Details

Time bar (total: 20.4s)

sample77.0ms

Algorithm
intervals
Results
15.0ms35×body2560valid
15.0ms190×body80valid
11.0ms29×body1280valid
7.0ms92×body80nan
5.0ms16×body640valid
2.0ms7×body320valid
1.0ms1×body5120valid
0.0ms3×body160valid

simplify162.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
01217
12117
24116
37516
48816
59616
done9616

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.4b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 3.0 a) c)
0.2b
(- (* b b) (* (* 3.0 a) c))
1.1b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
22.0b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite147.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×pow1
9×add-exp-log add-cbrt-cube
8×*-un-lft-identity add-log-exp
6×add-cube-cbrt
4×sqrt-prod
3×flip3-- associate-*r* pow-prod-down prod-exp flip-- cbrt-unprod
2×sub-neg sqrt-div diff-log difference-of-squares
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* *-commutative distribute-lft-out--
Counts
4 → 60
Calls
4 calls:
23.0ms
(* (* 3.0 a) c)
14.0ms
(- (* b b) (* (* 3.0 a) c))
78.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
29.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series263.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(* (* 3.0 a) c)
55.0ms
(- (* b b) (* (* 3.0 a) c))
96.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
85.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify3.7s

Counts
72 → 72
Iterations

Useful iterations: done (3.7s)

IterNodesCost
01201001
1276903
2928825
33466821
done5000815

prune244.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 11.4b

localize28.0ms

Local error

Found 4 expressions with local error:

1.0b
(+ (sqrt (- (* b b) (* (* 3.0 a) c))) b)
4.4b
(/ (/ (/ (- 0 (* (* 3.0 a) c)) (+ (sqrt (- (* b b) (* (* 3.0 a) c))) b)) 3.0) a)
8.1b
(/ (- 0 (* (* 3.0 a) c)) (+ (sqrt (- (* b b) (* (* 3.0 a) c))) b))
22.0b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite304.0ms

Algorithm
rewrite-expression-head
Rules
546×times-frac
327×*-un-lft-identity
246×add-sqr-sqrt
245×add-cube-cbrt
61×associate-/l*
41×distribute-lft-out
26×associate-/r/
18×div-inv
15×add-exp-log add-cbrt-cube
14×flip3-+ flip-+
7×cbrt-undiv div-exp associate-/r*
6×add-log-exp
5×pow1
4×div-sub distribute-frac-neg
3×sqrt-prod associate-/l/
2×flip3-- frac-2neg sub0-neg sqrt-div clear-num flip--
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 sum-log
Counts
4 → 318
Calls
4 calls:
40.0ms
(+ (sqrt (- (* b b) (* (* 3.0 a) c))) b)
135.0ms
(/ (/ (/ (- 0 (* (* 3.0 a) c)) (+ (sqrt (- (* b b) (* (* 3.0 a) c))) b)) 3.0) a)
76.0ms
(/ (- 0 (* (* 3.0 a) c)) (+ (sqrt (- (* b b) (* (* 3.0 a) c))) b))
15.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series728.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(+ (sqrt (- (* b b) (* (* 3.0 a) c))) b)
230.0ms
(/ (/ (/ (- 0 (* (* 3.0 a) c)) (+ (sqrt (- (* b b) (* (* 3.0 a) c))) b)) 3.0) a)
296.0ms
(/ (- 0 (* (* 3.0 a) c)) (+ (sqrt (- (* b b) (* (* 3.0 a) c))) b))
95.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.2s

Counts
330 → 330
Iterations

Useful iterations: 2 (1.1s)

IterNodesCost
060113349
1144412143
2467011831
done500111831

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 10.1b

localize25.0ms

Local error

Found 4 expressions with local error:

1.0b
(+ (sqrt (- (* b b) (* (* 3.0 a) c))) b)
3.2b
(/ (* a 3.0) (/ (+ (sqrt (- (* b b) (* (* 3.0 a) c))) b) c))
4.4b
(/ (/ (- 0 (/ (* a 3.0) (/ (+ (sqrt (- (* b b) (* (* 3.0 a) c))) b) c))) 3.0) a)
22.0b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite467.0ms

