Details

sample33.0ms

Algorithm

intervals

Results

14.0ms

256×

body

valid

simplify5.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
10	3779
9	2852
8	2267
7	1902
6	1547
5	966
4	418
3	167
2	72
1	38
0	18

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.9b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (+ z 6.012459259764103) z 3.350343815022304)
0.1b	(fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525)
0.1b	(fma (/ (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304)) y x)
16.3b	(/ (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

0.0ms	(fma (+ z 6.012459259764103) z 3.350343815022304)
0.0ms	(fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525)
0.0ms	(fma (/ (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304)) y x)
4.0ms	(/ (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304))

series368.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(fma (+ z 6.012459259764103) z 3.350343815022304)
49.0ms	(fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525)
186.0ms	(fma (/ (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304)) y x)
98.0ms	(/ (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304))

simplify1.7s

Counts

71 → 71

Iterations

Iter	Nodes
done	5002
3	2290
2	606
1	229
0	118

prune610.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525)
0.1b	(fma (/ 1 (/ (fma (+ z 6.012459259764103) z 3.350343815022304) (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525))) y x)
0.5b	(/ 1 (/ (fma (+ z 6.012459259764103) z 3.350343815022304) (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525)))
16.4b	(/ (fma (+ z 6.012459259764103) z 3.350343815022304) (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 127

Calls

4 calls:

0.0ms	(fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525)
0.0ms	(fma (/ 1 (/ (fma (+ z 6.012459259764103) z 3.350343815022304) (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525))) y x)
16.0ms	(/ 1 (/ (fma (+ z 6.012459259764103) z 3.350343815022304) (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525)))
8.0ms	(/ (fma (+ z 6.012459259764103) z 3.350343815022304) (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525))

series380.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525)
147.0ms	(fma (/ 1 (/ (fma (+ z 6.012459259764103) z 3.350343815022304) (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525))) y x)
80.0ms	(/ 1 (/ (fma (+ z 6.012459259764103) z 3.350343815022304) (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525)))
120.0ms	(/ (fma (+ z 6.012459259764103) z 3.350343815022304) (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525))

simplify1.2s

Counts

139 → 139

Iterations

Iter	Nodes
done	5001
2	2085
1	504
0	222

prune1.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 101.23733352003816 (* z z)) (/ 15.646356830292035 z))
0.4b	(/ 1 (+ 14.431876219268938 (- (/ 101.23733352003816 (* z z)) (/ 15.646356830292035 z))))
0.7b	(/ 101.23733352003816 (* z z))
1.7b	(fma (/ 1 (+ 14.431876219268938 (- (/ 101.23733352003816 (* z z)) (/ 15.646356830292035 z)))) y x)

rewrite212.0ms

Algorithm

rewrite-expression-head

Rules

127×	`times-frac`
115×	`*-un-lft-identity`
103×	`add-sqr-sqrt`
93×	`add-cube-cbrt`
91×	`prod-diff`
23×	`div-inv`
13×	`add-exp-log`
11×	`add-cbrt-cube`
8×	`distribute-lft-out`
7×	`fma-neg`
6×	`associate-/r` `associate-/l` `add-log-exp`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `div-exp` `log1p-expm1-u` `difference-of-squares`
3×	`cbrt-undiv`
2×	`clear-num` `frac-2neg` `associate-/r/`
1×	`rec-exp` `sub-neg` `flip3-+` `flip3--` `diff-log` `1-exp` `prod-exp` `frac-sub` `cbrt-unprod` `flip-+` `fma-udef` `pow-flip` `flip--` `inv-pow`

Counts

4 → 194

Calls

4 calls:

38.0ms	(- (/ 101.23733352003816 (* z z)) (/ 15.646356830292035 z))
158.0ms	(/ 1 (+ 14.431876219268938 (- (/ 101.23733352003816 (* z z)) (/ 15.646356830292035 z))))
6.0ms	(/ 101.23733352003816 (* z z))
0.0ms	(fma (/ 1 (+ 14.431876219268938 (- (/ 101.23733352003816 (* z z)) (/ 15.646356830292035 z)))) y x)

series279.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(- (/ 101.23733352003816 (* z z)) (/ 15.646356830292035 z))
54.0ms	(/ 1 (+ 14.431876219268938 (- (/ 101.23733352003816 (* z z)) (/ 15.646356830292035 z))))
36.0ms	(/ 101.23733352003816 (* z z))
97.0ms	(fma (/ 1 (+ 14.431876219268938 (- (/ 101.23733352003816 (* z z)) (/ 15.646356830292035 z)))) y x)

simplify2.1s

Counts

206 → 206

Iterations

Iter	Nodes
done	5001
2	3783
1	814
0	342

prune1.2s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1 (/ (fma (+ z 6.012459259764103) z 3.350343815022304) (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525)))
0.5b	(/ 1 (/ (fma (+ z 6.012459259764103) z 3.350343815022304) (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525)))
16.4b	(/ (fma (+ z 6.012459259764103) z 3.350343815022304) (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525))
16.4b	(/ (fma (+ z 6.012459259764103) z 3.350343815022304) (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

168×	`times-frac`
104×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
32×	`associate-/r*`
30×	`add-exp-log`
18×	`add-cbrt-cube`
16×	`div-exp`
12×	`div-inv` `associate-/l*`
8×	`cbrt-undiv`
6×	`pow1`
4×	`expm1-log1p-u` `rec-exp` `clear-num` `frac-2neg` `1-exp` `log1p-expm1-u` `add-log-exp`
2×	`associate-/r/` `pow-flip` `inv-pow`

Counts

4 → 214

Calls

4 calls:

8.0ms	(/ 1 (/ (fma (+ z 6.012459259764103) z 3.350343815022304) (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525)))
22.0ms	(/ 1 (/ (fma (+ z 6.012459259764103) z 3.350343815022304) (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525)))
7.0ms	(/ (fma (+ z 6.012459259764103) z 3.350343815022304) (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525))
7.0ms	(/ (fma (+ z 6.012459259764103) z 3.350343815022304) (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525))

series431.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(/ 1 (/ (fma (+ z 6.012459259764103) z 3.350343815022304) (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525)))
126.0ms	(/ 1 (/ (fma (+ z 6.012459259764103) z 3.350343815022304) (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525)))
98.0ms	(/ (fma (+ z 6.012459259764103) z 3.350343815022304) (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525))
95.0ms	(/ (fma (+ z 6.012459259764103) z 3.350343815022304) (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525))

simplify1.7s

Counts

226 → 226

Iterations

Iter	Nodes
done	5000
2	2125
1	434
0	189

prune2.4s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes522.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 15.4b

bsearch233.0ms

Steps

Iters	Range		Point
7	58098.925141855936	2373587.5359664164	774965.7572102336
10	-154130335284.9803	-27.16127718389199	-485777911.3922658

simplify14.0ms

Iterations

Iter	Nodes
done	41
1	41
0	34

end0.0ms

sample1.6s

Algorithm

intervals

Results

1.3s

8000×

body

valid