Details

analyze345.0ms (5.4%)

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)

sample135.0ms (2.1%)

Algorithm

1×

intervals

Results

16.0ms	123×	body	256	valid
10.0ms	276×	pre	128	true
8.0ms	42×	body	512	valid
6.0ms	91×	body	128	valid
1.0ms	20×	body	128	nan

Compiler

Compiled 66 to 48 computations (27.3% saved)

simplify367.0ms (5.8%)

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

53.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	53.0b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
	53.0b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))

Compiler

Compiled 111 to 74 computations (33.3% saved)

localize10.0ms (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))
✓	0.3b	(/.f64 1/3 a)
✓	28.0b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)

series152.0ms (2.4%)

Counts

4 → 76

Calls

4 calls:

87.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
54.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
10.0ms	(fma.f64 a (.f64 c -3) (.f64 b b))
2.0ms	(/.f64 1/3 a)

rewrite24.0ms (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:

8.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
6.0ms	(-.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))

simplify106.0ms (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

prune149.0ms (2.3%)

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
	1.2b	(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)))))))
▶	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))
	1.7b	(.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))

Compiler

Compiled 5863 to 3403 computations (42% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 a (.f64 c -3) (.f64 b b))
✓	0.3b	(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)

series16.0ms (0.3%)

Counts

2 → 48

Calls

2 calls:

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

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
10×	`times-frac_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`

Counts

2 → 44

Calls

2 calls:

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

simplify97.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

517×	`distribute-rgt-in_binary64`
506×	`associate-/l/_binary64`
492×	`associate-l_binary64`
430×	`associate-/r/_binary64`
383×	`associate-r_binary64`

Counts

92 → 79

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	85	1049
1	175	901
2	597	847
3	2395	797
4	4205	797
5	4724	797
6	5000	797
7	4845	797

prune130.0ms (2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	133	3	136
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	135	4	139

Error

Counts

139 → 4

Alt Table

Status	Error	Program
	0.6b	(/.f64 (.f64 (.f64 (.f64 -3 (.f64 c a)) (sqrt.f64 (/.f64 1/3 a))) (sqrt.f64 (/.f64 1/3 a))) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
	1.2b	(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)))))))
	25.3b	(/.f64 (expm1.f64 (log1p.f64 (.f64 1/3 (.f64 c -3)))) (+.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))

Compiler

Compiled 3949 to 2447 computations (38% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series354.0ms (5.6%)

Counts

3 → 60

Calls

3 calls:

253.0ms	(/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
56.0ms	(+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
45.0ms	(sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))

rewrite21.0ms (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:

6.0ms	(/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
3.0ms	(+.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)))

simplify167.0ms (2.6%)

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

prune192.0ms (3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

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

Error

Counts

251 → 4

Alt Table

Status	Error	Program
▶	0.2b	(/.f64 (neg.f64 c) (+.f64 (.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))
	1.2b	(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 (.f64 c c) a) (pow.f64 b 3)) -3/8 (.f64 -1/2 (/.f64 c b)))))
	0.5b	(/.f64 (neg.f64 c) (+.f64 (.f64 (fabs.f64 (cbrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))) (sqrt.f64 (cbrt.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))

Compiler

Compiled 6375 to 3438 computations (46.1% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))
✓	0.0b	(/.f64 (neg.f64 c) (+.f64 (.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 a (.f64 c -3) (.f64 b b))
✓	0.4b	(.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)))))

series303.0ms (4.8%)

Counts

2 → 40

Calls

2 calls:

259.0ms

(/.f64 (neg.f64 c) (+.f64 (*.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))

44.0ms

(*.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)))))

rewrite37.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

83×	`add-sqr-sqrt_binary64`
74×	`sqrt-prod_binary64`
37×	`*-un-lft-identity_binary64`
37×	`add-cube-cbrt_binary64`
32×	`sqrt-pow1_binary64`

Counts

2 → 146

Calls

2 calls:

11.0ms

(/.f64 (neg.f64 c) (+.f64 (*.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))

8.0ms

(*.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)))))

simplify149.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

383×	`fma-def_binary64`
274×	`div-sub_binary64`
243×	`associate-/l/_binary64`
172×	`fma-neg_binary64`
169×	`distribute-rgt-in_binary64`

Counts

186 → 231

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	269	5146
1	630	4865
2	2093	4598
3	4662	4574
4	5096	4574

prune338.0ms (5.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	370	1	371
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	371	4	375

Error

Counts

375 → 4

Alt Table

Status	Error	Program
✓	0.2b	(/.f64 (neg.f64 c) (+.f64 (.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))
	1.2b	(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 (.f64 c c) a) (pow.f64 b 3)) -3/8 (.f64 -1/2 (/.f64 c b)))))
	0.4b	(/.f64 -1 (/.f64 (+.f64 (.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) c))
✓	0.1b	(/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))

Compiler

Compiled 12641 to 7001 computations (44.6% saved)

regimes1.3s (20%)

Accuracy

Total 0.1b remaining (71.3%)

Threshold costs 0.1b (71.3%)

Counts

193 → 1

Compiler

Compiled 27732 to 18538 computations (33.2% 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

end0.0ms (0%)

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

sample1.9s (30.4%)

Algorithm

1×

intervals

Results

532.0ms	3815×	body	256	valid
368.0ms	1411×	body	512	valid
318.0ms	8767×	pre	128	true
199.0ms	2774×	body	128	valid
59.0ms	767×	body	128	nan

Compiler

Compiled 184 to 125 computations (32.1% saved)

Details

analyze345.0ms (5.4%)

sample135.0ms (2.1%)

simplify367.0ms (5.8%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

series152.0ms (2.4%)

rewrite24.0ms (0.4%)

simplify106.0ms (1.7%)

prune149.0ms (2.3%)

localize14.0ms (0.2%)

series16.0ms (0.3%)

rewrite8.0ms (0.1%)

simplify97.0ms (1.5%)

prune130.0ms (2%)

localize10.0ms (0.2%)

series354.0ms (5.6%)

rewrite21.0ms (0.3%)

simplify167.0ms (2.6%)

prune192.0ms (3%)

localize14.0ms (0.2%)

series303.0ms (4.8%)

rewrite37.0ms (0.6%)

simplify149.0ms (2.4%)

prune338.0ms (5.3%)

regimes1.3s (20%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.9s (30.4%)

Profiling