Details

analyze1.3s (20.6%)

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
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
3.5%	96.2%	0.2%	10
9.2%	90.6%	0.2%	11
13.7%	86%	0.2%	12
22.1%	77.7%	0.2%	13
23%	76.7%	0.2%	14

Compiler

Compiled 19 to 12 computations (36.8% saved)

sample1.4s (21.9%)

Results

898.0ms	6998×	body	128	valid
164.0ms	379×	body	1024	valid
135.0ms	467×	body	512	valid
107.0ms	766×	body	128	invalid
72.0ms	346×	body	256	valid
33.0ms	66×	body	2048	valid

Compiler

Compiled 38 to 24 computations (36.8% saved)

preprocess33.0ms (0.5%)

Algorithm

2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	209
0	5	5

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 18 to 11 computations (38.9% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	19

Stop Event

1×

saturated

Counts

1 → 1

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

17.7b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	17.7b	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

Compiler

Compiled 54 to 33 computations (38.9% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 z t) y)
✓	2.6b	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))
✓	11.6b	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))

series245.0ms (3.8%)

Counts

3 → 120

Calls

36 calls:

168.0ms	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))	a	inf
5.0ms	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))	y	inf
4.0ms	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))	t	-inf
4.0ms	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))	a	-inf
3.0ms	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))	z	inf

rewrite48.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

355×	`log-prod_binary64`
250×	`expm1-udef_binary64`
250×	`log1p-udef_binary64`
245×	`log-pow_binary64`
143×	`prod-diff_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	39
1	245	39
2	2868	39

Stop Event

1×	node limit

Counts

3 → 64

simplify678.0ms (10.4%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	178	3588
1	204	3588
2	221	3588
3	244	3588
4	277	3588
5	311	3588
6	351	3588
7	394	3588
8	444	3588
9	497	3588
10	557	3588
11	620	3588
12	690	3588
13	763	3588
14	843	3588
15	926	3588
16	1016	3588
17	1109	3588
18	1209	3588
19	1312	3588
20	1422	3588
21	1535	3588
22	1655	3588
23	1778	3588
24	1908	3588
25	2041	3588
26	2181	3588
27	2324	3588
28	2332	3588
29	2336	3588
30	2336	3588
31	2484	3588
32	2633	3588
33	2793	3588
34	2956	3588
35	3126	3588
36	3299	3588
37	3479	3588
38	3662	3588
39	3852	3588
40	4045	3588
41	4093	3588
42	4097	3588
43	4097	3588
44	4290	3588
45	4490	3588
46	4697	3588
47	4911	3588

Stop Event

1×	node limit

Counts

184 → 137

prune97.0ms (1.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	131	6	137
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	132	6	138

Error

0.7b

Counts

138 → 6

Alt Table

Status	Error	Program
	17.8b	(-.f64 (+.f64 x y) (/.f64 (pow.f64 (cbrt.f64 (*.f64 (-.f64 z t) y)) 3) (-.f64 a t)))
	37.4b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) (+.f64 (/.f64 (.f64 y (.f64 a z)) (pow.f64 t 2)) x)) (+.f64 (/.f64 (.f64 y (pow.f64 a 2)) (pow.f64 t 2)) (/.f64 (*.f64 a y) t)))
	27.4b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 a y) t))
▶	15.6b	(-.f64 (+.f64 x y) (/.f64 (*.f64 y z) (-.f64 a t)))
	40.9b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) y)
	26.8b	x

Compiler

Compiled 4311 to 1298 computations (69.9% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 x y) (/.f64 (*.f64 y z) (-.f64 a t)))
✓	6.6b	(/.f64 (*.f64 y z) (-.f64 a t))

series66.0ms (1%)

Counts

2 → 84

Calls

27 calls:

21.0ms	(-.f64 (+.f64 x y) (/.f64 (*.f64 y z) (-.f64 a t)))	z	inf
3.0ms	(/.f64 (*.f64 y z) (-.f64 a t))	z	-inf
2.0ms	(/.f64 (*.f64 y z) (-.f64 a t))	y	-inf
2.0ms	(-.f64 (+.f64 x y) (/.f64 (*.f64 y z) (-.f64 a t)))	a	0
2.0ms	(-.f64 (+.f64 x y) (/.f64 (*.f64 y z) (-.f64 a t)))	t	0

rewrite38.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

324×	`pow2_binary64`
318×	`log-prod_binary64`
227×	`pow1/3_binary64`
224×	`expm1-udef_binary64`
224×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	26
1	221	26
2	2555	26

