Details

analyze1.3s (16.8%)

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)

sample2.0s (26.3%)

Results

929.0ms	3120×	body	256	valid
843.0ms	5136×	body	128	valid
154.0ms	944×	body	128	invalid

Compiler

Compiled 106 to 76 computations (28.3% saved)

simplify351.0ms (4.5%)

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

44.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	44.3b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
▶	44.3b	(.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))
✓	0.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
✓	0.4b	(/.f64 1/3 a)
✓	39.1b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)

series161.0ms (2.1%)

Counts

4 → 76

Calls

4 calls:

91.0ms	(.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)
10.0ms	(fma.f64 a (.f64 c -3) (.f64 b b))
2.0ms	(/.f64 1/3 a)

rewrite24.0ms (0.3%)

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:

9.0ms	(.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))

simplify110.0ms (1.4%)

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

prune161.0ms (2.1%)

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
	44.3b	(.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)))
	3.6b	(.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))
	44.3b	(.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b) (/.f64 (sqrt.f64 1/3) (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 (sqrt.f64 1/3) (cbrt.f64 a)))
	3.2b	(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 (.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))
	4.5b	(.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))

Compiler

Compiled 6051 to 3531 computations (41.6% 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	(.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)

series16.0ms (0.2%)

Counts

2 → 48

Calls

2 calls:

10.0ms	(.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 (1.3%)

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

prune171.0ms (2.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	128	8	136
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	132	10	142

Error

0.0b

Counts

142 → 10

Alt Table

Status	Error	Program
	0.7b	(/.f64 (.f64 (.f64 (.f64 -3 (.f64 c a)) (sqrt.f64 1/3)) (/.f64 (sqrt.f64 1/3) a)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
	4.5b	(.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))
	0.7b	(/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (cbrt.f64 (pow.f64 (/.f64 1/3 a) 3))) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
	0.9b	(/.f64 (.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 (sqrt.f64 1/3) (sqrt.f64 a))) (/.f64 (sqrt.f64 1/3) (sqrt.f64 a))) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b))
	1.5b	(/.f64 (.f64 (.f64 (cbrt.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a))) (cbrt.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a)))) (cbrt.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))
	3.2b	(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 (.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a)) (+.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 c (.f64 a -3) (.f64 b b)) 3))) b))
	1.4b	(/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (.f64 (/.f64 1 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 1/3 (cbrt.f64 a)))) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
▶	0.2b	(/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
	1.4b	(/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (.f64 (/.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))

Compiler

Compiled 4399 to 2755 computations (37.4% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series356.0ms (4.6%)

Counts

3 → 60

Calls

3 calls:

259.0ms	(/.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)
44.0ms	(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:

7.0ms	(/.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)))

simplify173.0ms (2.2%)

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

prune213.0ms (2.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	241	6	247
Fresh	8	1	9
Picked	1	0	1
Done	0	0	0
Total	250	7	257

Error

0.0b

Counts

257 → 7

Alt Table

Status	Error	Program
▶	0.2b	(neg.f64 (/.f64 c (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)))
	3.2b	(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)))))
	1.4b	(/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (.f64 (/.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))
	0.6b	(.f64 (/.f64 -1 (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))) (/.f64 c (sqrt.f64 (+.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)))
	0.4b	(/.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))
	0.8b	(.f64 (/.f64 (sqrt.f64 c) (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))) (/.f64 (neg.f64 (sqrt.f64 c)) (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b))))

Compiler

Compiled 6592 to 3575 computations (45.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(sqrt.f64 (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 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))

series225.0ms (2.9%)

Counts

1 → 20

Calls

1 calls:

225.0ms

(/.f64 c (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b))

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`*-un-lft-identity_binary64`
12×	`times-frac_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
4×	`associate-/r*_binary64`

Counts

1 → 35

Calls

1 calls:

5.0ms

(/.f64 c (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b))

simplify82.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

603×	`fma-neg_binary64`
592×	`times-frac_binary64`
397×	`associate-/l*_binary64`
347×	`associate-/r*_binary64`
281×	`associate-r_binary64`

Counts

55 → 78

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	127	1736
1	329	1637
2	973	1583
3	4710	1581
4	5238	1581

prune180.0ms (2.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	197	1	198
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	198	7	205

Error

0.0b

Counts

205 → 7

Alt Table

Status	Error	Program
✓	0.2b	(neg.f64 (/.f64 c (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)))
	4.0b	(neg.f64 (/.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)))))
	3.2b	(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)))))
	1.4b	(/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (.f64 (/.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))
	0.6b	(.f64 (/.f64 -1 (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))) (/.f64 c (sqrt.f64 (+.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)))
	0.8b	(.f64 (/.f64 (sqrt.f64 c) (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))) (/.f64 (neg.f64 (sqrt.f64 c)) (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b))))

Compiler

Compiled 5026 to 2940 computations (41.5% saved)

regimes1.8s (23.9%)

Accuracy

Total 0.1b remaining (87.4%)

Threshold costs 0.1b (87.4%)

Counts

299 → 1

Compiler

Compiled 41817 to 27727 computations (33.7% 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

end142.0ms (1.8%)

Compiler: Compiled 247 to 162 computations (34.4% saved)

Details

analyze1.3s (16.8%)

sample2.0s (26.3%)

simplify351.0ms (4.5%)

prune4.0ms (0.1%)

localize10.0ms (0.1%)

series161.0ms (2.1%)

rewrite24.0ms (0.3%)

simplify110.0ms (1.4%)

prune161.0ms (2.1%)

localize14.0ms (0.2%)

series16.0ms (0.2%)

rewrite8.0ms (0.1%)

simplify97.0ms (1.3%)

prune171.0ms (2.2%)

localize11.0ms (0.1%)

series356.0ms (4.6%)

rewrite21.0ms (0.3%)

simplify173.0ms (2.2%)

prune213.0ms (2.8%)

localize10.0ms (0.1%)

series225.0ms (2.9%)

rewrite8.0ms (0.1%)

simplify82.0ms (1.1%)

prune180.0ms (2.3%)

regimes1.8s (23.9%)

simplify3.0ms (0%)

end142.0ms (1.8%)

Profiling