Details

Time bar (total: 3.8s)

analyze589.0ms

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
12.5%87.4%0.1%5
18.7%81.1%0.1%6
18.7%76.5%4.8%7
28.1%66.3%5.6%8
35.1%55%9.9%9
36.3%50.9%12.8%10
42.1%42.4%15.5%11
47.5%33.8%18.7%12
48.8%30.7%20.6%13
51.8%25.6%22.5%14

sample45.0ms

Algorithm
intervals
Results
11.0ms40×body2560valid
7.0ms157×body80valid
5.0ms25×body1280valid
2.0ms11×body640valid
2.0ms13×body320valid
1.0ms4×body5120valid
1.0ms18×body80nan
1.0ms13×body80invalid
1.0ms6×body160valid

simplify471.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (44.0ms)

IterNodesCost
071313
171313

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 33.5b

Counts
2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.2b
(- (* b_2 b_2) (* a c))
1.2b
(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
37×*-un-lft-identity
21×times-frac
17×add-cube-cbrt
10×distribute-lft-out-- add-log-exp difference-of-squares
8×sqrt-prod
7×associate-/l*
6×add-exp-log add-cbrt-cube
5×pow1 distribute-rgt-neg-in
4×flip3-- flip--
3×diff-log associate-/r*
2×sub-neg sqrt-div associate-/l/
1×cbrt-undiv associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub div-exp neg-log clear-num div-inv
Counts
4 → 89
Calls
4 calls:
30.0ms
(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
4.0ms
(- (* b_2 b_2) (* a c))
8.0ms
(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series58.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
7.0ms
(- (* b_2 b_2) (* a c))
13.0ms
(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify60.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
049361587
149361587

prune137.0ms

Filtered
72 candidates to 101 candidates (-40.3%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New929101
Fresh000
Picked101
Done000
Total939102

Merged error: 4.6b

Counts
102 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.6b
(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
8.3b
(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
22.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
66×times-frac
57×add-sqr-sqrt
42×*-un-lft-identity
28×add-cube-cbrt
18×add-exp-log add-cbrt-cube
14×difference-of-squares
13×associate-/l*
10×sqrt-prod associate-/r/
9×associate-/r*
7×cbrt-undiv flip3-- div-exp flip-- distribute-lft-out--
6×div-inv add-log-exp
5×pow1
2×frac-2neg sqrt-div prod-exp clear-num cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-/l/
Counts
4 → 126
Calls
4 calls:
7.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
12.0ms
(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.0ms
(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series121.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
39.0ms
(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
55.0ms
(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
12.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify52.0ms

Algorithm
egg-herbie
Counts
138 → 138
Iterations

Useful iterations: 0 (38.0ms)

IterNodesCost
050222592

prune144.0ms

Filtered
105 candidates to 138 candidates (-31.4%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1344138
Fresh448
Picked011
Done000
Total1389147

Merged error: 4.5b

Counts
147 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
1.2b
(- (* b_2 b_2) (* a c))
1.3b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
26×*-un-lft-identity
18×times-frac
16×add-cube-cbrt
10×difference-of-squares
8×sqrt-prod add-log-exp
6×add-exp-log associate-/r* add-cbrt-cube
5×pow1 distribute-lft-out--
4×flip3-- flip--
3×associate-/l*
2×sub-neg sqrt-div diff-log associate-/r/
1×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num div-inv
Counts
4 → 81
Calls
4 calls:
9.0ms
(/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms
(- (* b_2 b_2) (* a c))
7.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series80.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
7.0ms
(- (* b_2 b_2) (* a c))
13.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
12.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify60.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
048711374
148711374

prune107.0ms

Filtered
69 candidates to 93 candidates (-34.8%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New92193
Fresh077
Picked011
Done011
Total9210102

Merged error: 4.5b

Counts
102 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.6b
(* (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 a))
8.3b
(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
22.7b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
48×add-exp-log
40×add-sqr-sqrt
30×add-cbrt-cube
25×*-un-lft-identity
23×times-frac
17×prod-exp
16×add-cube-cbrt div-exp
13×associate-*r*
12×associate-*l*
9×cbrt-undiv cbrt-unprod
8×difference-of-squares
7×pow1 sqrt-prod
6×associate-/r* add-log-exp
4×flip3-- associate-/r/ flip-- distribute-lft-out--
3×rec-exp 1-exp div-inv unswap-sqr
2×sqrt-div
1×frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log associate-*r/ pow-prod-down associate-*l/ clear-num un-div-inv *-commutative associate-/l*
Counts
4 → 117
Calls
4 calls:
7.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
17.0ms
(* (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 a))
10.0ms
(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series120.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
41.0ms
(* (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 a))
54.0ms
(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
12.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify60.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
049501911
149501911

prune102.0ms

Filtered
87 candidates to 129 candidates (-48.3%)
Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New1290129
Fresh077
Picked011
Done022
Total12910139

Merged error: 4.5b

Counts
139 → 10

regimes256.0ms

Accuracy

95.1% (1.2b remaining)

Error of 6.9b against oracle of 5.7b and baseline of 29.9b

bsearch91.0ms

Steps
ItersRangePoint
8
4.135828598211903e+62
1.638872687017162e+65
7.216218674231209e+64
10
4.138459702640245e-217
1.0248084967234261e-206
5.910068292844364e-217
9
-3.822767888710634e+157
-9.931096313072362e+149
-9.503260830921614e+153

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
014554
114554

end0.0ms

sample1.1s

Algorithm
intervals
Results
262.0ms1066×body2560valid
229.0ms5183×body80valid
180.0ms872×body1280valid
68.0ms436×body640valid
35.0ms819×body80nan
32.0ms107×body5120valid
27.0ms226×body320valid
11.0ms244×body80invalid
9.0ms110×body160valid

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