Details

Time bar (total: 17.7s)

sample36.0ms

Algorithm
intervals
Results
7.0ms40×body2560valid
6.0ms196×body80valid
3.0ms20×body1280valid
3.0ms94×body80nan
2.0ms14×body640valid
1.0ms7×body320valid
0.0ms4×body160valid

simplify8.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0187
1327
2417
3447
4447

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.0b
(- (* b_2 b_2) (* a c))
1.2b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite104.0ms

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:
62.0ms
(/ (- (- 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)))

series262.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
35.0ms
(- (* b_2 b_2) (* a c))
73.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
65.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify116.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0368965
11213910
24761899
35002899

prune228.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.2b

localize10.0ms

Local error

Found 4 expressions with local error:

1.8b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.3b
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
12.1b
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
23.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite212.0ms

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:
42.0ms
(- (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))
12.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series493.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
158.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
194.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
66.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify100.0ms

Algorithm
egg-herbie
Counts
199 → 199
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
07302960
132002803
250012783

prune456.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.2b

localize13.0ms

Local error

Found 4 expressions with local error:

3.3b
(/ (/ (/ a (/ (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) c)) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
4.7b
(/ (/ a (/ (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) c)) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
23.7b
(sqrt (- (* b_2 b_2) (* a c)))
23.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
15078×times-frac
9183×add-sqr-sqrt
7371×*-un-lft-identity
6341×sqrt-prod
5561×add-cube-cbrt
1810×difference-of-squares
986×associate-/l*
905×distribute-lft-out--
190×div-inv
56×associate-/r/
27×add-exp-log add-cbrt-cube
16×cbrt-undiv div-exp
14×sqrt-div
12×associate-/r*
7×flip3-- flip--
6×pow1
4×add-log-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/l/
Counts
4 → 4612
Calls
4 calls:
349.0ms
(/ (/ (/ a (/ (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) c)) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
136.0ms
(/ (/ a (/ (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) c)) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))
11.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series453.0ms

Counts
4 → 12
Calls
4 calls:
145.0ms
(/ (/ (/ a (/ (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) c)) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
173.0ms
(/ (/ a (/ (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) c)) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
64.0ms
(sqrt (- (* b_2 b_2) (* a c)))
70.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.2s

Algorithm
egg-herbie
Counts
4624 → 4624
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
05001157496

prune10.7s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.2b

localize19.0ms

Local error

Found 4 expressions with local error:

16.0b
(cbrt (+ 0 (* a c)))
23.7b
(sqrt (- (* b_2 b_2) (* a c)))
23.7b
(sqrt (- (* b_2 b_2) (* a c)))
23.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×sqrt-prod
8×add-cube-cbrt *-un-lft-identity
7×pow1
6×sqrt-div
4×add-exp-log add-cbrt-cube add-log-exp
3×cbrt-prod rem-sqrt-square flip3-- sqrt-pow1 pow1/2 flip--
2×cbrt-div
1×flip3-+ pow1/3 flip-+
Counts
4 → 58
Calls
4 calls:
3.0ms
(cbrt (+ 0 (* a c)))
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series270.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(cbrt (+ 0 (* a c)))
62.0ms
(sqrt (- (* b_2 b_2) (* a c)))
67.0ms
(sqrt (- (* b_2 b_2) (* a c)))
67.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify43.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0226451
1823429
25002413

prune301.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 5.2b

regimes221.0ms

Accuracy

87.7% (3.3b remaining)

Error of 8.9b against oracle of 5.5b and baseline of 32.7b

bsearch134.0ms

Steps
ItersRangePoint
8
3.1248942757642245e+89
1.1714167766929137e+92
1.4947314724287081e+91
9
3.272370062612402e-294
2.4969690101927593e-289
1.0711388394770918e-291
8
-5.116786127313355e+101
-2.116985814268752e+98
-1.2900385447307874e+100

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04331
14331

end0.0ms

sample1.1s

Algorithm
intervals
Results
196.0ms1043×body2560valid
195.0ms5856×body80valid
140.0ms915×body1280valid
97.0ms2942×body80nan
55.0ms475×body640valid
23.0ms257×body320valid
22.0ms97×body5120valid
6.0ms96×body160valid