Details

Time bar (total: 14.7s)

sample50.0ms

Algorithm
intervals
Results
9.0ms36×body2560valid
9.0ms189×body80valid
5.0ms25×body1280valid
4.0ms104×body80nan
3.0ms16×body640valid
1.0ms6×body320valid
1.0ms2×body5120valid
0.0ms3×body160valid

simplify37.0ms

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

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.6b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.7b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.8b
(- (* b_2 b_2) (* a c))
26.2b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite127.0ms

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:
80.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
19.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
12.0ms
(- (* b_2 b_2) (* a c))
13.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series357.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
100.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
46.0ms
(- (* b_2 b_2) (* a c))
94.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.1s

Counts
103 → 103
Iterations
IterNodes
done5001
21521
1393
0158

prune588.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 7.5b

localize36.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b_2 b_2) (* a c))
2.8b
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
11.9b
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
26.2b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite187.0ms

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))
106.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
46.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
7.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series696.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(- (* b_2 b_2) (* a c))
222.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
314.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
97.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.4s

Counts
196 → 196
Iterations
IterNodes
done5002
24257
1770
0302

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
0.8b
(- (* b_2 b_2) (* c a))
16.0b
(/ (* c a) a)
26.2b
(sqrt (- (* b_2 b_2) (* c a)))

rewrite87.0ms

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:
60.0ms
(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
11.0ms
(- (* b_2 b_2) (* c a))
9.0ms
(/ (* c a) a)
7.0ms
(sqrt (- (* b_2 b_2) (* c a)))

series202.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
39.0ms
(- (* b_2 b_2) (* c a))
6.0ms
(/ (* c a) a)
82.0ms
(sqrt (- (* b_2 b_2) (* c a)))

simplify1.6s

Counts
75 → 75
Iterations
IterNodes
done5000
21547
1309
0125

prune389.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.4b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ c (- (sqrt (- (* b_2 b_2) (* c a))) b_2))
0.8b
(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
0.8b
(- (* b_2 b_2) (* c a))
26.2b
(sqrt (- (* b_2 b_2) (* c a)))

rewrite114.0ms

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:
38.0ms
(/ c (- (sqrt (- (* b_2 b_2) (* c a))) b_2))
61.0ms
(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
6.0ms
(- (* b_2 b_2) (* c a))
7.0ms
(sqrt (- (* b_2 b_2) (* c a)))

series540.0ms

Counts
4 → 12
Calls
4 calls:
285.0ms
(/ c (- (sqrt (- (* b_2 b_2) (* c a))) b_2))
113.0ms
(- (sqrt (- (* b_2 b_2) (* c a))) b_2)
62.0ms
(- (* b_2 b_2) (* c a))
79.0ms
(sqrt (- (* b_2 b_2) (* c a)))

simplify902.0ms

Counts
95 → 95
Iterations
IterNodes
done5000
21186
1339
0148

prune485.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 7.4b

regimes499.0ms

Accuracy

95.7% (1.0b remaining)

Error of 6.6b against oracle of 5.6b and baseline of 29.6b

bsearch189.0ms

Steps
ItersRangePoint
6
5.84949006905106e+100
6.027833473435204e+101
3.355858625783055e+101
9
-1.4598085821258646e-291
-1.0697531889019586e-297
-1.0850002786366243e-297
6
-1.7989235910837076e+89
-1.4585470499056154e+88
-1.7633154797394035e+89

simplify10.0ms

Iterations
IterNodes
done42
242
141
035

end0.0ms

sample2.8s

Algorithm
intervals
Results
930.0ms1063×body2560valid
535.0ms5821×body80valid
368.0ms950×body1280valid
250.0ms2885×body80nan
127.0ms116×body5120valid
115.0ms475×body640valid
46.0ms239×body320valid
13.0ms105×body160valid