Details

Time bar (total: 10.9s)

sample288.0ms

Algorithm
intervals
Results
47.0ms35×body1280valid
43.0ms168×body80valid
16.0ms33×body2560valid
7.0ms92×body80nan
5.0ms15×body640valid
4.0ms6×body5120valid
2.0ms9×body320valid
1.0ms8×body160valid

simplify10.0ms

Counts
1 → 1

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.6b

localize95.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.2b
(- (* b_2 b_2) (* a c))
2.0b
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite185.0ms

Algorithm
rewrite-expression-head
Rules
35×*-un-lft-identity
16×add-sqr-sqrt
15×add-cube-cbrt times-frac
10×distribute-lft-out add-log-exp
6×add-exp-log add-cbrt-cube
5×pow1 distribute-rgt-neg-in associate-/l*
3×associate-/r* sqrt-prod
2×neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div sum-log flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub div-exp neg-log clear-num div-inv
Counts
4 → 80
Calls
4 calls:
116.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
14.0ms
(- (* b_2 b_2) (* a c))
34.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
12.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series496.0ms

Counts
4 → 12
Calls
4 calls:
157.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
66.0ms
(- (* b_2 b_2) (* a c))
132.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
140.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify100.0ms

Counts
92 → 92

prune375.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.3b

localize24.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b_2 b_2) (* a c))
3.8b
(/ (/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
11.6b
(/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
24.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite243.0ms

Algorithm
rewrite-expression-head
Rules
74×times-frac
54×add-sqr-sqrt
53×*-un-lft-identity
29×add-cube-cbrt
18×add-exp-log add-cbrt-cube
14×associate-/l*
12×distribute-lft-out-- difference-of-squares
10×associate-/r* associate-/r/
9×sqrt-prod
7×cbrt-undiv flip3-- div-exp flip--
6×distribute-rgt-neg-in div-inv add-log-exp
5×pow1
2×frac-2neg sqrt-div prod-exp clear-num cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-/l/
Counts
4 → 130
Calls
4 calls:
14.0ms
(- (* b_2 b_2) (* a c))
121.0ms
(/ (/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
83.0ms
(/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
16.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series621.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(- (* b_2 b_2) (* a c))
239.0ms
(/ (/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
229.0ms
(/ (* a c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
91.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify79.0ms

Counts
142 → 142

prune493.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.2b

localize20.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b_2 b_2) (* a c))
3.8b
(/ (/ 1 (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (* a c))) a)
11.8b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (* a c))
24.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite311.0ms

Algorithm
rewrite-expression-head
Rules
337×times-frac
175×add-sqr-sqrt
174×*-un-lft-identity
118×add-cube-cbrt
45×associate-/l*
41×add-exp-log
28×distribute-lft-out-- difference-of-squares
24×div-exp
23×add-cbrt-cube
18×div-inv
17×sqrt-prod
14×distribute-rgt-neg-in
11×cbrt-undiv
6×add-log-exp
5×pow1
4×prod-exp associate-/r* associate-/r/
3×rec-exp flip3-- 1-exp flip-- associate-/l/
2×frac-2neg sqrt-div clear-num cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log div-sub
Counts
4 → 239
Calls
4 calls:
10.0ms
(- (* b_2 b_2) (* a c))
113.0ms
(/ (/ 1 (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (* a c))) a)
149.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (* a c))
18.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series426.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(- (* b_2 b_2) (* a c))
166.0ms
(/ (/ 1 (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (* a c))) a)
128.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (* a c))
83.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify124.0ms

Counts
251 → 251

prune946.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 7.2b

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 c))
0.7b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b
(- (* b_2 b_2) (* a c))
24.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite223.0ms

Algorithm
rewrite-expression-head
Rules
897×times-frac
528×add-sqr-sqrt
527×*-un-lft-identity
355×add-cube-cbrt
86×distribute-lft-out-- difference-of-squares
46×sqrt-prod
44×add-exp-log
43×distribute-rgt-neg-in div-inv
32×div-exp
29×associate-/r/
27×associate-/l*
17×flip3-- flip--
16×add-cbrt-cube
13×associate-/r*
10×add-log-exp
8×cbrt-undiv rec-exp 1-exp
5×pow1
3×diff-log
2×sub-neg sqrt-div
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 neg-log clear-num associate-/l/
Counts
4 → 468
Calls
4 calls:
111.0ms
(/ (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 c))
43.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
14.0ms
(- (* b_2 b_2) (* a c))
16.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series379.0ms

Counts
4 → 12
Calls
4 calls:
153.0ms
(/ (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 c))
90.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
44.0ms
(- (* b_2 b_2) (* a c))
91.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify162.0ms

Counts
480 → 480

prune1.3s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 7.2b

regimes339.0ms

Accuracy

94.5% (1.3b remaining)

Error of 6.8b against oracle of 5.5b and baseline of 29.5b

bsearch204.0ms

Steps
ItersRangePoint
5
1.2073698495971617e+61
2.9312978430050554e+61
2.5231041875643557e+61
8
-4.3193946104502796e-226
-4.381317687258745e-230
-7.892835993842436e-230
10
-3.742210988141449e+103
-1.1204690717208776e+87
-8.301687926884189e+98

simplify547.0ms

end0.0ms

sample2.8s

Algorithm
intervals
Results
799.0ms5871×body80valid
491.0ms1050×body2560valid
429.0ms895×body1280valid
202.0ms2846×body80nan
136.0ms101×body5120valid
107.0ms479×body640valid
51.0ms106×body160valid
35.0ms218×body320valid