Details

Time bar (total: 11.9s)

sample129.0ms

Algorithm
intervals
Results
26.0ms62×body80valid
21.0ms154×body160valid
19.0ms284×body80nan
17.0ms540×pre80true
8.0ms40×body320valid

simplify48.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
01217
12117
24116
37616
49616
510416
done10416

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 42.6b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (* b b) (* (* 3.0 a) c))
0.2b
(* (* 3.0 a) c)
0.3b
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
37.6b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

rewrite165.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
14×add-cbrt-cube add-exp-log
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×neg-sub0 cbrt-undiv sum-log flip3-+ div-exp associate-+l- flip-+ associate-/l/
1×+-commutative clear-num associate-/r* sub-neg frac-2neg flip3-- diff-log div-sub associate-*l* neg-log *-commutative div-inv flip--
Counts
4 → 73
Calls
4 calls:
13.0ms
(- (* b b) (* (* 3.0 a) c))
28.0ms
(* (* 3.0 a) c)
88.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
33.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

series366.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(- (* b b) (* (* 3.0 a) c))
23.0ms
(* (* 3.0 a) c)
144.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
130.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

simplify1.6s

Counts
85 → 85
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01541437
14371361
226251143
done50001139

prune520.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.5b

localize5.0ms

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

prune81.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.5b

localize12.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ (* a c) b)
0.3b
(* -1.5 (/ (* a c) b))
0.4b
(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
49×add-cbrt-cube add-exp-log
17×prod-exp cbrt-unprod
16×cbrt-undiv div-exp
10×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
7×times-frac associate-*r*
5×pow1
4×associate-/r*
3×associate-*l* div-inv add-log-exp
2×clear-num frac-2neg associate-*r/ associate-/l*
1×pow-prod-down *-commutative unswap-sqr associate-/l/
Counts
3 → 78
Calls
3 calls:
12.0ms
(/ (* a c) b)
24.0ms
(* -1.5 (/ (* a c) b))
26.0ms
(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))

series110.0ms

Counts
3 → 9
Calls
3 calls:
37.0ms
(/ (* a c) b)
49.0ms
(* -1.5 (/ (* a c) b))
24.0ms
(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))

simplify1.2s

Counts
87 → 87
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01231086
13911045
22789825
done5001761

prune432.0ms

Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 5.5b

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ c (sqrt b))
0.3b
(* -1.5 (/ a (sqrt b)))
0.4b
(* (* -1.5 (/ a (sqrt b))) (/ c (sqrt b)))
0.4b
(/ (* (* -1.5 (/ a (sqrt b))) (/ c (sqrt b))) (* 3.0 a))

rewrite172.0ms

Algorithm
rewrite-expression-head
Rules
97×add-cbrt-cube add-exp-log
57×times-frac
54×add-sqr-sqrt
46×*-un-lft-identity add-cube-cbrt
44×associate-*r*
39×prod-exp cbrt-unprod
31×cbrt-undiv div-exp sqrt-prod
11×pow1
7×associate-/r* associate-*r/
4×associate-*l* pow-prod-down div-inv associate-/l* add-log-exp
3×unswap-sqr associate-/l/
2×frac-times clear-num frac-2neg associate-*l/ *-commutative
Counts
4 → 173
Calls
4 calls:
10.0ms
(/ c (sqrt b))
19.0ms
(* -1.5 (/ a (sqrt b)))
62.0ms
(* (* -1.5 (/ a (sqrt b))) (/ c (sqrt b)))
64.0ms
(/ (* (* -1.5 (/ a (sqrt b))) (/ c (sqrt b))) (* 3.0 a))

series280.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(/ c (sqrt b))
75.0ms
(* -1.5 (/ a (sqrt b)))
79.0ms
(* (* -1.5 (/ a (sqrt b))) (/ c (sqrt b)))
54.0ms
(/ (* (* -1.5 (/ a (sqrt b))) (/ c (sqrt b))) (* 3.0 a))

simplify539.0ms

Counts
185 → 185
Iterations

Useful iterations: done (533.0ms)

IterNodesCost
03002922
19522668
done50012168

prune1.2s

Pruning

29 alts after pruning (28 fresh and 1 done)

Merged error: 5.5b

regimes969.0ms

Accuracy

14.6% (5.8b remaining)

Error of 10.8b against oracle of 5.0b and baseline of 11.8b

bsearch65.0ms

Steps
ItersRangePoint
4
0.03505168480040674
0.0561216462382886
0.035710121095340545

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02340
12840
done2840

end0.0ms

sample3.8s

Algorithm
intervals
Results
946.0ms4822×body160valid
693.0ms16308×pre80true
634.0ms8308×body80nan
535.0ms1770×body80valid
281.0ms1408×body320valid