Details

Time bar (total: 5.1s)

sample14.0ms

Algorithm
intervals
Results
6.0ms339×body80valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0143
1203
2223
3223

prune2.0ms

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: 5.6b

Counts
2 → 1

localize4.0ms

Local error

Found 1 expressions with local error:

5.2b
(* x (+ 1.0 (* y y)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
7×*-un-lft-identity
5×add-sqr-sqrt associate-*r*
4×associate-*l*
3×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
2×+-commutative distribute-rgt-in distribute-lft-in associate-*r/ distribute-lft-out
1×flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ add-log-exp unswap-sqr
Counts
1 → 26
Calls
1 calls:
9.0ms
(* x (+ 1.0 (* y y)))

series59.0ms

Counts
1 → 3
Calls
1 calls:
59.0ms
(* x (+ 1.0 (* y y)))

simplify81.0ms

Algorithm
egg-herbie
Counts
29 → 29
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
0140121
1687107
23153106
35003106

prune33.0ms

Filtered
29 candidates to 18 candidates (37.9%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New25429
Fresh000
Picked011
Done000
Total25530

Merged error: 5.4b

Counts
30 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(* x (sqrt (+ 1.0 (* y y))))
0.1b
(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ 1.0 (* y y))))
5.2b
(sqrt (+ 1.0 (* y y)))
5.2b
(sqrt (+ 1.0 (* y y)))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
35×*-un-lft-identity
32×sqrt-prod
29×associate-*l*
24×associate-*r*
18×sqrt-div
15×add-cube-cbrt
14×unswap-sqr
13×pow1
11×add-exp-log add-cbrt-cube
10×associate-*r/ distribute-lft-out
9×flip3-+ flip-+
4×frac-times pow-prod-down prod-exp cbrt-unprod add-log-exp
3×*-commutative
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l/
Counts
4 → 114
Calls
4 calls:
10.0ms
(* x (sqrt (+ 1.0 (* y y))))
23.0ms
(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ 1.0 (* y y))))
6.0ms
(sqrt (+ 1.0 (* y y)))
7.0ms
(sqrt (+ 1.0 (* y y)))

series221.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(* x (sqrt (+ 1.0 (* y y))))
59.0ms
(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ 1.0 (* y y))))
45.0ms
(sqrt (+ 1.0 (* y y)))
50.0ms
(sqrt (+ 1.0 (* y y)))

simplify52.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0325937
11343812
25001780

prune185.0ms

Filtered
126 candidates to 78 candidates (38.1%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1233126
Fresh213
Picked011
Done011
Total1256131

Merged error: 5.4b

Counts
131 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (sqrt (sqrt (+ 1.0 (* y y)))) 3)
2.2b
(* (* (pow (sqrt (sqrt (+ 1.0 (* y y)))) 3) 1) x)
5.2b
(sqrt (+ 1.0 (* y y)))
5.2b
(sqrt (+ 1.0 (* y y)))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
57×add-sqr-sqrt
54×associate-*l*
48×sqrt-prod
43×*-un-lft-identity
34×unpow-prod-down
31×unswap-sqr
20×add-exp-log
17×add-cube-cbrt
14×pow1
13×prod-exp
10×add-cbrt-cube
8×distribute-lft-out
6×sqrt-pow1 associate-*r* sqr-pow
5×pow-pow
4×pow1/2 sqrt-div add-log-exp
3×pow-to-exp pow-unpow 1-exp pow-prod-down pow-exp cbrt-unprod
2×rem-sqrt-square flip3-+ unpow3 *-commutative flip-+
1×sqrt-pow2 rem-cube-cbrt
Counts
4 → 133
Calls
4 calls:
9.0ms
(pow (sqrt (sqrt (+ 1.0 (* y y)))) 3)
25.0ms
(* (* (pow (sqrt (sqrt (+ 1.0 (* y y)))) 3) 1) x)
7.0ms
(sqrt (+ 1.0 (* y y)))
6.0ms
(sqrt (+ 1.0 (* y y)))

