Details

sample54.0ms

Algorithm

intervals

Results

28.0ms

265×

body

valid

simplify17.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (5.0ms)

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

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 28.4b

localize24.0ms

Local error

Found 2 expressions with local error:

0.5b	(+ (* a c) (* b d))
27.8b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite82.0ms

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:

9.0ms	(+ (* a c) (* b d))
72.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series182.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(+ (* a c) (* b d))
136.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify1.1s

Counts

53 → 53

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	89	972
1	248	818
2	1044	749
done	5000	747

prune331.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 18.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot c d)
0.0b	(fma a c (* b d))
0.2b	(* (/ 1 (hypot c d)) (/ (fma a c (* b d)) (hypot c d)))
17.6b	(/ (fma a c (* b d)) (hypot c d))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 107

Calls

4 calls:

0.0ms	(hypot c d)
0.0ms	(fma a c (* b d))
40.0ms	(* (/ 1 (hypot c d)) (/ (fma a c (* b d)) (hypot c d)))
5.0ms	(/ (fma a c (* b d)) (hypot c d))

series599.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(hypot c d)
58.0ms	(fma a c (* b d))
295.0ms	(* (/ 1 (hypot c d)) (/ (fma a c (* b d)) (hypot c d)))
186.0ms	(/ (fma a c (* b d)) (hypot c d))

simplify3.2s

Counts

119 → 119

Iterations

Useful iterations: 2 (412.0ms)

Iter	Nodes	Cost
0	146	1955
1	384	1841
2	2610	1579
done	5000	1579

prune440.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.5b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot c d)
0.1b	(/ (/ (fma d b (* c a)) (hypot c d)) (hypot c d))
0.5b	(fma d b (* c a))
17.6b	(/ (fma d b (* c a)) (hypot c d))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 121

Calls

4 calls:

0.0ms	(hypot c d)
12.0ms	(/ (/ (fma d b (* c a)) (hypot c d)) (hypot c d))
1.0ms	(fma d b (* c a))
10.0ms	(/ (fma d b (* c a)) (hypot c d))

series468.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(hypot c d)
168.0ms	(/ (/ (fma d b (* c a)) (hypot c d)) (hypot c d))
70.0ms	(fma d b (* c a))
144.0ms	(/ (fma d b (* c a)) (hypot c d))

simplify864.0ms

Counts

133 → 133

Iterations

Useful iterations: done (859.0ms)

Iter	Nodes	Cost
0	167	2544
1	363	2481
2	1778	2306
done	5002	2264

prune641.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 1.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1 (/ (hypot c d) (fma d b (* c a)))) (hypot c d))
0.2b	(/ 1 (/ (hypot c d) (fma d b (* c a))))
0.5b	(fma d b (* c a))
17.6b	(/ (hypot c d) (fma d b (* c a)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

480×	`times-frac`
239×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
50×	`associate-/l*`
36×	`add-exp-log`
23×	`div-inv`
22×	`div-exp`
20×	`add-cbrt-cube`
19×	`associate-/r*`
10×	`cbrt-undiv`
5×	`pow1` `associate-/r/`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num`
1×	`pow-flip` `fma-udef` `associate-/l/` `inv-pow`

Counts

4 → 319

Calls

4 calls:

24.0ms	(/ (/ 1 (/ (hypot c d) (fma d b (* c a)))) (hypot c d))
10.0ms	(/ 1 (/ (hypot c d) (fma d b (* c a))))
0.0ms	(fma d b (* c a))
5.0ms	(/ (hypot c d) (fma d b (* c a)))

series575.0ms

Counts

4 → 12

Calls

4 calls:

225.0ms	(/ (/ 1 (/ (hypot c d) (fma d b (* c a)))) (hypot c d))
190.0ms	(/ 1 (/ (hypot c d) (fma d b (* c a))))
48.0ms	(fma d b (* c a))
112.0ms	(/ (hypot c d) (fma d b (* c a)))

simplify865.0ms

Counts

331 → 331

Iterations

Useful iterations: done (854.0ms)

Iter	Nodes	Cost
0	458	8797
1	1312	7962
done	5000	7454

prune981.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 1.3b

regimes271.0ms

Accuracy

27.7% (10.6b remaining)

Error of 13.0b against oracle of 2.4b and baseline of 17.1b

bsearch90.0ms

Steps

Iters	Range		Point
8	1.267959276101694e+93	1.0044135886792885e+96	9.741722452995778e+95
7	-1.1968959000014948e+107	-2.2592652681113707e+105	-4.379830691407506e+106

simplify1.6s

Iterations

Useful iterations: 3 (13.0ms)

