Details

sample105.0ms

Algorithm

intervals

Results

21.0ms	270×	body	80	nan
18.0ms	104×	body	320	valid
15.0ms	526×	pre	80	true
12.0ms	99×	body	160	valid
4.0ms	19×	body	640	valid
2.0ms	34×	body	80	valid

simplify130.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	102
7	102
6	101
5	99
4	91
3	75
2	40
1	22
0	12

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 51.7b

localize24.0ms

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)
26.6b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

rewrite191.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
14×	`add-cbrt-cube` `add-exp-log`
10×	`add-sqr-sqrt` `fma-def` `add-cube-cbrt` `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×	`neg-sub0` `cbrt-undiv` `sum-log` `flip3-+` `div-exp` `associate-+l-` `flip-+` `associate-/l/`
1×	`+-commutative` `clear-num` `associate-/r` `neg-mul-1` `sub-neg` `frac-2neg` `flip3--` `fma-neg` `diff-log` `div-sub` `associate-l` `prod-diff` `neg-log` `-commutative` `div-inv` `flip--`

Counts

4 → 93

Calls

4 calls:

13.0ms	(- (* b b) (* (* 3.0 a) c))
105.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
26.0ms	(* (* 3.0 a) c)
43.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

series403.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(- (* b b) (* (* 3.0 a) c))
151.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
36.0ms	(* (* 3.0 a) c)
147.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

simplify1.8s

Counts

105 → 105

Iterations

Iter	Nodes
done	5002
2	1578
1	461
0	167

prune603.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite388.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
80×	`add-sqr-sqrt` `*-un-lft-identity`
40×	`add-cube-cbrt`
30×	`associate-/l*`
28×	`add-cbrt-cube` `add-exp-log`
20×	`distribute-lft-out--` `difference-of-squares`
14×	`pow1`
10×	`distribute-rgt-neg-in` `sqrt-prod`
8×	`associate-/r*` `prod-exp` `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--` `div-sub` `flip--` `associate-/l/`
2×	`clear-num` `frac-2neg` `associate-l` `*-commutative` `associate-+l-`
1×	`flip3-+` `flip-+`

Counts

4 → 167

Calls

4 calls:

14.0ms	(* (* 3.0 a) c)
20.0ms	(* (* 3.0 a) c)
153.0ms	(/ (+ (- (* b b) (* b b)) (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
193.0ms	(/ (/ (+ (- (* b b) (* b b)) (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

series543.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (* 3.0 a) c)
33.0ms	(* (* 3.0 a) c)
278.0ms	(/ (+ (- (* b b) (* b b)) (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
209.0ms	(/ (/ (+ (- (* b b) (* b b)) (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

simplify2.4s

Counts

179 → 179

Iterations

Iter	Nodes
done	5000
2	2099
1	667
0	247

prune985.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize53.0ms

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 (fma b b (* (- (* 3.0 a)) c)))))
0.4b	(/ (/ (* (- (* 3.0 a)) c) (- (- b) (sqrt (fma b b (* (- (* 3.0 a)) c))))) (- (* 3.0 a)))

rewrite171.0ms

Algorithm

rewrite-expression-head

Rules

134×	`times-frac`
78×	`add-sqr-sqrt`
74×	`*-un-lft-identity`
38×	`add-cube-cbrt`
25×	`distribute-rgt-neg-in`
22×	`add-cbrt-cube` `add-exp-log`
18×	`distribute-lft-out--` `difference-of-squares`
16×	`distribute-lft-neg-in` `neg-mul-1` `associate-/r/`
14×	`associate-/l*`
13×	`associate-/r*`
12×	`associate-l`
9×	`sqrt-prod` `div-inv`
8×	`pow1` `flip3--` `flip--`
7×	`cbrt-undiv` `div-exp`
6×	`associate-r`
4×	`distribute-lft-neg-out` `expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`distribute-frac-neg`
2×	`clear-num` `frac-2neg` `pow-prod-down` `*-commutative` `unswap-sqr`
1×	`associate-/l/`

Counts

4 → 199

Calls

4 calls:

19.0ms	(* (- (* 3.0 a)) c)
17.0ms	(* (- (* 3.0 a)) c)
45.0ms	(/ (* (- (* 3.0 a)) c) (- (- b) (sqrt (fma b b (* (- (* 3.0 a)) c)))))
76.0ms	(/ (/ (* (- (* 3.0 a)) c) (- (- b) (sqrt (fma b b (* (- (* 3.0 a)) c))))) (- (* 3.0 a)))

series527.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (- (* 3.0 a)) c)
40.0ms	(* (- (* 3.0 a)) c)
242.0ms	(/ (* (- (* 3.0 a)) c) (- (- b) (sqrt (fma b b (* (- (* 3.0 a)) c)))))
214.0ms	(/ (/ (* (- (* 3.0 a)) c) (- (- b) (sqrt (fma b b (* (- (* 3.0 a)) c))))) (- (* 3.0 a)))

simplify2.2s

Counts

211 → 211

Iterations

Iter	Nodes
done	5011
2	2963
1	728
0	284

prune1.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite993.0ms

Algorithm

rewrite-expression-head

Rules

13652×	`times-frac`
5723×	`add-sqr-sqrt`
5721×	`*-un-lft-identity`
3965×	`add-cube-cbrt`
1593×	`distribute-rgt-neg-in`
1154×	`distribute-lft-neg-in` `neg-mul-1`
878×	`distribute-lft-out--` `difference-of-squares`
439×	`sqrt-prod`
339×	`div-inv`
317×	`associate-/r/`
201×	`associate-/r*`
146×	`flip3--` `flip--`
43×	`add-exp-log`
34×	`add-cbrt-cube`
31×	`associate-/l*`
28×	`div-exp`
19×	`cbrt-undiv`
6×	`pow1` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `1-exp` `div-sub` `associate-r` `distribute-frac-neg`
2×	`neg-sub0`
1×	`distribute-lft-neg-out` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr` `associate-/l/`

Counts

4 → 4179

Calls

4 calls:

23.0ms	(/ c (- (- b) (sqrt (fma b b (* (- (* 3.0 a)) c)))))
8.0ms	(* (- (* 3.0 a)) c)
189.0ms	(/ (/ (- (* 3.0 a)) 1) (/ (- (* 3.0 a)) (/ c (- (- b) (sqrt (fma b b (* (- (* 3.0 a)) c)))))))
34.0ms	(/ (- (* 3.0 a)) (/ c (- (- b) (sqrt (fma b b (* (- (* 3.0 a)) c))))))

series1.2s

Counts

4 → 12

Calls

4 calls:

271.0ms	(/ c (- (- b) (sqrt (fma b b (* (- (* 3.0 a)) c)))))
25.0ms	(* (- (* 3.0 a)) c)
225.0ms	(/ (/ (- (* 3.0 a)) 1) (/ (- (* 3.0 a)) (/ c (- (- b) (sqrt (fma b b (* (- (* 3.0 a)) c)))))))
632.0ms	(/ (- (* 3.0 a)) (/ c (- (- b) (sqrt (fma b b (* (- (* 3.0 a)) c))))))

simplify7.7s

Counts

4191 → 4191

Iterations

Iter	Nodes
done	5286
0	5286

prune27.6s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes350.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	39
3	39
2	38
1	30
0	16

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.2s	7976×	body	80	nan
808.0ms	3556×	body	320	valid
597.0ms	15976×	pre	80	true
504.0ms	532×	body	640	valid
471.0ms	2995×	body	160	valid
57.0ms	917×	body	80	valid