Details

Time bar (total: 3.5s)

analyze520.0ms

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
18.7%81.1%0.1%6
26.5%67.1%6.4%7
35.1%58.5%6.4%8
41.3%49.9%8.7%9
46.4%40.2%13.4%10
50.8%34.2%15%11
55.2%26.7%18.1%12
57.4%22%20.6%13
59.8%17.9%22.3%14

sample38.0ms

Algorithm
intervals
Results
22.0ms256×body80valid
3.0ms31×body80nan
1.0ms18×body80invalid

simplify222.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (221.0ms)

IterNodesCost
0353237
1353237

prune17.0ms

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: 22.5b

Counts
2 → 2

localize22.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
1.2b
(- (* b b) (* (* 4.0 a) c))
25.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
25.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log flip3-- sqrt-div add-cbrt-cube flip--
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
Counts
4 → 52
Calls
4 calls:
4.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
6.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series57.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(- (* b b) (* (* 4.0 a) c))
8.0ms
(- (* b b) (* (* 4.0 a) c))
13.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify37.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 0 (31.0ms)

IterNodesCost
05017824

prune154.0ms

Filtered
54 candidates to 64 candidates (-18.5%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New60464
Fresh011
Picked101
Done000
Total61566

Merged error: 6.2b

Counts
66 → 5

localize26.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
2.3b
(* c (/ a b))
2.9b
(/ (* 2.0 c) (+ (neg b) (- (* 2.0 (* c (/ a b))) b)))
25.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
23×*-un-lft-identity
21×add-sqr-sqrt
15×add-cube-cbrt times-frac
14×add-exp-log add-cbrt-cube
13×associate-*r*
7×pow1
6×add-log-exp
5×associate-/r*
4×distribute-lft-out
3×cbrt-undiv div-exp associate-*l* prod-exp sqrt-prod cbrt-unprod
2×flip3-- distribute-rgt-neg-in sqrt-div associate-/r/ flip-- div-inv unswap-sqr
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 diff-log associate-*r/ pow-prod-down clear-num *-commutative flip-+ associate-/l*
Counts
4 → 85
Calls
4 calls:
4.0ms
(- (* b b) (* (* 4.0 a) c))
6.0ms
(* c (/ a b))
12.0ms
(/ (* 2.0 c) (+ (neg b) (- (* 2.0 (* c (/ a b))) b)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series52.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(- (* b b) (* (* 4.0 a) c))
5.0ms
(* c (/ a b))
25.0ms
(/ (* 2.0 c) (+ (neg b) (- (* 2.0 (* c (/ a b))) b)))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify42.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 0 (34.0ms)

IterNodesCost
055991108

prune193.0ms

Filtered
71 candidates to 97 candidates (-36.6%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New92597
Fresh134
Picked101
Done000
Total948102

Merged error: 6.2b

Counts
102 → 8

localize33.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
1.7b
(* c (* (/ (cbrt a) (cbrt b)) (/ (cbrt a) (cbrt b))))
2.9b
(/ (* 2.0 c) (+ (neg b) (- (* 2.0 (* (* c (* (/ (cbrt a) (cbrt b)) (/ (cbrt a) (cbrt b)))) (/ (cbrt a) (cbrt b)))) b)))
25.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
27×add-exp-log
19×add-cbrt-cube
16×*-un-lft-identity
10×pow1 add-sqr-sqrt prod-exp cbrt-unprod
8×add-cube-cbrt
6×cbrt-undiv div-exp add-log-exp
5×times-frac associate-/r*
4×associate-*r/ distribute-lft-out
3×associate-*l* pow-prod-down sqrt-prod
2×flip3-- distribute-rgt-neg-in sqrt-div associate-/r/ flip--
1×frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 diff-log associate-*r* associate-*l/ clear-num *-commutative flip-+ div-inv associate-/l* unswap-sqr
Counts
4 → 81
Calls
4 calls:
4.0ms
(- (* b b) (* (* 4.0 a) c))
14.0ms
(* c (* (/ (cbrt a) (cbrt b)) (/ (cbrt a) (cbrt b))))
30.0ms
(/ (* 2.0 c) (+ (neg b) (- (* 2.0 (* (* c (* (/ (cbrt a) (cbrt b)) (/ (cbrt a) (cbrt b)))) (/ (cbrt a) (cbrt b)))) b)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series74.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(- (* b b) (* (* 4.0 a) c))
29.0ms
(* c (* (/ (cbrt a) (cbrt b)) (/ (cbrt a) (cbrt b))))
23.0ms
(/ (* 2.0 c) (+ (neg b) (- (* 2.0 (* (* c (* (/ (cbrt a) (cbrt b)) (/ (cbrt a) (cbrt b)))) (/ (cbrt a) (cbrt b)))) b)))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify29.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 0 (20.0ms)

IterNodesCost
051981386

prune191.0ms

Filtered
65 candidates to 93 candidates (-43.1%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New91293
Fresh077
Picked101
Done000
Total929101

Merged error: 6.2b

Counts
101 → 9

localize29.0ms

Local error

Found 4 expressions with local error:

11.8b
(cbrt (/ a b))
11.8b
(cbrt (/ a b))
11.8b
(cbrt (/ a b))
25.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
39×cbrt-prod
27×add-sqr-sqrt times-frac
26×add-cube-cbrt *-un-lft-identity
5×pow1
4×add-exp-log add-cbrt-cube add-log-exp
3×cbrt-div pow1/3 sqrt-prod div-inv
2×sqrt-div
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 flip--
Counts
4 → 81
Calls
4 calls:
2.0ms
(cbrt (/ a b))
2.0ms
(cbrt (/ a b))
2.0ms
(cbrt (/ a b))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series53.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(cbrt (/ a b))
15.0ms
(cbrt (/ a b))
12.0ms
(cbrt (/ a b))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify58.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
05036833

prune154.0ms

Filtered
76 candidates to 93 candidates (-22.4%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New91293
Fresh178
Picked101
Done000
Total939102

Merged error: 6.2b

Counts
102 → 9

regimes309.0ms

Accuracy

92% (1.2b remaining)

Error of 6.9b against oracle of 5.7b and baseline of 20.9b

bsearch66.0ms

Steps
ItersRangePoint
9
4.395679495625736e+70
7.139682197070923e+77
4.864845683402437e+77
9
-6.141442921864838e+38
-1.3863181835697915e+33
-6.079179133751072e+38

simplify17.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (16.0ms)

IterNodesCost
0859132
1859132

end0.0ms

sample1.0s

Algorithm
intervals
Results
717.0ms8000×body80valid
58.0ms699×body80nan
32.0ms382×body80invalid

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