Details

sample143.0ms

Algorithm

intervals

Results

62.0ms	108×	body	2560	valid
28.0ms	70×	body	1280	valid
14.0ms	267×	body	80	nan
11.0ms	38×	body	640	valid
5.0ms	26×	body	320	valid
1.0ms	9×	body	160	valid
0.0ms	5×	body	80	valid

simplify776.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	20	14
2	43	14
3	84	14
4	155	14
5	252	14
6	934	14
done	5000	14

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize17.0ms

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)))

rewrite78.0ms

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×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `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 → 69

Calls

3 calls:

49.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
25.0ms	(* 5.0 (* v v))
1.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series154.0ms

Counts

3 → 9

Calls

3 calls:

101.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
48.0ms	(* 5.0 (* v v))
5.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify1.6s

Counts

78 → 78

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	145	1268
1	368	1227
2	1813	1122
done	5001	1118

prune245.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- 1.0 (* 5.0 (pow v 2))) (- (* v v) 1.0))
0.0b	(pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (* v v) 1.0)) 3)
0.2b	(* 5.0 (pow v 2))
0.4b	(acos (cbrt (pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (* v v) 1.0)) 3)))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt`
36×	`times-frac`
33×	`add-cube-cbrt` `*-un-lft-identity`
22×	`unpow-prod-down`
18×	`cube-prod`
14×	`add-exp-log`
11×	`add-cbrt-cube`
10×	`difference-of-squares`
8×	`associate-r`
6×	`associate-/r/`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `associate-/r*` `flip--` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-unpow` `associate-l` `pow-exp` `prod-exp` `div-inv` `associate-/l*` `sqr-pow`
2×	`cbrt-undiv` `pow-to-exp` `div-exp` `associate-/l/` `unpow2` `rem-cube-cbrt`
1×	`cube-div` `acos-asin` `cube-mult` `pow-pow` `frac-2neg` `unpow3` `div-sub` `clear-num` `*-commutative` `cbrt-unprod`

Counts

4 → 135

Calls

4 calls:

40.0ms	(/ (- 1.0 (* 5.0 (pow v 2))) (- (* v v) 1.0))
37.0ms	(pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (* v v) 1.0)) 3)
21.0ms	(* 5.0 (pow v 2))
1.0ms	(acos (cbrt (pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (* v v) 1.0)) 3)))

series338.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(/ (- 1.0 (* 5.0 (pow v 2))) (- (* v v) 1.0))
176.0ms	(pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (* v v) 1.0)) 3)
48.0ms	(* 5.0 (pow v 2))
8.0ms	(acos (cbrt (pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (* v v) 1.0)) 3)))

simplify2.1s

Counts

147 → 147

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	234	2992
1	841	2755
2	3954	2521
done	5000	2519

prune567.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.4b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 5.0 (pow v 2))
0.4b	(acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)))
1.0b	(cbrt (pow (acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0))) 3))
1.0b	(pow (acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0))) 3)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
12×	`cbrt-prod`
10×	`add-exp-log` `unpow-prod-down`
8×	`associate-r`
7×	`add-cbrt-cube`
6×	`cube-prod`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr` `sqr-pow`
3×	`pow-unpow` `associate-l` `prod-exp`
2×	`cube-mult` `pow-to-exp` `unpow3` `pow-exp` `unpow2`
1×	`acos-asin` `pow-pow` `pow1/3` `*-commutative` `rem-cbrt-cube` `cbrt-unprod` `rem-cube-cbrt`

Counts

4 → 87

Calls

4 calls:

13.0ms	(* 5.0 (pow v 2))
1.0ms	(acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)))
2.0ms	(cbrt (pow (acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0))) 3))
5.0ms	(pow (acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0))) 3)

series93.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* 5.0 (pow v 2))
5.0ms	(acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)))
7.0ms	(cbrt (pow (acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0))) 3))
53.0ms	(pow (acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0))) 3)

simplify1.3s

Counts

99 → 99

Iterations

Useful iterations: 2 (210.0ms)

Iter	Nodes	Cost
0	112	1838
1	258	1642
2	1293	1410
done	5003	1410

prune289.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.4b	(acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)))
1.0b	(cbrt (expm1 (log1p (pow (acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0))) 3))))
1.0b	(expm1 (log1p (pow (acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0))) 3)))
1.0b	(pow (acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0))) 3)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `unpow-prod-down` `pow-unpow` `cube-prod`
1×	`acos-asin` `cube-mult` `pow-to-exp` `expm1-log1p` `pow-pow` `pow1/3` `unpow3` `pow-exp` `expm1-udef` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 59

Calls

4 calls:

2.0ms	(acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)))
2.0ms	(cbrt (expm1 (log1p (pow (acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0))) 3))))
1.0ms	(expm1 (log1p (pow (acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0))) 3)))
5.0ms	(pow (acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0))) 3)

series825.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)))
516.0ms	(cbrt (expm1 (log1p (pow (acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0))) 3))))
242.0ms	(expm1 (log1p (pow (acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0))) 3)))
59.0ms	(pow (acos (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0))) 3)

simplify1.1s

Counts

71 → 71

Iterations

Useful iterations: 2 (137.0ms)

Iter	Nodes	Cost
0	72	1590
1	171	1372
2	806	1186
done	5002	1186

prune224.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.4b

regimes19.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	19
1	16	19
done	16	19

end0.0ms

sample5.7s

Algorithm

intervals

Results

1.8s	2948×	body	2560	valid
1.8s	2486×	body	1280	valid
858.0ms	1239×	body	640	valid
494.0ms	8126×	body	80	nan
138.0ms	660×	body	320	valid
111.0ms	427×	body	160	valid
23.0ms	240×	body	80	valid