Details

sample43.0ms

Algorithm

intervals

Results

22.0ms

271×

body

valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	21
2	21
1	17
0	11

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.0b

localize26.0ms

Local error

Found 1 expressions with local error:

22.6b

(/ (fma a c (* b d)) (fma d d (* c c)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt` `*-un-lft-identity` `times-frac` `add-cube-cbrt`
3×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l`
1×	`expm1-log1p-u` `pow1` `cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 29

Calls

1 calls:

8.0ms

(/ (fma a c (* b d)) (fma d d (* c c)))

series159.0ms

Counts

1 → 3

Calls

1 calls:

159.0ms

(/ (fma a c (* b d)) (fma d d (* c c)))

simplify1.9s

Counts

32 → 32

Iterations

Iter	Nodes
done	5000
4	4396
3	906
2	240
1	95
0	58

prune271.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 14.5b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot d c)
0.0b	(/ 1 (hypot d c))
0.3b	(* (/ 1 (hypot d c)) (/ (fma a c (* b d)) (hypot d c)))
14.2b	(/ (fma a c (* b d)) (hypot d c))

rewrite44.0ms

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` `unswap-sqr`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`rec-exp` `1-exp`
2×	`clear-num` `frac-2neg`
1×	`frac-times` `hypot-udef` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `pow-flip` `inv-pow`

Counts

4 → 130

Calls

4 calls:

0.0ms	(hypot d c)
5.0ms	(/ 1 (hypot d c))
26.0ms	(* (/ 1 (hypot d c)) (/ (fma a c (* b d)) (hypot d c)))
8.0ms	(/ (fma a c (* b d)) (hypot d c))

series620.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(hypot d c)
89.0ms	(/ 1 (hypot d c))
309.0ms	(* (/ 1 (hypot d c)) (/ (fma a c (* b d)) (hypot d c)))
157.0ms	(/ (fma a c (* b d)) (hypot d c))

simplify1.4s

Counts

142 → 142

Iterations

Iter	Nodes
done	5000
2	2850
1	407
0	154

prune861.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.4b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot d c)
0.0b	(hypot d c)
0.1b	(/ (/ (fma a c (* b d)) (hypot d c)) (hypot d c))
14.2b	(/ (fma a c (* b d)) (hypot d c))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 121

Calls

4 calls:

0.0ms	(hypot d c)
0.0ms	(hypot d c)
12.0ms	(/ (/ (fma a c (* b d)) (hypot d c)) (hypot d c))
4.0ms	(/ (fma a c (* b d)) (hypot d c))

series508.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(hypot d c)
68.0ms	(hypot d c)
204.0ms	(/ (/ (fma a c (* b d)) (hypot d c)) (hypot d c))
169.0ms	(/ (fma a c (* b d)) (hypot d c))

simplify889.0ms

Counts

133 → 133

Iterations

Iter	Nodes
done	5000
2	1628
1	355
0	161

prune958.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 6.4b

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (sqrt (hypot d c)))
0.3b	(* (/ 1 (sqrt (hypot d c))) (/ (/ (fma a c (* b d)) (sqrt (hypot d c))) (hypot d c)))
7.1b	(/ (fma a c (* b d)) (sqrt (hypot d c)))
7.3b	(/ (/ (fma a c (* b d)) (sqrt (hypot d c))) (hypot d c))

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

353×	`times-frac`
257×	`add-sqr-sqrt`
192×	`*-un-lft-identity`
184×	`add-cube-cbrt`
109×	`sqrt-prod`
70×	`associate-r`
54×	`add-exp-log`
34×	`add-cbrt-cube`
28×	`associate-/l*`
24×	`div-exp`
22×	`associate-l`
20×	`unswap-sqr`
15×	`associate-/r*`
14×	`cbrt-undiv`
12×	`prod-exp` `div-inv`
8×	`pow1`
6×	`cbrt-unprod`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `pow-flip`
1×	`frac-times` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `inv-pow` `associate-/l/`

Counts

4 → 340

Calls

4 calls:

