Details

Time bar (total: 6.0s)

sample27.0ms

Algorithm
intervals
Results
9.0ms246×body80valid
3.0ms18×body640valid
2.0ms10×body1280valid
1.0ms11×body320valid
0.0ms7×body160valid

simplify63.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0206
1456
21116
32886
47146
514986
634106
750016

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 27.1b

Counts
2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (- y z) (- t x))
1.4b
(+ x (/ (* (- y z) (- t x)) (- a z)))
20.9b
(/ (* (- y z) (- t x)) (- a z))

rewrite32.0ms

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:
9.0ms
(* (- y z) (- t x))
10.0ms
(+ x (/ (* (- y z) (- t x)) (- a z)))
12.0ms
(/ (* (- y z) (- t x)) (- a z))

series302.0ms

Counts
3 → 9
Calls
3 calls:
34.0ms
(* (- y z) (- t x))
145.0ms
(+ x (/ (* (- y z) (- t x)) (- a z)))
123.0ms
(/ (* (- y z) (- t x)) (- a z))

simplify54.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0466583
12158534
25001534

prune215.0ms

Filtered
90 candidates to 67 candidates (74.4%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New81990
Fresh000
Picked101
Done000
Total82991

Merged error: 4.2b

Counts
91 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (- a z))
0.5b
(cbrt (- a z))
0.9b
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
7.3b
(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite52.0ms

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:
3.0ms
(cbrt (- a z))
3.0ms
(cbrt (- a z))
37.0ms
(* (/ (- 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)))))

series732.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(cbrt (- a z))
145.0ms
(cbrt (- a z))
295.0ms
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
150.0ms
(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify85.0ms

Algorithm
egg-herbie
Counts
146 → 146
Iterations

Useful iterations: 2 (69.0ms)

IterNodesCost
07441831
132871663
250011576

prune397.0ms

Filtered
146 candidates to 103 candidates (70.5%)
Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New1388146
Fresh358
Picked011
Done000
Total14114155

Merged error: 4.1b

Counts
155 → 14

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (- y z))
0.5b
(cbrt (- y z))
0.8b
(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))
2.6b
(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
73×add-exp-log
35×add-cbrt-cube
32×prod-exp cbrt-unprod
22×cbrt-undiv div-exp
15×cbrt-prod add-sqr-sqrt *-un-lft-identity
14×associate-*l*
9×pow1 add-cube-cbrt
8×times-frac
6×cbrt-div add-log-exp
5×frac-times associate-*r/
3×flip3-- pow-prod-down associate-*l/ flip-- distribute-lft-out-- difference-of-squares
2×pow1/3 associate-/r/
1×+-commutative flip3-+ associate-*r* sum-log *-commutative flip-+ div-inv
Counts
4 → 103
Calls
4 calls:
3.0ms
(cbrt (- y z))
3.0ms
(cbrt (- y z))
34.0ms
(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))
3.0ms
(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

series727.0ms

Counts
4 → 12
Calls
4 calls:
147.0ms
(cbrt (- y z))
142.0ms
(cbrt (- y z))
288.0ms
(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))
149.0ms
(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

simplify72.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
06522061
124891608
250031462

prune305.0ms

Filtered
115 candidates to 70 candidates (60.9%)
Pruning

15 alts after pruning (13 fresh and 2 done)

PrunedKeptTotal
New1141115
Fresh01212
Picked011
Done011
Total11415129

Merged error: 4.1b

Counts
129 → 15

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (cbrt (- a z)))
0.6b
(cbrt (cbrt (- a z)))
0.6b
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))))
8.5b
(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
73×add-exp-log
44×cbrt-div
39×add-cbrt-cube
32×prod-exp cbrt-unprod
26×cbrt-prod
23×add-sqr-sqrt
22×cbrt-undiv div-exp
17×*-un-lft-identity associate-*l*
16×associate-/r/
14×flip3-- flip--
13×associate-*r*
11×add-cube-cbrt
10×times-frac
9×frac-times
6×pow1 add-log-exp
5×associate-*r/ associate-*l/
4×unswap-sqr
3×distribute-lft-out-- difference-of-squares
2×pow1/3 div-inv
1×+-commutative flip3-+ pow-prod-down sum-log *-commutative flip-+
Counts
4 → 123
Calls
4 calls:
4.0ms
(cbrt (cbrt (- a z)))
4.0ms
(cbrt (cbrt (- a z)))
42.0ms
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (cbrt (- a z))) (cbrt (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 (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

series743.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(cbrt (cbrt (- a z)))
148.0ms
(cbrt (cbrt (- a z)))
290.0ms
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))))
162.0ms
(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

simplify111.0ms

Algorithm
egg-herbie
Counts
135 → 135
Iterations

Useful iterations: 2 (85.0ms)

IterNodesCost
09042926
140512281
250022181

prune435.0ms

Filtered
135 candidates to 91 candidates (67.4%)
Pruning

15 alts after pruning (12 fresh and 3 done)

PrunedKeptTotal
New1332135
Fresh21012
Picked011
Done022
Total13515150

Merged error: 4.1b

Counts
150 → 15

regimes429.0ms

Accuracy

15% (6.6b remaining)

Error of 11.1b against oracle of 4.4b and baseline of 12.2b

bsearch108.0ms

Steps
ItersRangePoint
8
7.183280095972616e-88
1.620800228275719e-83
7.326026313435155e-88
8
-1.055386269196156e-138
-2.2766900434224755e-141
-7.395685414339779e-141

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04955
14955

end0.0ms

sample953.0ms

Algorithm
intervals
Results
304.0ms7797×body80valid
213.0ms221×body160valid
68.0ms488×body640valid
52.0ms296×body1280valid
44.0ms413×body320valid
4.0ms19×body2560valid

Profiling

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