Details

analyze461.0ms (7.4%)

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
0%	99.9%	0.1%	5
25%	74.9%	0.1%	6
37.4%	62.4%	0.1%	7
56.2%	43.7%	0.1%	8
56.2%	43.7%	0.1%	9
65.5%	34.3%	0.1%	10
76.5%	23.4%	0.1%	11
76.5%	23.4%	0.1%	12
81.9%	17.9%	0.1%	13
87.8%	12.1%	0.1%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample3.0s (47.8%)

Results

1.2s	1348×	body	1024	valid
1.2s	5881×	body	128	valid
477.0ms	683×	body	512	valid
108.0ms	339×	body	256	valid
7.0ms	5×	body	2048	valid

Compiler

Compiled 26 to 18 computations (30.8% saved)

preprocess21.0ms (0.3%)

Algorithm

2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	56
0	3	3

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 12 to 8 computations (33.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14

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

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))

Compiler

Compiled 36 to 24 computations (33.3% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sin.f64 y)
✓	0.0b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
✓	0.2b	(*.f64 z (sin.f64 y))

series21.0ms (0.3%)

Counts

3 → 64

Calls

18 calls:

3.0ms	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))	x	-inf
2.0ms	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))	z	-inf
1.0ms	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))	z	inf
1.0ms	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))	x	0
1.0ms	(*.f64 z (sin.f64 y))	z	-inf

rewrite45.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

827×	`log1p-expm1-u_binary64`
827×	`expm1-log1p-u_binary64`
99×	`add-sqr-sqrt_binary64`
94×	`add-cbrt-cube_binary64`
91×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	178	23
2	2047	23

Stop Event

1×	node limit

Counts

3 → 50

simplify564.0ms (9.1%)

Algorithm

1×	egg-herbie

Rules

1657×	`sqr-pow_binary64`
731×	`pow-sqr_binary64`
54×	`cube-prod_binary64`
54×	`cube-mult_binary64`
54×	`unpow3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	717
1	81	717
2	102	717
3	129	717
4	160	717
5	191	717
6	225	717
7	260	717
8	299	717
9	339	717
10	383	717
11	428	717
12	477	717
13	527	717
14	581	717
15	636	717
16	695	717
17	755	717
18	819	717
19	884	717
20	953	717
21	1023	717
22	1097	717
23	1172	717
24	1251	717
25	1331	717
26	1415	717
27	1500	717
28	1589	717
29	1679	717
30	1773	717
31	1868	717
32	1967	717
33	2067	717
34	2171	717
35	2276	717
36	2385	717
37	2389	717
38	2391	717
39	2391	717
40	2500	717
41	2612	717
42	2727	717
43	2846	717
44	2966	717
45	3090	717
46	3215	717
47	3344	717
48	3474	717
49	3608	717
50	3743	717
51	3882	717
52	4022	717
53	4166	717
54	4311	717
55	4315	717
56	4317	717
57	4317	717
58	4465	717
59	4613	717
60	4767	717
61	4922	717

Stop Event

1×	node limit

Counts

114 → 73

prune60.0ms (1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	67	6	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	6	74

Error

0.0b

Counts

74 → 6

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (expm1.f64 (log1p.f64 (sin.f64 y)))))
	5.0b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (log.f64 (exp.f64 (sin.f64 y)))))
	0.9b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 z (.f64 (cbrt.f64 (pow.f64 (sin.f64 y) 2)) (cbrt.f64 (sin.f64 y)))))
	28.5b	(pow.f64 (sqrt.f64 (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))) 2)
	27.3b	(-.f64 (+.f64 x (cos.f64 y)) (pow.f64 (sqrt.f64 (*.f64 z (sin.f64 y))) 2))
	46.6b	(.f64 -1 (.f64 (sin.f64 y) z))

Compiler

Compiled 1297 to 522 computations (59.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (expm1.f64 (log1p.f64 (sin.f64 y)))))
✓	0.2b	(*.f64 z (expm1.f64 (log1p.f64 (sin.f64 y))))
✓	0.2b	(expm1.f64 (log1p.f64 (sin.f64 y)))
✓	0.3b	(log1p.f64 (sin.f64 y))

series175.0ms (2.8%)

Counts

4 → 84

Calls

21 calls:

78.0ms	(log1p.f64 (sin.f64 y))	y	inf
70.0ms	(log1p.f64 (sin.f64 y))	y	-inf
3.0ms	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (expm1.f64 (log1p.f64 (sin.f64 y)))))	z	0
3.0ms	(*.f64 z (expm1.f64 (log1p.f64 (sin.f64 y))))	z	-inf
2.0ms	(log1p.f64 (sin.f64 y))	y	0

rewrite51.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

892×	`expm1-log1p-u_binary64`
891×	`log1p-expm1-u_binary64`
107×	`add-sqr-sqrt_binary64`
101×	`add-cbrt-cube_binary64`
98×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	28
1	198	28
2	2218	28

Stop Event

1×	node limit

Counts

4 → 64

simplify398.0ms (6.4%)

