Details

Time bar (total: 3.4s)

sample14.0ms

Algorithm
intervals
Results
6.0ms354×body80valid

simplify8.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0143
1233
2303
3313
4313

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.3b

localize8.0ms

Local error

Found 1 expressions with local error:

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

rewrite8.0ms

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

series52.0ms

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

simplify84.0ms

Algorithm
egg-herbie
Counts
27 → 27
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
0148123
1742103
23453100
35001100

prune58.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 4.2b

localize10.0ms

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)))

rewrite37.0ms

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:
9.0ms
(* x (sqrt (+ 1.0 (* y y))))
20.0ms
(* (* 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:
59.0ms
(* x (sqrt (+ 1.0 (* y y))))
58.0ms
(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ 1.0 (* y y))))
41.0ms
(sqrt (+ 1.0 (* y y)))
48.0ms
(sqrt (+ 1.0 (* y y)))

simplify50.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0318722
11367620
25002595

prune252.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 4.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (fabs (cbrt (+ 1.0 (* y y)))) (sqrt (cbrt (+ 1.0 (* y y)))))
4.0b
(sqrt (+ 1.0 (* y y)))
4.2b
(cbrt (+ 1.0 (* y y)))
4.2b
(cbrt (+ 1.0 (* y y)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
11×add-cube-cbrt *-un-lft-identity sqrt-prod
10×cbrt-prod
9×associate-*r*
7×pow1
6×add-exp-log cbrt-div add-cbrt-cube
4×expm1-log1p-u flip3-+ sqrt-div flip-+ log1p-expm1-u add-log-exp
3×associate-*l* unswap-sqr
2×pow1/3 associate-*r/
1×rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down prod-exp *-commutative cbrt-unprod hypot-def
Counts
4 → 78
Calls
4 calls:
11.0ms
(* (fabs (cbrt (+ 1.0 (* y y)))) (sqrt (cbrt (+ 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)))

series572.0ms

Counts
4 → 12
Calls
4 calls:
182.0ms
(* (fabs (cbrt (+ 1.0 (* y y)))) (sqrt (cbrt (+ 1.0 (* y y)))))
47.0ms
(sqrt (+ 1.0 (* y y)))
170.0ms
(cbrt (+ 1.0 (* y y)))
172.0ms
(cbrt (+ 1.0 (* y y)))

simplify55.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0471837
11844773
25001733

prune340.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 4.2b

localize23.0ms

Local error

Found 4 expressions with local error:

3.4b
(- (* (* y y) (* y y)) (* 1.0 (* y y)))
4.0b
(sqrt (+ 1.0 (* y y)))
6.1b
(sqrt (+ (* 1.0 1.0) (- (* (* y y) (* y y)) (* 1.0 (* y y)))))
7.7b
(/ (hypot (pow y 3) (pow 1.0 3/2)) (sqrt (+ (* 1.0 1.0) (- (* (* y y) (* y y)) (* 1.0 (* y y))))))

rewrite175.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity
18×times-frac sqrt-prod
6×pow1 add-exp-log sqrt-div associate-/r* add-cbrt-cube add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×flip3-+ flip-+ associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/ hypot-def
1×cbrt-undiv sub-neg sqrt-undiv hypot-udef flip3-- distribute-rgt-out-- frac-2neg fma-neg diff-log div-exp prod-diff clear-num flip-- div-inv
Counts
4 → 97
Calls
4 calls:
14.0ms
(- (* (* y y) (* y y)) (* 1.0 (* y y)))
3.0ms
(sqrt (+ 1.0 (* y y)))
81.0ms
(sqrt (+ (* 1.0 1.0) (- (* (* y y) (* y y)) (* 1.0 (* y y)))))
74.0ms
(/ (hypot (pow y 3) (pow 1.0 3/2)) (sqrt (+ (* 1.0 1.0) (- (* (* y y) (* y y)) (* 1.0 (* y y))))))

series480.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(- (* (* y y) (* y y)) (* 1.0 (* y y)))
47.0ms
(sqrt (+ 1.0 (* y y)))
80.0ms
(sqrt (+ (* 1.0 1.0) (- (* (* y y) (* y y)) (* 1.0 (* y y)))))
257.0ms
(/ (hypot (pow y 3) (pow 1.0 3/2)) (sqrt (+ (* 1.0 1.0) (- (* (* y y) (* y y)) (* 1.0 (* y y))))))

simplify62.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
04441486
117261374
250021351

prune440.0ms

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 4.2b

regimes110.0ms

Accuracy

0% (0.2b remaining)

Error of 5.4b against oracle of 5.2b and baseline of 5.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
083
183

end0.0ms

sample366.0ms

Algorithm
intervals
Results
196.0ms10750×body80valid