Stop Event

1×	node limit

Counts

2 → 48

simplify460.0ms (7.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	98	1962
1	122	1962
2	138	1962
3	161	1962
4	194	1962
5	228	1962
6	268	1962
7	311	1962
8	361	1962
9	414	1962
10	474	1962
11	537	1962
12	607	1962
13	680	1962
14	760	1962
15	843	1962
16	933	1962
17	1026	1962
18	1126	1962
19	1229	1962
20	1339	1962
21	1452	1962
22	1572	1962
23	1695	1962
24	1825	1962
25	1958	1962
26	2098	1962
27	2241	1962
28	2249	1962
29	2253	1962
30	2253	1962
31	2401	1962
32	2550	1962
33	2710	1962
34	2873	1962
35	3043	1962
36	3216	1962
37	3396	1962
38	3579	1962
39	3769	1962
40	3962	1962
41	4010	1962
42	4014	1962
43	4014	1962
44	4207	1962
45	4407	1962
46	4614	1962
47	4828	1962

Stop Event

1×	node limit

Counts

132 → 99

prune59.0ms (0.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	99	0	99
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	99	6	105

Error

0.7b

Counts

105 → 6

Alt Table

Status	Error	Program
▶	17.8b	(-.f64 (+.f64 x y) (/.f64 (pow.f64 (cbrt.f64 (*.f64 (-.f64 z t) y)) 3) (-.f64 a t)))
	37.4b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) (+.f64 (/.f64 (.f64 y (.f64 a z)) (pow.f64 t 2)) x)) (+.f64 (/.f64 (.f64 y (pow.f64 a 2)) (pow.f64 t 2)) (/.f64 (*.f64 a y) t)))
	27.4b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 a y) t))
✓	15.6b	(-.f64 (+.f64 x y) (/.f64 (*.f64 y z) (-.f64 a t)))
	40.9b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) y)
	26.8b	x

Compiler

Compiled 2523 to 765 computations (69.7% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(pow.f64 (cbrt.f64 (*.f64 (-.f64 z t) y)) 3)
✓	8.6b	(-.f64 (+.f64 x y) (/.f64 (pow.f64 (cbrt.f64 (*.f64 (-.f64 z t) y)) 3) (-.f64 a t)))
✓	11.6b	(/.f64 (pow.f64 (cbrt.f64 (*.f64 (-.f64 z t) y)) 3) (-.f64 a t))
✓	14.0b	(cbrt.f64 (*.f64 (-.f64 z t) y))

series572.0ms (8.8%)

Counts

4 → 124

Calls

45 calls:

136.0ms	(pow.f64 (cbrt.f64 (*.f64 (-.f64 z t) y)) 3)	t	0
63.0ms	(/.f64 (pow.f64 (cbrt.f64 (*.f64 (-.f64 z t) y)) 3) (-.f64 a t))	y	-inf
62.0ms	(-.f64 (+.f64 x y) (/.f64 (pow.f64 (cbrt.f64 (*.f64 (-.f64 z t) y)) 3) (-.f64 a t)))	y	-inf
57.0ms	(pow.f64 (cbrt.f64 (*.f64 (-.f64 z t) y)) 3)	z	0
56.0ms	(-.f64 (+.f64 x y) (/.f64 (pow.f64 (cbrt.f64 (*.f64 (-.f64 z t) y)) 3) (-.f64 a t)))	z	-inf

rewrite50.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

279×	`expm1-udef_binary64`
279×	`log1p-udef_binary64`
273×	`log-pow_binary64`
155×	`add-sqr-sqrt_binary64`
153×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	48
1	305	48
2	3311	48

Stop Event

1×	node limit

Counts

4 → 84

simplify574.0ms (8.8%)

Algorithm

1×	egg-herbie

Rules

1696×	`sqr-pow_binary64`
444×	`pow-sqr_binary64`
75×	`cube-mult_binary64`
75×	`unpow3_binary64`
72×	`cube-prod_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	283	4549
1	414	4549
2	519	4549
3	629	4549
4	751	4549
5	873	4549
6	1004	4549
7	1140	4549
8	1286	4549
9	1437	4549
10	1598	4549
11	1764	4549
12	1940	4549
13	2121	4549
14	2312	4549
15	2508	4549
16	2714	4549
17	2756	4549
18	2788	4549
19	2788	4549
20	2964	4549
21	3174	4549
22	3401	4549
23	3633	4549
24	3875	4549
25	4122	4549
26	4379	4549
27	4641	4549
28	4913	4549
29	4925	4549
30	4931	4549
31	4931	4549

