Details

sample95.0ms

Algorithm

intervals

Results

35.0ms	92×	body	2560	valid
21.0ms	78×	body	1280	valid
10.0ms	277×	body	80	nan
8.0ms	42×	body	640	valid
4.0ms	27×	body	320	valid
2.0ms	15×	body	160	valid
0.0ms	2×	body	80	valid

simplify3.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5018
8	4522
7	1213
6	455
5	218
4	138
3	77
2	42
1	20
0	9

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.6b

localize23.0ms

Local error

Found 2 expressions with local error:

0.2b	(* 5.0 (* v v))
0.6b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `add-cbrt-cube` `add-exp-log`
4×	`add-sqr-sqrt`
3×	`-un-lft-identity` `associate-l*` `pow-prod-down` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
2×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`acos-asin` `associate-r` `*-commutative` `unswap-sqr`

Counts

2 → 31

Calls

2 calls:

15.0ms	(* 5.0 (* v v))
1.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series39.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(* 5.0 (* v v))
5.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify3.1s

Counts

37 → 37

Iterations

Iter	Nodes
done	5001
3	1247
2	317
1	122
0	57

prune203.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.6b

localize43.0ms

Local error

Found 4 expressions with local error:

0.6b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
0.6b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
1.0b	(* (* (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (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))) (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

23×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
6×	`add-sqr-sqrt` `pow-plus` `pow-prod-up`
5×	`*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`pow2` `acos-asin` `pow3` `pow-sqr`
1×	`cbrt-prod` `pow1/3` `associate-l` `*-commutative` `rem-cbrt-cube` `unswap-sqr`

Counts

4 → 62

Calls

4 calls:

2.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
2.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
37.0ms	(* (* (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
23.0ms	(cbrt (* (* (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

series99.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
8.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
72.0ms	(* (* (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
11.0ms	(cbrt (* (* (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

simplify3.0s

Counts

74 → 74

Iterations

Iter	Nodes
done	5000
5	2279
4	1148
3	465
2	269
1	135
0	65

prune307.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.6b

localize39.0ms

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))))

rewrite20.0ms

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×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `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 → 81

Calls

4 calls:

14.0ms	(* (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))))
1.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))

series922.0ms

Counts

4 → 12

Calls

4 calls:

297.0ms	(* (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
190.0ms	(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))))
221.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))

simplify2.6s

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
4	2016
3	724
2	309
1	140
0	65

prune541.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.6b

localize119.0ms

Local error

Found 4 expressions with local error:

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))))
1.6b	(* (* (cbrt (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) (cbrt (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))) (* (cbrt (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) (cbrt (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

115×	`pow1`
49×	`pow-prod-up`
47×	`pow1/3`
33×	`pow-sqr`
32×	`pow-prod-down`
18×	`pow-plus`
16×	`add-exp-log`
13×	`pow2`
9×	`cbrt-prod`
8×	`add-cbrt-cube` `prod-exp` `cbrt-unprod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`swap-sqr` `associate-r` `associate-l` `*-commutative` `unswap-sqr`

Counts

4 → 115

Calls

4 calls:

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))))
1.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
82.0ms	(* (* (cbrt (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) (cbrt (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))) (* (cbrt (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) (cbrt (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))))

series1.2s

Counts

4 → 12

Calls

4 calls:

206.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
162.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
188.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
655.0ms	(* (* (cbrt (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) (cbrt (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))) (* (cbrt (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) (cbrt (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))))

simplify4.9s

Counts

127 → 127

Iterations

Iter	Nodes
done	5002
4	3381
3	906
2	391
1	209
0	83

prune564.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

regimes202.0ms

Accuracy

0% (0.0b remaining)

Error of 0.5b against oracle of 0.5b and baseline of 0.5b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	21
1	21
0	18

end0.0ms

sample5.2s

Algorithm

intervals

Results

2.1s	3063×	body	2560	valid
1.7s	2457×	body	1280	valid
514.0ms	8020×	body	80	nan
365.0ms	1250×	body	640	valid
168.0ms	629×	body	320	valid
64.0ms	414×	body	160	valid
15.0ms	187×	body	80	valid