Details

sample91.0ms

Algorithm

intervals

Results

18.0ms	144×	body	160	valid
16.0ms	255×	body	80	nan
15.0ms	511×	pre	80	true
7.0ms	112×	body	80	valid

simplify130.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	12	17
1	21	17
2	41	16
3	75	16
4	88	16
5	96	16
done	96	16

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 28.6b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.3b	(- (* b b) (* (* 3.0 a) c))
0.3b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
28.4b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

rewrite232.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

18.0ms	(* (* 3.0 a) c)
14.0ms	(- (* b b) (* (* 3.0 a) c))
141.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
56.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

series411.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (* 3.0 a) c)
67.0ms	(- (* b b) (* (* 3.0 a) c))
180.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
127.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

simplify1.6s

Counts

85 → 85

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	154	1437
1	410	1361
2	1541	1139
done	5000	1125

prune255.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.4b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
0.3b	(- (* b b) (* (* 3.0 a) c))
0.4b	(/ (/ (+ 0 (* c (* 3.0 a))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
0.4b	(/ (+ 0 (* c (* 3.0 a))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))

rewrite307.0ms

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:

35.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
8.0ms	(- (* b b) (* (* 3.0 a) c))
158.0ms	(/ (/ (+ 0 (* c (* 3.0 a))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
88.0ms	(/ (+ 0 (* c (* 3.0 a))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))

series780.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
77.0ms	(- (* b b) (* (* 3.0 a) c))
299.0ms	(/ (/ (+ 0 (* c (* 3.0 a))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
287.0ms	(/ (+ 0 (* c (* 3.0 a))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))

simplify1.7s

Counts

163 → 163

Iterations

Useful iterations: 2 (733.0ms)

Iter	Nodes	Cost
0	248	5048
1	617	4510
2	2607	4166
done	5000	4166

prune658.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (* b b) (* (* 3.0 a) c))
0.3b	(/ 1 (/ (* 3.0 a) (/ (* (* 3.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))))
0.3b	(/ (* 3.0 a) (/ (* (* 3.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
0.4b	(/ (* (* 3.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))

rewrite299.0ms

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*`
3×	`frac-2neg` `clear-num`
1×	`sub-neg` `pow-flip` `diff-log` `inv-pow`

Counts

4 → 223

Calls

4 calls:

16.0ms	(- (* b b) (* (* 3.0 a) c))
106.0ms	(/ 1 (/ (* 3.0 a) (/ (* (* 3.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))))
71.0ms	(/ (* 3.0 a) (/ (* (* 3.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
83.0ms	(/ (* (* 3.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))

series666.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(- (* b b) (* (* 3.0 a) c))
207.0ms	(/ 1 (/ (* 3.0 a) (/ (* (* 3.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))))
98.0ms	(/ (* 3.0 a) (/ (* (* 3.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
288.0ms	(/ (* (* 3.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))

simplify2.1s

Counts

235 → 235

Iterations

Useful iterations: 2 (815.0ms)

Iter	Nodes	Cost
0	344	7854
1	871	7255
2	3393	6153
done	5000	6153

prune720.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.2b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
0.2b	(/ c (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
0.3b	(- (* b b) (* (* 3.0 a) c))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt` `*-un-lft-identity`
21×	`times-frac`
17×	`add-cube-cbrt`
11×	`add-exp-log` `add-cbrt-cube`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
9×	`pow1`
7×	`associate-/r*`
5×	`distribute-rgt-neg-in` `sqrt-prod`
3×	`flip3--` `diff-log` `associate-r` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod` `associate-/l*`
2×	`sub-neg` `associate-/r/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `frac-2neg` `div-exp` `associate-l` `neg-log` `clear-num` `*-commutative` `div-inv`

Counts

4 → 93

Calls

4 calls:

31.0ms	(* (* 3.0 a) c)
31.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
59.0ms	(/ c (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
17.0ms	(- (* b b) (* (* 3.0 a) c))

series546.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (* 3.0 a) c)
117.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
335.0ms	(/ c (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
53.0ms	(- (* b b) (* (* 3.0 a) c))

simplify4.0s

Counts

105 → 105

Iterations

Useful iterations: done (4.0s)

Iter	Nodes	Cost
0	161	1923
1	370	1830
2	1203	1694
3	4371	1676
done	5001	1672

prune335.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

regimes173.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	17	27
1	24	25
done	24	25

end0.0ms

sample3.4s

Algorithm

intervals

Results

774.0ms	3549×	body	80	valid
740.0ms	4451×	body	160	valid
548.0ms	16506×	pre	80	true
519.0ms	8506×	body	80	nan