Details

analyze503.0ms (5.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
25%	74.9%	0.1%	4
37.4%	62.4%	0.1%	5
37.4%	62.4%	0.1%	6
37.4%	56.2%	6.4%	7
45.2%	48.4%	6.4%	8
49.1%	42.1%	8.7%	9
51.5%	35.1%	13.4%	10
58.1%	27.7%	14.2%	11
60.8%	22.6%	16.5%	12
62.3%	18.7%	19%	13
66.2%	14.4%	19.4%	14

Compiler

Compiled 21 to 15 computations (28.6% saved)

sample2.9s (29.9%)

Results

928.0ms	5655×	body	128	valid
717.0ms	1093×	body	2048	valid
500.0ms	638×	body	1024	valid
281.0ms	372×	body	4096	valid
144.0ms	341×	body	512	valid
112.0ms	668×	body	128	invalid
45.0ms	157×	body	256	valid

Compiler

Compiled 62 to 44 computations (29% saved)

simplify443.0ms (4.6%)

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

prune8.0ms (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

28.8b

Counts

3 → 2

Alt Table

Status	Error	Program
	28.9b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
▶	28.8b	(/.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)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 3 a) c)
✓	0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
✓	1.0b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
✓	25.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series161.0ms (1.7%)

Counts

4 → 100

Calls

4 calls:

74.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
69.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
11.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
7.0ms	(.f64 (.f64 3 a) c)

rewrite24.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
10×	`fma-def_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-log-exp_binary64`
10×	`pow1_binary64`

Counts

4 → 80

Calls

4 calls:

7.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
4.0ms	(.f64 (.f64 3 a) c)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
3.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

simplify196.0ms (2%)

Algorithm

1×	egg-herbie

Rules

677×	`fma-def_binary64`
621×	`fma-neg_binary64`
305×	`cancel-sign-sub-inv_binary64`
228×	`distribute-rgt-neg-in_binary64`
197×	`distribute-lft-neg-in_binary64`

Counts

180 → 168

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	201	2955
1	523	2836
2	1806	2732
3	4518	2728
4	4998	2728
5	4919	2728

prune307.0ms (3.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	157	11	168
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	158	12	170

Error

8.5b

Counts

170 → 12

Alt Table

Status	Error	Program
	39.3b	(/.f64 (/.f64 (.f64 3 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b))) (*.f64 3 a))
	34.4b	(/.f64 (+.f64 (neg.f64 b) (.f64 (.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b)) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b))) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b)))) (*.f64 3 a))
	36.5b	(/.f64 (+.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b)))) (*.f64 3 a))
	29.0b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 (.f64 3 a) (.f64 (cbrt.f64 c) (cbrt.f64 c))) (cbrt.f64 c))))) (.f64 3 a))
	46.5b	(/.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (*.f64 3 a))
▶	28.8b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -3))))) (*.f64 3 a))
	40.0b	(/.f64 (.f64 -2 b) (.f64 3 a))
	56.8b	(/.f64 (+.f64 (neg.f64 b) b) (*.f64 3 a))
	28.9b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
	40.0b	(/.f64 (cbrt.f64 (pow.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b) b) 3)) (*.f64 3 a))
	33.4b	(/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b) b))) (*.f64 3 a))
	52.6b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (/.f64 (fma.f64 (pow.f64 (.f64 c a) 3) -27 (pow.f64 b 6)) (fma.f64 3 (.f64 (.f64 c a) (fma.f64 3 (.f64 c a) (.f64 b b))) (pow.f64 b 4))))) (.f64 3 a))

Compiler

Compiled 4656 to 2736 computations (41.2% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 c (.f64 a -3))
✓	1.0b	(+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -3)))))
✓	1.0b	(fma.f64 b b (.f64 c (.f64 a -3)))
✓	25.0b	(sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -3))))

series248.0ms (2.6%)

Counts

4 → 100

Calls

4 calls:

125.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -3)))))
90.0ms	(sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -3))))
24.0ms	(fma.f64 b b (.f64 c (.f64 a -3)))
7.0ms	(.f64 c (.f64 a -3))

