Details

Time bar (total: 22.2s)

sample145.0ms

Algorithm
intervals
Results
44.0ms73×body1280valid
27.0ms63×body640valid
25.0ms258×body80valid
11.0ms42×body320valid
4.0ms19×body160valid

simplify256.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (50.0ms)

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

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma a1 a1 (* a2 a2))
0.1b
(* (cos th) (fma a1 a1 (* a2 a2)))
0.4b
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

rewrite57.0ms

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:
1.0ms
(fma a1 a1 (* a2 a2))
19.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
34.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

series505.0ms

Counts
3 → 9
Calls
3 calls:
52.0ms
(fma a1 a1 (* a2 a2))
144.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
309.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify3.1s

Counts
70 → 70
Iterations

Useful iterations: done (3.1s)

IterNodesCost
0103947
1201911
2750777
33465759
done5000758

prune260.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (hypot a2 a1) (cos th))
0.1b
(* (* (hypot a2 a1) (cos th)) (sqrt (fma a1 a1 (* a2 a2))))
0.4b
(/ (* (* (hypot a2 a1) (cos th)) (sqrt (fma a1 a1 (* a2 a2)))) (sqrt 2.0))
5.6b
(sqrt (fma a1 a1 (* a2 a2)))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
20×add-exp-log add-cbrt-cube
16×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
12×pow1 sqrt-prod
9×associate-*r*
7×prod-exp cbrt-unprod
6×times-frac associate-/r*
4×expm1-log1p-u associate-*l* pow-prod-down log1p-expm1-u add-log-exp
3×cbrt-undiv div-exp
2×*-commutative
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num fma-udef hypot-def div-inv associate-/l* unswap-sqr
Counts
4 → 90
Calls
4 calls:
17.0ms
(* (hypot a2 a1) (cos th))
28.0ms
(* (* (hypot a2 a1) (cos th)) (sqrt (fma a1 a1 (* a2 a2))))
45.0ms
(/ (* (* (hypot a2 a1) (cos th)) (sqrt (fma a1 a1 (* a2 a2)))) (sqrt 2.0))
3.0ms
(sqrt (fma a1 a1 (* a2 a2)))

series920.0ms

Counts
4 → 12
Calls
4 calls:
145.0ms
(* (hypot a2 a1) (cos th))
277.0ms
(* (* (hypot a2 a1) (cos th)) (sqrt (fma a1 a1 (* a2 a2))))
430.0ms
(/ (* (* (hypot a2 a1) (cos th)) (sqrt (fma a1 a1 (* a2 a2)))) (sqrt 2.0))
67.0ms
(sqrt (fma a1 a1 (* a2 a2)))

simplify2.0s

Counts
102 → 102
Iterations

Useful iterations: done (2.0s)

IterNodesCost
01371582
13011450
21078967
done5001965

prune430.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (hypot a2 a1) (cos th))
0.3b
(/ (* (hypot a2 a1) (cos th)) (/ (sqrt 2.0) (hypot a2 a1)))
0.5b
(/ (sqrt 2.0) (hypot a2 a1))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
76×times-frac
48×add-sqr-sqrt
46×add-cube-cbrt *-un-lft-identity
30×sqrt-prod
25×associate-/r*
19×add-exp-log add-cbrt-cube
7×cbrt-undiv div-exp associate-/l*
5×pow1
4×div-inv
3×expm1-log1p-u associate-*r* associate-*l* prod-exp cbrt-unprod log1p-expm1-u add-log-exp
2×frac-2neg clear-num
1×sqrt-undiv hypot-udef pow-prod-down associate-/r/ *-commutative unswap-sqr
Counts
3 → 128
Calls
3 calls:
9.0ms
(* (hypot a2 a1) (cos th))
18.0ms
(/ (* (hypot a2 a1) (cos th)) (/ (sqrt 2.0) (hypot a2 a1)))
7.0ms
(/ (sqrt 2.0) (hypot a2 a1))

series559.0ms

Counts
3 → 9
Calls
3 calls:
153.0ms
(* (hypot a2 a1) (cos th))
295.0ms
(/ (* (hypot a2 a1) (cos th)) (/ (sqrt 2.0) (hypot a2 a1)))
110.0ms
(/ (sqrt 2.0) (hypot a2 a1))

simplify2.3s

Counts
137 → 137
Iterations

Useful iterations: done (2.3s)

IterNodesCost
01892044
14041916
214941746
done50001744

prune480.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (hypot a2 a1) (cos th))
0.2b
(/ 2.0 (fma a2 a2 (* a1 a1)))
0.3b
(/ (* (hypot a2 a1) (cos th)) (sqrt (/ 2.0 (fma a2 a2 (* a1 a1)))))
5.8b
(sqrt (/ 2.0 (fma a2 a2 (* a1 a1))))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
53×times-frac
42×add-sqr-sqrt
39×sqrt-prod
37×add-cube-cbrt *-un-lft-identity
19×associate-/r*
13×add-exp-log add-cbrt-cube
7×pow1
5×div-inv
4×expm1-log1p-u log1p-expm1-u associate-/l* add-log-exp
3×cbrt-undiv div-exp associate-*r* associate-*l*
2×rem-sqrt-square frac-2neg sqrt-div prod-exp clear-num cbrt-unprod
1×sqrt-pow1 pow1/2 pow-prod-down associate-/r/ *-commutative unswap-sqr
Counts
4 → 126
Calls
4 calls:
17.0ms
(* (hypot a2 a1) (cos th))
10.0ms
(/ 2.0 (fma a2 a2 (* a1 a1)))
21.0ms
(/ (* (hypot a2 a1) (cos th)) (sqrt (/ 2.0 (fma a2 a2 (* a1 a1)))))
7.0ms
(sqrt (/ 2.0 (fma a2 a2 (* a1 a1))))

series771.0ms

Counts
4 → 12
Calls
4 calls:
168.0ms
(* (hypot a2 a1) (cos th))
78.0ms
(/ 2.0 (fma a2 a2 (* a1 a1)))
404.0ms
(/ (* (hypot a2 a1) (cos th)) (sqrt (/ 2.0 (fma a2 a2 (* a1 a1)))))
121.0ms
(sqrt (/ 2.0 (fma a2 a2 (* a1 a1))))

simplify3.0s

Counts
138 → 138
Iterations

Useful iterations: done (3.0s)

IterNodesCost
01932207
13372090
210561819
338231817
done50001816

prune647.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes217.0ms

Accuracy

0% (0.6b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 0.7b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01216
11316
done1316

end0.0ms

sample6.4s

Algorithm
intervals
Results
2.1s2544×body1280valid
1.4s2134×body640valid
1.2s8022×body80valid
738.0ms1074×body320valid
105.0ms520×body160valid