Details

sample31.0ms

Algorithm

intervals

Results

13.0ms

256×

body

valid

simplify373.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	9	19
1	19	18
2	39	18
3	77	18
4	128	18
5	184	18
6	211	18
7	216	18
done	216	18

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.9b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma x x (* (* y 4.0) y))
3.8b	(- (* x x) (* (* y 4.0) y))
33.3b	(/ (- (* x x) (* (* y 4.0) y)) (fma x x (* (* y 4.0) y)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1` `expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l`
2×	`flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `clear-num` `fma-udef` `div-inv`

Counts

3 → 58

Calls

3 calls:

0.0ms	(fma x x (* (* y 4.0) y))
9.0ms	(- (* x x) (* (* y 4.0) y))
24.0ms	(/ (- (* x x) (* (* y 4.0) y)) (fma x x (* (* y 4.0) y)))

series313.0ms

Counts

3 → 9

Calls

3 calls:

80.0ms	(fma x x (* (* y 4.0) y))
89.0ms	(- (* x x) (* (* y 4.0) y))
144.0ms	(/ (- (* x x) (* (* y 4.0) y)) (fma x x (* (* y 4.0) y)))

simplify2.9s

Counts

67 → 67

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	94	1321
1	225	1289
2	782	1165
3	3081	1163
done	5000	1162

prune235.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize0.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune4.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.6b

localize0.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune3.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.6b

localize21.0ms

Local error

Found 4 expressions with local error:

32.6b	(cbrt (- (* x x) (* (* y 4.0) y)))
32.6b	(cbrt (fma x x (* (* y 4.0) y)))
32.6b	(cbrt (fma x x (* (* y 4.0) y)))
32.6b	(cbrt (fma x x (* (* y 4.0) y)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `pow1/3` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-div`
1×	`flip3--` `flip--`

Counts

4 → 54

Calls

4 calls:

10.0ms	(cbrt (- (* x x) (* (* y 4.0) y)))
1.0ms	(cbrt (fma x x (* (* y 4.0) y)))
1.0ms	(cbrt (fma x x (* (* y 4.0) y)))
1.0ms	(cbrt (fma x x (* (* y 4.0) y)))

series690.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(cbrt (- (* x x) (* (* y 4.0) y)))
165.0ms	(cbrt (fma x x (* (* y 4.0) y)))
178.0ms	(cbrt (fma x x (* (* y 4.0) y)))
171.0ms	(cbrt (fma x x (* (* y 4.0) y)))

simplify4.0s

Counts

66 → 66

Iterations

Useful iterations: done (4.0s)

Iter	Nodes	Cost
0	88	965
1	188	948
2	493	861
3	1406	831
4	3804	819
done	5000	817

prune413.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0.6b

regimes188.0ms

Accuracy

58.5% (13.1b remaining)

Error of 13.4b against oracle of 0.3b and baseline of 31.8b

bsearch264.0ms

Steps

Iters	Range		Point
7	1.199445854275694e+37	2.5019551147159262e+39	2.3789718643835513e+39
7	1.5818187033891164e-118	3.8400264464765154e-116	1.7295951145279685e-117
9	-2.0471070403965084e-143	-2.153678170399452e-149	-8.489767143855688e-144
9	-4.450999065334776e+30	-6.7107616040613245e+25	-4.4113331927295025e+30
10	-5.053334512127192e+72	-6.261927662807804e+61	-2.353923326691391e+65

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	60
1	30	60
done	30	60

end0.0ms

sample611.0ms

Algorithm

intervals

Results

336.0ms

8000×

body

valid