Details

analyze654.0ms (6.2%)

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
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	74.9%	0.1%	6
25%	68.6%	6.4%	7
31.2%	62.4%	6.4%	8
36.7%	54.6%	8.7%	9
38.2%	48.4%	13.4%	10
42.7%	42.3%	15%	11
47.8%	34.1%	18.1%	12
49.1%	30.3%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 21 to 15 computations (28.6% saved)

sample2.6s (24.5%)

Results

760.0ms	1159×	body	2048	valid
727.0ms	5299×	body	128	valid
406.0ms	805×	body	1024	valid
274.0ms	425×	body	4096	valid
147.0ms	1081×	body	128	invalid
123.0ms	357×	body	512	valid
52.0ms	211×	body	256	valid

Compiler

Compiled 62 to 44 computations (29% saved)

simplify349.0ms (3.3%)

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%)

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

35.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	35.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
▶	35.2b	(/.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
✓	0.2b	(.f64 (.f64 3 a) c)
✓	0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
✓	0.8b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
✓	21.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series85.0ms (0.8%)

Counts

4 → 100

Calls

4 calls:

42.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
29.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
9.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
4.0ms	(.f64 (.f64 3 a) c)

rewrite23.0ms (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))))
6.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
4.0ms	(.f64 (.f64 3 a) c)
3.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

simplify122.0ms (1.1%)

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

prune174.0ms (1.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	158	10	168
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	159	11	170

Error

9.4b

Counts

170 → 11

Alt Table

Status	Error	Program
	42.6b	(/.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (*.f64 3 a))
	55.6b	(/.f64 (fma.f64 (sqrt.f64 b) (neg.f64 (sqrt.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
	35.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
	35.4b	(/.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))
▶	33.0b	(/.f64 (/.f64 (.f64 3 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b))) (*.f64 3 a))
	47.1b	(/.f64 (.f64 -2 b) (.f64 3 a))
	36.7b	(/.f64 (fma.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) (neg.f64 (cbrt.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (*.f64 3 a))
	35.3b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c))))) (.f64 3 a))
	35.9b	(/.f64 (+.f64 (neg.f64 b) (.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b)) (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b)))) (.f64 3 a))
	55.8b	(/.f64 (+.f64 (neg.f64 b) b) (*.f64 3 a))
	39.3b	(/.f64 (+.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b)))) (*.f64 3 a))

Compiler

Compiled 4580 to 2678 computations (41.5% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.9b	(-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b))
✓	1.6b	(/.f64 (/.f64 (.f64 3 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b))) (*.f64 3 a))
✓	7.1b	(/.f64 (.f64 3 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b)))
✓	11.2b	(sqrt.f64 (.f64 c (.f64 a -3)))

series706.0ms (6.7%)

Counts

4 → 42

Calls

4 calls:

321.0ms	(/.f64 (.f64 3 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b)))
258.0ms	(/.f64 (/.f64 (.f64 3 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b))) (*.f64 3 a))
114.0ms	(-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b))
14.0ms	(sqrt.f64 (.f64 c (.f64 a -3)))

rewrite49.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

53×	`*-un-lft-identity_binary64`
45×	`add-cbrt-cube_binary64`
45×	`add-exp-log_binary64`
43×	`add-sqr-sqrt_binary64`
33×	`add-cube-cbrt_binary64`

Counts

4 → 162

Calls

4 calls:

11.0ms	(-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b))
10.0ms	(/.f64 (/.f64 (.f64 3 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b))) (*.f64 3 a))
9.0ms	(/.f64 (.f64 3 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b)))
3.0ms	(sqrt.f64 (.f64 c (.f64 a -3)))

simplify157.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

440×	`times-frac_binary64`
424×	`fma-neg_binary64`
347×	`associate-/l*_binary64`
276×	`associate-/r*_binary64`
254×	`associate-r_binary64`

Counts

204 → 301

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	408	8024
1	1058	6261
2	4623	6255
3	4941	6255

prune238.0ms (2.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	296	5	301
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	301	11	312

