Details

analyze354.0ms (5.5%)

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)

sample143.0ms (2.2%)

Algorithm

1×

intervals

Results

16.0ms	127×	body	256	valid
12.0ms	288×	pre	128	true
8.0ms	40×	body	512	valid
7.0ms	89×	body	128	valid
2.0ms	32×	body	128	nan

Compiler

Compiled 66 to 48 computations (27.3% saved)

simplify357.0ms (5.5%)

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

53.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	53.0b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
▶	53.0b	(.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)
✓	29.7b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)

series171.0ms (2.6%)

Counts

4 → 76

Calls

4 calls:

103.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
56.0ms	(-.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)

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:

10.0ms	(.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))

simplify106.0ms (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

0.0b

Counts

223 → 6

Alt Table

Status	Error	Program
	2.3b	(.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))
▶	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))
	1.5b	(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)))))))
	53.0b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b) (.f64 (*.f64 (cbrt.f64 (/.f64 1/3 a)) (cbrt.f64 (/.f64 1/3 a))) (cbrt.f64 (/.f64 1/3 a))))
	52.3b	(.f64 (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)))) (neg.f64 b)) (/.f64 1/3 a))
	1.9b	(.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 6061 to 3535 computations (41.7% saved)

localize14.0ms (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)
	0.3b	(/.f64 1/3 a)

series71.0ms (1.1%)

Counts

3 → 68

Calls

3 calls:

54.0ms	(+.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)

rewrite14.0ms (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:

5.0ms	(.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a))
3.0ms	(+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
0.0ms	(fma.f64 a (*.f64 c -3) 0)

simplify78.0ms (1.2%)

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

prune175.0ms (2.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	157	5	162
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	161	7	168

Error

0.0b

Counts

168 → 7

Alt Table

Status	Error	Program
	0.6b	(/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a)) (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	(/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
	1.5b	(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 (/.f64 1 a))) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b))
	0.7b	(/.f64 (cbrt.f64 (.f64 (.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (fma.f64 a (.f64 c -3) 0)) (fma.f64 a (.f64 c -3) 0)) (/.f64 (.f64 (.f64 1/3 1/3) 1/3) (.f64 (.f64 a a) a)))) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
	0.8b	(/.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 -3 (.f64 c a)) (/.f64 1/3 a)) 3)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b))
	1.9b	(.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 5300 to 3283 computations (38.1% 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)))
	0.1b	(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))
	0.1b	(+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)

series303.0ms (4.7%)

Counts

2 → 40

Calls

2 calls:

257.0ms	(/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
46.0ms	(sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))

rewrite14.0ms (0.2%)

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)))

simplify121.0ms (1.9%)

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

prune216.0ms (3.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	241	6	247
Fresh	6	0	6
Picked	0	1	1
Done	0	0	0
Total	247	7	254

Error

Counts

254 → 7

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 (neg.f64 c) (.f64 (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)) (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b))))
	0.7b	(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))))
	1.5b	(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)))))
	1.8b	(/.f64 (neg.f64 c) (fma.f64 2 b (fma.f64 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)) -9/8 (.f64 (/.f64 (*.f64 c a) b) -3/2))))
	0.6b	(/.f64 (sqrt.f64 c) (/.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b) (neg.f64 (sqrt.f64 c))))
▶	0.4b	(/.f64 (neg.f64 c) (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))

Compiler

Compiled 6595 to 3544 computations (46.3% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(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)))))
✓	0.2b	(sqrt.f64 (cbrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))))
✓	0.5b	(.f64 (cbrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) (cbrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))))
✓	0.5b	(cbrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))

series253.0ms (3.9%)

Counts

4 → 144

Calls

4 calls:

73.0ms	(.f64 (cbrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) (cbrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))))
66.0ms	(sqrt.f64 (cbrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))))
57.0ms	(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)))))
57.0ms	(cbrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))

rewrite17.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
20×	`pow1_binary64`
15×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`

Counts

4 → 96

Calls

4 calls:

4.0ms	(.f64 (cbrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) (cbrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))))
3.0ms	(sqrt.f64 (cbrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))))
3.0ms	(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)))))
1.0ms	(cbrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))

simplify264.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

347×	`associate-/r*_binary64`
326×	`times-frac_binary64`
275×	`associate-l_binary64`
226×	`fma-def_binary64`
213×	`associate-/l*_binary64`

Counts

240 → 253

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	516	10223
1	1591	9919
2	5031	9919

prune532.0ms (8.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	377	0	377
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	377	7	384

Error

Counts

384 → 7

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 (neg.f64 c) (.f64 (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)) (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b))))
	0.7b	(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))))
	1.5b	(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)))))
	1.8b	(/.f64 (neg.f64 c) (fma.f64 2 b (fma.f64 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)) -9/8 (.f64 (/.f64 (*.f64 c a) b) -3/2))))
	0.6b	(/.f64 (sqrt.f64 c) (/.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b) (neg.f64 (sqrt.f64 c))))
✓	0.4b	(/.f64 (neg.f64 c) (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))

Compiler

Compiled 22331 to 13607 computations (39.1% saved)

regimes1.2s (18.2%)

Accuracy

Total 0.1b remaining (89.9%)

Threshold costs 0.1b (89.9%)

Counts

195 → 1

Compiler

Compiled 29393 to 19291 computations (34.4% 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)

sample1.9s (29.2%)

Algorithm

1×

intervals

Results

513.0ms	3735×	body	256	valid
338.0ms	8835×	pre	128	true
284.0ms	1482×	body	512	valid
191.0ms	2783×	body	128	valid
58.0ms	835×	body	128	nan

Compiler

Compiled 292 to 185 computations (36.6% saved)

Details

analyze354.0ms (5.5%)

sample143.0ms (2.2%)

simplify357.0ms (5.5%)

prune4.0ms (0.1%)

localize10.0ms (0.1%)

series171.0ms (2.6%)

rewrite25.0ms (0.4%)

simplify106.0ms (1.6%)

prune151.0ms (2.3%)

localize14.0ms (0.2%)

series71.0ms (1.1%)

rewrite14.0ms (0.2%)

simplify78.0ms (1.2%)

prune175.0ms (2.7%)

localize9.0ms (0.1%)

series303.0ms (4.7%)

rewrite14.0ms (0.2%)

simplify121.0ms (1.9%)

prune216.0ms (3.3%)

localize14.0ms (0.2%)

series253.0ms (3.9%)

rewrite17.0ms (0.3%)

simplify264.0ms (4.1%)

prune532.0ms (8.2%)

regimes1.2s (18.2%)

simplify3.0ms (0%)

end1.0ms (0%)

sample1.9s (29.2%)

Profiling