Details

sample45.0ms

Algorithm

intervals

Results

22.0ms

266×

body

valid

simplify16.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	11	15
1	17	13
2	21	13
done	21	13

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.8b

localize35.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x.re y.re) (* x.im y.im))
24.5b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`pow1` `expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `fma-def` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

2 → 47

Calls

2 calls:

8.0ms	(+ (* x.re y.re) (* x.im y.im))
43.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series132.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(+ (* x.re y.re) (* x.im y.im))
95.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify2.3s

Counts

53 → 53

Iterations

Useful iterations: 3 (997.0ms)

Iter	Nodes	Cost
0	90	972
1	247	818
2	964	747
3	4305	743
done	5000	743

prune202.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 15.8b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma y.re x.re (* x.im y.im))
0.2b	(* (/ 1 (hypot y.re y.im)) (/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im)))
15.4b	(/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
34×	`times-frac`
27×	`add-exp-log` `*-un-lft-identity`
25×	`add-cube-cbrt`
17×	`add-cbrt-cube`
13×	`associate-r` `associate-l`
9×	`div-exp`
8×	`prod-exp`
6×	`unswap-sqr`
5×	`pow1` `cbrt-undiv`
4×	`cbrt-unprod`
3×	`expm1-log1p-u` `associate-/r` `log1p-expm1-u` `div-inv` `associate-/l` `add-log-exp`
2×	`rec-exp` `1-exp`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative` `fma-udef`

Counts

3 → 97

Calls

3 calls:

0.0ms	(fma y.re x.re (* x.im y.im))
27.0ms	(* (/ 1 (hypot y.re y.im)) (/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im)))
5.0ms	(/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im))

series433.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(fma y.re x.re (* x.im y.im))
248.0ms	(* (/ 1 (hypot y.re y.im)) (/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im)))
142.0ms	(/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im))

simplify3.4s

Counts

106 → 106

Iterations

Useful iterations: done (3.4s)

Iter	Nodes	Cost
0	139	1895
1	373	1783
2	2784	1541
done	5000	1527

prune468.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 6.0b

localize29.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma y.im x.im (* x.re y.re))
0.0b	(/ (/ (fma y.im x.im (* x.re y.re)) (hypot y.re y.im)) (hypot y.re y.im))
15.4b	(/ (fma y.im x.im (* x.re y.re)) (hypot y.re y.im))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
53×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
16×	`associate-/l*`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*` `div-inv`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`fma-udef` `associate-/l/`

Counts

3 → 111

Calls

3 calls:

0.0ms	(fma y.im x.im (* x.re y.re))
20.0ms	(/ (/ (fma y.im x.im (* x.re y.re)) (hypot y.re y.im)) (hypot y.re y.im))
10.0ms	(/ (fma y.im x.im (* x.re y.re)) (hypot y.re y.im))

series381.0ms

Counts

3 → 9

Calls

3 calls:

69.0ms	(fma y.im x.im (* x.re y.re))
148.0ms	(/ (/ (fma y.im x.im (* x.re y.re)) (hypot y.re y.im)) (hypot y.re y.im))
164.0ms	(/ (fma y.im x.im (* x.re y.re)) (hypot y.re y.im))

simplify1.1s

Counts

120 → 120

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	160	2484
1	351	2423
2	1665	2254
done	5000	2206

prune613.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 1.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma y.im x.im (* x.re y.re))
0.0b	(/ (/ (/ (fma y.im x.im (* x.re y.re)) (sqrt (hypot y.re y.im))) (sqrt (hypot y.re y.im))) (hypot y.re y.im))
7.7b	(/ (/ (fma y.im x.im (* x.re y.re)) (sqrt (hypot y.re y.im))) (sqrt (hypot y.re y.im)))
7.9b	(/ (fma y.im x.im (* x.re y.re)) (sqrt (hypot y.re y.im)))

rewrite180.0ms

Algorithm

rewrite-expression-head

Rules

1644×	`times-frac`
785×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
624×	`sqrt-prod`
161×	`associate-/l*`
38×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
15×	`associate-/r*`
10×	`cbrt-undiv` `div-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`associate-/l/`
1×	`fma-udef`

Counts

4 → 794

Calls

4 calls:

