Details

Time bar (total: 4.6s)

sample40.0ms

Algorithm
intervals
Results
8.0ms34×body2560valid
7.0ms179×body80valid
5.0ms29×body1280valid
3.0ms85×body80nan
2.0ms17×body640valid
1.0ms5×body5120valid
1.0ms8×body320valid
0.0ms3×body160valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059

prune2.0ms

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: 35.9b

Counts
2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
1.0b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0b
(- (* b b) (* (* 4.0 a) c))
23.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite31.0ms

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:
11.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
6.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series284.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
75.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
42.0ms
(- (* b b) (* (* 4.0 a) c))
67.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify45.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0405779
11563685
25001674

prune206.0ms

Filtered
82 candidates to 63 candidates (76.8%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New74882
Fresh000
Picked101
Done000
Total75883

Merged error: 4.9b

Counts
83 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

2.8b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.2b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
11.1b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
23.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
84×add-sqr-sqrt
83×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
14×sqrt-prod
11×distribute-rgt-neg-in
8×associate-/r* add-log-exp
7×cbrt-undiv div-exp
6×associate-/r/
5×pow1 flip3-- flip--
4×div-inv
3×associate-/l/
2×frac-2neg sqrt-div diff-log prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 154
Calls
4 calls:
11.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
13.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series466.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
144.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
178.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
66.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify114.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 2 (91.0ms)

IterNodesCost
06512692
131392439
250022426

prune376.0ms

Filtered
166 candidates to 111 candidates (66.9%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1633166
Fresh167
Picked011
Done000
Total16410174

Merged error: 4.8b

Counts
174 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
1.0b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0b
(- (* b b) (* (* 4.0 a) c))
23.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
53×times-frac
45×*-un-lft-identity
26×add-sqr-sqrt
25×add-exp-log add-cube-cbrt
13×add-cbrt-cube
12×div-exp
11×associate-/r*
10×distribute-lft-out add-log-exp
9×associate-/r/
6×pow1
5×cbrt-undiv distribute-rgt-neg-in flip3-+ flip-+ div-inv
3×rec-exp 1-exp prod-exp sqrt-prod associate-/l*
2×flip3-- sqrt-div sum-log flip--
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 diff-log neg-log clear-num cbrt-unprod inv-pow
Counts
4 → 114
Calls
4 calls:
13.0ms
(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
8.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series332.0ms

Counts
4 → 12
Calls
4 calls:
138.0ms
(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
78.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
43.0ms
(- (* b b) (* (* 4.0 a) c))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify73.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
05251588
125701375
250011308

prune224.0ms

Filtered
126 candidates to 71 candidates (56.3%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New1251126
Fresh178
Picked011
Done011
Total12610136

Merged error: 4.8b

Counts
136 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (/ 1 (* 2.0 a)) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
1.0b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
1.0b
(- (* b b) (* (* 4.0 a) c))
23.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log
19×add-sqr-sqrt
13×add-cbrt-cube
12×*-un-lft-identity
10×prod-exp
8×add-cube-cbrt add-log-exp
7×pow1 associate-*l*
6×associate-*r*
5×flip3-- sqrt-prod flip--
4×sub-neg div-exp cbrt-unprod difference-of-squares
3×times-frac
2×cbrt-undiv distribute-rgt-in frac-times rec-exp distribute-lft-in sqrt-div diff-log 1-exp associate-*r/ distribute-lft-out--
1×rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down associate-*l/ *-commutative div-inv unswap-sqr
Counts
4 → 84
Calls
4 calls:
14.0ms
(* (/ 1 (* 2.0 a)) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
7.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
4.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series340.0ms

Counts
4 → 12
Calls
4 calls:
146.0ms
(* (/ 1 (* 2.0 a)) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
80.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
44.0ms
(- (* b b) (* (* 4.0 a) c))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify60.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
0453919
12109802
25001799

prune186.0ms

Filtered
96 candidates to 65 candidates (67.7%)
Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New96096
Fresh077
Picked011
Done022
Total9610106

Merged error: 4.8b

Counts
106 → 10

regimes217.0ms

Accuracy

85.7% (3.9b remaining)

Error of 9.3b against oracle of 5.4b and baseline of 32.6b

bsearch205.0ms

Steps
ItersRangePoint
9
14028.172733867412
3007116902181.375
4662246.201750503
8
-4.654091770266614e-259
-1.1349992526466847e-263
-3.0161999035837213e-263
10
-1.552489725432399e+46
-8.211399685419546e+34
-1.4899647929737788e+46

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04929
15129
25129

end0.0ms

sample1.2s

Algorithm
intervals
Results
257.0ms1101×body2560valid
236.0ms5800×body80valid
172.0ms887×body1280valid
113.0ms2958×body80nan
69.0ms469×body640valid
33.0ms117×body5120valid
27.0ms215×body320valid
11.0ms110×body160valid

Profiling

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