Details

sample55.0ms

Algorithm

intervals

Results

23.0ms

267×

body

valid

simplify144.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	11	15
1	21	14
2	40	14
3	56	14
4	76	14
5	90	14
6	94	14
done	94	14

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.1b

localize31.0ms

Local error

Found 2 expressions with local error:

0.2b	(- (* x.im y.re) (* x.re y.im))
27.6b	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.re y.re (* y.im y.im)))

rewrite72.0ms

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×	`associate-/r` `associate-/l`
2×	`pow1` `expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `clear-num` `div-inv`

Counts

2 → 48

Calls

2 calls:

27.0ms	(- (* x.im y.re) (* x.re y.im))
42.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.re y.re (* y.im y.im)))

series223.0ms

Counts

2 → 6

Calls

2 calls:

59.0ms	(- (* x.im y.re) (* x.re y.im))
164.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.re y.re (* y.im y.im)))

simplify2.2s

Counts

54 → 54

Iterations

Useful iterations: 3 (835.0ms)

Iter	Nodes	Cost
0	88	931
1	222	906
2	890	809
3	4246	807
done	5000	807

prune281.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 18.4b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (hypot y.re y.im))
0.2b	(- (* x.im y.re) (* x.re y.im))
0.2b	(* (/ 1 (hypot y.re y.im)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
18.0b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
43×	`times-frac`
36×	`*-un-lft-identity`
34×	`add-cube-cbrt`
32×	`add-exp-log`
20×	`add-cbrt-cube`
13×	`associate-r` `associate-l`
11×	`div-exp`
8×	`prod-exp`
7×	`pow1`
6×	`cbrt-undiv` `associate-/r` `associate-/l` `add-log-exp` `unswap-sqr`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `div-inv`
3×	`rec-exp` `1-exp`
2×	`flip3--` `frac-2neg` `clear-num` `flip--` `associate-/l/`
1×	`frac-times` `sub-neg` `pow-flip` `fma-neg` `diff-log` `div-sub` `associate-r/` `prod-diff` `pow-prod-down` `associate-l/` `*-commutative` `inv-pow`

Counts

4 → 139

Calls

4 calls:

10.0ms	(/ 1 (hypot y.re y.im))
16.0ms	(- (* x.im y.re) (* x.re y.im))
43.0ms	(* (/ 1 (hypot y.re y.im)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
25.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series605.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(/ 1 (hypot y.re y.im))
57.0ms	(- (* x.im y.re) (* x.re y.im))
261.0ms	(* (/ 1 (hypot y.re y.im)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
198.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify1.8s

Counts

151 → 151

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	178	2462
1	520	2280
2	3133	2015
done	5000	1997

prune718.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.8b

localize51.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- (* y.re x.im) (* y.im x.re)) (hypot y.re y.im)) (hypot y.re y.im))
0.2b	(- (* y.re x.im) (* y.im x.re))
18.0b	(/ (- (* y.re x.im) (* y.im x.re)) (hypot y.re y.im))

rewrite78.0ms

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`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `expm1-log1p-u` `div-sub` `log1p-expm1-u` `associate-/l/`
2×	`flip3--` `frac-2neg` `clear-num` `flip--`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff`

Counts

3 → 121

Calls

3 calls:

42.0ms	(/ (/ (- (* y.re x.im) (* y.im x.re)) (hypot y.re y.im)) (hypot y.re y.im))
8.0ms	(- (* y.re x.im) (* y.im x.re))
19.0ms	(/ (- (* y.re x.im) (* y.im x.re)) (hypot y.re y.im))

series397.0ms

Counts

3 → 9

Calls

3 calls:

170.0ms	(/ (/ (- (* y.re x.im) (* y.im x.re)) (hypot y.re y.im)) (hypot y.re y.im))
61.0ms	(- (* y.re x.im) (* y.im x.re))
166.0ms	(/ (- (* y.re x.im) (* y.im x.re)) (hypot y.re y.im))

simplify1.1s

Counts

130 → 130

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	185	2814
1	475	2738
2	2279	2556
done	5002	2506

