Details

analyze703.0ms (10.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
6.2%	93.6%	0.2%	8
25%	74.9%	0.2%	9
28.1%	71.7%	0.2%	10
29.6%	70.2%	0.2%	11
53%	46.8%	0.2%	12
71.3%	28.5%	0.2%	13
71.7%	28.1%	0.2%	14

Compiler

Compiled 20 to 12 computations (40% saved)

sample1.2s (18%)

Results

1.1s	8256×	body	128	valid
56.0ms	461×	body	128	invalid

Compiler

Compiled 40 to 24 computations (40% saved)

preprocess154.0ms (2.4%)

Algorithm

2×	egg-herbie

Rules

7×	`fma-neg_binary64`
7×	`fma-udef_binary64`
6×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	140
1	58	140
2	65	140
0	4	4

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 19 to 11 computations (42.1% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`fma-def_binary64`
1×	`fma-neg_binary64`
1×	`fma-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	20
1	15	20
2	16	20

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

26.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	26.1b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (fma.f64 c c (*.f64 d d)))

Compiler

Compiled 69 to 33 computations (52.2% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 b c) (.f64 a d))
✓	25.6b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (fma.f64 c c (*.f64 d d)))

series81.0ms (1.2%)

Counts

2 → 96

Calls

24 calls:

14.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (fma.f64 c c (*.f64 d d)))	b	-inf
10.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (fma.f64 c c (*.f64 d d)))	a	-inf
10.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (fma.f64 c c (*.f64 d d)))	b	0
9.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (fma.f64 c c (*.f64 d d)))	b	inf
9.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (fma.f64 c c (*.f64 d d)))	a	inf

rewrite41.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

380×	`unpow-prod-down_binary64`
305×	`pow2_binary64`
296×	`log-prod_binary64`
218×	`pow1/3_binary64`
218×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	30
1	217	29
2	2426	29

Stop Event

1×	node limit

Counts

2 → 67

simplify416.0ms (6.4%)

Algorithm

1×	egg-herbie

Rules

1734×	`sqr-pow_binary64`
834×	`pow-sqr_binary64`
82×	`cube-mult_binary64`
82×	`unpow3_binary64`
80×	`cube-prod_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	47	1734
1	72	1650
2	93	1650
3	114	1650
4	146	1650
5	180	1650
6	220	1650
7	263	1650
8	313	1650
9	366	1650
10	426	1650
11	489	1650
12	559	1650
13	632	1650
14	712	1650
15	795	1650
16	885	1650
17	978	1650
18	1078	1650
19	1181	1650
20	1291	1650
21	1404	1650
22	1524	1650
23	1647	1650
24	1777	1650
25	1910	1650
26	2050	1650
27	2193	1650
28	2201	1650
29	2205	1650
30	2205	1650
31	2353	1650
32	2502	1650
33	2662	1650
34	2825	1650
35	2995	1650
36	3168	1650
37	3348	1650
38	3531	1650
39	3721	1650
40	3914	1650
41	3962	1650
42	3966	1650
43	3966	1650
44	4159	1650
45	4359	1650
46	4566	1650
47	4780	1650
48	4997	1650

Stop Event

1×	node limit

Counts

163 → 90

prune63.0ms (1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	81	9	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	9	91

Error

3.5b

Counts

91 → 9

Alt Table

Status	Error	Program
▶	26.1b	(/.f64 (fma.f64 b c (neg.f64 (.f64 a d))) (fma.f64 c c (.f64 d d)))
	38.6b	(/.f64 (.f64 c b) (fma.f64 d d (.f64 c c)))
	37.8b	(pow.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b c) (.f64 a d))) (hypot.f64 c d)) 2)
	35.0b	(*.f64 -1 (/.f64 a d))
	42.5b	(/.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b c) (.f64 a d))) 2) (fma.f64 c c (*.f64 d d)))
	26.6b	(/.f64 (pow.f64 (cbrt.f64 (-.f64 (.f64 b c) (.f64 a d))) 3) (fma.f64 c c (*.f64 d d)))
	36.3b	(-.f64 (/.f64 b c) (/.f64 (*.f64 a d) (pow.f64 c 2)))
	38.4b	(/.f64 b c)
	38.9b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (.f64 b c) (.f64 a d)) (pow.f64 (hypot.f64 c d) 2)) 3))

Compiler

Compiled 2199 to 754 computations (65.7% saved)

localize9.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	25.6b	(/.f64 (fma.f64 b c (neg.f64 (.f64 a d))) (fma.f64 c c (.f64 d d)))

series83.0ms (1.3%)

Counts

1 → 48

Calls

12 calls:

25.0ms	(/.f64 (fma.f64 b c (neg.f64 (.f64 a d))) (fma.f64 c c (.f64 d d)))	a	0
11.0ms	(/.f64 (fma.f64 b c (neg.f64 (.f64 a d))) (fma.f64 c c (.f64 d d)))	b	0
9.0ms	(/.f64 (fma.f64 b c (neg.f64 (.f64 a d))) (fma.f64 c c (.f64 d d)))	b	-inf
9.0ms	(/.f64 (fma.f64 b c (neg.f64 (.f64 a d))) (fma.f64 c c (.f64 d d)))	b	inf
9.0ms	(/.f64 (fma.f64 b c (neg.f64 (.f64 a d))) (fma.f64 c c (.f64 d d)))	a	inf

rewrite164.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

814×	`log1p-expm1-u_binary64`
814×	`expm1-log1p-u_binary64`
110×	`add-sqr-sqrt_binary64`
101×	`add-log-exp_binary64`
100×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	203	19
2	2148	19

