Details

Time bar (total: 16.5s)

sample84.0ms

Algorithm
intervals
Results
18.0ms43×body2560valid
15.0ms32×body1280valid
11.0ms164×body80valid
5.0ms80×body80nan
4.0ms8×body5120valid
4.0ms16×body640valid
1.0ms7×body320valid
1.0ms6×body160valid

simplify115.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (16.0ms)

IterNodesCost
014365
124365
244325
378325
4102325
5111325
done111325

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.5b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0)
0.2b
(* (* 4.0 a) c)
1.5b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
21.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite526.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
27×*-un-lft-identity
18×times-frac
17×add-cube-cbrt
11×add-cbrt-cube add-exp-log
10×pow1 difference-of-squares
8×sqrt-prod
6×associate-/l* add-log-exp
5×distribute-lft-out--
3×associate-/r* flip3-- associate-*r* pow-prod-down prod-exp cbrt-unprod flip--
2×sqrt-div associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log div-sub div-exp associate-*l* *-commutative div-inv
Counts
4 → 90
Calls
4 calls:
76.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0)
26.0ms
(* (* 4.0 a) c)
408.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series386.0ms

Counts
4 → 12
Calls
4 calls:
141.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0)
37.0ms
(* (* 4.0 a) c)
115.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
92.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.7s

Counts
102 → 102
Iterations

Useful iterations: 2 (564.0ms)

IterNodesCost
017436258
143233986
2195033546
done500133546

prune651.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 10.3b

localize53.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt c)
0.6b
(cbrt c)
1.5b
(- (sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))) b)
21.2b
(sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))

rewrite67.0ms

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)
56.0ms
(- (sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))) b)
7.0ms
(sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))

series885.0ms

Counts
4 → 12
Calls
4 calls:
340.0ms
(cbrt c)
288.0ms
(cbrt c)
135.0ms
(- (sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))) b)
121.0ms
(sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))

simplify1.1s

Counts
64 → 64
Iterations

Useful iterations: 2 (294.0ms)

IterNodesCost
010422748
124520689
2100214931
done500014931

prune490.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 10.3b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (* 1 (- (sqrt (- (* b b) (* c (* 4.0 a)))) b)) 2.0)
0.2b
(* c (* 4.0 a))
1.5b
(- (sqrt (- (* b b) (* c (* 4.0 a)))) b)
21.2b
(sqrt (- (* b b) (* c (* 4.0 a))))

rewrite133.0ms

Algorithm
rewrite-expression-head
Rules
16×add-exp-log
14×add-cbrt-cube
13×add-sqr-sqrt
10×pow1 *-un-lft-identity
8×add-cube-cbrt
6×add-log-exp
5×prod-exp
4×sqrt-prod cbrt-unprod
3×associate-/r* times-frac flip3-- div-exp associate-*l* pow-prod-down flip--
2×cbrt-undiv sqrt-div associate-*r/ difference-of-squares associate-/l/
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log 1-exp associate-*r* *-commutative div-inv associate-/l* distribute-lft-out--
Counts
4 → 72
Calls
4 calls:
50.0ms
(/ (* 1 (- (sqrt (- (* b b) (* c (* 4.0 a)))) b)) 2.0)
21.0ms
(* c (* 4.0 a))
52.0ms
(- (sqrt (- (* b b) (* c (* 4.0 a)))) b)
7.0ms
(sqrt (- (* b b) (* c (* 4.0 a))))

series377.0ms

Counts
4 → 12
Calls
4 calls:
141.0ms
(/ (* 1 (- (sqrt (- (* b b) (* c (* 4.0 a)))) b)) 2.0)
34.0ms
(* c (* 4.0 a))
106.0ms
(- (sqrt (- (* b b) (* c (* 4.0 a)))) b)
97.0ms
(sqrt (- (* b b) (* c (* 4.0 a))))

simplify1.9s

Counts
84 → 84
Iterations

Useful iterations: 2 (532.0ms)

IterNodesCost
016825347
143622415
2200621854
done500121854

prune497.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 10.3b

localize101.0ms

Local error

Found 4 expressions with local error:

1.5b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
21.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite65.0ms

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:
39.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
7.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
7.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
8.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series397.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
101.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
79.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
100.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.0s

Counts
72 → 72
Iterations

Useful iterations: done (3.0s)

IterNodesCost
08123268
119920547
279220387
3445320227
done500020187

prune474.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 10.3b

regimes497.0ms

Accuracy

87.5% (2.8b remaining)

Error of 14.6b against oracle of 11.8b and baseline of 34.2b

bsearch121.0ms

Steps
ItersRangePoint
4
1.2765290296533779e-46
2.1214586855945932e-46
1.9152049814236774e-46
10
-1.1071683335692419e+166
-3.0632372757179626e+150
-1.3392371992290793e+154

simplify11.0ms

Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
030910
138869
239869
done39869

end0.0ms

sample2.8s

Algorithm
intervals
Results
617.0ms1094×body2560valid
498.0ms5792×body80valid
381.0ms243×body320valid
380.0ms887×body1280valid
258.0ms2874×body80nan
194.0ms467×body640valid
53.0ms108×body5120valid
19.0ms117×body160valid