Stop Event

1×	node limit

Counts

208 → 181

prune124.0ms (1.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	181	0	181
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	181	6	187

Error

0.7b

Counts

187 → 6

Alt Table

Status	Error	Program
✓	17.8b	(-.f64 (+.f64 x y) (/.f64 (pow.f64 (cbrt.f64 (*.f64 (-.f64 z t) y)) 3) (-.f64 a t)))
	37.4b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) (+.f64 (/.f64 (.f64 y (.f64 a z)) (pow.f64 t 2)) x)) (+.f64 (/.f64 (.f64 y (pow.f64 a 2)) (pow.f64 t 2)) (/.f64 (*.f64 a y) t)))
	27.4b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 a y) t))
✓	15.6b	(-.f64 (+.f64 x y) (/.f64 (*.f64 y z) (-.f64 a t)))
	40.9b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) y)
▶	26.8b	x

Compiler

Compiled 5949 to 2337 computations (60.7% saved)

localize1.0ms (0%)

prune3.0ms (0%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	3	3
Picked	1	1
Done	2	2
Total	6	6

Error

0.7b

Counts

6 → 6

Alt Table

Status	Error	Program
✓	17.8b	(-.f64 (+.f64 x y) (/.f64 (pow.f64 (cbrt.f64 (*.f64 (-.f64 z t) y)) 3) (-.f64 a t)))
	37.4b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) (+.f64 (/.f64 (.f64 y (.f64 a z)) (pow.f64 t 2)) x)) (+.f64 (/.f64 (.f64 y (pow.f64 a 2)) (pow.f64 t 2)) (/.f64 (*.f64 a y) t)))
	27.4b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 a y) t))
✓	15.6b	(-.f64 (+.f64 x y) (/.f64 (*.f64 y z) (-.f64 a t)))
	40.9b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) y)
✓	26.8b	x

Compiler

Compiled 119 to 76 computations (36.1% saved)

regimes560.0ms (8.6%)

Accuracy

Total 6.2b remaining (88%)

Threshold costs 0b (0%)

Counts

29 → 5

Compiler

Compiled 3456 to 2178 computations (37% saved)

bsearch1.0ms (0%)

Algorithm

4×	left-value

Calls

4 calls:

0.0ms	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))
0.0ms	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))
0.0ms	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))
0.0ms	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

Steps

Iters	Point		Range
1.290717785987541e+304	∈ [	1.290717785987541e+304	,	#hash((type . real) (value . +inf))	]
0.0	∈ [	0.0	,	1.2725898766180734e-239	]
-4.1468547448321337e-165	∈ [	-4.1468547448321337e-165	,	-2.872848349932294e-188	]
#hash((type . real) (value . -inf))	∈ [	#hash((type . real) (value . -inf))	,	-1.866989739836643e+301	]

Compiler

Compiled 18 to 11 computations (38.9% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	197
1	38	197

Stop Event

1×

saturated

end104.0ms (1.6%)

Stop Event

1×

fuel

Compiler

Compiled 395 to 154 computations (61% saved)

Details

analyze1.3s (20.6%)

sample1.4s (21.9%)

preprocess33.0ms (0.5%)

simplify5.0ms (0.1%)

prune2.0ms (0%)

localize9.0ms (0.1%)

series245.0ms (3.8%)

rewrite48.0ms (0.7%)

simplify678.0ms (10.4%)

prune97.0ms (1.5%)

localize7.0ms (0.1%)

series66.0ms (1%)

rewrite38.0ms (0.6%)

simplify460.0ms (7.1%)

prune59.0ms (0.9%)

localize14.0ms (0.2%)

series572.0ms (8.8%)

rewrite50.0ms (0.8%)

simplify574.0ms (8.8%)

prune124.0ms (1.9%)

localize1.0ms (0%)

prune3.0ms (0%)

regimes560.0ms (8.6%)

bsearch1.0ms (0%)

simplify3.0ms (0%)

end104.0ms (1.6%)

Profiling