Details

Time bar (total: 19.3s)

sample59.0ms

Algorithm
intervals
Results
16.0ms187×body80valid
8.0ms32×body2560valid
7.0ms32×body1280valid
4.0ms94×body80nan
2.0ms14×body640valid
1.0ms3×body5120valid
1.0ms6×body320valid
1.0ms6×body160valid

simplify38.0ms

Counts
1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b
(- (* b_2 b_2) (* a c))
1.4b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite190.0ms

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:
98.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
21.0ms
(- (* b_2 b_2) (* a c))
47.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
19.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series424.0ms

Counts
4 → 12
Calls
4 calls:
132.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
69.0ms
(- (* b_2 b_2) (* a c))
133.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
90.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.1s

Counts
103 → 103

prune425.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.3b

localize29.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b_2 b_2) (* c a))
2.5b
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* c a))) b_2)) a)
10.6b
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* c a))) b_2))
23.4b
(sqrt (- (* b_2 b_2) (* c a)))

rewrite297.0ms

Algorithm
rewrite-expression-head
Rules
162×times-frac
146×add-sqr-sqrt
113×*-un-lft-identity
81×add-cube-cbrt
32×difference-of-squares
27×associate-/l*
19×sqrt-prod
16×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 → 184
Calls
4 calls:
9.0ms
(- (* b_2 b_2) (* c a))
152.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* c a))) b_2)) a)
107.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* c a))) b_2))
20.0ms
(sqrt (- (* b_2 b_2) (* c a)))

series712.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(- (* b_2 b_2) (* c a))
248.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* c a))) b_2)) a)
306.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* c a))) b_2))
109.0ms
(sqrt (- (* b_2 b_2) (* c a)))

simplify1.8s

Counts
196 → 196

prune785.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b_2 b_2) (* c a))
2.5b
(/ a (/ (- (sqrt (- (* b_2 b_2) (* c a))) b_2) c))
2.5b
(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* c a))) b_2) c)) a)
23.4b
(sqrt (- (* b_2 b_2) (* c a)))

rewrite303.0ms

Algorithm
rewrite-expression-head
Rules
831×times-frac
545×add-sqr-sqrt
448×*-un-lft-identity
352×add-cube-cbrt
96×difference-of-squares
74×associate-/l*
51×sqrt-prod
48×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 → 437
Calls
4 calls:
9.0ms
(- (* b_2 b_2) (* c a))
74.0ms
(/ a (/ (- (sqrt (- (* b_2 b_2) (* c a))) b_2) c))
164.0ms
(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* c a))) b_2) c)) a)
10.0ms
(sqrt (- (* b_2 b_2) (* c a)))

series624.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(- (* b_2 b_2) (* c a))
282.0ms
(/ a (/ (- (sqrt (- (* b_2 b_2) (* c a))) b_2) c))
225.0ms
(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* c a))) b_2) c)) a)
78.0ms
(sqrt (- (* b_2 b_2) (* c a)))

simplify1.2s

Counts
449 → 449

prune1.9s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ 1 (- (sqrt (- (* b_2 b_2) (* c a))) b_2)) (/ 1 c))
0.4b
(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
0.8b
(- (* b_2 b_2) (* c a))
23.4b
(sqrt (- (* b_2 b_2) (* c a)))

rewrite255.0ms

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:
130.0ms
(/ (/ 1 (- (sqrt (- (* b_2 b_2) (* c a))) b_2)) (/ 1 c))
64.0ms
(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
9.0ms
(- (* b_2 b_2) (* c a))
10.0ms
(sqrt (- (* b_2 b_2) (* c a)))

series438.0ms

Counts
4 → 12
Calls
4 calls:
155.0ms
(/ (/ 1 (- (sqrt (- (* b_2 b_2) (* c a))) b_2)) (/ 1 c))
138.0ms
(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
40.0ms
(- (* b_2 b_2) (* c a))
104.0ms
(sqrt (- (* b_2 b_2) (* c a)))

simplify1.1s

Counts
435 → 435

prune1.6s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 6.2b

regimes371.0ms

Accuracy

96% (1.0b remaining)

Error of 6.4b against oracle of 5.4b and baseline of 30.1b

bsearch319.0ms

Steps
ItersRangePoint
10
1.1938117014962488e+94
7.783906932586822e+104
1.2945834219150715e+99
11
-8.569424948092005e-306
1.0003819803802923e-285
-6.186379766271726e-309
7
-9.035077376741492e+112
-5.081751909394618e+111
-6.075503372554189e+112

simplify1.5s

end0.0ms

sample2.9s

Algorithm
intervals
Results
617.0ms2856×body80nan
515.0ms5864×body80valid
511.0ms1075×body2560valid
321.0ms895×body1280valid
279.0ms443×body640valid
49.0ms107×body5120valid
41.0ms233×body320valid
14.0ms119×body160valid