Details

sample147.0ms

Algorithm

intervals

Results

31.0ms	121×	body	320	valid
23.0ms	272×	body	80	nan
22.0ms	528×	pre	80	true
15.0ms	85×	body	160	valid
6.0ms	18×	body	640	valid
3.0ms	32×	body	80	valid

simplify193.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	12	17
1	22	17
2	42	16
3	82	16
4	104	16
5	112	16
done	112	16

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.5b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* b b) (* (* 3.0 a) c))
0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.3b	(* (* 3.0 a) c)
25.7b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

rewrite216.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
14×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt` `add-cube-cbrt` `fma-def` `add-log-exp`
9×	`pow1`
6×	`distribute-rgt-neg-in` `distribute-lft-out`
5×	`times-frac` `associate-/l*`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-r` `pow-prod-down`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3-+` `div-exp` `sum-log` `flip-+` `associate-/l/`
1×	`+-commutative` `neg-mul-1` `sub-neg` `flip3--` `frac-2neg` `fma-neg` `diff-log` `div-sub` `associate-l` `prod-diff` `neg-log` `clear-num` `associate-/r` `-commutative` `flip--` `div-inv`

Counts

4 → 93

Calls

4 calls:

18.0ms	(- (* b b) (* (* 3.0 a) c))
129.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
22.0ms	(* (* 3.0 a) c)
42.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

series403.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(- (* b b) (* (* 3.0 a) c))
177.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
22.0ms	(* (* 3.0 a) c)
135.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

simplify1.6s

Counts

105 → 105

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	167	1559
1	440	1478
2	1684	1247
done	5000	1234

prune384.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite257.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
80×	`add-sqr-sqrt` `*-un-lft-identity`
40×	`add-cube-cbrt`
30×	`associate-/l*`
28×	`add-exp-log` `add-cbrt-cube`
20×	`distribute-lft-out--` `difference-of-squares`
14×	`pow1`
10×	`distribute-rgt-neg-in` `sqrt-prod`
8×	`prod-exp` `associate-/r*` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`associate-r` `pow-prod-down` `associate-/r/`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`flip3--` `flip--` `associate-/l/`
2×	`frac-2neg` `associate-l` `clear-num` `*-commutative`
1×	`flip3-+` `flip-+`

Counts

4 → 165

Calls

4 calls:

38.0ms	(* (* 3.0 a) c)
19.0ms	(* (* a c) 3.0)
71.0ms	(/ (+ 0 (* (* a c) 3.0)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
113.0ms	(/ (/ (+ 0 (* (* a c) 3.0)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

series528.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* (* 3.0 a) c)
22.0ms	(* (* a c) 3.0)
263.0ms	(/ (+ 0 (* (* a c) 3.0)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
214.0ms	(/ (/ (+ 0 (* (* a c) 3.0)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

simplify2.2s

Counts

177 → 177

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	255	4841
1	637	4352
2	2833	3973
done	5000	3971

prune704.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite462.0ms

Algorithm

rewrite-expression-head

Rules

438×	`times-frac`
272×	`add-sqr-sqrt` `*-un-lft-identity`
226×	`distribute-rgt-neg-in`
188×	`distribute-lft-neg-in`
120×	`add-cube-cbrt` `associate-/l*`
76×	`distribute-lft-out--` `difference-of-squares`
74×	`neg-mul-1`
38×	`sqrt-prod`
28×	`add-exp-log` `add-cbrt-cube`
19×	`associate-/r*`
14×	`pow1`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`associate-r` `pow-prod-down` `associate-/r/` `distribute-neg-frac`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`flip3--` `div-sub` `distribute-frac-neg` `flip--`
2×	`neg-sub0` `frac-2neg` `associate-l` `clear-num` `*-commutative`
1×	`associate-/l/`

Counts

4 → 442

Calls

4 calls:

36.0ms	(* (* 3.0 a) c)
35.0ms	(* (* 3.0 a) c)
134.0ms	(/ (- (* (* 3.0 a) c)) (- (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
200.0ms	(/ (/ (- (* (* 3.0 a) c)) (- (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) (* 3.0 a))

series591.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (* 3.0 a) c)
37.0ms	(* (* 3.0 a) c)
267.0ms	(/ (- (* (* 3.0 a) c)) (- (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
259.0ms	(/ (/ (- (* (* 3.0 a) c)) (- (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) (* 3.0 a))

simplify818.0ms

Counts

454 → 454

Iterations

Useful iterations: done (794.0ms)

Iter	Nodes	Cost
0	497	13875
1	1181	13569
done	5001	13177

prune1.5s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* b b) (* (* 3.0 a) c))
0.3b	(* (* 3.0 a) c)
0.4b	(/ (/ (- (* 3.0 a)) (- 1)) (/ (* 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))))))

rewrite671.0ms

Algorithm

rewrite-expression-head

Rules

7217×	`times-frac`
2568×	`add-sqr-sqrt` `*-un-lft-identity`
1764×	`add-cube-cbrt`
1125×	`distribute-rgt-neg-in`
924×	`distribute-lft-neg-in`
528×	`neg-mul-1`
402×	`distribute-lft-out--` `difference-of-squares`
201×	`sqrt-prod` `associate-/r/`
167×	`div-inv`
68×	`flip3--` `flip--`
65×	`associate-/l*`
62×	`add-exp-log` `add-cbrt-cube`
59×	`associate-/r*`
33×	`cbrt-undiv` `div-exp`
9×	`pow1` `prod-exp` `cbrt-unprod`
6×	`add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-r` `pow-prod-down`
2×	`frac-2neg` `div-sub` `distribute-frac-neg` `clear-num`
1×	`neg-sub0` `sub-neg` `fma-neg` `diff-log` `associate-l` `prod-diff` `*-commutative` `associate-/l/`

Counts

4 → 2292

Calls

4 calls:

18.0ms	(- (* b b) (* (* 3.0 a) c))
24.0ms	(* (* 3.0 a) c)
162.0ms	(/ (/ (- (* 3.0 a)) (- 1)) (/ (* 3.0 a) (/ c (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))))
56.0ms	(/ (* 3.0 a) (/ c (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))

series637.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(- (* b b) (* (* 3.0 a) c))
37.0ms	(* (* 3.0 a) c)
232.0ms	(/ (/ (- (* 3.0 a)) (- 1)) (/ (* 3.0 a) (/ c (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))))
284.0ms	(/ (* 3.0 a) (/ c (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))

simplify1.9s

Counts

2304 → 2304

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	2906	112382
done	5000	106425

prune10.6s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes191.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify9.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	18	27
1	29	26
2	33	26
done	33	26

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.2s	16319×	pre	80	true
957.0ms	3602×	body	320	valid
698.0ms	8319×	body	80	nan
582.0ms	2899×	body	160	valid
145.0ms	515×	body	640	valid
97.0ms	984×	body	80	valid