Details

Time bar (total: 17.8s)

sample283.0ms

Algorithm
intervals
Results
48.0ms28×body2560valid
17.0ms188×body80valid
17.0ms29×body1280valid
8.0ms95×body80nan
6.0ms17×body640valid
2.0ms8×body320valid
1.0ms6×body160valid
1.0ms2×body5120valid

simplify142.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
01013
11813
23213
34113
44413
done4413

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.7b

localize106.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b
(- (* b_2 b_2) (* a c))
1.7b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite248.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
37×*-un-lft-identity
21×times-frac
17×add-cube-cbrt
10×distribute-lft-out-- add-log-exp difference-of-squares
8×sqrt-prod
7×associate-/l*
6×add-exp-log add-cbrt-cube
5×pow1 distribute-rgt-neg-in
4×flip3-- flip--
3×diff-log associate-/r*
2×sub-neg sqrt-div associate-/l/
1×cbrt-undiv associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub div-exp neg-log clear-num div-inv
Counts
4 → 91
Calls
4 calls:
133.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
20.0ms
(- (* b_2 b_2) (* a c))
60.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series425.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
45.0ms
(- (* b_2 b_2) (* a c))
119.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
136.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify915.0ms

Counts
103 → 103
Iterations

Useful iterations: done (911.0ms)

IterNodesCost
01561821
13871727
215081613
done50011603

prune390.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.1b

localize14.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.3b
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
9.2b
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
23.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite353.0ms

Algorithm
rewrite-expression-head
Rules
162×times-frac
150×add-sqr-sqrt
115×*-un-lft-identity
81×add-cube-cbrt
34×difference-of-squares
27×associate-/l*
20×sqrt-prod
17×distribute-lft-out--
11×add-exp-log add-cbrt-cube
10×associate-/r/
9×associate-/r*
7×flip3-- flip--
6×div-inv add-log-exp
5×pow1
4×cbrt-undiv div-exp
3×associate-/l/
2×frac-2neg sqrt-div clear-num
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 187
Calls
4 calls:
81.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
143.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
103.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
16.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series677.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
221.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
269.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
89.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.4s

Counts
199 → 199
Iterations

Useful iterations: 2 (798.0ms)

IterNodesCost
03045659
17654902
241264722
done50014722

prune741.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.0b

localize38.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.4b
(* (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 a))
9.2b
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
23.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite460.0ms

Algorithm
rewrite-expression-head
Rules
83×add-sqr-sqrt
52×times-frac
51×*-un-lft-identity
33×add-cube-cbrt
28×add-exp-log
24×associate-*l*
18×add-cbrt-cube
16×difference-of-squares
13×associate-*r*
11×sqrt-prod
9×div-exp
8×prod-exp distribute-lft-out--
7×pow1
6×associate-/r* add-log-exp unswap-sqr
5×cbrt-undiv
4×flip3-- associate-/r/ flip-- cbrt-unprod
3×div-inv associate-/l*
2×rec-exp sqrt-div 1-exp associate-/l/
1×frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 diff-log associate-*r/ pow-prod-down associate-*l/ clear-num un-div-inv *-commutative flip-+
Counts
4 → 141
Calls
4 calls:
84.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
224.0ms
(* (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 a))
118.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
19.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series810.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
252.0ms
(* (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 a))
331.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
110.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify3.5s

Counts
153 → 153
Iterations

Useful iterations: 2 (798.0ms)

IterNodesCost
02503533
17303010
246052710
done50002710

prune590.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.0b

localize16.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.4b
(* (/ 1 (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (* a c))) (/ 1 a))
9.2b
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (* a c))
23.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite433.0ms

Algorithm
rewrite-expression-head
Rules
147×add-exp-log
80×add-sqr-sqrt
75×times-frac
70×div-exp
53×prod-exp
49×*-un-lft-identity
41×add-cbrt-cube
35×associate-*l*
31×add-cube-cbrt
22×rec-exp 1-exp
16×cbrt-undiv
13×associate-*r*
12×difference-of-squares
11×cbrt-unprod
9×pow1 sqrt-prod unswap-sqr
6×div-inv associate-/l* distribute-lft-out-- add-log-exp
3×flip3-- pow-prod-down flip--
2×pow-flip sqrt-div associate-/l/ inv-pow
1×frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub associate-*r/ associate-*l/ clear-num associate-/r* associate-/r/ un-div-inv *-commutative
Counts
4 → 180
Calls
4 calls:
61.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
189.0ms
(* (/ 1 (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (* a c))) (/ 1 a))
154.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (* a c))
10.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series537.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
150.0ms
(* (/ 1 (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (* a c))) (/ 1 a))
157.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (* a c))
124.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify648.0ms

Counts
192 → 192
Iterations

Useful iterations: done (642.0ms)

IterNodesCost
03234336
110773930
done50013412

prune512.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.0b

regimes358.0ms

Accuracy

85% (4.0b remaining)

Error of 9.4b against oracle of 5.4b and baseline of 32.3b

bsearch217.0ms

Steps
ItersRangePoint
10
1.3113650301339767e-12
0.01077406869848718
0.010648423176581222
9
-8.356775273780836e-234
-1.6460056981104342e-242
-1.8936269564254704e-242
6
-1.1000082512799256e+103
-1.2658565361216573e+102
-1.2929563087095085e+102

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03561
14261
done4261

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.1s1118×body2560valid
449.0ms5788×body80valid
395.0ms918×body1280valid
268.0ms3035×body80nan
160.0ms464×body640valid
47.0ms103×body5120valid
38.0ms218×body320valid
12.0ms97×body160valid