Details

analyze406.0ms (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)

sample55.0ms (0.9%)

Algorithm

1×

intervals

Results

14.0ms	117×	body	256	valid
10.0ms	51×	body	512	valid
9.0ms	282×	pre	128	true
8.0ms	88×	body	128	valid
2.0ms	26×	body	128	nan

Compiler

Compiled 66 to 48 computations (27.3% saved)

simplify371.0ms (6.1%)

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

52.7b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	52.7b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
	52.7b	(/.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)

localize11.0ms (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)
✓	24.9b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)

series152.0ms (2.5%)

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))
52.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
12.0ms	(fma.f64 a (.f64 c -3) (.f64 b b))
1.0ms	(/.f64 1/3 a)

rewrite22.0ms (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))
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))

simplify108.0ms (1.8%)

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

prune147.0ms (2.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	216	5	221
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	218	5	223

Error

0.0b

Counts

223 → 5

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)))))))
	52.6b	(.f64 (/.f64 (-.f64 (.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))) (.f64 b b)) (+.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))
	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))
	52.7b	(.f64 (-.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 c (.f64 a -3) (*.f64 b b)) 3))) b) (/.f64 1/3 a))

Compiler

Compiled 5989 to 3479 computations (41.9% saved)

localize13.0ms (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))
	0.4b	(/.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)

rewrite7.0ms (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)

simplify95.0ms (1.6%)

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

prune134.0ms (2.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	134	2	136
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	136	5	141

Error

0.0b

Counts

141 → 5

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)))))))
▶	0.6b	(/.f64 (cbrt.f64 (.f64 1/27 (.f64 (pow.f64 c 3) -27))) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
	0.7b	(/.f64 (.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 (sqrt.f64 1/3) 1)) (/.f64 (sqrt.f64 1/3) a)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b))
✓	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 4052 to 2522 computations (37.8% 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))
✓	0.2b	(*.f64 (pow.f64 c 3) -27)
✓	0.4b	(.f64 1/27 (.f64 (pow.f64 c 3) -27))
✓	0.6b	(cbrt.f64 (.f64 1/27 (.f64 (pow.f64 c 3) -27)))

series17.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

12.0ms	(cbrt.f64 (.f64 1/27 (.f64 (pow.f64 c 3) -27)))
3.0ms	(.f64 1/27 (.f64 (pow.f64 c 3) -27))
3.0ms	(*.f64 (pow.f64 c 3) -27)

rewrite16.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-exp-log_binary64`
15×	`associate-l_binary64`
15×	`add-sqr-sqrt_binary64`
10×	`prod-exp_binary64`
10×	`add-cbrt-cube_binary64`

Counts

3 → 65

Calls

3 calls:

4.0ms	(.f64 1/27 (.f64 (pow.f64 c 3) -27))
4.0ms	(*.f64 (pow.f64 c 3) -27)
3.0ms	(cbrt.f64 (.f64 1/27 (.f64 (pow.f64 c 3) -27)))

simplify102.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

903×	`fma-def_binary64`
429×	`log-prod_binary64`
427×	`exp-prod_binary64`
424×	`*-commutative_binary64`
272×	`unswap-sqr_binary64`

Counts

101 → 89

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	96	966
1	178	827
2	723	827
3	1393	803
4	3763	781
5	4778	781
6	4999	781
7	4892	781

prune110.0ms (1.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	112	6	118

Error

0.0b

Counts

118 → 6

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)))))))
✓	0.6b	(/.f64 (cbrt.f64 (.f64 1/27 (.f64 (pow.f64 c 3) -27))) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
▶	0.7b	(/.f64 (.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 (sqrt.f64 1/3) 1)) (/.f64 (sqrt.f64 1/3) a)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b))
✓	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))
	2.2b	(/.f64 (cbrt.f64 (.f64 1/27 (.f64 (pow.f64 c 3) -27))) (+.f64 (sqrt.f64 (exp.f64 (log.f64 (fma.f64 c (.f64 a -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 3097 to 2100 computations (32.2% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series46.0ms (0.8%)