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
10×	`fma-def_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`pow1_binary64`
9×	`add-cube-cbrt_binary64`

Counts

4 → 72

Calls

4 calls:

6.0ms	(.f64 c (.f64 a -3))
6.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -3)))))
1.0ms	(sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -3))))
0.0ms	(fma.f64 b b (.f64 c (.f64 a -3)))

simplify177.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

837×	`times-frac_binary64`
485×	`fma-neg_binary64`
405×	`fma-def_binary64`
173×	`cancel-sign-sub-inv_binary64`
131×	`distribute-rgt-in_binary64`

Counts

172 → 146

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	175	2790
1	449	2648
2	1475	2577
3	4583	2577
4	4958	2577

prune239.0ms (2.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	145	1	146
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	146	12	158

Error

8.5b

Counts

158 → 12

Alt Table

Status	Error	Program
	39.3b	(/.f64 (/.f64 (.f64 3 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b))) (*.f64 3 a))
	34.4b	(/.f64 (+.f64 (neg.f64 b) (.f64 (.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b)) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b))) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b)))) (*.f64 3 a))
	36.5b	(/.f64 (+.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b)))) (*.f64 3 a))
	33.4b	(/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b) b))) (*.f64 3 a))
	29.0b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 b b (.f64 (.f64 (cbrt.f64 c) (cbrt.f64 c)) (.f64 (cbrt.f64 c) (.f64 a -3)))))) (*.f64 3 a))
✓	28.8b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -3))))) (*.f64 3 a))
	40.0b	(/.f64 (.f64 -2 b) (.f64 3 a))
	56.8b	(/.f64 (+.f64 (neg.f64 b) b) (*.f64 3 a))
▶	28.9b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
	40.0b	(/.f64 (cbrt.f64 (pow.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b) b) 3)) (*.f64 3 a))
	46.5b	(/.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (*.f64 3 a))
	52.6b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (/.f64 (fma.f64 (pow.f64 (.f64 c a) 3) -27 (pow.f64 b 6)) (fma.f64 3 (.f64 (.f64 c a) (fma.f64 3 (.f64 c a) (.f64 b b))) (pow.f64 b 4))))) (.f64 3 a))

Compiler

Compiled 3968 to 2423 computations (38.9% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
✓	0.4b	(/.f64 1/3 a)
✓	1.0b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
✓	25.0b	(sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))

series344.0ms (3.6%)

Counts

4 → 60

Calls

4 calls:

143.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
111.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
86.0ms	(sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))
3.0ms	(/.f64 1/3 a)

rewrite36.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`add-sqr-sqrt_binary64`
40×	`*-un-lft-identity_binary64`
36×	`add-cube-cbrt_binary64`
19×	`times-frac_binary64`
18×	`prod-diff_binary64`

Counts

4 → 128

Calls

4 calls:

15.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
7.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
3.0ms	(/.f64 1/3 a)
1.0ms	(sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))

simplify153.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

446×	`fma-neg_binary64`
318×	`distribute-rgt-in_binary64`
276×	`cancel-sign-sub-inv_binary64`
271×	`neg-mul-1_binary64`
161×	`associate-r_binary64`

Counts

188 → 240

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	295	5224
1	709	4328
2	2581	4143
3	4488	4131
4	4864	4131

prune420.0ms (4.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	235	5	240
Fresh	6	4	10
Picked	1	0	1
Done	0	1	1
Total	242	10	252

Error

3.6b

Counts

252 → 10

Alt Table

Status	Error	Program
	39.3b	(/.f64 (/.f64 (.f64 3 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b))) (*.f64 3 a))
	40.0b	(.f64 (.f64 -2 b) (/.f64 1/3 a))
	33.5b	(/.f64 (.f64 (+.f64 (.f64 a (.f64 c -3)) 0) (/.f64 1/3 a)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b))
	41.5b	(*.f64 -1/2 (/.f64 c b))
✓	28.8b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -3))))) (*.f64 3 a))
	40.0b	(/.f64 (.f64 -2 b) (.f64 3 a))
	40.1b	(fma.f64 1/2 (/.f64 c b) (*.f64 (/.f64 b a) -2/3))
	40.0b	(/.f64 (cbrt.f64 (pow.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b) b) 3)) (*.f64 3 a))
	33.4b	(/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b) b))) (*.f64 3 a))
▶	28.9b	(/.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) 1/3) a)