Iter	Nodes	Cost
0	25	51
1	32	43
2	34	39
3	51	35
4	62	35
5	70	35
6	78	35
7	86	35
8	94	35
9	102	35
10	110	35
11	118	35
12	126	35
13	134	35
14	142	35
15	150	35
16	158	35
17	166	35
18	174	35
19	182	35
20	190	35
21	198	35
22	206	35
23	214	35
24	222	35
25	230	35
26	238	35
27	246	35
28	254	35
29	262	35
30	270	35
31	278	35
32	286	35
33	294	35
34	302	35
35	310	35
36	318	35
37	326	35
38	334	35
39	342	35
40	350	35
41	358	35
42	366	35
43	374	35
44	382	35
45	390	35
46	398	35
47	406	35
48	414	35
49	422	35
50	430	35
51	438	35
52	446	35
53	454	35
54	462	35
55	470	35
56	478	35
57	486	35
58	494	35
59	502	35
60	510	35
61	518	35
62	526	35
63	534	35
64	542	35
65	550	35
66	558	35
67	566	35
68	574	35
69	582	35
70	590	35
71	598	35
72	606	35
73	614	35
74	622	35
75	630	35
76	638	35
77	646	35
78	654	35
79	662	35
80	670	35
81	678	35
82	686	35
83	694	35
84	702	35
85	710	35
86	718	35
87	726	35
88	734	35
89	742	35
90	750	35
91	758	35
92	766	35
93	774	35
94	782	35
95	790	35
96	798	35
97	806	35
98	814	35
99	822	35
100	830	35
101	838	35
102	846	35
103	854	35
104	862	35
105	870	35
106	878	35
107	886	35
108	894	35
109	902	35
110	910	35
111	918	35
112	926	35
113	934	35
114	942	35
115	950	35
116	958	35
117	966	35
118	974	35
119	982	35
120	990	35
121	998	35
122	1006	35
123	1014	35
124	1022	35
125	1030	35
126	1038	35
127	1046	35
128	1054	35
129	1062	35
130	1070	35
131	1078	35
132	1086	35
133	1094	35
134	1102	35
135	1110	35
136	1118	35
137	1126	35
138	1134	35
139	1142	35
140	1150	35
141	1158	35
142	1166	35
143	1174	35
144	1182	35
145	1190	35
146	1198	35
147	1206	35
148	1214	35
149	1222	35
150	1230	35
151	1238	35
152	1246	35
153	1254	35
154	1262	35
155	1270	35
156	1278	35
157	1286	35
158	1294	35
159	1302	35
160	1310	35
161	1318	35
162	1326	35
163	1334	35
164	1342	35
165	1350	35
166	1358	35
167	1366	35
168	1374	35
169	1382	35
170	1390	35
171	1398	35
172	1406	35
173	1414	35
174	1422	35
175	1430	35
176	1438	35
177	1446	35
178	1454	35
179	1462	35
180	1470	35
181	1478	35
182	1486	35
183	1494	35
184	1502	35
185	1510	35
186	1518	35
187	1526	35
188	1534	35
189	1542	35
190	1550	35
191	1558	35
192	1566	35
193	1574	35
194	1582	35
195	1590	35
196	1598	35
197	1606	35
198	1614	35
199	1622	35
200	1630	35
201	1638	35
202	1646	35
203	1654	35
204	1662	35
205	1670	35
206	1678	35
207	1686	35
208	1694	35
209	1702	35
210	1710	35
211	1718	35
212	1726	35
213	1734	35
214	1742	35
215	1750	35
216	1758	35
217	1766	35
218	1774	35
219	1782	35
220	1790	35
221	1798	35
222	1806	35
223	1814	35
224	1822	35
225	1830	35
226	1838	35
227	1846	35
228	1854	35
229	1862	35
230	1870	35
231	1878	35
232	1886	35
233	1894	35
234	1902	35
235	1910	35
236	1918	35
237	1926	35
238	1934	35
239	1942	35
240	1950	35
241	1958	35
242	1966	35
243	1974	35
244	1982	35
245	1990	35
246	1998	35
247	2006	35
248	2014	35
249	2022	35
250	2030	35
251	2038	35
252	2046	35
253	2054	35
254	2062	35
255	2070	35
256	2078	35
257	2086	35
258	2094	35
259	2102	35
260	2110	35
261	2118	35
262	2126	35
263	2134	35
264	2142	35
265	2150	35
266	2158	35
267	2166	35
268	2174	35
269	2182	35
270	2190	35
271	2198	35
272	2206	35
273	2214	35
274	2222	35
275	2230	35
276	2238	35
277	2246	35
278	2254	35
279	2262	35
280	2270	35
281	2278	35
282	2286	35
283	2294	35
284	2302	35
285	2310	35
286	2318	35
287	2326	35
288	2334	35
289	2342	35
290	2350	35
291	2358	35
292	2366	35
293	2374	35
294	2382	35
295	2390	35
296	2398	35
297	2406	35
298	2414	35
299	2422	35
300	2430	35
301	2438	35
302	2446	35
303	2454	35
304	2462	35
305	2470	35
306	2478	35
307	2486	35
308	2494	35
309	2502	35
310	2510	35
311	2518	35
312	2526	35
313	2534	35
314	2542	35
315	2550	35
316	2558	35
317	2566	35
318	2574	35
319	2582	35
320	2590	35
321	2598	35
322	2606	35
323	2614	35
