Details

sample149.0ms

Algorithm

intervals

Results

46.0ms	563×	pre	80	true
26.0ms	307×	body	80	nan
26.0ms	150×	body	160	valid
9.0ms	106×	body	80	valid

simplify92.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	14	17
1	27	17
2	68	16
3	105	16
4	116	16
done	116	16

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.4b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b	(- (* b b) (* (* 4.0 a) c))
0.3b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
30.3b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite180.0ms

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:

19.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.0ms	(- (* b b) (* (* 4.0 a) c))
89.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
47.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series470.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
53.0ms	(- (* b b) (* (* 4.0 a) c))
160.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
154.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.7s

Counts

82 → 82

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	154	1565
1	961	1436
done	5001	1290

prune371.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.4b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite286.0ms

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:

30.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms	(- (* b b) (* (* 4.0 a) c))
106.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
128.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series641.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
74.0ms	(- (* b b) (* (* 4.0 a) c))
197.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
258.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify2.0m

Counts

163 → 163

Iterations

Useful iterations: done (2.0m)

Iter	Nodes	Cost
0	247	5048
done	5001	4497

prune727.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite338.0ms

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`
12×	`add-log-exp`
11×	`distribute-rgt-neg-in` `sqrt-prod`
8×	`associate-/r*`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
4×	`pow1` `flip3--` `flip--` `div-inv`
3×	`associate-/l/`
2×	`neg-sub0` `frac-2neg` `flip3-+` `diff-log` `neg-log` `prod-exp` `clear-num` `sum-log` `cbrt-unprod` `flip-+`
1×	`+-commutative` `associate--l-` `associate-+r-` `sub-neg` `unsub-neg`

Counts

4 → 154

Calls

4 calls:

33.0ms	(- (- b) (sqrt (+ (* b b) (- (* 4.0 (* a c))))))
19.0ms	(+ (* b b) (- (* 4.0 (* a c))))
150.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (+ (* b b) (- (* 4.0 (* a c))))))) (* 2.0 a))
129.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (+ (* b b) (- (* 4.0 (* a c)))))))

series667.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(- (- b) (sqrt (+ (* b b) (- (* 4.0 (* a c))))))
64.0ms	(+ (* b b) (- (* 4.0 (* a c))))
210.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (+ (* b b) (- (* 4.0 (* a c))))))) (* 2.0 a))
267.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (+ (* b b) (- (* 4.0 (* a c)))))))

simplify2.0m

Counts

166 → 166

Iterations

Useful iterations: done (2.0m)

Iter	Nodes	Cost
0	252	5275
done	5001	4526

prune804.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.2b	(- (* b b) (* 4.0 (* a c)))
0.3b	(/ (* 2.0 a) (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.3b	(/ (+ 0 (* (* 4.0 a) c)) (/ (* 2.0 a) (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))))

rewrite247.0ms

Algorithm

rewrite-expression-head

Rules

357×	`times-frac`
183×	`add-sqr-sqrt` `*-un-lft-identity`
107×	`add-cube-cbrt`
59×	`associate-/r*`
58×	`add-exp-log`
38×	`distribute-lft-out--` `difference-of-squares`
34×	`add-cbrt-cube`
33×	`div-exp`
19×	`distribute-rgt-neg-in` `sqrt-prod`
18×	`associate-/r/`
17×	`cbrt-undiv`
12×	`div-inv`
10×	`add-log-exp`
8×	`flip3--` `prod-exp` `flip--`
4×	`pow1` `rec-exp` `1-exp` `cbrt-unprod` `associate-/l*`
3×	`diff-log`
2×	`sub-neg` `frac-2neg` `clear-num` `associate-/l/`
1×	`associate--l-` `neg-sub0` `flip3-+` `neg-log` `flip-+`

Counts

4 → 266

Calls

4 calls:

30.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms	(- (* b b) (* 4.0 (* a c)))
61.0ms	(/ (* 2.0 a) (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
129.0ms	(/ (+ 0 (* (* 4.0 a) c)) (/ (* 2.0 a) (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))))

series566.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
55.0ms	(- (* b b) (* 4.0 (* a c)))
160.0ms	(/ (* 2.0 a) (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
221.0ms	(/ (+ 0 (* (* 4.0 a) c)) (/ (* 2.0 a) (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))))

simplify2.4m

Counts

278 → 278

Iterations

Useful iterations: done (2.4m)

Iter	Nodes	Cost
0	415	10005
done	5000	8946

prune761.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes131.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	21	27
1	28	25
done	28	25

end0.0ms

sample2.6s

Algorithm

intervals

Results

816.0ms	16589×	pre	80	true
572.0ms	8589×	body	80	nan
472.0ms	4475×	body	160	valid
192.0ms	3525×	body	80	valid