Details

analyze3.0s (16%)

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
12.5%	87.3%	0.2%	9
12.5%	87.3%	0.2%	10
18.7%	81.1%	0.2%	11
18.7%	81.1%	0.2%	12
18.7%	81.1%	0.2%	13
20.5%	79.3%	0.2%	14

Compiler

Compiled 35 to 24 computations (31.4% saved)

sample2.0s (11%)

Results

1.7s	8096×	body	128	valid
79.0ms	88×	body	1024	invalid
69.0ms	346×	body	128	invalid
53.0ms	62×	body	1024	valid
47.0ms	88×	body	512	invalid
40.0ms	66×	body	512	valid
21.0ms	57×	body	256	invalid
16.0ms	15×	body	2048	invalid
10.0ms	28×	body	256	valid
6.0ms	4×	body	2048	valid

Compiler

Compiled 70 to 48 computations (31.4% saved)

preprocess72.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

1390×	`sqr-pow_binary64`
960×	`pow-sqr_binary64`
90×	`exp-prod_binary64`
31×	`exp-diff_binary64`
10×	`rem-sqrt-square_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	154	495
1	217	495
2	285	495
3	339	495
4	440	495
5	579	495
6	790	495
7	1143	495
8	1756	495
9	2869	495
10	3570	495
11	3590	495
12	3590	495
0	5	5

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 34 to 23 computations (32.4% saved)

simplify41.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1596×	`sqr-pow_binary64`
1373×	`pow-sqr_binary64`
13×	`exp-prod_binary64`
3×	`exp-diff_binary64`
1×	`rem-sqrt-square_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	45
1	30	45
2	42	45
3	51	45
4	65	45
5	82	45
6	108	45
7	146	45
8	210	45
9	324	45
10	528	45
11	907	45
12	1608	45
13	2939	45
14	3864	45
15	3866	45
16	3866	45

Stop Event

1×	node limit

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

15.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	15.3b	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))

Compiler

Compiled 102 to 69 computations (32.4% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 K (+.f64 m n))
✓	0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
✓	0.0b	(exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n)))))
✓	36.6b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series91.0ms (0.5%)

Counts

4 → 168

Calls

42 calls:

8.0ms	(exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n)))))	M
7.0ms	(exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n)))))	m
7.0ms	(exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n)))))	l
7.0ms	(exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n)))))	n
6.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))	K

rewrite56.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

235×	`add-sqr-sqrt_binary64`
235×	`prod-diff_binary64`
227×	`log1p-expm1-u_binary64`
227×	`expm1-log1p-u_binary64`
225×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	63
1	428	63
2	4891	63

Stop Event

1×	node limit

Counts

4 → 60

simplify412.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

1412×	`sqr-pow_binary64`
967×	`pow-sqr_binary64`
95×	`fma-def_binary64`
50×	`cube-mult_binary64`
50×	`unpow3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	350	7652
1	511	7482
2	579	7482
3	658	7482
4	760	7482
5	882	7482
6	1053	7482
7	1295	7482
8	1664	7482
9	2250	7482
10	3235	7482
11	3847	7482
12	3863	7482
13	3865	7482
14	3865	7482

Stop Event

1×	node limit

Counts

228 → 164

prune236.0ms (1.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	158	6	164
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	159	6	165

Error

1.4b

Counts

165 → 6

Alt Table

Status	Error	Program
	35.7b	(.f64 (cos.f64 (-.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 K (+.f64 m n)) 3)) 2) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
	11.1b	(.f64 (cos.f64 (-.f64 (.f64 1/2 (*.f64 n K)) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
	15.3b	(.f64 (.f64 (pow.f64 (cbrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))) 2) (cbrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)))) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
	15.3b	(.f64 (-.f64 (exp.f64 (log1p.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)))) 1) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
	29.9b	(.f64 (cos.f64 (-.f64 (/.f64 (expm1.f64 (log1p.f64 (.f64 K (+.f64 m n)))) 2) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
▶	1.8b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))

Compiler

Compiled 10958 to 5291 computations (51.7% saved)

localize33.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (+.f64 m n) 2) M)
✓	0.0b	(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))
	0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
	0.0b	(exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n)))))

series80.0ms (0.4%)

