Details

Time bar (total: 3.8s)

sample24.0ms

Algorithm
intervals
Results
13.0ms478×body80valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0154
1254
2274
3274

prune5.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112

Merged error: 0.0b

Counts
2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b
(* x (+ 2.0 x))
0.0b
(+ (* y y) (* x (+ 2.0 x)))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt *-un-lft-identity
4×pow1 add-exp-log add-cube-cbrt associate-*r* add-cbrt-cube add-log-exp
3×associate-*l*
2×distribute-rgt-in associate-+r+ distribute-lft-in flip3-+ associate-*r/ flip-+
1×+-commutative pow-prod-down prod-exp sum-log *-commutative cbrt-unprod distribute-lft-out unswap-sqr
Counts
2 → 36
Calls
2 calls:
6.0ms
(* x (+ 2.0 x))
5.0ms
(+ (* y y) (* x (+ 2.0 x)))

series94.0ms

Counts
2 → 6
Calls
2 calls:
50.0ms
(* x (+ 2.0 x))
44.0ms
(+ (* y y) (* x (+ 2.0 x)))

simplify47.0ms

Algorithm
egg-herbie
Counts
42 → 42
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0206183
11038169
25001169

prune73.0ms

Filtered
42 candidates to 27 candidates (64.3%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New40242
Fresh000
Picked011
Done000
Total40343

Merged error: 0.0b

Counts
43 → 3

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ (* y y) (* x (+ 2.0 x))))
0.0b
(+ (* y y) (* x (+ 2.0 x)))
0.0b
(+ (* y y) (* x (+ 2.0 x)))
0.1b
(* (sqrt (+ (* y y) (* x (+ 2.0 x)))) (sqrt (+ (* y y) (* x (+ 2.0 x)))))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
21×sqrt-prod
20×pow1
14×sqrt-div
13×add-cube-cbrt *-un-lft-identity
9×sqrt-pow1 flip3-+ pow1/2 flip-+
8×swap-sqr add-log-exp
6×add-exp-log associate-*r* associate-*l* add-cbrt-cube
5×pow-prod-up
4×frac-times associate-+r+ unswap-sqr
3×pow-prod-down pow-sqr
2×+-commutative distribute-rgt-in distribute-lft-in associate-*r/ associate-*l/ sum-log
1×pow2 rem-sqrt-square pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 98
Calls
4 calls:
4.0ms
(sqrt (+ (* y y) (* x (+ 2.0 x))))
5.0ms
(+ (* y y) (* x (+ 2.0 x)))
5.0ms
(+ (* y y) (* x (+ 2.0 x)))
13.0ms
(* (sqrt (+ (* y y) (* x (+ 2.0 x)))) (sqrt (+ (* y y) (* x (+ 2.0 x)))))

series258.0ms

Counts
4 → 12
Calls
4 calls:
140.0ms
(sqrt (+ (* y y) (* x (+ 2.0 x))))
37.0ms
(+ (* y y) (* x (+ 2.0 x)))
37.0ms
(+ (* y y) (* x (+ 2.0 x)))
43.0ms
(* (sqrt (+ (* y y) (* x (+ 2.0 x)))) (sqrt (+ (* y y) (* x (+ 2.0 x)))))

simplify60.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0246902
11085806
25001779

prune200.0ms

Filtered
110 candidates to 61 candidates (55.5%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1091110
Fresh011
Picked101
Done011
Total1103113

Merged error: 0.0b

Counts
113 → 3

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (sqrt (+ (* y y) (* x (+ 2.0 x)))))
0.0b
(sqrt (sqrt (+ (* y y) (* x (+ 2.0 x)))))
0.1b
(* (sqrt (+ (* y y) (* x (+ 2.0 x)))) (* (sqrt (sqrt (+ (* y y) (* x (+ 2.0 x))))) (sqrt (sqrt (+ (* y y) (* x (+ 2.0 x)))))))
0.4b
(* (sqrt (sqrt (+ (* y y) (* x (+ 2.0 x))))) (sqrt (sqrt (+ (* y y) (* x (+ 2.0 x))))))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
122×sqrt-div
91×sqrt-pow1 sqrt-prod
69×pow1
60×add-sqr-sqrt
47×pow1/2
39×pow-prod-up
35×flip3-+ flip-+
32×frac-times
22×add-cube-cbrt *-un-lft-identity
17×swap-sqr
16×associate-*r/
15×associate-*l*
12×pow-prod-down
11×add-exp-log pow-sqr add-cbrt-cube unswap-sqr
10×associate-*r* associate-*l/
4×rem-sqrt-square prod-exp cbrt-unprod add-log-exp
3×sqrt-unprod
2×*-commutative
1×pow2 pow-plus rem-square-sqrt
Counts
4 → 197
Calls
4 calls:
5.0ms
(sqrt (sqrt (+ (* y y) (* x (+ 2.0 x)))))
5.0ms
(sqrt (sqrt (+ (* y y) (* x (+ 2.0 x)))))
26.0ms
(* (sqrt (+ (* y y) (* x (+ 2.0 x)))) (* (sqrt (sqrt (+ (* y y) (* x (+ 2.0 x))))) (sqrt (sqrt (+ (* y y) (* x (+ 2.0 x)))))))
17.0ms
(* (sqrt (sqrt (+ (* y y) (* x (+ 2.0 x))))) (sqrt (sqrt (+ (* y y) (* x (+ 2.0 x))))))

