Details

Time bar (total: 7.7s)

sample113.0ms

Algorithm
intervals
Results
36.0ms88×body1280valid
30.0ms89×body640valid
19.0ms245×body80valid
8.0ms35×body320valid
3.0ms21×body160valid

simplify19.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0267
1576
2876
31146
41326
51516
61716
71736
81736

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma a1 a1 (* a2 a2))
0.2b
(* (cos th) (fma a1 a1 (* a2 a2)))
0.6b
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×add-exp-log add-cbrt-cube
9×add-cube-cbrt *-un-lft-identity
6×times-frac associate-/r* sqrt-prod
5×pow1
3×expm1-log1p-u associate-*r* associate-*l* fma-udef log1p-expm1-u add-log-exp
2×cbrt-undiv div-exp prod-exp cbrt-unprod
1×distribute-rgt-in frac-2neg distribute-lft-in pow-prod-down clear-num *-commutative div-inv associate-/l* unswap-sqr
Counts
3 → 61
Calls
3 calls:
0.0ms
(fma a1 a1 (* a2 a2))
3.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
5.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

series366.0ms

Counts
3 → 9
Calls
3 calls:
34.0ms
(fma a1 a1 (* a2 a2))
108.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
223.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify35.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0205467
11002399
25001393

prune188.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma a1 a1 (* a2 a2))
0.2b
(* (cos th) (/ (fma a1 a1 (* a2 a2)) (sqrt 2.0)))
0.6b
(/ (fma a1 a1 (* a2 a2)) (sqrt 2.0))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
38×times-frac
32×add-cube-cbrt *-un-lft-identity
22×associate-*r* sqrt-prod
10×add-exp-log add-cbrt-cube
6×associate-/r*
5×pow1
3×expm1-log1p-u associate-*l* log1p-expm1-u associate-/l* add-log-exp unswap-sqr
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv
1×frac-2neg associate-*r/ pow-prod-down clear-num *-commutative fma-udef
Counts
3 → 95
Calls
3 calls:
0.0ms
(fma a1 a1 (* a2 a2))
11.0ms
(* (cos th) (/ (fma a1 a1 (* a2 a2)) (sqrt 2.0)))
3.0ms
(/ (fma a1 a1 (* a2 a2)) (sqrt 2.0))

series359.0ms

Counts
3 → 9
Calls
3 calls:
40.0ms
(fma a1 a1 (* a2 a2))
216.0ms
(* (cos th) (/ (fma a1 a1 (* a2 a2)) (sqrt 2.0)))
103.0ms
(/ (fma a1 a1 (* a2 a2)) (sqrt 2.0))

simplify42.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0258819
11145718
25001693

prune461.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos th) (* (/ (hypot a1 a2) (sqrt (sqrt 2.0))) (/ (hypot a1 a2) (sqrt (sqrt 2.0)))))
0.2b
(/ (hypot a1 a2) (sqrt (sqrt 2.0)))
0.2b
(/ (hypot a1 a2) (sqrt (sqrt 2.0)))
0.5b
(* (/ (hypot a1 a2) (sqrt (sqrt 2.0))) (/ (hypot a1 a2) (sqrt (sqrt 2.0))))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
240×sqrt-prod
230×add-sqr-sqrt
222×times-frac
137×add-cube-cbrt *-un-lft-identity
49×swap-sqr
38×add-exp-log add-cbrt-cube
34×associate-*l*
32×associate-*r*
18×associate-/r*
17×unswap-sqr
16×pow1
13×prod-exp cbrt-unprod
10×cbrt-undiv div-exp
6×sqrt-undiv hypot-udef div-inv associate-/l*
5×associate-*r/
4×expm1-log1p-u pow-prod-down log1p-expm1-u add-log-exp
2×frac-times frac-2neg associate-*l/ clear-num *-commutative
1×pow2 pow-plus sqrt-unprod rem-square-sqrt pow-sqr pow-prod-up
Counts
4 → 293
Calls
4 calls:
36.0ms
(* (cos th) (* (/ (hypot a1 a2) (sqrt (sqrt 2.0))) (/ (hypot a1 a2) (sqrt (sqrt 2.0)))))
4.0ms
(/ (hypot a1 a2) (sqrt (sqrt 2.0)))
4.0ms
(/ (hypot a1 a2) (sqrt (sqrt 2.0)))
37.0ms
(* (/ (hypot a1 a2) (sqrt (sqrt 2.0))) (/ (hypot a1 a2) (sqrt (sqrt 2.0))))

