Details

Time bar (total: 10.3s)

sample345.0ms

Algorithm
intervals
Results
7.0ms187×body80valid
6.0ms36×body2560valid
4.0ms26×body1280valid
2.0ms19×body640valid
2.0ms73×body80nan
0.0ms5×body320valid
0.0ms1×body5120valid
0.0ms2×body160valid

simplify33.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (22.0ms)

IterNodesCost
0147
1227
2257
3277
4297
5297
done297

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.8b
(- (* b_2 b_2) (* a c))
21.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite110.0ms

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:
66.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
21.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
8.0ms
(- (* b_2 b_2) (* a c))
11.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series282.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
75.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
35.0ms
(- (* b_2 b_2) (* a c))
77.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify40.0ms

Counts
92 → 92
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0358790
11261727
25001705
done5001705

prune228.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.6b

localize12.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.2b
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
7.9b
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
21.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite172.0ms

Algorithm
rewrite-expression-head
Rules
186×times-frac
158×add-sqr-sqrt
157×*-un-lft-identity
89×add-cube-cbrt
34×distribute-lft-out-- difference-of-squares
30×associate-/l*
20×sqrt-prod
17×distribute-rgt-neg-in
11×add-exp-log add-cbrt-cube
10×associate-/r* associate-/r/
8×add-log-exp
7×flip3-- flip--
6×div-inv
5×pow1
4×cbrt-undiv div-exp
3×associate-/l/
2×frac-2neg sqrt-div diff-log clear-num
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 206
Calls
4 calls:
22.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
77.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
51.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
11.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series455.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
144.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
174.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
65.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify110.0ms

Counts
218 → 218
Iterations

Useful iterations: 2 (85.0ms)

IterNodesCost
07413477
133293295
250013269
done50013269

prune491.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.6b

localize14.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0b
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
3.2b
(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
21.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite197.0ms

Algorithm
rewrite-expression-head
Rules
951×times-frac
589×add-sqr-sqrt
588×*-un-lft-identity
392×add-cube-cbrt
98×distribute-lft-out-- difference-of-squares
83×associate-/l*
52×sqrt-prod
49×distribute-rgt-neg-in
28×associate-/r*
22×div-inv
18×add-exp-log add-cbrt-cube
9×cbrt-undiv div-exp
8×add-log-exp
5×pow1 associate-/r/
2×flip3-- frac-2neg sqrt-div diff-log clear-num flip--
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 neg-log associate-/l/
Counts
4 → 491
Calls
4 calls:
22.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
43.0ms
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
81.0ms
(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series484.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
187.0ms
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
157.0ms
(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
67.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify96.0ms

Counts
503 → 503
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
015828734
150018085
done50018085

prune1.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.6b

localize14.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.4b
(/ (/ (cbrt a) (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) (cbrt a))
1.4b
(/ (cbrt a) (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
21.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite339.0ms

Algorithm
rewrite-expression-head
Rules
3159×times-frac
1858×add-sqr-sqrt
1857×*-un-lft-identity
1265×add-cube-cbrt
1071×cbrt-prod
296×distribute-lft-out-- difference-of-squares
161×associate-/l*
151×sqrt-prod
148×distribute-rgt-neg-in
58×div-inv
31×associate-/r*
18×add-exp-log
11×add-cbrt-cube
9×cbrt-undiv div-exp
8×associate-/r/ add-log-exp
5×pow1
2×flip3-- frac-2neg sqrt-div diff-log clear-num flip--
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 neg-log associate-/l/
Counts
4 → 1337
Calls
4 calls:
21.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
107.0ms
(/ (/ (cbrt a) (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) (cbrt a))
47.0ms
(/ (cbrt a) (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
8.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series645.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
159.0ms
(/ (/ (cbrt a) (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) (cbrt a))
358.0ms
(/ (cbrt a) (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
60.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify263.0ms

Counts
1349 → 1349
Iterations

Useful iterations: 1 (50.0ms)

IterNodesCost
0303331518
1500231220
done500231220

prune3.6s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 3.6b

regimes235.0ms

Accuracy

94.8% (1.3b remaining)

Error of 6.7b against oracle of 5.5b and baseline of 29.9b

bsearch105.0ms

Steps
ItersRangePoint
6
1.4800420954007604e+99
6.083502279918113e+99
3.1053591122253717e+99
6
6.848468298883923e-306
1.066878005244536e-304
7.378256006970051e-306
9
-1.8974141771495474e+104
-5.663418186450483e+98
-1.3630271318813635e+101

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04326
14526
24526
done4526

end0.0ms

sample1.0s

Algorithm
intervals
Results
200.0ms1108×body2560valid
184.0ms5758×body80valid
129.0ms916×body1280valid
88.0ms2868×body80nan
56.0ms489×body640valid
23.0ms105×body5120valid
19.0ms224×body320valid
6.0ms103×body160valid