Counts

2 → 84

Calls

21 calls:

36.0ms	(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))	M	inf
5.0ms	(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))	l	0
4.0ms	(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))	l	inf
4.0ms	(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))	l	-inf
3.0ms	(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))	M	0

rewrite44.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

301×	`expm1-udef_binary64`
301×	`log1p-udef_binary64`
182×	`prod-diff_binary64`
167×	`add-sqr-sqrt_binary64`
164×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	36
1	309	36
2	3531	36

Stop Event

1×	node limit

Counts

2 → 48

simplify5.6s (30.1%)

Algorithm

1×	egg-herbie

Rules

1623×	`sqr-pow_binary64`
34×	`fma-def_binary64`
5×	`fma-neg_binary64`
5×	`fma-udef_binary64`
3×	`rem-sqrt-square_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	79	1988
1	119	1926
2	145	1926
3	159	1926
4	172	1926
5	181	1926
6	190	1926
7	199	1926
8	208	1926
9	217	1926
10	226	1926
11	235	1926
12	244	1926
13	253	1926
14	262	1926
15	271	1926
16	280	1926
17	289	1926
18	298	1926
19	307	1926
20	316	1926
21	325	1926
22	334	1926
23	343	1926
24	352	1926
25	361	1926
26	370	1926
27	379	1926
28	388	1926
29	397	1926
30	406	1926
31	415	1926
32	424	1926
33	433	1926
34	442	1926
35	451	1926
36	460	1926
37	469	1926
38	478	1926
39	487	1926
40	496	1926
41	505	1926
42	514	1926
43	523	1926
44	532	1926
45	541	1926
46	550	1926
47	559	1926
48	568	1926
49	577	1926
50	586	1926
51	595	1926
52	604	1926
53	613	1926
54	622	1926
55	631	1926
56	640	1926
57	649	1926
58	658	1926
59	667	1926
60	676	1926
61	685	1926
62	694	1926
63	703	1926
64	712	1926
65	721	1926
66	730	1926
67	739	1926
68	748	1926
69	757	1926
70	766	1926
71	775	1926
72	784	1926
73	793	1926
74	802	1926
75	811	1926
76	820	1926
77	829	1926
78	838	1926
79	847	1926
80	856	1926
81	865	1926
82	874	1926
83	883	1926
84	892	1926
85	901	1926
86	910	1926
87	919	1926
88	928	1926
89	937	1926
90	946	1926
91	955	1926
92	964	1926
93	973	1926
94	982	1926
95	991	1926
96	1000	1926
97	1009	1926
98	1018	1926
99	1027	1926
100	1036	1926
101	1045	1926
102	1054	1926
103	1063	1926
104	1072	1926
105	1081	1926
106	1090	1926
107	1099	1926
108	1108	1926
109	1117	1926
110	1126	1926
111	1135	1926
112	1144	1926
113	1153	1926
114	1162	1926
115	1171	1926
116	1180	1926
117	1189	1926
118	1198	1926
119	1207	1926
120	1216	1926
121	1225	1926
122	1234	1926
123	1243	1926
124	1252	1926
125	1261	1926
126	1270	1926
127	1279	1926
128	1288	1926
129	1297	1926
130	1306	1926
131	1315	1926
132	1324	1926
133	1333	1926
134	1342	1926
135	1351	1926
136	1360	1926
137	1369	1926
138	1378	1926
139	1387	1926
140	1396	1926
141	1405	1926
142	1414	1926
143	1423	1926
144	1432	1926
145	1441	1926
146	1450	1926
147	1459	1926
148	1468	1926
149	1477	1926
150	1486	1926
151	1495	1926
152	1504	1926
153	1513	1926
154	1522	1926
155	1531	1926
156	1540	1926
157	1549	1926
158	1558	1926
159	1567	1926
160	1576	1926
161	1585	1926
162	1594	1926
163	1603	1926
164	1612	1926
165	1621	1926
166	1630	1926
167	1639	1926
168	1648	1926
169	1657	1926
170	1666	1926
171	1675	1926
172	1684	1926
173	1693	1926
174	1702	1926
175	1711	1926
176	1720	1926
177	1729	1926
178	1738	1926
179	1747	1926
180	1756	1926
181	1765	1926
182	1774	1926
183	1783	1926
184	1792	1926
185	1801	1926
186	1810	1926
187	1819	1926
188	1828	1926
189	1837	1926
190	1846	1926
191	1855	1926
192	1864	1926
193	1873	1926
194	1882	1926
195	1891	1926
196	1900	1926
197	1909	1926
198	1918	1926
199	1927	1926
200	1936	1926
201	1945	1926
202	1954	1926
203	1963	1926
204	1972	1926
205	1981	1926
206	1990	1926
207	1999	1926
208	2008	1926
209	2017	1926
210	2026	1926
211	2035	1926
212	2044	1926
213	2053	1926
214	2062	1926
215	2071	1926
216	2080	1926
217	2089	1926
218	2098	1926
219	2107	1926
220	2116	1926
221	2125	1926
222	2134	1926
223	2143	1926
224	2152	1926
225	2161	1926
226	2170	1926
227	2179	1926
228	2188	1926
229	2197	1926
230	2206	1926
231	2215	1926
232	2224	1926
233	2233	1926
234	2242	1926
235	2251	1926
236	2260	1926
237	2269	1926
238	2278	1926
239	2287	1926
240	2296	1926
241	2305	1926
242	2314	1926
243	2323	1926
244	2332	1926
245	2341	1926