Error

4.2b

Counts

312 → 11

Alt Table

Status	Error	Program
	58.3b	(/.f64 (/.f64 (.f64 3 (.f64 c a)) (.f64 1/2 (/.f64 (pow.f64 (sqrt.f64 (.f64 -3 (.f64 c a))) 2) b))) (.f64 3 a))
	36.7b	(/.f64 (fma.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) (neg.f64 (cbrt.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (*.f64 3 a))
	37.3b	(*.f64 -1/2 (/.f64 c b))
	47.1b	(/.f64 (.f64 -2 b) (.f64 3 a))
	42.6b	(/.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (*.f64 3 a))
	35.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
	35.3b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c))))) (.f64 3 a))
	33.0b	(/.f64 (sqrt.f64 (/.f64 (.f64 3 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b)))) (/.f64 (.f64 3 a) (sqrt.f64 (/.f64 (.f64 3 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (*.f64 a -3))) b))))))
	53.3b	(.f64 -2/3 (/.f64 (.f64 c b) (*.f64 c a)))
▶	32.9b	(.f64 1 (/.f64 (/.f64 (.f64 c a) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 (.f64 c a) -3)) b))) a))
	39.3b	(/.f64 (+.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -3))) b)))) (*.f64 3 a))

Compiler

Compiled 11916 to 7109 computations (40.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.9b	(-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 (.f64 c a) -3)) b))
✓	1.5b	(/.f64 (/.f64 (.f64 c a) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 (*.f64 c a) -3)) b))) a)
✓	7.1b	(/.f64 (.f64 c a) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 (*.f64 c a) -3)) b)))
✓	11.2b	(sqrt.f64 (.f64 (.f64 c a) -3))

series697.0ms (6.6%)

Counts

4 → 42

Calls

4 calls:

319.0ms	(/.f64 (.f64 c a) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 (*.f64 c a) -3)) b)))
248.0ms	(/.f64 (/.f64 (.f64 c a) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 (*.f64 c a) -3)) b))) a)
115.0ms	(-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 (.f64 c a) -3)) b))
14.0ms	(sqrt.f64 (.f64 (.f64 c a) -3))

rewrite42.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`*-un-lft-identity_binary64`
66×	`times-frac_binary64`
64×	`add-sqr-sqrt_binary64`
50×	`add-cube-cbrt_binary64`
30×	`prod-diff_binary64`

Counts

4 → 176

Calls

4 calls:

9.0ms	(/.f64 (/.f64 (.f64 c a) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 (*.f64 c a) -3)) b))) a)
8.0ms	(/.f64 (.f64 c a) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 (*.f64 c a) -3)) b)))
5.0ms	(-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 (.f64 c a) -3)) b))
3.0ms	(sqrt.f64 (.f64 (.f64 c a) -3))

simplify183.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

508×	`fma-neg_binary64`
288×	`times-frac_binary64`
241×	`associate-/l*_binary64`
237×	`sub-neg_binary64`
184×	`associate-r_binary64`

Counts

218 → 280

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	409	8065
1	1038	6656
2	3934	6153
3	4719	6147
4	4914	6147

prune241.0ms (2.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	274	6	280
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	280	11	291

Error

4.2b

Counts

291 → 11

Alt Table

Status	Error	Program
	33.0b	(.f64 1 (/.f64 (/.f64 (.f64 c a) (-.f64 (neg.f64 b) (hypot.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 c a) -3))) (sqrt.f64 (sqrt.f64 (.f64 (*.f64 c a) -3)))) b))) a))
	47.1b	(.f64 1 (/.f64 (.f64 2 (*.f64 1 (/.f64 b -3))) a))
▶	29.7b	(.f64 1 (.f64 1 (/.f64 c (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 (.f64 c a) -3)) b)))))
	35.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
	34.6b	(.f64 1 (expm1.f64 (log1p.f64 (/.f64 c (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 (*.f64 c a) -3)) b))))))
	47.3b	(.f64 1 (fma.f64 2 (.f64 1 (/.f64 b (.f64 a -3))) (.f64 1/2 (/.f64 c b))))
	37.3b	(*.f64 -1/2 (/.f64 c b))
	42.6b	(/.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (*.f64 3 a))
	58.3b	(/.f64 (/.f64 (.f64 3 (.f64 c a)) (.f64 1/2 (/.f64 (pow.f64 (sqrt.f64 (.f64 -3 (.f64 c a))) 2) b))) (.f64 3 a))
	35.3b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c))))) (.f64 3 a))
	47.1b	(.f64 1 (.f64 2 (.f64 1 (/.f64 b (.f64 a -3)))))

