Details

Time bar (total: 20.4s)

sample168.0ms

Algorithm
intervals
Results
61.0ms85×body1280valid
34.0ms250×body80valid
28.0ms55×body640valid
13.0ms35×body320valid
5.0ms21×body160valid

simplify237.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (9.0ms)

IterNodesCost
01219
12613
25712
38712
411412
513212
615012
717012
817212
done17212

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize26.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma a1 a1 (* a2 a2))
0.2b
(* (cos th) (fma a1 a1 (* a2 a2)))
0.4b
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

rewrite31.0ms

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))
15.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
14.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

series597.0ms

Counts
3 → 9
Calls
3 calls:
62.0ms
(fma a1 a1 (* a2 a2))
191.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
343.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify3.2s

Counts
70 → 70
Iterations

Useful iterations: done (3.2s)

IterNodesCost
0103947
1201911
2750777
33465759
done5000758

prune291.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

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)))
0.4b
(/ (fma a1 a1 (* a2 a2)) (sqrt 2.0))

rewrite73.0ms

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:
1.0ms
(fma a1 a1 (* a2 a2))
44.0ms
(* (cos th) (/ (fma a1 a1 (* a2 a2)) (sqrt 2.0)))
21.0ms
(/ (fma a1 a1 (* a2 a2)) (sqrt 2.0))

series563.0ms

Counts
3 → 9
Calls
3 calls:
74.0ms
(fma a1 a1 (* a2 a2))
323.0ms
(* (cos th) (/ (fma a1 a1 (* a2 a2)) (sqrt 2.0)))
166.0ms
(/ (fma a1 a1 (* a2 a2)) (sqrt 2.0))

simplify2.5s

Counts
104 → 104
Iterations

Useful iterations: done (2.5s)

IterNodesCost
01311616
12531531
28621325
329581317
done50001313

prune419.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite324.0ms

Algorithm
rewrite-expression-head
Rules
1137×sqrt-prod
1119×times-frac
625×add-sqr-sqrt
578×add-cube-cbrt *-un-lft-identity
283×associate-*r*
34×associate-/l*
22×div-inv
20×add-exp-log add-cbrt-cube
18×associate-/r*
13×unswap-sqr
7×cbrt-undiv div-exp
6×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*l* prod-exp cbrt-unprod
2×frac-2neg clear-num
1×associate-*r/ pow-prod-down *-commutative fma-udef associate-/l/
Counts
4 → 716
Calls
4 calls:
1.0ms
(fma a1 a1 (* a2 a2))
190.0ms
(* (cos th) (/ (/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
37.0ms
(/ (/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
8.0ms
(/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0)))

series730.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(fma a1 a1 (* a2 a2))
329.0ms
(* (cos th) (/ (/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
123.0ms
(/ (/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
212.0ms
(/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0)))

simplify2.2s

Counts
728 → 728
Iterations

Useful iterations: done (2.1s)

IterNodesCost
060518939
1142916385
2344514246
done500014052

prune1.7s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sqrt (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))
0.3b
(/ (/ (sqrt (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.3b
(* (* (cos th) (hypot a2 a1)) (/ (/ (sqrt (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
4.0b
(sqrt (fma a1 a1 (* a2 a2)))

rewrite570.0ms

Algorithm
rewrite-expression-head
Rules
2688×sqrt-prod
2124×times-frac
1102×add-sqr-sqrt
1101×add-cube-cbrt *-un-lft-identity
526×associate-*r*
64×associate-/l*
32×add-exp-log add-cbrt-cube
22×div-inv
18×associate-/r*
10×pow1 cbrt-undiv div-exp
9×prod-exp cbrt-unprod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×sqrt-undiv pow-prod-down
2×frac-2neg clear-num
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ associate-*l* *-commutative fma-udef hypot-def associate-/l/
Counts
4 → 1259
Calls
4 calls:
10.0ms
(/ (sqrt (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))
70.0ms
(/ (/ (sqrt (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
261.0ms
(* (* (cos th) (hypot a2 a1)) (/ (/ (sqrt (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
3.0ms
(sqrt (fma a1 a1 (* a2 a2)))

series952.0ms

Counts
4 → 12
Calls
4 calls:
237.0ms
(/ (sqrt (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))
178.0ms
(/ (/ (sqrt (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
473.0ms
(* (* (cos th) (hypot a2 a1)) (/ (/ (sqrt (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
64.0ms
(sqrt (fma a1 a1 (* a2 a2)))

simplify2.5s

Counts
1271 → 1271
Iterations

Useful iterations: done (2.4s)

IterNodesCost
087237667
1252031404
done500024309

prune3.3s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes3.0ms