Details

Time bar (total: 5.2s)

analyze738.0ms

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
0%99.9%0.1%5
12.5%87.4%0.1%6
20.3%73.3%6.4%7
27.3%66.3%6.4%8
38.2%53%8.7%9
46%40.6%13.4%10
49.9%35.1%15%11
54.9%26.9%18.1%12
57.4%22%20.6%13
59.7%18%22.4%14

sample42.0ms

Algorithm
intervals
Results
23.0ms256×body80valid
2.0ms25×body80nan
2.0ms17×body80invalid

simplify359.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03518
16618
211618
314418
415918
516118
616118

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 17.6b

Counts
2 → 1

localize44.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* (* 4.0 a) c))
1.1b
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity add-log-exp
8×add-sqr-sqrt
6×pow1 add-cube-cbrt sqrt-prod
4×add-exp-log sqrt-div add-cbrt-cube
3×flip3-- flip--
2×rem-sqrt-square sqrt-pow1 pow1/2 sum-log distribute-lft-out
1×+-commutative neg-sub0 associate-+l- sub-neg distribute-rgt-neg-in flip3-+ diff-log neg-log flip-+
Counts
4 → 57
Calls
4 calls:
4.0ms
(- (* b b) (* (* 4.0 a) c))
8.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
6.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series60.0ms

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))))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify119.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 3 (113.0ms)

IterNodesCost
0231533
1909501
24047489
35001486

prune183.0ms

Filtered
55 candidates to 69 candidates (-25.5%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New62769
Fresh000
Picked101
Done000
Total63770

Merged error: 9.1b

Counts
70 → 7

localize25.0ms

Local error

Found 4 expressions with local error:

8.4b
(- (neg b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
21.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×sqrt-prod
8×add-log-exp
7×pow1 add-cube-cbrt *-un-lft-identity
6×sqrt-div
4×add-exp-log flip3-- add-cbrt-cube flip--
3×rem-sqrt-square sqrt-pow1 pow1/2
2×diff-log
1×associate--l- neg-sub0 sub-neg neg-log difference-of-squares
Counts
4 → 60
Calls
4 calls:
4.0ms
(- (neg b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series60.0ms

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

simplify109.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 3 (101.0ms)

IterNodesCost
0221722
1829631
23533612
35001592

prune237.0ms

Filtered
60 candidates to 72 candidates (-20.0%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New70272
Fresh336
Picked011
Done000
Total73679

Merged error: 9.0b

Counts
79 → 6

localize30.0ms

Local error

Found 4 expressions with local error:

1.1b
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.6b
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
5.8b
(/ (* a c) b)
21.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log add-cbrt-cube
13×*-un-lft-identity
10×add-sqr-sqrt
9×add-cube-cbrt
8×add-log-exp
6×times-frac associate-/r*
5×pow1
4×cbrt-undiv div-exp
3×sqrt-prod
2×flip3-- frac-2neg sqrt-div prod-exp clear-num sum-log associate-/r/ flip-- cbrt-unprod div-inv distribute-lft-out associate-/l*
1×+-commutative neg-sub0 associate-+l- rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 74
Calls
4 calls:
8.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
4.0ms
(/ (* a c) b)
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series54.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.0ms
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
5.0ms
(/ (* a c) b)
15.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify53.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
0455639
12202559
25001554

prune181.0ms

Filtered
66 candidates to 86 candidates (-30.3%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New81586
Fresh134
Picked101
Done011
Total83992

Merged error: 8.0b

Counts
92 → 9

localize34.0ms

Local error

Found 4 expressions with local error:

1.1b
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.8b
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
4.6b
(/ (* 2.0 c) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) (* 2 b)))
21.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
31×times-frac
30×add-exp-log
26×*-un-lft-identity
23×add-cbrt-cube
22×add-cube-cbrt associate-*r*
11×cbrt-prod
9×cbrt-undiv div-exp prod-exp cbrt-unprod
8×add-log-exp
7×pow1 associate-*l*
6×unswap-sqr
3×associate-/r* sqrt-prod div-inv
2×flip3-- sqrt-div sum-log associate-/r/ flip-- distribute-lft-out
1×+-commutative neg-sub0 frac-times associate-+l- rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 flip3-+ pow1/2 associate-*r/ pow-prod-down neg-log associate-*l/ clear-num *-commutative flip-+ associate-/l*
Counts
4 → 112
Calls
4 calls:
8.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
15.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
14.0ms
(/ (* 2.0 c) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) (* 2 b)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series65.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
10.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
25.0ms
(/ (* 2.0 c) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) (* 2 b)))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify89.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
07501328
137781149
250021094

prune200.0ms

Filtered
91 candidates to 124 candidates (-36.3%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1204124
Fresh167
Picked101
Done011
Total12211133

Merged error: 8.0b

Counts
133 → 11

regimes352.0ms

Accuracy

93.4% (0.9b remaining)

Error of 7.8b against oracle of 6.9b and baseline of 19.9b

bsearch564.0ms

Steps
ItersRangePoint
7
6.097468680748611e+144
7.971380955179317e+146
2.3115674843061896e+145
9
-1.8218028511812e+159
-1.5632542644097195e+153
-1.3391262166790126e+154

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06172
16172

end0.0ms

analyze503.0ms

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
0%99.9%0.1%5
12.5%87.4%0.1%6
20.3%73.3%6.4%7
27.3%66.3%6.4%8
38.2%53%8.7%9
46%40.6%13.4%10
49.9%35.1%15%11
54.9%26.9%18.1%12
57.4%22%20.6%13
59.7%18%22.4%14

sample992.0ms

Algorithm
intervals
Results
704.0ms8000×body80valid
56.0ms645×body80nan
33.0ms386×body80invalid

Profiling

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