Details

Time bar (total: 3.9s)

analyze263.0ms

Algorithm
search

sample41.0ms

Algorithm
intervals
Results
15.0ms138×body160valid
8.0ms289×pre80true
6.0ms118×body80valid
2.0ms33×body80nan

simplify9.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 26.8b

Counts
2 → 1

localize12.0ms

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))
26.6b
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite27.0ms

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))))

series65.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
8.0ms
(- (* b b) (* (* 4.0 a) c))
25.0ms
(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
18.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify44.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0396773
11550683
25001673

prune118.0ms

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

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New79382
Fresh000
Picked011
Done000
Total79483

Merged error: 0.3b

Counts
83 → 4

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* b b) (* (* 4.0 a) c))
0.2b
(- (neg b) (sqrt (- (* 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))
0.4b
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite46.0ms

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:
4.0ms
(- (* b b) (* (* 4.0 a) c))
8.0ms
(- (neg b) (sqrt (- (* 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)))))

series126.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(- (* b b) (* (* 4.0 a) c))
17.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
42.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
59.0ms
(/ (+ 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 (90.0ms)

IterNodesCost
06432666
132102408
250012396

prune313.0ms

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

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New15310163
Fresh202
Picked101
Done101
Total15710167

Merged error: 0.0b

Counts
167 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* b b) (* (* 4.0 a) c))
0.2b
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.4b
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.4b
(* (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
66×add-sqr-sqrt
61×*-un-lft-identity
51×add-exp-log
46×times-frac
29×add-cube-cbrt
27×associate-*l* add-cbrt-cube
20×prod-exp
16×div-exp distribute-lft-out-- difference-of-squares
10×add-log-exp
8×cbrt-undiv distribute-rgt-neg-in sqrt-prod cbrt-unprod
7×associate-*r* associate-/r*
6×pow1
4×rec-exp flip3-- 1-exp associate-/r/ flip--
3×diff-log div-inv associate-/l*
2×sub-neg associate-/l/ unswap-sqr
1×associate--l- neg-sub0 frac-times frac-2neg flip3-+ associate-*r/ pow-prod-down neg-log associate-*l/ clear-num un-div-inv *-commutative flip-+
Counts
4 → 146
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
8.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
13.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
19.0ms
(* (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))

series125.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(- (* b b) (* (* 4.0 a) c))
15.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
59.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
43.0ms
(* (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))

simplify143.0ms

Algorithm
egg-herbie
Counts
158 → 158
Iterations

Useful iterations: 2 (120.0ms)

IterNodesCost
07362389
139832051
250022044

prune274.0ms

Filtered
100 candidates to 158 candidates (-58.0%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1562158
Fresh189
Picked011
Done000
Total15711168

Merged error: 0b

Counts
168 → 11

localize15.0ms

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

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
48×add-sqr-sqrt
47×*-un-lft-identity
43×times-frac
33×add-exp-log add-cbrt-cube
19×add-cube-cbrt
14×distribute-lft-out-- difference-of-squares
13×cbrt-undiv div-exp
10×sqrt-prod add-log-exp
9×prod-exp cbrt-unprod div-inv
7×distribute-rgt-neg-in associate-/r*
5×pow1 associate-/l*
4×flip3-- flip--
3×diff-log
2×sub-neg sqrt-div associate-/r/
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 neg-log clear-num associate-/l/
Counts
4 → 119
Calls
4 calls:
3.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
3.0ms
(- (* b b) (* (* 4.0 a) c))
8.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
15.0ms
(/ (/ (* 4.0 (* a c)) (* 2.0 a)) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series83.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(- (* b b) (* (* 4.0 a) c))
16.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms
(/ (/ (* 4.0 (* a c)) (* 2.0 a)) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify111.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 2 (92.0ms)

IterNodesCost
06631963
141431725
250011724

prune168.0ms

Filtered
80 candidates to 131 candidates (-63.8%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New1301131
Fresh189
Picked011
Done011
Total13111142

Merged error: 0b

Counts
142 → 11

regimes246.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02212
12212

end0.0ms

analyze260.0ms

Algorithm
search

sample1.2s

Algorithm
intervals
Results
559.0ms4418×body160valid
256.0ms8845×pre80true
178.0ms3582×body80valid
43.0ms845×body80nan

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