Counts

3 → 48

Calls

3 calls:

32.0ms	(.f64 (.f64 (fma.f64 a (*.f64 c -3) 0) (/.f64 (sqrt.f64 1/3) 1)) (/.f64 (sqrt.f64 1/3) a))
11.0ms	(.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 (sqrt.f64 1/3) 1))
3.0ms	(/.f64 (sqrt.f64 1/3) a)

rewrite31.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`times-frac_binary64`
57×	`add-sqr-sqrt_binary64`
47×	`*-un-lft-identity_binary64`
45×	`add-cube-cbrt_binary64`
44×	`associate-r_binary64`

Counts

3 → 140

Calls

3 calls:

11.0ms	(.f64 (.f64 (fma.f64 a (*.f64 c -3) 0) (/.f64 (sqrt.f64 1/3) 1)) (/.f64 (sqrt.f64 1/3) a))
7.0ms	(.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 (sqrt.f64 1/3) 1))
3.0ms	(/.f64 (sqrt.f64 1/3) a)

simplify127.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

609×	`times-frac_binary64`
499×	`associate-/r/_binary64`
338×	`*-commutative_binary64`
296×	`log-prod_binary64`
277×	`associate-/l/_binary64`

Counts

188 → 188

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	162	2969
1	329	2520
2	1251	2493
3	3341	2229
4	4769	2229
5	4822	2229

prune242.0ms (4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	207	0	207
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	207	6	213

Error

0.0b

Counts

213 → 6

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)))))))
✓	0.6b	(/.f64 (cbrt.f64 (.f64 1/27 (.f64 (pow.f64 c 3) -27))) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
✓	0.7b	(/.f64 (.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 (sqrt.f64 1/3) 1)) (/.f64 (sqrt.f64 1/3) a)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b))
✓	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))
	2.2b	(/.f64 (cbrt.f64 (.f64 1/27 (.f64 (pow.f64 c 3) -27))) (+.f64 (sqrt.f64 (exp.f64 (log.f64 (fma.f64 c (.f64 a -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 7322 to 5121 computations (30.1% saved)

regimes1.9s (30.9%)

Accuracy

Total 0.1b remaining (64.9%)

Threshold costs 0.1b (64.9%)

Counts

294 → 1

Compiler

Compiled 46067 to 33025 computations (28.3% 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	14	21
1	21	21
2	25	21
3	28	21
4	30	21
5	31	21
6	30	21

end1.0ms (0%)

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

sample1.9s (31.9%)

Algorithm

1×

intervals

Results

604.0ms	3768×	body	256	valid
306.0ms	8826×	pre	128	true
281.0ms	1459×	body	512	valid
186.0ms	2773×	body	128	valid
52.0ms	826×	body	128	nan

Compiler

Compiled 267 to 191 computations (28.5% saved)

Details

analyze406.0ms (6.7%)

sample55.0ms (0.9%)

simplify371.0ms (6.1%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

series152.0ms (2.5%)

rewrite22.0ms (0.4%)

simplify108.0ms (1.8%)

prune147.0ms (2.4%)

localize13.0ms (0.2%)

series16.0ms (0.3%)

rewrite7.0ms (0.1%)

simplify95.0ms (1.6%)

prune134.0ms (2.2%)

localize14.0ms (0.2%)

series17.0ms (0.3%)

rewrite16.0ms (0.3%)

simplify102.0ms (1.7%)

prune110.0ms (1.8%)

localize17.0ms (0.3%)

series46.0ms (0.8%)

rewrite31.0ms (0.5%)

simplify127.0ms (2.1%)

prune242.0ms (4%)

regimes1.9s (30.9%)

simplify3.0ms (0%)

end1.0ms (0%)

sample1.9s (31.9%)

Profiling