series416.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(sqrt (sqrt (+ (* y y) (* x (+ 2.0 x)))))
118.0ms
(sqrt (sqrt (+ (* y y) (* x (+ 2.0 x)))))
39.0ms
(* (sqrt (+ (* y y) (* x (+ 2.0 x)))) (* (sqrt (sqrt (+ (* y y) (* x (+ 2.0 x))))) (sqrt (sqrt (+ (* y y) (* x (+ 2.0 x)))))))
140.0ms
(* (sqrt (sqrt (+ (* y y) (* x (+ 2.0 x))))) (sqrt (sqrt (+ (* y y) (* x (+ 2.0 x))))))

simplify103.0ms

Algorithm
egg-herbie
Counts
209 → 209
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
05472564
120442212
250012176

prune400.0ms

Filtered
209 candidates to 102 candidates (48.8%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New2081209
Fresh101
Picked011
Done011
Total2093212

Merged error: 0b

Counts
212 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (sqrt (sqrt (+ (* y y) (* x (+ 2.0 x))))))
0.1b
(* (sqrt (+ (* y y) (* x (+ 2.0 x)))) (* (pow (sqrt (sqrt (sqrt (+ (* y y) (* x (+ 2.0 x)))))) 3) (sqrt (sqrt (sqrt (+ (* y y) (* x (+ 2.0 x))))))))
0.2b
(* (pow (sqrt (sqrt (sqrt (+ (* y y) (* x (+ 2.0 x)))))) 3) (sqrt (sqrt (sqrt (+ (* y y) (* x (+ 2.0 x)))))))
0.6b
(pow (sqrt (sqrt (sqrt (+ (* y y) (* x (+ 2.0 x)))))) 3)

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
222×sqrt-prod
174×sqrt-div
110×add-sqr-sqrt
40×unpow-prod-down cube-prod unswap-sqr
36×associate-*l*
35×flip3-+ flip-+
32×frac-times
31×add-cube-cbrt *-un-lft-identity
26×cube-div
20×add-exp-log
18×sqrt-pow1
16×associate-*r/
14×pow1
13×associate-*r*
12×add-cbrt-cube
10×associate-*l/ prod-exp
7×pow-pow
6×pow1/2 sqr-pow
4×cbrt-unprod add-log-exp
3×pow-to-exp rem-sqrt-square pow-unpow pow-exp
2×cube-mult unpow3 *-commutative
1×pow-plus pow-prod-down pow-prod-up sqrt-pow2 rem-cube-cbrt
Counts
4 → 229
Calls
4 calls:
7.0ms
(sqrt (sqrt (sqrt (+ (* y y) (* x (+ 2.0 x))))))
27.0ms
(* (sqrt (+ (* y y) (* x (+ 2.0 x)))) (* (pow (sqrt (sqrt (sqrt (+ (* y y) (* x (+ 2.0 x)))))) 3) (sqrt (sqrt (sqrt (+ (* y y) (* x (+ 2.0 x))))))))
25.0ms
(* (pow (sqrt (sqrt (sqrt (+ (* y y) (* x (+ 2.0 x)))))) 3) (sqrt (sqrt (sqrt (+ (* y y) (* x (+ 2.0 x)))))))
14.0ms
(pow (sqrt (sqrt (sqrt (+ (* y y) (* x (+ 2.0 x)))))) 3)

series479.0ms

Counts
4 → 12
Calls
4 calls:
137.0ms
(sqrt (sqrt (sqrt (+ (* y y) (* x (+ 2.0 x))))))
39.0ms
(* (sqrt (+ (* y y) (* x (+ 2.0 x)))) (* (pow (sqrt (sqrt (sqrt (+ (* y y) (* x (+ 2.0 x)))))) 3) (sqrt (sqrt (sqrt (+ (* y y) (* x (+ 2.0 x))))))))
135.0ms
(* (pow (sqrt (sqrt (sqrt (+ (* y y) (* x (+ 2.0 x)))))) 3) (sqrt (sqrt (sqrt (+ (* y y) (* x (+ 2.0 x)))))))
167.0ms
(pow (sqrt (sqrt (sqrt (+ (* y y) (* x (+ 2.0 x)))))) 3)

simplify156.0ms

Algorithm
egg-herbie
Counts
241 → 241
Iterations

Useful iterations: 2 (113.0ms)

IterNodesCost
07454397
131543933
250023519

prune581.0ms

Filtered
241 candidates to 121 candidates (50.2%)
Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New2410241
Fresh000
Picked011
Done022
Total2413244

Merged error: 0b

Counts
244 → 3

regimes50.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0104
1104

end0.0ms

sample593.0ms

Algorithm
intervals
Results
370.0ms14063×body80valid