Details

Time bar (total: 2.6s)

sample13.0ms

Algorithm
intervals
Results
5.0ms327×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: 7.6b

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ 1.0 (* y y))
7.1b
(* x (+ 1.0 (* y y)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt
5×add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log add-cbrt-cube add-log-exp
3×fma-def associate-*r* associate-*l*
2×expm1-log1p-u flip3-+ associate-*r/ flip-+ log1p-expm1-u
1×+-commutative distribute-rgt-in distribute-lft-in pow-prod-down prod-exp sum-log *-commutative cbrt-unprod unswap-sqr
Counts
2 → 40
Calls
2 calls:
2.0ms
(+ 1.0 (* y y))
7.0ms
(* x (+ 1.0 (* y y)))

series90.0ms

Counts
2 → 6
Calls
2 calls:
32.0ms
(+ 1.0 (* y y))
58.0ms
(* x (+ 1.0 (* y y)))

simplify94.0ms

Algorithm
egg-herbie
Counts
46 → 46
Iterations

Useful iterations: 3 (90.0ms)

IterNodesCost
0176185
1831149
23617145
35001144

prune95.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.4b

localize4.0ms

Local error

Found 1 expressions with local error:

7.1b
(* x (fma y y 1.0))

rewrite4.0ms

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×fma-udef
1×distribute-rgt-in expm1-log1p-u distribute-lft-in pow-prod-down prod-exp *-commutative cbrt-unprod log1p-expm1-u add-log-exp unswap-sqr
Counts
1 → 22
Calls
1 calls:
3.0ms
(* x (fma y y 1.0))

series55.0ms

Counts
1 → 3
Calls
1 calls:
55.0ms
(* x (fma y y 1.0))

simplify40.0ms

Algorithm
egg-herbie
Counts
25 → 25
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
08387
134175
2157975
3500175

prune42.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 7.4b

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))))
7.1b
(sqrt (+ 1.0 (* y y)))
7.1b
(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)))

series214.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(* x (sqrt (+ 1.0 (* y y))))
58.0ms
(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ 1.0 (* y y))))
42.0ms
(sqrt (+ 1.0 (* y y)))
46.0ms
(sqrt (+ 1.0 (* y y)))

simplify46.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0318722
11367620
25002595

prune264.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 7.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* x (sqrt (sqrt (+ 1.0 (* y y))))) (hypot (sqrt 1.0) y))
0.1b
(* (* (* x (sqrt (sqrt (+ 1.0 (* y y))))) (hypot (sqrt 1.0) y)) (sqrt (sqrt (+ 1.0 (* y y)))))
7.1b
(sqrt (+ 1.0 (* y y)))
7.1b
(sqrt (+ 1.0 (* y y)))

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
32×sqrt-div
20×pow1
18×add-exp-log add-cbrt-cube
15×sqrt-prod
14×add-sqr-sqrt
12×associate-*r*
10×add-cube-cbrt *-un-lft-identity associate-*r/ associate-*l/
9×flip3-+ pow-prod-down prod-exp cbrt-unprod flip-+
4×expm1-log1p-u frac-times log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* *-commutative hypot-def
Counts
4 → 95
Calls
4 calls:
20.0ms
(* (* x (sqrt (sqrt (+ 1.0 (* y y))))) (hypot (sqrt 1.0) y))
81.0ms
(* (* (* x (sqrt (sqrt (+ 1.0 (* y y))))) (hypot (sqrt 1.0) y)) (sqrt (sqrt (+ 1.0 (* y y)))))
3.0ms
(sqrt (+ 1.0 (* y y)))
3.0ms
(sqrt (+ 1.0 (* y y)))

series675.0ms

Counts
4 → 12
Calls
4 calls:
293.0ms
(* (* x (sqrt (sqrt (+ 1.0 (* y y))))) (hypot (sqrt 1.0) y))
290.0ms
(* (* (* x (sqrt (sqrt (+ 1.0 (* y y))))) (hypot (sqrt 1.0) y)) (sqrt (sqrt (+ 1.0 (* y y)))))
43.0ms
(sqrt (+ 1.0 (* y y)))
48.0ms
(sqrt (+ 1.0 (* y y)))

simplify71.0ms

Algorithm
egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
05031174
122851049
25001930

prune358.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes46.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0136
1136

end0.0ms

sample341.0ms

Algorithm
intervals
Results
184.0ms10636×body80valid