Details

analyze3.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1

Compiler

Compiled 38 to 21 computations (44.7% saved)

sample2.0s (26.6%)

Results

2.0s

8256×

body

128

valid

Compiler

Compiled 76 to 42 computations (44.7% saved)

preprocess12.0ms (0.2%)

Algorithm

2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	72
0	2	2

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 23 to 10 computations (56.5% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	36

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

0.7b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.7b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))

Compiler

Compiled 69 to 30 computations (56.5% saved)

localize33.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(*.f32 x (PI.f32))
✓	0.4b	(sin.f32 (.f32 (.f32 x (PI.f32)) tau))
✓	0.4b	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
✓	0.4b	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))

series41.0ms (0.5%)

Counts

4 → 72

Calls

18 calls:

6.0ms	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))	x	-inf
5.0ms	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))	tau	-inf
4.0ms	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))	tau	inf
4.0ms	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))	x	inf
3.0ms	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))	x	0

rewrite41.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

748×	`log1p-expm1-u_binary32`
748×	`expm1-log1p-u_binary32`
181×	`expm1-udef_binary32`
181×	`log1p-udef_binary32`
100×	`add-sqr-sqrt_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	49
1	181	49
2	1933	49

Stop Event

1×	node limit

Counts

4 → 61

simplify317.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

1701×	`sqr-pow_binary32`
723×	`pow-sqr_binary32`
90×	`cube-prod_binary32`
90×	`cube-mult_binary32`
90×	`unpow3_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	78	1330
1	138	1330
2	178	1330
3	224	1330
4	284	1330
5	353	1330
6	426	1330
7	509	1330
8	597	1330
9	695	1330
10	798	1330
11	911	1330
12	1029	1330
13	1157	1330
14	1290	1330
15	1433	1330
16	1581	1330
17	1739	1330
18	1902	1330
19	2075	1330
20	2253	1330
21	2265	1330
22	2271	1330
23	2271	1330
24	2456	1330
25	2643	1330
26	2846	1330
27	3054	1330
28	3272	1330
29	3495	1330
30	3728	1330
31	3966	1330
32	4214	1330
33	4226	1330
34	4232	1330
35	4232	1330
36	4482	1330
37	4739	1330

Stop Event

1×	node limit

Counts

133 → 84

prune211.0ms (2.8%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	113	16	129
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	114	16	130

Error

0.2b

Counts

130 → 16

Alt Table

Status	Error	Program
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))))
	0.8b	(.f32 (-.f32 (exp.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)))) 1) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (pow.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32)))) 3))
	1.1b	(.f32 (/.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) 3) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	2.1b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (-.f32 (fma.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (pow.f32 x 4)) 1) (fma.f32 1/5040 (.f32 (pow.f32 (PI.f32) 6) (pow.f32 x 6)) (.f32 1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 x x))))))
	1.2b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (pow.f32 (cbrt.f32 (.f32 x (PI.f32))) 3) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
▶	0.7b	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.6b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (pow.f32 (pow.f32 (*.f32 x (PI.f32)) 3) 1/3)))
	0.9b	(.f32 (pow.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))) 3) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	3.8b	(.f32 (-.f32 (+.f32 1 (.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (.f32 (pow.f32 tau 4) (pow.f32 x 4))))) (fma.f32 1/5040 (.f32 (pow.f32 (PI.f32) 6) (.f32 (pow.f32 tau 6) (pow.f32 x 6))) (.f32 1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 tau tau) (.f32 x x)))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	5.7b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (-.f32 (exp.f32 (log1p.f32 (.f32 x (PI.f32)))) 1)) (*.f32 x (PI.f32))))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.0b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (pow.f32 (sqrt.f32 (.f32 x (PI.f32))) 2)) (*.f32 x (PI.f32))))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (-.f32 (exp.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))) 1))
	5.6b	(.f32 (/.f32 (sin.f32 (.f32 (log.f32 (+.f32 1 (expm1.f32 (.f32 x (PI.f32))))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.8b	(.f32 (/.f32 (expm1.f32 (log1p.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))

Compiler

Compiled 4309 to 1383 computations (67.9% saved)

localize43.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f32 (PI.f32) (.f32 tau x))
✓	0.4b	(sin.f32 (.f32 (PI.f32) (.f32 tau x)))
	0.4b	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
✓	0.4b	(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))

series57.0ms (0.7%)

