Details

Time bar (total: 8.8s)

sample288.0ms

Algorithm
intervals
Results
8.0ms39×body2560valid
6.0ms191×body80valid
4.0ms82×body80nan
3.0ms19×body1280valid
2.0ms16×body640valid
1.0ms8×body320valid
0.0ms2×body5120valid
0.0ms2×body160valid

simplify16.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0187
1327
2417
3447
4447

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 29.8b

Counts
2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.2b
(- (* b_2 b_2) (* a c))
0.9b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
19.8b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
88×add-sqr-sqrt
53×*-un-lft-identity
30×difference-of-squares
22×sqrt-prod
21×times-frac
18×distribute-lft-out--
17×add-cube-cbrt
14×unswap-sqr
10×add-log-exp
8×associate-*l*
7×associate-/l*
6×add-exp-log add-cbrt-cube
5×pow1 distribute-rgt-neg-in
4×flip3-- swap-sqr *-commutative 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 → 120
Calls
4 calls:
29.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
15.0ms
(- (* b_2 b_2) (* a c))
38.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
17.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series272.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
34.0ms
(- (* b_2 b_2) (* a c))
75.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
74.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify51.0ms

Algorithm
egg-herbie
Counts
132 → 132
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
04091177
113581122
250021109

prune209.0ms

Filtered
132 candidates to 81 candidates (61.4%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1257132
Fresh000
Picked011
Done000
Total1258133

Merged error: 4.4b

Counts
133 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.0b
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
9.5b
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
19.8b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite125.0ms

Algorithm
rewrite-expression-head
Rules
297×*-un-lft-identity
258×times-frac
243×add-sqr-sqrt
105×add-cube-cbrt
66×difference-of-squares
64×distribute-lft-out
46×associate-/l*
45×sqrt-prod
36×associate-*l*
32×distribute-lft-out--
20×associate-/l/
15×associate-/r*
11×add-exp-log add-cbrt-cube
10×associate-/r/
7×flip3-- flip-- unswap-sqr
6×div-inv add-log-exp
5×pow1
4×cbrt-undiv div-exp
3×frac-2neg clear-num
2×flip3-+ sqrt-div swap-sqr *-commutative flip-+
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
Counts
4 → 278
Calls
4 calls:
21.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
40.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
30.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
15.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series501.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
161.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
199.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
66.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify126.0ms

Algorithm
egg-herbie
Counts
290 → 290
Iterations

Useful iterations: 2 (90.0ms)

IterNodesCost
07894143
134343915
250023895

prune398.0ms

Filtered
290 candidates to 161 candidates (55.5%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New2873290
Fresh246
Picked101
Done101
Total2917298

Merged error: 4.3b

Counts
298 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.0b
(/ (* (+ 0 (* a c)) (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
9.5b
(* (+ 0 (* a c)) (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
19.8b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite151.0ms

Algorithm
rewrite-expression-head
Rules
263×add-sqr-sqrt
211×times-frac
193×*-un-lft-identity
120×associate-*r*
114×add-cube-cbrt
57×associate-/l*
54×difference-of-squares
48×frac-times
41×associate-/l/
39×associate-/r* sqrt-prod
34×associate-*l*
28×add-exp-log
26×flip3-+ flip-+ distribute-lft-out--
24×associate-*r/
22×unswap-sqr
18×add-cbrt-cube
10×associate-/r/ distribute-lft-out
9×div-exp clear-num
8×prod-exp
7×pow1 flip3-- frac-2neg *-commutative flip--
6×un-div-inv div-inv add-log-exp
5×cbrt-undiv
4×associate-*l/ cbrt-unprod
2×rec-exp sqrt-div 1-exp swap-sqr
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log pow-prod-down
Counts
4 → 342
Calls
4 calls:
21.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
50.0ms
(/ (* (+ 0 (* a c)) (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
38.0ms
(* (+ 0 (* a c)) (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
15.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series501.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
162.0ms
(/ (* (+ 0 (* a c)) (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
200.0ms
(* (+ 0 (* a c)) (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
62.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify74.0ms

Algorithm
egg-herbie
Counts
354 → 354
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
012634615
150014245

prune537.0ms

Filtered
354 candidates to 211 candidates (59.6%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New3540354
Fresh066
Picked011
Done000
Total3547361

Merged error: 4.3b

Counts
361 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.0b
(/ (/ 1 (/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)) a)
2.0b
(/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)
19.8b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite322.0ms

Algorithm
rewrite-expression-head
Rules
3378×times-frac
1967×add-sqr-sqrt
1655×*-un-lft-identity
1353×add-cube-cbrt
399×associate-/l*
304×difference-of-squares
168×associate-/r/
164×sqrt-prod
156×associate-/l/
151×distribute-lft-out--
103×associate-/r*
66×div-inv
41×add-exp-log
28×div-exp
23×add-cbrt-cube
13×cbrt-undiv
12×frac-2neg clear-num
7×flip3-- flip-- unswap-sqr
6×add-log-exp
5×pow1
4×associate-*l*
3×rec-exp 1-exp
2×sqrt-div div-sub swap-sqr *-commutative
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
Counts
4 → 1291
Calls
4 calls:
27.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
93.0ms
(/ (/ 1 (/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)) a)
33.0ms
(/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)
15.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series353.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
102.0ms
(/ (/ 1 (/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)) a)
107.0ms
(/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)
69.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify242.0ms

Algorithm
egg-herbie
Counts
1303 → 1303
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
0500124461

prune3.1s

Filtered
1303 candidates to 906 candidates (69.5%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New130301303
Fresh055
Picked011
Done011
Total130371310

Merged error: 4.3b

Counts
1310 → 7

regimes180.0ms

Accuracy

88.3% (3.1b remaining)

Error of 8.9b against oracle of 5.8b and baseline of 32.0b

bsearch128.0ms

Steps
ItersRangePoint
7
8.175350185103435e+71
1.3253879264775672e+74
1.2930490387792999e+74
10
5.8218956722497675e-180
2.5852304699661686e-169
8.336053356425346e-180
6
-221896.37464641608
-35733.850999515795
-113859.44661823702

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04124
14124

end0.0ms

sample1.0s

Algorithm
intervals
Results
221.0ms1069×body2560valid
196.0ms5865×body80valid
151.0ms907×body1280valid
96.0ms2978×body80nan
55.0ms413×body640valid
23.0ms94×body5120valid
23.0ms239×body320valid
7.0ms117×body160valid