Details

Time bar (total: 2.7s)

sample13.0ms

Algorithm
intervals
Results
6.0ms342×body80valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0143
1203
2223
3223

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.3b

localize4.0ms

Local error

Found 1 expressions with local error:

4.1b
(* x (+ 1.0 (* y y)))

rewrite11.0ms

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:
7.0ms
(* x (+ 1.0 (* y y)))

series53.0ms

Counts
1 → 3
Calls
1 calls:
52.0ms
(* x (+ 1.0 (* y y)))

simplify79.0ms

Algorithm
egg-herbie
Counts
25 → 25
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
0144115
1712101
23303100
35003100

prune45.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 4.2b

localize7.0ms

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))))
4.0b
(sqrt (+ 1.0 (* y y)))
4.0b
(sqrt (+ 1.0 (* y y)))

rewrite39.0ms

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:
12.0ms
(* x (sqrt (+ 1.0 (* y y))))
19.0ms
(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ 1.0 (* y y))))
3.0ms
(sqrt (+ 1.0 (* y y)))
3.0ms
(sqrt (+ 1.0 (* y y)))

series207.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(* x (sqrt (+ 1.0 (* y y))))
53.0ms
(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ 1.0 (* y y))))
47.0ms
(sqrt (+ 1.0 (* y y)))
42.0ms
(sqrt (+ 1.0 (* y y)))

simplify41.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0306681
11316604
25002594

prune206.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 4.2b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* x (sqrt (sqrt (+ 1.0 (* y y))))) (sqrt (sqrt (+ 1.0 (* y y)))))
4.0b
(sqrt (+ 1.0 (* y y)))
4.0b
(sqrt (+ 1.0 (* y y)))
4.0b
(sqrt (+ 1.0 (* y y)))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
30×sqrt-div
18×sqrt-prod
13×add-sqr-sqrt
12×pow1
10×add-cube-cbrt *-un-lft-identity
9×add-exp-log flip3-+ associate-*r* add-cbrt-cube flip-+
8×associate-*r/
4×frac-times add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down prod-exp cbrt-unprod
2×associate-*l/
1×associate-*l* *-commutative
Counts
4 → 77
Calls
4 calls:
30.0ms
(* (* x (sqrt (sqrt (+ 1.0 (* y y))))) (sqrt (sqrt (+ 1.0 (* y y)))))
3.0ms
(sqrt (+ 1.0 (* y y)))
3.0ms
(sqrt (+ 1.0 (* y y)))
3.0ms
(sqrt (+ 1.0 (* y y)))

series380.0ms

Counts
4 → 12
Calls
4 calls:
239.0ms
(* (* x (sqrt (sqrt (+ 1.0 (* y y))))) (sqrt (sqrt (+ 1.0 (* y y)))))
43.0ms
(sqrt (+ 1.0 (* y y)))
51.0ms
(sqrt (+ 1.0 (* y y)))
46.0ms
(sqrt (+ 1.0 (* y y)))

simplify123.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0298736
11063653
24704639
35001639

prune238.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 4.2b

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)
1.9b
(* (+ (pow 1.0 3) (pow (* y y) 3)) x)
14.0b
(/ (* (+ (pow 1.0 3) (pow (* y y) 3)) x) (+ (* (pow y 2) (- (pow y 2) 1.0)) (* 1.0 1.0)))

rewrite99.0ms

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:
25.0ms
(* (pow y 2) (- (pow y 2) 1.0))
3.0ms
(pow (* y y) 3)
41.0ms
(* (+ (pow 1.0 3) (pow (* y y) 3)) x)
28.0ms
(/ (* (+ (pow 1.0 3) (pow (* y y) 3)) x) (+ (* (pow y 2) (- (pow y 2) 1.0)) (* 1.0 1.0)))

series258.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(* (pow y 2) (- (pow y 2) 1.0))
44.0ms
(pow (* y y) 3)
32.0ms
(* (+ (pow 1.0 3) (pow (* y y) 3)) x)
103.0ms
(/ (* (+ (pow 1.0 3) (pow (* y y) 3)) x) (+ (* (pow y 2) (- (pow y 2) 1.0)) (* 1.0 1.0)))

simplify84.0ms

Algorithm
egg-herbie
Counts
123 → 123
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
0494869
12549741
25001736

prune333.0ms

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 4.2b

regimes97.0ms

Accuracy

0% (0.2b remaining)

Error of 5.2b against oracle of 5.1b and baseline of 5.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
083
183

end0.0ms

sample327.0ms

Algorithm
intervals
Results
177.0ms10669×body80valid