Details

Time bar (total: 10.8s)

sample3.6s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 1.062012%

Guaranteed chance to sample good point: 19.272054%

Results
8.0ms205×body80valid
2.0ms18×body640valid
2.0ms21×body320valid
1.0ms25×body80invalid
1.0ms5×body1280valid
0.0ms7×body160valid

simplify64.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0206
1456
21116
32886
47146
514986
634106
750016

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 22.6b

Counts
2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (- y z) (- t x))
2.1b
(+ x (/ (* (- y z) (- t x)) (- a z)))
14.2b
(/ (* (- y z) (- t x)) (- a z))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt *-un-lft-identity
13×flip3-- flip--
10×add-exp-log add-cbrt-cube
8×frac-times associate-/l/
7×add-cube-cbrt
5×pow1 times-frac associate-*r* associate-*l* associate-/r* add-log-exp
4×associate-*r/ associate-*l/ distribute-lft-out-- difference-of-squares
2×cbrt-undiv distribute-rgt-in sub-neg distribute-lft-in div-exp prod-exp associate-/r/ cbrt-unprod
1×+-commutative frac-2neg flip3-+ pow-prod-down clear-num sum-log *-commutative flip-+ div-inv distribute-lft-out associate-/l* unswap-sqr
Counts
3 → 81
Calls
3 calls:
8.0ms
(* (- y z) (- t x))
7.0ms
(+ x (/ (* (- y z) (- t x)) (- a z)))
16.0ms
(/ (* (- y z) (- t x)) (- a z))

series92.0ms

Counts
3 → 9
Calls
3 calls:
9.0ms
(* (- y z) (- t x))
50.0ms
(+ x (/ (* (- y z) (- t x)) (- a z)))
33.0ms
(/ (* (- y z) (- t x)) (- a z))

simplify51.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0466583
12158534
25001534

prune147.0ms

Filtered
67 candidates to 90 candidates (-34.3%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New781290
Fresh000
Picked101
Done000
Total791291

Merged error: 5.2b

Counts
91 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- a z))
0.6b
(cbrt (- a z))
2.6b
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
9.9b
(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
75×add-sqr-sqrt
59×*-un-lft-identity
52×times-frac
46×associate-*r*
37×cbrt-prod
27×add-cube-cbrt
25×add-exp-log
18×cbrt-div add-cbrt-cube
17×associate-*l*
16×distribute-lft-out-- difference-of-squares
10×associate-/r/
9×flip3-- flip--
8×prod-exp cbrt-unprod
7×cbrt-undiv div-exp
6×pow1 add-log-exp unswap-sqr
5×frac-times
3×associate-*r/ associate-*l/
2×pow1/3 div-inv
1×+-commutative flip3-+ pow-prod-down sum-log *-commutative flip-+
Counts
4 → 134
Calls
4 calls:
5.0ms
(cbrt (- a z))
3.0ms
(cbrt (- a z))
33.0ms
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
3.0ms
(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

series156.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(cbrt (- a z))
25.0ms
(cbrt (- a z))
56.0ms
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
48.0ms
(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify96.0ms

Algorithm
egg-herbie
Counts
146 → 146
Iterations

Useful iterations: 2 (81.0ms)

IterNodesCost
07521839
133201671
250011580

prune195.0ms

Filtered
103 candidates to 146 candidates (-41.7%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New1397146
Fresh2911
Picked101
Done000
Total14216158

Merged error: 5.2b

Counts
158 → 16

localize28.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- a z))
0.6b
(cbrt (- a z))
1.3b
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))))
9.9b
(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
40×add-exp-log
36×cbrt-div
26×add-sqr-sqrt
22×add-cbrt-cube
17×associate-*l*
16×*-un-lft-identity times-frac associate-*r* associate-/r/
15×prod-exp cbrt-unprod
14×flip3-- flip--
13×cbrt-prod
12×cbrt-undiv div-exp
10×add-cube-cbrt
9×frac-times
6×pow1 add-log-exp unswap-sqr
5×associate-*r/ associate-*l/
3×distribute-lft-out-- difference-of-squares
2×pow1/3 div-inv
1×+-commutative flip3-+ pow-prod-down sum-log *-commutative flip-+
Counts
4 → 110
Calls
4 calls:
3.0ms
(cbrt (- a z))
3.0ms
(cbrt (- a z))
30.0ms
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))))
3.0ms
(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

series246.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(cbrt (- a z))
26.0ms
(cbrt (- a z))
140.0ms
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))))
52.0ms
(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

simplify89.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 2 (71.0ms)

IterNodesCost
08892531
133872166
250012124

prune195.0ms

Filtered
91 candidates to 122 candidates (-34.1%)
Pruning

16 alts after pruning (15 fresh and 1 done)

PrunedKeptTotal
New1220122
Fresh01515
Picked011
Done000
Total12216138

Merged error: 5.2b

Counts
138 → 16

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- t x) (- a z))
3.6b
(+ x (* (- y z) (/ (- t x) (- a z))))
7.3b
(* (- y z) (/ (- t x) (- a z)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
78×add-sqr-sqrt
73×*-un-lft-identity
51×times-frac
31×associate-*r*
27×add-cube-cbrt
23×distribute-lft-out-- difference-of-squares
10×add-exp-log add-cbrt-cube
5×pow1 flip3-- associate-*l* associate-/r* flip-- associate-/l* add-log-exp
4×associate-/r/
2×cbrt-undiv frac-times div-exp associate-*l/ prod-exp cbrt-unprod div-inv associate-/l/ unswap-sqr
1×+-commutative frac-2neg flip3-+ div-sub associate-*r/ pow-prod-down clear-num sum-log *-commutative flip-+
Counts
3 → 119
Calls
3 calls:
7.0ms
(/ (- t x) (- a z))
3.0ms
(+ x (* (- y z) (/ (- t x) (- a z))))
16.0ms
(* (- y z) (/ (- t x) (- a z)))

series96.0ms

Counts
3 → 9
Calls
3 calls:
12.0ms
(/ (- t x) (- a z))
50.0ms
(+ x (* (- y z) (/ (- t x) (- a z))))
33.0ms
(* (- y z) (/ (- t x) (- a z)))

simplify50.0ms

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0473869
12012820
25002820

prune97.0ms

Filtered
86 candidates to 128 candidates (-48.8%)
Pruning

14 alts after pruning (12 fresh and 2 done)

PrunedKeptTotal
New1262128
Fresh41014
Picked011
Done011
Total13014144

Merged error: 5.2b

Counts
144 → 14

regimes597.0ms

Accuracy

18.6% (6.5b remaining)

Error of 10.7b against oracle of 4.2b and baseline of 12.2b

bsearch71.0ms

Steps
ItersRangePoint
9
2.0529702004354465e-172
2.9482605613054127e-167
8.63734572451516e-169
10
-1.4480657668471456e-121
-2.413242020705684e-134
-2.632869011778878e-126

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04134
14134

end0.0ms

sample4.7s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 1.062012%

Guaranteed chance to sample good point: 19.272054%

Results
272.0ms6565×body80valid
72.0ms494×body640valid
52.0ms1125×body80invalid
47.0ms274×body1280valid
42.0ms408×body320valid
17.0ms242×body160valid
4.0ms17×body2560valid

Profiling

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