prune670.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.8b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (hypot y.re y.im))
0.1b	(/ (* (- (* y.re x.im) (* y.im x.re)) (/ 1 (hypot y.re y.im))) (hypot y.re y.im))
0.2b	(- (* y.re x.im) (* y.im x.re))
18.2b	(* (- (* y.re x.im) (* y.im x.re)) (/ 1 (hypot y.re y.im)))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
29×	`add-sqr-sqrt`
23×	`*-un-lft-identity` `times-frac`
22×	`add-cube-cbrt`
20×	`add-cbrt-cube`
13×	`associate-r`
11×	`div-exp`
8×	`prod-exp`
7×	`pow1`
6×	`cbrt-undiv` `associate-/r*` `associate-/l/` `add-log-exp`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `frac-times` `associate-l/` `cbrt-unprod` `log1p-expm1-u` `associate-/l`
3×	`rec-exp` `1-exp` `associate-l` `div-inv` `unswap-sqr`
2×	`frac-2neg` `associate-*r/` `clear-num` `un-div-inv`
1×	`sub-neg` `pow-flip` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `*-commutative` `inv-pow`

Counts

4 → 124

Calls

4 calls:

5.0ms	(/ 1 (hypot y.re y.im))
40.0ms	(/ (* (- (* y.re x.im) (* y.im x.re)) (/ 1 (hypot y.re y.im))) (hypot y.re y.im))
10.0ms	(- (* y.re x.im) (* y.im x.re))
33.0ms	(* (- (* y.re x.im) (* y.im x.re)) (/ 1 (hypot y.re y.im)))

series502.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(/ 1 (hypot y.re y.im))
198.0ms	(/ (* (- (* y.re x.im) (* y.im x.re)) (/ 1 (hypot y.re y.im))) (hypot y.re y.im))
59.0ms	(- (* y.re x.im) (* y.im x.re))
142.0ms	(* (- (* y.re x.im) (* y.im x.re)) (/ 1 (hypot y.re y.im)))

simplify3.4s

Counts

136 → 136

Iterations

Useful iterations: done (3.4s)

Iter	Nodes	Cost
0	161	2024
1	449	1874
2	3415	1546
done	5001	1534

prune753.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.8b

regimes422.0ms

Accuracy

34.8% (7.0b remaining)

Error of 13.0b against oracle of 6.0b and baseline of 16.8b

bsearch117.0ms

Steps

Iters	Range		Point
8	7.303045123672125e+120	2.905736802042024e+124	7.341181395987439e+123
9	-6.003682551293429e+100	-2.18566872581121e+95	-5.9418984653554864e+100

simplify2.0s

Iterations

Useful iterations: 3 (7.0ms)