0.0ms	(fma y.im x.im (* x.re y.re))
70.0ms	(/ (/ (/ (fma y.im x.im (* x.re y.re)) (sqrt (hypot y.re y.im))) (sqrt (hypot y.re y.im))) (hypot y.re y.im))
18.0ms	(/ (/ (fma y.im x.im (* x.re y.re)) (sqrt (hypot y.re y.im))) (sqrt (hypot y.re y.im)))
13.0ms	(/ (fma y.im x.im (* x.re y.re)) (sqrt (hypot y.re y.im)))

series554.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(fma y.im x.im (* x.re y.re))
166.0ms	(/ (/ (/ (fma y.im x.im (* x.re y.re)) (sqrt (hypot y.re y.im))) (sqrt (hypot y.re y.im))) (hypot y.re y.im))
136.0ms	(/ (/ (fma y.im x.im (* x.re y.re)) (sqrt (hypot y.re y.im))) (sqrt (hypot y.re y.im)))
208.0ms	(/ (fma y.im x.im (* x.re y.re)) (sqrt (hypot y.re y.im)))

simplify1.6s

Counts

806 → 806

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	830	30039
1	2223	27030
done	5000	25807

prune3.6s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 1.2b

regimes379.0ms

Accuracy

24.3% (10.9b remaining)

Error of 13.4b against oracle of 2.4b and baseline of 16.9b

bsearch278.0ms

Steps

Iters	Range		Point
9	1.2564916464665883e+128	1.0940963542127011e+133	1.0484121450209069e+133
9	4.62518452031582e-213	7.833661410696538e-206	4.694847582105376e-213
8	1.1699336559244646e-236	7.187404175808244e-234	6.370255659610306e-234
8	-5.1848556793692505e+109	-3.3364575624134836e+106	-3.114802040969311e+109