Counts

3 → 16

Calls

18 calls:

20.0ms	(sin.f32 (.f32 (PI.f32) (.f32 tau x)))	tau	-inf
6.0ms	(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))	tau	-inf
5.0ms	(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))	x	-inf
4.0ms	(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))	tau	inf
4.0ms	(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))	x	inf

rewrite46.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

595×	`log1p-expm1-u_binary32`
595×	`expm1-log1p-u_binary32`
200×	`pow2_binary32`
198×	`log-prod_binary32`
154×	`log-pow_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	38
1	145	38
2	1544	38

Stop Event

1×	node limit

Counts

3 → 58

simplify225.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

1701×	`sqr-pow_binary32`
771×	`pow-sqr_binary32`
93×	`cube-prod_binary32`
93×	`cube-mult_binary32`
93×	`unpow3_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	584
1	119	584
2	159	584
3	205	584
4	265	584
5	334	584
6	407	584
7	490	584
8	578	584
9	676	584
10	779	584
11	892	584
12	1010	584
13	1138	584
14	1271	584
15	1414	584
16	1562	584
17	1720	584
18	1883	584
19	2056	584
20	2234	584
21	2246	584
22	2252	584
23	2252	584
24	2437	584
25	2624	584
26	2827	584
27	3035	584
28	3253	584
29	3476	584
30	3709	584
31	3947	584
32	4195	584
33	4207	584
34	4213	584
35	4213	584
36	4463	584
37	4720	584
38	4988	584

Stop Event

1×	node limit

Counts

74 → 71

prune139.0ms (1.8%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	103	8	111
Fresh	6	9	15
Picked	1	0	1
Done	0	0	0
Total	110	17	127

Error

0.2b

Counts

127 → 17

Alt Table

Status	Error	Program
	0.8b	(.f32 (-.f32 (exp.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))))) 1) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (pow.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32)))) 3))
	0.9b	(.f32 (pow.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))) 3) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	3.8b	(.f32 (-.f32 (+.f32 1 (.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (.f32 (pow.f32 tau 4) (pow.f32 x 4))))) (fma.f32 1/5040 (.f32 (pow.f32 (PI.f32) 6) (.f32 (pow.f32 tau 6) (pow.f32 x 6))) (.f32 1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 tau tau) (.f32 x x)))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	5.7b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (-.f32 (exp.f32 (log1p.f32 (.f32 x (PI.f32)))) 1)) (*.f32 x (PI.f32))))
	1.0b	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (pow.f32 (sqrt.f32 (.f32 (PI.f32) (.f32 tau x))) 2)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))))
	1.0b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (pow.f32 (sqrt.f32 (.f32 x (PI.f32))) 2)) (*.f32 x (PI.f32))))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (-.f32 (exp.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))) 1))
	1.2b	(.f32 (+.f32 (log.f32 (sqrt.f32 (exp.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))))) (log.f32 (sqrt.f32 (exp.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	4.8b	(.f32 (/.f32 (log.f32 (exp.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))))) (.f32 (PI.f32) (.f32 tau x))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.1b	(.f32 (/.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x)))) 3) (.f32 (PI.f32) (.f32 tau x))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.4b	(.f32 (+.f32 (log.f32 (pow.f32 (cbrt.f32 (exp.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))))) 2)) (log.f32 (cbrt.f32 (exp.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.6b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (pow.f32 (pow.f32 (*.f32 x (PI.f32)) 3) 1/3)))
	5.6b	(.f32 (/.f32 (sin.f32 (.f32 (log.f32 (+.f32 1 (expm1.f32 (.f32 x (PI.f32))))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.1b	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (pow.f32 (cbrt.f32 (.f32 (PI.f32) (.f32 tau x))) 3)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
▶	0.7b	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))) (cbrt.f32 (/.f32 (pow.f32 (sin.f32 (.f32 x (PI.f32))) 3) (pow.f32 (*.f32 x (PI.f32)) 3))))

Compiler

Compiled 4132 to 1340 computations (67.6% saved)

localize635.0ms (8.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.4b	(sin.f32 (.f32 (PI.f32) (.f32 tau x)))
	0.4b	(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x)))
✓	0.7b	(pow.f32 (sin.f32 (*.f32 x (PI.f32))) 3)
✓	0.8b	(pow.f32 (*.f32 x (PI.f32)) 3)

series18.0ms (0.2%)