Iter	Nodes	Cost
0	26	58
1	34	46
2	36	40
3	55	34
4	66	34
5	74	34
6	82	34
7	90	34
8	98	34
9	106	34
10	114	34
11	122	34
12	130	34
13	138	34
14	146	34
15	154	34
16	162	34
17	170	34
18	178	34
19	186	34
20	194	34
21	202	34
22	210	34
23	218	34
24	226	34
25	234	34
26	242	34
27	250	34
28	258	34
29	266	34
30	274	34
31	282	34
32	290	34
33	298	34
34	306	34
35	314	34
36	322	34
37	330	34
38	338	34
39	346	34
40	354	34
41	362	34
42	370	34
43	378	34
44	386	34
45	394	34
46	402	34
47	410	34
48	418	34
49	426	34
50	434	34
51	442	34
52	450	34
53	458	34
54	466	34
55	474	34
56	482	34
57	490	34
58	498	34
59	506	34
60	514	34
61	522	34
62	530	34
63	538	34
64	546	34
65	554	34
66	562	34
67	570	34
68	578	34
69	586	34
70	594	34
71	602	34
72	610	34
73	618	34
74	626	34
75	634	34
76	642	34
77	650	34
78	658	34
79	666	34
80	674	34
81	682	34
82	690	34
83	698	34
84	706	34
85	714	34
86	722	34
87	730	34
88	738	34
89	746	34
90	754	34
91	762	34
92	770	34
93	778	34
94	786	34
95	794	34
96	802	34
97	810	34
98	818	34
99	826	34
100	834	34
101	842	34
102	850	34
103	858	34
104	866	34
105	874	34
106	882	34
107	890	34
108	898	34
109	906	34
110	914	34
111	922	34
112	930	34
113	938	34
114	946	34
115	954	34
116	962	34
117	970	34
118	978	34
119	986	34
120	994	34
121	1002	34
122	1010	34
123	1018	34
124	1026	34
125	1034	34
126	1042	34
127	1050	34
128	1058	34
129	1066	34
130	1074	34
131	1082	34
132	1090	34
133	1098	34
134	1106	34
135	1114	34
136	1122	34
137	1130	34
138	1138	34
139	1146	34
140	1154	34
141	1162	34
142	1170	34
143	1178	34
144	1186	34
145	1194	34
146	1202	34
147	1210	34
148	1218	34
149	1226	34
150	1234	34
151	1242	34
152	1250	34
153	1258	34
154	1266	34
155	1274	34
156	1282	34
157	1290	34
158	1298	34
159	1306	34
160	1314	34
161	1322	34
162	1330	34
163	1338	34
164	1346	34
165	1354	34
166	1362	34
167	1370	34
168	1378	34
169	1386	34
170	1394	34
171	1402	34
172	1410	34
173	1418	34
174	1426	34
175	1434	34
176	1442	34
177	1450	34
178	1458	34
179	1466	34
180	1474	34
181	1482	34
182	1490	34
183	1498	34
184	1506	34
185	1514	34
186	1522	34
187	1530	34
188	1538	34
189	1546	34
190	1554	34
191	1562	34
192	1570	34
193	1578	34
194	1586	34
195	1594	34
196	1602	34
197	1610	34
198	1618	34
199	1626	34
200	1634	34
201	1642	34
202	1650	34
203	1658	34
204	1666	34
205	1674	34
206	1682	34
207	1690	34
208	1698	34
209	1706	34
210	1714	34
211	1722	34
212	1730	34
213	1738	34
214	1746	34
215	1754	34
216	1762	34
217	1770	34
218	1778	34
219	1786	34
220	1794	34
221	1802	34
222	1810	34
223	1818	34
224	1826	34
225	1834	34
226	1842	34
227	1850	34
228	1858	34
229	1866	34
230	1874	34
231	1882	34
232	1890	34
233	1898	34
234	1906	34
235	1914	34
236	1922	34
237	1930	34
238	1938	34
239	1946	34
240	1954	34
241	1962	34
242	1970	34
243	1978	34
244	1986	34
245	1994	34
246	2002	34
247	2010	34
248	2018	34
249	2026	34
250	2034	34
251	2042	34
252	2050	34
253	2058	34
254	2066	34
255	2074	34
256	2082	34
257	2090	34
258	2098	34
259	2106	34
260	2114	34
261	2122	34
262	2130	34
263	2138	34
264	2146	34
265	2154	34
266	2162	34
267	2170	34
268	2178	34
269	2186	34
270	2194	34
271	2202	34
272	2210	34
273	2218	34
274	2226	34
275	2234	34
276	2242	34
277	2250	34
278	2258	34
279	2266	34
280	2274	34
281	2282	34
282	2290	34
283	2298	34
284	2306	34
285	2314	34
286	2322	34
287	2330	34
288	2338	34
289	2346	34
290	2354	34
291	2362	34
292	2370	34
293	2378	34
294	2386	34
295	2394	34
296	2402	34
297	2410	34
298	2418	34
299	2426	34
300	2434	34
301	2442	34
302	2450	34
303	2458	34
304	2466	34
305	2474	34
306	2482	34
307	2490	34
308	2498	34
309	2506	34
310	2514	34
311	2522	34
312	2530	34
313	2538	34
314	2546	34
315	2554	34
316	2562	34
317	2570	34
318	2578	34
319	2586	34
320	2594	34
321	2602	34
322	2610	34
323	2618	34
