Details

sample136.0ms

Algorithm

intervals

Results

32.0ms	30×	body	1280	valid
30.0ms	38×	body	2560	valid
27.0ms	189×	body	80	valid
12.0ms	87×	body	80	nan
10.0ms	15×	body	640	valid
3.0ms	6×	body	320	valid
2.0ms	2×	body	5120	valid

simplify117.0ms

Counts: 1 → 1

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.3b

localize30.0ms

Local error

Found 4 expressions with local error:

22.6b	(sqrt (- (* b b) (* (* 4 a) c)))
0.3b	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
0.2b	(- (* b b) (* (* 4 a) c))
0.1b	(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) (* 2 a))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
7×	`add-cube-cbrt`
6×	`times-frac` `sqrt-prod` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `insert-posit16` `flip--`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 76

Calls

4 calls:

Slowest

74.0ms	(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) (* 2 a))
58.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
9.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
7.0ms	(- (* b b) (* (* 4 a) c))

series405.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

135.0ms	(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) (* 2 a))
116.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
93.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
60.0ms	(- (* b b) (* (* 4 a) c))

simplify2.0s

Counts: 88 → 88

prune963.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.8b

localize40.0ms

Local error

Found 4 expressions with local error:

22.6b	(sqrt (- (* b b) (* (* 4 a) c)))
5.2b	(- (/ (sqrt (- (* b b) (* (* 4 a) c))) (* 2 a)) (/ b (* 2 a)))
0.2b	(- (* b b) (* (* 4 a) c))
0.1b	(/ (sqrt (- (* b b) (* (* 4 a) c))) (* 2 a))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
12×	`add-sqr-sqrt`
9×	`add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `sqrt-prod`
8×	`times-frac` `add-log-exp`
6×	`associate-/l*`
5×	`pow1`
4×	`flip3--` `sqrt-div` `insert-posit16` `flip--`
3×	`div-inv`
2×	`cbrt-undiv` `sub-neg` `diff-log` `div-exp` `distribute-lft-out--` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `distribute-rgt-out--` `pow1/2` `prod-exp` `frac-sub` `cbrt-unprod` `sub-div` `difference-of-squares`

Counts

4 → 78

Calls

4 calls:

Slowest

46.0ms	(- (/ (sqrt (- (* b b) (* (* 4 a) c))) (* 2 a)) (/ b (* 2 a)))
28.0ms	(/ (sqrt (- (* b b) (* (* 4 a) c))) (* 2 a))
9.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
7.0ms	(- (* b b) (* (* 4 a) c))

series461.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

154.0ms	(/ (sqrt (- (* b b) (* (* 4 a) c))) (* 2 a))
140.0ms	(- (/ (sqrt (- (* b b) (* (* 4 a) c))) (* 2 a)) (/ b (* 2 a)))
109.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
58.0ms	(- (* b b) (* (* 4 a) c))

simplify1.9s

Counts: 90 → 90

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.8b

localize52.0ms

Local error

Found 4 expressions with local error:

22.6b	(sqrt (- (* b b) (* (* 4 a) c)))
10.2b	(- (/ 1 (/ (* 2 a) (sqrt (- (* b b) (* (* 4 a) c))))) (/ b (* 2 a)))
0.2b	(/ 1 (/ (* 2 a) (sqrt (- (* b b) (* (* 4 a) c)))))
0.2b	(- (* b b) (* (* 4 a) c))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

62×	`times-frac`
38×	`add-sqr-sqrt`
34×	`*-un-lft-identity`
30×	`add-cube-cbrt`
25×	`add-exp-log`
15×	`sqrt-prod`
13×	`add-cbrt-cube`
12×	`associate-/r*` `div-exp`
10×	`sqrt-div`
9×	`associate-/r/`
8×	`add-log-exp`
7×	`flip3--` `flip--`
6×	`pow1` `div-inv`
5×	`cbrt-undiv`
4×	`insert-posit16`
3×	`rec-exp` `1-exp` `prod-exp` `associate-/l*` `difference-of-squares`
2×	`sub-neg` `diff-log` `distribute-lft-out--`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `frac-sub` `cbrt-unprod` `pow-flip` `inv-pow`

