Details

Time bar (total: 4.2s)

sample249.0ms

Algorithm
intervals
Results
188.0ms9×body320valid
10.0ms37×body2560valid
9.0ms171×body80valid
7.0ms33×body1280valid
4.0ms85×body80nan
3.0ms15×body640valid
1.0ms2×body5120valid
0.0ms4×body160valid

simplify265.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (18.0ms)

IterNodesCost
0187
1327
2417
3447
4447

prune5.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 37.2b

Counts
2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b
(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b
(- (* b_2 b_2) (* a c))
26.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite32.0ms

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:
10.0ms
(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms
(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms
(- (* b_2 b_2) (* a c))
7.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series66.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
14.0ms
(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms
(- (* b_2 b_2) (* a c))
22.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify43.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0360964
11233910
25002901

prune143.0ms

Filtered
103 candidates to 72 candidates (30.1%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New949103
Fresh000
Picked101
Done000
Total959104

Merged error: 7.5b

Counts
104 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b_2 b_2) (* a c))
2.1b
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
11.7b
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
26.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite43.0ms

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:
3.0ms
(- (* b_2 b_2) (* a c))
15.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
13.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series116.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(- (* b_2 b_2) (* a c))
40.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
57.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
12.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify104.0ms

Algorithm
egg-herbie
Counts
196 → 196
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
07042894
131122747
250012727

prune232.0ms

Filtered
196 candidates to 144 candidates (26.5%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1915196
Fresh448
Picked011
Done000
Total19510205

Merged error: 7.4b

Counts
205 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b_2 b_2) (* a c))
2.1b
(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
3.0b
(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
26.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite74.0ms

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:
3.0ms
(- (* b_2 b_2) (* a c))
22.0ms
(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
11.0ms
(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series113.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(- (* b_2 b_2) (* a c))
38.0ms
(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
55.0ms
(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
12.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify94.0ms

Algorithm
egg-herbie
Counts
449 → 449
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
015307327
150016764

prune311.0ms

Filtered
449 candidates to 297 candidates (33.9%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New4490449
Fresh088
Picked011
Done011
Total44910459

Merged error: 7.4b

Counts
459 → 10

localize24.0ms

Local error

Found 4 expressions with local error:

2.8b
(* (/ (/ 1 (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) (* (cbrt a) (cbrt a))) (/ (* a c) (* (cbrt a) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))))
11.0b
(/ (* a c) (* (cbrt a) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))))
26.0b
(sqrt (- (* b_2 b_2) (* a c)))
26.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
248×add-exp-log
114×add-cbrt-cube
105×prod-exp
100×div-exp
71×times-frac
59×cbrt-unprod
54×cbrt-undiv
52×add-sqr-sqrt
37×associate-*l*
32×*-un-lft-identity
29×sqrt-prod
24×add-cube-cbrt
10×rec-exp sqrt-div 1-exp
8×pow1
7×associate-*r*
6×associate-/r/ difference-of-squares unswap-sqr
5×flip3-- associate-*r/ flip--
4×div-inv add-log-exp
3×distribute-lft-out--
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times frac-2neg pow-prod-down associate-*l/ clear-num associate-/r* *-commutative associate-/l*
Counts
4 → 185
Calls
4 calls:
36.0ms
(* (/ (/ 1 (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) (* (cbrt a) (cbrt a))) (/ (* a c) (* (cbrt a) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))))
12.0ms
(/ (* a c) (* (cbrt a) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series205.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(* (/ (/ 1 (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) (* (cbrt a) (cbrt a))) (/ (* a c) (* (cbrt a) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))))
146.0ms
(/ (* a c) (* (cbrt a) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))))
13.0ms
(sqrt (- (* b_2 b_2) (* a c)))
16.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify57.0ms

Algorithm
egg-herbie
Counts
197 → 197
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
012094471
150023637

prune150.0ms

Filtered
197 candidates to 103 candidates (47.7%)
Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New1970197
Fresh077
Picked011
Done022
Total19710207

Merged error: 7.4b

Counts
207 → 10

regimes259.0ms

Accuracy

87.7% (2.9b remaining)

Error of 8.8b against oracle of 6.0b and baseline of 29.2b

bsearch88.0ms

Steps
ItersRangePoint
7
1.5733488064158731e+78
9.799352262304037e+79
1.2245621006229754e+79
9
4.4115275333905e-304
6.739992957276137e-299
8.54980141829627e-301
8
-86.2311277262396
-0.006735307951909714
-22.48003364851449

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03620
13620

end0.0ms

sample1.4s

Algorithm
intervals
Results
280.0ms1064×body2560valid
249.0ms1150×body1280valid
242.0ms5300×body80valid
112.0ms2606×body80nan
92.0ms549×body640valid
34.0ms273×body320valid
33.0ms105×body5120valid
10.0ms113×body160valid

Profiling

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