Algorithm
rewrite-expression-head
Rules
157×times-frac
115×*-un-lft-identity
102×add-sqr-sqrt
77×add-cube-cbrt
21×add-exp-log add-cbrt-cube
20×associate-/l*
19×associate-/r*
12×distribute-lft-out-- difference-of-squares
9×cbrt-undiv div-exp
8×div-inv
7×distribute-lft-out
6×add-log-exp
5×pow1
3×sqrt-prod
2×frac-2neg sqrt-div div-sub distribute-frac-neg prod-exp clear-num cbrt-unprod
1×+-commutative rem-sqrt-square flip3-- sqrt-pow1 flip3-+ sub0-neg pow1/2 sum-log associate-/r/ flip-- flip-+ associate-/l/
Counts
4 → 175
Calls
4 calls:
39.0ms
(+ (sqrt (- (* b b) (* (* 3.0 a) c))) b)
86.0ms
(/ (* a 3.0) (/ (+ (sqrt (- (* b b) (* (* 3.0 a) c))) b) c))
316.0ms
(/ (/ (- 0 (/ (* a 3.0) (/ (+ (sqrt (- (* b b) (* (* 3.0 a) c))) b) c))) 3.0) a)
11.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series775.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(+ (sqrt (- (* b b) (* (* 3.0 a) c))) b)
322.0ms
(/ (* a 3.0) (/ (+ (sqrt (- (* b b) (* (* 3.0 a) c))) b) c))
222.0ms
(/ (/ (- 0 (/ (* a 3.0) (/ (+ (sqrt (- (* b b) (* (* 3.0 a) c))) b) c))) 3.0) a)
96.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.5s

Counts
187 → 187
Iterations

Useful iterations: 2 (695.0ms)

IterNodesCost
03705971
19045625
228825235
done50005235

prune712.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 9.5b

localize40.0ms

Local error

Found 4 expressions with local error:

1.0b
(+ (sqrt (- (* b b) (* (* 3.0 a) c))) b)
3.2b
(/ (* a 3.0) (/ (+ (sqrt (- (* b b) (* (* 3.0 a) c))) b) c))
4.4b
(* (/ (- 0 (/ (* a 3.0) (/ (+ (sqrt (- (* b b) (* (* 3.0 a) c))) b) c))) 3.0) (/ 1 a))
22.0b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite551.0ms

Algorithm
rewrite-expression-head
Rules
71×times-frac
61×add-sqr-sqrt
59×*-un-lft-identity
38×add-exp-log
37×add-cube-cbrt
28×add-cbrt-cube
19×associate-*l*
16×associate-/r*
14×div-exp
13×associate-*r*
10×cbrt-undiv prod-exp
7×pow1 distribute-lft-out
6×cbrt-unprod add-log-exp unswap-sqr
5×div-inv
3×sqrt-prod distribute-lft-out-- difference-of-squares
2×rec-exp sqrt-div 1-exp
1×+-commutative distribute-lft-neg-out frac-times rem-sqrt-square flip3-- frac-2neg sqrt-pow1 flip3-+ sub0-neg pow1/2 associate-*r/ distribute-frac-neg pow-prod-down associate-*l/ clear-num sum-log associate-/r/ un-div-inv *-commutative flip-- flip-+ associate-/l*
Counts
4 → 143
Calls
4 calls:
64.0ms
(+ (sqrt (- (* b b) (* (* 3.0 a) c))) b)
74.0ms
(/ (* a 3.0) (/ (+ (sqrt (- (* b b) (* (* 3.0 a) c))) b) c))
366.0ms
(* (/ (- 0 (/ (* a 3.0) (/ (+ (sqrt (- (* b b) (* (* 3.0 a) c))) b) c))) 3.0) (/ 1 a))
34.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series795.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(+ (sqrt (- (* b b) (* (* 3.0 a) c))) b)
310.0ms
(/ (* a 3.0) (/ (+ (sqrt (- (* b b) (* (* 3.0 a) c))) b) c))
234.0ms
(* (/ (- 0 (/ (* a 3.0) (/ (+ (sqrt (- (* b b) (* (* 3.0 a) c))) b) c))) 3.0) (/ 1 a))
134.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.6s

Counts
155 → 155
Iterations

Useful iterations: 2 (823.0ms)

IterNodesCost
03114175
18493847
227103338
done50003338

prune657.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 9.4b

regimes478.0ms

Accuracy

89.8% (2.4b remaining)

Error of 12.0b against oracle of 9.7b and baseline of 32.8b

bsearch278.0ms

Steps
ItersRangePoint
7
1.138038992187667e+117
2.1492991228689436e+118
2.048582467390677e+118
8
-5.159206870984134e-258
-3.0781728110121473e-262
-3.1477801358310677e-262
9
-6.354265220965125e+156
-1.769171722317776e+149
-1.1399756785205677e+154

simplify27.0ms

Iterations

Useful iterations: 5 (22.0ms)

IterNodesCost
048108
160106
272106
385106
490106
593105
done93105

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.0s5881×body80valid
685.0ms1076×body2560valid
465.0ms849×body1280valid
255.0ms2915×body80nan
246.0ms467×body640valid
55.0ms106×body5120valid
44.0ms214×body320valid
18.0ms121×body160valid