11.0ms	(/ 1 (sqrt (hypot d c)))
82.0ms	(* (/ 1 (sqrt (hypot d c))) (/ (/ (fma a c (* b d)) (sqrt (hypot d c))) (hypot d c)))
10.0ms	(/ (fma a c (* b d)) (sqrt (hypot d c)))
23.0ms	(/ (/ (fma a c (* b d)) (sqrt (hypot d c))) (hypot d c))

series965.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(/ 1 (sqrt (hypot d c)))
266.0ms	(* (/ 1 (sqrt (hypot d c))) (/ (/ (fma a c (* b d)) (sqrt (hypot d c))) (hypot d c)))
288.0ms	(/ (fma a c (* b d)) (sqrt (hypot d c)))
277.0ms	(/ (/ (fma a c (* b d)) (sqrt (hypot d c))) (hypot d c))

simplify618.0ms

Counts

352 → 352

Iterations

Iter	Nodes
done	5001
1	1300
0	405

prune2.2s

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 6.4b

regimes575.0ms

Accuracy

34.8% (7.4b remaining)

Error of 13.4b against oracle of 6.0b and baseline of 17.3b

bsearch124.0ms

Steps

Iters	Range		Point
6	7.997843383138597e+191	8.056208352901572e+192	8.747123436813268e+191
10	-3.959953710600684e+125	-7.632284195501427e+113	-2.0458466692374305e+123

