Details

Time bar (total: 48.4s)

sample282.0ms

Algorithm
intervals
Results
86.0ms41×body10240exit
63.0ms51×body1280valid
35.0ms48×body640valid
16.0ms34×body320valid
16.0ms103×body80valid
16.0ms5×body2560valid
9.0ms81×body80nan
5.0ms15×body160valid
5.0ms7×body640nan
2.0ms2×body1280nan
1.0ms5×body160nan
0.0ms1×body320nan

simplify18.1s

Counts
1 → 1
Iterations
IterNodes
done5000
2304994
2294969
2284959
2274946
2264940
2254919
2244909
2234892
2224886
2214861
2204855
2194842
2184836
2174815
2164805
2154788
2144782
2134757
2124751
2114738
2104732
2094711
2084701
2074684
2064678
2054653
2044647
2034634
2024628
2014607
2004597
1994580
1984574
1974549
1964541
1954528
1944522
1934501
1924495
1914478
1904472
1894447
1884441
1874428
1864422
1854401
1844391
1834374
1824368
1814343
1804337
1794324
1784318
1774297
1764289
1754272
1744266
1734241
1724235
1714222
1704216
1694195
1684185
1674168
1664162
1654137
1644131
1634118
1624112
1614091
1604083
1594066
1584060
1574035
1564025
1554012
1544006
1533985
1523975
1513958
1503952
1493927
1483917
1473904
1463898
1453877
1443871
1433854
1423848
1413823
1403813
1393800
1383794
1373773
1363767
1353750
1343744
1333719
1323711
1313698
1303692
1293671
1283663
1273646
1263640
1253615
1243605
1233592
1223586
1213565
1203559
1193542
1183536
1173511
1163501
1153488
1143482
1133461
1123453
1113436
1103430
1093405
1083395
1073382
1063376
1053355
1043345
1033328
1023322
1013297
1003291
993278
983272
973251
963241
953224
943218
933193
923185
913172
903166
893145
883137
873120
863114
853089
843083
833070
823064
813043
803033
793016
783010
772985
762979
752966
742960
732939
722933
712916
702910
692885
682877
672864
662858
652837
642827
632810
622804
612779
602771
592758
582752
572731
562723
552706
542700
532675
522669
512656
502650
492629
482619
472602
462596
452571
442565
432552
422546
412525
402517
392500
382494
372469
362461
352448
342442
332421
322413
312396
302390
292365
282359
272346
262340
252319
242309
232292
222286
212261
202253
192240
182234
172213
162187
152170
142164
132139
122095
111735
101206
9788
8572
7448
6253
5127
477
353
235
120
012

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.4b

localize15.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ (log (fma (expm1 z) y 1.0)) t)
4.5b
(log (fma (expm1 z) y 1.0))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt *-un-lft-identity times-frac add-cube-cbrt
7×pow1
5×add-exp-log log-pow
4×add-cbrt-cube associate-/l*
3×log-prod associate-/r*
2×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
1×cbrt-undiv clear-num frac-2neg div-exp rem-log-exp div-inv
Counts
2 → 49
Calls
2 calls:
6.0ms
(/ (log (fma (expm1 z) y 1.0)) t)
1.0ms
(log (fma (expm1 z) y 1.0))

series265.0ms

Counts
2 → 6
Calls
2 calls:
175.0ms
(/ (log (fma (expm1 z) y 1.0)) t)
89.0ms
(log (fma (expm1 z) y 1.0))

simplify2.1s

Counts
55 → 55
Iterations
IterNodes
done5005
32443
2786
1283
0130

prune447.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.7b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (fma (expm1 z) y 1.0))
0.1b
(/ (+ (log (sqrt (fma (expm1 z) y 1.0))) (log (sqrt (fma (expm1 z) y 1.0)))) t)
4.6b
(log (sqrt (fma (expm1 z) y 1.0)))
4.6b
(log (sqrt (fma (expm1 z) y 1.0)))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
94×log-pow
80×*-un-lft-identity
78×times-frac
73×pow1
57×add-sqr-sqrt
56×add-cube-cbrt
40×distribute-rgt-out
32×distribute-lft-out
27×sqrt-pow1 pow1/2
26×associate-/l*
12×log-prod
9×sqrt-prod
8×distribute-lft1-in distribute-rgt1-in add-exp-log
6×add-cbrt-cube
4×expm1-log1p-u count-2 insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r*
2×rem-log-exp associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg flip3-+ div-exp flip-+ div-inv
Counts
4 → 180
Calls
4 calls:
1.0ms
(sqrt (fma (expm1 z) y 1.0))
52.0ms
(/ (+ (log (sqrt (fma (expm1 z) y 1.0))) (log (sqrt (fma (expm1 z) y 1.0)))) t)
4.0ms
(log (sqrt (fma (expm1 z) y 1.0)))
4.0ms
(log (sqrt (fma (expm1 z) y 1.0)))

