Details

sample143.0ms

Algorithm

intervals

Results

32.0ms	47×	body	320	valid
24.0ms	157×	body	160	valid
22.0ms	541×	pre	80	true
22.0ms	285×	body	80	nan
4.0ms	52×	body	80	valid

simplify84.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	12	17
1	22	17
2	42	16
3	82	16
4	104	16
5	112	16
done	112	16

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.9b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* b b) (* (* 3.0 a) c))
0.3b	(* (* 3.0 a) c)
0.3b	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
40.1b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

rewrite211.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
21×	`add-cube-cbrt`
19×	`prod-diff`
15×	`sqrt-prod`
14×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
8×	`add-log-exp`
7×	`fma-neg`
6×	`times-frac` `associate-/l*` `difference-of-squares`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`flip3--` `associate-r` `pow-prod-down` `flip--` `distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `diff-log` `div-exp` `associate-/l/`
1×	`frac-2neg` `div-sub` `associate-l` `clear-num` `associate-/r` `-commutative` `div-inv`

Counts

4 → 109

Calls

4 calls:

10.0ms	(- (* b b) (* (* 3.0 a) c))
20.0ms	(* (* 3.0 a) c)
108.0ms	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
67.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

series415.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- (* b b) (* (* 3.0 a) c))
38.0ms	(* (* 3.0 a) c)
180.0ms	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
118.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

simplify1.9s

Counts

121 → 121

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	201	2338
1	495	2065
2	1668	1747
done	5000	1676

prune400.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 4.7b

localize6.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify1.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune59.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 4.7b

localize9.0ms

Local error

Found 3 expressions with local error:

0.3b	(/ (* a c) b)
0.3b	(* -1.5 (/ (* a c) b))
0.3b	(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-exp-log` `add-cbrt-cube`
17×	`prod-exp` `cbrt-unprod`
16×	`cbrt-undiv` `div-exp`
10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`times-frac` `associate-r`
5×	`pow1`
4×	`associate-/r*`
3×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`frac-2neg` `associate-r/` `clear-num` `associate-/l`
1×	`pow-prod-down` `*-commutative` `associate-/l/` `unswap-sqr`

Counts

3 → 84

Calls

3 calls:

21.0ms	(/ (* a c) b)
24.0ms	(* -1.5 (/ (* a c) b))
34.0ms	(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))

series124.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(/ (* a c) b)
48.0ms	(* -1.5 (/ (* a c) b))
28.0ms	(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))

simplify1.1s

Counts

93 → 93

Iterations

Useful iterations: 2 (346.0ms)

Iter	Nodes	Cost
0	129	1138
1	353	1097
2	1740	813
done	5000	813

prune311.0ms

Pruning

29 alts after pruning (28 fresh and 1 done)

Merged error: 4.6b

localize8.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (/ (* a c) b) a)
0.3b	(/ (* a c) b)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
20×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
16×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/l*`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r*` `div-inv`
2×	`pow1` `expm1-log1p-u` `frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
1×	`associate-/l/`

Counts

2 → 73

Calls

2 calls:

17.0ms	(/ (/ (* a c) b) a)
11.0ms	(/ (* a c) b)

series45.0ms

Counts

2 → 6

Calls

2 calls:

15.0ms	(/ (/ (* a c) b) a)
29.0ms	(/ (* a c) b)

simplify1.8s

Counts

79 → 79

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	121	831
1	285	794
2	902	708
done	5000	632

prune266.0ms

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 4.6b

regimes409.0ms

Accuracy

8.6% (6.2b remaining)

Error of 11.3b against oracle of 5.0b and baseline of 11.9b

bsearch31.0ms

Steps

Iters	Range		Point
4	0.1732461128728932	0.24673157795888256	0.17554253365683037

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	27
1	25	27
2	33	27
done	33	27

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.1s	4906×	body	160	valid
677.0ms	8337×	body	80	nan
625.0ms	16337×	pre	80	true
232.0ms	1319×	body	320	valid
173.0ms	1775×	body	80	valid