Details

sample115.0ms

Algorithm

intervals

Results

38.0ms	84×	body	2560	valid
33.0ms	95×	body	1280	valid
12.0ms	262×	body	80	nan
8.0ms	36×	body	640	valid
4.0ms	22×	body	320	valid
2.0ms	14×	body	160	valid
0.0ms	5×	body	80	valid

simplify508.0ms

Counts

1 → 1

Iterations

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

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

rewrite70.0ms

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:

40.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
25.0ms	(* 5.0 (* v v))
2.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series173.0ms

Counts

3 → 9

Calls

3 calls:

127.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
38.0ms	(* 5.0 (* v v))
8.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify1.1s

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
2	1987
1	366
0	139

prune391.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize33.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (/ (- 1.0 (* (* 5.0 v) v)) (- (pow v 4) (* 1.0 1.0))) (+ (* v v) 1.0))
0.1b	(* (* 5.0 v) v)
0.4b	(acos (* (/ (- 1.0 (* (* 5.0 v) v)) (- (pow v 4) (* 1.0 1.0))) (+ (* v v) 1.0)))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
25×	`associate-l`
19×	`times-frac`
15×	`*-un-lft-identity` `add-cube-cbrt`
13×	`add-cbrt-cube` `add-exp-log`
10×	`pow1`
9×	`difference-of-squares`
6×	`associate-r`
5×	`prod-exp` `cbrt-unprod`
4×	`pow-prod-down`
3×	`unpow-prod-down` `add-log-exp` `sqr-pow`
2×	`frac-times` `flip3-+` `associate-r/` `associate-/r/` `-commutative` `flip-+` `unswap-sqr`
1×	`distribute-rgt-in` `acos-asin` `cbrt-undiv` `distribute-lft-in` `flip3--` `div-exp` `associate-*l/` `div-inv` `flip--`

Counts

3 → 75

Calls

3 calls:

100.0ms	(* (/ (- 1.0 (* (* 5.0 v) v)) (- (pow v 4) (* 1.0 1.0))) (+ (* v v) 1.0))
27.0ms	(* (* 5.0 v) v)
3.0ms	(acos (* (/ (- 1.0 (* (* 5.0 v) v)) (- (pow v 4) (* 1.0 1.0))) (+ (* v v) 1.0)))

series233.0ms

Counts

3 → 9

Calls

3 calls:

188.0ms	(* (/ (- 1.0 (* (* 5.0 v) v)) (- (pow v 4) (* 1.0 1.0))) (+ (* v v) 1.0))
36.0ms	(* (* 5.0 v) v)
8.0ms	(acos (* (/ (- 1.0 (* (* 5.0 v) v)) (- (pow v 4) (* 1.0 1.0))) (+ (* v v) 1.0)))

simplify2.3s

Counts

84 → 84

Iterations

Iter	Nodes
done	5000
2	4290
1	674
0	187

prune716.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize34.0ms

Local error

Found 4 expressions with local error:

0.4b	(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)))))

rewrite30.0ms

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))))
21.0ms	(* (sqrt (acos (/ (- 1.0 (* (* 5.0 v) v)) (- (* v v) 1.0)))) (sqrt (acos (/ (- 1.0 (* (* 5.0 v) v)) (- (* v v) 1.0)))))

series67.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(acos (/ (- 1.0 (* (* 5.0 v) v)) (- (* v v) 1.0)))
20.0ms	(sqrt (acos (/ (- 1.0 (* (* 5.0 v) v)) (- (* v v) 1.0))))
34.0ms	(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)))))

simplify4.4s

Counts

95 → 95

Iterations

Iter	Nodes
done	5001
3	3580
2	559
1	148
0	72

prune435.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.4b

localize91.0ms

Local error

Found 4 expressions with local error:

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

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

75×	`sqrt-prod`
63×	`add-sqr-sqrt`
24×	`associate-l` `unswap-sqr`
18×	`unpow-prod-down` `cube-prod`
16×	`*-un-lft-identity` `add-cube-cbrt`
9×	`associate-r` `add-exp-log`
6×	`pow1` `add-cbrt-cube`
4×	`add-log-exp` `sqr-pow`
3×	`prod-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`acos-asin` `cube-mult` `pow-to-exp` `unpow3` `pow-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 103

Calls

4 calls:

1.0ms	(acos (/ (- 1.0 (* (* v v) 5.0)) (- (* v v) 1.0)))
1.0ms	(sqrt (acos (/ (- 1.0 (* (* 5.0 v) v)) (- (* v v) 1.0))))
1.0ms	(sqrt (acos (/ (- 1.0 (* (* v v) 5.0)) (- (* v v) 1.0))))
33.0ms	(* (pow (sqrt (sqrt (acos (/ (- 1.0 (* (* v v) 5.0)) (- (* v v) 1.0))))) 3) (sqrt (sqrt (acos (/ (- 1.0 (* (* 5.0 v) v)) (- (* v v) 1.0))))))

series49.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(acos (/ (- 1.0 (* (* v v) 5.0)) (- (* v v) 1.0)))
19.0ms	(sqrt (acos (/ (- 1.0 (* (* 5.0 v) v)) (- (* v v) 1.0))))
20.0ms	(sqrt (acos (/ (- 1.0 (* (* v v) 5.0)) (- (* v v) 1.0))))
5.0ms	(* (pow (sqrt (sqrt (acos (/ (- 1.0 (* (* v v) 5.0)) (- (* v v) 1.0))))) 3) (sqrt (sqrt (acos (/ (- 1.0 (* (* 5.0 v) v)) (- (* v v) 1.0))))))

simplify3.9s

Counts

115 → 115

Iterations

Iter	Nodes
done	5000
2	1312
1	239
0	115

prune617.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.4b

regimes64.0ms

Accuracy

0% (0.0b remaining)

Error of 0.6b against oracle of 0.5b and baseline of 0.6b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	27
1	27
0	24

end0.0ms

sample5.6s

Algorithm

intervals

Results

2.3s	3026×	body	2560	valid
1.0s	2444×	body	1280	valid
873.0ms	1280×	body	640	valid
624.0ms	8221×	body	80	nan
171.0ms	610×	body	320	valid
97.0ms	442×	body	160	valid
16.0ms	198×	body	80	valid