Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 16 to 13 computations (18.8% saved)

sample1.2s (22.7%)

Results

925.0ms	8256×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 47 to 38 computations (19.1% saved)

simplify225.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

2682×	`fma-neg_binary64`
690×	`times-frac_binary64`
636×	`fma-def_binary64`
533×	`sub-neg_binary64`
432×	`distribute-rgt-neg-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	21
1	25	19
2	45	17
3	65	17
4	78	17
5	89	17
6	129	17
7	180	17
8	288	17
9	497	17
10	671	17
11	811	17
12	976	17
13	1611	17
14	3407	17
15	3743	17
16	3727	17
17	3787	17
18	3819	17
19	3887	17
20	3898	17
21	4186	17
22	4220	17
23	4236	17
24	4236	17
25	4236	17
26	6212	17

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

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))

Compiler

Compiled 53 to 40 computations (24.5% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 4 (sqrt.f64 x) (+.f64 x 1))
✓	0.1b	(fma.f64 6 x -6)
✓	0.1b	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))

series22.0ms (0.4%)

Counts

3 → 18

Calls

3 calls:

16.0ms	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
5.0ms	(fma.f64 4 (sqrt.f64 x) (+.f64 x 1))
2.0ms	(fma.f64 6 x -6)

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
5×	`add-cbrt-cube_binary64`

Counts

3 → 49

Calls

3 calls:

2.0ms	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
0.0ms	(fma.f64 6 x -6)
0.0ms	(fma.f64 4 (sqrt.f64 x) (+.f64 x 1))

simplify90.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

492×	`div-sub_binary64`
426×	`fma-neg_binary64`
384×	`*-commutative_binary64`
348×	`distribute-rgt-in_binary64`
336×	`distribute-lft-in_binary64`

Counts

67 → 64

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	67	1136
1	110	1034
2	285	1034
3	751	1025
4	2413	1025
5	3154	1025
6	4752	1025
7	4942	1025

prune65.0ms (1.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	59	5	64
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	59	6	65

Error

Counts

65 → 6

Alt Table

Status	Error	Program
▶	0.3b	(/.f64 (/.f64 (fma.f64 6 x -6) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))
	1.6b	(.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 6 x -6)) (cbrt.f64 (fma.f64 6 x -6))) (*.f64 (cbrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (cbrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))) (/.f64 (cbrt.f64 (fma.f64 6 x -6)) (cbrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
✓	0.1b	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
	2.6b	(/.f64 (fma.f64 6 x -6) (expm1.f64 (log1p.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
	19.1b	(/.f64 (cbrt.f64 (.f64 (.f64 (fma.f64 6 x -6) (fma.f64 6 x -6)) (fma.f64 6 x -6))) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
	1.5b	(.f64 (.f64 (cbrt.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) (cbrt.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))) (cbrt.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))

Compiler

Compiled 1508 to 1092 computations (27.6% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 4 (sqrt.f64 x) (+.f64 x 1))
	0.1b	(fma.f64 6 x -6)
✓	0.2b	(/.f64 (/.f64 (fma.f64 6 x -6) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))
✓	0.2b	(/.f64 (fma.f64 6 x -6) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))

series52.0ms (1%)

Counts

2 → 4

Calls

2 calls:

38.0ms	(/.f64 (fma.f64 6 x -6) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))
14.0ms	(/.f64 (/.f64 (fma.f64 6 x -6) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))

rewrite51.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

276×	`times-frac_binary64`
154×	`*-un-lft-identity_binary64`
154×	`add-sqr-sqrt_binary64`
154×	`add-cube-cbrt_binary64`
144×	`sqrt-prod_binary64`

Counts

2 → 218

Calls

2 calls:

12.0ms	(/.f64 (/.f64 (fma.f64 6 x -6) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))
3.0ms	(/.f64 (fma.f64 6 x -6) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))

simplify386.0ms (7.3%)

Algorithm

1×	egg-herbie

Rules

773×	`div-sub_binary64`
525×	`distribute-rgt-in_binary64`
521×	`distribute-lft-in_binary64`
501×	`associate-/l/_binary64`
344×	`*-commutative_binary64`

Counts

222 → 237

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	213	12510
1	440	12127
2	839	10983
3	2014	10448
4	3676	10416
5	4472	8736
6	4775	8472
7	5752	8472

prune306.0ms (5.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	276	3	279
Fresh	3	1	4
Picked	0	1	1
Done	0	1	1
Total	279	6	285

Error

Counts

285 → 6

Alt Table

Status	Error	Program
▶	0.3b	(*.f64 (/.f64 (fma.f64 6 x -6) 1) (/.f64 (/.f64 1 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
✓	0.3b	(/.f64 (/.f64 (fma.f64 6 x -6) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))
✓	0.1b	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
	0.8b	(*.f64 (/.f64 1 (cbrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) (/.f64 (fma.f64 6 x -6) (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) 4)))
	10.5b	(/.f64 (cbrt.f64 (pow.f64 (/.f64 (fma.f64 6 x -6) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) 3)) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))
	1.5b	(.f64 (.f64 (cbrt.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) (cbrt.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))) (cbrt.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))

Compiler

Compiled 10889 to 7896 computations (27.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 6 x -6)
✓	0.2b	(/.f64 1 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))
✓	0.2b	(*.f64 (/.f64 (fma.f64 6 x -6) 1) (/.f64 (/.f64 1 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
✓	0.3b	(/.f64 (/.f64 1 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))

series67.0ms (1.3%)

Counts

3 → 7

Calls

3 calls:

