Details

Time bar (total: 11.7s)

sample103.0ms

Algorithm
intervals
Results
33.0ms144×body160valid
15.0ms273×body80nan
14.0ms529×pre80true
8.0ms39×body320valid
4.0ms73×body80valid

simplify117.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
01217
12217
24216
38316
411216
512016
done12016

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.8b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (* b b) (* (* 3.0 a) c))
0.3b
(* (* 3.0 a) c)
0.3b
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
38.5b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

rewrite229.0ms

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))
36.0ms
(* (* 3.0 a) c)
117.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
53.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

series354.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(- (* b b) (* (* 3.0 a) c))
35.0ms
(* (* 3.0 a) c)
158.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
101.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

simplify1.9s

Counts
105 → 105
Iterations

Useful iterations: done (1.9s)

IterNodesCost
01671559
14721480
227811251
done50011244

prune351.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.3b

localize4.0ms

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

prune61.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.3b

localize19.0ms

Local error

Found 3 expressions with local error:

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

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
49×add-exp-log add-cbrt-cube
17×prod-exp cbrt-unprod
16×cbrt-undiv div-exp
10×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
7×times-frac associate-*r*
5×pow1
4×associate-/r*
3×expm1-log1p-u associate-*l* log1p-expm1-u div-inv add-log-exp
2×frac-2neg associate-*r/ clear-num associate-/l*
1×pow-prod-down *-commutative associate-/l/ unswap-sqr
Counts
3 → 84
Calls
3 calls:
46.0ms
(* -1.5 (/ (* a c) b))
21.0ms
(/ (* a c) b)
47.0ms
(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))

series117.0ms

Counts
3 → 9
Calls
3 calls:
46.0ms
(* -1.5 (/ (* a c) b))
33.0ms
(/ (* a c) b)
38.0ms
(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))

simplify1.5s

Counts
93 → 93
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01291138
14011097
22854869
done5001853

prune309.0ms

Pruning

24 alts after pruning (23 fresh and 1 done)

Merged error: 5.2b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite596.0ms

Algorithm
rewrite-expression-head
Rules
97×add-exp-log add-cbrt-cube
57×times-frac
54×add-sqr-sqrt
46×add-cube-cbrt *-un-lft-identity
44×associate-*r*
39×prod-exp cbrt-unprod
31×cbrt-undiv div-exp sqrt-prod
11×pow1
7×associate-*r/ associate-/r*
4×expm1-log1p-u associate-*l* pow-prod-down log1p-expm1-u div-inv associate-/l* add-log-exp
3×associate-/l/ unswap-sqr
2×frac-times frac-2neg associate-*l/ clear-num *-commutative
Counts
4 → 181
Calls
4 calls:
9.0ms
(/ c (sqrt b))
61.0ms
(* (* -1.5 (/ a (sqrt b))) (/ c (sqrt b)))
32.0ms
(* -1.5 (/ a (sqrt b)))
486.0ms
(/ (* (* -1.5 (/ a (sqrt b))) (/ c (sqrt b))) (* 3.0 a))

series237.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(/ c (sqrt b))
56.0ms
(* (* -1.5 (/ a (sqrt b))) (/ c (sqrt b)))
86.0ms
(* -1.5 (/ a (sqrt b)))
48.0ms
(/ (* (* -1.5 (/ a (sqrt b))) (/ c (sqrt b))) (* 3.0 a))

simplify550.0ms

Counts
193 → 193
Iterations

Useful iterations: done (544.0ms)

IterNodesCost
03083002
19762744
done50012248

prune662.0ms

Pruning

29 alts after pruning (28 fresh and 1 done)

Merged error: 5.2b

regimes558.0ms

Accuracy

8.2% (6.4b remaining)

Error of 11.5b against oracle of 5.1b and baseline of 12.1b

bsearch37.0ms

Steps
ItersRangePoint
4
0.12472275306628457
0.2162455449205228
0.12731425734469268

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02340
12840
done2840

end0.0ms

sample3.8s

Algorithm
intervals
Results
970.0ms8249×body80nan
929.0ms4887×body160valid
626.0ms16249×pre80true
341.0ms1298×body320valid
113.0ms1815×body80valid