Details

Time bar (total: 12.0s)

sample107.0ms

Algorithm
intervals
Results
42.0ms135×body160valid
15.0ms537×pre80true
15.0ms281×body80nan
10.0ms60×body320valid
4.0ms61×body80valid

simplify74.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
01217
12117
24116
37516
48816
59616
done9616

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 44.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) 3.0)
0.3b
(/ (/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) 3.0) a)
0.3b
(* (* 3.0 a) c)
37.5b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

rewrite349.0ms

Algorithm
rewrite-expression-head
Rules
156×times-frac
147×add-sqr-sqrt
113×*-un-lft-identity
79×add-cube-cbrt
34×difference-of-squares
28×associate-/l*
17×sqrt-prod distribute-lft-out--
16×add-exp-log add-cbrt-cube
9×pow1
6×associate-/r* div-inv add-log-exp
4×cbrt-undiv div-exp
3×div-sub associate-*r* pow-prod-down prod-exp cbrt-unprod associate-/l/
2×flip3-- frac-2neg clear-num flip--
1×sub-neg diff-log associate-*l* *-commutative
Counts
4 → 182
Calls
4 calls:
104.0ms
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) 3.0)
120.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) 3.0) a)
30.0ms
(* (* 3.0 a) c)
83.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

series374.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) 3.0)
134.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) 3.0) a)
35.0ms
(* (* 3.0 a) c)
102.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

simplify1.7s

Counts
194 → 194
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02874775
16894627
219844417
done50004407

prune660.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 5.1b

localize8.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify0.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
done00

prune60.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 5.1b

localize14.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (* a c) b)
0.2b
(/ (* -0.5 (/ (* a c) b)) a)

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
21×add-exp-log add-cbrt-cube
8×cbrt-undiv div-exp
6×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac associate-/r*
5×prod-exp cbrt-unprod
2×pow1 frac-2neg clear-num div-inv associate-/l* add-log-exp
1×associate-*r/ associate-/l/
Counts
2 → 47
Calls
2 calls:
19.0ms
(/ (* a c) b)
36.0ms
(/ (* -0.5 (/ (* a c) b)) a)

series67.0ms

Counts
2 → 6
Calls
2 calls:
37.0ms
(/ (* a c) b)
29.0ms
(/ (* -0.5 (/ (* a c) b)) a)

simplify1.2s

Counts
53 → 53
Iterations

Useful iterations: done (1.2s)

IterNodesCost
097568
1253547
21082427
done5001353

prune158.0ms

Pruning

26 alts after pruning (25 fresh and 1 done)

Merged error: 5.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (* a c) b)
0.3b
(/ -0.5 (sqrt a))
0.3b
(* (/ -0.5 (sqrt a)) (/ (/ (* a c) b) (sqrt a)))
0.3b
(/ (/ (* a c) b) (sqrt a))

rewrite118.0ms

Algorithm
rewrite-expression-head
Rules
174×times-frac
121×add-sqr-sqrt
91×add-cube-cbrt *-un-lft-identity
72×sqrt-prod
52×add-exp-log add-cbrt-cube
46×associate-*r*
22×cbrt-undiv div-exp associate-*l*
18×div-inv
15×associate-/r*
12×prod-exp cbrt-unprod
11×associate-/l*
9×unswap-sqr
6×pow1
4×add-log-exp
3×frac-2neg clear-num
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative associate-/l/
Counts
4 → 237
Calls
4 calls:
10.0ms
(/ (* a c) b)
8.0ms
(/ -0.5 (sqrt a))
72.0ms
(* (/ -0.5 (sqrt a)) (/ (/ (* a c) b) (sqrt a)))
17.0ms
(/ (/ (* a c) b) (sqrt a))

series287.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(/ (* a c) b)
67.0ms
(/ -0.5 (sqrt a))
91.0ms
(* (/ -0.5 (sqrt a)) (/ (/ (* a c) b) (sqrt a)))
104.0ms
(/ (/ (* a c) b) (sqrt a))

simplify2.0s

Counts
249 → 249
Iterations

Useful iterations: 2 (934.0ms)

IterNodesCost
03333746
19503436
232843092
done50013092

prune766.0ms

Pruning

34 alts after pruning (33 fresh and 1 done)

Merged error: 5.0b

regimes485.0ms

Accuracy

11% (6.2b remaining)

Error of 11.1b against oracle of 4.9b and baseline of 11.9b

bsearch37.0ms

Steps
ItersRangePoint
5
6.650147488704243e-06
1.5219671990751255e-05
6.724747266396374e-06

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02039
12439
done2439

end0.0ms

sample3.5s

Algorithm
intervals
Results
961.0ms16347×pre80true
796.0ms4896×body160valid
531.0ms1771×body80valid
519.0ms8347×body80nan
259.0ms1333×body320valid