Details

Time bar (total: 9.9s)

sample309.0ms

Algorithm
intervals
Results
10.0ms187×body80valid
8.0ms35×body2560valid
6.0ms31×body1280valid
4.0ms95×body80nan
2.0ms11×body640valid
1.0ms3×body5120valid
0.0ms4×body320valid
0.0ms4×body160valid

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0187
1327
2417
3447
4447

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 35.5b

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
(- (* b_2 b_2) (* a c))
1.0b
(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite48.0ms

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:
25.0ms
(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
4.0ms
(- (* b_2 b_2) (* a c))
9.0ms
(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series278.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
37.0ms
(- (* b_2 b_2) (* a c))
76.0ms
(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
75.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify44.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0360964
11233910
25002901

prune238.0ms

Filtered
103 candidates to 72 candidates (69.9%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New9310103
Fresh000
Picked101
Done000
Total9410104

Merged error: 6.4b

Counts
104 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.7b
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
11.6b
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
24.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite47.0ms

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:
7.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
15.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
11.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series590.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
201.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
248.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
67.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify108.0ms

Algorithm
egg-herbie
Counts
199 → 199
Iterations

Useful iterations: 2 (82.0ms)

IterNodesCost
07042957
130982807
250012787

prune445.0ms

Filtered
199 candidates to 148 candidates (74.4%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1963199
Fresh369
Picked101
Done000
Total2009209

Merged error: 6.4b

Counts
209 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.1b
(/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)
2.7b
(/ (/ 1 (/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)) a)
24.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite202.0ms

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)
13.0ms
(/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)
59.0ms
(/ (/ 1 (/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)) a)
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series367.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
107.0ms
(/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)
114.0ms
(/ (/ 1 (/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)) a)
70.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify251.0ms

Algorithm
egg-herbie
Counts
1037 → 1037
Iterations

Useful iterations: 1 (74.0ms)

IterNodesCost
0423521055
1500120463

prune2.1s

Filtered
1037 candidates to 577 candidates (55.6%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New103611037
Fresh178
Picked011
Done000
Total103791046

Merged error: 6.4b

Counts
1046 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

4.8b
(/ (/ 1 (/ (/ (- (exp (log (sqrt (- (* b_2 b_2) (* a c))))) b_2) a) c)) a)
5.6b
(exp (log (sqrt (- (* b_2 b_2) (* a c)))))
17.0b
(- (exp (log (sqrt (- (* b_2 b_2) (* a c))))) b_2)
24.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite222.0ms

Algorithm
rewrite-expression-head
Rules
3330×times-frac
1934×add-sqr-sqrt
1497×*-un-lft-identity
1279×add-cube-cbrt
327×difference-of-squares
242×associate-/l*
224×log-prod exp-sum
115×sqrt-prod
109×distribute-lft-out--
53×div-inv
36×add-exp-log
25×div-exp
18×add-cbrt-cube
10×cbrt-undiv
7×pow1
6×exp-prod add-log-exp
4×sqrt-div associate-/r/
3×rec-exp flip3-- 1-exp associate-/r* log-pow flip--
2×log-div sqrt-pow1 pow1/2 exp-diff
1×sub-neg rem-sqrt-square frac-2neg diff-log clear-num rem-exp-log associate-/l/
Counts
4 → 1049
Calls
4 calls:
67.0ms
(/ (/ 1 (/ (/ (- (exp (log (sqrt (- (* b_2 b_2) (* a c))))) b_2) a) c)) a)
6.0ms
(exp (log (sqrt (- (* b_2 b_2) (* a c)))))
10.0ms
(- (exp (log (sqrt (- (* b_2 b_2) (* a c))))) b_2)
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series324.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(/ (/ 1 (/ (/ (- (exp (log (sqrt (- (* b_2 b_2) (* a c))))) b_2) a) c)) a)
67.0ms
(exp (log (sqrt (- (* b_2 b_2) (* a c)))))
74.0ms
(- (exp (log (sqrt (- (* b_2 b_2) (* a c))))) b_2)
69.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify271.0ms

Algorithm
egg-herbie
Counts
1061 → 1061
Iterations

Useful iterations: 1 (73.0ms)

IterNodesCost
0489225552
1500124913

prune2.4s

Filtered
1061 candidates to 546 candidates (51.5%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New105921061
Fresh077
Picked101
Done011
Total1060101070

Merged error: 6.4b

Counts
1070 → 10

regimes250.0ms

Accuracy

88.9% (3.0b remaining)

Error of 8.3b against oracle of 5.3b and baseline of 32.1b

bsearch147.0ms

Steps
ItersRangePoint
9
1.554603894687908e+31
4.1009785056144894e+37
4.056542178957228e+37
10
-2.544310204335198e-304
3.947659886945619e-296
1.593881270757566e-307
6
-1.3831374154076917e+37
-1.925364763132006e+36
-1.0455454844483269e+37

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04124
14124

end0.0ms

sample1.2s

Algorithm
intervals
Results
276.0ms1115×body2560valid
242.0ms5858×body80valid
168.0ms864×body1280valid
117.0ms2878×body80nan
69.0ms429×body640valid
32.0ms110×body5120valid
27.0ms233×body320valid
8.0ms105×body160valid

Profiling

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