Details

Time bar (total: 4.5s)

sample40.0ms

Algorithm
intervals
Results
9.0ms34×body2560valid
6.0ms187×body80valid
4.0ms29×body1280valid
3.0ms99×body80nan
2.0ms16×body640valid
2.0ms7×body5120valid
1.0ms7×body320valid
0.0ms2×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: 32.7b

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.5b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.6b
(- (* b_2 b_2) (* a c))
20.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite107.0ms

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)
22.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
8.0ms
(- (* b_2 b_2) (* a c))
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series253.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
73.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
34.0ms
(- (* b_2 b_2) (* a c))
61.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify39.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0368965
11241910
25001901

prune242.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.5b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.6b
(- (* b_2 b_2) (* a c))
20.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite97.0ms

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:
49.0ms
(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
23.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
8.0ms
(- (* b_2 b_2) (* a c))
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series277.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
73.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
34.0ms
(- (* b_2 b_2) (* a c))
64.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify69.0ms

Algorithm
egg-herbie
Counts
189 → 189
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
05912458
127062226
250012071

prune278.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sqrt 1) (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.5b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.6b
(- (* b_2 b_2) (* a c))
20.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
309×times-frac
227×add-sqr-sqrt
226×*-un-lft-identity
138×add-cube-cbrt
109×sqrt-prod
44×distribute-lft-out-- difference-of-squares
27×associate-/r*
22×distribute-rgt-neg-in
15×associate-/r/
10×flip3-- flip-- add-log-exp
9×add-exp-log add-cbrt-cube
8×div-inv
6×associate-/l*
5×pow1
3×cbrt-undiv diff-log div-exp
2×sub-neg sqrt-div
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 neg-log clear-num
Counts
4 → 255
Calls
4 calls:
49.0ms
(/ (sqrt 1) (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
23.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
11.0ms
(- (* b_2 b_2) (* a c))
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series279.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(/ (sqrt 1) (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
74.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
34.0ms
(- (* b_2 b_2) (* a c))
66.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify84.0ms

Algorithm
egg-herbie
Counts
267 → 267
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
07064393
133593820
250013457

prune484.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.9b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* b_2 b_2) (* a c))) a)
0.6b
(- (* b_2 b_2) (* a c))
7.2b
(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
20.6b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
38×*-un-lft-identity
37×times-frac
24×add-cube-cbrt
17×sqrt-prod
8×add-log-exp
7×distribute-lft-out--
6×add-exp-log add-cbrt-cube associate-/l* difference-of-squares
5×pow1
4×flip3-- sqrt-div flip--
3×distribute-rgt-neg-in associate-/r* div-inv
2×sub-neg diff-log associate-/l/
1×cbrt-undiv associate--l- neg-sub0 rem-sqrt-square distribute-rgt-out-- frac-2neg sqrt-pow1 pow1/2 div-sub div-exp clear-num frac-sub sub-div
Counts
4 → 97
Calls
4 calls:
17.0ms
(/ (sqrt (- (* b_2 b_2) (* a c))) a)
8.0ms
(- (* b_2 b_2) (* a c))
70.0ms
(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
11.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series283.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(/ (sqrt (- (* b_2 b_2) (* a c))) a)
34.0ms
(- (* b_2 b_2) (* a c))
85.0ms
(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
63.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify131.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
03921006
11202962
24466947
35001947

prune226.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.9b

regimes220.0ms

Accuracy

88.8% (3.2b remaining)

Error of 8.5b against oracle of 5.3b and baseline of 33.7b

bsearch131.0ms

Steps
ItersRangePoint
7
2.5938763934072053e+128
9.952100372240566e+129
5.3798698575955895e+128
9
-2.600157470066103e-290
-1.3231854596579914e-298
-2.1982985618064027e-291
9
-1.2811458506798908e+27
-4.2272303889279916e+20
-3.1202666053494416e+25

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04729
14929
24929

end0.0ms

sample1.0s

Algorithm
intervals
Results
181.0ms5788×body80valid
181.0ms1040×body2560valid
127.0ms916×body1280valid
87.0ms2947×body80nan
53.0ms434×body640valid
29.0ms125×body5120valid
21.0ms256×body320valid
11.0ms148×body160valid