Details

sample54.0ms

Algorithm

intervals

Results

21.0ms	273×	body	80	valid
7.0ms	76×	body	80	nan

simplify221.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	20	38
1	35	38
2	66	37
3	116	37
4	139	37
5	151	37
6	153	37
done	153	37

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.0b

localize156.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
0.7b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
25.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
25.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite177.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
10×	`add-log-exp`
8×	`sqrt-prod`
6×	`pow1` `add-cube-cbrt`
4×	`add-exp-log` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `difference-of-squares`
3×	`diff-log` `distribute-lft-out--`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`associate--l-` `neg-sub0` `distribute-rgt-neg-in` `neg-log`

Counts

4 → 63

Calls

4 calls:

80.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
49.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
19.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series510.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
127.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
113.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
139.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.9s

Counts

75 → 75

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	106	1330
1	241	1181
2	748	1110
3	2669	1090
done	5001	1085

prune436.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.2b

localize134.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.1b	(/ (- (- (* 2.0 (/ (* a c) b)) b) b) (* 2.0 a))
6.5b	(/ (* a c) b)
25.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite440.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
14×	`add-exp-log` `add-cbrt-cube`
9×	`add-cube-cbrt`
8×	`times-frac` `add-log-exp`
6×	`associate-/l*`
5×	`pow1`
4×	`cbrt-undiv` `div-exp` `associate-/r*` `sqrt-prod` `distribute-lft-out--` `difference-of-squares`
3×	`flip3--` `flip--`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l/`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `pow1/2` `div-sub` `neg-log`

Counts

4 → 82

Calls

4 calls:

34.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
360.0ms	(/ (- (- (* 2.0 (/ (* a c) b)) b) b) (* 2.0 a))
20.0ms	(/ (* a c) b)
19.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series333.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
121.0ms	(/ (- (- (* 2.0 (/ (* a c) b)) b) b) (* 2.0 a))
25.0ms	(/ (* a c) b)
83.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.2s

Counts

94 → 94

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	188	1545
1	470	1455
2	1662	1289
done	5001	1268

prune574.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.6b

localize133.0ms

Local error

Found 3 expressions with local error:

0.3b	(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.7b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
25.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
8×	`add-exp-log` `add-cbrt-cube`
7×	`times-frac` `associate-/r*` `add-log-exp`
6×	`add-cube-cbrt` `sqrt-prod` `distribute-lft-out--` `difference-of-squares`
4×	`pow1`
3×	`flip3--` `distribute-rgt-neg-in` `flip--`
2×	`cbrt-undiv` `sqrt-div` `diff-log` `div-exp` `associate-/r/`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

3 → 64

Calls

3 calls:

69.0ms	(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
38.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series515.0ms

Counts

3 → 9

Calls

3 calls:

289.0ms	(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
111.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
115.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.5s

Counts

73 → 73

Iterations

Useful iterations: 3 (1.6s)

Iter	Nodes	Cost
0	139	1473
1	344	1372
2	1159	1228
3	4537	1210
done	5002	1210

prune409.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.4b

localize141.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.7b	(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
3.1b	(/ (- (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b) b) (* 2.0 a))
25.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite2.5s

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
33×	`times-frac`
30×	`add-exp-log` `*-un-lft-identity`
23×	`add-cbrt-cube`
22×	`add-cube-cbrt` `associate-r`
11×	`cbrt-prod`
9×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
8×	`add-log-exp`
7×	`pow1` `associate-l`
6×	`unswap-sqr`
5×	`associate-/l*`
4×	`sqrt-prod` `distribute-lft-out--` `difference-of-squares`
3×	`flip3--` `flip--` `div-inv`
2×	`sqrt-div` `diff-log` `associate-/l/`
1×	`associate--l-` `neg-sub0` `frac-times` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `associate-r/` `pow-prod-down` `neg-log` `associate-l/` `clear-num` `associate-/r` `-commutative`

Counts

4 → 120

Calls

4 calls:

27.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
70.0ms	(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
2.3s	(/ (- (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b) b) (* 2.0 a))
20.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series492.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
82.0ms	(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
173.0ms	(/ (- (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b) b) (* 2.0 a))
109.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.6s

Counts

132 → 132

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	273	2657
1	747	2530
2	2852	2020
done	5000	1820

prune838.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.1b

regimes343.0ms

Accuracy

89.6% (1.5b remaining)

Error of 7.7b against oracle of 6.2b and baseline of 20.8b

bsearch268.0ms

Steps

Iters	Range		Point
5	1.0433798175544735e+152	3.237299440315181e+152	1.1155337065557208e+152
8	-1.173014798652874e+100	-8.67642318333193e+96	-1.1200838301149146e+100

simplify29.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	49	150
1	57	150
done	57	150

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.2s	8717×	body	80	valid
400.0ms	2914×	body	80	nan