Details

sample76.0ms

Algorithm

intervals

Results

17.0ms	137×	body	160	valid
15.0ms	266×	body	80	nan
12.0ms	522×	pre	80	true
6.0ms	119×	body	80	valid

simplify84.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	14	17
1	25	17
2	46	16
3	87	16
4	120	16
5	129	16
done	129	16

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.1b

localize14.0ms

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))
28.0b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
6×	`distribute-rgt-neg-in` `distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-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` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 90

Calls

4 calls:

13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
74.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
9.0ms	(- (* b b) (* (* 4.0 a) c))
30.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series438.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
159.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
67.0ms	(- (* b b) (* (* 4.0 a) c))
96.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.5s

Counts

102 → 102

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	167	1697
1	450	1588
2	2152	1361
done	5001	1352

prune300.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.3b	(/ (/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.3b	(- (* b b) (* (* 4.0 a) c))
0.4b	(/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite289.0ms

Algorithm

rewrite-expression-head

Rules

123×	`add-sqr-sqrt` `*-un-lft-identity`
90×	`times-frac`
79×	`add-cube-cbrt`
61×	`prod-diff`
41×	`sqrt-prod`
32×	`distribute-rgt-neg-in`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
18×	`add-exp-log` `add-cbrt-cube`
11×	`fma-neg`
10×	`add-log-exp`
8×	`associate-/r*`
7×	`cbrt-undiv` `neg-mul-1` `div-exp`
6×	`associate-/r/`
5×	`flip3--` `flip--`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `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 → 231

Calls

4 calls:

53.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
112.0ms	(/ (/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
9.0ms	(- (* b b) (* (* 4.0 a) c))
94.0ms	(/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series590.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
211.0ms	(/ (/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
55.0ms	(- (* b b) (* (* 4.0 a) c))
223.0ms	(/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify477.0ms

Counts

243 → 243

Iterations

Useful iterations: done (464.0ms)

Iter	Nodes	Cost
0	339	10026
1	858	7622
done	5000	6606

prune853.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (/ (* 2.0 a) (/ (* (* 4.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))
0.3b	(/ (* 2.0 a) (/ (* (* 4.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.3b	(- (* b b) (* (* 4.0 a) c))
0.4b	(/ (* (* 4.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite320.0ms

Algorithm

rewrite-expression-head

Rules

168×	`times-frac`
153×	`add-exp-log`
87×	`add-cbrt-cube`
77×	`div-exp`
73×	`add-sqr-sqrt` `*-un-lft-identity`
43×	`prod-exp`
41×	`add-cube-cbrt`
40×	`cbrt-undiv`
38×	`associate-/r*`
23×	`cbrt-unprod`
20×	`associate-/r/`
16×	`distribute-lft-out--` `difference-of-squares`
13×	`div-inv`
9×	`rec-exp` `1-exp`
8×	`flip3--` `distribute-rgt-neg-in` `sqrt-prod` `flip--`
6×	`add-log-exp`
5×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`frac-2neg` `clear-num`
1×	`sub-neg` `pow-flip` `fma-neg` `diff-log` `prod-diff` `inv-pow`

Counts

4 → 233

Calls

4 calls:

92.0ms	(/ 1 (/ (* 2.0 a) (/ (* (* 4.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))
116.0ms	(/ (* 2.0 a) (/ (* (* 4.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
16.0ms	(- (* b b) (* (* 4.0 a) c))
68.0ms	(/ (* (* 4.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series627.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(/ 1 (/ (* 2.0 a) (/ (* (* 4.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))
119.0ms	(/ (* 2.0 a) (/ (* (* 4.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
76.0ms	(- (* b b) (* (* 4.0 a) c))
248.0ms	(/ (* (* 4.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify602.0ms

Counts

245 → 245

Iterations

Useful iterations: done (593.0ms)

Iter	Nodes	Cost
0	368	8040
1	1137	7437
done	5001	6505

prune890.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize50.0ms

Local error

Found 4 expressions with local error:

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

rewrite891.0ms

Algorithm

rewrite-expression-head

Rules

8920×	`times-frac`
3989×	`add-sqr-sqrt` `*-un-lft-identity`
2953×	`add-cube-cbrt`
518×	`distribute-lft-out--` `difference-of-squares`
463×	`div-inv`
288×	`associate-/r/`
259×	`distribute-rgt-neg-in` `sqrt-prod`
137×	`add-exp-log`
120×	`associate-/r*`
100×	`div-exp`
87×	`flip3--` `flip--`
65×	`add-cbrt-cube`
43×	`cbrt-undiv`
32×	`associate-/l*`
9×	`rec-exp` `1-exp` `prod-exp`
6×	`add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`frac-2neg` `clear-num` `cbrt-unprod`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff` `associate-/l/`

Counts

4 → 2595

Calls

4 calls:

54.0ms	(/ c (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
202.0ms	(/ (/ 1 (/ 2.0 (* 4.0 a))) (/ a (/ c (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))
95.0ms	(/ a (/ c (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
19.0ms	(- (* b b) (* (* 4.0 a) c))

series787.0ms

Counts

4 → 12

Calls

4 calls:

265.0ms	(/ c (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
223.0ms	(/ (/ 1 (/ 2.0 (* 4.0 a))) (/ a (/ c (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))
245.0ms	(/ a (/ c (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
53.0ms	(- (* b b) (* (* 4.0 a) c))

simplify2.0s

Counts

2607 → 2607

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	3240	134177
done	5000	127310

prune12.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes200.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	25
1	23	25
done	23	25

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.0s	8578×	body	80	nan
604.0ms	4399×	body	160	valid
602.0ms	16578×	pre	80	true
323.0ms	3601×	body	80	valid