Details

Time bar (total: 15.5s)

sample129.0ms

Algorithm
intervals
Results
30.0ms116×body80valid
25.0ms140×body160valid
24.0ms261×body80nan
19.0ms517×pre80true

simplify131.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (10.0ms)

IterNodesCost
014365
125365
246325
386325
4119325
5128325
done128325

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.4b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.2b
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
29.3b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

rewrite200.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
135×add-sqr-sqrt
108×*-un-lft-identity
82×add-cube-cbrt
28×sqrt-prod
26×difference-of-squares
22×associate-/l*
19×prod-diff
13×distribute-lft-out--
9×add-cbrt-cube add-exp-log
8×add-log-exp
7×fma-neg
5×pow1 div-inv
4×expm1-log1p-u log1p-expm1-u
3×cbrt-undiv associate-/r* flip3-- div-exp flip--
2×sub-neg sqrt-div diff-log div-sub
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 associate-/l/
Counts
4 → 183
Calls
4 calls:
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
13.0ms
(- (* b b) (* (* 4.0 a) c))
108.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
61.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

series441.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
77.0ms
(- (* b b) (* (* 4.0 a) c))
142.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
119.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

simplify2.4s

Counts
195 → 195
Iterations

Useful iterations: done (2.4s)

IterNodesCost
0321102660
181795887
2389991777
done500091727

prune1.1s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 9.1b

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

prune187.0ms

Pruning

27 alts after pruning (26 fresh and 1 done)

Merged error: 9.1b

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
27×add-cbrt-cube add-exp-log
20×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
13×cbrt-undiv div-exp
8×associate-/l*
6×associate-/r* div-inv
5×prod-exp cbrt-unprod
2×expm1-log1p-u pow1 clear-num frac-2neg log1p-expm1-u add-log-exp
1×associate-/l/
Counts
2 → 77
Calls
2 calls:
16.0ms
(/ (* a c) b)
23.0ms
(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)

series71.0ms

Counts
2 → 6
Calls
2 calls:
32.0ms
(/ (* a c) b)
39.0ms
(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)

simplify1.7s

Counts
83 → 83
Iterations

Useful iterations: done (1.7s)

IterNodesCost
017124170
146522409
2294022008
done500221848

prune468.0ms

Pruning

38 alts after pruning (37 fresh and 1 done)

Merged error: 9.1b

localize16.0ms

Local error

Found 3 expressions with local error:

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

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
86×add-exp-log
69×times-frac
49×div-exp
44×add-cbrt-cube
37×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
23×cbrt-undiv
17×prod-exp
13×associate-/l*
11×associate-/r* div-inv
7×cbrt-unprod
6×rec-exp 1-exp
4×pow1
3×expm1-log1p-u clear-num frac-2neg log1p-expm1-u add-log-exp
1×associate-/r/ pow-flip inv-pow associate-/l/
Counts
3 → 143
Calls
3 calls:
32.0ms
(/ (/ (* -2.0 (/ 1 (/ b (* a c)))) 2.0) a)
6.0ms
(/ b (* a c))
14.0ms
(/ 1 (/ b (* a c)))

series72.0ms

Counts
3 → 9
Calls
3 calls:
23.0ms
(/ (/ (* -2.0 (/ 1 (/ b (* a c)))) 2.0) a)
23.0ms
(/ b (* a c))
26.0ms
(/ 1 (/ b (* a c)))

simplify2.7s

Counts
152 → 152
Iterations

Useful iterations: 2 (946.0ms)

IterNodesCost
026646674
172538664
2450534546
done500034546

prune663.0ms

Pruning

40 alts after pruning (39 fresh and 1 done)

Merged error: 9.1b

regimes1.2s

Accuracy

42.5% (7.8b remaining)

Error of 17.0b against oracle of 9.2b and baseline of 22.8b

bsearch24.0ms

Steps
ItersRangePoint
0
2072.609825166481
2177.5484668538597
2125.0791460101705
0
248.9628020274003
252.65350759806194
250.80815481273112
1
52.78857874562935
56.54518336069951
53.72772989939689

simplify55.0ms

Iterations

Useful iterations: 0 (9.0ms)

IterNodesCost
0301014
1391014
2421014
3451014
done451014

end0.0ms

sample3.7s

Algorithm
intervals
Results
982.0ms8619×body80nan
972.0ms16619×pre80true
947.0ms4454×body160valid
280.0ms3546×body80valid