Details

Time bar (total: 3.8s)

analyze467.0ms

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

sample44.0ms

Algorithm
intervals
Results
10.0ms25×body2560valid
9.0ms173×body80valid
6.0ms26×body1280valid
4.0ms20×body640valid
1.0ms10×body320valid
1.0ms21×body80nan
1.0ms13×body80invalid
0.0ms1×body5120valid
0.0ms1×body160valid

simplify181.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (180.0ms)

IterNodesCost
0178416
1178416

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: 35.0b

Counts
2 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.3b
(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
0.6b
(- (* b b) (* (* 3.0 a) c))
23.7b
(sqrt (- (* b b) (* (* 3.0 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 → 69
Calls
4 calls:
13.0ms
(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
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)))

series61.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
14.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
8.0ms
(- (* b b) (* (* 3.0 a) c))
14.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify41.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
058991226

prune154.0ms

Filtered
64 candidates to 81 candidates (-26.6%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New74781
Fresh101
Picked011
Done000
Total75883

Merged error: 7.0b

Counts
83 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))
3.0b
(/ (/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))) (* 3.0 a))
11.3b
(/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c))))))
23.7b
(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
45×add-exp-log add-cbrt-cube
34×times-frac
32×add-sqr-sqrt
31×*-un-lft-identity
17×cbrt-undiv div-exp
14×associate-/l*
13×prod-exp cbrt-unprod
11×add-cube-cbrt
10×distribute-lft-out-- difference-of-squares
8×associate-/r* sqrt-prod add-log-exp
6×associate-/r/
5×pow1 flip3-- distribute-rgt-neg-in flip--
4×div-inv
2×frac-2neg sqrt-div diff-log clear-num
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 neg-log associate-/l/
Counts
4 → 119
Calls
4 calls:
8.0ms
(- (neg b) (sqrt (- (* 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))))))
6.0ms
(sqrt (- (* b b) (* 3.0 (* a c))))

series129.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))
42.0ms
(/ (/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))) (* 3.0 a))
56.0ms
(/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c))))))
14.0ms
(sqrt (- (* b b) (* 3.0 (* a c))))

simplify74.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 0 (59.0ms)

IterNodesCost
049732553
149732553

prune173.0ms

Filtered
84 candidates to 131 candidates (-56.0%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1301131
Fresh156
Picked011
Done011
Total1318139

Merged error: 6.9b

Counts
139 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(* 3.0 (* a c))
0.6b
(- (* b b) (* 3.0 (* a c)))
1.0b
(- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))
23.7b
(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))
4.0ms
(- (* 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))))

series44.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(* 3.0 (* a c))
9.0ms
(- (* b b) (* 3.0 (* a c)))
15.0ms
(- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))
16.0ms
(sqrt (- (* b b) (* 3.0 (* a c))))

simplify48.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
04956873
14956873

prune106.0ms

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

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New71273
Fresh145
Picked011
Done022
Total72981

Merged error: 6.9b

Counts
81 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(* 3.0 (* a c))
0.3b
(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
0.6b
(- (* b b) (* 3.0 (* a c)))
23.7b
(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×pow1
9×add-exp-log add-cbrt-cube
8×*-un-lft-identity add-log-exp
6×add-cube-cbrt
4×sqrt-prod
3×flip3-- associate-*l* pow-prod-down prod-exp flip-- cbrt-unprod
2×sub-neg sqrt-div diff-log difference-of-squares
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r* *-commutative distribute-lft-out--
Counts
4 → 58
Calls
4 calls:
5.0ms
(* 3.0 (* a c))
7.0ms
(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
4.0ms
(- (* b b) (* 3.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 3.0 (* a c))))

series42.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(* 3.0 (* a c))
16.0ms
(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
8.0ms
(- (* b b) (* 3.0 (* a c)))
14.0ms
(sqrt (- (* b b) (* 3.0 (* a c))))

simplify45.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 0 (38.0ms)

IterNodesCost
04938809
14938809

prune84.0ms

Filtered
49 candidates to 70 candidates (-42.9%)
Pruning

11 alts after pruning (7 fresh and 4 done)

PrunedKeptTotal
New68270
Fresh055
Picked011
Done033
Total681179

Merged error: 6.9b

Counts
79 → 11

regimes581.0ms

Accuracy

94.4% (1.4b remaining)

Error of 7.3b against oracle of 5.9b and baseline of 30.4b

bsearch104.0ms

Steps
ItersRangePoint
8
2.4167607848118348e+59
3.829298897716676e+62
3.786479868770222e+62
10
3.752519867813892e-287
5.802439856157935e-271
3.821524395718537e-287
11
-4.070625519422487e+144
-3.762618123328472e+124
-6.393909460190851e+142

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
015959
115959

end0.0ms

sample1.3s

Algorithm
intervals
Results
302.0ms994×body2560valid
285.0ms5191×body80valid
221.0ms890×body1280valid
90.0ms469×body640valid
43.0ms112×body5120valid
33.0ms668×body80nan
32.0ms223×body320valid
20.0ms376×body80invalid
14.0ms121×body160valid

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