Details

Time bar (total: 8.9s)

sample281.0ms

Algorithm
intervals
Results
8.0ms182×body80valid
7.0ms33×body2560valid
5.0ms31×body1280valid
3.0ms85×body80nan
2.0ms17×body640valid
1.0ms10×body320valid
0.0ms1×body5120valid
0.0ms2×body160valid

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0157
1237
2307
3327
4347
5347

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: 35.4b

Counts
2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.9b
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b
(- (* b_2 b_2) (* a c))
23.2b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
38×*-un-lft-identity
19×add-sqr-sqrt
18×add-cube-cbrt
15×times-frac
10×fma-def distribute-lft-out add-log-exp
8×distribute-rgt-neg-in
6×add-exp-log add-cbrt-cube
5×pow1 associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-neg-in associate-/r* sqrt-prod
2×neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div sum-log flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub div-exp prod-diff neg-log clear-num div-inv
Counts
4 → 100
Calls
4 calls:
25.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms
(- (* b_2 b_2) (* a c))
6.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series270.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
72.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
38.0ms
(- (* b_2 b_2) (* a c))
70.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify46.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0389850
11366779
25001753

prune293.0ms

Filtered
112 candidates to 88 candidates (78.6%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New10210112
Fresh000
Picked101
Done000
Total10310113

Merged error: 7.9b

Counts
113 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b_2 b_2) (* a c))
3.6b
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
13.1b
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
23.2b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
186×times-frac
154×add-sqr-sqrt
153×*-un-lft-identity
89×add-cube-cbrt
32×distribute-lft-out-- difference-of-squares
30×associate-/l*
19×sqrt-prod
16×distribute-rgt-neg-in
11×add-exp-log add-cbrt-cube
10×associate-/r* associate-/r/
7×flip3-- flip--
6×div-inv add-log-exp
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
3×associate-/l/
2×frac-2neg sqrt-div clear-num
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 fma-neg diff-log prod-diff flip-+
Counts
4 → 210
Calls
4 calls:
4.0ms
(- (* b_2 b_2) (* a c))
17.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
15.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series401.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(- (* b_2 b_2) (* a c))
137.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
168.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
62.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify120.0ms

Algorithm
egg-herbie
Counts
222 → 222
Iterations

Useful iterations: 2 (90.0ms)

IterNodesCost
07613434
134903258
250023250

prune497.0ms

Filtered
222 candidates to 152 candidates (68.5%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New2193222
Fresh279
Picked011
Done000
Total22111232

Merged error: 7.8b

Counts
232 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b_2 b_2) (* a c))
1.8b
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
3.6b
(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
23.2b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
951×times-frac
585×add-sqr-sqrt
584×*-un-lft-identity
392×add-cube-cbrt
96×distribute-lft-out-- difference-of-squares
83×associate-/l*
51×sqrt-prod
48×distribute-rgt-neg-in
28×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/
4×expm1-log1p-u log1p-expm1-u
2×flip3-- frac-2neg sqrt-div clear-num flip--
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff associate-/l/
Counts
4 → 495
Calls
4 calls:
4.0ms
(- (* b_2 b_2) (* a c))
14.0ms
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
29.0ms
(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series419.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(- (* b_2 b_2) (* a c))
176.0ms
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
152.0ms
(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
58.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify108.0ms

Algorithm
egg-herbie
Counts
507 → 507
Iterations

Useful iterations: 1 (36.0ms)

IterNodesCost
015618690
150018042

prune1.0s

Filtered
507 candidates to 308 candidates (60.7%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New5061507
Fresh279
Picked101
Done011
Total5099518

Merged error: 7.8b

Counts
518 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.7b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b
(/ (/ (cbrt a) (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) (cbrt a))
1.0b
(- (* b_2 b_2) (* a c))
23.2b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite210.0ms

Algorithm
rewrite-expression-head
Rules
2862×times-frac
1686×add-sqr-sqrt
1685×*-un-lft-identity
1177×add-cube-cbrt
993×cbrt-prod
254×distribute-lft-out-- difference-of-squares
160×sqrt-prod
155×associate-/l*
148×distribute-rgt-neg-in
61×prod-diff
50×div-inv
21×distribute-lft-neg-in
13×add-exp-log
11×fma-neg
10×add-log-exp
8×add-cbrt-cube
7×neg-mul-1 associate-/r/
6×cbrt-undiv div-exp associate-/r*
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×flip3-- diff-log flip--
2×sub-neg sqrt-div
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 neg-log clear-num associate-/l/
Counts
4 → 1233
Calls
4 calls:
10.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
50.0ms
(/ (/ (cbrt a) (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) (cbrt a))
6.0ms
(- (* b_2 b_2) (* a c))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series303.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
147.0ms
(/ (/ (cbrt a) (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) (cbrt a))
35.0ms
(- (* b_2 b_2) (* a c))
57.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify292.0ms

Algorithm
egg-herbie
Counts
1245 → 1245
Iterations

Useful iterations: 1 (60.0ms)

IterNodesCost
0310530009
1500228173

prune3.0s

Filtered
1245 candidates to 712 candidates (57.2%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New124501245
Fresh077
Picked011
Done011
Total124591254

Merged error: 7.8b

Counts
1254 → 9

regimes195.0ms

Accuracy

92.6% (1.8b remaining)

Error of 7.6b against oracle of 5.8b and baseline of 30.4b

bsearch129.0ms

Steps
ItersRangePoint
7
6.184155830638016e+27
1.3306260697673677e+30
2.0732437802605094e+28
8
8.801855242554939e-263
2.6053624752067433e-259
8.94594987092143e-263
8
-1.109941606813071e+113
-3.739307379384431e+110
-2.7467723558510264e+111

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04326
14526
24526

end0.0ms

sample1.0s

Algorithm
intervals
Results
209.0ms1067×body2560valid
199.0ms5875×body80valid
143.0ms883×body1280valid
90.0ms2893×body80nan
55.0ms445×body640valid
27.0ms103×body5120valid
23.0ms223×body320valid
7.0ms114×body160valid