Details

Time bar (total: 17.7s)

sample63.0ms

Algorithm
intervals
Results
15.0ms191×body80valid
11.0ms39×body2560valid
6.0ms119×body80nan
6.0ms26×body1280valid
3.0ms15×body640valid
1.0ms8×body320valid
0.0ms1×body5120valid
0.0ms1×body160valid

simplify29.0ms

Counts
1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.5b

localize19.0ms

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))
1.0b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
25.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite171.0ms

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:
84.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
9.0ms
(- (* b_2 b_2) (* a c))
56.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
15.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series370.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
57.0ms
(- (* b_2 b_2) (* a c))
110.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
82.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.2s

Counts
103 → 103

prune382.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.9b

localize16.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.9b
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
11.4b
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
25.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite315.0ms

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:
64.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
143.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
89.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
10.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series717.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
237.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
285.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
84.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.6s

Counts
199 → 199

prune774.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.9b

localize27.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.8b
(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
3.9b
(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
25.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite376.0ms

Algorithm
rewrite-expression-head
Rules
831×times-frac
549×add-sqr-sqrt
450×*-un-lft-identity
352×add-cube-cbrt
98×difference-of-squares
74×associate-/l*
52×sqrt-prod
49×distribute-lft-out--
25×associate-/r*
22×div-inv
18×add-exp-log add-cbrt-cube
9×cbrt-undiv div-exp
6×add-log-exp
5×pow1 associate-/r/
2×flip3-- frac-2neg sqrt-div clear-num flip--
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-/l/
Counts
4 → 440
Calls
4 calls:
86.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
92.0ms
(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
112.0ms
(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
13.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series736.0ms

Counts
4 → 12
Calls
4 calls:
136.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
300.0ms
(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
218.0ms
(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
82.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.0s

Counts
452 → 452

prune1.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 c))
0.6b
(- (* b_2 b_2) (* a c))
1.2b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
25.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite261.0ms

Algorithm
rewrite-expression-head
Rules
789×times-frac
493×add-sqr-sqrt
406×*-un-lft-identity
320×add-cube-cbrt
86×difference-of-squares
46×sqrt-prod
44×add-exp-log
43×distribute-lft-out--
40×div-inv
32×div-exp
29×associate-/r/
24×associate-/l*
17×flip3-- flip--
16×add-cbrt-cube
13×associate-/r*
8×cbrt-undiv rec-exp 1-exp add-log-exp
5×pow1
2×sub-neg sqrt-div diff-log
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/l/
Counts
4 → 423
Calls
4 calls:
139.0ms
(/ (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 c))
10.0ms
(- (* b_2 b_2) (* a c))
58.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series420.0ms

Counts
4 → 12
Calls
4 calls:
153.0ms
(/ (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 c))
48.0ms
(- (* b_2 b_2) (* a c))
111.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
108.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify867.0ms

Counts
435 → 435

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.9b

regimes321.0ms

Accuracy

93.6% (1.6b remaining)

Error of 7.1b against oracle of 5.5b and baseline of 30.3b

bsearch232.0ms

Steps
ItersRangePoint
8
1.890514070312107e+96
2.5656331724562416e+99
5.5575580047450245e+97
9
-2.5272618514179185e-248
-3.416338979747681e-256
-1.3591367057663401e-248
10
-2.112704124357506e+75
-5.879772917858402e+57
-2.0612055510809406e+75

simplify1.3s

end0.0ms

sample2.6s

Algorithm
intervals
Results
880.0ms1074×body2560valid
450.0ms5908×body80valid
299.0ms863×body1280valid
177.0ms3023×body80nan
136.0ms460×body640valid
83.0ms119×body5120valid
35.0ms225×body320valid
13.0ms121×body160valid