Stop Event

1×	node limit

Counts

1 → 16

simplify348.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

1734×	`sqr-pow_binary64`
874×	`pow-sqr_binary64`
82×	`cube-prod_binary64`
82×	`cube-mult_binary64`
82×	`unpow3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	45	1308
1	68	1224
2	88	1224
3	109	1224
4	141	1224
5	175	1224
6	215	1224
7	258	1224
8	308	1224
9	361	1224
10	421	1224
11	484	1224
12	554	1224
13	627	1224
14	707	1224
15	790	1224
16	880	1224
17	973	1224
18	1073	1224
19	1176	1224
20	1286	1224
21	1399	1224
22	1519	1224
23	1642	1224
24	1772	1224
25	1905	1224
26	2045	1224
27	2188	1224
28	2196	1224
29	2200	1224
30	2200	1224
31	2348	1224
32	2497	1224
33	2657	1224
34	2820	1224
35	2990	1224
36	3163	1224
37	3343	1224
38	3526	1224
39	3716	1224
40	3909	1224
41	3957	1224
42	3961	1224
43	3961	1224
44	4154	1224
45	4354	1224
46	4561	1224
47	4775	1224
48	4992	1224

Stop Event

1×	node limit

Counts

64 → 36

prune206.0ms (3.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	36	0	36
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	36	9	45

Error

3.5b

Counts

45 → 9

Alt Table

Status	Error	Program
✓	26.1b	(/.f64 (fma.f64 b c (neg.f64 (.f64 a d))) (fma.f64 c c (.f64 d d)))
	38.6b	(/.f64 (.f64 c b) (fma.f64 d d (.f64 c c)))
	37.8b	(pow.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b c) (.f64 a d))) (hypot.f64 c d)) 2)
	35.0b	(*.f64 -1 (/.f64 a d))
	42.5b	(/.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b c) (.f64 a d))) 2) (fma.f64 c c (*.f64 d d)))
▶	26.6b	(/.f64 (pow.f64 (cbrt.f64 (-.f64 (.f64 b c) (.f64 a d))) 3) (fma.f64 c c (*.f64 d d)))
	36.3b	(-.f64 (/.f64 b c) (/.f64 (*.f64 a d) (pow.f64 c 2)))
	38.4b	(/.f64 b c)
	38.9b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (.f64 b c) (.f64 a d)) (pow.f64 (hypot.f64 c d) 2)) 3))

Compiler

Compiled 901 to 423 computations (53.1% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (.f64 b c) (.f64 a d))
✓	0.5b	(pow.f64 (cbrt.f64 (-.f64 (.f64 b c) (.f64 a d))) 3)
✓	16.5b	(cbrt.f64 (-.f64 (.f64 b c) (.f64 a d)))
✓	25.6b	(/.f64 (pow.f64 (cbrt.f64 (-.f64 (.f64 b c) (.f64 a d))) 3) (fma.f64 c c (*.f64 d d)))

series1.2s (18.7%)

Counts

3 → 80

Calls

36 calls:

431.0ms	(pow.f64 (cbrt.f64 (-.f64 (.f64 b c) (.f64 a d))) 3)	a
211.0ms	(pow.f64 (cbrt.f64 (-.f64 (.f64 b c) (.f64 a d))) 3)	d
205.0ms	(cbrt.f64 (-.f64 (.f64 b c) (.f64 a d)))	d
70.0ms	(pow.f64 (cbrt.f64 (-.f64 (.f64 b c) (.f64 a d))) 3)	c
70.0ms	(pow.f64 (cbrt.f64 (-.f64 (.f64 b c) (.f64 a d))) 3)	b

rewrite50.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

338×	`log-prod_binary64`
245×	`log-pow_binary64`
243×	`pow1/3_binary64`
243×	`expm1-udef_binary64`
243×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	42
1	275	41
2	2842	41

Stop Event

1×	node limit

Counts

3 → 78

simplify529.0ms (8.1%)

Algorithm

1×	egg-herbie

Rules

1729×	`sqr-pow_binary64`
528×	`pow-sqr_binary64`
88×	`cube-prod_binary64`
88×	`cube-mult_binary64`
88×	`unpow3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	158	3740
1	288	3656
2	386	3656
3	487	3656
4	606	3656
5	728	3656
6	862	3656
7	1003	3656
8	1157	3656
9	1318	3656
10	1492	3656
11	1673	3656
12	1867	3656
13	2068	3656
14	2282	3656
15	2503	3656
16	2519	3656
17	2527	3656
18	2527	3656
19	2757	3656
20	2990	3656
21	3244	3656
22	3505	3656
23	3779	3656
24	4060	3656
25	4354	3656
26	4416	3656
27	4470	3656
28	4470	3656
29	4718	3656

