Details

Time bar (total: 10.1s)

sample43.0ms

Algorithm
intervals
Results
9.0ms37×body2560valid
7.0ms177×body80valid
6.0ms31×body1280valid
3.0ms92×body80nan
2.0ms16×body640valid
1.0ms5×body5120valid
1.0ms6×body320valid
0.0ms3×body160valid

simplify53.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
01417
12417
24416
37816
49016
59816
done9816

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
0.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
0.8b
(- (* b b) (* (* 4.0 a) c))
27.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
121×add-sqr-sqrt
94×*-un-lft-identity
68×add-cube-cbrt
26×difference-of-squares
22×associate-/l*
16×sqrt-prod
13×distribute-lft-out--
9×add-exp-log add-cbrt-cube
8×add-log-exp
5×pow1 div-inv
3×cbrt-undiv flip3-- div-exp associate-/r* flip--
2×sub-neg sqrt-div diff-log div-sub
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/l/
Counts
4 → 149
Calls
4 calls:
37.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
20.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
3.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series307.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
80.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
46.0ms
(- (* b b) (* (* 4.0 a) c))
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify938.0ms

Counts
161 → 161
Iterations

Useful iterations: done (933.0ms)

IterNodesCost
02804083
16653911
219753753
done50003752

prune455.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ a (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0)))
0.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
0.8b
(- (* b b) (* (* 4.0 a) c))
27.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
693×times-frac
438×add-sqr-sqrt
363×*-un-lft-identity
289×add-cube-cbrt
74×difference-of-squares
71×associate-/r*
40×sqrt-prod
37×distribute-lft-out--
25×add-exp-log
17×div-inv
15×div-exp
13×add-cbrt-cube
8×add-log-exp
6×pow1 cbrt-undiv
5×associate-/r/
3×rec-exp flip3-- 1-exp flip-- associate-/l*
2×sub-neg sqrt-div diff-log
1×rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 clear-num inv-pow
Counts
4 → 354
Calls
4 calls:
34.0ms
(/ 1 (/ a (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0)))
18.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
3.0ms
(- (* b b) (* (* 4.0 a) c))
6.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series340.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(/ 1 (/ a (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0)))
80.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
44.0ms
(- (* b b) (* (* 4.0 a) c))
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.1s

Counts
366 → 366
Iterations

Useful iterations: 2 (1.4s)

IterNodesCost
057111964
1134610919
2382310033
done500010033

prune549.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
0.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
0.8b
(- (* b b) (* (* 4.0 a) c))
27.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
121×add-sqr-sqrt
94×*-un-lft-identity
68×add-cube-cbrt
26×difference-of-squares
22×associate-/l*
16×sqrt-prod
13×distribute-lft-out--
9×add-exp-log add-cbrt-cube
8×add-log-exp
5×pow1 div-inv
3×cbrt-undiv flip3-- div-exp associate-/r* flip--
2×sub-neg sqrt-div diff-log div-sub
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/l/
Counts
4 → 149
Calls
4 calls:
36.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
22.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
2.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series317.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
83.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
50.0ms
(- (* b b) (* (* 4.0 a) c))
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify949.0ms

Counts
161 → 161
Iterations

Useful iterations: done (943.0ms)

IterNodesCost
02804083
16653911
219753753
done50003752

prune438.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.9b

localize19.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* (* 4.0 a) c))
0.8b
(- (* b b) (* (* 4.0 a) c))
27.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
27.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log flip3-- sqrt-div add-cbrt-cube flip--
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
Counts
4 → 54
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
2.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series237.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(- (* b b) (* (* 4.0 a) c))
49.0ms
(- (* b b) (* (* 4.0 a) c))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.3s

Counts
66 → 66
Iterations

Useful iterations: done (1.3s)

IterNodesCost
0621010
1150930
2520834
32068834
done5001832

prune258.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 3.9b

regimes262.0ms

Accuracy

85.2% (4.2b remaining)

Error of 9.8b against oracle of 5.6b and baseline of 33.8b

bsearch133.0ms

Steps
ItersRangePoint
11
4.489865195692553e-133
5.932607888300091e-106
2.0569776426586135e-106
8
-6.10058349091927e+155
-9.408528429616011e+151
-7.93152454634662e+153

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
02942
13738
done3738

end0.0ms

sample1.2s

Algorithm
intervals
Results
247.0ms1046×body2560valid
239.0ms5918×body80valid
164.0ms861×body1280valid
109.0ms2864×body80nan
71.0ms452×body640valid
32.0ms113×body5120valid
26.0ms230×body320valid
8.0ms100×body160valid