Details

analyze343.0ms (5.2%)

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)

sample138.0ms (2.1%)

Algorithm

1×

intervals

Results

16.0ms	121×	body	256	valid
10.0ms	290×	pre	128	true
7.0ms	36×	body	512	valid
6.0ms	99×	body	128	valid
2.0ms	34×	body	128	nan

Compiler

Compiled 66 to 48 computations (27.3% saved)

simplify356.0ms (5.4%)

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

50.9b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	50.9b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
	50.9b	(/.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)
✓	27.4b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)

series161.0ms (2.4%)

Counts

4 → 76

Calls

4 calls:

90.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
58.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
11.0ms	(fma.f64 a (.f64 c -3) (.f64 b b))
1.0ms	(/.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:

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 (1.6%)

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

prune151.0ms (2.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	215	6	221
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	217	6	223

Error

0.1b

Counts

223 → 6

Alt Table

Status	Error	Program
	50.9b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (exp.f64 (log.f64 (/.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))
	1.9b	(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)))))))
	3.7b	(fma.f64 (/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3)) -3/8 (*.f64 -1/2 (/.f64 c b)))
	2.4b	(.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))
	50.9b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b) (.f64 (*.f64 (cbrt.f64 1/3) (cbrt.f64 1/3)) (/.f64 (cbrt.f64 1/3) a)))

Compiler

Compiled 5991 to 3495 computations (41.7% 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))
✓	0.3b	(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)

series437.0ms (6.6%)

Counts

3 → 68

Calls

3 calls:

420.0ms	(/.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))
6.0ms	(.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a))
0.0ms	(fma.f64 a (*.f64 c -3) 0)

simplify103.0ms (1.6%)

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

prune162.0ms (2.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	178	4	182
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	182	6	188

Error

0.0b

Counts

188 → 6

Alt Table

Status	Error	Program
	1.9b	(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)))))
	50.9b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b) (.f64 (*.f64 (cbrt.f64 1/3) (cbrt.f64 1/3)) (/.f64 (cbrt.f64 1/3) a)))
	0.6b	(.f64 (/.f64 (fma.f64 a (.f64 c -3) 0) 1) (/.f64 (/.f64 1/3 a) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)))
	1.5b	(.f64 (.f64 (cbrt.f64 (/.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))) (cbrt.f64 (/.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)))) (cbrt.f64 (/.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))))
	3.7b	(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))

Compiler

Compiled 5813 to 3537 computations (39.2% 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	(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))

series388.0ms (5.9%)

Counts

3 → 60

Calls

3 calls:

288.0ms	(/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
53.0ms	(+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
47.0ms	(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))
4.0ms	(+.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)))

simplify175.0ms (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

prune195.0ms (2.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	243	4	247
Fresh	4	1	5
Picked	0	1	1
Done	0	0	0
Total	247	6	253

Error

Counts

253 → 6

Alt Table

Status	Error	Program
	3.7b	(fma.f64 (/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3)) -3/8 (*.f64 -1/2 (/.f64 c b)))
	0.4b	(/.f64 -1 (/.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b) c))
	2.4b	(/.f64 (neg.f64 c) (fma.f64 b 2 (fma.f64 (/.f64 (.f64 (.f64 c c) (.f64 a a)) (pow.f64 b 3)) -9/8 (.f64 (*.f64 (/.f64 c b) a) -3/2))))
▶	0.2b	(/.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)))
✓	0.1b	(/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))

Compiler

Compiled 6391 to 3448 computations (46% saved)

localize11.0ms (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)

series394.0ms (6%)

Counts

3 → 108

Calls

3 calls:

233.0ms

(/.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))

106.0ms

(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))))

rewrite14.0ms (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:

3.0ms

(/.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))

1.0ms

(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)

simplify213.0ms (3.2%)

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

prune462.0ms (7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	428	0	428
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	428	6	434

Error

Counts

434 → 6

Alt Table

Status	Error	Program
	3.7b	(fma.f64 (/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3)) -3/8 (*.f64 -1/2 (/.f64 c b)))
	0.4b	(/.f64 -1 (/.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b) c))
	2.4b	(/.f64 (neg.f64 c) (fma.f64 b 2 (fma.f64 (/.f64 (.f64 (.f64 c c) (.f64 a a)) (pow.f64 b 3)) -9/8 (.f64 (*.f64 (/.f64 c b) a) -3/2))))
✓	0.2b	(/.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)))
✓	0.1b	(/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))

Compiler

Compiled 20419 to 12850 computations (37.1% saved)

regimes715.0ms (10.8%)

Accuracy

Total 0.1b remaining (85.6%)

Threshold costs 0.1b (85.6%)

Counts

115 → 1

Compiler

Compiled 16827 to 11208 computations (33.4% 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)

sample2.0s (30.1%)

Algorithm

1×

intervals

Results

491.0ms	3783×	body	256	valid
335.0ms	8762×	pre	128	true
302.0ms	1429×	body	512	valid
190.0ms	2788×	body	128	valid
48.0ms	762×	body	128	nan

Compiler

Compiled 193 to 130 computations (32.6% saved)

Details

analyze343.0ms (5.2%)

sample138.0ms (2.1%)

simplify356.0ms (5.4%)

prune4.0ms (0.1%)

localize10.0ms (0.1%)

series161.0ms (2.4%)

rewrite25.0ms (0.4%)

simplify108.0ms (1.6%)

prune151.0ms (2.3%)

localize13.0ms (0.2%)

series437.0ms (6.6%)

rewrite19.0ms (0.3%)

simplify103.0ms (1.6%)

prune162.0ms (2.4%)

localize10.0ms (0.1%)

series388.0ms (5.9%)

rewrite21.0ms (0.3%)

simplify175.0ms (2.6%)

prune195.0ms (2.9%)

localize11.0ms (0.2%)

series394.0ms (6%)

rewrite14.0ms (0.2%)

simplify213.0ms (3.2%)

prune462.0ms (7%)

regimes715.0ms (10.8%)

simplify3.0ms (0%)

end1.0ms (0%)

sample2.0s (30.1%)

Profiling