Details

sample238.0ms

Algorithm

intervals

Results

21.0ms	118×	body	320	valid
14.0ms	469×	pre	80	true
13.0ms	213×	body	80	nan
12.0ms	98×	body	160	valid
2.0ms	11×	body	640	valid
2.0ms	29×	body	80	valid

simplify102.0ms

Counts: 1 → 1

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.2b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b	(- (* b b) (* (* 4.0 a) c))
0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
28.5b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
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×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 70

Calls

4 calls:

23.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
17.0ms	(- (* b b) (* (* 4.0 a) c))
96.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
32.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series427.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
49.0ms	(- (* b b) (* (* 4.0 a) c))
169.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
129.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify696.0ms

Counts: 82 → 82

prune323.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize47.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b	(- (* b b) (* (* 4.0 a) c))
0.3b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.3b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

rewrite281.0ms

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-exp-log` `add-cbrt-cube`
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×	`sub-neg` `frac-2neg` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `flip3-+` `neg-log` `flip-+`

Counts

4 → 151

Calls

4 calls:

38.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms	(- (* b b) (* (* 4.0 a) c))
87.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
140.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

series653.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
62.0ms	(- (* b b) (* (* 4.0 a) c))
255.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
208.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

simplify2.0s

Counts: 163 → 163

prune622.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite393.0ms

Algorithm

rewrite-expression-head

Rules

389×	`times-frac`
281×	`add-sqr-sqrt`
255×	`*-un-lft-identity`
169×	`add-cube-cbrt`
117×	`add-exp-log`
85×	`associate-r`
77×	`add-cbrt-cube`
62×	`div-exp`
42×	`distribute-lft-out--` `difference-of-squares`
37×	`cbrt-undiv`
33×	`associate-/l*`
27×	`prod-exp`
26×	`associate-l`
21×	`distribute-rgt-neg-in` `sqrt-prod`
19×	`div-inv`
17×	`cbrt-unprod`
16×	`associate-/r/`
11×	`associate-/r*`
8×	`unswap-sqr`
7×	`flip3--` `flip--`
6×	`pow1`
5×	`rec-exp` `1-exp`
4×	`add-log-exp`
3×	`frac-2neg` `clear-num`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `associate-/l/`

Counts

4 → 360

Calls

4 calls:

97.0ms	(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
8.0ms	(/ 2.0 (* a c))
12.0ms	(/ 4.0 (/ 2.0 (* a c)))
226.0ms	(* (/ 4.0 (/ 2.0 (* a c))) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

series457.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
39.0ms	(/ 2.0 (* a c))
44.0ms	(/ 4.0 (/ 2.0 (* a c)))
201.0ms	(* (/ 4.0 (/ 2.0 (* a c))) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

simplify959.0ms

Counts: 372 → 372

prune1.5s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite714.0ms

Algorithm

rewrite-expression-head

Rules

1148×	`times-frac`
668×	`add-sqr-sqrt`
600×	`*-un-lft-identity`
512×	`add-cube-cbrt`
134×	`associate-l`
117×	`add-exp-log`
85×	`associate-r`
77×	`add-cbrt-cube`
69×	`div-exp`
49×	`associate-/r*`
44×	`div-inv`
43×	`associate-/l*`
42×	`cbrt-undiv` `distribute-lft-out--` `difference-of-squares`
21×	`distribute-rgt-neg-in` `sqrt-prod`
20×	`prod-exp`
16×	`associate-/r/` `unswap-sqr`
12×	`cbrt-unprod`
7×	`flip3--` `flip--`
6×	`pow1`
5×	`rec-exp` `1-exp`
4×	`add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`associate-/l/`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 669

Calls

4 calls:

109.0ms	(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
24.0ms	(/ 4.0 (/ (/ 2.0 a) c))
24.0ms	(/ (/ 2.0 a) c)
466.0ms	(* (/ 4.0 (/ (/ 2.0 a) c)) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

series473.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
33.0ms	(/ 4.0 (/ (/ 2.0 a) c))
34.0ms	(/ (/ 2.0 a) c)
219.0ms	(* (/ 4.0 (/ (/ 2.0 a) c)) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

simplify1.3s

Counts: 681 → 681

prune3.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes136.0ms

Accuracy

83.8% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.7s

end0.0ms

sample4.6s

Algorithm

intervals

Results

1.8s	3640×	body	320	valid
700.0ms	8070×	body	80	nan
629.0ms	16070×	pre	80	true
476.0ms	2964×	body	160	valid
207.0ms	482×	body	640	valid
60.0ms	914×	body	80	valid