Details

Time bar (total: 5.4s)

sample26.0ms

Algorithm
intervals
Results
9.0ms247×body80valid
1.0ms14×body320valid
1.0ms10×body640valid
1.0msbody1280valid
1.0msbody160valid

simplify73.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0236
1446
21226
33276
48686
517276
635446
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: 11.6b

Counts
2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- t x) (- a z))
4.5b
(+ x (* (- y z) (/ (- t x) (- a z))))
4.8b
(* (- y z) (/ (- t x) (- a z)))

rewrite33.0ms

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
pow1 flip3-- associate-*l* associate-/r* flip-- associate-/l* add-log-exp
associate-/r/
cbrt-undiv frac-times div-exp associate-*l/ prod-exp cbrt-unprod div-inv associate-/l/ unswap-sqr
+-commutative frac-2neg flip3-+ div-sub associate-*r/ pow-prod-down clear-num sum-log *-commutative flip-+
Counts
3 → 119
Calls
3 calls:
8.0ms
(/ (- t x) (- a z))
3.0ms
(+ x (* (- y z) (/ (- t x) (- a z))))
17.0ms
(* (- y z) (/ (- t x) (- a z)))

series319.0ms

Counts
3 → 9
Calls
3 calls:
50.0ms
(/ (- t x) (- a z))
144.0ms
(+ x (* (- y z) (/ (- t x) (- a z))))
124.0ms
(* (- y z) (/ (- t x) (- a z)))

simplify53.0ms

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0473869
12012820
25002820

prune310.0ms

Filtered
128 candidates to 88 candidates (68.8%)
Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New11414128
Fresh000
Picked011
Done000
Total11415129

Merged error: 3.1b

Counts
129 → 15

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- t x))
0.6b
(cbrt (- t x))
0.6b
(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
6.4b
(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
22×add-exp-log
17×add-sqr-sqrt
16×cbrt-div
14×*-un-lft-identity add-cbrt-cube
13×associate-*r*
10×cbrt-prod flip3-- flip--
prod-exp cbrt-unprod
add-cube-cbrt associate-/r/
pow1 frac-times add-log-exp
associate-*l*
cbrt-undiv div-exp associate-*l/
associate-*r/ distribute-lft-out-- difference-of-squares
times-frac pow1/3 unswap-sqr
+-commutative flip3-+ pow-prod-down sum-log *-commutative flip-+ div-inv
Counts
4 → 85
Calls
4 calls:
3.0ms
(cbrt (- t x))
3.0ms
(cbrt (- t x))
24.0ms
(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
3.0ms
(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

series696.0ms

Counts
4 → 12
Calls
4 calls:
144.0ms
(cbrt (- t x))
141.0ms
(cbrt (- t x))
264.0ms
(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
147.0ms
(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

simplify70.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
06801363
126541151
250011129

prune320.0ms

Filtered
97 candidates to 74 candidates (76.3%)
Pruning

15 alts after pruning (13 fresh and 2 done)

PrunedKeptTotal
New96197
Fresh11213
Picked011
Done011
Total9715112

Merged error: 3.1b

Counts
112 → 15

localize24.0ms

Local error

Found 4 expressions with local error:

0.9b
(cbrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
0.9b
(cbrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
0.9b
(cbrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
7.9b
(+ x (* (* (* (- y z) (* (cbrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (cbrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))))) (cbrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
39×cbrt-prod cbrt-div
24×associate-/r/
18×flip3-- flip--
12×frac-times
add-sqr-sqrt add-cube-cbrt *-un-lft-identity
associate-*r/ associate-*l/ add-log-exp
pow1 add-exp-log add-cbrt-cube
times-frac pow1/3 div-inv
+-commutative flip3-+ sum-log flip-+
Counts
4 → 77
Calls
4 calls:
20.0ms
(cbrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
18.0ms
(cbrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
17.0ms
(cbrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
4.0ms
(+ x (* (* (* (- y z) (* (cbrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (cbrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))))) (cbrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

series717.0ms

Counts
4 → 12
Calls
4 calls:
186.0ms
(cbrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
193.0ms
(cbrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
185.0ms
(cbrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
152.0ms
(+ x (* (* (* (- y z) (* (cbrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (cbrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))))) (cbrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

simplify50.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
03722240
110022012
250011948

prune399.0ms

Filtered
89 candidates to 75 candidates (84.3%)
Pruning

15 alts after pruning (12 fresh and 3 done)

PrunedKeptTotal
New88189
Fresh11112
Picked011
Done022
Total8915104

Merged error: 2.4b

Counts
104 → 15

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (- a z))
0.2b
(* (- t x) (/ 1 (- a z)))
4.8b
(* (- y z) (* (- t x) (/ 1 (- a z))))
5.7b
(+ x (* (- y z) (* (- t x) (/ 1 (- a z)))))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
50×add-sqr-sqrt
44×*-un-lft-identity
32×add-exp-log times-frac
25×add-cube-cbrt
22×associate-*r*
20×frac-times add-cbrt-cube
17×flip3-- flip--
13×prod-exp
12×pow1
10×associate-*r/ associate-*l* associate-*l/
distribute-lft-out-- difference-of-squares
cbrt-unprod
div-exp add-log-exp
associate-/r*
pow-prod-down associate-/r/ un-div-inv
cbrt-undiv rec-exp 1-exp associate-/l* unswap-sqr
*-commutative div-inv
+-commutative pow-flip frac-2neg flip3-+ clear-num sum-log flip-+ inv-pow
Counts
4 → 146
Calls
4 calls:
6.0ms
(/ 1 (- a z))
14.0ms
(* (- t x) (/ 1 (- a z)))
18.0ms
(* (- y z) (* (- t x) (/ 1 (- a z))))
4.0ms
(+ x (* (- y z) (* (- t x) (/ 1 (- a z)))))

series559.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(/ 1 (- a z))
51.0ms
(* (- t x) (/ 1 (- a z)))
127.0ms
(* (- y z) (* (- t x) (/ 1 (- a z))))
346.0ms
(+ x (* (- y z) (* (- t x) (/ 1 (- a z)))))

simplify74.0ms

Algorithm
egg-herbie
Counts
158 → 158
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
05851025
12810908
25002863

prune268.0ms

Filtered
158 candidates to 97 candidates (61.4%)
Pruning

16 alts after pruning (12 fresh and 4 done)

PrunedKeptTotal
New1562158
Fresh11011
Picked011
Done033
Total15716173

Merged error: 2.4b

Counts
173 → 16

regimes435.0ms

Accuracy

61.9% (3.3b remaining)

Error of 6.6b against oracle of 3.3b and baseline of 12.0b

bsearch3.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04137
14137

end0.0ms

sample771.0ms

Algorithm
intervals
Results
304.0ms7832×body80valid
62.0ms449×body640valid
54.0ms295×body1280valid
42.0ms402×body320valid
18.0ms262×body160valid
4.0ms17×body2560valid

Profiling

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