Details

analyze363.0ms (5.3%)

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)

sample2.4s (34.5%)

Results

1.1s	4077×	body	256	valid
573.0ms	1463×	body	512	valid
420.0ms	2716×	body	128	valid
129.0ms	851×	body	128	invalid

Compiler

Compiled 106 to 76 computations (28.3% saved)

simplify357.0ms (5.2%)

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

55.4b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	55.4b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
	55.4b	(/.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 (0.1%)

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)
✓	25.7b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)

series153.0ms (2.2%)

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))
55.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
9.0ms	(fma.f64 a (.f64 c -3) (.f64 b b))
1.0ms	(/.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))
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))

simplify103.0ms (1.5%)

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

prune146.0ms (2.1%)

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
	1.8b	(.f64 (fma.f64 -3/2 (/.f64 (.f64 c a) b) (fma.f64 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)) -9/8 (.f64 (/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)) -27/16))) (/.f64 1/3 a))
	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)))))))
	55.7b	(.f64 (.f64 (+.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))) (sqrt.f64 b)) (-.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))) (sqrt.f64 b))) (/.f64 1/3 a))
	55.4b	(.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))

Compiler

Compiled 5987 to 3469 computations (42.1% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series63.0ms (0.9%)

Counts

3 → 68

Calls

3 calls:

48.0ms	(+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
9.0ms	(.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a))
7.0ms	(fma.f64 a (*.f64 c -3) 0)

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 64

Calls

3 calls:

6.0ms	(+.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)

simplify86.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

623×	`times-frac_binary64`
538×	`associate-/l*_binary64`
487×	`fma-def_binary64`
394×	`associate-/r*_binary64`
151×	`distribute-rgt-in_binary64`

Counts

132 → 129

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	165	1963
1	414	1772
2	1326	1748
3	4883	1748
4	4961	1748

prune158.0ms (2.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	158	4	162
Fresh	3	1	4
Picked	0	1	1
Done	0	0	0
Total	161	6	167

Error

0.0b

Counts

167 → 6

Alt Table

Status	Error	Program
	0.7b	(/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a)) (fma.f64 (sqrt.f64 (.f64 (cbrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) (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))
	1.4b	(/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a)) (-.f64 (.f64 2 b) (fma.f64 3/2 (/.f64 (.f64 c a) b) (fma.f64 9/8 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)) (.f64 27/16 (/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)))))))
	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)))))))
▶	0.1b	(/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
	1.5b	(/.f64 (.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 (sqrt.f64 1/3) (.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 (sqrt.f64 1/3) (cbrt.f64 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))

Compiler

Compiled 5207 to 3208 computations (38.4% saved)

localize9.0ms (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)))
✓	0.0b	(/.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))
	0.1b	(+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)

series278.0ms (4.1%)

Counts

2 → 40

Calls

2 calls:

236.0ms	(/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
42.0ms	(sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))

rewrite19.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`*-un-lft-identity_binary64`
40×	`times-frac_binary64`
30×	`add-sqr-sqrt_binary64`
29×	`add-cube-cbrt_binary64`
15×	`distribute-lft-neg-in_binary64`

Counts

2 → 87

Calls

2 calls:

6.0ms	(/.f64 (neg.f64 c) (+.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)))

simplify114.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

349×	`fma-def_binary64`
320×	`associate-/r/_binary64`
306×	`div-sub_binary64`
243×	`associate-/l/_binary64`
221×	`fma-neg_binary64`

Counts

127 → 173

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	228	3973
1	566	3858
2	1878	3711
3	4616	3705
4	5106	3705

prune212.0ms (3.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	243	4	247
Fresh	4	0	4
Picked	1	0	1
Done	1	0	1
Total	249	4	253

Error

Counts

253 → 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))
	0.6b	(cbrt.f64 (/.f64 (.f64 (.f64 (neg.f64 c) (neg.f64 c)) (neg.f64 c)) (.f64 (.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)) (+.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)))
	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 (.f64 c c) a) (pow.f64 b 3)) -3/8 (.f64 -1/2 (/.f64 c b)))))

Compiler

Compiled 6414 to 3441 computations (46.4% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (+.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 (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)))

series439.0ms (6.4%)

Counts

2 → 40

Calls

2 calls:

249.0ms	(.f64 (neg.f64 c) (/.f64 1 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b)))
190.0ms	(/.f64 1 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))

rewrite21.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`*-un-lft-identity_binary64`
29×	`add-sqr-sqrt_binary64`
26×	`times-frac_binary64`
22×	`add-cube-cbrt_binary64`
18×	`associate-r_binary64`

Counts

2 → 90

Calls

2 calls:

10.0ms	(.f64 (neg.f64 c) (/.f64 1 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b)))
5.0ms	(/.f64 1 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))

simplify111.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

757×	`associate-/l*_binary64`
355×	`fma-def_binary64`
204×	`fma-neg_binary64`
155×	`associate-/r/_binary64`
153×	`distribute-lft-neg-out_binary64`

Counts

130 → 173

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	191	3644
1	543	3338
2	1781	3216
3	4895	3208
4	4940	3208

prune201.0ms (3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	247	0	247
Fresh	0	3	3
Picked	0	1	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))
	0.6b	(cbrt.f64 (/.f64 (.f64 (.f64 (neg.f64 c) (neg.f64 c)) (neg.f64 c)) (.f64 (.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)) (+.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)))
	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 (.f64 c c) a) (pow.f64 b 3)) -3/8 (.f64 -1/2 (/.f64 c b)))))

Compiler

Compiled 6616 to 3793 computations (42.7% saved)

regimes1.5s (21.4%)

Accuracy

Total 0.1b remaining (75.3%)

Threshold costs 0.1b (75.3%)

Counts

247 → 1

Compiler

Compiled 35961 to 23838 computations (33.7% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-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	24	21
2	28	21
3	31	21
4	32	21
5	31	21

end93.0ms (1.4%)

Compiler: Compiled 164 to 105 computations (36% saved)

Details

analyze363.0ms (5.3%)

sample2.4s (34.5%)

simplify357.0ms (5.2%)

prune4.0ms (0.1%)

localize10.0ms (0.1%)

series153.0ms (2.2%)

rewrite24.0ms (0.4%)

simplify103.0ms (1.5%)

prune146.0ms (2.1%)

localize12.0ms (0.2%)

series63.0ms (0.9%)

rewrite15.0ms (0.2%)

simplify86.0ms (1.3%)

prune158.0ms (2.3%)

localize9.0ms (0.1%)

series278.0ms (4.1%)

rewrite19.0ms (0.3%)

simplify114.0ms (1.7%)

prune212.0ms (3.1%)

localize10.0ms (0.1%)

series439.0ms (6.4%)

rewrite21.0ms (0.3%)

simplify111.0ms (1.6%)

prune201.0ms (3%)

regimes1.5s (21.4%)

simplify3.0ms (0%)

end93.0ms (1.4%)

Profiling