Details

Time bar (total: 22.3s)

sample93.0ms

Algorithm
intervals
Results
23.0ms99×body80nan
18.0ms193×body80valid
17.0ms30×body2560valid
12.0ms26×body1280valid
5.0ms12×body640valid
3.0ms5×body5120valid
1.0ms5×body320valid
0.0ms1×body160valid

simplify79.0ms

Counts
1 → 1
Iterations
IterNodes
895
795
694
592
484
367
243
124
014

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.6b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) a)
0.2b
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
0.6b
(- (* b b) (* (* 4 a) c))
24.5b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite154.0ms

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-cbrt-cube add-exp-log associate-/l*
5×pow1 distribute-lft-out--
4×flip3-- insert-posit16 flip--
3×associate-/r*
2×sub-neg sqrt-div diff-log associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-sub div-exp div-inv
Counts
4 → 88
Calls
4 calls:
102.0ms
(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) a)
36.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
7.0ms
(- (* b b) (* (* 4 a) c))
7.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series442.0ms

Counts
4 → 12
Calls
4 calls:
133.0ms
(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) a)
123.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
70.0ms
(- (* b b) (* (* 4 a) c))
115.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.6s

Counts
100 → 100
Iterations
IterNodes
33741
21117
1393
0161

prune972.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.9b

localize58.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* (* 4 a) c))
0.6b
(- (* b b) (* (* 4 a) c))
24.5b
(sqrt (- (* b b) (* (* 4 a) c)))
24.5b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
6×pow1 *-un-lft-identity add-cube-cbrt sqrt-prod
4×flip3-- add-cbrt-cube sqrt-div add-exp-log insert-posit16 flip--
2×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log
Counts
4 → 58
Calls
4 calls:
19.0ms
(- (* b b) (* (* 4 a) c))
13.0ms
(- (* b b) (* (* 4 a) c))
14.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
14.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series362.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(- (* b b) (* (* 4 a) c))
79.0ms
(- (* b b) (* (* 4 a) c))
108.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
107.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify4.5s

Counts
70 → 70
Iterations
IterNodes
47462
31987
2522
1156
063

prune1.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.9b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* b b) (* (* 4 a) c))) a)
0.6b
(- (* b b) (* (* 4 a) c))
6.7b
(- (/ (sqrt (- (* b b) (* (* 4 a) c))) a) (/ b a))
24.5b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt
31×times-frac
30×*-un-lft-identity
22×add-cube-cbrt
17×sqrt-prod
8×add-log-exp
6×add-cbrt-cube add-exp-log associate-/l* difference-of-squares
5×pow1
4×flip3-- sqrt-div insert-posit16 flip-- distribute-lft-out--
3×associate-/r* div-inv
2×sub-neg diff-log associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 distribute-rgt-out-- pow1/2 div-exp frac-sub sub-div
Counts
4 → 97
Calls
4 calls:
21.0ms
(/ (sqrt (- (* b b) (* (* 4 a) c))) a)
7.0ms
(- (* b b) (* (* 4 a) c))
50.0ms
(- (/ (sqrt (- (* b b) (* (* 4 a) c))) a) (/ b a))
12.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series469.0ms

Counts
4 → 12
Calls
4 calls:
146.0ms
(/ (sqrt (- (* b b) (* (* 4 a) c))) a)
66.0ms
(- (* b b) (* (* 4 a) c))
150.0ms
(- (/ (sqrt (- (* b b) (* (* 4 a) c))) a) (/ b a))
108.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.5s

Counts
109 → 109
Iterations
IterNodes
33407
21131
1408
0179

prune1.4s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.9b

localize49.0ms

Local error

Found 4 expressions with local error:

24.5b
(sqrt (* (* (cbrt (- (* b b) (* (* 4 a) c))) (cbrt (- (* b b) (* (* 4 a) c)))) (cbrt (- (* b b) (* (* 4 a) c)))))
25.3b
(cbrt (- (* b b) (* (* 4 a) c)))
25.3b
(cbrt (- (* b b) (* (* 4 a) c)))
25.3b
(cbrt (- (* b b) (* (* 4 a) c)))

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
60×cbrt-div
30×flip3-- flip--
28×frac-times
26×sqrt-div
24×pow1
15×sqrt-pow1
14×associate-*l/
12×pow1/3
9×cbrt-prod pow-prod-up
8×associate-*r/
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×pow-plus
5×pow-prod-down
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×pow-sqr
2×pow2
1×pow1/2 pow3 sqrt-prod
Counts
4 → 93
Calls
4 calls:
82.0ms
(sqrt (* (* (cbrt (- (* b b) (* (* 4 a) c))) (cbrt (- (* b b) (* (* 4 a) c)))) (cbrt (- (* b b) (* (* 4 a) c)))))
5.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
5.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
5.0ms
(cbrt (- (* b b) (* (* 4 a) c)))

series596.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(sqrt (* (* (cbrt (- (* b b) (* (* 4 a) c))) (cbrt (- (* b b) (* (* 4 a) c)))) (cbrt (- (* b b) (* (* 4 a) c)))))
158.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
162.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
142.0ms
(cbrt (- (* b b) (* (* 4 a) c)))

simplify916.0ms

Counts
105 → 105
Iterations
IterNodes
32014
2728
1342
0188

prune1.9s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 5.9b

regimes422.0ms

Accuracy

83.5% (4.6b remaining)

Error of 10.4b against oracle of 5.8b and baseline of 33.5b

bsearch198.0ms

Steps
ItersRangePoint
6
3.7222086374392734e-21
4.963951531010332e-20
3.821014310434392e-21
10
-3.568388406125044e+108
-3.585760457965514e+97
-5.571206846913461e+106

simplify6.0ms

Iterations
IterNodes
232
132
028

end0.0ms

sample5.1s

Algorithm
intervals
Results
1.5s5860×body80valid
1.1s1029×body2560valid
842.0ms2862×body80nan
704.0ms889×body1280valid
304.0ms469×body640valid
108.0ms107×body5120valid
79.0ms199×body320valid
39.0ms141×body160valid