Details

sample130.0ms

Algorithm

intervals

Results

26.0ms	148×	body	160	valid
23.0ms	286×	body	80	nan
21.0ms	542×	pre	80	true
15.0ms	59×	body	320	valid
4.0ms	49×	body	80	valid

simplify233.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	102
7	102
6	101
5	99
4	91
3	75
2	40
1	22
0	12

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 46.9b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* b b) (* (* a 3.0) c))
0.2b	(* (* a 3.0) c)
0.3b	(/ (- (sqrt (- (* b b) (* (* a 3.0) c))) b) (* a 3.0))
38.9b	(- (sqrt (- (* b b) (* (* a 3.0) c))) b)

rewrite376.0ms

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:

18.0ms	(- (* b b) (* (* a 3.0) c))
41.0ms	(* (* a 3.0) c)
197.0ms	(/ (- (sqrt (- (* b b) (* (* a 3.0) c))) b) (* a 3.0))
112.0ms	(- (sqrt (- (* b b) (* (* a 3.0) c))) b)

series478.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(- (* b b) (* (* a 3.0) c))
36.0ms	(* (* a 3.0) c)
204.0ms	(/ (- (sqrt (- (* b b) (* (* a 3.0) c))) b) (* a 3.0))
155.0ms	(- (sqrt (- (* b b) (* (* a 3.0) c))) b)

simplify3.1s

Counts

121 → 121

Iterations

Iter	Nodes
done	5006
2	1864
1	541
0	202

prune990.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 4.2b

localize13.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify1.0ms

Counts

0 → 0

Iterations

Iter	Nodes
done	0
0	0

prune155.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 4.2b

localize60.0ms

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)) (* a 3.0))

rewrite115.0ms

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)
37.0ms	(* -1.5 (/ (* a c) b))
47.0ms	(/ (* -1.5 (/ (* a c) b)) (* a 3.0))

series130.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(/ (* a c) b)
55.0ms	(* -1.5 (/ (* a c) b))
36.0ms	(/ (* -1.5 (/ (* a c) b)) (* a 3.0))

simplify2.8s

Counts

93 → 93

Iterations

Iter	Nodes
done	5085
2	2286
1	385
0	129

prune907.0ms

Pruning

28 alts after pruning (27 fresh and 1 done)

Merged error: 4.1b

localize105.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (* a a) a) (* (* c c) c))
0.4b	(/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))
0.4b	(/ (* (* (* -1.5 -1.5) -1.5) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* (* a a) a) (* (* 3.0 3.0) 3.0)))
0.6b	(cbrt (/ (* (* (* -1.5 -1.5) -1.5) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* (* a a) a) (* (* 3.0 3.0) 3.0))))

rewrite3.6s

Algorithm

rewrite-expression-head

Rules

10719×	`add-exp-log` `add-cbrt-cube`
7866×	`prod-exp` `cbrt-unprod`
1870×	`cbrt-undiv` `div-exp`
128×	`pow1`
52×	`pow-prod-down`
40×	`pow-plus` `pow-prod-up`
8×	`pow2` `pow-sqr`
5×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `div-inv`
2×	`frac-2neg` `pow3` `clear-num` `associate-/r` `associate-/l`
1×	`cbrt-div` `pow1/3` `associate-r/` `associate-r` `associate-l` `-commutative` `associate-/l/`

Counts

4 → 2051

Calls

4 calls:

259.0ms	(* (* (* a a) a) (* (* c c) c))
260.0ms	(/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))
1.0s	(/ (* (* (* -1.5 -1.5) -1.5) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* (* a a) a) (* (* 3.0 3.0) 3.0)))
951.0ms	(cbrt (/ (* (* (* -1.5 -1.5) -1.5) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* (* a a) a) (* (* 3.0 3.0) 3.0))))

series618.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(* (* (* a a) a) (* (* c c) c))
192.0ms	(/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))
165.0ms	(/ (* (* (* -1.5 -1.5) -1.5) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* (* a a) a) (* (* 3.0 3.0) 3.0)))
130.0ms	(cbrt (/ (* (* (* -1.5 -1.5) -1.5) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* (* a a) a) (* (* 3.0 3.0) 3.0))))

simplify31.8s

Counts

2063 → 2063

Iterations

Iter	Nodes
done	5004
1	2178
0	1393

prune1.1s

Pruning

35 alts after pruning (34 fresh and 1 done)

Merged error: 4.1b

regimes1.4s

Accuracy

14.9% (6.0b remaining)

Error of 11.1b against oracle of 5.1b and baseline of 12.2b

bsearch45.0ms

Steps

Iters	Range		Point
3	8.811935278252425e-05	0.00011572818137097542	8.984490456930244e-05

simplify10.0ms

Iterations

Iter	Nodes
done	28
1	28
0	22

end0.0ms

sample4.7s

Algorithm

intervals

Results

1.4s	8304×	body	80	nan
1.2s	4842×	body	160	valid
908.0ms	16304×	pre	80	true
331.0ms	1331×	body	320	valid
199.0ms	1827×	body	80	valid