Details

Time bar (total: 3.1s)

sample15.0ms

Algorithm
intervals
Results
7.0ms349×body80valid

simplify8.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0143
1233
2303
3313
4313

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.6b

localize5.0ms

Local error

Found 1 expressions with local error:

5.2b
(* 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 expm1-log1p-u distribute-lft-in flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ log1p-expm1-u add-log-exp unswap-sqr
Counts
1 → 24
Calls
1 calls:
5.0ms
(* x (+ 1.0 (* y y)))

series56.0ms

Counts
1 → 3
Calls
1 calls:
56.0ms
(* x (+ 1.0 (* y y)))

simplify83.0ms

Algorithm
egg-herbie
Counts
27 → 27
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
0148123
1742103
23453100
35001100

prune64.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.4b

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

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
18×sqrt-div
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×expm1-log1p-u frac-times associate-*l* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l/ *-commutative hypot-def unswap-sqr
Counts
4 → 93
Calls
4 calls:
6.0ms
(* x (sqrt (+ 1.0 (* y y))))
13.0ms
(* (* 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)))

series211.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(* x (sqrt (+ 1.0 (* y y))))
52.0ms
(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ 1.0 (* y y))))
56.0ms
(sqrt (+ 1.0 (* y y)))
41.0ms
(sqrt (+ 1.0 (* y y)))

simplify42.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0318722
11367620
25002595

prune250.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* (* (fabs (cbrt (+ 1.0 (* y y)))) x) (sqrt (cbrt (+ 1.0 (* y y))))) (sqrt (+ 1.0 (* y y))))
5.2b
(sqrt (+ 1.0 (* y y)))
5.4b
(cbrt (+ 1.0 (* y y)))
5.4b
(cbrt (+ 1.0 (* y y)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
14×pow1 sqrt-div
13×add-exp-log add-cbrt-cube
11×add-sqr-sqrt
10×cbrt-div
9×add-cube-cbrt *-un-lft-identity flip3-+ flip-+
8×associate-*r/
6×cbrt-prod associate-*r* pow-prod-down prod-exp sqrt-prod cbrt-unprod
4×expm1-log1p-u frac-times log1p-expm1-u add-log-exp
2×pow1/3 associate-*l/
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* *-commutative hypot-def
Counts
4 → 82
Calls
4 calls:
15.0ms
(* (* (* (fabs (cbrt (+ 1.0 (* y y)))) x) (sqrt (cbrt (+ 1.0 (* y y))))) (sqrt (+ 1.0 (* y y))))
3.0ms
(sqrt (+ 1.0 (* y y)))
2.0ms
(cbrt (+ 1.0 (* y y)))
2.0ms
(cbrt (+ 1.0 (* y y)))

series691.0ms

Counts
4 → 12
Calls
4 calls:
322.0ms
(* (* (* (fabs (cbrt (+ 1.0 (* y y)))) x) (sqrt (cbrt (+ 1.0 (* y y))))) (sqrt (+ 1.0 (* y y))))
41.0ms
(sqrt (+ 1.0 (* y y)))
169.0ms
(cbrt (+ 1.0 (* y y)))
159.0ms
(cbrt (+ 1.0 (* y y)))

simplify67.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
05151111
123521003
25001982

prune376.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 5.4b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (* x (fma y y 1.0)) (- 1.0 (pow y 2)))
5.2b
(* x (fma y y 1.0))
10.3b
(/ (* (* x (fma y y 1.0)) (- 1.0 (pow y 2))) (- 1.0 (* y y)))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
48×prod-diff
46×add-sqr-sqrt
38×*-un-lft-identity
36×add-cube-cbrt
27×distribute-rgt-in distribute-lft-in
19×add-exp-log unpow-prod-down add-cbrt-cube
11×associate-*r*
10×pow1
7×prod-exp cbrt-unprod unpow2 sqr-pow
6×difference-of-squares
4×times-frac associate-*r/ associate-*l* pow-prod-down associate-/r*
3×cbrt-undiv expm1-log1p-u flip3-- div-exp flip-- log1p-expm1-u add-log-exp
2×sub-neg associate-/r/ *-commutative fma-udef associate-/l/
1×frac-2neg clear-num div-inv associate-/l* distribute-lft-out-- unswap-sqr
Counts
3 → 132
Calls
3 calls:
11.0ms
(* (* x (fma y y 1.0)) (- 1.0 (pow y 2)))
4.0ms
(* x (fma y y 1.0))
15.0ms
(/ (* (* x (fma y y 1.0)) (- 1.0 (pow y 2))) (- 1.0 (* y y)))

series288.0ms

Counts
3 → 9
Calls
3 calls:
172.0ms
(* (* x (fma y y 1.0)) (- 1.0 (pow y 2)))
57.0ms
(* x (fma y y 1.0))
59.0ms
(/ (* (* x (fma y y 1.0)) (- 1.0 (pow y 2))) (- 1.0 (* y y)))

simplify110.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 1 (20.0ms)

IterNodesCost
07651656
139851124
250011124

prune229.0ms

Pruning

7 alts after pruning (3 fresh and 4 done)

Merged error: 5.4b

regimes120.0ms

Accuracy

0% (0.2b remaining)

Error of 5.5b against oracle of 5.3b and baseline of 5.5b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
083
183

end0.0ms

sample375.0ms

Algorithm
intervals
Results
209.0ms10656×body80valid