Details

Time bar (total: 4.8s)

analyze475.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
25%74.9%0.1%5
25%74.9%0.1%6
25%68.6%6.4%7
31.2%62.4%6.4%8
36.7%54.6%8.7%9
38.2%48.4%13.4%10
42.7%42.3%15%11
47.8%34.1%18.1%12
49.1%30.3%20.5%13
51.9%25.8%22.3%14

sample45.0ms

Algorithm
intervals
Results
10.0ms32×body2560valid
9.0ms163×body80valid
7.0ms27×body1280valid
3.0ms14×body640valid
2.0ms5×body5120valid
2.0ms12×body320valid
1.0ms18×body80nan
1.0ms11×body80invalid
0.0ms3×body160valid

simplify3.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
02717
12717

prune11.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 36.5b

Counts
2 → 2

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.6b
(- (* b b) (* (* 3.0 a) c))
1.6b
(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
26.0b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite30.0ms

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 → 69
Calls
4 calls:
14.0ms
(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
3.0ms
(- (* b b) (* (* 3.0 a) c))
8.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series65.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
9.0ms
(- (* b b) (* (* 3.0 a) c))
15.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
15.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify51.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
050221266

prune176.0ms

Filtered
63 candidates to 81 candidates (-28.6%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New711081
Fresh101
Picked101
Done000
Total731083

Merged error: 8.0b

Counts
83 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* 3.0 (* a c)))
4.1b
(/ (/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))) (* 3.0 a))
11.4b
(/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c))))))
26.0b
(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
45×add-exp-log add-cbrt-cube
34×times-frac
28×add-sqr-sqrt
27×*-un-lft-identity
17×cbrt-undiv div-exp
14×associate-/l*
13×prod-exp cbrt-unprod
11×add-cube-cbrt
8×associate-/r* distribute-lft-out-- difference-of-squares
7×sqrt-prod
6×associate-/r/ add-log-exp
5×pow1 flip3-- flip--
4×distribute-rgt-neg-in div-inv
2×frac-2neg sqrt-div clear-num
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-/l/
Counts
4 → 113
Calls
4 calls:
4.0ms
(- (* b b) (* 3.0 (* a c)))
16.0ms
(/ (/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))) (* 3.0 a))
13.0ms
(/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c))))))
4.0ms
(sqrt (- (* b b) (* 3.0 (* a c))))

series128.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(- (* b b) (* 3.0 (* a c)))
46.0ms
(/ (/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))) (* 3.0 a))
58.0ms
(/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c))))))
15.0ms
(sqrt (- (* b b) (* 3.0 (* a c))))

simplify50.0ms

Algorithm
egg-herbie
Counts
125 → 125
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
050432308

prune185.0ms

Filtered
79 candidates to 125 candidates (-58.2%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1241125
Fresh279
Picked011
Done000
Total1269135

Merged error: 7.9b

Counts
135 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(* 3.0 (* a c))
0.3b
(- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))
0.6b
(- (* b b) (* 3.0 (* a c)))
26.0b
(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×pow1 *-un-lft-identity add-log-exp
9×add-exp-log add-cbrt-cube
6×add-cube-cbrt
4×sqrt-prod
3×flip3-- diff-log associate-*l* pow-prod-down prod-exp flip-- cbrt-unprod
2×sub-neg sqrt-div distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 pow1/2 associate-*r* neg-log *-commutative
Counts
4 → 61
Calls
4 calls:
5.0ms
(* 3.0 (* a c))
8.0ms
(- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))
4.0ms
(- (* b b) (* 3.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 3.0 (* a c))))

series44.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(* 3.0 (* a c))
16.0ms
(- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))
9.0ms
(- (* b b) (* 3.0 (* a c)))
16.0ms
(sqrt (- (* b b) (* 3.0 (* a c))))

simplify62.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 0 (55.0ms)

IterNodesCost
04960873
14960873

prune111.0ms

Filtered
51 candidates to 73 candidates (-43.1%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New72173
Fresh167
Picked011
Done011
Total73982

Merged error: 7.9b

Counts
82 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 1 3.0) (/ (+ (sqrt (- (* b b) (* 3.0 (* a c)))) (neg b)) a))
0.6b
(- (* b b) (* 3.0 (* a c)))
1.6b
(+ (sqrt (- (* b b) (* 3.0 (* a c)))) (neg b))
26.0b
(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt *-un-lft-identity
31×times-frac
26×add-exp-log
21×add-cube-cbrt
19×associate-*r*
16×add-cbrt-cube
13×associate-*l*
10×add-log-exp
8×div-exp prod-exp distribute-lft-out
7×pow1
6×unswap-sqr
4×cbrt-undiv distribute-rgt-neg-in cbrt-unprod
3×sqrt-prod
2×rec-exp flip3-- sqrt-div 1-exp sum-log flip-- div-inv
1×+-commutative neg-sub0 frac-times associate-+r- sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log associate-*r/ unsub-neg pow-prod-down neg-log associate-*l/ *-commutative flip-+
Counts
4 → 104
Calls
4 calls:
21.0ms
(* (/ 1 3.0) (/ (+ (sqrt (- (* b b) (* 3.0 (* a c)))) (neg b)) a))
3.0ms
(- (* b b) (* 3.0 (* a c)))
8.0ms
(+ (sqrt (- (* b b) (* 3.0 (* a c)))) (neg b))
4.0ms
(sqrt (- (* b b) (* 3.0 (* a c))))

series65.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(* (/ 1 3.0) (/ (+ (sqrt (- (* b b) (* 3.0 (* a c)))) (neg b)) a))
9.0ms
(- (* b b) (* 3.0 (* a c)))
15.0ms
(+ (sqrt (- (* b b) (* 3.0 (* a c)))) (neg b))
14.0ms
(sqrt (- (* b b) (* 3.0 (* a c))))

simplify60.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 0 (46.0ms)

IterNodesCost
049131834
149131834

prune156.0ms

Filtered
80 candidates to 116 candidates (-45.0%)
Pruning

11 alts after pruning (8 fresh and 3 done)

PrunedKeptTotal
New1124116
Fresh246
Picked011
Done022
Total11411125

Merged error: 7.9b

Counts
125 → 11

regimes307.0ms

Accuracy

93.1% (1.6b remaining)

Error of 7.3b against oracle of 5.6b and baseline of 29.5b

bsearch892.0ms

Steps
ItersRangePoint
9
1.9843643632770458e+70
5.8890617205900905e+75
4.796343227814801e+75
9
-1.9054288369633496e-226
-6.648278717872741e-233
-7.408184693465228e-233
11
-6.191066304504855e+51
-7.078127003988134e+31
-6.094184368017698e+51

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04562
14562

end0.0ms

analyze468.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
25%74.9%0.1%5
25%74.9%0.1%6
25%68.6%6.4%7
31.2%62.4%6.4%8
36.7%54.6%8.7%9
38.2%48.4%13.4%10
42.7%42.3%15%11
47.8%34.1%18.1%12
49.1%30.3%20.5%13
51.9%25.8%22.3%14

sample1.3s

Algorithm
intervals
Results
331.0ms1046×body2560valid
286.0ms5177×body80valid
230.0ms880×body1280valid
88.0ms437×body640valid
38.0ms98×body5120valid
36.0ms220×body320valid
34.0ms637×body80nan
23.0ms425×body80invalid
15.0ms142×body160valid

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