Details

analyze347.0ms (4.9%)

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)

sample141.0ms (2%)

Algorithm

1×

intervals

Results

16.0ms	128×	body	256	valid
10.0ms	284×	pre	128	true
9.0ms	42×	body	512	valid
6.0ms	86×	body	128	valid
2.0ms	28×	body	128	nan

Compiler

Compiled 66 to 48 computations (27.3% saved)

simplify359.0ms (5%)

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

prune4.0ms (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

53.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	53.1b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
▶	53.1b	(.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)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 a (.f64 c -3) (.f64 b b))
✓	0.1b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
✓	0.3b	(/.f64 1/3 a)
✓	26.8b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)

series162.0ms (2.3%)

Counts

4 → 76

Calls

4 calls:

89.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
60.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
11.0ms	(fma.f64 a (.f64 c -3) (.f64 b b))
2.0ms	(/.f64 1/3 a)

rewrite25.0ms (0.4%)

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:

9.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
4.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
2.0ms	(/.f64 1/3 a)
0.0ms	(fma.f64 a (.f64 c -3) (.f64 b b))

simplify114.0ms (1.6%)

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

prune152.0ms (2.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	218	3	221
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	220	3	223

Error

0.0b

Counts

223 → 3

Alt Table

Status	Error	Program
▶	0.4b	(/.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))
	1.0b	(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)))))))
	53.1b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 (/.f64 1/3 (sqrt.f64 a)) (sqrt.f64 a)))

Compiler

Compiled 5799 to 3357 computations (42.1% saved)

localize13.0ms (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))
✓	0.2b	(fma.f64 a (*.f64 c -3) 0)
✓	0.3b	(.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a))
	0.3b	(/.f64 1/3 a)

series335.0ms (4.7%)

Counts

3 → 68

Calls

3 calls:

319.0ms	(/.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))
11.0ms	(.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a))
5.0ms	(fma.f64 a (*.f64 c -3) 0)

rewrite19.0ms (0.3%)

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:

7.0ms	(/.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))
7.0ms	(.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a))
0.0ms	(fma.f64 a (*.f64 c -3) 0)

simplify105.0ms (1.5%)

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

prune174.0ms (2.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	178	4	182
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	181	4	185

Error

0.0b

Counts

185 → 4

Alt Table

Status	Error	Program
▶	0.1b	(/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
	0.5b	(/.f64 1 (/.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b) (.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a))))
	0.8b	(/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (.f64 (/.f64 (sqrt.f64 1/3) (sqrt.f64 a)) (/.f64 (sqrt.f64 1/3) (sqrt.f64 a)))) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b))
	1.0b	(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)))))

Compiler

Compiled 5643 to 3423 computations (39.3% saved)

localize10.0ms (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	(+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
	0.1b	(fma.f64 a (.f64 c -3) (.f64 b b))
✓	0.1b	(/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))

series353.0ms (5%)

Counts

3 → 60

Calls

3 calls:

250.0ms	(/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
52.0ms	(+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
51.0ms	(sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))

rewrite22.0ms (0.3%)

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:

7.0ms	(/.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)))

simplify170.0ms (2.4%)

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

prune203.0ms (2.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	244	3	247
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	247	4	251

Error

Counts

251 → 4

Alt Table

Status	Error	Program
	0.3b	(/.f64 -1 (/.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b) c))
	1.0b	(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) (fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))) b))
	0.3b	(.f64 (neg.f64 c) (/.f64 1 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b)))

Compiler

Compiled 6368 to 3437 computations (46% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series400.0ms (5.6%)

Counts

3 → 108

Calls

3 calls:

240.0ms

(/.f64 (neg.f64 c) (fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b)))) b))

105.0ms

(fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b)))) b)

55.0ms

(sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))))

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`times-frac_binary64`
30×	`add-sqr-sqrt_binary64`
28×	`*-un-lft-identity_binary64`
28×	`add-cube-cbrt_binary64`
12×	`distribute-lft-neg-in_binary64`

Counts

3 → 90

Calls

3 calls:

4.0ms

(/.f64 (neg.f64 c) (fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b)))) b))

3.0ms

(sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))))

0.0ms

(fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b)))) b)

simplify218.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

830×	`times-frac_binary64`
291×	`fma-def_binary64`
207×	`*-commutative_binary64`
133×	`distribute-neg-in_binary64`
131×	`sub-neg_binary64`

Counts

198 → 304

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	675	10375
1	2159	10029
2	4979	10029
3	5000	10029

prune464.0ms (6.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	428	0	428
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	428	4	432

Error

Counts

432 → 4

Alt Table

Status	Error	Program
	0.3b	(/.f64 -1 (/.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b) c))
	1.0b	(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) (fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))) b))
	0.3b	(.f64 (neg.f64 c) (/.f64 1 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b)))

Compiler

Compiled 20399 to 12839 computations (37.1% saved)

regimes1.3s (18.9%)

Accuracy

Total 0.1b remaining (80.8%)

Threshold costs 0.1b (80.8%)

Counts

234 → 1

Compiler

Compiled 32517 to 21553 computations (33.7% saved)

simplify4.0ms (0.1%)

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)

sample1.9s (27.3%)

Algorithm

1×

intervals

Results

616.0ms	3863×	body	256	valid
305.0ms	8803×	pre	128	true
301.0ms	1509×	body	512	valid
179.0ms	2628×	body	128	valid
52.0ms	803×	body	128	nan

Compiler

Compiled 173 to 119 computations (31.2% saved)

Details

analyze347.0ms (4.9%)

sample141.0ms (2%)

simplify359.0ms (5%)

prune4.0ms (0.1%)

localize10.0ms (0.1%)

series162.0ms (2.3%)

rewrite25.0ms (0.4%)

simplify114.0ms (1.6%)

prune152.0ms (2.1%)

localize13.0ms (0.2%)

series335.0ms (4.7%)

rewrite19.0ms (0.3%)

simplify105.0ms (1.5%)

prune174.0ms (2.4%)

localize10.0ms (0.1%)

series353.0ms (5%)

rewrite22.0ms (0.3%)

simplify170.0ms (2.4%)

prune203.0ms (2.8%)

localize13.0ms (0.2%)

series400.0ms (5.6%)

rewrite17.0ms (0.2%)

simplify218.0ms (3.1%)

prune464.0ms (6.5%)

regimes1.3s (18.9%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.9s (27.3%)

Profiling