Details

analyze604.0ms (6.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

Compiler

Compiled 43 to 31 computations (27.9% saved)

sample195.0ms (2.2%)

Algorithm

1×

intervals

Results

28.0ms	115×	body	256	valid
17.0ms	51×	body	512	valid
17.0ms	280×	pre	128	true
10.0ms	90×	body	128	valid
3.0ms	24×	body	128	nan

Compiler

Compiled 66 to 48 computations (27.3% saved)

simplify390.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

1968×	`fma-neg_binary64`
1363×	`fma-def_binary64`
898×	`div-sub_binary64`
743×	`associate-/l*_binary64`
567×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	26
1	30	22
2	64	22
3	135	22
4	201	22
5	335	22
6	554	22
7	929	22
8	1477	22
9	2115	22
10	2599	22
11	2554	22
12	2602	22
13	2671	22
14	3117	22
15	2327	22
16	2375	22
17	2383	22
18	2389	22
19	2395	22
20	2397	22
21	2397	22
22	2585	22
23	2685	22
24	2619	22
25	2631	22
26	2661	22
27	2677	22
28	2707	22
29	2707	22
30	2751	22
31	2851	22
32	2827	22
33	2827	22
34	2638	22

prune8.0ms (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

51.8b

Counts

3 → 2

Alt Table

Status	Error	Program
	51.8b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
▶	51.8b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))

Compiler

Compiled 111 to 74 computations (33.3% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 a (.f64 c -3) (.f64 b b))
✓	0.2b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
✓	0.4b	(/.f64 1/3 a)
✓	25.1b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)

series266.0ms (3%)

Counts

4 → 76

Calls

4 calls:

151.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
92.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
20.0ms	(fma.f64 a (.f64 c -3) (.f64 b b))
3.0ms	(/.f64 1/3 a)

rewrite44.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`add-sqr-sqrt_binary64`
39×	`*-un-lft-identity_binary64`
35×	`add-cube-cbrt_binary64`
19×	`times-frac_binary64`
18×	`prod-diff_binary64`

Counts

4 → 123

Calls

4 calls:

18.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
8.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
4.0ms	(/.f64 1/3 a)
1.0ms	(fma.f64 a (.f64 c -3) (.f64 b b))

simplify149.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

797×	`fma-def_binary64`
340×	`distribute-rgt-in_binary64`
235×	`cancel-sign-sub-inv_binary64`
185×	`fma-neg_binary64`
160×	`associate-r_binary64`

Counts

199 → 221

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	283	5008
1	661	4039
2	2464	3848
3	4911	3848

prune155.0ms (1.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	217	4	221
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	219	4	223

Error

0.0b

Counts

223 → 4

Alt Table

Status	Error	Program
	2.3b	(.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (fma.f64 9/8 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)) (fma.f64 27/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)) (.f64 405/128 (/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7)))))) (/.f64 1/3 a))
	1.8b	(neg.f64 (fma.f64 9/16 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) (fma.f64 135/128 (/.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) (fma.f64 1/2 (/.f64 c b) (.f64 3/8 (/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3)))))))
	51.8b	(.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)) (cbrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))) (cbrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b))) (/.f64 1/3 a))
▶	0.5b	(/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))

Compiler

Compiled 5953 to 3457 computations (41.9% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
✓	0.3b	(fma.f64 a (*.f64 c -3) 0)
✓	0.3b	(.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a))
	0.4b	(/.f64 1/3 a)

series342.0ms (3.8%)

Counts

3 → 68

Calls

3 calls:

324.0ms	(/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
10.0ms	(.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a))
8.0ms	(fma.f64 a (*.f64 c -3) 0)

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
17×	`*-un-lft-identity_binary64`
17×	`add-cbrt-cube_binary64`
17×	`add-exp-log_binary64`
14×	`times-frac_binary64`

Counts

3 → 74

Calls

3 calls:

8.0ms	(/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
5.0ms	(.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a))
0.0ms	(fma.f64 a (*.f64 c -3) 0)

simplify99.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

561×	`associate-/l/_binary64`
487×	`div-sub_binary64`
483×	`fma-def_binary64`
201×	`distribute-rgt-in_binary64`
155×	`associate-/l*_binary64`

Counts

142 → 149

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	202	3063
1	529	2602
2	1978	2548
3	4289	2542
4	5631	2542

prune165.0ms (1.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	179	3	182
Fresh	3	0	3
Picked	1	0	1
Done	0	0	0
Total	183	3	186

Error

Counts

186 → 3

Alt Table

Status	Error	Program
	1.8b	(fma.f64 (/.f64 (.f64 (pow.f64 c 3) (.f64 a a)) (pow.f64 b 5)) -9/16 (fma.f64 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7)) -135/128 (fma.f64 (/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3)) -3/8 (.f64 -1/2 (/.f64 c b)))))
▶	0.1b	(/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
	0.7b	(/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 (/.f64 1/3 (sqrt.f64 a)) (sqrt.f64 a))) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))

Compiler

Compiled 5581 to 3377 computations (39.5% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))
	0.1b	(fma.f64 a (.f64 c -3) (.f64 b b))
✓	0.1b	(+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
✓	0.1b	(/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))

series463.0ms (5.2%)

Counts

3 → 60

Calls

3 calls:

248.0ms	(/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
171.0ms	(+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
44.0ms	(sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))

rewrite20.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`*-un-lft-identity_binary64`
40×	`times-frac_binary64`
33×	`add-sqr-sqrt_binary64`
32×	`add-cube-cbrt_binary64`
15×	`distribute-lft-neg-in_binary64`

