f64 (fma.f64 x x -1))

rewrite23.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

33.4b

Rules

6×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-log-exp_binary64`
3×	`fma-def_binary64`

Counts

2 → 32

Calls

2 calls:

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

Compiler

Compiled 426 to 285 computations (33.1% saved)

series23.0ms (0.5%)

Error

Counts

2 → 13

Calls

2 calls:

9.0ms	(sqrt.f64 (fma.f64 x x -1))
6.0ms	(+.f64 x (sqrt.f64 (fma.f64 x x -1)))

Compiler

Compiled 357 to 286 computations (19.9% saved)

simplify65.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

774×	`times-frac_binary64`
432×	`fma-def_binary64`
391×	`fma-neg_binary64`
358×	`distribute-rgt-in_binary64`
295×	`cancel-sign-sub-inv_binary64`

Counts

45 → 17

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	68	482
1	163	455
2	360	454
3	833	452
4	2088	452
5	4258	452
6	4863	452

prune14.0ms (0.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	16	1	17
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	16	3	19

Error

Counts

19 → 3

Alt Table

Status	Error	Program
	33.4b	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
✓	33.4b	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
▶	0.5b	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))

Compiler

Compiled 247 to 174 computations (29.6% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(fma.f64 x 2 (/.f64 -1/2 x))
0.0b	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

3×	`add-exp-log_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`log-prod_binary64`
3×	`add-cube-cbrt_binary64`

Counts

2 → 24

Calls

2 calls:

1.0ms	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))
0.0ms	(fma.f64 x 2 (/.f64 -1/2 x))

Compiler

Compiled 296 to 226 computations (23.6% saved)

series18.0ms (0.4%)

Error

Counts

2 → 10

Calls

2 calls:

8.0ms	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))
7.0ms	(fma.f64 x 2 (/.f64 -1/2 x))

Compiler

Compiled 224 to 188 computations (16.1% saved)

simplify40.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

756×	`distribute-rgt-in_binary64`
713×	`distribute-lft-in_binary64`
231×	`times-frac_binary64`
145×	`associate-l_binary64`
128×	`distribute-rgt-out_binary64`

Counts

34 → 12

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	54	437
1	88	378
2	163	378
3	433	378
4	1541	378
5	5134	378

prune7.0ms (0.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	12	0	12
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	12	3	15

Error

Counts

15 → 3

Alt Table

Status	Error	Program
▶	33.4b	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
✓	33.4b	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
✓	0.5b	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))

Compiler

Compiled 113 to 84 computations (25.7% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
0.0b	(-.f64 (*.f64 x x) 1)
31.1b	(sqrt.f64 (-.f64 (*.f64 x x) 1))

rewrite80.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

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

Counts

3 → 62

Calls

3 calls:

6.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
5.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))
4.0ms	(-.f64 (*.f64 x x) 1)

Compiler

Compiled 929 to 589 computations (36.6% saved)

series26.0ms (0.6%)

Error

Counts

3 → 19

Calls

3 calls:

6.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))
6.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
6.0ms	(-.f64 (*.f64 x x) 1)

Compiler

Compiled 455 to 363 computations (20.2% saved)

simplify76.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

841×	`fma-neg_binary64`
803×	`distribute-rgt-in_binary64`
703×	`distribute-lft-in_binary64`
199×	`fma-def_binary64`
168×	`associate-l_binary64`

Counts

81 → 62

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	102	766
1	226	707
2	574	706
3	1807	704
4	4898	704
5	5236	704

prune22.0ms (0.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	62	0	62
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	62	3	65

Error

Counts

65 → 3

Alt Table

Status	Error	Program
	33.4b	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
	33.4b	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
	0.5b	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))

Compiler

Compiled 602 to 419 computations (30.4% saved)

regimes87.0ms (2%)

Accuracy

Total 0.2b remaining (79.4%)

Threshold costs 0.2b (79.4%)

Compiler

Compiled 231 to 166 computations (28.1% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-commutative_binary64`
1×	`distribute-neg-frac_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	10	12
2	18	12
3	20	12
4	21	12
5	20	12

end0.0ms (0%)

Compiler: Compiled 9 to 6 computations (33.3% saved)

sample2.1s (49.4%)

Algorithm

1×

intervals

Results

786.0ms	3987×	body	2048	nan
416.0ms	8000×	body	128	valid
315.0ms	2022×	body	1024	nan
115.0ms	971×	body	512	nan
45.0ms	520×	body	256	nan
23.0ms	498×	body	128	nan
2.0ms	9×	body	4096	nan

Compiler

Compiled 48 to 34 computations (29.2% saved)

Details

analyze957.0ms (22.3%)

sample533.0ms (12.4%)

simplify162.0ms (3.8%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

rewrite23.0ms (0.5%)

series23.0ms (0.5%)

simplify65.0ms (1.5%)

prune14.0ms (0.3%)

localize5.0ms (0.1%)

rewrite13.0ms (0.3%)

series18.0ms (0.4%)

simplify40.0ms (0.9%)

prune7.0ms (0.2%)

localize7.0ms (0.2%)

rewrite80.0ms (1.9%)

series26.0ms (0.6%)

simplify76.0ms (1.8%)

prune22.0ms (0.5%)

regimes87.0ms (2%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample2.1s (49.4%)

Profiling