Details

Time bar (total: 20.4s)

sample98.0ms

Algorithm
intervals
Results
47.0ms76×body1280valid
17.0ms45×body640valid
13.0ms31×body2560valid
4.0ms17×body320valid
4.0ms70×body80valid
2.0ms17×body160valid

simplify3.0ms

Counts
1 → 1
Iterations
IterNodes
done10
110
07

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.2b

localize11.0ms

Local error

Found 3 expressions with local error:

0.9b
(+ x (sqrt (fma x x 1.0)))
2.9b
(log (+ x (sqrt (fma x x 1.0))))
15.4b
(sqrt (fma x x 1.0))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
add-sqr-sqrt
add-cube-cbrt
pow1 add-log-exp
log-prod add-exp-log
expm1-log1p-u fma-def add-cbrt-cube sqrt-prod log1p-expm1-u
log-div flip3-+ flip-+ distribute-lft-out
+-commutative rem-sqrt-square sum-log sqrt-pow1 pow1/2 rem-log-exp log-pow
Counts
3 → 49
Calls
3 calls:
6.0ms
(+ x (sqrt (fma x x 1.0)))
5.0ms
(log (+ x (sqrt (fma x x 1.0))))
1.0ms
(sqrt (fma x x 1.0))

series466.0ms

Counts
3 → 9
Calls
3 calls:
95.0ms
(+ x (sqrt (fma x x 1.0)))
301.0ms
(log (+ x (sqrt (fma x x 1.0))))
69.0ms
(sqrt (fma x x 1.0))

simplify1.2s

Counts
58 → 58
Iterations
IterNodes
done5001
21087
1289
0126

prune418.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 2 expressions with local error:

0.1b
(fma (/ (/ (* (* x x) x) 1.0) (sqrt 1.0)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))
0.1b
(* (* x x) x)

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
21×pow1
add-cbrt-cube add-exp-log
pow-plus pow-prod-up
add-sqr-sqrt
*-un-lft-identity associate-*r* pow-prod-down prod-exp add-cube-cbrt cbrt-unprod
pow2 expm1-log1p-u pow-sqr log1p-expm1-u add-log-exp
associate-*l* pow3 *-commutative fma-udef unswap-sqr
Counts
2 → 40
Calls
2 calls:
0.0ms
(fma (/ (/ (* (* x x) x) 1.0) (sqrt 1.0)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))
15.0ms
(* (* x x) x)

series233.0ms

Counts
2 → 6
Calls
2 calls:
169.0ms
(fma (/ (/ (* (* x x) x) 1.0) (sqrt 1.0)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))
64.0ms
(* (* x x) x)

simplify991.0ms

Counts
46 → 46
Iterations
IterNodes
done5000
2791
1139
060

prune200.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 0.0625 (pow x 5))
0.4b
(/ 0.125 (* (* x x) x))
12.2b
(log (- (- (/ 0.125 (* (* x x) x)) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
19.0b
(- (- (/ 0.125 (* (* x x) x)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))

rewrite975.0ms

Algorithm
rewrite-expression-head
Rules
358×add-sqr-sqrt
284×times-frac
270×*-un-lft-identity
241×prod-diff
208×add-cube-cbrt
93×associate--l+
68×unpow-prod-down
60×difference-of-squares
32×distribute-lft-out--
28×div-inv
24×sqr-pow
19×add-exp-log
15×add-cbrt-cube
log-prod add-log-exp
associate-/r* frac-sub
fma-neg div-exp associate-/l*
pow1 log-div
expm1-log1p-u cbrt-undiv flip3-- log1p-expm1-u flip--
diff-log prod-exp cbrt-unprod
clear-num sub-neg frac-2neg
associate--l- pow-to-exp rem-log-exp pow-exp log-pow
Counts
4 → 371
Calls
4 calls:
11.0ms
(/ 0.0625 (pow x 5))
29.0ms
(/ 0.125 (* (* x x) x))
335.0ms
(log (- (- (/ 0.125 (* (* x x) x)) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
547.0ms
(- (- (/ 0.125 (* (* x x) x)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))

series538.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(/ 0.0625 (pow x 5))
61.0ms
(/ 0.125 (* (* x x) x))
320.0ms
(log (- (- (/ 0.125 (* (* x x) x)) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
78.0ms
(- (- (/ 0.125 (* (* x x) x)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))

