Details

sample175.0ms

Algorithm

intervals

Results

70.0ms	99×	body	2560	valid
40.0ms	82×	body	1280	valid
17.0ms	251×	body	80	nan
14.0ms	40×	body	640	valid
5.0ms	19×	body	320	valid
2.0ms	12×	body	160	valid
0.0ms	4×	body	80	valid

simplify799.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	906
5	235
4	146
3	77
2	42
1	19
0	9

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize27.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.2b	(* 5.0 (* v v))
0.5b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
13×	`*-un-lft-identity` `add-cube-cbrt`
12×	`times-frac`
10×	`add-cbrt-cube` `add-exp-log`
8×	`pow1`
4×	`associate-/r*` `difference-of-squares`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `associate-/l*` `add-log-exp`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`acos-asin` `cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `associate-r` `*-commutative` `div-inv` `unswap-sqr`

Counts

3 → 63

Calls

3 calls:

23.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
23.0ms	(* 5.0 (* v v))
2.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series132.0ms

Counts

3 → 9

Calls

3 calls:

95.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
30.0ms	(* 5.0 (* v v))
8.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify1.5s

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
2	1987
1	366
0	139

prune283.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* v v) (* (* v v) (* v v)))
0.0b	(* 4.0 (+ (* v v) (* (* v v) (* v v))))
0.1b	(* (* v v) (* v v))
0.5b	(acos (- (* 4.0 (+ (* v v) (* (* v v) (* v v)))) 1.0))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

117×	`pow1`
36×	`pow-prod-up`
24×	`pow-prod-down`
22×	`pow-sqr`
18×	`pow-plus` `add-cbrt-cube` `add-exp-log`
13×	`pow2`
9×	`prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt`
6×	`*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
5×	`associate-r`
4×	`associate-l`
2×	`flip3-+` `distribute-rgt1-in` `associate-r/` `-commutative` `flip-+` `unswap-sqr`
1×	`distribute-rgt-in` `acos-asin` `+-commutative` `sum-log` `distribute-lft-in` `swap-sqr`

Counts

4 → 106

Calls

4 calls:

7.0ms	(+ (* v v) (* (* v v) (* v v)))
21.0ms	(* 4.0 (+ (* v v) (* (* v v) (* v v))))
30.0ms	(* (* v v) (* v v))
2.0ms	(acos (- (* 4.0 (+ (* v v) (* (* v v) (* v v)))) 1.0))

series267.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(+ (* v v) (* (* v v) (* v v)))
115.0ms	(* 4.0 (+ (* v v) (* (* v v) (* v v))))
37.0ms	(* (* v v) (* v v))
6.0ms	(acos (- (* 4.0 (+ (* v v) (* (* v v) (* v v)))) 1.0))

simplify2.6s

Counts

118 → 118

Iterations

Iter	Nodes
done	5000
2	2771
1	371
0	112

prune345.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize41.0ms

Local error

Found 4 expressions with local error:

0.5b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
1.0b	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0b	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0b	(* (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
14×	`*-un-lft-identity` `add-cube-cbrt`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-cbrt-cube` `associate-r` `associate-l` `add-exp-log`
5×	`pow-prod-up`
4×	`add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square`
1×	`pow2` `acos-asin` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 83

Calls

4 calls:

2.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
2.0ms	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
2.0ms	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
28.0ms	(* (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

series63.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
19.0ms	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
31.0ms	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
9.0ms	(* (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

simplify1.8s

Counts

95 → 95

Iterations

Iter	Nodes
done	5000
2	847
1	155
0	71

prune394.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.5b

localize52.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
1.0b	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0b	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0b	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

18.0ms	(* (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
1.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
2.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))

series899.0ms

Counts

4 → 12

Calls

4 calls:

255.0ms	(* (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
203.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
226.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
214.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))

simplify2.3s

Counts

85 → 85

Iterations

Iter	Nodes
done	5001
2	644
1	137
0	61

prune372.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.5b

regimes258.0ms

Accuracy

0% (0.2b remaining)

Error of 0.8b against oracle of 0.6b and baseline of 0.8b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	11
1	11
0	9

end0.0ms

sample5.7s

Algorithm

intervals

Results

2.4s	3049×	body	2560	valid
1.7s	2440×	body	1280	valid
494.0ms	8164×	body	80	nan
400.0ms	1214×	body	640	valid
136.0ms	629×	body	320	valid
110.0ms	451×	body	160	valid
18.0ms	217×	body	80	valid