Algorithm

1×	egg-herbie

Rules

1658×	`sqr-pow_binary64`
731×	`pow-sqr_binary64`
54×	`cube-prod_binary64`
54×	`cube-mult_binary64`
54×	`unpow3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	845
1	99	845
2	121	845
3	150	845
4	182	845
5	213	845
6	247	845
7	282	845
8	321	845
9	361	845
10	405	845
11	450	845
12	499	845
13	549	845
14	603	845
15	658	845
16	717	845
17	777	845
18	841	845
19	906	845
20	975	845
21	1045	845
22	1119	845
23	1194	845
24	1273	845
25	1353	845
26	1437	845
27	1522	845
28	1611	845
29	1701	845
30	1795	845
31	1890	845
32	1989	845
33	2089	845
34	2193	845
35	2298	845
36	2407	845
37	2411	845
38	2413	845
39	2413	845
40	2522	845
41	2634	845
42	2749	845
43	2868	845
44	2988	845
45	3112	845
46	3237	845
47	3366	845
48	3496	845
49	3630	845
50	3765	845
51	3904	845
52	4044	845
53	4188	845
54	4333	845
55	4337	845
56	4339	845
57	4339	845
58	4487	845
59	4635	845
60	4789	845
61	4944	845

Stop Event

1×	node limit

Counts

148 → 95

prune95.0ms (1.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	95	6	101

Error

0.0b

Counts

101 → 6

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (expm1.f64 (log1p.f64 (sin.f64 y)))))
	5.0b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (log.f64 (exp.f64 (sin.f64 y)))))
▶	0.9b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 z (.f64 (cbrt.f64 (pow.f64 (sin.f64 y) 2)) (cbrt.f64 (sin.f64 y)))))
	28.5b	(pow.f64 (sqrt.f64 (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))) 2)
	27.3b	(-.f64 (+.f64 x (cos.f64 y)) (pow.f64 (sqrt.f64 (*.f64 z (sin.f64 y))) 2))
	46.6b	(.f64 -1 (.f64 (sin.f64 y) z))

Compiler

Compiled 1652 to 692 computations (58.1% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (sin.f64 y) 2)
✓	0.3b	(*.f64 (cbrt.f64 (pow.f64 (sin.f64 y) 2)) (cbrt.f64 (sin.f64 y)))
✓	0.6b	(cbrt.f64 (sin.f64 y))
✓	13.4b	(cbrt.f64 (pow.f64 (sin.f64 y) 2))

series108.0ms (1.7%)

Counts

4 → 32

Calls

12 calls:

30.0ms	(cbrt.f64 (pow.f64 (sin.f64 y) 2))	y	-inf
29.0ms	(cbrt.f64 (pow.f64 (sin.f64 y) 2))	y	inf
18.0ms	(cbrt.f64 (sin.f64 y))	y	-inf
18.0ms	(cbrt.f64 (sin.f64 y))	y	inf
5.0ms	(pow.f64 (sin.f64 y) 2)	y	inf

rewrite42.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

454×	`log1p-expm1-u_binary64`
454×	`expm1-log1p-u_binary64`
428×	`pow1_binary64`
163×	`unpow-prod-down_binary64`
144×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	22
1	147	22
2	1271	22

Stop Event

1×	node limit

Counts

4 → 133

simplify266.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

1651×	`sqr-pow_binary64`
677×	`pow-sqr_binary64`
51×	`cube-prod_binary64`
51×	`cube-mult_binary64`
51×	`unpow3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	42	252
1	80	248
2	120	248
3	158	248
4	197	248
5	239	248
6	281	248
7	327	248
8	374	248
9	425	248
10	477	248
11	533	248
12	590	248
13	651	248
14	713	248
15	779	248
16	846	248
17	917	248
18	989	248
19	1065	248
20	1142	248
21	1223	248
22	1305	248
23	1391	248
24	1478	248
25	1569	248
26	1661	248
27	1757	248
28	1854	248
29	1955	248
30	2057	248
31	2163	248
32	2270	248
33	2381	248
34	2493	248
35	2497	248
36	2499	248
37	2499	248
38	2614	248
39	2729	248
40	2850	248
41	2972	248
42	3098	248
43	3225	248
44	3356	248
45	3488	248
46	3624	248
47	3761	248
48	3902	248
49	4044	248
50	4190	248
51	4337	248
52	4488	248
53	4492	248
54	4494	248
55	4494	248
56	4645	248
57	4799	248
58	4956	248

Stop Event

1×	node limit

Counts

165 → 148

prune120.0ms (1.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	148	0	148
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	148	6	154

Error

0.0b

Counts

154 → 6

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (expm1.f64 (log1p.f64 (sin.f64 y)))))
▶	5.0b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (log.f64 (exp.f64 (sin.f64 y)))))
✓	0.9b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 z (.f64 (cbrt.f64 (pow.f64 (sin.f64 y) 2)) (cbrt.f64 (sin.f64 y)))))
	28.5b	(pow.f64 (sqrt.f64 (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))) 2)
	27.3b	(-.f64 (+.f64 x (cos.f64 y)) (pow.f64 (sqrt.f64 (*.f64 z (sin.f64 y))) 2))
	46.6b	(.f64 -1 (.f64 (sin.f64 y) z))

