Details

Time bar (total: 3.8s)

analyze276.0ms

Algorithm
search

sample49.0ms

Algorithm
intervals
Results
17.0ms123×body320valid
9.0ms97×body160valid
8.0ms281×pre80true
2.0ms9×body640valid
1.0ms27×body80valid
1.0ms25×body80nan

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 52.5b

Counts
2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.1b
(- (* b b) (* (* 4.0 a) c))
28.2b
(+ (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)))
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))))

series63.0ms

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

simplify43.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0396773
11550683
25001673

prune120.0ms

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

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New79382
Fresh000
Picked101
Done000
Total80383

Merged error: 0.1b

Counts
83 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b
(- (* 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)))))

rewrite48.0ms

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))
14.0ms
(/ (+ 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))
42.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
58.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify115.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (90.0ms)

IterNodesCost
06432666
132102408
250012396

prune277.0ms

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

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1585163
Fresh112
Picked011
Done000
Total1597166

Merged error: 0.0b

Counts
166 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite40.0ms

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:
8.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
13.0ms
(* a (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
14.0ms
(/ (* 4.0 (* a c)) (* a (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series94.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
28.0ms
(* a (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
8.0ms
(- (* b b) (* (* 4.0 a) c))
43.0ms
(/ (* 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 (77.0ms)

IterNodesCost
05181106
13294871
25002864

prune146.0ms

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

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New95297
Fresh145
Picked101
Done011
Total977104

Merged error: 0b

Counts
104 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* 1 (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) c)
0.1b
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ 4.0 (/ (* 1 (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) c))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
26×add-sqr-sqrt *-un-lft-identity
23×add-exp-log
22×add-cube-cbrt
18×add-cbrt-cube
10×div-exp associate-/r* add-log-exp
7×cbrt-undiv
6×div-inv
4×pow1 prod-exp associate-/l*
3×flip3-- diff-log flip--
2×sub-neg frac-2neg 1-exp associate-*r/ clear-num cbrt-unprod associate-/l/ distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 distribute-rgt-neg-in neg-log sqrt-prod associate-/r/
Counts
4 → 103
Calls
4 calls:
11.0ms
(/ (* 1 (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) c)
8.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(- (* b b) (* (* 4.0 a) c))
12.0ms
(/ 4.0 (/ (* 1 (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) c))

series75.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(/ (* 1 (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) c)
15.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms
(- (* b b) (* (* 4.0 a) c))
34.0ms
(/ 4.0 (/ (* 1 (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) c))

simplify71.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
05931359
125121192
250011191

prune169.0ms

Filtered
85 candidates to 115 candidates (-35.3%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New1141115
Fresh145
Picked011
Done011
Total1157122

Merged error: 0b

Counts
122 → 7

regimes192.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02311
12311

end0.0ms

analyze273.0ms

Algorithm
search

sample1.4s

Algorithm
intervals
Results
515.0ms3579×body320valid
294.0ms3021×body160valid
263.0ms8770×pre80true
87.0ms454×body640valid
47.0ms946×body80valid
37.0ms770×body80nan

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