246	2350	1926
247	2359	1926
248	2368	1926
249	2377	1926
250	2386	1926
251	2395	1926
252	2404	1926
253	2413	1926
254	2422	1926
255	2431	1926
256	2440	1926
257	2449	1926
258	2458	1926
259	2467	1926
260	2476	1926
261	2485	1926
262	2494	1926
263	2503	1926
264	2512	1926
265	2521	1926
266	2530	1926
267	2539	1926
268	2548	1926
269	2557	1926
270	2566	1926
271	2575	1926
272	2584	1926
273	2593	1926
274	2602	1926
275	2611	1926
276	2620	1926
277	2629	1926
278	2638	1926
279	2647	1926
280	2656	1926
281	2665	1926
282	2674	1926
283	2683	1926
284	2692	1926
285	2701	1926
286	2710	1926
287	2719	1926
288	2728	1926
289	2737	1926
290	2746	1926
291	2755	1926
292	2764	1926
293	2773	1926
294	2782	1926
295	2791	1926
296	2800	1926
297	2809	1926
298	2818	1926
299	2827	1926
300	2836	1926
301	2845	1926
302	2854	1926
303	2863	1926
304	2872	1926
305	2881	1926
306	2890	1926
307	2899	1926
308	2908	1926
309	2917	1926
310	2926	1926
311	2935	1926
312	2944	1926
313	2953	1926
314	2962	1926
315	2971	1926
316	2980	1926
317	2989	1926
318	2998	1926
319	3007	1926
320	3016	1926
321	3025	1926
322	3034	1926
323	3043	1926
324	3052	1926
325	3061	1926
326	3070	1926
327	3079	1926
328	3088	1926
329	3097	1926
330	3106	1926
331	3115	1926
332	3124	1926
333	3133	1926
334	3134	1926
335	3142	1926
336	3150	1926
337	3158	1926
338	3166	1926
339	3174	1926
340	3182	1926
341	3196	1926
342	3205	1926
343	3214	1926
344	3223	1926
345	3232	1926
346	3241	1926
347	3250	1926
348	3259	1926
349	3268	1926
350	3277	1926
351	3286	1926
352	3295	1926
353	3304	1926
354	3313	1926
355	3322	1926
356	3331	1926
357	3340	1926
358	3349	1926
359	3358	1926
360	3367	1926
361	3376	1926
362	3385	1926
363	3394	1926
364	3403	1926
365	3412	1926
366	3421	1926
367	3430	1926
368	3439	1926
369	3448	1926
370	3457	1926
371	3466	1926
372	3475	1926
373	3484	1926
374	3493	1926
375	3502	1926
376	3511	1926
377	3520	1926
378	3529	1926
379	3538	1926
380	3547	1926
381	3556	1926
382	3565	1926
383	3574	1926
384	3583	1926
385	3592	1926
386	3601	1926
387	3610	1926
388	3619	1926
389	3628	1926
390	3637	1926
391	3646	1926
392	3655	1926
393	3664	1926
394	3673	1926
395	3682	1926
396	3691	1926
397	3700	1926
398	3709	1926
399	3718	1926
400	3727	1926
401	3736	1926
402	3745	1926
403	3754	1926
404	3763	1926
405	3772	1926
406	3781	1926
407	3790	1926
408	3799	1926
409	3808	1926
410	3817	1926
411	3826	1926
412	3835	1926
413	3844	1926
414	3853	1926
415	3862	1926
416	3871	1926
417	3880	1926
418	3889	1926
419	3898	1926
420	3907	1926
421	3916	1926
422	3925	1926
423	3934	1926
424	3943	1926
425	3952	1926
426	3961	1926
427	3970	1926
428	3979	1926
429	3988	1926
430	3997	1926
431	4006	1926
432	4015	1926
433	4024	1926
434	4033	1926
435	4042	1926
436	4051	1926
437	4060	1926
438	4069	1926
439	4078	1926
440	4087	1926
441	4096	1926
442	4105	1926
443	4114	1926
444	4123	1926
445	4132	1926
446	4141	1926
447	4150	1926
448	4159	1926
449	4168	1926
450	4177	1926
451	4186	1926
452	4195	1926
453	4204	1926
454	4213	1926
455	4222	1926
456	4231	1926
457	4240	1926
458	4249	1926
459	4258	1926
460	4267	1926
461	4276	1926
462	4285	1926
463	4294	1926
464	4303	1926
465	4312	1926
466	4321	1926
467	4330	1926
468	4339	1926
469	4348	1926
470	4357	1926
471	4366	1926
472	4375	1926
473	4384	1926
474	4393	1926
475	4402	1926
476	4411	1926
477	4420	1926
478	4429	1926
479	4438	1926
480	4447	1926
481	4456	1926
482	4465	1926
483	4474	1926
484	4483	1926
485	4492	1926
486	4501	1926
487	4510	1926
488	4519	1926
489	4528	1926
490	4537	1926
491	4546	1926
492	4555	1926
493	4564	1926
494	4573	1926
495	4582	1926
496	4591	1926
497	4600	1926
498	4609	1926
499	4618	1926
500	4627	1926
501	4636	1926
502	4645	1926
503	4654	1926
504	4663	1926
505	4672	1926
506	4681	1926
507	4690	1926
508	4699	1926
509	4708	1926
510	4717	1926
511	4726	1926
512	4735	1926
513	4744	1926
514	4753	1926
515	4762	1926
516	4771	1926
517	4780	1926
518	4789	1926
519	4798	1926
520	4807	1926
521	4816	1926
522	4825	1926
523	4834	1926
524	4843	1926
525	4852	1926
526	4861	1926
527	4870	1926
528	4879	1926
529	4888	1926
530	4897	1926
531	4906	1926
532	4915	1926
533	4924	1926
534	4933	1926
535	4942	1926
536	4951	1926
537	4960	1926
538	4969	1926
539	4978	1926
540	4987	1926
541	4996	1926

