Details

Time bar (total: 3.4s)

sample14.0ms

Algorithm
intervals
Results
6.0ms349×body80valid

simplify9.0ms

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

localize8.0ms

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)))

series52.0ms

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

simplify81.0ms

Algorithm
egg-herbie
Counts
27 → 27
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
0148123
1742103
23453100
35001100

prune66.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.4b

localize11.0ms

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)))

rewrite24.0ms

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))))
10.0ms
(* (* 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:
61.0ms
(* x (sqrt (+ 1.0 (* y y))))
59.0ms
(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ 1.0 (* y y))))
48.0ms
(sqrt (+ 1.0 (* y y)))
43.0ms
(sqrt (+ 1.0 (* y y)))

simplify45.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0318722
11367620
25002595

prune286.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.4b

localize17.0ms

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)))

rewrite23.0ms

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:
13.0ms
(* (* (* (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)))
3.0ms
(cbrt (+ 1.0 (* y y)))

series917.0ms

Counts
4 → 12
Calls
4 calls:
521.0ms
(* (* (* (fabs (cbrt (+ 1.0 (* y y)))) x) (sqrt (cbrt (+ 1.0 (* y y))))) (sqrt (+ 1.0 (* y y))))
48.0ms
(sqrt (+ 1.0 (* y y)))
172.0ms
(cbrt (+ 1.0 (* y y)))
176.0ms
(cbrt (+ 1.0 (* y y)))

simplify70.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
05151111
123521003
25001985

prune381.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 5.4b

localize11.0ms

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)))

rewrite40.0ms

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:
12.0ms
(* (* x (fma y y 1.0)) (- 1.0 (pow y 2)))
4.0ms
(* x (fma y y 1.0))
16.0ms
(/ (* (* x (fma y y 1.0)) (- 1.0 (pow y 2))) (- 1.0 (* y y)))

series278.0ms

Counts
3 → 9
Calls
3 calls:
168.0ms
(* (* x (fma y y 1.0)) (- 1.0 (pow y 2)))
57.0ms
(* x (fma y y 1.0))
53.0ms
(/ (* (* x (fma y y 1.0)) (- 1.0 (pow y 2))) (- 1.0 (* y y)))

simplify106.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 1 (19.0ms)

IterNodesCost
07651658
140941124
250011124

prune242.0ms

Pruning

7 alts after pruning (3 fresh and 4 done)

Merged error: 5.4b

regimes125.0ms

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

sample352.0ms

Algorithm
intervals
Results
191.0ms10656×body80valid