series1.2s

Counts
4 → 12
Calls
4 calls:
132.0ms
(sqrt (fma (expm1 z) y 1.0))
678.0ms
(/ (+ (log (sqrt (fma (expm1 z) y 1.0))) (log (sqrt (fma (expm1 z) y 1.0)))) t)
161.0ms
(log (sqrt (fma (expm1 z) y 1.0)))
181.0ms
(log (sqrt (fma (expm1 z) y 1.0)))

simplify4.0s

Counts
192 → 192
Iterations
IterNodes
done5008
23261
1992
0376

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.7b

localize56.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cbrt (fma (expm1 z) y 1.0)) (cbrt (fma (expm1 z) y 1.0)))
4.6b
(log (sqrt (fma (expm1 z) y 1.0)))
4.6b
(log (sqrt (* (cbrt (fma (expm1 z) y 1.0)) (cbrt (fma (expm1 z) y 1.0)))))
4.6b
(log (sqrt (cbrt (fma (expm1 z) y 1.0))))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
24×pow1
19×cbrt-prod log-prod
18×*-un-lft-identity log-pow add-cube-cbrt
13×pow1/3
12×sqrt-pow1
10×sqrt-prod
9×add-exp-log
6×swap-sqr associate-*r* associate-*l*
4×expm1-log1p-u add-cbrt-cube pow-prod-down pow-sqr pow-prod-up insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×pow1/2 rem-log-exp
2×pow2 pow-plus
1×prod-exp *-commutative cbrt-unprod
Counts
4 → 113
Calls
4 calls:
18.0ms
(* (cbrt (fma (expm1 z) y 1.0)) (cbrt (fma (expm1 z) y 1.0)))
14.0ms
(log (sqrt (fma (expm1 z) y 1.0)))
10.0ms
(log (sqrt (* (cbrt (fma (expm1 z) y 1.0)) (cbrt (fma (expm1 z) y 1.0)))))
2.0ms
(log (sqrt (cbrt (fma (expm1 z) y 1.0))))

series746.0ms

Counts
4 → 12
Calls
4 calls:
167.0ms
(* (cbrt (fma (expm1 z) y 1.0)) (cbrt (fma (expm1 z) y 1.0)))
212.0ms
(log (sqrt (fma (expm1 z) y 1.0)))
162.0ms
(log (sqrt (* (cbrt (fma (expm1 z) y 1.0)) (cbrt (fma (expm1 z) y 1.0)))))
204.0ms
(log (sqrt (cbrt (fma (expm1 z) y 1.0))))

simplify4.7s

Counts
125 → 125
Iterations
IterNodes
done5002
23513
11003
0360

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.7b

localize51.0ms

Local error

Found 4 expressions with local error:

1.1b
(pow (fma (expm1 z) y 1.0) 2/3)
4.6b
(log (sqrt (fma (expm1 z) y 1.0)))
4.6b
(log (sqrt (pow (fma (expm1 z) y 1.0) 2/3)))
4.6b
(log (sqrt (cbrt (fma (expm1 z) y 1.0))))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
25×log-prod
16×sqrt-prod
14×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
10×pow1 log-pow
8×add-exp-log
6×unpow-prod-down
4×expm1-log1p-u sqrt-pow1 add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-prod pow-unpow pow1/2 rem-log-exp
2×sqr-pow
1×pow-to-exp pow-pow pow1/3 pow-exp
Counts
4 → 88
Calls
4 calls:
2.0ms
(pow (fma (expm1 z) y 1.0) 2/3)
2.0ms
(log (sqrt (fma (expm1 z) y 1.0)))
9.0ms
(log (sqrt (pow (fma (expm1 z) y 1.0) 2/3)))
2.0ms
(log (sqrt (cbrt (fma (expm1 z) y 1.0))))

series556.0ms

Counts
4 → 12
Calls
4 calls:
135.0ms
(pow (fma (expm1 z) y 1.0) 2/3)
159.0ms
(log (sqrt (fma (expm1 z) y 1.0)))
138.0ms
(log (sqrt (pow (fma (expm1 z) y 1.0) 2/3)))
123.0ms
(log (sqrt (cbrt (fma (expm1 z) y 1.0))))

simplify3.5s

Counts
100 → 100
Iterations
IterNodes
done5010
22901
1851
0333

prune827.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.7b

regimes493.0ms

Accuracy

43.4% (4.2b remaining)

Error of 8.2b against oracle of 4.0b and baseline of 11.5b

bsearch386.0ms

Steps
ItersRangePoint
6
1.9206664796388615e-37
7.890820011983143e-37
3.023041139807338e-37
9
3.8348011439366415e-102
6.242787085476989e-93
1.8362327647799437e-96
10
-0.0018335887134067947
-2.9762919585783795e-22
-1.4203884136029791e-18

simplify19.0ms

Iterations
IterNodes
done64
164
057

end0.0ms

sample8.3s

Algorithm
intervals
Results
3.0s1493×body10240exit
1.7s1420×body1280valid
1.2s1507×body640valid
532.0ms3607×body80valid
442.0ms914×body320valid
303.0ms2533×body80nan
201.0ms78×body2560valid
170.0ms496×body160valid
155.0ms245×body640nan
88.0ms162×body320nan
77.0ms105×body1280nan
27.0ms117×body160nan