Details

Time bar (total: 2.9s)

sample14.0ms

Algorithm
intervals
Results
6.0ms328×body80valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0143
1203
2223
3223

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: 6.3b

Counts
2 → 1

localize4.0ms

Local error

Found 1 expressions with local error:

5.9b
(* x (+ 1.0 (* y y)))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt
3×pow1 add-exp-log add-cube-cbrt *-un-lft-identity associate-*r* associate-*l* add-cbrt-cube
2×associate-*r/
1×distribute-rgt-in distribute-lft-in flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ add-log-exp unswap-sqr
Counts
1 → 22
Calls
1 calls:
5.0ms
(* x (+ 1.0 (* y y)))

series55.0ms

Counts
1 → 3
Calls
1 calls:
55.0ms
(* x (+ 1.0 (* y y)))

simplify78.0ms

Algorithm
egg-herbie
Counts
25 → 25
Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
0144115
1712101
23303100
35003100

prune39.0ms

Filtered
25 candidates to 17 candidates (68.0%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New20525
Fresh000
Picked011
Done000
Total20626

Merged error: 6.1b

Counts
26 → 6

localize6.0ms

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))))
5.9b
(sqrt (+ 1.0 (* y y)))
5.9b
(sqrt (+ 1.0 (* y y)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
18×sqrt-div
17×add-sqr-sqrt
13×pow1 sqrt-prod
12×associate-*r*
11×add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
10×associate-*r/
9×flip3-+ flip-+
4×frac-times associate-*l* pow-prod-down prod-exp cbrt-unprod add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l/ *-commutative unswap-sqr
Counts
4 → 83
Calls
4 calls:
6.0ms
(* x (sqrt (+ 1.0 (* y y))))
10.0ms
(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ 1.0 (* y y))))
2.0ms
(sqrt (+ 1.0 (* y y)))
5.0ms
(sqrt (+ 1.0 (* y y)))

series198.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(* x (sqrt (+ 1.0 (* y y))))
51.0ms
(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ 1.0 (* y y))))
45.0ms
(sqrt (+ 1.0 (* y y)))
41.0ms
(sqrt (+ 1.0 (* y y)))

simplify43.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0306681
11316604
25002594

prune174.0ms

Filtered
95 candidates to 67 candidates (70.5%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New93295
Fresh044
Picked011
Done011
Total938101

Merged error: 6.1b

Counts
101 → 8

localize8.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.6b
(cbrt x)
1.9b
(* (cbrt x) (+ 1.0 (* y y)))
4.2b
(* (* (cbrt x) (cbrt x)) (* (cbrt x) (+ 1.0 (* y y))))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
18×pow1 add-exp-log
13×add-sqr-sqrt
11×add-cbrt-cube
10×cbrt-prod
9×add-cube-cbrt *-un-lft-identity pow-prod-down prod-exp cbrt-unprod
7×associate-*l*
6×associate-*r/
5×distribute-rgt-in distribute-lft-in
4×associate-*r* add-log-exp
2×flip3-+ pow1/3 *-commutative flip-+ unswap-sqr
Counts
4 → 76
Calls
4 calls:
1.0ms
(cbrt x)
1.0ms
(cbrt x)
6.0ms
(* (cbrt x) (+ 1.0 (* y y)))
11.0ms
(* (* (cbrt x) (cbrt x)) (* (cbrt x) (+ 1.0 (* y y))))

series632.0ms

Counts
4 → 12
Calls
4 calls:
178.0ms
(cbrt x)
177.0ms
(cbrt x)
200.0ms
(* (cbrt x) (+ 1.0 (* y y)))
78.0ms
(* (* (cbrt x) (cbrt x)) (* (cbrt x) (+ 1.0 (* y y))))

simplify52.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
0320581
11613442
25003395

prune343.0ms

Filtered
88 candidates to 60 candidates (68.2%)
Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New88088
Fresh055
Picked011
Done022
Total88896

Merged error: 6.1b

Counts
96 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (pow y 2) (- (pow y 2) 1.0))
0.2b
(pow (* y y) 3)
1.0b
(* (+ (pow 1.0 3) (pow (* y y) 3)) x)
14.3b
(/ (* (+ (pow 1.0 3) (pow (* y y) 3)) x) (+ (* (pow y 2) (- (pow y 2) 1.0)) (* 1.0 1.0)))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
19×add-exp-log
16×*-un-lft-identity add-cbrt-cube
14×pow1
13×associate-*l*
12×add-cube-cbrt
11×associate-*r*
6×unpow-prod-down pow-pow prod-exp
5×unswap-sqr
4×associate-*l/ cbrt-unprod add-log-exp difference-of-squares sqr-pow
3×pow-unpow flip3-+ times-frac pow-exp associate-/r* flip-+ unpow2
2×cbrt-undiv distribute-rgt-in pow-to-exp sub-neg distribute-lft-in associate-*r/ div-exp pow-prod-down associate-/r/ *-commutative associate-/l/ rem-cube-cbrt
1×pow2 cube-mult flip3-- frac-2neg pow-plus unpow3 cube-prod clear-num pow-sqr sum-cubes pow-prod-up flip-- div-inv distribute-lft-out associate-/l* distribute-lft-out--
Counts
4 → 111
Calls
4 calls:
10.0ms
(* (pow y 2) (- (pow y 2) 1.0))
4.0ms
(pow (* y y) 3)
11.0ms
(* (+ (pow 1.0 3) (pow (* y y) 3)) x)
19.0ms
(/ (* (+ (pow 1.0 3) (pow (* y y) 3)) x) (+ (* (pow y 2) (- (pow y 2) 1.0)) (* 1.0 1.0)))

series261.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(* (pow y 2) (- (pow y 2) 1.0))
42.0ms
(pow (* y y) 3)
32.0ms
(* (+ (pow 1.0 3) (pow (* y y) 3)) x)
104.0ms
(/ (* (+ (pow 1.0 3) (pow (* y y) 3)) x) (+ (* (pow y 2) (- (pow y 2) 1.0)) (* 1.0 1.0)))

simplify91.0ms

Algorithm
egg-herbie
Counts
123 → 123
Iterations

Useful iterations: 2 (79.0ms)

IterNodesCost
0494869
12549741
25001736

prune270.0ms

Filtered
123 candidates to 84 candidates (68.3%)
Pruning

8 alts after pruning (4 fresh and 4 done)

PrunedKeptTotal
New1230123
Fresh044
Picked011
Done033
Total1238131

Merged error: 6.1b

Counts
131 → 8

regimes125.0ms

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

sample345.0ms

Algorithm
intervals
Results
190.0ms10613×body80valid