Details

Time bar (total: 42.9s)

sample139.0ms

Algorithm
intervals
Results
43.0ms64×body1280valid
35.0ms249×body80valid
25.0ms54×body640valid
9.0ms27×body320valid
3.0ms13×body160valid

simplify495.0ms

Counts
1 → 1
Iterations
IterNodes
done134
7134
6122
5110
498
380
255
126
012

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize18.0ms

Local error

Found 2 expressions with local error:

0.3b
(/ (cos th) (/ (sqrt 2) (fma a1 a1 (* a2 a2))))
0.4b
(/ (sqrt 2) (fma a1 a1 (* a2 a2)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
156×times-frac
92×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
48×sqrt-prod
25×associate-/r*
9×add-cbrt-cube add-exp-log associate-/l*
6×div-inv
4×cbrt-undiv div-exp
2×expm1-log1p-u pow1 clear-num frac-2neg insert-posit16 log1p-expm1-u add-log-exp
1×associate-/r/
Counts
2 → 151
Calls
2 calls:
10.0ms
(/ (cos th) (/ (sqrt 2) (fma a1 a1 (* a2 a2))))
5.0ms
(/ (sqrt 2) (fma a1 a1 (* a2 a2)))

series330.0ms

Counts
2 → 6
Calls
2 calls:
241.0ms
(/ (cos th) (/ (sqrt 2) (fma a1 a1 (* a2 a2))))
89.0ms
(/ (sqrt 2) (fma a1 a1 (* a2 a2)))

simplify1.6s

Counts
157 → 157
Iterations
IterNodes
done5004
21635
1553
0226

prune863.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 2 expressions with local error:

0.1b
(* (cos th) (/ (fma a1 a1 (* a2 a2)) (sqrt 2)))
0.4b
(/ (fma a1 a1 (* a2 a2)) (sqrt 2))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
38×times-frac
31×*-un-lft-identity add-cube-cbrt
22×associate-*r* sqrt-prod
9×add-cbrt-cube add-exp-log
6×associate-/r*
4×pow1
3×associate-*l* associate-/l* unswap-sqr
2×expm1-log1p-u cbrt-undiv div-exp prod-exp cbrt-unprod insert-posit16 log1p-expm1-u div-inv add-log-exp
1×clear-num frac-2neg pow-prod-down associate-*r/ *-commutative
Counts
2 → 87
Calls
2 calls:
17.0ms
(* (cos th) (/ (fma a1 a1 (* a2 a2)) (sqrt 2)))
5.0ms
(/ (fma a1 a1 (* a2 a2)) (sqrt 2))

series432.0ms

Counts
2 → 6
Calls
2 calls:
278.0ms
(* (cos th) (/ (fma a1 a1 (* a2 a2)) (sqrt 2)))
154.0ms
(/ (fma a1 a1 (* a2 a2)) (sqrt 2))

simplify2.0s

Counts
93 → 93
Iterations
IterNodes
done5003
32298
2791
1277
0127

prune512.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (sqrt (fma a1 a1 (* a2 a2))) (/ (sqrt 2) (sqrt (fma a1 a1 (* a2 a2)))))
0.5b
(/ (sqrt 2) (sqrt (fma a1 a1 (* a2 a2))))
7.8b
(sqrt (fma a1 a1 (* a2 a2)))
7.8b
(sqrt (fma a1 a1 (* a2 a2)))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
528×times-frac
423×sqrt-prod
293×add-sqr-sqrt
291×*-un-lft-identity add-cube-cbrt
46×associate-/r*
12×associate-/l*
11×add-cbrt-cube add-exp-log
9×div-inv
6×pow1
4×expm1-log1p-u cbrt-undiv div-exp insert-posit16 log1p-expm1-u add-log-exp
3×sqrt-undiv
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 fma-udef hypot-def
1×associate-/r/
Counts
4 → 403
Calls
4 calls:
8.0ms
(/ (sqrt (fma a1 a1 (* a2 a2))) (/ (sqrt 2) (sqrt (fma a1 a1 (* a2 a2)))))
5.0ms
(/ (sqrt 2) (sqrt (fma a1 a1 (* a2 a2))))
1.0ms
(sqrt (fma a1 a1 (* a2 a2)))
1.0ms
(sqrt (fma a1 a1 (* a2 a2)))

series347.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(/ (sqrt (fma a1 a1 (* a2 a2))) (/ (sqrt 2) (sqrt (fma a1 a1 (* a2 a2)))))
112.0ms
(/ (sqrt 2) (sqrt (fma a1 a1 (* a2 a2))))
65.0ms
(sqrt (fma a1 a1 (* a2 a2)))
54.0ms
(sqrt (fma a1 a1 (* a2 a2)))

simplify2.1s

Counts
415 → 415
Iterations
IterNodes
done5001
21993
1921
0370

prune1.9s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (cbrt (sqrt 2)) (sqrt (fma a1 a1 (* a2 a2))))
0.3b
(/ (/ (sqrt (fma a1 a1 (* a2 a2))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) (/ (cbrt (sqrt 2)) (sqrt (fma a1 a1 (* a2 a2)))))
7.8b
(sqrt (fma a1 a1 (* a2 a2)))
7.8b
(sqrt (fma a1 a1 (* a2 a2)))

rewrite275.0ms

Algorithm
rewrite-expression-head
Rules
8912×times-frac
3456×sqrt-prod
3418×add-sqr-sqrt
3416×*-un-lft-identity add-cube-cbrt
1770×cbrt-prod
463×div-inv
64×associate-/r*
60×associate-/r/
56×associate-/l*
54×add-exp-log
37×div-exp
29×add-cbrt-cube
23×cbrt-undiv
6×pow1
4×expm1-log1p-u 1-exp prod-exp insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 cbrt-unprod fma-udef hypot-def
1×associate-/l/
Counts
4 → 2984
Calls
4 calls:
6.0ms
(/ (cbrt (sqrt 2)) (sqrt (fma a1 a1 (* a2 a2))))
19.0ms
(/ (/ (sqrt (fma a1 a1 (* a2 a2))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) (/ (cbrt (sqrt 2)) (sqrt (fma a1 a1 (* a2 a2)))))
1.0ms
(sqrt (fma a1 a1 (* a2 a2)))
1.0ms
(sqrt (fma a1 a1 (* a2 a2)))

series644.0ms

Counts
4 → 12
Calls
4 calls:
332.0ms
(/ (cbrt (sqrt 2)) (sqrt (fma a1 a1 (* a2 a2))))
161.0ms
(/ (/ (sqrt (fma a1 a1 (* a2 a2))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) (/ (cbrt (sqrt 2)) (sqrt (fma a1 a1 (* a2 a2)))))
52.0ms
(sqrt (fma a1 a1 (* a2 a2)))
99.0ms
(sqrt (fma a1 a1 (* a2 a2)))

simplify4.7s

Counts
2996 → 2996
Iterations
IterNodes
done5001
02814

prune20.0s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes560.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify5.0ms

Iterations
IterNodes
done11
111
010

end0.0ms

sample5.8s

Algorithm
intervals
Results
2.4s2488×body1280valid
1.4s2069×body640valid
1.1s7948×body80valid
398.0ms1037×body320valid
161.0ms511×body160valid