Details

analyze384.0ms (4.9%)

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 (31.4%)

Results

1.1s	3902×	body	256	valid
638.0ms	1510×	body	512	valid
455.0ms	2844×	body	128	valid
126.0ms	816×	body	128	invalid

Compiler

Compiled 106 to 76 computations (28.3% saved)

simplify346.0ms (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

53.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	53.0b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
	53.0b	(/.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)
✓	25.0b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)

series161.0ms (2.1%)

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))
57.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
12.0ms	(fma.f64 a (.f64 c -3) (.f64 b b))
2.0ms	(/.f64 1/3 a)

rewrite25.0ms (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:

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))

simplify112.0ms (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

prune148.0ms (1.9%)

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
	53.0b	(.f64 (.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 a) (cbrt.f64 a)))) (/.f64 (cbrt.f64 1/3) (cbrt.f64 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))
	1.8b	(fma.f64 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) -9/16 (fma.f64 (/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3)) -3/8 (*.f64 -1/2 (/.f64 c b))))
	5.9b	(*.f64 -1/2 (/.f64 c b))
	2.0b	(.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))
	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))

Compiler

Compiled 5995 to 3489 computations (41.8% 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	(.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)

series334.0ms (4.3%)

Counts

3 → 68

Calls

3 calls:

318.0ms	(/.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))
9.0ms	(.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a))
6.0ms	(fma.f64 a (*.f64 c -3) 0)

rewrite19.0ms (0.2%)

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)

simplify100.0ms (1.3%)

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

prune171.0ms (2.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	177	5	182
Fresh	4	1	5
Picked	1	0	1
Done	0	0	0
Total	182	6	188

Error

0.0b

Counts

188 → 6

Alt Table

Status	Error	Program
	0.6b	(.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a)) (/.f64 1 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b)))
	1.8b	(fma.f64 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) -9/16 (fma.f64 (/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3)) -3/8 (*.f64 -1/2 (/.f64 c b))))
	1.4b	(/.f64 (.f64 (.f64 (.f64 -3 (.f64 c a)) (.f64 (cbrt.f64 (/.f64 1/3 a)) (cbrt.f64 (/.f64 1/3 a)))) (cbrt.f64 (/.f64 1/3 a))) (+.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))
	0.6b	(/.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a)))
	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))

Compiler

Compiled 5727 to 3481 computations (39.2% 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)))
✓	0.1b	(+.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))

series352.0ms (4.5%)

Counts

3 → 60

Calls

3 calls:

252.0ms	(/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
56.0ms	(+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
43.0ms	(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))
3.0ms	(+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
3.0ms	(sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))

simplify171.0ms (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

prune194.0ms (2.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	246	1	247
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	248	5	253

Error

Counts

253 → 5

Alt Table

Status	Error	Program
	0.6b	(.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a)) (/.f64 1 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b)))
	1.8b	(fma.f64 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) -9/16 (fma.f64 (/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3)) -3/8 (*.f64 -1/2 (/.f64 c b))))
▶	0.6b	(.f64 (/.f64 (sqrt.f64 c) 1) (/.f64 (neg.f64 (sqrt.f64 c)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b)))
	1.4b	(/.f64 (.f64 (.f64 (.f64 -3 (.f64 c a)) (.f64 (cbrt.f64 (/.f64 1/3 a)) (cbrt.f64 (/.f64 1/3 a)))) (cbrt.f64 (/.f64 1/3 a))) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b))
	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))

Compiler

Compiled 6438 to 3491 computations (45.8% saved)

localize13.0ms (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)
	0.1b	(fma.f64 a (.f64 c -3) (.f64 b b))
✓	0.3b	(/.f64 (neg.f64 (sqrt.f64 c)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
✓	0.4b	(.f64 (/.f64 (sqrt.f64 c) 1) (/.f64 (neg.f64 (sqrt.f64 c)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b)))

series755.0ms (9.7%)

Counts

2 → 36

Calls

2 calls:

452.0ms

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

302.0ms

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

rewrite78.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

164×	`*-un-lft-identity_binary64`
159×	`times-frac_binary64`
123×	`add-sqr-sqrt_binary64`
94×	`add-cube-cbrt_binary64`
70×	`associate-r_binary64`

Counts

2 → 229

Calls

2 calls:

34.0ms

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

10.0ms

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

simplify203.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

567×	`fma-def_binary64`
298×	`associate-/l*_binary64`
276×	`associate-r_binary64`
262×	`div-sub_binary64`
242×	`associate-l_binary64`

Counts

265 → 338

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	334	9027
1	862	8669
2	3639	8348
3	4967	8348

prune295.0ms (3.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	413	1	414
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	414	5	419

Error

Counts

419 → 5

Alt Table

Status	Error	Program
	0.6b	(.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a)) (/.f64 1 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b)))
	1.8b	(fma.f64 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) -9/16 (fma.f64 (/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3)) -3/8 (*.f64 -1/2 (/.f64 c b))))
✓	0.6b	(.f64 (/.f64 (sqrt.f64 c) 1) (/.f64 (neg.f64 (sqrt.f64 c)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b)))
	0.6b	(.f64 (/.f64 (sqrt.f64 c) 1) (/.f64 (neg.f64 (sqrt.f64 c)) (+.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 c (.f64 a -3) (*.f64 b b)) 3))) b)))
	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))

Compiler

Compiled 13527 to 6946 computations (48.7% saved)

regimes1.3s (16.8%)

Accuracy

Total 0.1b remaining (62.9%)

Threshold costs 0.1b (62.9%)

Counts

221 → 1

Compiler

Compiled 29338 to 19567 computations (33.3% 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	13	22
1	21	22
2	25	22
3	28	22
4	29	22
5	29	22

end101.0ms (1.3%)

Compiler: Compiled 172 to 118 computations (31.4% saved)

Details

analyze384.0ms (4.9%)

sample2.4s (31.4%)

simplify346.0ms (4.5%)

prune4.0ms (0.1%)

localize10.0ms (0.1%)

series161.0ms (2.1%)

rewrite25.0ms (0.3%)

simplify112.0ms (1.4%)

prune148.0ms (1.9%)

localize13.0ms (0.2%)

series334.0ms (4.3%)

rewrite19.0ms (0.2%)

simplify100.0ms (1.3%)

prune171.0ms (2.2%)

localize11.0ms (0.1%)

series352.0ms (4.5%)

rewrite21.0ms (0.3%)

simplify171.0ms (2.2%)

prune194.0ms (2.5%)

localize13.0ms (0.2%)

series755.0ms (9.7%)

rewrite78.0ms (1%)

simplify203.0ms (2.6%)

prune295.0ms (3.8%)

regimes1.3s (16.8%)

simplify3.0ms (0%)

end101.0ms (1.3%)

Profiling