Details

Time bar (total: 16.2s)

sample80.0ms

Algorithm
intervals
Results
15.0ms188×body80valid
12.0ms27×body2560valid
10.0ms30×body1280valid
8.0ms95×body80nan
5.0ms17×body640valid
1.0ms8×body320valid
1.0ms2×body5120valid
1.0ms6×body160valid

simplify219.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01417
12817
26417
311417
414117
515117
615517
done15517

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.7b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.6b
(- (* b b) (* 4.0 (* a c)))
1.6b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite211.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×add-cube-cbrt times-frac associate-/l*
6×sqrt-prod distribute-lft-out-- difference-of-squares
5×pow1
4×flip3-- flip--
3×distribute-rgt-neg-in diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 77
Calls
4 calls:
113.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
19.0ms
(- (* b b) (* 4.0 (* a c)))
56.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
18.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series394.0ms

Counts
4 → 12
Calls
4 calls:
127.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
65.0ms
(- (* b b) (* 4.0 (* a c)))
103.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
98.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify911.0ms

Counts
89 → 89
Iterations

Useful iterations: done (908.0ms)

IterNodesCost
01571750
14181650
216441474
done50001466

prune369.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.1b

localize36.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
2.3b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
9.2b
(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
23.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite351.0ms

Algorithm
rewrite-expression-head
Rules
81×add-sqr-sqrt
78×times-frac
58×*-un-lft-identity
36×add-cube-cbrt
27×associate-/l*
22×difference-of-squares
18×add-exp-log add-cbrt-cube
14×sqrt-prod
11×distribute-lft-out--
7×cbrt-undiv div-exp associate-/r*
6×associate-/r/ add-log-exp
5×pow1 flip3-- flip--
4×div-inv
3×associate-/l/
2×frac-2neg sqrt-div prod-exp clear-num cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 141
Calls
4 calls:
57.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
152.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
108.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
28.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series809.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
283.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
336.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
94.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.3s

Counts
153 → 153
Iterations

Useful iterations: 2 (786.0ms)

IterNodesCost
02504579
16494063
236203761
done50013761

prune656.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.0b

localize56.0ms

Local error

Found 4 expressions with local error:

9.2b
(/ (+ 0 (* 4.0 (* a c))) (- (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))) b))
9.4b
(- (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))) b)
23.7b
(cbrt (- (* b b) (* 4.0 (* a c))))
23.7b
(cbrt (- (* b b) (* 4.0 (* a c))))

rewrite151.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
6×add-exp-log cbrt-prod add-cbrt-cube add-log-exp
4×pow1 cbrt-div flip3-- flip--
3×associate-/r* associate-/l*
2×pow1/3 associate-/r/ associate-/l/
1×cbrt-undiv sub-neg frac-2neg flip3-+ diff-log div-exp clear-num flip-+ div-inv
Counts
4 → 69
Calls
4 calls:
94.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))) b))
40.0ms
(- (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))) b)
7.0ms
(cbrt (- (* b b) (* 4.0 (* a c))))
7.0ms
(cbrt (- (* b b) (* 4.0 (* a c))))

series1.5s

Counts
4 → 12
Calls
4 calls:
1.0s
(/ (+ 0 (* 4.0 (* a c))) (- (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))) b))
150.0ms
(- (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))) b)
161.0ms
(cbrt (- (* b b) (* 4.0 (* a c))))
162.0ms
(cbrt (- (* b b) (* 4.0 (* a c))))

simplify1.6s

Counts
81 → 81
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02283002
16182842
229142523
done50002511

prune532.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.0b

localize33.0ms

Local error

Found 4 expressions with local error:

13.3b
(cbrt (+ 0 (* 4.0 (* a c))))
13.3b
(cbrt (* 4.0 (* a c)))
23.7b
(cbrt (- (* b b) (* 4.0 (* a c))))
23.7b
(cbrt (- (* b b) (* 4.0 (* a c))))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
10×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×cbrt-div
4×pow1 add-exp-log pow1/3 add-cbrt-cube add-log-exp
2×flip3-- flip--
1×flip3-+ flip-+
Counts
4 → 48
Calls
4 calls:
3.0ms
(cbrt (+ 0 (* 4.0 (* a c))))
13.0ms
(cbrt (* 4.0 (* a c)))
9.0ms
(cbrt (- (* b b) (* 4.0 (* a c))))
16.0ms
(cbrt (- (* b b) (* 4.0 (* a c))))

series529.0ms

Counts
4 → 12
Calls
4 calls:
155.0ms
(cbrt (+ 0 (* 4.0 (* a c))))
136.0ms
(cbrt (* 4.0 (* a c)))
121.0ms
(cbrt (- (* b b) (* 4.0 (* a c))))
118.0ms
(cbrt (- (* b b) (* 4.0 (* a c))))

simplify703.0ms

Counts
60 → 60
Iterations

Useful iterations: done (701.0ms)

IterNodesCost
0121953
1283885
2982792
done5000769

prune525.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.0b

regimes304.0ms

Accuracy

83.5% (4.5b remaining)

Error of 9.9b against oracle of 5.4b and baseline of 32.4b

bsearch320.0ms

Steps
ItersRangePoint
10
1.3113650301339767e-12
0.01077406869848718
0.010648423176581222
10
-7.839332307815203e-146
-4.567075081547058e-160
-1.2965847557848701e-151
6
-1.1000082512799256e+103
-1.2658565361216573e+102
-4.884773494239208e+102

simplify8.0ms

Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
03771
14669
24769
done4769

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.3s1112×body2560valid
588.0ms5790×body80valid
405.0ms923×body1280valid
316.0ms3037×body80nan
140.0ms463×body640valid
110.0ms103×body5120valid
49.0ms214×body320valid
15.0ms100×body160valid