Details

Time bar (total: 17.2s)

sample107.0ms

Algorithm
intervals
Results
19.0ms33×body2560valid
17.0ms35×body1280valid
16.0ms168×body80valid
9.0ms92×body80nan
6.0ms15×body640valid
4.0ms6×body5120valid
3.0ms9×body320valid
1.0ms8×body160valid

simplify139.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (16.0ms)

IterNodesCost
01417
12417
24416
37816
49116
59916
done9916

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.6b

localize395.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
1.2b
(- (* b b) (* (* 4.0 a) c))
2.0b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite225.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
13×*-un-lft-identity
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×add-cube-cbrt
6×times-frac sqrt-prod associate-/l* difference-of-squares
5×pow1
4×flip3-- flip--
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 → 72
Calls
4 calls:
122.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
18.0ms
(- (* b b) (* (* 4.0 a) c))
64.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
19.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series430.0ms

Counts
4 → 12
Calls
4 calls:
174.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
79.0ms
(- (* b b) (* (* 4.0 a) c))
92.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
84.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.3s

Counts
84 → 84
Iterations

Useful iterations: 3 (1.6s)

IterNodesCost
01541592
13861488
212331332
346481324
done50021324

prune391.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.4b

localize4.0ms

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

prune28.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.4b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0)
1.2b
(- (* b b) (* (* 4.0 a) c))
2.0b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite243.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
26×*-un-lft-identity
18×times-frac
16×add-cube-cbrt
10×difference-of-squares
8×sqrt-prod add-log-exp
6×add-exp-log add-cbrt-cube associate-/l*
5×pow1 distribute-lft-out--
4×flip3-- flip--
3×associate-/r*
2×sub-neg sqrt-div diff-log associate-/l/
1×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub div-exp clear-num div-inv
Counts
4 → 84
Calls
4 calls:
137.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0)
9.0ms
(- (* b b) (* (* 4.0 a) c))
62.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
31.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series461.0ms

Counts
4 → 12
Calls
4 calls:
141.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0)
79.0ms
(- (* b b) (* (* 4.0 a) c))
124.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
117.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.9s

Counts
96 → 96
Iterations

Useful iterations: done (2.9s)

IterNodesCost
01531884
13541770
210051654
332211647
done50021641

prune383.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 7.3b

localize33.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
3.8b
(/ (/ (/ (- 0 (* (* 4.0 a) c)) (+ (sqrt (- (* b b) (* (* 4.0 a) c))) b)) 2.0) a)
11.8b
(/ (- 0 (* (* 4.0 a) c)) (+ (sqrt (- (* b b) (* (* 4.0 a) c))) b))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite295.0ms

Algorithm
rewrite-expression-head
Rules
546×times-frac
325×*-un-lft-identity
246×add-sqr-sqrt
245×add-cube-cbrt
61×associate-/l*
40×distribute-lft-out
26×associate-/r/
18×div-inv
15×add-exp-log add-cbrt-cube
13×flip3-+ flip-+
7×cbrt-undiv div-exp associate-/r*
6×add-log-exp
5×pow1
4×div-sub distribute-frac-neg
3×flip3-- sqrt-prod flip-- associate-/l/
2×frac-2neg sub0-neg sqrt-div clear-num
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
Counts
4 → 318
Calls
4 calls:
14.0ms
(- (* b b) (* (* 4.0 a) c))
160.0ms
(/ (/ (/ (- 0 (* (* 4.0 a) c)) (+ (sqrt (- (* b b) (* (* 4.0 a) c))) b)) 2.0) a)
72.0ms
(/ (- 0 (* (* 4.0 a) c)) (+ (sqrt (- (* b b) (* (* 4.0 a) c))) b))
15.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series784.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(- (* b b) (* (* 4.0 a) c))
286.0ms
(/ (/ (/ (- 0 (* (* 4.0 a) c)) (+ (sqrt (- (* b b) (* (* 4.0 a) c))) b)) 2.0) a)
327.0ms
(/ (- 0 (* (* 4.0 a) c)) (+ (sqrt (- (* b b) (* (* 4.0 a) c))) b))
106.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.1s

Counts
330 → 330
Iterations

Useful iterations: done (1.0s)

IterNodesCost
060513290
1145212101
done500011803

prune1.8s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 7.2b

regimes339.0ms

Accuracy

88.1% (3.2b remaining)

Error of 8.8b against oracle of 5.6b and baseline of 32.5b

bsearch331.0ms

Steps
ItersRangePoint
5
1.2073698495971617e+61
2.9312978430050554e+61
1.3572844331324948e+61
9
6.262918217783262e-188
1.0824447814377013e-180
2.71836077956275e-181
10
-3.742210988141449e+103
-1.1204690717208776e+87
-8.301687926884189e+98

simplify29.0ms

Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
03566
14165
24965
35765
45965
done5965

end0.0ms

sample3.5s

Algorithm
intervals
Results
694.0ms1051×body2560valid
655.0ms480×body640valid
647.0ms5870×body80valid
431.0ms893×body1280valid
267.0ms2845×body80nan
91.0ms98×body5120valid
49.0ms218×body320valid
17.0ms108×body160valid