Details

Time bar (total: 5.5s)

sample42.0ms

Algorithm
intervals
Results
8.0ms192×body80valid
7.0ms33×body2560valid
5.0ms26×body1280valid
4.0ms113×body80nan
1.0ms10×body640valid
1.0ms4×body5120valid
1.0ms9×body320valid
1.0ms7×body160valid

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0289
1649
21149
31359
41449
51489
61489

prune3.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 34.4b

Counts
2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.4b
(- (* b b) (* 4.0 (* a c)))
2.0b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.9b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite135.0ms

Algorithm
rewrite-expression-head
Rules
205×add-sqr-sqrt
114×*-un-lft-identity
84×times-frac
58×difference-of-squares
44×unswap-sqr
42×add-cube-cbrt
36×sqrt-prod distribute-lft-out--
32×associate-*l*
24×associate-*r*
14×distribute-rgt-neg-in *-commutative
12×associate-/r*
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×associate-/l*
6×swap-sqr
5×pow1
4×flip3-- flip--
3×diff-log
2×cbrt-undiv associate--l- neg-sub0 sub-neg sqrt-div div-sub div-exp associate-/l/
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 neg-log prod-exp clear-num cbrt-unprod div-inv
Counts
4 → 204
Calls
4 calls:
44.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
22.0ms
(- (* b b) (* 4.0 (* a c)))
34.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
26.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series311.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
51.0ms
(- (* b b) (* 4.0 (* a c)))
82.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
79.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify82.0ms

Algorithm
egg-herbie
Counts
216 → 216
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
07282859
127642769
250012764

prune562.0ms

Filtered
216 candidates to 120 candidates (44.4%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New2088216
Fresh000
Picked101
Done000
Total2098217

Merged error: 5.0b

Counts
217 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a)
0.4b
(- (* b b) (* 4.0 (* a c)))
2.0b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.9b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite127.0ms

Algorithm
rewrite-expression-head
Rules
128×add-sqr-sqrt
53×*-un-lft-identity
40×difference-of-squares
36×unswap-sqr
27×sqrt-prod
21×times-frac
18×distribute-lft-out--
17×add-cube-cbrt
10×add-log-exp
8×associate-*l*
7×associate-/l*
6×add-exp-log swap-sqr *-commutative add-cbrt-cube
5×pow1 distribute-rgt-neg-in
4×flip3-- flip--
3×diff-log associate-/r*
2×associate--l- neg-sub0 sub-neg sqrt-div div-sub associate-/l/
1×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp neg-log clear-num div-inv
Counts
4 → 130
Calls
4 calls:
37.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a)
24.0ms
(- (* b b) (* 4.0 (* a c)))
34.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
25.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series298.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a)
49.0ms
(- (* b b) (* 4.0 (* a c)))
79.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
75.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify55.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
04491499
114971433
250011420

prune232.0ms

Filtered
142 candidates to 85 candidates (40.1%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1375142
Fresh527
Picked011
Done000
Total1428150

Merged error: 5.0b

Counts
150 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ a (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.4b
(- (* b b) (* 4.0 (* a c)))
2.0b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.9b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite140.0ms

Algorithm
rewrite-expression-head
Rules
226×add-sqr-sqrt
165×times-frac
152×*-un-lft-identity
79×add-cube-cbrt
58×difference-of-squares
36×sqrt-prod distribute-lft-out-- unswap-sqr
34×associate-/r*
21×associate-/r/
15×add-exp-log
14×distribute-rgt-neg-in
10×add-log-exp
9×add-cbrt-cube
8×associate-*l*
7×flip3-- div-exp flip-- associate-/l*
6×pow1 swap-sqr *-commutative
5×div-inv
3×cbrt-undiv diff-log clear-num
2×sub-neg rec-exp frac-2neg sqrt-div 1-exp remove-double-div
1×associate--l- neg-sub0 rem-sqrt-square pow-flip sqrt-pow1 pow1/2 neg-log inv-pow
Counts
4 → 229
Calls
4 calls:
46.0ms
(/ 1 (/ a (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
22.0ms
(- (* b b) (* 4.0 (* a c)))
36.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series322.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(/ 1 (/ a (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
47.0ms
(- (* b b) (* 4.0 (* a c)))
82.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
77.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify92.0ms

Algorithm
egg-herbie
Counts
241 → 241
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
06763178
130742922
250022772

prune297.0ms

Filtered
241 candidates to 103 candidates (57.3%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2383241
Fresh246
Picked101
Done011
Total2418249

Merged error: 5.0b

Counts
249 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

1.8b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
5.6b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) a)
8.8b
(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
22.9b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite166.0ms

Algorithm
rewrite-expression-head
Rules
297×*-un-lft-identity
263×add-sqr-sqrt
258×times-frac
105×add-cube-cbrt
71×difference-of-squares
64×distribute-lft-out
50×sqrt-prod
46×associate-/l*
36×associate-*l*
32×distribute-lft-out--
20×associate-/l/
18×unswap-sqr
15×associate-/r*
11×add-exp-log add-cbrt-cube
10×associate-/r/
7×flip3-- flip--
6×div-inv add-log-exp
5×pow1
4×cbrt-undiv div-exp
3×frac-2neg swap-sqr clear-num *-commutative
2×flip3-+ sqrt-div flip-+
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
Counts
4 → 283
Calls
4 calls:
32.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
49.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) a)
43.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
23.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series555.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
175.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) a)
218.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
77.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify135.0ms

Algorithm
egg-herbie
Counts
295 → 295
Iterations

Useful iterations: 2 (93.0ms)

IterNodesCost
08224969
136524715
250024692

prune455.0ms

Filtered
295 candidates to 163 candidates (44.7%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New2932295
Fresh156
Picked011
Done011
Total2949303

Merged error: 5.0b

Counts
303 → 9

regimes221.0ms

Accuracy

85.1% (4.3b remaining)

Error of 9.8b against oracle of 5.5b and baseline of 34.3b

bsearch60.0ms

Steps
ItersRangePoint
0
1.3836563058951246e+50
1.390978468581987e+50
1.3873173872385558e+50
9
-2.816841330355383e-75
-7.368877589091801e-81
-1.0996442222619662e-75

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03216
13216

end0.0ms

sample1.2s

Algorithm
intervals
Results
265.0ms1103×body2560valid
233.0ms5872×body80valid
167.0ms890×body1280valid
107.0ms2796×body80nan
73.0ms453×body640valid
31.0ms102×body5120valid
26.0ms231×body320valid
9.0ms116×body160valid