simplify1.4s

Iterations

Iter	Nodes
done	5001
621	4999
620	4991
619	4983
618	4975
617	4967
616	4959
615	4951
614	4943
613	4935
612	4927
611	4919
610	4911
609	4903
608	4895
607	4887
606	4879
605	4871
604	4863
603	4855
602	4847
601	4839
600	4831
599	4823
598	4815
597	4807
596	4799
595	4791
594	4783
593	4775
592	4767
591	4759
590	4751
589	4743
588	4735
587	4727
586	4719
585	4711
584	4703
583	4695
582	4687
581	4679
580	4671
579	4663
578	4655
577	4647
576	4639
575	4631
574	4623
573	4615
572	4607
571	4599
570	4591
569	4583
568	4575
567	4567
566	4559
565	4551
564	4543
563	4535
562	4527
561	4519
560	4511
559	4503
558	4495
557	4487
556	4479
555	4471
554	4463
553	4455
552	4447
551	4439
550	4431
549	4423
548	4415
547	4407
546	4399
545	4391
544	4383
543	4375
542	4367
541	4359
540	4351
539	4343
538	4335
537	4327
536	4319
535	4311
534	4303
533	4295
532	4287
531	4279
530	4271
529	4263
528	4255
527	4247
526	4239
525	4231
524	4223
523	4215
522	4207
521	4199
520	4191
519	4183
518	4175
517	4167
516	4159
515	4151
514	4143
513	4135
512	4127
511	4119
510	4111
509	4103
508	4095
507	4087
506	4079
505	4071
504	4063
503	4055
502	4047
501	4039
500	4031
499	4023
498	4015
497	4007
496	3999
495	3991
494	3983
493	3975
492	3967
491	3959
490	3951
489	3943
488	3935
487	3927
486	3919
485	3911
484	3903
483	3895
482	3887
481	3879
480	3871
479	3863
478	3855
477	3847
476	3839
475	3831
474	3823
473	3815
472	3807
471	3799
470	3791
469	3783
468	3775
467	3767
466	3759
465	3751
464	3743
463	3735
462	3727
461	3719
460	3711
459	3703
458	3695
457	3687
456	3679
455	3671
454	3663
453	3655
452	3647
451	3639
450	3631
449	3623
448	3615
447	3607
446	3599
445	3591
444	3583
443	3575
442	3567
441	3559
440	3551
439	3543
438	3535
437	3527
436	3519
435	3511
434	3503
433	3495
432	3487
431	3479
430	3471
429	3463
428	3455
427	3447
426	3439
425	3431
424	3423
423	3415
422	3407
421	3399
420	3391
419	3383
418	3375
417	3367
416	3359
415	3351
414	3343
413	3335
412	3327
411	3319
410	3311
409	3303
408	3295
407	3287
406	3279
405	3271
404	3263
403	3255
402	3247
401	3239
400	3231
399	3223
398	3215
397	3207
396	3199
395	3191
394	3183
393	3175
392	3167
391	3159
390	3151
389	3143
388	3135
387	3127
386	3119
385	3111
384	3103
383	3095
382	3087
381	3079
380	3071
379	3063
378	3055
377	3047
376	3039
375	3031
374	3023
373	3015
372	3007
371	2999
370	2991
369	2983
368	2975
367	2967
366	2959
365	2951
364	2943
363	2935
362	2927
361	2919
360	2911
359	2903
358	2895
357	2887
356	2879
355	2871
354	2863
353	2855
352	2847
351	2839
350	2831
349	2823
348	2815
347	2807
346	2799
345	2791
344	2783
343	2775
342	2767
341	2759
340	2751
339	2743
338	2735
337	2727
336	2719
335	2711
334	2703
333	2695
332	2687
331	2679
330	2671
329	2663
328	2655
327	2647
326	2639
325	2631
324	2623
323	2615
322	2607
321	2599
320	2591
319	2583
318	2575
317	2567
316	2559
315	2551
314	2543
313	2535
312	2527
311	2519
310	2511
309	2503
308	2495
307	2487
306	2479
305	2471
304	2463
303	2455
302	2447
301	2439
300	2431
299	2423
298	2415
297	2407
296	2399
295	2391
294	2383
293	2375
292	2367
291	2359
290	2351
289	2343
288	2335
287	2327
286	2319
285	2311
284	2303
283	2295
282	2287
281	2279
280	2271
279	2263
278	2255
277	2247
276	2239
275	2231
274	2223
273	2215
272	2207
271	2199
270	2191
269	2183
268	2175
267	2167
266	2159
265	2151
264	2143
263	2135
262	2127
261	2119
260	2111
259	2103
258	2095
257	2087
256	2079
255	2071
254	2063
253	2055
252	2047
251	2039
250	2031
249	2023
248	2015
247	2007
246	1999
245	1991
244	1983
243	1975
242	1967
241	1959
240	1951
239	1943
238	1935
237	1927
236	1919
235	1911
234	1903
233	1895
232	1887
231	1879
230	1871
229	1863
228	1855
227	1847
226	1839
225	1831
224	1823
223	1815
222	1807
221	1799
220	1791
219	1783
218	1775
217	1767
216	1759
215	1751
214	1743
213	1735
212	1727
211	1719
210	1711
209	1703
208	1695
207	1687
206	1679
205	1671
204	1663
203	1655
202	1647
201	1639
200	1631
199	1623
198	1615
197	1607
196	1599
195	1591
194	1583
193	1575
192	1567
191	1559
190	1551
189	1543
188	1535
187	1527
186	1519
185	1511
184	1503
183	1495
182	1487
181	1479
180	1471
179	1463
178	1455
177	1447
176	1439
175	1431
174	1423
173	1415
172	1407
171	1399
170	1391
169	1383
168	1375
167	1367
166	1359
165	1351
164	1343
163	1335
162	1327
161	1319
160	1311
159	1303
158	1295
157	1287
156	1279
155	1271
154	1263
153	1255
152	1247
151	1239
150	1231
149	1223
148	1215
147	1207
146	1199
145	1191
144	1183
143	1175
142	1167
141	1159
140	1151
139	1143
138	1135
137	1127
136	1119
135	1111
134	1103
133	1095
132	1087
131	1079
130	1071
129	1063
128	1055
127	1047
126	1039
125	1031
124	1023
123	1015
122	1007
121	999
120	991
119	983
118	975
117	967
116	959
115	951
114	943
113	935
112	927
111	919
110	911
109	903
108	895
107	887
106	879
105	871
104	863
103	855
102	847
101	839
100	831
99	823
98	815
97	807
96	799
95	791
94	783
93	775
92	767
91	759
90	751
89	743
88	735
87	727
86	719
85	711
84	703
83	695
82	687
81	679
80	671
79	663
78	655
77	647
76	639
75	631
74	623
73	615
72	607
71	599
70	591
69	583
68	575
67	567
66	559
65	551
64	543
63	535
62	527
61	519
60	511
59	503
58	495
57	487
56	479
55	471
54	463
53	455
52	447
51	439
50	431
49	423
48	415
47	407
46	399
45	391
44	383
43	375
42	367
41	359
40	351
39	343
38	335
37	327
36	319
35	311
34	303
33	295
32	287
31	279
30	271
29	263
28	255
27	247
26	239
25	231
24	223
23	215
22	207
21	199
20	191
19	183
18	175
17	167
16	159
15	151
14	143
13	135
12	127
11	119
10	111
9	103
8	95
7	87
6	79
5	71
4	63
3	53
2	41
1	31
0	24

end0.0ms

sample994.0ms

Algorithm

intervals

Results

684.0ms

8463×

body

valid