Details

sample41.0ms

Algorithm

intervals

Results

17.0ms

256×

body

valid

simplify5.2s

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

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (+ z 6.012459259764103) z 3.350343815022304)
0.0b	(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)
16.1b	(/ (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304))

rewrite6.0ms

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))

series390.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(fma (+ z 6.012459259764103) z 3.350343815022304)
54.0ms	(fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525)
175.0ms	(fma (/ (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304)) y x)
124.0ms	(/ (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304))

simplify1.3s

Counts

71 → 71

Iterations

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

prune527.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (+ z 6.012459259764103) z 3.350343815022304)
0.0b	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
5.1b	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
17.9b	(* (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `add-cube-cbrt`
19×	`times-frac`
13×	`associate-r`
11×	`add-cbrt-cube` `add-exp-log`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-l` `associate-/l`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `fma-udef` `div-inv` `unswap-sqr`
1×	`clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `-commutative`

Counts

4 → 83

Calls

4 calls:

0.0ms	(fma (+ z 6.012459259764103) z 3.350343815022304)
0.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
4.0ms	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
12.0ms	(* (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)))

series322.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(fma (+ z 6.012459259764103) z 3.350343815022304)
51.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
100.0ms	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
126.0ms	(* (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)))

simplify816.0ms

Counts

95 → 95

Iterations

Iter	Nodes
done	5001
2	1368
1	356
0	156

prune664.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (cbrt (pow (/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304)) 3)) y x)
0.5b	(cbrt (pow (/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304)) 3))
0.6b	(pow (/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304)) 3)
16.1b	(/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

45×	`times-frac`
42×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
32×	`cbrt-prod`
26×	`unpow-prod-down` `cube-prod`
9×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `associate-/r` `associate-/l`
2×	`cube-div` `cube-mult` `cbrt-undiv` `unpow3` `div-exp` `pow-exp` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `cbrt-div` `clear-num` `pow-pow` `frac-2neg` `pow1/3` `rem-cbrt-cube` `fma-udef`

Counts

4 → 131

Calls

4 calls:

0.0ms	(fma (cbrt (pow (/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304)) 3)) y x)
5.0ms	(cbrt (pow (/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304)) 3))
5.0ms	(pow (/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304)) 3)
6.0ms	(/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304))

series616.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(fma (cbrt (pow (/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304)) 3)) y x)
137.0ms	(cbrt (pow (/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304)) 3))
154.0ms	(pow (/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304)) 3)
138.0ms	(/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304))

simplify1.6s

Counts

143 → 143

Iterations

Iter	Nodes
done	5001
2	2803
1	549
0	194

prune979.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
0.1b	(fma (/ 1 (/ (fma (+ z 6.012459259764103) z 3.350343815022304) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525))) y x)
0.5b	(/ 1 (/ (fma (+ z 6.012459259764103) z 3.350343815022304) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)))
16.1b	(/ (fma (+ z 6.012459259764103) z 3.350343815022304) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525))

rewrite34.0ms

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

series400.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
153.0ms	(fma (/ 1 (/ (fma (+ z 6.012459259764103) z 3.350343815022304) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525))) y x)
112.0ms	(/ 1 (/ (fma (+ z 6.012459259764103) z 3.350343815022304) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)))
100.0ms	(/ (fma (+ z 6.012459259764103) z 3.350343815022304) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525))

simplify1.1s

Counts

139 → 139

Iterations

Iter	Nodes
done	5001
2	2085
1	504
0	222

prune756.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes497.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 16.2b

bsearch223.0ms

Steps

Iters	Range		Point
11	11826.435389185313	5.566453567611273e+27	14154540400533552.0
9	-633385646006946.0	-496427297.3881253	-4347718231920.455

simplify4.0ms

Iterations

Iter	Nodes
done	41
1	41
0	32

end0.0ms

sample1.6s

Algorithm

intervals

Results

1.3s

8000×

body

valid