324	2622	35
325	2630	35
326	2638	35
327	2646	35
328	2654	35
329	2662	35
330	2670	35
331	2678	35
332	2686	35
333	2694	35
334	2702	35
335	2710	35
336	2718	35
337	2726	35
338	2734	35
339	2742	35
340	2750	35
341	2758	35
342	2766	35
343	2774	35
344	2782	35
345	2790	35
346	2798	35
347	2806	35
348	2814	35
349	2822	35
350	2830	35
351	2838	35
352	2846	35
353	2854	35
354	2862	35
355	2870	35
356	2878	35
357	2886	35
358	2894	35
359	2902	35
360	2910	35
361	2918	35
362	2926	35
363	2934	35
364	2942	35
365	2950	35
366	2958	35
367	2966	35
368	2974	35
369	2982	35
370	2990	35
371	2998	35
372	3006	35
373	3014	35
374	3022	35
375	3030	35
376	3038	35
377	3046	35
378	3054	35
379	3062	35
380	3070	35
381	3078	35
382	3086	35
383	3094	35
384	3102	35
385	3110	35
386	3118	35
387	3126	35
388	3134	35
389	3142	35
390	3150	35
391	3158	35
392	3166	35
393	3174	35
394	3182	35
395	3190	35
396	3198	35
397	3206	35
398	3214	35
399	3222	35
400	3230	35
401	3238	35
402	3246	35
403	3254	35
404	3262	35
405	3270	35
406	3278	35
407	3286	35
408	3294	35
409	3302	35
410	3310	35
411	3318	35
412	3326	35
413	3334	35
414	3342	35
415	3350	35
416	3358	35
417	3366	35
418	3374	35
419	3382	35
420	3390	35
421	3398	35
422	3406	35
423	3414	35
424	3422	35
425	3430	35
426	3438	35
427	3446	35
428	3454	35
429	3462	35
430	3470	35
431	3478	35
432	3486	35
433	3494	35
434	3502	35
435	3510	35
436	3518	35
437	3526	35
438	3534	35
439	3542	35
440	3550	35
441	3558	35
442	3566	35
443	3574	35
444	3582	35
445	3590	35
446	3598	35
447	3606	35
448	3614	35
449	3622	35
450	3630	35
451	3638	35
452	3646	35
453	3654	35
454	3662	35
455	3670	35
456	3678	35
457	3686	35
458	3694	35
459	3702	35
460	3710	35
461	3718	35
462	3726	35
463	3734	35
464	3742	35
465	3750	35
466	3758	35
467	3766	35
468	3774	35
469	3782	35
470	3790	35
471	3798	35
472	3806	35
473	3814	35
474	3822	35
475	3830	35
476	3838	35
477	3846	35
478	3854	35
479	3862	35
480	3870	35
481	3878	35
482	3886	35
483	3894	35
484	3902	35
485	3910	35
486	3918	35
487	3926	35
488	3934	35
489	3942	35
490	3950	35
491	3958	35
492	3966	35
493	3974	35
494	3982	35
495	3990	35
496	3998	35
497	4006	35
498	4014	35
499	4022	35
500	4030	35
501	4038	35
502	4046	35
503	4054	35
504	4062	35
505	4070	35
506	4078	35
507	4086	35
508	4094	35
509	4102	35
510	4110	35
511	4118	35
512	4126	35
513	4134	35
514	4142	35
515	4150	35
516	4158	35
517	4166	35
518	4174	35
519	4182	35
520	4190	35
521	4198	35
522	4206	35
523	4214	35
524	4222	35
525	4230	35
526	4238	35
527	4246	35
528	4254	35
529	4262	35
530	4270	35
531	4278	35
532	4286	35
533	4294	35
534	4302	35
535	4310	35
536	4318	35
537	4326	35
538	4334	35
539	4342	35
540	4350	35
541	4358	35
542	4366	35
543	4374	35
544	4382	35
545	4390	35
546	4398	35
547	4406	35
548	4414	35
549	4422	35
550	4430	35
551	4438	35
552	4446	35
553	4454	35
554	4462	35
555	4470	35
556	4478	35
557	4486	35
558	4494	35
559	4502	35
560	4510	35
561	4518	35
562	4526	35
563	4534	35
564	4542	35
565	4550	35
566	4558	35
567	4566	35
568	4574	35
569	4582	35
570	4590	35
571	4598	35
572	4606	35
573	4614	35
574	4622	35
575	4630	35
576	4638	35
577	4646	35
578	4654	35
579	4662	35
580	4670	35
581	4678	35
582	4686	35
583	4694	35
584	4702	35
585	4710	35
586	4718	35
587	4726	35
588	4734	35
589	4742	35
590	4750	35
591	4758	35
592	4766	35
593	4774	35
594	4782	35
595	4790	35
596	4798	35
597	4806	35
598	4814	35
599	4822	35
600	4830	35
601	4838	35
602	4846	35
603	4854	35
604	4862	35
605	4870	35
606	4878	35
607	4886	35
608	4894	35
609	4902	35
610	4910	35
611	4918	35
612	4926	35
613	4934	35
614	4942	35
615	4950	35
616	4958	35
617	4966	35
618	4974	35
619	4982	35
620	4990	35
621	4998	35
done	5000	35

end0.0ms

sample1.2s

Algorithm

intervals

Results

829.0ms

8462×

body

valid