324	2626	34
325	2634	34
326	2642	34
327	2650	34
328	2658	34
329	2666	34
330	2674	34
331	2682	34
332	2690	34
333	2698	34
334	2706	34
335	2714	34
336	2722	34
337	2730	34
338	2738	34
339	2746	34
340	2754	34
341	2762	34
342	2770	34
343	2778	34
344	2786	34
345	2794	34
346	2802	34
347	2810	34
348	2818	34
349	2826	34
350	2834	34
351	2842	34
352	2850	34
353	2858	34
354	2866	34
355	2874	34
356	2882	34
357	2890	34
358	2898	34
359	2906	34
360	2914	34
361	2922	34
362	2930	34
363	2938	34
364	2946	34
365	2954	34
366	2962	34
367	2970	34
368	2978	34
369	2986	34
370	2994	34
371	3002	34
372	3010	34
373	3018	34
374	3026	34
375	3034	34
376	3042	34
377	3050	34
378	3058	34
379	3066	34
380	3074	34
381	3082	34
382	3090	34
383	3098	34
384	3106	34
385	3114	34
386	3122	34
387	3130	34
388	3138	34
389	3146	34
390	3154	34
391	3162	34
392	3170	34
393	3178	34
394	3186	34
395	3194	34
396	3202	34
397	3210	34
398	3218	34
399	3226	34
400	3234	34
401	3242	34
402	3250	34
403	3258	34
404	3266	34
405	3274	34
406	3282	34
407	3290	34
408	3298	34
409	3306	34
410	3314	34
411	3322	34
412	3330	34
413	3338	34
414	3346	34
415	3354	34
416	3362	34
417	3370	34
418	3378	34
419	3386	34
420	3394	34
421	3402	34
422	3410	34
423	3418	34
424	3426	34
425	3434	34
426	3442	34
427	3450	34
428	3458	34
429	3466	34
430	3474	34
431	3482	34
432	3490	34
433	3498	34
434	3506	34
435	3514	34
436	3522	34
437	3530	34
438	3538	34
439	3546	34
440	3554	34
441	3562	34
442	3570	34
443	3578	34
444	3586	34
445	3594	34
446	3602	34
447	3610	34
448	3618	34
449	3626	34
450	3634	34
451	3642	34
452	3650	34
453	3658	34
454	3666	34
455	3674	34
456	3682	34
457	3690	34
458	3698	34
459	3706	34
460	3714	34
461	3722	34
462	3730	34
463	3738	34
464	3746	34
465	3754	34
466	3762	34
467	3770	34
468	3778	34
469	3786	34
470	3794	34
471	3802	34
472	3810	34
473	3818	34
474	3826	34
475	3834	34
476	3842	34
477	3850	34
478	3858	34
479	3866	34
480	3874	34
481	3882	34
482	3890	34
483	3898	34
484	3906	34
485	3914	34
486	3922	34
487	3930	34
488	3938	34
489	3946	34
490	3954	34
491	3962	34
492	3970	34
493	3978	34
494	3986	34
495	3994	34
496	4002	34
497	4010	34
498	4018	34
499	4026	34
500	4034	34
501	4042	34
502	4050	34
503	4058	34
504	4066	34
505	4074	34
506	4082	34
507	4090	34
508	4098	34
509	4106	34
510	4114	34
511	4122	34
512	4130	34
513	4138	34
514	4146	34
515	4154	34
516	4162	34
517	4170	34
518	4178	34
519	4186	34
520	4194	34
521	4202	34
522	4210	34
523	4218	34
524	4226	34
525	4234	34
526	4242	34
527	4250	34
528	4258	34
529	4266	34
530	4274	34
531	4282	34
532	4290	34
533	4298	34
534	4306	34
535	4314	34
536	4322	34
537	4330	34
538	4338	34
539	4346	34
540	4354	34
541	4362	34
542	4370	34
543	4378	34
544	4386	34
545	4394	34
546	4402	34
547	4410	34
548	4418	34
549	4426	34
550	4434	34
551	4442	34
552	4450	34
553	4458	34
554	4466	34
555	4474	34
556	4482	34
557	4490	34
558	4498	34
559	4506	34
560	4514	34
561	4522	34
562	4530	34
563	4538	34
564	4546	34
565	4554	34
566	4562	34
567	4570	34
568	4578	34
569	4586	34
570	4594	34
571	4602	34
572	4610	34
573	4618	34
574	4626	34
575	4634	34
576	4642	34
577	4650	34
578	4658	34
579	4666	34
580	4674	34
581	4682	34
582	4690	34
583	4698	34
584	4706	34
585	4714	34
586	4722	34
587	4730	34
588	4738	34
589	4746	34
590	4754	34
591	4762	34
592	4770	34
593	4778	34
594	4786	34
595	4794	34
596	4802	34
597	4810	34
598	4818	34
599	4826	34
600	4834	34
601	4842	34
602	4850	34
603	4858	34
604	4866	34
605	4874	34
606	4882	34
607	4890	34
608	4898	34
609	4906	34
610	4914	34
611	4922	34
612	4930	34
613	4938	34
614	4946	34
615	4954	34
616	4962	34
617	4970	34
618	4978	34
619	4986	34
620	4994	34
done	5000	34

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.0s

8517×

body

valid