Details

Time bar (total: 3.7s)

sample42.0ms

Algorithm
intervals
Results
9.0ms248×body80valid
2.0ms16×body640valid
2.0ms11×body1280valid
2.0ms15×body320valid
1.0ms7×body160valid
0.0ms2×body2560valid

simplify71.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0236
1446
21226
33276
48686
517276
635446
750016

prune4.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 17.5b

Counts
2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- t x) (- a z))
5.6b
(+ x (* (- y z) (/ (- t x) (- a z))))
6.2b
(* (- y z) (/ (- t x) (- a z)))

rewrite32.0ms

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))
4.0ms
(+ x (* (- y z) (/ (- t x) (- a z))))
16.0ms
(* (- y z) (/ (- t x) (- a z)))

series101.0ms

Counts
3 → 9
Calls
3 calls:
14.0ms
(/ (- t x) (- a z))
49.0ms
(+ x (* (- y z) (/ (- t x) (- a z))))
37.0ms
(* (- y z) (/ (- t x) (- a z)))

simplify52.0ms

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0473869
12012820
25002820

prune187.0ms

Filtered
128 candidates to 88 candidates (31.3%)
Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New11513128
Fresh000
Picked011
Done000
Total11514129

Merged error: 5.1b

Counts
129 → 14

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (- a z))
0.6b
(* (cbrt (- a z)) (cbrt (- a z)))
1.8b
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
10.5b
(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
96×add-sqr-sqrt
78×*-un-lft-identity
60×cbrt-prod
54×associate-*r*
52×times-frac
34×add-cube-cbrt
28×cbrt-div
27×add-exp-log
25×associate-*l*
21×distribute-lft-out--
19×difference-of-squares
18×add-cbrt-cube
14×flip3-- flip--
13×pow1
10×swap-sqr associate-/r/ unswap-sqr
9×frac-times prod-exp cbrt-unprod
7×cbrt-undiv pow1/3 div-exp
6×add-log-exp
5×associate-*r/ associate-*l/
3×pow-prod-down
2×pow-sqr *-commutative pow-prod-up div-inv
1×+-commutative pow2 flip3-+ pow-plus sum-log flip-+
Counts
4 → 175
Calls
4 calls:
3.0ms
(cbrt (- a z))
10.0ms
(* (cbrt (- a z)) (cbrt (- a z)))
39.0ms
(* (/ (- 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)))))

series164.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(cbrt (- a z))
30.0ms
(* (cbrt (- a z)) (cbrt (- a z)))
57.0ms
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
52.0ms
(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify109.0ms

Algorithm
egg-herbie
Counts
187 → 187
Iterations

Useful iterations: 2 (91.0ms)

IterNodesCost
08722188
141561999
250031875

prune220.0ms

Filtered
187 candidates to 124 candidates (33.7%)
Pruning

15 alts after pruning (13 fresh and 2 done)

PrunedKeptTotal
New1843187
Fresh21012
Picked011
Done011
Total18615201

Merged error: 5.1b

Counts
201 → 15

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (cbrt (- a z)) (cbrt (- a z)))
1.5b
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (- t x))
5.4b
(/ (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (- t x)) (cbrt (- a z)))
10.5b
(+ x (/ (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (- t x)) (cbrt (- a z))))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
47×add-sqr-sqrt
43×*-un-lft-identity
38×cbrt-prod
29×add-exp-log
26×cbrt-div
25×associate-*l*
19×add-cube-cbrt add-cbrt-cube
17×flip3-- flip--
14×times-frac
13×pow1 associate-*r*
12×frac-times
10×swap-sqr associate-/r/ distribute-lft-out--
9×prod-exp cbrt-unprod
8×cbrt-undiv associate-*r/ div-exp associate-/r* difference-of-squares
6×pow1/3 associate-*l/ add-log-exp unswap-sqr
5×associate-/l/
3×pow-prod-down
2×distribute-rgt-in sub-neg distribute-lft-in pow-sqr *-commutative pow-prod-up div-inv
1×+-commutative pow2 frac-2neg flip3-+ pow-plus clear-num sum-log flip-+ distribute-lft-out associate-/l*
Counts
4 → 158
Calls
4 calls:
11.0ms
(* (cbrt (- a z)) (cbrt (- a z)))
21.0ms
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (- t x))
21.0ms
(/ (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (- t x)) (cbrt (- a z)))
8.0ms
(+ x (/ (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (- t x)) (cbrt (- a z))))

series201.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(* (cbrt (- a z)) (cbrt (- a z)))
70.0ms
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (- t x))
55.0ms
(/ (* (/ (- 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))))

simplify101.0ms

Algorithm
egg-herbie
Counts
170 → 170
Iterations

Useful iterations: 2 (82.0ms)

IterNodesCost
07831900
136711698
250031600

prune207.0ms

Filtered
170 candidates to 112 candidates (34.1%)
Pruning

15 alts after pruning (12 fresh and 3 done)

PrunedKeptTotal
New1700170
Fresh01212
Picked011
Done022
Total17015185

Merged error: 5.1b

Counts
185 → 15

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (- a z))
0.3b
(* (- t x) (/ 1 (- a z)))
6.2b
(* (- y z) (* (- t x) (/ 1 (- a z))))
6.6b
(+ x (* (- y z) (* (- t x) (/ 1 (- a z)))))

rewrite44.0ms

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/
9×distribute-lft-out-- difference-of-squares
7×cbrt-unprod
6×div-exp add-log-exp
5×associate-/r*
4×pow-prod-down associate-/r/ un-div-inv
3×cbrt-undiv rec-exp 1-exp associate-/l* unswap-sqr
2×*-commutative div-inv
1×+-commutative pow-flip frac-2neg flip3-+ clear-num sum-log flip-+ inv-pow
Counts
4 → 146
Calls
4 calls:
6.0ms
(/ 1 (- a z))
13.0ms
(* (- t x) (/ 1 (- a z)))
15.0ms
(* (- y z) (* (- t x) (/ 1 (- a z))))
4.0ms
(+ x (* (- y z) (* (- t x) (/ 1 (- a z)))))

series103.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(/ 1 (- a z))
12.0ms
(* (- t x) (/ 1 (- a z)))
36.0ms
(* (- y z) (* (- t x) (/ 1 (- a z))))
50.0ms
(+ 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

prune130.0ms

Filtered
158 candidates to 95 candidates (39.9%)
Pruning

13 alts after pruning (10 fresh and 3 done)

PrunedKeptTotal
New1571158
Fresh2911
Picked101
Done033
Total16013173

Merged error: 5.1b

Counts
173 → 13

regimes716.0ms

Accuracy

51.2% (4.0b remaining)

Error of 8.2b against oracle of 4.1b and baseline of 12.4b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03931
13931

end0.0ms

sample1.0s

Algorithm
intervals
Results
302.0ms7759×body80valid
72.0ms457×body640valid
51.0ms282×body1280valid
45.0ms394×body320valid
19.0ms265×body160valid
6.0ms15×body2560valid

Profiling

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