Details

analyze7.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
12.5%	25%	62.5%	4
18.7%	12.5%	68.8%	5
21.9%	6.2%	71.9%	6
23.4%	3.1%	73.5%	7
24.2%	1.6%	74.2%	8
24.6%	0.8%	74.6%	9
24.8%	0.4%	74.8%	10
24.9%	0.2%	74.9%	11
24.9%	0.1%	75%	12
25%	0%	75%	13
25%	0%	75%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample1.3s (46.6%)

Results

1.1s	8256×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify203.0ms (7.4%)

Algorithm

1×	egg-herbie

Rules

1115×	`distribute-rgt-neg-in_binary64`
788×	`distribute-rgt-out--_binary64`
692×	`unsub-neg_binary64`
492×	`fma-neg_binary64`
461×	`distribute-neg-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	18	20
2	24	20
3	34	20
4	50	20
5	73	20
6	113	20
7	247	20
8	452	20
9	742	20
10	1560	20
11	2338	20
12	2392	20
13	2628	20
14	2776	20
15	2774	20
16	2851	20
17	3110	20
18	3673	20
19	4665	20
20	4910	20
21	4952	20
22	4963	20
23	4960	20
24	6208	20

prune2.0ms (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

0.0b

Counts

2 → 1

Alt Table

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

Compiler

Compiled 42 to 30 computations (28.6% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

series21.0ms (0.8%)

Counts

3 → 36

Calls

3 calls:

9.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
7.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
5.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))

rewrite52.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

70×	`*-un-lft-identity_binary64`
59×	`times-frac_binary64`
46×	`add-sqr-sqrt_binary64`
36×	`add-cube-cbrt_binary64`
26×	`sqrt-prod_binary64`

Counts

3 → 119

Calls

3 calls:

20.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
19.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
5.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)

simplify110.0ms (4%)

Algorithm

1×	egg-herbie

Rules

465×	`fma-def_binary64`
447×	`associate-/r*_binary64`
391×	`fma-neg_binary64`
328×	`associate-r_binary64`
326×	`associate-l_binary64`

Counts

155 → 205

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	236	3253
1	554	3089
2	1498	3048
3	4497	3013
4	4940	3013

prune157.0ms (5.7%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	204	1	205
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	205	1	206

Error

Counts

206 → 1

Alt Table

Status	Error	Program
▶	0b	(log.f64 (+.f64 (/.f64 1 x) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))) (/.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) x))))

Compiler

Compiled 4357 to 2963 computations (32% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) x)
✓	0.0b	(sqrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))
✓	0.0b	(+.f64 (/.f64 1 x) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))) (/.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) x)))
✓	0.0b	(.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))) (/.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) x))

series29.0ms (1.1%)

Counts

4 → 48

Calls

4 calls:

10.0ms	(/.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) x)
7.0ms	(.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))) (/.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) x))
6.0ms	(sqrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))
5.0ms	(+.f64 (/.f64 1 x) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))) (/.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) x)))

rewrite55.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

139×	`sqrt-prod_binary64`
105×	`add-sqr-sqrt_binary64`
84×	`times-frac_binary64`
70×	`*-un-lft-identity_binary64`
61×	`add-cube-cbrt_binary64`

Counts

4 → 199

Calls

4 calls:

18.0ms	(.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))) (/.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) x))
6.0ms	(+.f64 (/.f64 1 x) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))) (/.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) x)))
6.0ms	(/.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) x)
3.0ms	(sqrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))

simplify184.0ms (6.7%)

Algorithm

1×	egg-herbie

Rules

874×	`fma-def_binary64`
481×	`cancel-sign-sub-inv_binary64`
320×	`fma-neg_binary64`
201×	`sub-neg_binary64`
189×	`distribute-rgt-neg-in_binary64`

Counts

247 → 327

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	341	6604
1	871	6023
2	2766	5800
3	4864	5800
4	4977	5800

prune308.0ms (11.2%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	378	0	378
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	378	1	379

Error

Counts

379 → 1

Alt Table

Status	Error	Program
✓	0b	(log.f64 (+.f64 (/.f64 1 x) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))) (/.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) x))))

Compiler

Compiled 12512 to 8670 computations (30.7% saved)

regimes263.0ms (9.6%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0.0b (0%)

Counts

80 → 1

Compiler

Compiled 4423 to 3314 computations (25.1% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
3×	`*-commutative_binary64`
3×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	35
1	21	35
2	27	35
3	31	35
4	33	35
5	32	35

end51.0ms (1.8%)

Compiler: Compiled 69 to 48 computations (30.4% saved)

Details

analyze7.0ms (0.3%)

sample1.3s (46.6%)

simplify203.0ms (7.4%)

prune2.0ms (0.1%)

localize9.0ms (0.3%)

series21.0ms (0.8%)

rewrite52.0ms (1.9%)

simplify110.0ms (4%)

prune157.0ms (5.7%)

localize11.0ms (0.4%)

series29.0ms (1.1%)

rewrite55.0ms (2%)

simplify184.0ms (6.7%)

prune308.0ms (11.2%)

regimes263.0ms (9.6%)

simplify3.0ms (0.1%)

end51.0ms (1.8%)

Profiling