series641.0ms

Counts
4 → 12
Calls
4 calls:
242.0ms
(pow (sqrt (sqrt (+ 1.0 (* y y)))) 3)
304.0ms
(* (* (pow (sqrt (sqrt (+ 1.0 (* y y)))) 3) 1) x)
49.0ms
(sqrt (+ 1.0 (* y y)))
46.0ms
(sqrt (+ 1.0 (* y y)))

simplify74.0ms

Algorithm
egg-herbie
Counts
145 → 145
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
05871117
124641011
25001978

prune289.0ms

Filtered
145 candidates to 87 candidates (40.0%)
Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New1450145
Fresh033
Picked011
Done022
Total1456151

Merged error: 5.4b

Counts
151 → 6

localize20.0ms

Local error

Found 4 expressions with local error:

4.4b
(- (* (* y y) (* y y)) (* 1.0 (* y y)))
5.2b
(sqrt (+ 1.0 (* y y)))
6.6b
(sqrt (+ (* 1.0 1.0) (- (* (* y y) (* y y)) (* 1.0 (* y y)))))
10.5b
(/ (* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ (pow 1.0 3) (pow (* y y) 3)))) (sqrt (+ (* 1.0 1.0) (- (* (* y y) (* y y)) (* 1.0 (* y y))))))

rewrite909.0ms

Algorithm
rewrite-expression-head
Rules
2395×*-un-lft-identity
1615×associate-*l*
1512×add-sqr-sqrt
1194×sqrt-prod
840×times-frac
733×unswap-sqr
723×distribute-lft-out
562×associate-*r*
544×distribute-lft-out--
253×add-cube-cbrt
230×*-commutative
228×swap-sqr
222×difference-of-squares
84×unpow-prod-down pow-unpow sum-cubes
79×distribute-rgt-out--
42×associate-/l*
20×associate-/r*
18×sqrt-div
13×add-exp-log add-cbrt-cube
9×flip3-+ flip-+
8×associate-*r/ associate-/l/
6×pow1 add-log-exp
4×frac-times
3×cbrt-undiv div-exp prod-exp cbrt-unprod
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l/ associate-/r/
1×sub-neg flip3-- frac-2neg diff-log clear-num flip-- div-inv
Counts
4 → 1303
Calls
4 calls:
112.0ms
(- (* (* y y) (* y y)) (* 1.0 (* y y)))
6.0ms
(sqrt (+ 1.0 (* y y)))
286.0ms
(sqrt (+ (* 1.0 1.0) (- (* (* y y) (* y y)) (* 1.0 (* y y)))))
346.0ms
(/ (* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ (pow 1.0 3) (pow (* y y) 3)))) (sqrt (+ (* 1.0 1.0) (- (* (* y y) (* y y)) (* 1.0 (* y y))))))

series553.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(- (* (* y y) (* y y)) (* 1.0 (* y y)))
45.0ms
(sqrt (+ 1.0 (* y y)))
81.0ms
(sqrt (+ (* 1.0 1.0) (- (* (* y y) (* y y)) (* 1.0 (* y y)))))
330.0ms
(/ (* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ (pow 1.0 3) (pow (* y y) 3)))) (sqrt (+ (* 1.0 1.0) (- (* (* y y) (* y y)) (* 1.0 (* y y))))))

simplify322.0ms

Algorithm
egg-herbie
Counts
1315 → 1315
Iterations

Useful iterations: 1 (47.0ms)

IterNodesCost
0167030064
1500228350

prune1.1s

Filtered
1315 candidates to 196 candidates (85.1%)
Pruning

6 alts after pruning (2 fresh and 4 done)

PrunedKeptTotal
New131501315
Fresh022
Picked011
Done033
Total131561321

Merged error: 5.4b

Counts
1321 → 6

regimes110.0ms

Accuracy

0% (0.2b remaining)

Error of 5.2b against oracle of 5.0b and baseline of 5.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
083
183

end0.0ms

sample344.0ms

Algorithm
intervals
Results
186.0ms10603×body80valid