Details

Time bar (total: 10.8s)

sample43.0ms

Algorithm
intervals
Results
8.0ms37×body2560valid
7.0ms177×body80valid
6.0ms31×body1280valid
3.0ms92×body80nan
2.0ms16×body640valid
1.0ms5×body5120valid
1.0ms6×body320valid
0.0ms3×body160valid

simplify52.0ms

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

localize13.0ms

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)))

rewrite77.0ms

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:
40.0ms
(/ (/ (- (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)))

series316.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
83.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
52.0ms
(- (* b b) (* (* 4.0 a) c))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify939.0ms

Counts
161 → 161
Iterations

Useful iterations: done (928.0ms)

IterNodesCost
02804083
16653911
219753753
done50003752

prune487.0ms

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)))

rewrite95.0ms

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:
40.0ms
(/ 1 (/ a (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0)))
19.0ms
(- (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)))

series350.0ms

Counts
4 → 12
Calls
4 calls:
148.0ms
(/ 1 (/ a (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0)))
82.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
44.0ms
(- (* b b) (* (* 4.0 a) c))
76.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.0s

Counts
366 → 366
Iterations

Useful iterations: 2 (1.4s)

IterNodesCost
057111964
1134610919
2382310033
done500010033

prune763.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ a (/ 1 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)))

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
726×times-frac
480×add-sqr-sqrt
387×*-un-lft-identity
295×add-cube-cbrt
92×difference-of-squares
49×sqrt-prod
46×distribute-lft-out--
44×associate-/r*
29×div-inv
19×add-exp-log
13×add-cbrt-cube
11×div-exp
8×associate-/r/ add-log-exp
6×cbrt-undiv associate-/l*
5×pow1
4×flip3-- flip--
2×sub-neg sqrt-div diff-log associate-/l/
1×rem-sqrt-square rec-exp frac-2neg sqrt-pow1 pow1/2 1-exp div-sub clear-num
Counts
4 → 378
Calls
4 calls:
57.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ a (/ 1 2.0)))
19.0ms
(- (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)))

series306.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ a (/ 1 2.0)))
79.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
44.0ms
(- (* b b) (* (* 4.0 a) c))
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.2s

Counts
390 → 390
Iterations

Useful iterations: done (1.1s)

IterNodesCost
060213610
1171112335
done500111507

prune644.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.9b

localize14.0ms

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)))

rewrite15.0ms

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))
3.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series235.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(- (* b b) (* (* 4.0 a) c))
44.0ms
(- (* b b) (* (* 4.0 a) c))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.3s

Counts
66 → 66
Iterations

Useful iterations: done (1.3s)

IterNodesCost
0621010
1150930
2520834
32068834
done5001832

prune245.0ms

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: 0 (1.0ms)

IterNodesCost
02840
13440
done3440

end0.0ms

sample1.2s

Algorithm
intervals
Results
246.0ms1046×body2560valid
238.0ms5918×body80valid
158.0ms861×body1280valid
110.0ms2864×body80nan
67.0ms452×body640valid
31.0ms113×body5120valid
28.0ms230×body320valid
7.0ms100×body160valid