Stop Event

1×	node limit

Counts

158 → 124

prune116.0ms (1.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	168	1	169
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	169	9	178

Error

3.5b

Counts

178 → 9

Alt Table

Status	Error	Program
✓	26.1b	(/.f64 (fma.f64 b c (neg.f64 (.f64 a d))) (fma.f64 c c (.f64 d d)))
	38.6b	(/.f64 (.f64 c b) (fma.f64 d d (.f64 c c)))
	37.8b	(pow.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b c) (.f64 a d))) (hypot.f64 c d)) 2)
▶	35.0b	(*.f64 -1 (/.f64 a d))
	46.0b	(/.f64 (pow.f64 (/.f64 (cbrt.f64 (-.f64 (pow.f64 (.f64 b c) 3) (pow.f64 (.f64 a d) 3))) (cbrt.f64 (+.f64 (pow.f64 (.f64 b c) 2) (+.f64 (pow.f64 (.f64 a d) 2) (.f64 (.f64 b c) (.f64 a d)))))) 3) (fma.f64 c c (.f64 d d)))
	42.5b	(/.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b c) (.f64 a d))) 2) (fma.f64 c c (*.f64 d d)))
	36.3b	(-.f64 (/.f64 b c) (/.f64 (*.f64 a d) (pow.f64 c 2)))
	38.4b	(/.f64 b c)
	38.9b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (.f64 b c) (.f64 a d)) (pow.f64 (hypot.f64 c d) 2)) 3))

Compiler

Compiled 5197 to 2118 computations (59.2% saved)

localize8.0ms (0.1%)

prune5.0ms (0.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	7	7
Picked	1	1
Done	1	1
Total	9	9

Error

3.5b

Counts

9 → 9

Alt Table

Status	Error	Program
✓	26.1b	(/.f64 (fma.f64 b c (neg.f64 (.f64 a d))) (fma.f64 c c (.f64 d d)))
	38.6b	(/.f64 (.f64 c b) (fma.f64 d d (.f64 c c)))
	37.8b	(pow.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b c) (.f64 a d))) (hypot.f64 c d)) 2)
✓	35.0b	(*.f64 -1 (/.f64 a d))
	46.0b	(/.f64 (pow.f64 (/.f64 (cbrt.f64 (-.f64 (pow.f64 (.f64 b c) 3) (pow.f64 (.f64 a d) 3))) (cbrt.f64 (+.f64 (pow.f64 (.f64 b c) 2) (+.f64 (pow.f64 (.f64 a d) 2) (.f64 (.f64 b c) (.f64 a d)))))) 3) (fma.f64 c c (.f64 d d)))
	42.5b	(/.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b c) (.f64 a d))) 2) (fma.f64 c c (*.f64 d d)))
	36.3b	(-.f64 (/.f64 b c) (/.f64 (*.f64 a d) (pow.f64 c 2)))
	38.4b	(/.f64 b c)
	38.9b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (.f64 b c) (.f64 a d)) (pow.f64 (hypot.f64 c d) 2)) 3))

Compiler

Compiled 168 to 105 computations (37.5% saved)

regimes911.0ms (13.9%)

Accuracy

Total 10.4b remaining (72.2%)

Threshold costs 0b (0%)

Counts

50 → 5

Compiler

Compiled 6013 to 3524 computations (41.4% saved)

bsearch86.0ms (1.3%)

Algorithm

4×	binary-search

Calls

4 calls:

24.0ms	d
23.0ms	d
22.0ms	d
15.0ms	d

Steps

Iters	Point		Range
5.131772163378566e+121	∈ [	9.109824581873085e+117	,	9.07981629889916e+121	]
3.216419037427215e-136	∈ [	1.762110471008832e-136	,	1.145135322564555e-135	]
-2.5191708025146317e-157	∈ [	-1.1707068543614303e-156	,	-5.771789708303048e-161	]
-2.4710460232761658e+98	∈ [	-5.187816570186289e+98	,	-4.666706069647747e+96	]

Compiler

Compiled 5 to 4 computations (20% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	94

Stop Event

1×

saturated

end130.0ms (2%)

Stop Event

1×

fuel

Compiler

Compiled 306 to 169 computations (44.8% saved)

Details

analyze703.0ms (10.8%)

sample1.2s (18%)

preprocess154.0ms (2.4%)

simplify4.0ms (0.1%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series81.0ms (1.2%)

rewrite41.0ms (0.6%)

simplify416.0ms (6.4%)

prune63.0ms (1%)

localize9.0ms (0.1%)

series83.0ms (1.3%)

rewrite164.0ms (2.5%)

simplify348.0ms (5.3%)

prune206.0ms (3.2%)

localize12.0ms (0.2%)

series1.2s (18.7%)

rewrite50.0ms (0.8%)

simplify529.0ms (8.1%)

prune116.0ms (1.8%)

localize8.0ms (0.1%)

prune5.0ms (0.1%)

regimes911.0ms (13.9%)

bsearch86.0ms (1.3%)

simplify5.0ms (0.1%)

end130.0ms (2%)

Profiling