Details

Time bar (total: 19.1s)

sample174.0ms

Algorithm
intervals
Results
17.0ms190×body80valid
17.0ms36×body2560valid
11.0ms28×body1280valid
7.0ms92×body80nan
5.0ms16×body640valid
2.0ms7×body320valid
1.0ms1×body5120valid
0.0ms3×body160valid

simplify108.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (17.0ms)

IterNodesCost
01013
11413
22212
32512
42712
52912
done2912

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.2b
(- (* b_2 b_2) (* a c))
1.1b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite246.0ms

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-exp-log add-cbrt-cube associate-/l*
5×pow1 distribute-lft-out--
4×flip3-- flip--
3×associate-/r*
2×sub-neg sqrt-div diff-log associate-/l/
1×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub div-exp clear-num div-inv
Counts
4 → 84
Calls
4 calls:
135.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
16.0ms
(- (* b_2 b_2) (* a c))
67.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
19.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series428.0ms

Counts
4 → 12
Calls
4 calls:
151.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
60.0ms
(- (* b_2 b_2) (* a c))
125.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
92.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.2s

Counts
96 → 96
Iterations

Useful iterations: done (2.2s)

IterNodesCost
01541624
13611526
29271426
323271418
done50001410

prune414.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.6b

localize20.0ms

Local error

Found 4 expressions with local error:

1.0b
(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.4b
(/ (/ (- 0 (* c a)) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
8.1b
(/ (- 0 (* c a)) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))
22.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite250.0ms

Algorithm
rewrite-expression-head
Rules
114×times-frac
99×*-un-lft-identity
66×add-sqr-sqrt
65×add-cube-cbrt
21×associate-/l*
17×distribute-lft-out
11×add-exp-log add-cbrt-cube
10×associate-/r/
7×associate-/r*
6×flip3-+ flip-+ div-inv add-log-exp
5×pow1
4×cbrt-undiv div-exp
3×div-sub distribute-frac-neg sqrt-prod associate-/l/
2×flip3-- frac-2neg sub0-neg sqrt-div clear-num flip--
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 sum-log
Counts
4 → 156
Calls
4 calls:
48.0ms
(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
107.0ms
(/ (/ (- 0 (* c a)) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
78.0ms
(/ (- 0 (* c a)) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))
10.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series715.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
259.0ms
(/ (/ (- 0 (* c a)) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
271.0ms
(/ (- 0 (* c a)) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))
89.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.8s

Counts
168 → 168
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02714493
16804026
221523822
done50003772

prune766.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 4.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ c (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))
0.2b
(- (* b_2 b_2) (* a c))
1.0b
(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite118.0ms

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity
15×add-sqr-sqrt
14×add-cube-cbrt
12×times-frac
8×add-log-exp
6×add-exp-log add-cbrt-cube
5×pow1 distribute-lft-out
4×associate-/r*
3×sqrt-prod associate-/l*
2×flip3-- flip3-+ sqrt-div associate-/r/ flip-- flip-+
1×cbrt-undiv +-commutative sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-exp clear-num sum-log div-inv
Counts
4 → 72
Calls
4 calls:
58.0ms
(/ c (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))
8.0ms
(- (* b_2 b_2) (* a c))
37.0ms
(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
10.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series468.0ms

Counts
4 → 12
Calls
4 calls:
240.0ms
(/ c (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))
57.0ms
(- (* b_2 b_2) (* a c))
94.0ms
(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
77.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify4.2s

Counts
84 → 84
Iterations

Useful iterations: done (4.2s)

IterNodesCost
01281320
12791222
27121124
317011121
443721109
done50001107

prune349.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 4.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* b_2 b_2) (* a c))
0.7b
(/ 1 (/ (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))) c))
1.0b
(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
22.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
96×times-frac
80×*-un-lft-identity
55×add-sqr-sqrt
54×add-cube-cbrt
16×associate-/r*
15×add-exp-log
13×distribute-lft-out
9×add-cbrt-cube
8×add-log-exp
7×div-exp
6×pow1
5×div-inv
3×cbrt-undiv sqrt-prod associate-/l*
2×rec-exp flip3-- sqrt-div 1-exp flip--
1×+-commutative sub-neg rem-sqrt-square pow-flip frac-2neg sqrt-pow1 flip3-+ pow1/2 diff-log clear-num sum-log associate-/r/ flip-+ inv-pow
Counts
4 → 127
Calls
4 calls:
8.0ms
(- (* b_2 b_2) (* a c))
37.0ms
(/ 1 (/ (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))) c))
35.0ms
(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series421.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(- (* b_2 b_2) (* a c))
162.0ms
(/ 1 (/ (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))) c))
109.0ms
(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
110.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.4s

Counts
139 → 139
Iterations

Useful iterations: done (2.4s)

IterNodesCost
02222867
15082523
211432282
326692248
done50002241

prune357.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 4.5b

regimes164.0ms

Accuracy

96.3% (0.9b remaining)

Error of 6.2b against oracle of 5.3b and baseline of 30.2b

bsearch204.0ms

Steps
ItersRangePoint
9
1.3206820209921783e+153
1.5782810135998455e+159
2.3222513364549933e+153
5
-1.6644721232883786e-209
-7.804748171248596e-210
-7.907890444019499e-210
9
-6.354265220965125e+156
-1.769171722317776e+149
-1.0084023741576003e+154

simplify9.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03562
14556
25756
done5756

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.1s1077×body2560valid
548.0ms850×body1280valid
426.0ms5880×body80valid
222.0ms466×body640valid
201.0ms2914×body80nan
57.0ms107×body5120valid
44.0ms212×body320valid
17.0ms123×body160valid