Counts

2 → 24

Calls

6 calls:

6.0ms	(pow.f32 (sin.f32 (*.f32 x (PI.f32))) 3)	x	0
3.0ms	(pow.f32 (sin.f32 (*.f32 x (PI.f32))) 3)	x	-inf
2.0ms	(pow.f32 (sin.f32 (*.f32 x (PI.f32))) 3)	x	inf
2.0ms	(pow.f32 (*.f32 x (PI.f32)) 3)	x	-inf
2.0ms	(pow.f32 (*.f32 x (PI.f32)) 3)	x	0

rewrite32.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

584×	`log1p-expm1-u_binary32`
584×	`expm1-log1p-u_binary32`
197×	`log-prod_binary32`
189×	`pow2_binary32`
136×	`log-pow_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	157	18
2	1604	18

Stop Event

1×	node limit

Counts

2 → 32

simplify849.0ms (11.1%)

Algorithm

1×	egg-herbie

Rules

1494×	`sqr-pow_binary32`
3×	`cube-mult_binary32`
3×	`unpow3_binary32`
2×	`fma-def_binary32`
1×	`fma-neg_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	346
1	73	346
2	104	346
3	134	346
4	164	346
5	194	346
6	224	346
7	254	346
8	284	346
9	314	346
10	344	346
11	374	346
12	404	346
13	434	346
14	464	346
15	494	346
16	524	346
17	554	346
18	584	346
19	614	346
20	644	346
21	674	346
22	704	346
23	734	346
24	764	346
25	794	346
26	824	346
27	854	346
28	884	346
29	914	346
30	944	346
31	974	346
32	1004	346
33	1034	346
34	1064	346
35	1094	346
36	1124	346
37	1154	346
38	1184	346
39	1214	346
40	1244	346
41	1274	346
42	1304	346
43	1334	346
44	1364	346
45	1394	346
46	1424	346
47	1454	346
48	1484	346
49	1514	346
50	1544	346
51	1574	346
52	1604	346
53	1634	346
54	1664	346
55	1694	346
56	1724	346
57	1754	346
58	1784	346
59	1814	346
60	1844	346
61	1874	346
62	1904	346
63	1934	346
64	1964	346
65	1994	346
66	2024	346
67	2054	346
68	2084	346
69	2114	346
70	2144	346
71	2174	346
72	2204	346
73	2234	346
74	2264	346
75	2294	346
76	2324	346
77	2354	346
78	2384	346
79	2414	346
80	2444	346
81	2474	346
82	2504	346
83	2534	346
84	2564	346
85	2594	346
86	2624	346
87	2654	346
88	2684	346
89	2714	346
90	2744	346
91	2774	346
92	2804	346
93	2834	346
94	2864	346
95	2894	346
96	2924	346
97	2954	346
98	2984	346
99	3014	346
100	3044	346
101	3074	346
102	3104	346
103	3134	346
104	3164	346
105	3194	346
106	3224	346
107	3254	346
108	3284	346
109	3314	346
110	3344	346
111	3374	346
112	3378	346
113	3404	346
114	3430	346
115	3456	346
116	3482	346
117	3508	346
118	3534	346
119	3584	346
120	3614	346
121	3644	346
122	3674	346
123	3704	346
124	3734	346
125	3764	346
126	3794	346
127	3824	346
128	3854	346
129	3884	346
130	3914	346
131	3944	346
132	3974	346
133	4004	346
134	4034	346
135	4064	346
136	4094	346
137	4124	346
138	4154	346
139	4184	346
140	4214	346
141	4244	346
142	4274	346
143	4304	346
144	4334	346
145	4364	346
146	4394	346
147	4424	346
148	4454	346
149	4484	346
150	4514	346
151	4544	346
152	4574	346
153	4604	346
154	4634	346
155	4664	346
156	4694	346
157	4724	346
158	4754	346
159	4784	346
160	4814	346
161	4844	346
162	4874	346
163	4904	346
164	4934	346
165	4964	346
166	4994	346

Stop Event

1×	node limit

Counts

56 → 38

prune131.0ms (1.7%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	88	4	92
Fresh	3	13	16
Picked	1	0	1
Done	0	0	0
Total	92	17	109