simplify2.4s

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	32	85
1	40	70
2	52	60
3	64	60
4	74	60
5	82	60
6	90	60
7	98	60
8	106	60
9	114	60
10	122	60
11	130	60
12	138	60
13	146	60
14	154	60
15	162	60
16	170	60
17	178	60
18	186	60
19	194	60
20	202	60
21	210	60
22	218	60
23	226	60
24	234	60
25	242	60
26	250	60
27	258	60
28	266	60
29	274	60
30	282	60
31	290	60
32	298	60
33	306	60
34	314	60
35	322	60
36	330	60
37	338	60
38	346	60
39	354	60
40	362	60
41	370	60
42	378	60
43	386	60
44	394	60
45	402	60
46	410	60
47	418	60
48	426	60
49	434	60
50	442	60
51	450	60
52	458	60
53	466	60
54	474	60
55	482	60
56	490	60
57	498	60
58	506	60
59	514	60
60	522	60
61	530	60
62	538	60
63	546	60
64	554	60
65	562	60
66	570	60
67	578	60
68	586	60
69	594	60
70	602	60
71	610	60
72	618	60
73	626	60
74	634	60
75	642	60
76	650	60
77	658	60
78	666	60
79	674	60
80	682	60
81	690	60
82	698	60
83	706	60
84	714	60
85	722	60
86	730	60
87	738	60
88	746	60
89	754	60
90	762	60
91	770	60
92	778	60
93	786	60
94	794	60
95	802	60
96	810	60
97	818	60
98	826	60
99	834	60
100	842	60
101	850	60
102	858	60
103	866	60
104	874	60
105	882	60
106	890	60
107	898	60
108	906	60
109	914	60
110	922	60
111	930	60
112	938	60
113	946	60
114	954	60
115	962	60
116	970	60
117	978	60
118	986	60
119	994	60
120	1002	60
121	1010	60
122	1018	60
123	1026	60
124	1034	60
125	1042	60
126	1050	60
127	1058	60
128	1066	60
129	1074	60
130	1082	60
131	1090	60
132	1098	60
133	1106	60
134	1114	60
135	1122	60
136	1130	60
137	1138	60
138	1146	60
139	1154	60
140	1162	60
141	1170	60
142	1178	60
143	1186	60
144	1194	60
145	1202	60
146	1210	60
147	1218	60
148	1226	60
149	1234	60
150	1242	60
151	1250	60
152	1258	60
153	1266	60
154	1274	60
155	1282	60
156	1290	60
157	1298	60
158	1306	60
159	1314	60
160	1322	60
161	1330	60
162	1338	60
163	1346	60
164	1354	60
165	1362	60
166	1370	60
167	1378	60
168	1386	60
169	1394	60
170	1402	60
171	1410	60
172	1418	60
173	1426	60
174	1434	60
175	1442	60
176	1450	60
177	1458	60
178	1466	60
179	1474	60
180	1482	60
181	1490	60
182	1498	60
183	1506	60
184	1514	60
185	1522	60
186	1530	60
187	1538	60
188	1546	60
189	1554	60
190	1562	60
191	1570	60
192	1578	60
193	1586	60
194	1594	60
195	1602	60
196	1610	60
197	1618	60
198	1626	60
199	1634	60
200	1642	60
201	1650	60
202	1658	60
203	1666	60
204	1674	60
205	1682	60
206	1690	60
207	1698	60
208	1706	60
209	1714	60
210	1722	60
211	1730	60
212	1738	60
213	1746	60
214	1754	60
215	1762	60
216	1770	60
217	1778	60
218	1786	60
219	1794	60
220	1802	60
221	1810	60
222	1818	60
223	1826	60
224	1834	60
225	1842	60
226	1850	60
227	1858	60
228	1866	60
229	1874	60
230	1882	60
231	1890	60
232	1898	60
233	1906	60
234	1914	60
235	1922	60
236	1930	60
237	1938	60
238	1946	60
239	1954	60
240	1962	60
241	1970	60
242	1978	60
243	1986	60
244	1994	60
245	2002	60
246	2010	60
247	2018	60
248	2026	60
249	2034	60
250	2042	60
251	2050	60
252	2058	60
253	2066	60
254	2074	60
255	2082	60
256	2090	60
257	2098	60
258	2106	60
259	2114	60
260	2122	60
261	2130	60
262	2138	60
263	2146	60
264	2154	60
265	2162	60
266	2170	60
267	2178	60
268	2186	60
269	2194	60
270	2202	60
271	2210	60
272	2218	60
273	2226	60
274	2234	60
275	2242	60
276	2250	60
277	2258	60
278	2266	60
279	2274	60
280	2282	60
281	2290	60
282	2298	60
283	2306	60
284	2314	60
285	2322	60
286	2330	60
287	2338	60
288	2346	60
289	2354	60
290	2362	60
291	2370	60
292	2378	60
293	2386	60
294	2394	60
295	2402	60
296	2410	60
297	2418	60
298	2426	60
299	2434	60
300	2442	60
301	2450	60
302	2458	60
303	2466	60
304	2474	60
305	2482	60
306	2490	60
307	2498	60
308	2506	60
309	2514	60
310	2522	60
311	2530	60
312	2538	60
313	2546	60
314	2554	60
315	2562	60
316	2570	60
317	2578	60
318	2586	60
319	2594	60
320	2602	60
