Details

sample32.0ms

Algorithm

intervals

Results

14.0ms	278×	body	80	valid
3.0ms	76×	body	80	nan

simplify82.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	20	38
1	35	38
2	65	37
3	114	37
4	136	37
5	148	37
6	149	37
done	149	37

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.6b

localize109.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b b) (* (* 4.0 a) c))
1.6b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

3.0ms	(- (* b b) (* (* 4.0 a) c))
13.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
7.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series254.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (* b b) (* (* 4.0 a) c))
74.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
65.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
70.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.5s

Counts

72 → 72

Iterations

Useful iterations: 3 (457.0ms)

Iter	Nodes	Cost
0	97	1211
1	228	1091
2	772	1009
3	3155	998
done	5000	998

prune278.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.0b

localize117.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.7b	(/ (* a c) b)
4.8b	(/ (/ (- (- (* 2.0 (/ (* a c) b)) b) b) 2.0) a)
24.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 149

Calls

4 calls:

12.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(/ (* a c) b)
93.0ms	(/ (/ (- (- (* 2.0 (/ (* a c) b)) b) b) 2.0) a)
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series248.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
19.0ms	(/ (* a c) b)
79.0ms	(/ (/ (- (- (* 2.0 (/ (* a c) b)) b) b) 2.0) a)
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify884.0ms

Counts

161 → 161

Iterations

Useful iterations: 2 (331.0ms)

Iter	Nodes	Cost
0	309	3560
1	733	3400
2	2685	3238
done	5000	3238

prune757.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.6b

localize111.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 4.0 a) c)
0.4b	(- (* b b) (* (* 4.0 a) c))
1.6b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 63

Calls

4 calls:

6.0ms	(* (* 4.0 a) c)
3.0ms	(- (* b b) (* (* 4.0 a) c))
12.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series205.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (* 4.0 a) c)
42.0ms	(- (* b b) (* (* 4.0 a) c))
73.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
69.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify543.0ms

Counts

75 → 75

Iterations

Useful iterations: done (541.0ms)

Iter	Nodes	Cost
0	126	1083
1	298	989
2	1084	899
done	5001	893

prune247.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.6b

localize115.0ms

Local error

Found 4 expressions with local error:

15.6b	(cbrt (* (* 4.0 a) c))
15.6b	(cbrt (* (* 4.0 a) c))
15.6b	(cbrt (* (* 4.0 a) c))
24.7b	(sqrt (- (* b b) (* (* (cbrt (* (* 4.0 a) c)) (cbrt (* (* 4.0 a) c))) (cbrt (* (* 4.0 a) c)))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--`

Counts

4 → 42

Calls

4 calls:

5.0ms	(cbrt (* (* 4.0 a) c))
5.0ms	(cbrt (* (* 4.0 a) c))
5.0ms	(cbrt (* (* 4.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* (cbrt (* (* 4.0 a) c)) (cbrt (* (* 4.0 a) c))) (cbrt (* (* 4.0 a) c)))))

series410.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(cbrt (* (* 4.0 a) c))
96.0ms	(cbrt (* (* 4.0 a) c))
95.0ms	(cbrt (* (* 4.0 a) c))
127.0ms	(sqrt (- (* b b) (* (* (cbrt (* (* 4.0 a) c)) (cbrt (* (* 4.0 a) c))) (cbrt (* (* 4.0 a) c)))))

simplify700.0ms

Counts

54 → 54

Iterations

Useful iterations: done (698.0ms)

Iter	Nodes	Cost
0	88	981
1	206	897
2	519	529
3	1760	514
done	5001	513

prune247.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.6b

regimes195.0ms

Accuracy

92.2% (1.1b remaining)

Error of 7.9b against oracle of 6.8b and baseline of 21.1b

bsearch196.0ms

Steps

Iters	Range		Point
8	1.5276508475467709e+44	4.1560730947117816e+46	4.047592289682709e+46
11	-1.829086240692416e+154	-2.187052964502477e+134	-8.555281377770497e+140

simplify11.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	49	149
1	56	149
done	56	149

end0.0ms

sample832.0ms

Algorithm

intervals

Results

444.0ms	8732×	body	80	valid
142.0ms	2861×	body	80	nan