Error

0.1b

Counts

109 → 17

Alt Table

Status	Error	Program
	0.8b	(.f32 (-.f32 (exp.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))))) 1) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (pow.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32)))) 3))
	4.8b	(.f32 (/.f32 (log.f32 (+.f32 1 (expm1.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x)))))) (.f32 (PI.f32) (.f32 tau x))) (cbrt.f32 (/.f32 (pow.f32 (sin.f32 (.f32 x (PI.f32))) 3) (pow.f32 (*.f32 x (PI.f32)) 3))))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (-.f32 (exp.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))) 1))
▶	0.7b	(.f32 (cbrt.f32 (/.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) 3) (pow.f32 (.f32 (PI.f32) (.f32 tau x)) 3))) (cbrt.f32 (/.f32 (pow.f32 (sin.f32 (.f32 x (PI.f32))) 3) (pow.f32 (*.f32 x (PI.f32)) 3))))
	1.4b	(.f32 (+.f32 (log.f32 (pow.f32 (cbrt.f32 (exp.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))))) 2)) (log.f32 (cbrt.f32 (exp.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	17.5b	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))) (cbrt.f32 (/.f32 (+.f32 (log.f32 (sqrt.f32 (exp.f32 (pow.f32 (sin.f32 (.f32 x (PI.f32))) 3)))) (log.f32 (sqrt.f32 (exp.f32 (pow.f32 (sin.f32 (.f32 x (PI.f32))) 3))))) (pow.f32 (.f32 x (PI.f32)) 3))))
	0.9b	(.f32 (pow.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))) 3) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	3.8b	(.f32 (-.f32 (+.f32 1 (.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (.f32 (pow.f32 tau 4) (pow.f32 x 4))))) (fma.f32 1/5040 (.f32 (pow.f32 (PI.f32) 6) (.f32 (pow.f32 tau 6) (pow.f32 x 6))) (.f32 1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 tau tau) (.f32 x x)))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	5.7b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (-.f32 (exp.f32 (log1p.f32 (.f32 x (PI.f32)))) 1)) (*.f32 x (PI.f32))))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))))
	1.0b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (pow.f32 (sqrt.f32 (.f32 x (PI.f32))) 2)) (*.f32 x (PI.f32))))
	16.6b	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))) (cbrt.f32 (/.f32 (log.f32 (exp.f32 (pow.f32 (sin.f32 (.f32 x (PI.f32))) 3))) (pow.f32 (*.f32 x (PI.f32)) 3))))
	1.1b	(.f32 (/.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x)))) 3) (.f32 (PI.f32) (.f32 tau x))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.6b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (pow.f32 (pow.f32 (*.f32 x (PI.f32)) 3) 1/3)))
	5.6b	(.f32 (/.f32 (sin.f32 (.f32 (log.f32 (+.f32 1 (expm1.f32 (.f32 x (PI.f32))))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.1b	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (pow.f32 (cbrt.f32 (.f32 (PI.f32) (.f32 tau x))) 3)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))

Compiler

Compiled 4184 to 1843 computations (56% saved)

localize66.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.7b	(pow.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) 3)
	0.7b	(pow.f32 (sin.f32 (*.f32 x (PI.f32))) 3)
✓	0.7b	(pow.f32 (.f32 (PI.f32) (.f32 tau x)) 3)
	0.8b	(pow.f32 (*.f32 x (PI.f32)) 3)

series48.0ms (0.6%)

Counts

2 → 32

Calls

12 calls:

6.0ms	(pow.f32 (.f32 (PI.f32) (.f32 tau x)) 3)	x	0
6.0ms	(pow.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) 3)	tau	0
6.0ms	(pow.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) 3)	x	0
4.0ms	(pow.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) 3)	tau	inf
4.0ms	(pow.f32 (.f32 (PI.f32) (.f32 tau x)) 3)	x	-inf

rewrite40.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

728×	`log1p-expm1-u_binary32`
728×	`expm1-log1p-u_binary32`
168×	`expm1-udef_binary32`
168×	`log1p-udef_binary32`
97×	`add-sqr-sqrt_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	24
1	193	24
2	1983	24

Stop Event

1×	node limit

Counts

2 → 29

simplify981.0ms (12.8%)

