Details

sample45.0ms

Algorithm

intervals

Results

9.0ms	143×	body	160	valid
9.0ms	514×	pre	80	true
8.0ms	258×	body	80	nan
4.0ms	113×	body	80	valid

simplify54.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	12	17
1	22	17
2	42	16
3	82	16
4	100	16
5	108	16
done	108	16

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.8b

localize9.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* 3.0 a) c)
0.3b	(- (* b b) (* (* 3.0 a) c))
0.3b	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
27.7b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

rewrite84.0ms

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:

7.0ms	(* (* 3.0 a) c)
3.0ms	(- (* b b) (* (* 3.0 a) c))
45.0ms	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
25.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

series247.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (* 3.0 a) c)
44.0ms	(- (* b b) (* (* 3.0 a) c))
107.0ms	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
77.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

simplify1.0s

Counts

121 → 121

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	201	2338
1	500	2065
2	1802	1747
done	5000	1728

prune262.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 8.7b

localize3.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify1.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune37.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 8.7b

localize9.0ms

Local error

Found 3 expressions with local error:

0.3b	(/ (* a c) b)
0.3b	(* -1.5 (/ (* a c) b))
0.4b	(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))

rewrite24.0ms

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:

3.0ms	(/ (* a c) b)
9.0ms	(* -1.5 (/ (* a c) b))
9.0ms	(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))

series69.0ms

Counts

3 → 9

Calls

3 calls:

22.0ms	(/ (* a c) b)
27.0ms	(* -1.5 (/ (* a c) b))
20.0ms	(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))

simplify951.0ms

Counts

93 → 93

Iterations

Useful iterations: 2 (182.0ms)

Iter	Nodes	Cost
0	129	1138
1	383	1097
2	1928	813
done	5001	813

prune191.0ms

Pruning

29 alts after pruning (28 fresh and 1 done)

Merged error: 8.6b

localize7.0ms

Local error

Found 3 expressions with local error:

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

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 73

Calls

3 calls:

13.0ms	(/ (* -1.5 (* a c)) (* (* 3.0 a) b))
7.0ms	(* (* 3.0 a) b)
6.0ms	(* -1.5 (* a c))

series63.0ms

Counts

3 → 9

Calls

3 calls:

20.0ms	(/ (* -1.5 (* a c)) (* (* 3.0 a) b))
22.0ms	(* (* 3.0 a) b)
21.0ms	(* -1.5 (* a c))

simplify1.5s

Counts

82 → 82

Iterations

Useful iterations: 2 (256.0ms)

Iter	Nodes	Cost
0	113	1002
1	358	967
2	2379	687
done	5001	687

prune104.0ms

Pruning

32 alts after pruning (31 fresh and 1 done)

Merged error: 8.5b

regimes554.0ms

Accuracy

36.5% (8.5b remaining)

Error of 17.5b against oracle of 9.0b and baseline of 22.3b

bsearch23.0ms

Steps

Iters	Range		Point
0	4947.217786474198	5174.453079191142	5060.8354328326695
1	496.22568619109217	534.3448668414316	520.8714932266197
2	19.91577405755974	23.2074174531597	20.327229482009734

simplify8.0ms

Iterations

Useful iterations: done (8.0ms)

Iter	Nodes	Cost
0	26	80
1	33	76
2	36	48
3	39	48
done	39	47

end0.0ms

sample1.3s

Algorithm

intervals

Results

297.0ms	16441×	pre	80	true
291.0ms	4542×	body	160	valid
263.0ms	8441×	body	80	nan
113.0ms	3458×	body	80	valid