27.0ms

(/.f64 (/.f64 1 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))

25.0ms

(/.f64 1 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))

15.0ms

(*.f64 (/.f64 (fma.f64 6 x -6) 1) (/.f64 (/.f64 1 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))

rewrite152.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Rules

603×	`times-frac_binary64`
408×	`add-sqr-sqrt_binary64`
309×	`*-un-lft-identity_binary64`
291×	`sqrt-prod_binary64`
285×	`add-cube-cbrt_binary64`

Counts

3 → 452

Calls

3 calls:

44.0ms

(*.f64 (/.f64 (fma.f64 6 x -6) 1) (/.f64 (/.f64 1 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))

14.0ms

(/.f64 (/.f64 1 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))

4.0ms

(/.f64 1 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))

simplify493.0ms (9.3%)

Algorithm

1×	egg-herbie

Rules

739×	`fma-def_binary64`
585×	`associate-/l*_binary64`
253×	`associate-/r/_binary64`
247×	`fma-neg_binary64`
228×	`distribute-rgt-in_binary64`

Counts

459 → 492

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	206	17267
1	412	16339
2	1283	14973
3	2731	14678
4	3466	14662
5	4910	14662
6	5002	14662

prune749.0ms (14.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	504	2	506
Fresh	2	1	3
Picked	1	0	1
Done	0	2	2
Total	507	5	512

Error

Counts

512 → 5

Alt Table

Status	Error	Program
▶	0.3b	(.f64 (/.f64 (fma.f64 6 x -6) 1) (/.f64 1 (.f64 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))))
✓	0.3b	(/.f64 (/.f64 (fma.f64 6 x -6) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))
✓	0.1b	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
	0.4b	(*.f64 (/.f64 (fma.f64 6 x -6) 1) (/.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))) (/.f64 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (sqrt.f64 (/.f64 1 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))))))
	1.5b	(.f64 (.f64 (cbrt.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) (cbrt.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))) (cbrt.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))

Compiler

Compiled 21899 to 16402 computations (25.1% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (*.f64 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
	0.1b	(fma.f64 6 x -6)
✓	0.2b	(.f64 (/.f64 (fma.f64 6 x -6) 1) (/.f64 1 (.f64 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))))
✓	0.3b	(*.f64 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))

series38.0ms (0.7%)

Counts

3 → 9

Calls

3 calls:

18.0ms

(*.f64 (/.f64 (fma.f64 6 x -6) 1) (/.f64 1 (*.f64 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))))

14.0ms

(/.f64 1 (*.f64 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))

5.0ms

(*.f64 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))

rewrite41.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

80×	`add-exp-log_binary64`
56×	`add-sqr-sqrt_binary64`
36×	`pow1_binary64`
34×	`prod-exp_binary64`
31×	`add-cbrt-cube_binary64`

Counts

3 → 166

Calls

3 calls:

12.0ms

(*.f64 (/.f64 (fma.f64 6 x -6) 1) (/.f64 1 (*.f64 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))))

8.0ms

(/.f64 1 (*.f64 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))

5.0ms

(*.f64 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))

simplify165.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

722×	`fma-def_binary64`
605×	`times-frac_binary64`
340×	`associate-l_binary64`
255×	`associate-r_binary64`
211×	`associate-/l*_binary64`

Counts

175 → 221

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	140	3324
1	219	2827
2	729	2773
3	3199	2622
4	4521	2609
5	4974	2609
6	4994	2609
7	4929	2609

prune293.0ms (5.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	235	0	235
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	235	5	240

Error

Counts

240 → 5

Alt Table

Status	Error	Program
✓	0.3b	(.f64 (/.f64 (fma.f64 6 x -6) 1) (/.f64 1 (.f64 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))))
✓	0.3b	(/.f64 (/.f64 (fma.f64 6 x -6) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))
✓	0.1b	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
	0.4b	(*.f64 (/.f64 (fma.f64 6 x -6) 1) (/.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))) (/.f64 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (sqrt.f64 (/.f64 1 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))))))
	1.5b	(.f64 (.f64 (cbrt.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) (cbrt.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))) (cbrt.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))

Compiler

Compiled 7430 to 5596 computations (24.7% saved)

regimes740.0ms (13.9%)

Accuracy

Total 0.1b remaining (44.2%)

Threshold costs 0.1b (44.2%)

Counts

326 → 1

Compiler

Compiled 18719 to 14854 computations (20.6% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	17
1	13	17
2	17	17
3	19	17
4	20	17
5	20	17

end116.0ms (2.2%)

Compiler: Compiled 171 to 130 computations (24% saved)

Details

analyze3.0ms (0.1%)

sample1.2s (22.7%)

simplify225.0ms (4.2%)

prune3.0ms (0.1%)

localize8.0ms (0.1%)

series22.0ms (0.4%)

rewrite5.0ms (0.1%)

simplify90.0ms (1.7%)

prune65.0ms (1.2%)

localize9.0ms (0.2%)

series52.0ms (1%)

rewrite51.0ms (1%)

simplify386.0ms (7.3%)

prune306.0ms (5.8%)

localize11.0ms (0.2%)

series67.0ms (1.3%)

rewrite152.0ms (2.9%)

simplify493.0ms (9.3%)

prune749.0ms (14.1%)

localize11.0ms (0.2%)

series38.0ms (0.7%)

rewrite41.0ms (0.8%)

simplify165.0ms (3.1%)

prune293.0ms (5.5%)

regimes740.0ms (13.9%)

simplify3.0ms (0%)

end116.0ms (2.2%)

Profiling