Details

sample41.0ms

Algorithm

intervals

Results

19.0ms

256×

body

valid

simplify6.7s

Counts

1 → 1

Iterations

Useful iterations: 3 (51.0ms)

Iter	Nodes	Cost
0	18	21
1	38	18
2	72	18
3	167	17
4	415	17
5	944	17
6	1502	17
7	1837	17
8	2224	17
9	2802	17
10	3764	17
done	5000	17

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (+ z 6.012459259764103) z 3.350343815022304)
0.1b	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
3.6b	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
15.9b	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

0.0ms	(fma (+ z 6.012459259764103) z 3.350343815022304)
0.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
5.0ms	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
0.0ms	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

series355.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(fma (+ z 6.012459259764103) z 3.350343815022304)
42.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
92.0ms	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
199.0ms	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify2.7s

Counts

71 → 71

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	129	985
1	251	962
2	768	866
3	3365	855
done	5000	851

prune340.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (+ z 6.012459259764103) z 3.350343815022304)
0.1b	(fma z (fma z 0.0692910599291889 0.4917317610505968) 0.279195317918525)
3.6b	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
15.9b	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma z (fma z 0.0692910599291889 0.4917317610505968) 0.279195317918525) x)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

0.0ms	(fma (+ z 6.012459259764103) z 3.350343815022304)
1.0ms	(fma z (fma z 0.0692910599291889 0.4917317610505968) 0.279195317918525)
8.0ms	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
1.0ms	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma z (fma z 0.0692910599291889 0.4917317610505968) 0.279195317918525) x)

series307.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(fma (+ z 6.012459259764103) z 3.350343815022304)
30.0ms	(fma z (fma z 0.0692910599291889 0.4917317610505968) 0.279195317918525)
88.0ms	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
160.0ms	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma z (fma z 0.0692910599291889 0.4917317610505968) 0.279195317918525) x)

simplify2.5s

Counts

71 → 71

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	129	985
1	251	962
2	768	866
3	3365	855
done	5000	851

prune302.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)))
14.2b	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
14.2b	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
15.9b	(fma (/ (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (fma z (fma z 0.0692910599291889 0.4917317610505968) 0.279195317918525) x)

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

258×	`times-frac`
145×	`add-sqr-sqrt`
143×	`add-cube-cbrt` `*-un-lft-identity`
138×	`sqrt-prod`
22×	`associate-/l*`
9×	`add-exp-log` `add-cbrt-cube`
8×	`div-inv`
6×	`pow1` `associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`frac-2neg` `clear-num` `fma-udef` `associate-/l/`

Counts

4 → 217

Calls

4 calls:

33.0ms	(/ (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)))
3.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
3.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
1.0ms	(fma (/ (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (fma z (fma z 0.0692910599291889 0.4917317610505968) 0.279195317918525) x)

series385.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(/ (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)))
71.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
72.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
166.0ms	(fma (/ (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (fma z (fma z 0.0692910599291889 0.4917317610505968) 0.279195317918525) x)

simplify1.4s

Counts

229 → 229

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	318	7057
1	751	6040
2	3433	5656
done	5000	5354

prune953.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

14.2b	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
14.7b	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
14.7b	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
15.9b	(fma (/ (/ (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (fabs (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) (sqrt (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) (fma z (fma z 0.0692910599291889 0.4917317610505968) 0.279195317918525) x)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-prod`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
2×	`pow1/3`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

4 → 51

Calls

4 calls:

3.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
2.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
1.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
1.0ms	(fma (/ (/ (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (fabs (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) (sqrt (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) (fma z (fma z 0.0692910599291889 0.4917317610505968) 0.279195317918525) x)

series1.2s

Counts

4 → 12

Calls

4 calls:

61.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
496.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
147.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
493.0ms	(fma (/ (/ (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (fabs (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) (sqrt (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) (fma z (fma z 0.0692910599291889 0.4917317610505968) 0.279195317918525) x)

simplify2.0s

Counts

63 → 63

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	134	1247
1	306	1188
2	997	1058
3	4147	1021
done	5000	1014

prune470.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes218.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 16.9b

bsearch181.0ms

Steps

Iters	Range		Point
9	7337.051904760935	9334432389.324938	131692816.82489662
9	-4159660869929146.0	-8119328.430348501	-191257685.2125228

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	28	47
1	40	39
done	40	39

end0.0ms

sample1.2s

Algorithm

intervals

Results

799.0ms

8000×

body

valid