Details

Time bar (total: 6.0s)

analyze589.0ms

Algorithm
search

sample42.0ms

Algorithm
intervals
Results
8.0ms31×body2560valid
7.0ms31×body1280valid
7.0ms160×body80valid
3.0ms18×body640valid
2.0ms5×body5120valid
1.0ms28×body80nan
1.0ms9×body320valid
0.0ms6×body80invalid
0.0ms2×body160valid

simplify397.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0187
1327
2417
3447
4447

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 33.4b

Counts
2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b
(- (* b_2 b_2) (* a c))
0.5b
(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.3b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite47.0ms

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:
9.0ms
(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms
(- (* b_2 b_2) (* a c))
8.0ms
(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
5.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series60.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
7.0ms
(- (* b_2 b_2) (* a c))
14.0ms
(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify41.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0360964
11233910
25002901

prune140.0ms

Filtered
72 candidates to 103 candidates (-43.1%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New958103
Fresh000
Picked101
Done000
Total968104

Merged error: 4.9b

Counts
104 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

1.8b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.1b
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
9.4b
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
21.3b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
162×times-frac
150×add-sqr-sqrt
115×*-un-lft-identity
81×add-cube-cbrt
34×difference-of-squares
27×associate-/l*
20×sqrt-prod
17×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 → 187
Calls
4 calls:
6.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
14.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
3.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series122.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
41.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
53.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
16.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify104.0ms

Algorithm
egg-herbie
Counts
199 → 199
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
07042957
130982807
250012787

prune228.0ms

Filtered
148 candidates to 199 candidates (-34.5%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1954199
Fresh347
Picked011
Done000
Total1989207

Merged error: 4.8b

Counts
207 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

1.8b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.5b
(/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)
3.1b
(/ (/ 1 (/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)) a)
21.3b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite195.0ms

Algorithm
rewrite-expression-head
Rules
3063×times-frac
1689×add-sqr-sqrt
1446×*-un-lft-identity
1204×add-cube-cbrt
242×difference-of-squares
237×associate-/l*
124×sqrt-prod
121×distribute-lft-out--
58×div-inv
41×add-exp-log
28×div-exp
23×add-cbrt-cube
13×cbrt-undiv
6×associate-/r* add-log-exp
5×pow1
4×associate-/r/
3×rec-exp 1-exp
2×flip3-- frac-2neg sqrt-div div-sub clear-num flip-- associate-/l/
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
Counts
4 → 1025
Calls
4 calls:
7.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
17.0ms
(/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)
52.0ms
(/ (/ 1 (/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)) a)
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series69.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.0ms
(/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)
23.0ms
(/ (/ 1 (/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)) a)
12.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify248.0ms

Algorithm
egg-herbie
Counts
1037 → 1037
Iterations

Useful iterations: 1 (71.0ms)

IterNodesCost
0422921054
1500120466

prune920.0ms

Filtered
576 candidates to 1037 candidates (-80.0%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New103701037
Fresh077
Picked011
Done011
Total103791046

Merged error: 4.8b

Counts
1046 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* b_2 b_2) (* a c))
1.8b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
14.2b
(* (* a c) (/ (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a))
21.3b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
126×times-frac
101×add-sqr-sqrt
80×*-un-lft-identity
76×associate-*r*
60×add-cube-cbrt
39×add-exp-log
25×add-cbrt-cube
20×difference-of-squares
15×prod-exp
13×sqrt-prod
12×div-exp
10×pow1 distribute-lft-out--
9×cbrt-unprod
8×add-log-exp
6×cbrt-undiv flip3-- associate-/r/ flip--
4×div-inv
3×pow-prod-down
2×sub-neg rec-exp sqrt-div diff-log 1-exp
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ associate-*l* *-commutative
Counts
4 → 146
Calls
4 calls:
3.0ms
(- (* b_2 b_2) (* a c))
6.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.0ms
(* (* a c) (/ (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a))
3.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series71.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(- (* b_2 b_2) (* a c))
13.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
39.0ms
(* (* a c) (/ (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a))
12.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify110.0ms

Algorithm
egg-herbie
Counts
158 → 158
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
08981588
149881371
250021371

prune134.0ms

Filtered
103 candidates to 158 candidates (-53.4%)
Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New1580158
Fresh066
Picked011
Done022
Total1589167

Merged error: 4.8b

Counts
167 → 9

regimes284.0ms

Accuracy

87.9% (3.3b remaining)

Error of 8.9b against oracle of 5.7b and baseline of 32.6b

bsearch586.0ms

Steps
ItersRangePoint
9
3.9505087361995763e+37
1.2035772986465193e+45
1.3904002231562079e+44
9
6.482434630622566e-303
6.527526308554541e-295
6.632006754206088e-298
6
-7.205443943730628e+56
-1.0679482755853425e+56
-1.2574409554595683e+56

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04224
14224

end0.0ms

analyze385.0ms

Algorithm
search

sample1.1s

Algorithm
intervals
Results
272.0ms1074×body2560valid
216.0ms5104×body80valid
178.0ms890×body1280valid
72.0ms456×body640valid
37.0ms124×body5120valid
33.0ms813×body80nan
27.0ms227×body320valid
11.0ms251×body80invalid
10.0ms125×body160valid

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