321	2610	60
322	2618	60
323	2626	60
324	2634	60
325	2642	60
326	2650	60
327	2658	60
328	2666	60
329	2674	60
330	2682	60
331	2690	60
332	2698	60
333	2706	60
334	2714	60
335	2722	60
336	2730	60
337	2738	60
338	2746	60
339	2754	60
340	2762	60
341	2770	60
342	2778	60
343	2786	60
344	2794	60
345	2802	60
346	2810	60
347	2818	60
348	2826	60
349	2834	60
350	2842	60
351	2850	60
352	2858	60
353	2866	60
354	2874	60
355	2882	60
356	2890	60
357	2898	60
358	2906	60
359	2914	60
360	2922	60
361	2930	60
362	2938	60
363	2946	60
364	2954	60
365	2962	60
366	2970	60
367	2978	60
368	2986	60
369	2994	60
370	3002	60
371	3010	60
372	3018	60
373	3026	60
374	3034	60
375	3042	60
376	3050	60
377	3058	60
378	3066	60
379	3074	60
380	3082	60
381	3090	60
382	3098	60
383	3106	60
384	3114	60
385	3122	60
386	3130	60
387	3138	60
388	3146	60
389	3154	60
390	3162	60
391	3170	60
392	3178	60
393	3186	60
394	3194	60
395	3202	60
396	3210	60
397	3218	60
398	3226	60
399	3234	60
400	3242	60
401	3250	60
402	3258	60
403	3266	60
404	3274	60
405	3282	60
406	3290	60
407	3298	60
408	3306	60
409	3314	60
410	3322	60
411	3330	60
412	3338	60
413	3346	60
414	3354	60
415	3362	60
416	3370	60
417	3378	60
418	3386	60
419	3394	60
420	3402	60
421	3410	60
422	3418	60
423	3426	60
424	3434	60
425	3442	60
426	3450	60
427	3458	60
428	3466	60
429	3474	60
430	3482	60
431	3490	60
432	3498	60
433	3506	60
434	3514	60
435	3522	60
436	3530	60
437	3538	60
438	3546	60
439	3554	60
440	3562	60
441	3570	60
442	3578	60
443	3586	60
444	3594	60
445	3602	60
446	3610	60
447	3618	60
448	3626	60
449	3634	60
450	3642	60
451	3650	60
452	3658	60
453	3666	60
454	3674	60
455	3682	60
456	3690	60
457	3698	60
458	3706	60
459	3714	60
460	3722	60
461	3730	60
462	3738	60
463	3746	60
464	3754	60
465	3762	60
466	3770	60
467	3778	60
468	3786	60
469	3794	60
470	3802	60
471	3810	60
472	3818	60
473	3826	60
474	3834	60
475	3842	60
476	3850	60
477	3858	60
478	3866	60
479	3874	60
480	3882	60
481	3890	60
482	3898	60
483	3906	60
484	3914	60
485	3922	60
486	3930	60
487	3938	60
488	3946	60
489	3954	60
490	3962	60
491	3970	60
492	3978	60
493	3986	60
494	3994	60
495	4002	60
496	4010	60
497	4018	60
498	4026	60
499	4034	60
500	4042	60
501	4050	60
502	4058	60
503	4066	60
504	4074	60
505	4082	60
506	4090	60
507	4098	60
508	4106	60
509	4114	60
510	4122	60
511	4130	60
512	4138	60
513	4146	60
514	4154	60
515	4162	60
516	4170	60
517	4178	60
518	4186	60
519	4194	60
520	4202	60
521	4210	60
522	4218	60
523	4226	60
524	4234	60
525	4242	60
526	4250	60
527	4258	60
528	4266	60
529	4274	60
530	4282	60
531	4290	60
532	4298	60
533	4306	60
534	4314	60
535	4322	60
536	4330	60
537	4338	60
538	4346	60
539	4354	60
540	4362	60
541	4370	60
542	4378	60
543	4386	60
544	4394	60
545	4402	60
546	4410	60
547	4418	60
548	4426	60
549	4434	60
550	4442	60
551	4450	60
552	4458	60
553	4466	60
554	4474	60
555	4482	60
556	4490	60
557	4498	60
558	4506	60
559	4514	60
560	4522	60
561	4530	60
562	4538	60
563	4546	60
564	4554	60
565	4562	60
566	4570	60
567	4578	60
568	4586	60
569	4594	60
570	4602	60
571	4610	60
572	4618	60
573	4626	60
574	4634	60
575	4642	60
576	4650	60
577	4658	60
578	4666	60
579	4674	60
580	4682	60
581	4690	60
582	4698	60
583	4706	60
584	4714	60
585	4722	60
586	4730	60
587	4738	60
588	4746	60
589	4754	60
590	4762	60
591	4770	60
592	4778	60
593	4786	60
594	4794	60
595	4802	60
596	4810	60
597	4818	60
598	4826	60
599	4834	60
600	4842	60
601	4850	60
602	4858	60
603	4866	60
604	4874	60
605	4882	60
606	4890	60
607	4898	60
608	4906	60
609	4914	60
610	4922	60
611	4930	60
612	4938	60
613	4946	60
614	4954	60
615	4962	60
616	4970	60
617	4978	60
618	4986	60
619	4994	60
done	5000	60

end0.0ms

sample1.4s

Algorithm

intervals

Results

815.0ms

8411×

body

valid