Details

sample77.0ms

Algorithm

intervals

Results

16.0ms	190×	body	80	valid
13.0ms	38×	body	2560	valid
11.0ms	36×	body	1280	valid
5.0ms	79×	body	80	nan
2.0ms	11×	body	640	valid
2.0ms	4×	body	5120	valid
1.0ms	5×	body	320	valid
0.0ms	2×	body	160	valid

simplify108.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	14	17
1	24	17
2	44	16
3	79	16
4	99	16
5	107	16
done	107	16

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
0.2b	(- (* b b) (* (* 4.0 a) c))
0.8b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite200.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

109.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
9.0ms	(- (* b b) (* (* 4.0 a) c))
66.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series444.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
60.0ms	(- (* b b) (* (* 4.0 a) c))
126.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
106.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.1s

Counts

84 → 84

Iterations

Useful iterations: 2 (281.0ms)

Iter	Nodes	Cost
0	154	1592
1	405	1496
2	1789	1332
done	5001	1332

prune333.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
0.2b	(- (* b b) (* (* 4.0 a) c))
0.8b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

60×	`times-frac`
47×	`add-sqr-sqrt`
36×	`*-un-lft-identity`
26×	`add-cube-cbrt`
25×	`add-exp-log`
13×	`add-cbrt-cube`
12×	`div-exp` `associate-/r*`
10×	`difference-of-squares`
9×	`associate-/r/`
8×	`sqrt-prod` `add-log-exp`
7×	`flip3--` `flip--`
6×	`pow1`
5×	`cbrt-undiv` `div-inv` `distribute-lft-out--`
3×	`rec-exp` `1-exp` `prod-exp` `associate-/l*`
2×	`sub-neg` `sqrt-div` `diff-log`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `cbrt-unprod` `inv-pow`

Counts

4 → 118

Calls

4 calls:

82.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
12.0ms	(- (* b b) (* (* 4.0 a) c))
64.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series487.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
71.0ms	(- (* b b) (* (* 4.0 a) c))
118.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
100.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.7s

Counts

130 → 130

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	220	3137
1	571	2809
2	2756	2613
done	5002	2611

prune377.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* (* 4.0 a) c))
0.2b	(* (/ 1 (* 2.0 a)) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
0.8b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite306.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
19×	`add-sqr-sqrt`
13×	`add-cbrt-cube`
12×	`*-un-lft-identity`
10×	`prod-exp`
8×	`add-cube-cbrt` `add-log-exp`
7×	`pow1` `associate-l`
6×	`associate-r`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`sub-neg` `div-exp` `cbrt-unprod` `difference-of-squares`
3×	`times-frac`
2×	`cbrt-undiv` `distribute-rgt-in` `frac-times` `rec-exp` `distribute-lft-in` `sqrt-div` `diff-log` `1-exp` `associate-*r/` `distribute-lft-out--`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-l/` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 84

Calls

4 calls:

17.0ms	(- (* b b) (* (* 4.0 a) c))
225.0ms	(* (/ 1 (* 2.0 a)) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
50.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series546.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(- (* b b) (* (* 4.0 a) c))
219.0ms	(* (/ 1 (* 2.0 a)) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
128.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
133.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.1s

Counts

96 → 96

Iterations

Useful iterations: 2 (385.0ms)

Iter	Nodes	Cost
0	171	1924
1	487	1781
2	2603	1511
done	5000	1511

prune361.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
0.2b	(- (* b b) (* (* 4.0 a) c))
0.8b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite210.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

120.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
8.0ms	(- (* b b) (* (* 4.0 a) c))
68.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series401.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
66.0ms	(- (* b b) (* (* 4.0 a) c))
103.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
93.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.2s

Counts

84 → 84

Iterations

Useful iterations: 2 (309.0ms)

Iter	Nodes	Cost
0	154	1592
1	405	1496
2	1789	1332
done	5001	1332

prune332.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 5.5b

regimes247.0ms

Accuracy

84.6% (4.3b remaining)

Error of 10.3b against oracle of 6.0b and baseline of 33.8b

bsearch222.0ms

Steps

Iters	Range		Point
9	3.58845601849977e-79	3.3299624871078663e-72	2.071930020515771e-74
9	-7.561250615295736e+156	-1.350243324689865e+150	-4.919628179067154e+153

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	33	50
1	43	38
done	43	38

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.1s	5922×	body	80	valid
612.0ms	1053×	body	2560	valid
589.0ms	458×	body	640	valid
481.0ms	906×	body	1280	valid
264.0ms	2894×	body	80	nan
82.0ms	85×	body	5120	valid
77.0ms	220×	body	320	valid
18.0ms	121×	body	160	valid