Details

Time bar (total: 44.8s)

sample78.0ms

Algorithm
intervals
Results
19.0ms541×pre80true
14.0ms285×body80nan
13.0ms142×body160valid
6.0ms41×body320valid
3.0ms73×body80valid

simplify9.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059

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: 40.8b

Counts
2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.2b
(- (* b b) (* (* 4.0 a) c))
36.4b
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
10×add-log-exp
add-exp-log add-cbrt-cube
add-sqr-sqrt
add-cube-cbrt
distribute-lft-out
pow1 times-frac associate-/l*
distribute-rgt-neg-in sqrt-prod
cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
+-commutative sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 70
Calls
4 calls:
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms
(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
3.0ms
(- (* b b) (* (* 4.0 a) c))
7.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series61.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
25.0ms
(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms
(- (* b b) (* (* 4.0 a) c))
15.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify44.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0396773
11550683
25001673

prune127.0ms

Filtered
82 candidates to 63 candidates (23.2%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New77582
Fresh000
Picked101
Done000
Total78583

Merged error: 0.2b

Counts
83 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.2b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.3b
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
82×add-sqr-sqrt *-un-lft-identity
38×add-cube-cbrt
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
11×distribute-rgt-neg-in sqrt-prod
10×add-log-exp
associate-/r*
cbrt-undiv div-exp
associate-/r/
flip3-- flip--
pow1 div-inv
diff-log associate-/l/
sub-neg frac-2neg prod-exp clear-num cbrt-unprod
associate--l- neg-sub0 flip3-+ neg-log flip-+
Counts
4 → 151
Calls
4 calls:
10.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
16.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
12.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series124.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms
(- (* b b) (* (* 4.0 a) c))
45.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
56.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify112.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (89.0ms)

IterNodesCost
06432666
132102408
250012396

prune295.0ms

Filtered
163 candidates to 106 candidates (35.0%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New15310163
Fresh314
Picked101
Done000
Total15711168

Merged error: 0b

Counts
168 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* b b) (* (* 4.0 a) c))
0.2b
(/ (* 2.0 a) (* 4.0 (* a c)))
0.2b
(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.3b
(* (/ (* 2.0 a) (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
152×add-exp-log
92×add-cbrt-cube
73×prod-exp
46×div-exp
41×cbrt-unprod
26×cbrt-undiv
14×add-sqr-sqrt
12×*-un-lft-identity
pow1
add-cube-cbrt rec-exp 1-exp
associate-*r*
add-log-exp
flip3-- times-frac associate-*l* associate-/r/ flip--
frac-times associate-*r/ associate-/l*
sub-neg div-inv
distribute-rgt-in pow-flip frac-2neg distribute-lft-in pow-prod-down associate-*l/ clear-num associate-/r* distribute-lft-out-- difference-of-squares
distribute-rgt-neg-in diff-log sqrt-prod *-commutative inv-pow unswap-sqr
Counts
4 → 139
Calls
4 calls:
4.0ms
(- (* b b) (* (* 4.0 a) c))
7.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
16.0ms
(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
17.0ms
(* (/ (* 2.0 a) (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series82.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(- (* b b) (* (* 4.0 a) c))
2.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
46.0ms
(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
25.0ms
(* (/ (* 2.0 a) (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify38.0ms

Algorithm
egg-herbie
Counts
151 → 151
Iterations

Useful iterations: 1 (21.0ms)

IterNodesCost
08162130
150011586

prune167.0ms

Filtered
151 candidates to 72 candidates (52.3%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1474151
Fresh6410
Picked101
Done000
Total1548162

Merged error: 0b

Counts
162 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (/ 1 (/ 2.0 4.0)) (/ 1 c)) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.2b
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b
(/ (/ 1 (/ 2.0 4.0)) (/ 1 c))
0.2b
(- (* b b) (* (* 4.0 a) c))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
20548×times-frac
9815×add-sqr-sqrt *-un-lft-identity
7499×add-cube-cbrt
1158×distribute-lft-out-- difference-of-squares
879×div-inv
621×associate-/l*
579×distribute-rgt-neg-in sqrt-prod
200×add-exp-log
169×div-exp
129×associate-/r/
54×add-cbrt-cube
37×cbrt-undiv
30×rec-exp 1-exp
20×associate-/r*
10×add-log-exp
pow1
flip3-- diff-log flip--
sub-neg frac-2neg clear-num associate-/l/
associate--l- neg-sub0 neg-log
Counts
4 → 5377
Calls
4 calls:
166.0ms
(/ (/ (/ 1 (/ 2.0 4.0)) (/ 1 c)) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
10.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.0ms
(/ (/ 1 (/ 2.0 4.0)) (/ 1 c))
3.0ms
(- (* b b) (* (* 4.0 a) c))

series77.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(/ (/ (/ 1 (/ 2.0 4.0)) (/ 1 c)) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
15.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.0ms
(/ (/ 1 (/ 2.0 4.0)) (/ 1 c))
9.0ms
(- (* b b) (* (* 4.0 a) c))

simplify1.3s

Algorithm
egg-herbie
Counts
5389 → 5389
Iterations

Useful iterations: 0 (68.0ms)

IterNodesCost
05494146352

prune38.7s

Filtered
5389 candidates to 2863 candidates (46.9%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New538815389
Fresh167
Picked101
Done000
Total539075397

Merged error: 0b

Counts
5397 → 7

regimes182.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0179
1179

end0.0ms

sample2.2s

Algorithm
intervals
Results
468.0ms4839×body160valid
460.0ms16519×pre80true
404.0ms8519×body80nan
194.0ms1327×body320valid
89.0ms1834×body80valid

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