Compiler

Compiled 2967 to 1381 computations (53.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (log.f64 (exp.f64 (sin.f64 y)))))
✓	0.1b	(exp.f64 (sin.f64 y))
✓	0.2b	(*.f64 z (log.f64 (exp.f64 (sin.f64 y))))
✓	2.4b	(log.f64 (exp.f64 (sin.f64 y)))

series23.0ms (0.4%)

Counts

4 → 76

Calls

21 calls:

3.0ms	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (log.f64 (exp.f64 (sin.f64 y)))))	x	0
2.0ms	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (log.f64 (exp.f64 (sin.f64 y)))))	x	inf
1.0ms	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (log.f64 (exp.f64 (sin.f64 y)))))	z	0
1.0ms	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (log.f64 (exp.f64 (sin.f64 y)))))	x	-inf
1.0ms	(*.f64 z (log.f64 (exp.f64 (sin.f64 y))))	z	-inf

rewrite51.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

884×	`log1p-expm1-u_binary64`
884×	`expm1-log1p-u_binary64`
107×	`add-sqr-sqrt_binary64`
101×	`add-cbrt-cube_binary64`
98×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	28
1	199	28
2	2207	28

Stop Event

1×	node limit

Counts

4 → 67

simplify412.0ms (6.6%)

Algorithm

1×	egg-herbie

Rules

1658×	`sqr-pow_binary64`
731×	`pow-sqr_binary64`
54×	`cube-prod_binary64`
54×	`cube-mult_binary64`
54×	`unpow3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	781
1	91	781
2	113	781
3	141	781
4	171	781
5	202	781
6	236	781
7	271	781
8	310	781
9	350	781
10	394	781
11	439	781
12	488	781
13	538	781
14	592	781
15	647	781
16	706	781
17	766	781
18	830	781
19	895	781
20	964	781
21	1034	781
22	1108	781
23	1183	781
24	1262	781
25	1342	781
26	1426	781
27	1511	781
28	1600	781
29	1690	781
30	1784	781
31	1879	781
32	1978	781
33	2078	781
34	2182	781
35	2287	781
36	2396	781
37	2400	781
38	2402	781
39	2402	781
40	2511	781
41	2623	781
42	2738	781
43	2857	781
44	2977	781
45	3101	781
46	3226	781
47	3355	781
48	3485	781
49	3619	781
50	3754	781
51	3893	781
52	4033	781
53	4177	781
54	4322	781
55	4326	781
56	4328	781
57	4328	781
58	4476	781
59	4624	781
60	4778	781
61	4933	781

Stop Event

1×	node limit

Counts

143 → 96

prune71.0ms (1.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	96	6	102

Error

0.0b

Counts

102 → 6

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (expm1.f64 (log1p.f64 (sin.f64 y)))))
✓	5.0b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (log.f64 (exp.f64 (sin.f64 y)))))
✓	0.9b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 z (.f64 (cbrt.f64 (pow.f64 (sin.f64 y) 2)) (cbrt.f64 (sin.f64 y)))))
	28.5b	(pow.f64 (sqrt.f64 (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))) 2)
	27.3b	(-.f64 (+.f64 x (cos.f64 y)) (pow.f64 (sqrt.f64 (*.f64 z (sin.f64 y))) 2))
	46.6b	(.f64 -1 (.f64 (sin.f64 y) z))

Compiler

Compiled 1568 to 615 computations (60.8% saved)

regimes120.0ms (1.9%)

Accuracy

Total 0.0b remaining (43.8%)

Threshold costs 0.0b (43.8%)

Counts

22 → 1

Compiler

Compiled 1227 to 827 computations (32.6% saved)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14

Stop Event

1×

saturated

end96.0ms (1.5%)

Stop Event

1×

fuel

Compiler

Compiled 110 to 78 computations (29.1% saved)

Details

analyze461.0ms (7.4%)

sample3.0s (47.8%)

preprocess21.0ms (0.3%)

simplify4.0ms (0.1%)

prune2.0ms (0%)

localize9.0ms (0.1%)

series21.0ms (0.3%)

rewrite45.0ms (0.7%)

simplify564.0ms (9.1%)

prune60.0ms (1%)

localize11.0ms (0.2%)

series175.0ms (2.8%)

rewrite51.0ms (0.8%)

simplify398.0ms (6.4%)

prune95.0ms (1.5%)

localize14.0ms (0.2%)

series108.0ms (1.7%)

rewrite42.0ms (0.7%)

simplify266.0ms (4.3%)

prune120.0ms (1.9%)

localize12.0ms (0.2%)

series23.0ms (0.4%)

rewrite51.0ms (0.8%)

simplify412.0ms (6.6%)

prune71.0ms (1.1%)

regimes120.0ms (1.9%)

simplify1.0ms (0%)

end96.0ms (1.5%)

Profiling