Details

Time bar (total: 12.2s)

sample140.0ms

Algorithm
intervals
Results
38.0ms155×body160valid
22.0ms253×body80nan
20.0ms509×pre80true
9.0ms33×body320valid
6.0ms68×body80valid

simplify158.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
01417
12517
24616
38716
412016
512916
done12916

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.5b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.2b
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
37.8b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

rewrite280.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
27×*-un-lft-identity
21×add-cube-cbrt
19×prod-diff
18×sqrt-prod
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×fma-neg
6×times-frac associate-/l* difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×distribute-lft-out--
2×cbrt-undiv sub-neg sqrt-div diff-log div-exp associate-/l/
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 106
Calls
4 calls:
20.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
18.0ms
(- (* b b) (* (* 4.0 a) c))
159.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
78.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

series462.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
65.0ms
(- (* b b) (* (* 4.0 a) c))
170.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
116.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

simplify1.8s

Counts
118 → 118
Iterations

Useful iterations: done (1.8s)

IterNodesCost
01952476
15182183
224661866
done50021794

prune460.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 6.2b

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

prune46.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 6.2b

localize9.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (* -2.0 (/ (* a c) b)) (* 2.0 a))
0.3b
(/ (* a c) b)

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
39×add-exp-log add-cbrt-cube
14×cbrt-undiv div-exp
13×prod-exp cbrt-unprod
4×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac associate-/r*
2×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u div-inv associate-/l* add-log-exp
1×associate-*r/ associate-/l/
Counts
2 → 55
Calls
2 calls:
30.0ms
(/ (* -2.0 (/ (* a c) b)) (* 2.0 a))
10.0ms
(/ (* a c) b)

series68.0ms

Counts
2 → 6
Calls
2 calls:
34.0ms
(/ (* -2.0 (/ (* a c) b)) (* 2.0 a))
34.0ms
(/ (* a c) b)

simplify1.5s

Counts
61 → 61
Iterations

Useful iterations: done (1.5s)

IterNodesCost
0111818
1352787
22559605
done5001559

prune253.0ms

Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 6.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(log1p (/ (* a c) b))
0.2b
(/ (* -2.0 (expm1 (log1p (/ (* a c) b)))) (* 2.0 a))
0.3b
(/ (* a c) b)
0.3b
(expm1 (log1p (/ (* a c) b)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
21×add-exp-log add-cbrt-cube
6×cbrt-undiv add-sqr-sqrt add-cube-cbrt *-un-lft-identity div-exp
5×expm1-log1p-u prod-exp cbrt-unprod
4×pow1 times-frac associate-/r* log1p-expm1-u add-log-exp
2×frac-2neg clear-num div-inv associate-/l*
1×log1p-udef expm1-log1p log1p-expm1 expm1-udef
Counts
4 → 68
Calls
4 calls:
0.0ms
(log1p (/ (* a c) b))
13.0ms
(/ (* -2.0 (expm1 (log1p (/ (* a c) b)))) (* 2.0 a))
10.0ms
(/ (* a c) b)
0.0ms
(expm1 (log1p (/ (* a c) b)))

series363.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(log1p (/ (* a c) b))
122.0ms
(/ (* -2.0 (expm1 (log1p (/ (* a c) b)))) (* 2.0 a))
22.0ms
(/ (* a c) b)
133.0ms
(expm1 (log1p (/ (* a c) b)))

simplify1.3s

Counts
80 → 80
Iterations

Useful iterations: done (1.3s)

IterNodesCost
0146972
1372851
22085697
done5000677

prune313.0ms

Pruning

25 alts after pruning (24 fresh and 1 done)

Merged error: 6.1b

regimes499.0ms

Accuracy

12.6% (6.0b remaining)

Error of 11.2b against oracle of 5.2b and baseline of 12.0b

bsearch3.0ms

Steps
ItersRangePoint
0
0.0031282979026107443
0.0031669466915584974
0.003147622297084621

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02238
12738
done2738

end0.0ms

sample4.4s

Algorithm
intervals
Results
1.0s16243×pre80true
907.0ms4898×body160valid
737.0ms1316×body320valid
677.0ms8243×body80nan
234.0ms1786×body80valid