Details

Time bar (total: 4.5s)

sample328.0ms

Algorithm
intervals
Results
7.0ms41×body2560valid
7.0ms187×body80valid
3.0ms20×body1280valid
3.0ms86×body80nan
1.0ms12×body640valid
1.0ms10×body320valid
1.0ms3×body5120valid
0.0ms4×body160valid

simplify33.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0187
1327
2417
3447
4447

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b
(- (* b_2 b_2) (* a c))
1.4b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite109.0ms

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:
65.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms
(- (* b_2 b_2) (* a c))
22.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
11.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series235.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
29.0ms
(- (* b_2 b_2) (* a c))
63.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
67.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify42.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0368965
11241910
25001901

prune255.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.6b
(- (* b_2 b_2) (* a c))
1.4b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
165×times-frac
130×add-sqr-sqrt
129×*-un-lft-identity
77×add-cube-cbrt
27×associate-/r*
26×distribute-lft-out-- difference-of-squares
16×sqrt-prod
15×add-exp-log
13×distribute-rgt-neg-in
10×add-log-exp
9×associate-/r/ add-cbrt-cube
7×flip3-- div-exp flip--
6×pow1
5×div-inv
3×cbrt-undiv diff-log associate-/l*
2×sub-neg rec-exp sqrt-div 1-exp
1×associate--l- neg-sub0 rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 neg-log clear-num inv-pow
Counts
4 → 177
Calls
4 calls:
46.0ms
(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
7.0ms
(- (* b_2 b_2) (* a c))
22.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
11.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series236.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
31.0ms
(- (* b_2 b_2) (* a c))
59.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
56.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify73.0ms

Algorithm
egg-herbie
Counts
189 → 189
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
05912458
127062226
250012071

prune293.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.1b

localize14.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.0b
(sqrt (- (* b_2 b_2) (* a c)))
22.0b
(sqrt (- (* b_2 b_2) (* a c)))
22.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
11×*-un-lft-identity
10×sqrt-prod
8×add-log-exp
7×pow1 add-cube-cbrt
6×sqrt-div
4×add-exp-log flip3-- add-cbrt-cube flip--
3×rem-sqrt-square sqrt-pow1 pow1/2
2×diff-log distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 sub-neg distribute-rgt-neg-in neg-log
Counts
4 → 63
Calls
4 calls:
24.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
8.0ms
(sqrt (- (* b_2 b_2) (* a c)))
8.0ms
(sqrt (- (* b_2 b_2) (* a c)))
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series223.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
55.0ms
(sqrt (- (* b_2 b_2) (* a c)))
55.0ms
(sqrt (- (* b_2 b_2) (* a c)))
53.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify71.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 3 (65.0ms)

IterNodesCost
0201523
1699504
22378493
35002489

prune255.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.1b

localize20.0ms

Local error

Found 4 expressions with local error:

1.8b
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
15.8b
(- (pow b_2 2) (pow b_2 2))
16.0b
(/ (* 1 (+ (- (pow b_2 2) (pow b_2 2)) (* a c))) a)
22.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite166.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
23×*-un-lft-identity
22×unpow-prod-down
16×difference-of-squares
15×add-cube-cbrt
12×unpow2 sqr-pow
11×add-exp-log
10×distribute-rgt-out-- add-log-exp
9×add-cbrt-cube
8×distribute-lft-out--
5×pow1
3×times-frac div-exp associate-/r* sqrt-prod
2×cbrt-undiv flip3-- flip3-+ sqrt-div associate-*r/ prod-exp sum-log flip-- flip-+ associate-/l/ distribute-lft-out
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 pow1/2 +-inverses diff-log 1-exp neg-log clear-num cbrt-unprod div-inv associate-/l*
Counts
4 → 101
Calls
4 calls:
20.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
18.0ms
(- (pow b_2 2) (pow b_2 2))
116.0ms
(/ (* 1 (+ (- (pow b_2 2) (pow b_2 2)) (* a c))) a)
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series128.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0ms
(- (pow b_2 2) (pow b_2 2))
8.0ms
(/ (* 1 (+ (- (pow b_2 2) (pow b_2 2)) (* a c))) a)
56.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify185.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (177.0ms)

IterNodesCost
0507577
13397452
25001411

prune270.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.1b

regimes227.0ms

Accuracy

95.1% (1.2b remaining)

Error of 6.8b against oracle of 5.6b and baseline of 29.5b

bsearch116.0ms

Steps
ItersRangePoint
7
7.363656180201337e+60
1.0503009045500217e+63
1.0273828621120979e+63
8
2.5487727292066854e-249
1.8198961796190227e-246
1.0545287641463871e-247
8
-5.3591540899030606e+132
-7.727081080122102e+128
-5.005006561769842e+132

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03922
13922

end0.0ms

sample1.0s

Algorithm
intervals
Results
195.0ms1090×body2560valid
180.0ms5869×body80valid
129.0ms859×body1280valid
79.0ms2802×body80nan
55.0ms457×body640valid
30.0ms120×body5120valid
19.0ms231×body320valid
6.0ms110×body160valid