simplify1.2s

Counts
383 → 383
Iterations
IterNodes
done5001
11483
0584

prune2.4s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (sqrt 0.5) x)
12.2b
(log (+ (fma 0.125 (/ 1 (* (* x x) x)) (- (* (/ (sqrt 0.5) x) (/ (sqrt 0.5) 1)))) (- (fma (- (/ (sqrt 0.5) x)) (/ (sqrt 0.5) 1) (* (/ (sqrt 0.5) x) (/ (sqrt 0.5) 1))) (/ 0.0625 (pow x 5)))))
19.0b
(+ (fma 0.125 (/ 1 (* (* x x) x)) (- (* (/ (sqrt 0.5) x) (/ (sqrt 0.5) 1)))) (- (fma (- (/ (sqrt 0.5) x)) (/ (sqrt 0.5) 1) (* (/ (sqrt 0.5) x) (/ (sqrt 0.5) 1))) (/ 0.0625 (pow x 5))))
60.2b
(fma (- (/ (sqrt 0.5) x)) (/ (sqrt 0.5) 1) (* (/ (sqrt 0.5) x) (/ (sqrt 0.5) 1)))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
98×*-un-lft-identity
88×add-sqr-sqrt add-cube-cbrt
81×times-frac
78×associate-+r+
75×prod-diff
27×unpow-prod-down
12×sqrt-prod
add-log-exp sqr-pow
add-exp-log
add-cbrt-cube associate-/l*
pow1 log-prod
expm1-log1p-u log1p-expm1-u div-inv distribute-lft-out
associate-/r* fma-def fma-udef
log-div sum-log flip3-+ flip-+ distribute-lft-out--
cbrt-undiv +-commutative associate-+l+ clear-num associate-+r- sub-neg frac-2neg diff-log div-exp rem-log-exp associate--l+ log-pow
Counts
4 → 168
Calls
4 calls:
5.0ms
(/ (sqrt 0.5) x)
42.0ms
(log (+ (fma 0.125 (/ 1 (* (* x x) x)) (- (* (/ (sqrt 0.5) x) (/ (sqrt 0.5) 1)))) (- (fma (- (/ (sqrt 0.5) x)) (/ (sqrt 0.5) 1) (* (/ (sqrt 0.5) x) (/ (sqrt 0.5) 1))) (/ 0.0625 (pow x 5)))))
48.0ms
(+ (fma 0.125 (/ 1 (* (* x x) x)) (- (* (/ (sqrt 0.5) x) (/ (sqrt 0.5) 1)))) (- (fma (- (/ (sqrt 0.5) x)) (/ (sqrt 0.5) 1) (* (/ (sqrt 0.5) x) (/ (sqrt 0.5) 1))) (/ 0.0625 (pow x 5))))
0.0ms
(fma (- (/ (sqrt 0.5) x)) (/ (sqrt 0.5) 1) (* (/ (sqrt 0.5) x) (/ (sqrt 0.5) 1)))

series983.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(/ (sqrt 0.5) x)
437.0ms
(log (+ (fma 0.125 (/ 1 (* (* x x) x)) (- (* (/ (sqrt 0.5) x) (/ (sqrt 0.5) 1)))) (- (fma (- (/ (sqrt 0.5) x)) (/ (sqrt 0.5) 1) (* (/ (sqrt 0.5) x) (/ (sqrt 0.5) 1))) (/ 0.0625 (pow x 5)))))
286.0ms
(+ (fma 0.125 (/ 1 (* (* x x) x)) (- (* (/ (sqrt 0.5) x) (/ (sqrt 0.5) 1)))) (- (fma (- (/ (sqrt 0.5) x)) (/ (sqrt 0.5) 1) (* (/ (sqrt 0.5) x) (/ (sqrt 0.5) 1))) (/ 0.0625 (pow x 5))))
198.0ms
(fma (- (/ (sqrt 0.5) x)) (/ (sqrt 0.5) 1) (* (/ (sqrt 0.5) x) (/ (sqrt 0.5) 1)))

simplify2.5s

Counts
180 → 180
Iterations
IterNodes
done5000
24124
11033
0439

prune1.1s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes65.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 31.2b

bsearch130.0ms

Steps
ItersRangePoint
10
2.777137017098532e-16
1126.7541422477805
0.9010700472866574
9
-291337.82152789796
-0.7274215675205146
-1.0196402015835608

simplify3.6s

Iterations
IterNodes
done5000
13064999
13054995
13044991
13034987
13024983
13014979
13004977
12994972
12984970
12974965
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3421351
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3281296
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3101230
3091225
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3011196
3001192
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2831128
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2791112
2781108
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2751097
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2731089
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2701078
2691074
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2641056
2631054
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2591038
2581034
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2531016
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246989
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241972
240967
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238959
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236951
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219887
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214869
213865
212861
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209849
208847
207842
206840
205835
204831
203827
202823
201819
200817
199812
198810
197805
196801
195797
194793
193789
192785
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190778
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187767
186763
185759
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183751
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179736
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169696
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167688
166684
165680
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160662
159657
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157650
156648
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154639
153635
152631
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150623
149621
148616
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146608
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144600
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113481
112477
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110469
109467
108462
107460
106455
105451
104447
103443
102439
101435
100433
99428
98426
97421
96417
95413
94409
93405
92401
91397
90393
89391
88386
87382
86378
85374
84370
83366
82364
81359
80357
79352
78348
77344
76340
75336
74334
73331
72328
71323
70319
69315
68311
67307
66305
65300
64298
63293
62289
61285
60281
59277
58273
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56266
55264
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53255
52251
51247
50243
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48237
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46228
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43216
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41208
40204
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37193
36191
35188
34183
33181
32178
31173
30169
29165
28161
27157
26153
25149
24145
23143
22138
21136
20131
19127
18123
17119
16117
15112
14110
13105
12101
1197
1093
989
885
783
678
576
471
369
264
154
043

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.4s2341×body1280valid
781.0ms1573×body640valid
285.0ms763×body2560valid
258.0ms806×body320valid
91.0ms2086×body80valid
47.0ms431×body160valid