Details

sample167.0ms

Algorithm

intervals

Results

71.0ms	108×	body	2560	valid
33.0ms	70×	body	1280	valid
17.0ms	267×	body	80	nan
13.0ms	38×	body	640	valid
7.0ms	26×	body	320	valid
2.0ms	9×	body	160	valid
0.0ms	5×	body	80	valid

simplify693.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	19	14
2	42	14
3	77	14
4	146	14
5	233	14
6	901	14
done	5000	14

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize9.0ms

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))
0.4b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
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×	`cbrt-undiv` `acos-asin` `frac-2neg` `div-sub` `div-exp` `associate-r` `clear-num` `*-commutative` `div-inv` `unswap-sqr`

Counts

3 → 63

Calls

3 calls:

34.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
20.0ms	(* 5.0 (* v v))
1.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series179.0ms

Counts

3 → 9

Calls

3 calls:

144.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
30.0ms	(* 5.0 (* v v))
5.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify1.4s

Counts

72 → 72

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	139	1198
1	366	1162
2	1989	1056
done	5000	1052

prune287.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (* v v) 1.0) (sqrt (- 1.0 (* 5.0 (* v v)))))
0.2b	(* 5.0 (* v v))
0.2b	(* 5.0 (* v v))
0.4b	(acos (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (/ (- (* v v) 1.0) (sqrt (- 1.0 (* 5.0 (* v v)))))))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
24×	`times-frac`
23×	`add-cube-cbrt` `*-un-lft-identity`
16×	`add-exp-log` `add-cbrt-cube`
15×	`sqrt-prod`
14×	`pow1`
7×	`difference-of-squares`
6×	`associate-l` `pow-prod-down` `prod-exp` `associate-/r*` `cbrt-unprod`
4×	`associate-/l*` `add-log-exp`
2×	`flip3--` `sqrt-div` `associate-r` `associate-/r/` `*-commutative` `flip--` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `acos-asin` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 97

Calls

4 calls:

40.0ms	(/ (- (* v v) 1.0) (sqrt (- 1.0 (* 5.0 (* v v)))))
19.0ms	(* 5.0 (* v v))
40.0ms	(* 5.0 (* v v))
2.0ms	(acos (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (/ (- (* v v) 1.0) (sqrt (- 1.0 (* 5.0 (* v v)))))))

series332.0ms

Counts

4 → 12

Calls

4 calls:

246.0ms	(/ (- (* v v) 1.0) (sqrt (- 1.0 (* 5.0 (* v v)))))
41.0ms	(* 5.0 (* v v))
40.0ms	(* 5.0 (* v v))
5.0ms	(acos (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (/ (- (* v v) 1.0) (sqrt (- 1.0 (* 5.0 (* v v)))))))

simplify1.4s

Counts

109 → 109

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	189	2031
1	476	1910
2	2235	1680
done	5002	1678

prune403.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.4b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 5.0 (* v v))
0.4b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
1.0b	(cbrt (pow (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) 3))
1.0b	(pow (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) 3)

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod` `add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`unpow-prod-down` `cube-prod`
4×	`add-log-exp`
3×	`pow-unpow` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`cube-mult` `unpow3` `sqr-pow`
1×	`acos-asin` `pow-to-exp` `pow-pow` `pow1/3` `associate-r` `pow-exp` `*-commutative` `rem-cbrt-cube` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 71

Calls

4 calls:

33.0ms	(* 5.0 (* v v))
2.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
5.0ms	(cbrt (pow (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) 3))
6.0ms	(pow (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) 3)

series118.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* 5.0 (* v v))
5.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
5.0ms	(cbrt (pow (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) 3))
81.0ms	(pow (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) 3)

simplify1.4s

Counts

83 → 83

Iterations

Useful iterations: 2 (243.0ms)

Iter	Nodes	Cost
0	93	1656
1	256	1514
2	1513	1257
done	5001	1257

prune232.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.4b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 5.0 (* v v))
0.4b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
1.0b	(cbrt (cbrt (pow (pow (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) 3) 3)))
1.0b	(pow (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) 3)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

63×	`cbrt-prod`
21×	`unpow-prod-down` `cube-prod`
17×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
10×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`cube-mult` `unpow3` `add-log-exp` `sqr-pow`
3×	`pow-unpow` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
1×	`acos-asin` `pow-to-exp` `pow-pow` `pow1/3` `associate-r` `pow-exp` `*-commutative` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 91

Calls

4 calls:

21.0ms	(* 5.0 (* v v))
1.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
9.0ms	(cbrt (cbrt (pow (pow (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) 3) 3)))
3.0ms	(pow (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) 3)

series128.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* 5.0 (* v v))
8.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
9.0ms	(cbrt (cbrt (pow (pow (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) 3) 3)))
82.0ms	(pow (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) 3)

simplify3.6s

Counts

103 → 103

Iterations

Useful iterations: 2 (512.0ms)

Iter	Nodes	Cost
0	134	2689
1	382	2188
2	2082	1868
done	5000	1868

prune253.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.4b

regimes88.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	10	14
done	10	14

end0.0ms

sample5.3s

Algorithm

intervals

Results

2.6s	2948×	body	2560	valid
1.2s	2486×	body	1280	valid
493.0ms	8126×	body	80	nan
412.0ms	1239×	body	640	valid
136.0ms	660×	body	320	valid
59.0ms	427×	body	160	valid
20.0ms	240×	body	80	valid