Algorithm

1×	egg-herbie

Rules

1656×	`sqr-pow_binary32`
3×	`cube-mult_binary32`
3×	`unpow3_binary32`
2×	`fma-def_binary32`
1×	`fma-neg_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	796
1	85	796
2	122	796
3	158	796
4	194	796
5	230	796
6	266	796
7	302	796
8	338	796
9	374	796
10	410	796
11	446	796
12	482	796
13	518	796
14	554	796
15	590	796
16	626	796
17	662	796
18	698	796
19	734	796
20	770	796
21	806	796
22	842	796
23	878	796
24	914	796
25	950	796
26	986	796
27	1022	796
28	1058	796
29	1094	796
30	1130	796
31	1166	796
32	1202	796
33	1238	796
34	1274	796
35	1310	796
36	1346	796
37	1382	796
38	1418	796
39	1454	796
40	1490	796
41	1526	796
42	1562	796
43	1598	796
44	1634	796
45	1670	796
46	1706	796
47	1742	796
48	1778	796
49	1814	796
50	1850	796
51	1886	796
52	1922	796
53	1958	796
54	1994	796
55	2030	796
56	2066	796
57	2102	796
58	2138	796
59	2174	796
60	2210	796
61	2246	796
62	2282	796
63	2318	796
64	2354	796
65	2390	796
66	2426	796
67	2462	796
68	2498	796
69	2534	796
70	2570	796
71	2606	796
72	2642	796
73	2678	796
74	2714	796
75	2750	796
76	2786	796
77	2822	796
78	2858	796
79	2894	796
80	2930	796
81	2966	796
82	3002	796
83	3038	796
84	3042	796
85	3074	796
86	3106	796
87	3138	796
88	3170	796
89	3202	796
90	3234	796
91	3290	796
92	3326	796
93	3362	796
94	3398	796
95	3434	796
96	3470	796
97	3506	796
98	3542	796
99	3578	796
100	3614	796
101	3650	796
102	3686	796
103	3722	796
104	3758	796
105	3794	796
106	3830	796
107	3866	796
108	3902	796
109	3938	796
110	3974	796
111	4010	796
112	4046	796
113	4082	796
114	4118	796
115	4154	796
116	4190	796
117	4226	796
118	4262	796
119	4298	796
120	4334	796
121	4370	796
122	4406	796
123	4442	796
124	4478	796
125	4514	796
126	4550	796
127	4586	796
128	4622	796
129	4658	796
130	4694	796
131	4730	796
132	4766	796
133	4802	796
134	4838	796
135	4874	796
136	4910	796
137	4946	796
138	4982	796

Stop Event

1×	node limit

Counts

61 → 35

prune125.0ms (1.6%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	71	2	73
Fresh	1	15	16
Picked	0	1	1
Done	0	0	0
Total	72	18	90