Stop Event

1×	node limit

Counts

132 → 96

prune297.0ms (1.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	187	2	189
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	188	7	195

Error

1.4b

Counts

195 → 7

Alt Table

Status	Error	Program
	35.7b	(.f64 (cos.f64 (-.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 K (+.f64 m n)) 3)) 2) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
	11.1b	(.f64 (cos.f64 (-.f64 (.f64 1/2 (*.f64 n K)) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
	33.6b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (neg.f64 (pow.f64 (fma.f64 (pow.f64 (cbrt.f64 (-.f64 (/.f64 (+.f64 m n) 2) M)) 2) (cbrt.f64 (-.f64 (/.f64 (+.f64 m n) 2) M)) (fma.f64 (neg.f64 (sqrt.f64 M)) (sqrt.f64 M) M)) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
▶	1.8b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (neg.f64 (sqrt.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 4))) (-.f64 l (fabs.f64 (-.f64 m n))))))
	15.3b	(.f64 (.f64 (pow.f64 (cbrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))) 2) (cbrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)))) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
	15.3b	(.f64 (-.f64 (exp.f64 (log1p.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)))) 1) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
	29.9b	(.f64 (cos.f64 (-.f64 (/.f64 (expm1.f64 (log1p.f64 (.f64 K (+.f64 m n)))) 2) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))

