Details

analyze380.0ms (5.1%)

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 (32%)

Results

1.1s	3809×	body	256	valid
607.0ms	1497×	body	512	valid
473.0ms	2950×	body	128	valid
131.0ms	886×	body	128	invalid

Compiler

Compiled 106 to 76 computations (28.3% saved)

simplify349.0ms (4.7%)

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

51.4b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	51.4b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
	51.4b	(/.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)

localize9.0ms (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)
✓	25.3b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)

series104.0ms (1.4%)

Counts

4 → 76

Calls

4 calls:

56.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
36.0ms	(-.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)

rewrite27.0ms (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))

simplify100.0ms (1.3%)

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

prune153.0ms (2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	217	4	221
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	219	4	223

Error

0.0b

Counts

223 → 4

Alt Table

Status	Error	Program
▶	0.4b	(/.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))
	2.5b	(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)))))))
	51.4b	(.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b) (sqrt.f64 (/.f64 1/3 a))) (sqrt.f64 (/.f64 1/3 a)))
	3.6b	(.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 5883 to 3415 computations (42% 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))
✓	0.2b	(.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)

series185.0ms (2.5%)

Counts

3 → 68

Calls

3 calls:

169.0ms	(/.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))
10.0ms	(.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))
5.0ms	(.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a))
0.0ms	(fma.f64 a (*.f64 c -3) 0)

simplify92.0ms (1.2%)

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

prune169.0ms (2.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	178	4	182
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	181	5	186

Error

0.0b

Counts

186 → 5

Alt Table

Status	Error	Program
	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))
	0.5b	(/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) 1/3) (.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) a))
	2.5b	(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 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))
	3.6b	(.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 5709 to 3465 computations (39.3% saved)

localize11.0ms (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 (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 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))

series194.0ms (2.6%)

Counts

3 → 60

Calls

3 calls:

130.0ms	(/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
36.0ms	(+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
29.0ms	(sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))

rewrite20.0ms (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))
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)))

simplify159.0ms (2.1%)

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

prune189.0ms (2.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	246	1	247
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	247	5	252

Error

Counts

252 → 5

Alt Table

Status	Error	Program
	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))
	0.5b	(/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) 1/3) (.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) a))
✓	0.1b	(/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
	3.6b	(.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 (neg.f64 c) (+.f64 (pow.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) 3) (pow.f64 b 3))) (+.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 (.f64 b b) (.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))))

Compiler

Compiled 6465 to 3490 computations (46% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) 3)
✓	0.3b	(/.f64 (neg.f64 c) (+.f64 (pow.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) 3) (pow.f64 b 3)))
✓	0.3b	(.f64 (/.f64 (neg.f64 c) (+.f64 (pow.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) 3) (pow.f64 b 3))) (+.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 (.f64 b b) (.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))))
✓	25.4b	(-.f64 (.f64 b b) (.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))

series492.0ms (6.6%)

Counts

4 → 80

Calls

4 calls:

224.0ms	(.f64 (/.f64 (neg.f64 c) (+.f64 (pow.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) 3) (pow.f64 b 3))) (+.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 (.f64 b b) (.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))))
131.0ms	(/.f64 (neg.f64 c) (+.f64 (pow.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) 3) (pow.f64 b 3)))
84.0ms	(pow.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) 3)
51.0ms	(-.f64 (.f64 b b) (.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))

rewrite119.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

299×	`*-un-lft-identity_binary64`
181×	`times-frac_binary64`
105×	`distribute-lft-out_binary64`
96×	`associate-l_binary64`
94×	`add-sqr-sqrt_binary64`

Counts

4 → 302

Calls

4 calls:

36.0ms	(.f64 (/.f64 (neg.f64 c) (+.f64 (pow.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) 3) (pow.f64 b 3))) (+.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 (.f64 b b) (.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))))
15.0ms	(/.f64 (neg.f64 c) (+.f64 (pow.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) 3) (pow.f64 b 3)))
4.0ms	(pow.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) 3)
3.0ms	(-.f64 (.f64 b b) (.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))

simplify243.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

333×	`fma-def_binary64`
299×	`associate-/l*_binary64`
294×	`distribute-rgt-in_binary64`
265×	`distribute-lft-in_binary64`
248×	`times-frac_binary64`

Counts

382 → 433

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	507	17645
1	1676	16753
2	5084	16753

prune584.0ms (7.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	433	0	433
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	433	5	438

Error

Counts

438 → 5

Alt Table

Status	Error	Program
	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))
	0.5b	(/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) 1/3) (.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) a))
✓	0.1b	(/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
	3.6b	(.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 (neg.f64 c) (+.f64 (pow.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) 3) (pow.f64 b 3))) (+.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 (.f64 b b) (.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))))

Compiler

Compiled 30170 to 15882 computations (47.4% saved)

regimes1.3s (18%)

Accuracy

Total 0.1b remaining (77.4%)

Threshold costs 0.1b (77.4%)

Counts

217 → 1

Compiler

Compiled 32687 to 21533 computations (34.1% saved)

simplify2.0ms (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

end113.0ms (1.5%)

Compiler: Compiled 201 to 128 computations (36.3% saved)

Details

analyze380.0ms (5.1%)

sample2.4s (32%)

simplify349.0ms (4.7%)

prune4.0ms (0.1%)

localize9.0ms (0.1%)

series104.0ms (1.4%)

rewrite27.0ms (0.4%)

simplify100.0ms (1.3%)

prune153.0ms (2%)

localize13.0ms (0.2%)

series185.0ms (2.5%)

rewrite19.0ms (0.3%)

simplify92.0ms (1.2%)

prune169.0ms (2.3%)

localize11.0ms (0.1%)

series194.0ms (2.6%)

rewrite20.0ms (0.3%)

simplify159.0ms (2.1%)

prune189.0ms (2.5%)

localize20.0ms (0.3%)

series492.0ms (6.6%)

rewrite119.0ms (1.6%)

simplify243.0ms (3.2%)

prune584.0ms (7.8%)

regimes1.3s (18%)

simplify2.0ms (0%)

end113.0ms (1.5%)

Profiling