Error

0.1b

Counts

90 → 18

Alt Table

Status	Error	Program
	0.8b	(.f32 (-.f32 (exp.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))))) 1) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (pow.f32 (cbrt.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32)))) 3))
	4.8b	(.f32 (/.f32 (log.f32 (+.f32 1 (expm1.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x)))))) (.f32 (PI.f32) (.f32 tau x))) (cbrt.f32 (/.f32 (pow.f32 (sin.f32 (.f32 x (PI.f32))) 3) (pow.f32 (*.f32 x (PI.f32)) 3))))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (-.f32 (exp.f32 (log1p.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))) 1))
	17.7b	(.f32 (cbrt.f32 (/.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) 3) (pow.f32 (.f32 (PI.f32) (.f32 tau x)) 3))) (cbrt.f32 (/.f32 (+.f32 (log.f32 (pow.f32 (cbrt.f32 (exp.f32 (pow.f32 (sin.f32 (.f32 x (PI.f32))) 3))) 2)) (log.f32 (cbrt.f32 (exp.f32 (pow.f32 (sin.f32 (.f32 x (PI.f32))) 3))))) (pow.f32 (.f32 x (PI.f32)) 3))))
✓	0.7b	(.f32 (cbrt.f32 (/.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) 3) (pow.f32 (.f32 (PI.f32) (.f32 tau x)) 3))) (cbrt.f32 (/.f32 (pow.f32 (sin.f32 (.f32 x (PI.f32))) 3) (pow.f32 (*.f32 x (PI.f32)) 3))))
	0.7b	(.f32 (cbrt.f32 (/.f32 (pow.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) 3) (.f32 (pow.f32 (.f32 (PI.f32) (.f32 tau x)) 3/2) (pow.f32 (.f32 (PI.f32) (.f32 tau x)) 3/2)))) (cbrt.f32 (/.f32 (pow.f32 (sin.f32 (.f32 x (PI.f32))) 3) (pow.f32 (.f32 x (PI.f32)) 3))))
	1.1b	(.f32 (/.f32 (pow.f32 (cbrt.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x)))) 3) (.f32 (PI.f32) (.f32 tau x))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.4b	(.f32 (+.f32 (log.f32 (pow.f32 (cbrt.f32 (exp.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))))) 2)) (log.f32 (cbrt.f32 (exp.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	17.5b	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))) (cbrt.f32 (/.f32 (+.f32 (log.f32 (sqrt.f32 (exp.f32 (pow.f32 (sin.f32 (.f32 x (PI.f32))) 3)))) (log.f32 (sqrt.f32 (exp.f32 (pow.f32 (sin.f32 (.f32 x (PI.f32))) 3))))) (pow.f32 (.f32 x (PI.f32)) 3))))
	3.8b	(.f32 (-.f32 (+.f32 1 (.f32 1/120 (.f32 (pow.f32 (PI.f32) 4) (.f32 (pow.f32 tau 4) (pow.f32 x 4))))) (fma.f32 1/5040 (.f32 (pow.f32 (PI.f32) 6) (.f32 (pow.f32 tau 6) (pow.f32 x 6))) (.f32 1/6 (.f32 (pow.f32 (PI.f32) 2) (.f32 (.f32 tau tau) (.f32 x x)))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	5.7b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (-.f32 (exp.f32 (log1p.f32 (.f32 x (PI.f32)))) 1)) (*.f32 x (PI.f32))))
	0.9b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (log.f32 (exp.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))))
	1.0b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (pow.f32 (sqrt.f32 (.f32 x (PI.f32))) 2)) (*.f32 x (PI.f32))))
	16.6b	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (.f32 (PI.f32) (.f32 tau x))) (cbrt.f32 (/.f32 (log.f32 (exp.f32 (pow.f32 (sin.f32 (.f32 x (PI.f32))) 3))) (pow.f32 (*.f32 x (PI.f32)) 3))))
	1.6b	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (pow.f32 (pow.f32 (*.f32 x (PI.f32)) 3) 1/3)))
	5.6b	(.f32 (/.f32 (sin.f32 (.f32 (log.f32 (+.f32 1 (expm1.f32 (.f32 x (PI.f32))))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	1.1b	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 tau x))) (pow.f32 (cbrt.f32 (.f32 (PI.f32) (.f32 tau x))) 3)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))

Compiler

Compiled 3407 to 1728 computations (49.3% saved)

regimes1.2s (15.6%)

Accuracy

Total 0.6b remaining (79.3%)

Threshold costs 0.6b (79.3%)

Counts

196 → 1

Compiler

Compiled 25360 to 14280 computations (43.7% saved)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	64

Stop Event

1×

saturated

end319.0ms (4.2%)

Stop Event

1×

fuel

Compiler

Compiled 666 to 378 computations (43.2% saved)

Details

analyze3.0ms (0%)

sample2.0s (26.6%)

preprocess12.0ms (0.2%)

simplify7.0ms (0.1%)

prune2.0ms (0%)

localize33.0ms (0.4%)

series41.0ms (0.5%)

rewrite41.0ms (0.5%)

simplify317.0ms (4.1%)

prune211.0ms (2.8%)

localize43.0ms (0.6%)

series57.0ms (0.7%)

rewrite46.0ms (0.6%)

simplify225.0ms (2.9%)

prune139.0ms (1.8%)

localize635.0ms (8.3%)

series18.0ms (0.2%)

rewrite32.0ms (0.4%)

simplify849.0ms (11.1%)

prune131.0ms (1.7%)

localize66.0ms (0.9%)

series48.0ms (0.6%)

rewrite40.0ms (0.5%)

simplify981.0ms (12.8%)

prune125.0ms (1.6%)

regimes1.2s (15.6%)

simplify1.0ms (0%)

end319.0ms (4.2%)

Profiling