Counts

4 → 125

Calls

4 calls:

Slowest

76.0ms	(- (/ 1 (/ (* 2 a) (sqrt (- (* b b) (* (* 4 a) c))))) (/ b (* 2 a)))
29.0ms	(/ 1 (/ (* 2 a) (sqrt (- (* b b) (* (* 4 a) c)))))
14.0ms	(- (* b b) (* (* 4 a) c))
7.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series421.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

128.0ms	(/ 1 (/ (* 2 a) (sqrt (- (* b b) (* (* 4 a) c)))))
123.0ms	(- (/ 1 (/ (* 2 a) (sqrt (- (* b b) (* (* 4 a) c))))) (/ b (* 2 a)))
111.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
59.0ms	(- (* b b) (* (* 4 a) c))

simplify599.0ms

Counts: 137 → 137

prune1.5s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.8b

localize55.0ms

Local error

Found 4 expressions with local error:

22.6b	(sqrt (- (* b b) (* (* 4 a) c)))
22.6b	(sqrt (- (* b b) (* (* 4 a) c)))
13.7b	(- (* (* 1/2 (sqrt (sqrt (- (* b b) (* (* 4 a) c))))) (/ 1 (/ a (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))) (/ b (* 2 a)))
0.3b	(* (* 1/2 (sqrt (sqrt (- (* b b) (* (* 4 a) c))))) (/ 1 (/ a (sqrt (sqrt (- (* b b) (* (* 4 a) c)))))))

rewrite225.0ms

Algorithm

rewrite-expression-head

Rules

180×	`times-frac`
104×	`associate-r`
99×	`add-sqr-sqrt`
97×	`*-un-lft-identity` `add-cube-cbrt`
87×	`sqrt-prod`
49×	`add-exp-log`
32×	`sqrt-div`
25×	`add-cbrt-cube`
21×	`prod-exp`
14×	`div-exp`
11×	`pow1`
10×	`flip3--` `associate-*r/` `flip--`
9×	`cbrt-unprod`
7×	`associate-/r/`
6×	`cbrt-undiv` `frac-sub` `add-log-exp`
4×	`frac-times` `rec-exp` `1-exp` `associate-*l/` `insert-posit16` `div-inv`
3×	`pow-prod-down`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `un-div-inv`
1×	`sub-neg` `diff-log` `associate-l` `*-commutative`

Counts

4 → 193

Calls

4 calls:

Slowest

121.0ms	(* (* 1/2 (sqrt (sqrt (- (* b b) (* (* 4 a) c))))) (/ 1 (/ a (sqrt (sqrt (- (* b b) (* (* 4 a) c)))))))
80.0ms	(- (* (* 1/2 (sqrt (sqrt (- (* b b) (* (* 4 a) c))))) (/ 1 (/ a (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))) (/ b (* 2 a)))
8.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
7.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series601.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

208.0ms	(* (* 1/2 (sqrt (sqrt (- (* b b) (* (* 4 a) c))))) (/ 1 (/ a (sqrt (sqrt (- (* b b) (* (* 4 a) c)))))))
172.0ms	(- (* (* 1/2 (sqrt (sqrt (- (* b b) (* (* 4 a) c))))) (/ 1 (/ a (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))) (/ b (* 2 a)))
113.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
108.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify656.0ms

Counts: 205 → 205

prune3.2s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 5.8b

regimes390.0ms

Accuracy

83.4% (4.6b remaining)

Error of 10.6b against oracle of 6.0b and baseline of 33.5b

bsearch247.0ms

end0.0ms

sample4.8s

Algorithm

intervals

Results

1.5s	1070×	body	2560	valid
1.3s	5902×	body	80	valid
654.0ms	864×	body	1280	valid
443.0ms	2867×	body	80	nan
283.0ms	458×	body	640	valid
122.0ms	102×	body	5120	valid
78.0ms	207×	body	320	valid
28.0ms	112×	body	160	valid