Details

Time bar (total: 4.9s)

sample38.0ms

Algorithm
intervals
Results
7.0ms40×body2560valid
6.0ms187×body80valid
5.0ms31×body1280valid
3.0ms96×body80nan
2.0ms8×body5120valid
1.0ms9×body640valid
1.0ms6×body320valid
0.0ms3×body160valid

simplify9.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0187
1327
2417
3447
4447

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b
(- (* b_2 b_2) (* a c))
0.9b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
28.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite101.0ms

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:
60.0ms
(/ (- (- 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))))
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series230.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
30.0ms
(- (* b_2 b_2) (* a c))
65.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
57.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify41.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0368965
11241910
25001901

prune242.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.4b

localize11.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.6b
(/ (/ (+ 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))
28.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite208.0ms

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:
41.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
92.0ms
(/ (/ (+ 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))
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series437.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
143.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
173.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
53.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify102.0ms

Algorithm
egg-herbie
Counts
199 → 199
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
07302960
132002803
250012783

prune485.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.3b

localize13.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.1b
(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
3.6b
(/ (* 1 (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))) a)
28.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite136.0ms

Algorithm
rewrite-expression-head
Rules
141×times-frac
123×add-sqr-sqrt
96×*-un-lft-identity
70×add-cube-cbrt
32×add-exp-log
26×difference-of-squares
25×associate-/r*
23×add-cbrt-cube
16×div-exp sqrt-prod
13×distribute-lft-out--
10×cbrt-undiv
6×prod-exp div-inv add-log-exp
5×pow1
4×associate-/l*
3×1-exp cbrt-unprod
2×flip3-- frac-2neg sqrt-div clear-num flip--
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-*r/ associate-/r/ associate-/l/
Counts
4 → 165
Calls
4 calls:
40.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
42.0ms
(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
37.0ms
(/ (* 1 (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))) a)
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series399.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
155.0ms
(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
120.0ms
(/ (* 1 (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))) a)
57.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify90.0ms

Algorithm
egg-herbie
Counts
177 → 177
Iterations

Useful iterations: 2 (71.0ms)

IterNodesCost
08032218
136682058
250012035

prune406.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 1 (/ (* 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) c))
0.8b
(- (* b_2 b_2) (* a c))
1.4b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
28.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
33×times-frac
32×add-exp-log
26×add-sqr-sqrt
23×*-un-lft-identity
21×add-cube-cbrt
17×div-exp
13×add-cbrt-cube
8×add-log-exp
7×1-exp associate-/r*
6×pow1 prod-exp
5×cbrt-undiv div-inv
4×rec-exp sqrt-prod
3×flip3-- flip-- associate-/l*
2×sub-neg sqrt-div diff-log difference-of-squares
1×rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 clear-num associate-/r/ cbrt-unprod distribute-lft-out-- inv-pow
Counts
4 → 101
Calls
4 calls:
44.0ms
(/ 1 (/ (* 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) c))
8.0ms
(- (* b_2 b_2) (* a c))
43.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series241.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(/ 1 (/ (* 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) c))
34.0ms
(- (* b_2 b_2) (* a c))
61.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
57.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify55.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
05041009
11998871
25001827

prune182.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 8.3b

regimes194.0ms

Accuracy

95.2% (1.2b remaining)

Error of 6.7b against oracle of 5.6b and baseline of 29.8b

bsearch87.0ms

Steps
ItersRangePoint
6
4.231934083523606e+52
2.717919616353272e+53
1.0271211196326774e+53
3
2.62163126713661e-290
3.6876397702511455e-290
3.354512113027853e-290
8
-4.3398659734944224e+136
-1.0492990687338703e+133
-7.056049990712678e+135

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04122
14322
24322

end0.0ms

sample1.0s

Algorithm
intervals
Results
192.0ms1050×body2560valid
191.0ms5881×body80valid
139.0ms923×body1280valid
84.0ms2795×body80nan
49.0ms425×body640valid
28.0ms111×body5120valid
20.0ms232×body320valid
6.0ms102×body160valid