Details

Time bar (total: 19.1s)

sample101.0ms

Algorithm
intervals
Results
51.0ms270×body80valid
13.0ms100×body80nan

simplify246.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
02038
13538
26637
311637
415037
516437
616637
done16637

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.2b

localize168.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* (* 4.0 a) c))
1.0b
(- (* b b) (* (* 4.0 a) c))
25.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
25.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log flip3-- sqrt-div add-cbrt-cube flip--
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
Counts
4 → 54
Calls
4 calls:
17.0ms
(- (* b b) (* (* 4.0 a) c))
16.0ms
(- (* b b) (* (* 4.0 a) c))
16.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series360.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(- (* b b) (* (* 4.0 a) c))
58.0ms
(- (* b b) (* (* 4.0 a) c))
90.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
151.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify4.1s

Counts
66 → 66
Iterations

Useful iterations: 2 (126.0ms)

IterNodesCost
0621010
1165930
2739834
34972834
done5001834

prune440.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 9.1b

localize160.0ms

Local error

Found 4 expressions with local error:

8.4b
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
25.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
25.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
25.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×sqrt-prod
8×add-log-exp
7×pow1 add-cube-cbrt *-un-lft-identity
6×sqrt-div
4×add-exp-log flip3-- add-cbrt-cube flip--
3×rem-sqrt-square sqrt-pow1 pow1/2
2×diff-log
1×associate--l- neg-sub0 sub-neg neg-log difference-of-squares
Counts
4 → 60
Calls
4 calls:
14.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
17.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series375.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
106.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
82.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
84.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify593.0ms

Counts
72 → 72
Iterations

Useful iterations: done (590.0ms)

IterNodesCost
0901506
12361066
29821000
done5001992

prune566.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 9.1b

localize134.0ms

Local error

Found 4 expressions with local error:

14.3b
(- (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))) b)
25.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
25.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
25.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×sqrt-prod
7×pow1 add-cube-cbrt *-un-lft-identity
6×sqrt-div add-log-exp
4×add-exp-log flip3-- add-cbrt-cube flip--
3×rem-sqrt-square sqrt-pow1 pow1/2
1×sub-neg diff-log difference-of-squares
Counts
4 → 58
Calls
4 calls:
78.0ms
(- (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))) b)
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series404.0ms

Counts
4 → 12
Calls
4 calls:
121.0ms
(- (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))) b)
94.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
93.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
96.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.6s

Counts
70 → 70
Iterations

Useful iterations: 3 (1.3s)

IterNodesCost
0841388
12171004
2829942
34569936
done5000936

prune571.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 9.1b

localize207.0ms

Local error

Found 4 expressions with local error:

25.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
25.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
26.1b
(cbrt (- (* b b) (* (* 4.0 a) c)))
26.1b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite465.0ms

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:
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
428.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
12.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series566.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
101.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
184.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
166.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify2.7s

Counts
68 → 68
Iterations

Useful iterations: done (2.7s)

IterNodesCost
0901160
12111076
2700976
33606966
done5001942

prune591.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 9.1b

regimes296.0ms

Accuracy

92.7% (0.9b remaining)

Error of 8.4b against oracle of 7.5b and baseline of 20.1b

bsearch246.0ms

Steps
ItersRangePoint
8
1.051086597250448e+104
4.713735678910177e+106
1.5438258933175616e+106
8
-2.1489000102508758e+104
-1.471055469501053e+100
-2.1102147844326466e+104

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
042129
149129
done49129

end0.0ms

sample2.0s

Algorithm
intervals
Results
1.1s8674×body80valid
377.0ms2905×body80nan