Details

Time bar (total: 16.8s)

sample64.0ms

Algorithm
intervals
Results
14.0ms24×body1280valid
10.0ms186×body80valid
9.0ms29×body2560valid
6.0ms102×body80nan
3.0ms14×body640valid
2.0ms5×body5120valid
1.0ms9×body320valid
0.0ms4×body160valid

simplify95.0ms

Counts
1 → 1
Iterations
IterNodes
done107
5107
499
379
244
124
014

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
0.6b
(- (* b b) (* (* 4.0 a) c))
1.3b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite192.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
121×add-sqr-sqrt
94×*-un-lft-identity
68×add-cube-cbrt
26×difference-of-squares
22×associate-/l*
16×sqrt-prod
13×distribute-lft-out--
9×add-cbrt-cube add-exp-log
8×add-log-exp
5×pow1 div-inv
3×cbrt-undiv associate-/r* flip3-- div-exp flip--
2×sub-neg sqrt-div diff-log div-sub
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 associate-/l/
Counts
4 → 149
Calls
4 calls:
115.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
12.0ms
(- (* b b) (* (* 4.0 a) c))
47.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
7.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series498.0ms

Counts
4 → 12
Calls
4 calls:
151.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
71.0ms
(- (* b b) (* (* 4.0 a) c))
147.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
129.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

Counts
161 → 161
Iterations
IterNodes
done5001
23078
1690
0280

prune1.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.7b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ 1 1) (* (/ a (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) 2.0))
0.6b
(- (* b b) (* 4.0 (* a c)))
1.3b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
22.9b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
64×add-exp-log
40×div-exp
31×times-frac
25×add-cbrt-cube
24×add-sqr-sqrt
21×*-un-lft-identity
19×add-cube-cbrt
15×1-exp
14×prod-exp
13×associate-/l*
11×cbrt-undiv
8×add-log-exp
6×rec-exp
5×pow1
4×sqrt-prod cbrt-unprod
3×flip3-- div-inv flip--
2×sub-neg sqrt-div diff-log difference-of-squares
1×rem-sqrt-square clear-num associate-/r* frac-2neg sqrt-pow1 pow1/2 associate-*l/ associate-/r/ distribute-lft-out-- associate-/l/
Counts
4 → 108
Calls
4 calls:
41.0ms
(/ (/ 1 1) (* (/ a (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) 2.0))
11.0ms
(- (* b b) (* 4.0 (* a c)))
39.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
9.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series501.0ms

Counts
4 → 12
Calls
4 calls:
242.0ms
(/ (/ 1 1) (* (/ a (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) 2.0))
64.0ms
(- (* b b) (* 4.0 (* a c)))
105.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
90.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.7s

Counts
120 → 120
Iterations
IterNodes
done5000
23037
1676
0224

prune475.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.7b

localize48.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
1.3b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
22.9b
(sqrt (- (* b b) (* 4.0 (* a c))))
22.9b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite150.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×*-un-lft-identity
8×sqrt-prod add-log-exp
6×pow1 add-cube-cbrt
4×flip3-- add-cbrt-cube sqrt-div add-exp-log flip-- difference-of-squares
2×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log distribute-lft-out--
Counts
4 → 60
Calls
4 calls:
60.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
63.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
12.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
12.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series464.0ms

Counts
4 → 12
Calls
4 calls:
132.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
119.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
110.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
103.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.7s

Counts
72 → 72
Iterations
IterNodes
done5001
34455
2793
1198
080

prune534.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 5.6b

localize47.0ms

Local error

Found 4 expressions with local error:

7.6b
(- (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))) b)
22.9b
(sqrt (- (* b b) (* 4.0 (* a c))))
23.8b
(cbrt (- (* b b) (* 4.0 (* a c))))
23.8b
(cbrt (- (* b b) (* 4.0 (* a c))))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
7×*-un-lft-identity add-cube-cbrt
6×cbrt-prod add-log-exp
5×pow1
4×cbrt-div flip3-- add-cbrt-cube add-exp-log flip--
3×sqrt-prod
2×pow1/3 sqrt-div
1×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log
Counts
4 → 53
Calls
4 calls:
28.0ms
(- (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))) b)
12.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
9.0ms
(cbrt (- (* b b) (* 4.0 (* a c))))
9.0ms
(cbrt (- (* b b) (* 4.0 (* a c))))

series539.0ms

Counts
4 → 12
Calls
4 calls:
140.0ms
(- (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))) b)
129.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
116.0ms
(cbrt (- (* b b) (* 4.0 (* a c))))
153.0ms
(cbrt (- (* b b) (* 4.0 (* a c))))

simplify728.0ms

Counts
65 → 65
Iterations
IterNodes
done5000
21205
1346
0139

prune665.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 5.6b

regimes490.0ms

Accuracy

83.4% (4.7b remaining)

Error of 10.2b against oracle of 5.5b and baseline of 33.9b

bsearch191.0ms

Steps
ItersRangePoint
9
7.013128997607284e-77
5.714800893424793e-72
3.3620065154544137e-75
9
-3.792961868720521e+75
-7.261872368850313e+67
-3.5695008721667037e+75

simplify4.0ms

Iterations
IterNodes
done37
137
030

end0.0ms

sample3.8s

Algorithm
intervals
Results
1.2s5961×body80valid
722.0ms877×body1280valid
688.0ms1054×body2560valid
267.0ms2946×body80nan
140.0ms455×body640valid
97.0ms111×body160valid
70.0ms97×body5120valid
46.0ms214×body320valid