Details

Time bar (total: 14.6s)

sample85.0ms

Algorithm
intervals
Results
17.0ms37×body2560valid
14.0ms182×body80valid
12.0ms31×body1280valid
6.0ms22×body640valid
6.0ms89×body80nan
2.0ms9×body320valid
1.0ms3×body160valid
1.0ms1×body5120valid

simplify37.0ms

Counts
1 → 1
Iterations
IterNodes
done44
444
341
232
118
010

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.2b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.2b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.4b
(- (* b_2 b_2) (* a c))
22.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite158.0ms

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-cbrt-cube add-exp-log
5×pow1 distribute-rgt-neg-in
4×flip3-- flip--
3×associate-/r* diff-log
2×sub-neg sqrt-div associate-/l/
1×associate--l- neg-sub0 cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-sub div-exp neg-log div-inv
Counts
4 → 91
Calls
4 calls:
66.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
35.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
12.0ms
(- (* b_2 b_2) (* a c))
40.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series429.0ms

Counts
4 → 12
Calls
4 calls:
154.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
95.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
65.0ms
(- (* b_2 b_2) (* a c))
115.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.3s

Counts
103 → 103
Iterations
IterNodes
done5001
21521
1393
0158

prune635.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.1b

localize21.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (* b_2 b_2) (* a c))
4.2b
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
8.9b
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
22.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite215.0ms

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-cbrt-cube add-exp-log
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×clear-num frac-2neg sqrt-div
1×rem-sqrt-square sub-neg sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 184
Calls
4 calls:
12.0ms
(- (* b_2 b_2) (* a c))
113.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
67.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
11.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series717.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(- (* b_2 b_2) (* a c))
277.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
299.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
78.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.3s

Counts
196 → 196
Iterations
IterNodes
done5002
24257
1770
0302

prune1.3s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
1.4b
(- (* b_2 b_2) (* c a))
13.2b
(/ (* c a) a)
22.7b
(sqrt (- (* b_2 b_2) (* c a)))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
9×*-un-lft-identity add-cbrt-cube add-exp-log
8×add-log-exp
7×add-cube-cbrt
5×pow1
4×sqrt-prod
3×associate-/r* times-frac flip3-- flip--
2×cbrt-undiv sub-neg sqrt-div diff-log div-exp difference-of-squares
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 prod-exp cbrt-unprod div-inv associate-/l* distribute-lft-out--
Counts
4 → 63
Calls
4 calls:
71.0ms
(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
10.0ms
(- (* b_2 b_2) (* c a))
14.0ms
(/ (* c a) a)
8.0ms
(sqrt (- (* b_2 b_2) (* c a)))

series271.0ms

Counts
4 → 12
Calls
4 calls:
122.0ms
(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
61.0ms
(- (* b_2 b_2) (* c a))
7.0ms
(/ (* c a) a)
80.0ms
(sqrt (- (* b_2 b_2) (* c a)))

simplify1.5s

Counts
75 → 75
Iterations
IterNodes
done5000
21547
1309
0125

prune369.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ c (- (sqrt (- (* b_2 b_2) (* c a))) b_2))
0.2b
(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
1.4b
(- (* b_2 b_2) (* c a))
22.7b
(sqrt (- (* b_2 b_2) (* c a)))

rewrite134.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
26×*-un-lft-identity
18×times-frac
16×add-cube-cbrt
10×difference-of-squares
8×sqrt-prod add-log-exp
6×associate-/r* add-cbrt-cube add-exp-log
5×pow1 distribute-lft-out--
4×flip3-- flip--
3×associate-/l*
2×sub-neg sqrt-div diff-log associate-/r/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-exp div-inv
Counts
4 → 83
Calls
4 calls:
37.0ms
(/ c (- (sqrt (- (* b_2 b_2) (* c a))) b_2))
64.0ms
(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
12.0ms
(- (* b_2 b_2) (* c a))
16.0ms
(sqrt (- (* b_2 b_2) (* c a)))

series463.0ms

Counts
4 → 12
Calls
4 calls:
219.0ms
(/ c (- (sqrt (- (* b_2 b_2) (* c a))) b_2))
98.0ms
(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
43.0ms
(- (* b_2 b_2) (* c a))
103.0ms
(sqrt (- (* b_2 b_2) (* c a)))

simplify895.0ms

Counts
95 → 95
Iterations
IterNodes
done5000
21186
1339
0148

prune607.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.0b

regimes428.0ms

Accuracy

95.9% (1.0b remaining)

Error of 7.0b against oracle of 6.0b and baseline of 29.9b

bsearch203.0ms

Steps
ItersRangePoint
5
2.6243927093659187e+107
5.901159163981397e+107
5.8304273320174675e+107
9
5.804049448362254e-224
5.063540901645884e-216
6.138409820727008e-224
8
-2.748004767191833e+152
-1.058878950082428e+148
-3.055872925556576e+149

simplify7.0ms

Iterations
IterNodes
done38
238
137
032

end0.0ms

sample2.4s

Algorithm
intervals
Results
818.0ms1019×body2560valid
394.0ms5889×body80valid
387.0ms891×body1280valid
180.0ms2880×body80nan
135.0ms461×body640valid
60.0ms98×body5120valid
34.0ms223×body320valid
12.0ms117×body160valid