Details

sample131.0ms

Algorithm

intervals

Results

42.0ms	146×	body	160	valid
25.0ms	318×	body	80	nan
18.0ms	574×	pre	80	true
9.0ms	110×	body	80	valid

simplify87.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	111
5	111
4	102
3	78
2	44
1	24
0	14

prune30.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.5b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.3b	(- (* b b) (* (* 4.0 a) c))
28.3b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
89.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms	(- (* b b) (* (* 4.0 a) c))
21.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series408.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
122.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
65.0ms	(- (* b b) (* (* 4.0 a) c))
126.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify885.0ms

Counts

82 → 82

Iterations

Iter	Nodes
done	5000
2	1894
1	419
0	154

prune539.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.4b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (- b) (sqrt (- (* b b) (* 4.0 (* c a)))))
0.2b	(/ (/ (+ 0 (* 4.0 (* c a))) (- (- b) (sqrt (- (* b b) (* 4.0 (* c a)))))) (* 2.0 a))
0.3b	(- (* b b) (* 4.0 (* c a)))
0.3b	(/ (+ 0 (* 4.0 (* c a))) (- (- b) (sqrt (- (* b b) (* 4.0 (* c a))))))

rewrite207.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 151

Calls

4 calls:

28.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* c a)))))
100.0ms	(/ (/ (+ 0 (* 4.0 (* c a))) (- (- b) (sqrt (- (* b b) (* 4.0 (* c a)))))) (* 2.0 a))
10.0ms	(- (* b b) (* 4.0 (* c a)))
60.0ms	(/ (+ 0 (* 4.0 (* c a))) (- (- b) (sqrt (- (* b b) (* 4.0 (* c a))))))

series743.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* c a)))))
276.0ms	(/ (/ (+ 0 (* 4.0 (* c a))) (- (- b) (sqrt (- (* b b) (* 4.0 (* c a)))))) (* 2.0 a))
72.0ms	(- (* b b) (* 4.0 (* c a)))
265.0ms	(/ (+ 0 (* 4.0 (* c a))) (- (- b) (sqrt (- (* b b) (* 4.0 (* c a))))))

simplify1.7s

Counts

163 → 163

Iterations

Iter	Nodes
done	5001
2	3980
1	655
0	247

prune925.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (+ b (sqrt (- (* b b) (* 4.0 (* c a)))))) (* a 4.0))
0.3b	(- (* b b) (* 4.0 (* c a)))
0.3b	(/ (/ (- (+ b (sqrt (- (* b b) (* 4.0 (* c a)))))) (* a 4.0)) c)
0.3b	(/ 1 (/ (/ (- (+ b (sqrt (- (* b b) (* 4.0 (* c a)))))) (* a 4.0)) c))

rewrite369.0ms

Algorithm

rewrite-expression-head

Rules

600×	`times-frac`
284×	`*-un-lft-identity`
212×	`add-sqr-sqrt` `add-cube-cbrt`
72×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
56×	`associate-/r*`
52×	`add-exp-log`
36×	`distribute-lft-out`
32×	`add-cbrt-cube`
31×	`associate-/l*`
30×	`div-exp`
23×	`div-inv`
18×	`neg-mul-1`
16×	`cbrt-undiv`
6×	`add-log-exp`
5×	`pow1` `prod-exp`
4×	`rec-exp` `1-exp`
3×	`clear-num` `frac-2neg` `div-sub` `distribute-frac-neg` `cbrt-unprod` `associate-/l/`
2×	`neg-sub0` `distribute-neg-frac`
1×	`sub-neg` `flip3-+` `flip3--` `diff-log` `associate-/r/` `flip-+` `pow-flip` `flip--` `inv-pow`

Counts

4 → 381

Calls

4 calls:

89.0ms	(/ (- (+ b (sqrt (- (* b b) (* 4.0 (* c a)))))) (* a 4.0))
14.0ms	(- (* b b) (* 4.0 (* c a)))
145.0ms	(/ (/ (- (+ b (sqrt (- (* b b) (* 4.0 (* c a)))))) (* a 4.0)) c)
79.0ms	(/ 1 (/ (/ (- (+ b (sqrt (- (* b b) (* 4.0 (* c a)))))) (* a 4.0)) c))

series556.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(/ (- (+ b (sqrt (- (* b b) (* 4.0 (* c a)))))) (* a 4.0))
56.0ms	(- (* b b) (* 4.0 (* c a)))
130.0ms	(/ (/ (- (+ b (sqrt (- (* b b) (* 4.0 (* c a)))))) (* a 4.0)) c)
254.0ms	(/ 1 (/ (/ (- (+ b (sqrt (- (* b b) (* 4.0 (* c a)))))) (* a 4.0)) c))

simplify915.0ms

Counts

393 → 393

Iterations

Iter	Nodes
done	5001
1	1625
0	554

prune2.0s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize65.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (sqrt (- (* b b) (* (* a c) 4.0))) b)
0.2b	(/ (* (/ 1 (/ -1 a)) (/ 1 (/ (/ (+ (sqrt (- (* b b) (* (* a c) 4.0))) b) 4.0) c))) (* 2.0 a))
0.3b	(- (* b b) (* (* a c) 4.0))
0.3b	(/ 1 (/ (/ (+ (sqrt (- (* b b) (* (* a c) 4.0))) b) 4.0) c))

rewrite247.0ms

Algorithm

rewrite-expression-head

Rules

788×	`add-exp-log`
507×	`div-exp`
493×	`times-frac`
295×	`*-un-lft-identity`
221×	`add-sqr-sqrt` `add-cube-cbrt`
211×	`prod-exp`
162×	`add-cbrt-cube`
92×	`cbrt-undiv`
85×	`rec-exp` `1-exp`
53×	`associate-/r*`
37×	`cbrt-unprod` `distribute-lft-out`
18×	`div-inv`
8×	`add-log-exp`
5×	`pow1`
4×	`associate-/l*` `associate-/l/`
2×	`clear-num` `frac-2neg`
1×	`frac-times` `+-commutative` `sum-log` `sub-neg` `flip3-+` `flip3--` `diff-log` `associate-l/` `associate-r/` `associate-/r/` `un-div-inv` `flip-+` `pow-flip` `flip--` `inv-pow`

Counts

4 → 445

Calls

4 calls:

40.0ms	(+ (sqrt (- (* b b) (* (* a c) 4.0))) b)
79.0ms	(/ (* (/ 1 (/ -1 a)) (/ 1 (/ (/ (+ (sqrt (- (* b b) (* (* a c) 4.0))) b) 4.0) c))) (* 2.0 a))
11.0ms	(- (* b b) (* (* a c) 4.0))
62.0ms	(/ 1 (/ (/ (+ (sqrt (- (* b b) (* (* a c) 4.0))) b) 4.0) c))

series652.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(+ (sqrt (- (* b b) (* (* a c) 4.0))) b)
277.0ms	(/ (* (/ 1 (/ -1 a)) (/ 1 (/ (/ (+ (sqrt (- (* b b) (* (* a c) 4.0))) b) 4.0) c))) (* 2.0 a))
71.0ms	(- (* b b) (* (* a c) 4.0))
181.0ms	(/ 1 (/ (/ (+ (sqrt (- (* b b) (* (* a c) 4.0))) b) 4.0) c))

simplify2.3s

Counts

457 → 457

Iterations

Iter	Nodes
done	5000
1	2909
0	790

prune1.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes297.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	27
1	27
0	20

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.1s	16646×	pre	80	true
841.0ms	8646×	body	80	nan
805.0ms	4367×	body	160	valid
308.0ms	3633×	body	80	valid