Compiler

Compiled 9799 to 4603 computations (53% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 4)
✓	0.0b	(-.f64 (neg.f64 (sqrt.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 4))) (-.f64 l (fabs.f64 (-.f64 m n))))
✓	0.0b	(exp.f64 (-.f64 (neg.f64 (sqrt.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 4))) (-.f64 l (fabs.f64 (-.f64 m n)))))
✓	12.5b	(sqrt.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 4))

series148.0ms (0.8%)

Counts

4 → 168

Calls

42 calls:

8.0ms	(exp.f64 (-.f64 (neg.f64 (sqrt.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 4))) (-.f64 l (fabs.f64 (-.f64 m n)))))	M	0
7.0ms	(exp.f64 (-.f64 (neg.f64 (sqrt.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 4))) (-.f64 l (fabs.f64 (-.f64 m n)))))	l	0
7.0ms	(exp.f64 (-.f64 (neg.f64 (sqrt.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 4))) (-.f64 l (fabs.f64 (-.f64 m n)))))	m	0
7.0ms	(exp.f64 (-.f64 (neg.f64 (sqrt.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 4))) (-.f64 l (fabs.f64 (-.f64 m n)))))	n	0
7.0ms	(-.f64 (neg.f64 (sqrt.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 4))) (-.f64 l (fabs.f64 (-.f64 m n))))	l	inf

rewrite67.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

338×	`expm1-udef_binary64`
338×	`log1p-udef_binary64`
188×	`add-sqr-sqrt_binary64`
187×	`log1p-expm1-u_binary64`
187×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	80
1	363	80
2	4025	80

Stop Event

1×	node limit

Counts

4 → 74

simplify521.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

1359×	`sqr-pow_binary64`
942×	`pow-sqr_binary64`
168×	`fma-def_binary64`
42×	`exp-prod_binary64`
40×	`cube-mult_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	400	10009
1	622	9777
2	700	9777
3	771	9777
4	861	9777
5	970	9777
6	1125	9777
7	1349	9777
8	1697	9777
9	2260	9777
10	3219	9777
11	3823	9777
12	3837	9777
13	3839	9777
14	3839	9777

Stop Event

1×	node limit

Counts

242 → 218

prune361.0ms (1.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	218	0	218
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	218	7	225

Error

1.4b

Counts

225 → 7

Alt Table

Status	Error	Program
	35.7b	(.f64 (cos.f64 (-.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 K (+.f64 m n)) 3)) 2) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
▶	11.1b	(.f64 (cos.f64 (-.f64 (.f64 1/2 (*.f64 n K)) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
	33.6b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (neg.f64 (pow.f64 (fma.f64 (pow.f64 (cbrt.f64 (-.f64 (/.f64 (+.f64 m n) 2) M)) 2) (cbrt.f64 (-.f64 (/.f64 (+.f64 m n) 2) M)) (fma.f64 (neg.f64 (sqrt.f64 M)) (sqrt.f64 M) M)) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
✓	1.8b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (neg.f64 (sqrt.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 4))) (-.f64 l (fabs.f64 (-.f64 m n))))))
	15.3b	(.f64 (.f64 (pow.f64 (cbrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))) 2) (cbrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)))) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
	15.3b	(.f64 (-.f64 (exp.f64 (log1p.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)))) 1) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
	29.9b	(.f64 (cos.f64 (-.f64 (/.f64 (expm1.f64 (log1p.f64 (.f64 K (+.f64 m n)))) 2) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))

Compiler

Compiled 12639 to 6302 computations (50.1% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))
	0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
	0.0b	(exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n)))))
✓	27.7b	(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))

series9.0ms (0%)

Counts

1 → 12

Calls

9 calls:

2.0ms	(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))	n	0
2.0ms	(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))	K	0
1.0ms	(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))	M	0
1.0ms	(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))	n	-inf
1.0ms	(cos.f64 (-.f64 (.f64 1/2 (.f64 n K)) M))	n	inf

rewrite34.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

817×	`log1p-expm1-u_binary64`
817×	`expm1-log1p-u_binary64`
101×	`add-sqr-sqrt_binary64`
95×	`add-cbrt-cube_binary64`
94×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	12
1	182	12
2	2023	12