Compiler

Compiled 6572 to 3865 computations (41.2% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) 1/3) a)
✓	0.2b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) 1/3)
	1.0b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
	25.0b	(sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))

series261.0ms (2.7%)

Counts

2 → 40

Calls

2 calls:

140.0ms	(/.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) 1/3) a)
121.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) 1/3)

rewrite26.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
8×	`*-un-lft-identity_binary64`
6×	`associate-l_binary64`

Counts

2 → 50

Calls

2 calls:

11.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) 1/3)
9.0ms	(/.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) 1/3) a)

simplify132.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

540×	`associate-/r*_binary64`
488×	`fma-def_binary64`
267×	`associate-/r/_binary64`
266×	`associate-/l/_binary64`
223×	`distribute-rgt-in_binary64`

Counts

90 → 126

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	199	2742
1	568	2518
2	1957	2427
3	5268	2427

prune199.0ms (2.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	241	1	242
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	242	10	252

Error

3.5b

Counts

252 → 10

Alt Table

Status	Error	Program
	39.3b	(/.f64 (/.f64 (.f64 3 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b))) (*.f64 3 a))
	40.0b	(.f64 (.f64 -2 b) (/.f64 1/3 a))
	33.5b	(/.f64 (.f64 (+.f64 (.f64 a (.f64 c -3)) 0) (/.f64 1/3 a)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b))
	41.5b	(*.f64 -1/2 (/.f64 c b))
✓	28.8b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -3))))) (*.f64 3 a))
	40.0b	(/.f64 (.f64 -2 b) (.f64 3 a))
	40.0b	(/.f64 (.f64 (cbrt.f64 (pow.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -3)))) b) 3)) 1/3) a)
	40.1b	(fma.f64 1/2 (/.f64 c b) (*.f64 (/.f64 b a) -2/3))
	33.4b	(/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b) b))) (*.f64 3 a))
✓	28.9b	(/.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) 1/3) a)

Compiler

Compiled 6561 to 3840 computations (41.5% saved)

regimes2.5s (26%)

Accuracy

Total 2.9b remaining (37.3%)

Threshold costs 0b (0%)

Counts

128 → 4

Compiler

Compiled 15629 to 10823 computations (30.8% saved)

bsearch128.0ms (1.3%)

Steps

Iters	Range		Point
4	3.805784381602972e+45	6.516529514186632e+45	5.17555123963869e+45
6	1.123098274182808e-169	1.236058523118014e-168	1.1498395275009536e-168
8	-2.728471400924003e+154	-4.3643145321831494e+150	-8.182845608862169e+150

Compiler

Compiled 4 to 3 computations (25% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary64`
3×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`unsub-neg_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	42	91
1	55	89
2	58	89
3	59	89
4	59	89

end148.0ms (1.5%)

Compiler: Compiled 295 to 206 computations (30.2% saved)

Details

analyze503.0ms (5.2%)

sample2.9s (29.9%)

simplify443.0ms (4.6%)

prune8.0ms (0.1%)

localize21.0ms (0.2%)

series161.0ms (1.7%)

rewrite24.0ms (0.2%)

simplify196.0ms (2%)

prune307.0ms (3.2%)

localize23.0ms (0.2%)

series248.0ms (2.6%)

rewrite19.0ms (0.2%)

simplify177.0ms (1.8%)

prune239.0ms (2.5%)

localize19.0ms (0.2%)

series344.0ms (3.6%)

rewrite36.0ms (0.4%)

simplify153.0ms (1.6%)

prune420.0ms (4.3%)

localize20.0ms (0.2%)

series261.0ms (2.7%)

rewrite26.0ms (0.3%)

simplify132.0ms (1.4%)

prune199.0ms (2.1%)

regimes2.5s (26%)

bsearch128.0ms (1.3%)

simplify7.0ms (0.1%)

end148.0ms (1.5%)

Profiling