Details

Time bar (total: 2.9s)

sample23.0ms

Algorithm
intervals
Results
15.0ms333×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: 5.1b

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ 1.0 (* y y))
4.8b
(* x (+ 1.0 (* y y)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt
4×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
3×associate-*r* associate-*l*
2×flip3-+ associate-*r/ flip-+
1×+-commutative distribute-rgt-in distribute-lft-in pow-prod-down prod-exp sum-log *-commutative cbrt-unprod unswap-sqr
Counts
2 → 33
Calls
2 calls:
2.0ms
(+ 1.0 (* y y))
7.0ms
(* x (+ 1.0 (* y y)))

series87.0ms

Counts
2 → 6
Calls
2 calls:
32.0ms
(+ 1.0 (* y y))
56.0ms
(* x (+ 1.0 (* y y)))

simplify87.0ms

Algorithm
egg-herbie
Counts
39 → 39
Iterations

Useful iterations: 2 (22.0ms)

IterNodesCost
0168171
1790152
23413149
35001149

prune82.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 4.9b

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))))
4.7b
(sqrt (+ 1.0 (* y y)))
4.7b
(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:
9.0ms
(* 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)))

series210.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(* x (sqrt (+ 1.0 (* y y))))
53.0ms
(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ 1.0 (* y y))))
49.0ms
(sqrt (+ 1.0 (* y y)))
45.0ms
(sqrt (+ 1.0 (* y y)))

simplify43.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0306681
11316604
25002594

prune203.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 4.9b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (sqrt (+ 1.0 (* y y))))) (sqrt (sqrt (+ 1.0 (* y y)))))
4.7b
(sqrt (+ 1.0 (* y y)))
4.7b
(sqrt (+ 1.0 (* y y)))
4.7b
(sqrt (+ 1.0 (* y y)))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
96×sqrt-div
30×flip3-+ flip-+
28×frac-times
26×associate-*r/
18×sqrt-prod
16×pow1
14×associate-*l/
13×add-exp-log add-sqr-sqrt add-cbrt-cube
10×add-cube-cbrt *-un-lft-identity
9×associate-*r*
6×pow-prod-down prod-exp cbrt-unprod
4×add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
1×associate-*l* *-commutative
Counts
4 → 98
Calls
4 calls:
74.0ms
(* (* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (sqrt (+ 1.0 (* y y))))) (sqrt (sqrt (+ 1.0 (* y y)))))
2.0ms
(sqrt (+ 1.0 (* y y)))
2.0ms
(sqrt (+ 1.0 (* y y)))
3.0ms
(sqrt (+ 1.0 (* y y)))

series190.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(* (* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (sqrt (+ 1.0 (* y y))))) (sqrt (sqrt (+ 1.0 (* y y)))))
47.0ms
(sqrt (+ 1.0 (* y y)))
42.0ms
(sqrt (+ 1.0 (* y y)))
47.0ms
(sqrt (+ 1.0 (* y y)))

simplify256.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
04481458
117471223
250011105

prune297.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 4.9b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (pow y 2) 1.0)
0.1b
(pow (+ (pow y 2) 1.0) 3)
4.8b
(* x (cbrt (pow (+ (pow y 2) 1.0) 3)))
7.7b
(cbrt (pow (+ (pow y 2) 1.0) 3))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
32×cbrt-prod
29×*-un-lft-identity
24×add-sqr-sqrt
17×associate-*r*
15×add-cube-cbrt
13×unpow-prod-down cube-prod
7×pow1 add-exp-log distribute-lft-out
6×cube-div add-cbrt-cube add-log-exp
5×unswap-sqr
4×cbrt-div flip3-+ flip-+ sqr-pow
3×cube-mult pow-unpow unpow3 associate-*l*
2×associate-*r/
1×+-commutative pow-to-exp pow-pow pow1/3 pow-prod-down pow-exp prod-exp sum-log *-commutative rem-cbrt-cube cbrt-unprod rem-cube-cbrt
Counts
4 → 102
Calls
4 calls:
6.0ms
(+ (pow y 2) 1.0)
11.0ms
(pow (+ (pow y 2) 1.0) 3)
47.0ms
(* x (cbrt (pow (+ (pow y 2) 1.0) 3)))
10.0ms
(cbrt (pow (+ (pow y 2) 1.0) 3))

series181.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(+ (pow y 2) 1.0)
55.0ms
(pow (+ (pow y 2) 1.0) 3)
53.0ms
(* x (cbrt (pow (+ (pow y 2) 1.0) 3)))
37.0ms
(cbrt (pow (+ (pow y 2) 1.0) 3))

simplify55.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0283550
11425513
25001502

prune204.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 4.9b

regimes83.0ms

Accuracy

0% (0.2b remaining)

Error of 5.3b against oracle of 5.1b and baseline of 5.3b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0118
1118

end0.0ms

sample654.0ms

Algorithm
intervals
Results
490.0ms10635×body80valid