Stop Event

1×	node limit

Counts

1 → 18

simplify201.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

1800×	`sqr-pow_binary64`
822×	`pow-sqr_binary64`
99×	`cube-prod_binary64`
99×	`cube-mult_binary64`
99×	`unpow3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	368
1	80	368
2	100	368
3	128	368
4	171	368
5	218	368
6	274	368
7	335	368
8	406	368
9	482	368
10	568	368
11	659	368
12	760	368
13	866	368
14	982	368
15	1103	368
16	1234	368
17	1370	368
18	1516	368
19	1667	368
20	1828	368
21	1994	368
22	2170	368
23	2182	368
24	2188	368
25	2188	368
26	2366	368
27	2551	368
28	2747	368
29	2953	368
30	3164	368
31	3385	368
32	3611	368
33	3847	368
34	4088	368
35	4100	368
36	4106	368
37	4106	368
38	4354	368
39	4604	368
40	4870	368

Stop Event

1×	node limit

Counts

30 → 32

prune330.0ms (1.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	181	3	184
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	183	8	191

Error

1.4b

Counts

191 → 8

Alt Table

Status	Error	Program
✓	1.8b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (neg.f64 (sqrt.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 4))) (-.f64 l (fabs.f64 (-.f64 m n))))))
	11.1b	(.f64 (-.f64 (exp.f64 (log1p.f64 (cos.f64 (-.f64 (.f64 1/2 (*.f64 n K)) M)))) 1) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
	33.6b	(*.f64 (cos.f64 M) (exp.f64 (-.f64 (neg.f64 (pow.f64 (fma.f64 (pow.f64 (cbrt.f64 (-.f64 (/.f64 (+.f64 m n) 2) M)) 2) (cbrt.f64 (-.f64 (/.f64 (+.f64 m n) 2) M)) (fma.f64 (neg.f64 (sqrt.f64 M)) (sqrt.f64 M) M)) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
	11.1b	(.f64 (log.f64 (exp.f64 (cos.f64 (-.f64 (.f64 1/2 (*.f64 n K)) M)))) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
	11.3b	(.f64 (sqrt.f64 (pow.f64 (cos.f64 (-.f64 (.f64 1/2 (*.f64 n K)) M)) 2)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
	15.3b	(.f64 (.f64 (pow.f64 (cbrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))) 2) (cbrt.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)))) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
	29.9b	(.f64 (cos.f64 (-.f64 (/.f64 (expm1.f64 (log1p.f64 (.f64 K (+.f64 m n)))) 2) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))
	35.7b	(.f64 (cos.f64 (-.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 K (+.f64 m n)) 3)) 2) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)) (-.f64 l (fabs.f64 (-.f64 m n))))))

Compiler

Compiled 10741 to 5211 computations (51.5% saved)

regimes4.7s (25.3%)

Accuracy

Total 0.2b remaining (15.3%)

Threshold costs 0.2b (15.3%)

Counts

117 → 1

Compiler

Compiled 20354 to 14652 computations (28% saved)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	38

Stop Event

1×

saturated

end190.0ms (1%)

Stop Event

1×

fuel

Compiler

Compiled 357 to 255 computations (28.6% saved)

Details

analyze3.0s (16%)

sample2.0s (11%)

preprocess72.0ms (0.4%)

simplify41.0ms (0.2%)

prune2.0ms (0%)

localize17.0ms (0.1%)

series91.0ms (0.5%)

rewrite56.0ms (0.3%)

simplify412.0ms (2.2%)

prune236.0ms (1.3%)

localize33.0ms (0.2%)

series80.0ms (0.4%)

rewrite44.0ms (0.2%)

simplify5.6s (30.1%)

prune297.0ms (1.6%)

localize15.0ms (0.1%)

series148.0ms (0.8%)

rewrite67.0ms (0.4%)

simplify521.0ms (2.8%)

prune361.0ms (1.9%)

localize20.0ms (0.1%)

series9.0ms (0%)

rewrite34.0ms (0.2%)

simplify201.0ms (1.1%)

prune330.0ms (1.8%)

regimes4.7s (25.3%)

simplify1.0ms (0%)

end190.0ms (1%)

Profiling