Details

sample25.0ms

Algorithm

intervals

Results

10.0ms

256×

body

valid

simplify2.8s

Counts

1 → 1

Iterations

Useful iterations: 3 (29.0ms)

Iter	Nodes	Cost
0	18	21
1	38	18
2	72	18
3	164	17
4	339	17
5	596	17
6	819	17
7	926	17
8	1192	17
9	1633	17
10	1697	17
11	1698	17
done	1698	17

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.9b

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)
1.9b	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
13.3b	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 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:

5.0ms	(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)

series280.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(fma (+ z 6.012459259764103) z 3.350343815022304)
29.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
74.0ms	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
154.0ms	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify818.0ms

Counts

71 → 71

Iterations

Useful iterations: done (816.0ms)

Iter	Nodes	Cost
0	129	985
1	246	962
2	572	857
3	1554	852
done	5000	849

prune276.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

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)
1.9b	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
13.3b	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma z (fma z 0.0692910599291889 0.4917317610505968) 0.279195317918525) x)

rewrite11.0ms

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

series282.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(fma (+ z 6.012459259764103) z 3.350343815022304)
30.0ms	(fma z (fma z 0.0692910599291889 0.4917317610505968) 0.279195317918525)
74.0ms	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
155.0ms	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma z (fma z 0.0692910599291889 0.4917317610505968) 0.279195317918525) x)

simplify816.0ms

Counts

71 → 71

Iterations

Useful iterations: done (813.0ms)

Iter	Nodes	Cost
0	129	985
1	246	962
2	572	857
3	1554	852
done	5000	849

prune257.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)))
11.9b	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
11.9b	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
13.3b	(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)

rewrite38.0ms

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:

18.0ms	(/ (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)))
2.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
2.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
0.0ms	(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)

series359.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(/ (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)))
57.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
65.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
157.0ms	(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)

simplify1.9s

Counts

229 → 229

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	318	7057
1	707	6040
2	1460	5562
3	3794	5281
done	5000	5143

prune633.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

11.9b	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
11.9b	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
11.9b	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
13.3b	(fma (/ (/ 1 (* (cbrt (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (cbrt (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))))) (/ (pow (cbrt (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) 4) y)) (fma z (fma z 0.0692910599291889 0.4917317610505968) 0.279195317918525) x)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 55

Calls

4 calls:

1.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
2.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
2.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
0.0ms	(fma (/ (/ 1 (* (cbrt (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (cbrt (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))))) (/ (pow (cbrt (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) 4) y)) (fma z (fma z 0.0692910599291889 0.4917317610505968) 0.279195317918525) x)

series284.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
64.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
58.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
106.0ms	(fma (/ (/ 1 (* (cbrt (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (cbrt (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))))) (/ (pow (cbrt (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) 4) y)) (fma z (fma z 0.0692910599291889 0.4917317610505968) 0.279195317918525) x)

simplify966.0ms

Counts

67 → 67

Iterations

Useful iterations: done (957.0ms)

Iter	Nodes	Cost
0	81	1162
1	168	1094
2	418	885
3	1244	820
done	5000	740

prune364.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes216.0ms

Accuracy

98.2% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 16.8b

bsearch124.0ms

Steps

Iters	Range		Point
9	8.870965552829853	38818986.17800169	32935595.478218053
4	-5.212707364099186e+60	-3.221273438315299e+60	-3.283505748496046e+60

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

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

end0.0ms

sample569.0ms

Algorithm

intervals

Results

336.0ms

8000×

body

valid