Details

Time bar (total: 15.1s)

sample106.0ms

Algorithm
intervals
Results
22.0ms178×body80valid
20.0ms40×body2560valid
15.0ms36×body1280valid
7.0ms88×body80nan
5.0ms15×body640valid
2.0ms7×body320valid
1.0ms2×body5120valid
0.0ms2×body160valid

simplify76.0ms

Counts
1 → 1
Iterations
IterNodes
done104
5104
496
376
241
121
012

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.2b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* b b) (* (* 3.0 a) c))
0.2b
(* (* 3.0 a) c)
0.7b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
24.4b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×pow1
9×add-cbrt-cube add-exp-log
8×*-un-lft-identity add-log-exp
6×add-cube-cbrt
4×sqrt-prod
3×flip3-- associate-*r* pow-prod-down prod-exp cbrt-unprod flip--
2×sub-neg sqrt-div diff-log difference-of-squares
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* *-commutative distribute-lft-out--
Counts
4 → 60
Calls
4 calls:
6.0ms
(- (* b b) (* (* 3.0 a) c))
13.0ms
(* (* 3.0 a) c)
45.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
13.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series334.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(- (* b b) (* (* 3.0 a) c))
33.0ms
(* (* 3.0 a) c)
119.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
113.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.2s

Counts
72 → 72
Iterations
IterNodes
done5001
21549
1302
0120

prune412.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 13.0b

localize67.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt c)
0.6b
(cbrt c)
0.7b
(- (sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))) b)
24.4b
(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
9×*-un-lft-identity
7×add-cube-cbrt
6×cbrt-prod add-log-exp
5×pow1
4×add-cbrt-cube add-exp-log sqrt-prod
2×flip3-- pow1/3 sqrt-div flip-- difference-of-squares
1×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log distribute-lft-out--
Counts
4 → 52
Calls
4 calls:
1.0ms
(cbrt c)
1.0ms
(cbrt c)
45.0ms
(- (sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))) b)
7.0ms
(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))

series771.0ms

Counts
4 → 12
Calls
4 calls:
270.0ms
(cbrt c)
220.0ms
(cbrt c)
146.0ms
(- (sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))) b)
135.0ms
(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))

simplify1.0s

Counts
64 → 64
Iterations
IterNodes
done5000
21002
1245
0104

prune483.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 13.0b

localize102.0ms

Local error

Found 4 expressions with local error:

0.7b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
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)))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
10×sqrt-prod
9×*-un-lft-identity
7×pow1 add-cube-cbrt
6×sqrt-div add-log-exp
4×flip3-- add-cbrt-cube add-exp-log flip--
3×rem-sqrt-square sqrt-pow1 pow1/2
2×difference-of-squares
1×sub-neg diff-log distribute-lft-out--
Counts
4 → 60
Calls
4 calls:
45.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
7.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
10.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
8.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series382.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
84.0ms
(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)))

simplify2.8s

Counts
72 → 72
Iterations
IterNodes
done5000
34453
2792
1199
081

prune557.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 13.0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c)))))
9.2b
(- (* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c))))) b)
25.2b
(cbrt (- (* b b) (* (* 3.0 a) c)))
25.2b
(cbrt (- (* b b) (* (* 3.0 a) c)))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×cbrt-prod *-un-lft-identity add-cube-cbrt
9×associate-*r*
8×sqrt-prod
6×pow1 cbrt-div add-cbrt-cube add-exp-log add-log-exp
4×flip3-- flip--
3×associate-*l* unswap-sqr
2×pow1/3 sqrt-div associate-*r/
1×sub-neg diff-log pow-prod-down prod-exp *-commutative cbrt-unprod
Counts
4 → 66
Calls
4 calls:
24.0ms
(* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c)))))
40.0ms
(- (* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c))))) b)
8.0ms
(cbrt (- (* b b) (* (* 3.0 a) c)))
9.0ms
(cbrt (- (* b b) (* (* 3.0 a) c)))

series552.0ms

Counts
4 → 12
Calls
4 calls:
180.0ms
(* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c)))))
128.0ms
(- (* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c))))) b)
110.0ms
(cbrt (- (* b b) (* (* 3.0 a) c)))
134.0ms
(cbrt (- (* b b) (* (* 3.0 a) c)))

simplify1.5s

Counts
78 → 78
Iterations
IterNodes
done5001
21419
1371
0159

prune583.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 13.0b

regimes420.0ms

Accuracy

84.1% (3.5b remaining)

Error of 15.6b against oracle of 12.1b and baseline of 33.9b

bsearch186.0ms

Steps
ItersRangePoint
9
1.3779648538499424e-26
8.898381193664584e-21
4.106481463860357e-26
8
-3.204967514759302e+157
-9.685109581380507e+154
-9.772692982051752e+154

simplify6.0ms

Iterations
IterNodes
done36
136
030

end0.0ms

sample3.1s

Algorithm
intervals
Results
605.0ms5900×body80valid
555.0ms450×body640valid
506.0ms1053×body2560valid
363.0ms898×body1280valid
355.0ms2831×body80nan
56.0ms111×body5120valid
43.0ms240×body320valid
13.0ms103×body160valid