Details

Time bar (total: 3.8s)

analyze270.0ms

Algorithm
search

sample45.0ms

Algorithm
intervals
Results
18.0ms160×body160valid
8.0ms279×pre80true
4.0ms31×body320valid
3.0ms65×body80valid
1.0ms23×body80nan

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 42.2b

Counts
2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.2b
(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
39.2b
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
8×add-sqr-sqrt
7×add-cube-cbrt
6×distribute-lft-out
5×pow1 times-frac associate-/l*
3×distribute-rgt-neg-in sqrt-prod
2×cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
1×+-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:
3.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
3.0ms
(- (* b b) (* (* 4.0 a) c))
11.0ms
(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
7.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series64.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
8.0ms
(- (* b b) (* (* 4.0 a) c))
27.0ms
(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
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

prune131.0ms

Filtered
63 candidates to 82 candidates (-30.2%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New77582
Fresh000
Picked101
Done000
Total78583

Merged error: 0.3b

Counts
83 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ (/ (+ 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)))))

rewrite45.0ms

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
8×associate-/r*
7×cbrt-undiv div-exp
6×associate-/r/
5×flip3-- flip--
4×pow1 div-inv
3×diff-log associate-/l/
2×sub-neg frac-2neg prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 flip3-+ neg-log flip-+
Counts
4 → 151
Calls
4 calls:
8.0ms
(- (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)))))

series133.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms
(- (* b b) (* (* 4.0 a) c))
50.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
60.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify113.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (91.0ms)

IterNodesCost
06432667
132102408
250012396

prune312.0ms

Filtered
106 candidates to 163 candidates (-53.8%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New15211163
Fresh224
Picked101
Done000
Total15513168

Merged error: 0.0b

Counts
168 → 13

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(* a (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.1b
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.4b
(/ (* 4.0 (* a c)) (* a (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
27×add-exp-log add-cbrt-cube
16×add-sqr-sqrt
14×*-un-lft-identity
10×prod-exp cbrt-unprod add-log-exp
7×associate-*r*
6×pow1 cbrt-undiv add-cube-cbrt div-exp
4×sub-neg flip3-- associate-*r/ flip-- distribute-lft-out-- difference-of-squares
3×diff-log associate-*l*
2×distribute-rgt-in distribute-rgt-neg-in distribute-lft-in sqrt-prod associate-/r/
1×associate--l- neg-sub0 frac-2neg times-frac pow-prod-down neg-log clear-num associate-/r* *-commutative div-inv associate-/l* unswap-sqr
Counts
4 → 85
Calls
4 calls:
10.0ms
(* a (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
8.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
15.0ms
(/ (* 4.0 (* a c)) (* a (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series95.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(* a (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
15.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0ms
(- (* b b) (* (* 4.0 a) c))
42.0ms
(/ (* 4.0 (* a c)) (* a (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify88.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
05181106
13294871
25002864

prune159.0ms

Filtered
62 candidates to 97 candidates (-56.5%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New94397
Fresh4812
Picked011
Done000
Total9812110

Merged error: 0b

Counts
110 → 12

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ (* -1 (* a b)) (* a (neg (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.2b
(* a (neg (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.4b
(/ (* 4.0 (* a c)) (+ (* -1 (* a b)) (* a (neg (sqrt (- (* b b) (* (* 4.0 a) c)))))))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
16×associate-*r*
15×add-exp-log add-cbrt-cube
14×add-sqr-sqrt
12×add-cube-cbrt *-un-lft-identity
8×add-log-exp
6×pow1 distribute-lft-neg-in distribute-rgt-neg-in sqrt-prod
4×prod-exp distribute-rgt-neg-out cbrt-unprod
3×cbrt-undiv times-frac div-exp associate-*l* associate-/r*
2×flip3-- flip3-+ sqrt-div associate-*r/ associate-/r/ flip-- flip-+ distribute-neg-frac
1×+-commutative neg-mul-1 sub-neg distribute-neg-out frac-2neg mul-1-neg diff-log unsub-neg pow-prod-down clear-num sum-log *-commutative div-inv associate-/l* unswap-sqr
Counts
4 → 85
Calls
4 calls:
5.0ms
(+ (* -1 (* a b)) (* a (neg (sqrt (- (* b b) (* (* 4.0 a) c))))))
8.0ms
(* a (neg (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms
(- (* b b) (* (* 4.0 a) c))
9.0ms
(/ (* 4.0 (* a c)) (+ (* -1 (* a b)) (* a (neg (sqrt (- (* b b) (* (* 4.0 a) c)))))))

series119.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(+ (* -1 (* a b)) (* a (neg (sqrt (- (* b b) (* (* 4.0 a) c))))))
20.0ms
(* a (neg (sqrt (- (* b b) (* (* 4.0 a) c)))))
8.0ms
(- (* b b) (* (* 4.0 a) c))
67.0ms
(/ (* 4.0 (* a c)) (+ (* -1 (* a b)) (* a (neg (sqrt (- (* b b) (* (* 4.0 a) c)))))))

simplify81.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
05241116
12722928
25001909

prune142.0ms

Filtered
72 candidates to 97 candidates (-34.7%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New96197
Fresh2810
Picked011
Done101
Total9910109

Merged error: 0b

Counts
109 → 10

regimes220.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03213
13813
23813

end0.0ms

analyze262.0ms

Algorithm
search

sample1.3s

Algorithm
intervals
Results
490.0ms4841×body160valid
258.0ms8906×pre80true
191.0ms1305×body320valid
95.0ms1854×body80valid
44.0ms906×body80nan

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