series709.0ms

Counts
4 → 12
Calls
4 calls:
246.0ms
(* (cos th) (* (/ (hypot a1 a2) (sqrt (sqrt 2.0))) (/ (hypot a1 a2) (sqrt (sqrt 2.0)))))
164.0ms
(/ (hypot a1 a2) (sqrt (sqrt 2.0)))
165.0ms
(/ (hypot a1 a2) (sqrt (sqrt 2.0)))
134.0ms
(* (/ (hypot a1 a2) (sqrt (sqrt 2.0))) (/ (hypot a1 a2) (sqrt (sqrt 2.0))))

simplify103.0ms

Algorithm
egg-herbie
Counts
305 → 305
Iterations

Useful iterations: 2 (69.0ms)

IterNodesCost
07143973
134883509
250013477

prune659.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos th) (/ (* (hypot a1 a2) (/ (hypot a1 a2) (sqrt (sqrt 2.0)))) (sqrt (sqrt 2.0))))
0.2b
(/ (* (hypot a1 a2) (/ (hypot a1 a2) (sqrt (sqrt 2.0)))) (sqrt (sqrt 2.0)))
0.2b
(* (hypot a1 a2) (/ (hypot a1 a2) (sqrt (sqrt 2.0))))
0.2b
(/ (hypot a1 a2) (sqrt (sqrt 2.0)))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
93×sqrt-prod
75×times-frac
70×add-sqr-sqrt
57×add-cube-cbrt *-un-lft-identity
44×associate-*r*
34×add-exp-log add-cbrt-cube
18×associate-/r*
10×cbrt-undiv div-exp prod-exp cbrt-unprod
8×pow1
6×associate-*l*
5×hypot-udef unswap-sqr
4×expm1-log1p-u sqrt-undiv log1p-expm1-u div-inv associate-/l* add-log-exp
3×associate-*r/
2×frac-2neg sqrt-unprod pow-prod-down clear-num *-commutative
1×associate-/l/
Counts
4 → 185
Calls
4 calls:
25.0ms
(* (cos th) (/ (* (hypot a1 a2) (/ (hypot a1 a2) (sqrt (sqrt 2.0)))) (sqrt (sqrt 2.0))))
10.0ms
(/ (* (hypot a1 a2) (/ (hypot a1 a2) (sqrt (sqrt 2.0)))) (sqrt (sqrt 2.0)))
15.0ms
(* (hypot a1 a2) (/ (hypot a1 a2) (sqrt (sqrt 2.0))))
7.0ms
(/ (hypot a1 a2) (sqrt (sqrt 2.0)))

series732.0ms

Counts
4 → 12
Calls
4 calls:
244.0ms
(* (cos th) (/ (* (hypot a1 a2) (/ (hypot a1 a2) (sqrt (sqrt 2.0)))) (sqrt (sqrt 2.0))))
127.0ms
(/ (* (hypot a1 a2) (/ (hypot a1 a2) (sqrt (sqrt 2.0)))) (sqrt (sqrt 2.0)))
190.0ms
(* (hypot a1 a2) (/ (hypot a1 a2) (sqrt (sqrt 2.0))))
171.0ms
(/ (hypot a1 a2) (sqrt (sqrt 2.0)))

simplify74.0ms

Algorithm
egg-herbie
Counts
197 → 197
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
05181991
126881702
250021577

prune460.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes174.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01411
11411

end0.0ms

sample2.9s

Algorithm
intervals
Results
1.0s2509×body1280valid
634.0ms7918×body80valid
599.0ms2065×body640valid
227.0ms1063×body320valid
78.0ms500×body160valid