Compiler

Compiled 10830 to 5984 computations (44.7% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 c (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 (.f64 c a) -3)) b)))
✓	0.3b	(.f64 (.f64 c a) -3)
	0.9b	(-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 (.f64 c a) -3)) b))
	11.2b	(sqrt.f64 (.f64 (.f64 c a) -3))

series259.0ms (2.4%)

Counts

2 → 38

Calls

2 calls:

254.0ms	(/.f64 c (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 (.f64 c a) -3)) b)))
5.0ms	(.f64 (.f64 c a) -3)

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`*-un-lft-identity_binary64`
22×	`add-sqr-sqrt_binary64`
18×	`times-frac_binary64`
14×	`add-cube-cbrt_binary64`
9×	`add-cbrt-cube_binary64`

Counts

2 → 63

Calls

2 calls:

5.0ms	(/.f64 c (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 (.f64 c a) -3)) b)))
4.0ms	(.f64 (.f64 c a) -3)

simplify83.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

625×	`associate-/l*_binary64`
467×	`associate-/r*_binary64`
354×	`fma-neg_binary64`
229×	`fma-def_binary64`
215×	`associate-*l/_binary64`

Counts

101 → 115

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	186	2398
1	455	2148
2	1501	2116
3	4776	2112
4	4960	2112

prune180.0ms (1.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	214	2	216
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	217	10	227

Error

4.2b

Counts

227 → 10

Alt Table

Status	Error	Program
	33.0b	(.f64 1 (/.f64 (/.f64 (.f64 c a) (-.f64 (neg.f64 b) (hypot.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 c a) -3))) (sqrt.f64 (sqrt.f64 (.f64 (*.f64 c a) -3)))) b))) a))
	47.1b	(.f64 1 (/.f64 (.f64 2 (*.f64 1 (/.f64 b -3))) a))
✓	29.7b	(.f64 1 (.f64 1 (/.f64 c (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 (.f64 c a) -3)) b)))))
	35.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
	34.6b	(.f64 1 (expm1.f64 (log1p.f64 (/.f64 c (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 (*.f64 c a) -3)) b))))))
	47.3b	(.f64 1 (fma.f64 2 (.f64 1 (/.f64 b (.f64 a -3))) (.f64 1/2 (/.f64 c b))))
	35.3b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c))))) (.f64 3 a))
	37.3b	(.f64 1 (.f64 1 (/.f64 c (*.f64 b -2))))
	51.0b	(.f64 1 (.f64 1 (/.f64 c (/.f64 (.f64 -3/2 (.f64 c a)) b))))
	47.1b	(.f64 1 (.f64 2 (.f64 1 (/.f64 b (.f64 a -3)))))

Compiler

Compiled 7614 to 4625 computations (39.3% saved)

regimes3.5s (32.6%)

Accuracy

Total 4.3b remaining (42.6%)

Threshold costs 0b (0%)

Counts

180 → 3

Compiler

Compiled 21388 to 14922 computations (30.2% saved)

bsearch72.0ms (0.7%)

Steps

Iters	Range		Point
5	1.8116479780854882e-99	6.715617076880025e-99	4.913578702369731e-99
10	-4.664788915091569e+159	-1.346939172091467e+144	-8.620998372327297e+152

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

12×	`*-commutative_binary64`
7×	`+-commutative_binary64`
6×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	33	55
1	50	53
2	61	53
3	74	53
4	80	53
5	83	53
6	84	53
7	82	53

end160.0ms (1.5%)

Compiler: Compiled 262 to 191 computations (27.1% saved)

Details

analyze654.0ms (6.2%)

sample2.6s (24.5%)

simplify349.0ms (3.3%)

prune4.0ms (0%)

localize9.0ms (0.1%)

series85.0ms (0.8%)

rewrite23.0ms (0.2%)

simplify122.0ms (1.1%)

prune174.0ms (1.6%)

localize14.0ms (0.1%)

series706.0ms (6.7%)

rewrite49.0ms (0.5%)

simplify157.0ms (1.5%)

prune238.0ms (2.3%)

localize11.0ms (0.1%)

series697.0ms (6.6%)

rewrite42.0ms (0.4%)

simplify183.0ms (1.7%)

prune241.0ms (2.3%)

localize12.0ms (0.1%)

series259.0ms (2.4%)

rewrite14.0ms (0.1%)

simplify83.0ms (0.8%)

prune180.0ms (1.7%)

regimes3.5s (32.6%)

bsearch72.0ms (0.7%)

simplify4.0ms (0%)

end160.0ms (1.5%)

Profiling