Details

Time bar (total: 16.5s)

sample72.0ms

Algorithm
intervals
Results
41.0ms280×body80valid
6.0ms78×body80nan

simplify206.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (11.0ms)

IterNodesCost
02038
13838
27837
313637
416337
517537
617937
done17937

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.7b

localize141.0ms

Local error

Found 4 expressions with local error:

0.3b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.8b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
22.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite126.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
12×*-un-lft-identity
10×add-log-exp
8×sqrt-prod
6×pow1 add-cube-cbrt
4×add-exp-log flip3-- sqrt-div add-cbrt-cube flip-- difference-of-squares
3×diff-log distribute-lft-out--
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2
1×associate--l- neg-sub0 distribute-rgt-neg-in neg-log
Counts
4 → 63
Calls
4 calls:
34.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
54.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
18.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
19.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series491.0ms

Counts
4 → 12
Calls
4 calls:
143.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
138.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
111.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
99.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify737.0ms

Counts
75 → 75
Iterations

Useful iterations: done (735.0ms)

IterNodesCost
01061330
12501189
210961110
done50001095

prune517.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.7b

localize140.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
22.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite96.0ms

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×add-exp-log flip3-- add-cbrt-cube 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:
64.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series814.0ms

Counts
4 → 12
Calls
4 calls:
131.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
82.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
496.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
104.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.6s

Counts
72 → 72
Iterations

Useful iterations: done (3.6s)

IterNodesCost
0811194
11991044
2776982
34387976
done5000971

prune471.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.7b

localize164.0ms

Local error

Found 4 expressions with local error:

22.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.2b
(cbrt (- (* b b) (* (* 4.0 a) c)))
23.2b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×pow1 cbrt-prod sqrt-prod
4×add-exp-log cbrt-div flip3-- sqrt-div add-cbrt-cube flip-- add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 56
Calls
4 calls:
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
13.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
8.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
7.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series520.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
95.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
149.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
165.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify2.8s

Counts
68 → 68
Iterations

Useful iterations: done (2.8s)

IterNodesCost
0901160
12111076
2700976
33606966
done5001942

prune684.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.7b

localize174.0ms

Local error

Found 4 expressions with local error:

6.2b
(- (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))) b)
22.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.2b
(cbrt (- (* b b) (* (* 4.0 a) c)))
23.2b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×cbrt-prod add-log-exp
5×pow1
4×add-exp-log cbrt-div flip3-- add-cbrt-cube flip--
3×sqrt-prod
2×pow1/3 sqrt-div
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
Counts
4 → 53
Calls
4 calls:
35.0ms
(- (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))) b)
25.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
6.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
7.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series534.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(- (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))) b)
107.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
158.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
154.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify923.0ms

Counts
65 → 65
Iterations

Useful iterations: done (919.0ms)

IterNodesCost
01411448
13461385
212741185
done50001141

prune470.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 6.7b

regimes252.0ms

Accuracy

88.1% (1.4b remaining)

Error of 9.3b against oracle of 7.9b and baseline of 19.7b

bsearch219.0ms

Steps
ItersRangePoint
8
3932480935863.943
2020002846347102.2
2000198799923726.5
7
-1.350243324689865e+150
-5.880305990614135e+148
-1.3219792860639911e+149

simplify22.0ms

Iterations

Useful iterations: 0 (15.0ms)

IterNodesCost
045144
154144
done54144

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.3s8666×body80valid
370.0ms2861×body80nan