Details

Time bar (total: 23.5s)

sample76.0ms

Algorithm
intervals
Results
31.0ms33×body2560valid
8.0ms168×body80valid
8.0ms35×body1280valid
4.0ms92×body80nan
3.0ms15×body640valid
2.0ms6×body5120valid
1.0ms9×body320valid
1.0ms8×body160valid

simplify86.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
01217
12117
24116
37516
48816
59616
done9616

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 36.6b

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
1.2b
(- (* b b) (* (* 3.0 a) c))
2.0b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
24.4b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite131.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
8×add-sqr-sqrt
7×add-cube-cbrt
6×distribute-lft-out
5×pow1 times-frac associate-/l*
3×distribute-rgt-neg-in sqrt-prod
2×cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
1×+-commutative sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 70
Calls
4 calls:
73.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
13.0ms
(- (* b b) (* (* 3.0 a) c))
34.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
10.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series433.0ms

Counts
4 → 12
Calls
4 calls:
146.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
64.0ms
(- (* b b) (* (* 3.0 a) c))
114.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
109.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.3s

Counts
82 → 82
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01541565
13951463
213051247
done50011235

prune288.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.3b

localize27.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 3.0 a) c))
3.9b
(/ (/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
11.6b
(/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
24.4b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite218.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
80×add-sqr-sqrt
79×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
20×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
13×sqrt-prod
10×distribute-rgt-neg-in
8×associate-/r*
7×cbrt-undiv div-exp
6×associate-/r/ add-log-exp
5×pow1 flip3-- flip--
4×div-inv
3×associate-/l/
2×frac-2neg sqrt-div prod-exp clear-num cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 148
Calls
4 calls:
9.0ms
(- (* b b) (* (* 3.0 a) c))
106.0ms
(/ (/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
79.0ms
(/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
17.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series637.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(- (* b b) (* (* 3.0 a) c))
206.0ms
(/ (/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
266.0ms
(/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
110.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.3s

Counts
160 → 160
Iterations

Useful iterations: 2 (575.0ms)

IterNodesCost
02484912
16074364
224394036
done50004036

prune597.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 7.2b

localize29.0ms

Local error

Found 4 expressions with local error:

10.8b
(/ (/ (* (* 3.0 a) c) (cbrt (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
24.4b
(sqrt (- (* b b) (* (* 3.0 a) c)))
24.4b
(sqrt (- (* b b) (* (* 3.0 a) c)))
24.4b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
88×times-frac
55×add-sqr-sqrt
52×*-un-lft-identity
36×add-cube-cbrt
28×cbrt-prod
18×add-exp-log
16×associate-/l*
15×add-cbrt-cube
13×sqrt-prod
8×cbrt-div associate-/r/ distribute-lft-out-- difference-of-squares
7×pow1 cbrt-undiv flip3-- div-exp flip--
6×sqrt-div
5×div-inv
4×distribute-rgt-neg-in add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2 prod-exp associate-/r* cbrt-unprod
1×frac-2neg clear-num associate-/l/
Counts
4 → 131
Calls
4 calls:
83.0ms
(/ (/ (* (* 3.0 a) c) (cbrt (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
19.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
10.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
11.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series8.4s

Counts
4 → 12
Calls
4 calls:
8.2s
(/ (/ (* (* 3.0 a) c) (cbrt (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
77.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
83.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
101.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.5s

Counts
143 → 143
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02764007
16793698
223543537
done50003533

prune949.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 7.2b

localize38.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 3.0 a) c))
3.8b
(/ (/ (* (* 3.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a)
11.6b
(/ (* (* 3.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
24.4b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite265.0ms

Algorithm
rewrite-expression-head
Rules
74×times-frac
54×add-sqr-sqrt
53×*-un-lft-identity
29×add-cube-cbrt
27×add-exp-log add-cbrt-cube
14×associate-/l*
12×distribute-lft-out-- difference-of-squares
10×cbrt-undiv div-exp associate-/r* associate-/r/
9×sqrt-prod
7×flip3-- flip--
6×distribute-rgt-neg-in prod-exp cbrt-unprod div-inv add-log-exp
5×pow1
2×frac-2neg sqrt-div clear-num
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-/l/
Counts
4 → 134
Calls
4 calls:
17.0ms
(- (* b b) (* (* 3.0 a) c))
101.0ms
(/ (/ (* (* 3.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a)
102.0ms
(/ (* (* 3.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
33.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series717.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(- (* b b) (* (* 3.0 a) c))
248.0ms
(/ (/ (* (* 3.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a)
266.0ms
(/ (* (* 3.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
114.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.6s

Counts
146 → 146
Iterations

Useful iterations: 2 (565.0ms)

IterNodesCost
02514073
16463815
227233419
done50013419

prune571.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 7.2b

regimes526.0ms

Accuracy

87.8% (3.3b remaining)

Error of 8.9b against oracle of 5.6b and baseline of 32.5b

bsearch316.0ms

Steps
ItersRangePoint
5
1.2073698495971617e+61
2.9312978430050554e+61
1.4079722485425759e+61
9
6.262918217783262e-188
1.0824447814377013e-180
2.6052409935806966e-181
10
-3.742210988141449e+103
-1.1204690717208776e+87
-8.594947000714855e+98

simplify10.0ms

Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
03669
14267
done4267

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.0s5868×body80valid
622.0ms1051×body2560valid
338.0ms2845×body80nan
306.0ms891×body1280valid
189.0ms480×body640valid
91.0ms100×body5120valid
86.0ms217×body320valid
20.0ms111×body160valid