Details

Time bar (total: 10.6s)

sample88.0ms

Algorithm
intervals
Results
20.0ms569×pre80true
19.0ms313×body80nan
16.0ms135×body160valid
8.0ms121×body80valid

simplify124.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (10.0ms)

IterNodesCost
01417
12517
24616
38616
410816
511616
done11616

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
0.3b
(- (* b b) (* (* 4.0 a) c))
27.1b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

rewrite227.0ms

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:
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
126.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
12.0ms
(- (* b b) (* (* 4.0 a) c))
71.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

series427.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
154.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
71.0ms
(- (* b b) (* (* 4.0 a) c))
90.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

simplify1.2s

Counts
118 → 118
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01952476
14802169
214461861
done50001789

prune427.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 8.3b

localize6.0ms

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

prune51.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 8.3b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite40.0ms

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:
10.0ms
(/ (* a c) b)
27.0ms
(/ (* -2.0 (/ (* a c) b)) (* 2.0 a))

series57.0ms

Counts
2 → 6
Calls
2 calls:
31.0ms
(/ (* a c) b)
26.0ms
(/ (* -2.0 (/ (* a c) b)) (* 2.0 a))

simplify922.0ms

Counts
61 → 61
Iterations

Useful iterations: 2 (254.0ms)

IterNodesCost
0111818
1314787
21621559
done5001559

prune242.0ms

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 8.3b

localize10.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ (* -2.0 (/ 1 (/ b (* a c)))) (* 2.0 a))
0.2b
(/ b (* a c))
0.3b
(/ 1 (/ b (* a c)))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
128×add-exp-log
62×add-cbrt-cube
60×div-exp
41×prod-exp
37×times-frac
27×cbrt-undiv
21×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
17×cbrt-unprod
9×rec-exp 1-exp associate-/r*
7×div-inv associate-/l*
4×pow1
3×expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
2×associate-/l/
1×pow-flip associate-*r/ associate-/r/ un-div-inv inv-pow
Counts
3 → 130
Calls
3 calls:
45.0ms
(/ (* -2.0 (/ 1 (/ b (* a c)))) (* 2.0 a))
9.0ms
(/ b (* a c))
25.0ms
(/ 1 (/ b (* a c)))

series107.0ms

Counts
3 → 9
Calls
3 calls:
30.0ms
(/ (* -2.0 (/ 1 (/ b (* a c)))) (* 2.0 a))
39.0ms
(/ b (* a c))
37.0ms
(/ 1 (/ b (* a c)))

simplify1.5s

Counts
139 → 139
Iterations

Useful iterations: 2 (459.0ms)

IterNodesCost
02081950
15081724
220101236
done50001236

prune277.0ms

Pruning

32 alts after pruning (32 fresh and 0 done)

Merged error: 8.3b

regimes674.0ms

Accuracy

42.5% (7.9b remaining)

Error of 16.9b against oracle of 9.0b and baseline of 22.8b

bsearch30.0ms

Steps
ItersRangePoint
2
21798.380384010838
25007.94249627011
22199.575648043246

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02238
12738
done2738

end0.0ms

sample4.1s

Algorithm
intervals
Results
1.4s8809×body80nan
944.0ms4481×body160valid
856.0ms16809×pre80true
327.0ms3519×body80valid