Counts

3 → 107

Calls

3 calls:

6.0ms	(/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
5.0ms	(+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
1.0ms	(sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))

simplify188.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

473×	`fma-def_binary64`
278×	`div-sub_binary64`
247×	`associate-/l/_binary64`
187×	`cancel-sign-sub-inv_binary64`
166×	`distribute-rgt-neg-out_binary64`

Counts

167 → 223

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	253	4899
1	638	4739
2	2058	4559
3	4528	4553
4	4983	4553
5	4903	4553

prune225.0ms (2.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	247	0	247
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	247	3	250

Error

Counts

250 → 3

Alt Table

Status	Error	Program
	1.8b	(fma.f64 (/.f64 (.f64 (pow.f64 c 3) (.f64 a a)) (pow.f64 b 5)) -9/16 (fma.f64 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7)) -135/128 (fma.f64 (/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3)) -3/8 (.f64 -1/2 (/.f64 c b)))))
✓	0.1b	(/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
▶	0.7b	(/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 (/.f64 1/3 (sqrt.f64 a)) (sqrt.f64 a))) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))

Compiler

Compiled 6313 to 3402 computations (46.1% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(fma.f64 a (*.f64 c -3) 0)
✓	0.3b	(.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 (/.f64 1/3 (sqrt.f64 a)) (sqrt.f64 a)))
✓	0.3b	(/.f64 (/.f64 1/3 (sqrt.f64 a)) (sqrt.f64 a))
✓	0.4b	(/.f64 1/3 (sqrt.f64 a))

series50.0ms (0.6%)

Counts

3 → 28

Calls

3 calls:

21.0ms	(.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 (/.f64 1/3 (sqrt.f64 a)) (sqrt.f64 a)))
17.0ms	(/.f64 1/3 (sqrt.f64 a))
11.0ms	(/.f64 (/.f64 1/3 (sqrt.f64 a)) (sqrt.f64 a))

rewrite90.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

526×	`times-frac_binary64`
303×	`add-sqr-sqrt_binary64`
279×	`*-un-lft-identity_binary64`
279×	`add-cube-cbrt_binary64`
269×	`sqrt-prod_binary64`

Counts

3 → 382

Calls

3 calls:

30.0ms	(.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 (/.f64 1/3 (sqrt.f64 a)) (sqrt.f64 a)))
8.0ms	(/.f64 (/.f64 1/3 (sqrt.f64 a)) (sqrt.f64 a))
3.0ms	(/.f64 1/3 (sqrt.f64 a))

simplify363.0ms (4%)

Algorithm

1×	egg-herbie

Rules

714×	`associate-/r/_binary64`
666×	`fma-def_binary64`
344×	`distribute-rgt-in_binary64`
316×	`*-commutative_binary64`
289×	`fma-neg_binary64`

Counts

410 → 455

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	307	8934
1	672	8289
2	2026	7891
3	2880	7843
4	3937	7827
5	4795	7527
6	4993	7527
7	4783	7527

prune459.0ms (5.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	474	0	474
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	474	3	477

Error

Counts

477 → 3

Alt Table

Status	Error	Program
	1.8b	(fma.f64 (/.f64 (.f64 (pow.f64 c 3) (.f64 a a)) (pow.f64 b 5)) -9/16 (fma.f64 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7)) -135/128 (fma.f64 (/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3)) -3/8 (.f64 -1/2 (/.f64 c b)))))
✓	0.1b	(/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
✓	0.7b	(/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 (/.f64 1/3 (sqrt.f64 a)) (sqrt.f64 a))) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))

Compiler

Compiled 17341 to 9458 computations (45.5% saved)

regimes2.8s (31%)

Accuracy

Total 0.0b remaining (59.2%)

Threshold costs 0.0b (59.2%)

Counts

379 → 1

Compiler

Compiled 60417 to 40713 computations (32.6% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	21
1	20	21
2	24	21
3	27	21
4	28	21
5	28	21

end1.0ms (0%)

Compiler: Compiled 17 to 11 computations (35.3% saved)

sample1.8s (20.4%)

Algorithm

1×

intervals

Results

507.0ms	3791×	body	256	valid
321.0ms	8849×	pre	128	true
296.0ms	1490×	body	512	valid
193.0ms	2719×	body	128	valid
57.0ms	849×	body	128	nan

Compiler

Compiled 154 to 107 computations (30.5% saved)

Details

analyze604.0ms (6.7%)

sample195.0ms (2.2%)

simplify390.0ms (4.3%)

prune8.0ms (0.1%)

localize21.0ms (0.2%)

series266.0ms (3%)

rewrite44.0ms (0.5%)

simplify149.0ms (1.7%)

prune155.0ms (1.7%)

localize14.0ms (0.2%)

series342.0ms (3.8%)

rewrite19.0ms (0.2%)

simplify99.0ms (1.1%)

prune165.0ms (1.8%)

localize11.0ms (0.1%)

series463.0ms (5.2%)

rewrite20.0ms (0.2%)

simplify188.0ms (2.1%)

prune225.0ms (2.5%)

localize15.0ms (0.2%)

series50.0ms (0.6%)

rewrite90.0ms (1%)

simplify363.0ms (4%)

prune459.0ms (5.1%)

regimes2.8s (31%)

simplify3.0ms (0%)

end1.0ms (0%)

sample1.8s (20.4%)

Profiling