Details

Time bar (total: 20.5s)

sample142.0ms

Algorithm
intervals
Results
42.0ms86×body1280valid
39.0ms66×body640valid
23.0ms284×body80valid
7.0ms30×body320valid
3.0ms15×body160valid

simplify207.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (9.0ms)

IterNodesCost
01219
12613
25712
38712
411412
513212
615112
717312
817512
done17512

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×add-exp-log add-cbrt-cube
8×add-cube-cbrt *-un-lft-identity
6×times-frac associate-/r* sqrt-prod
4×pow1
3×associate-*r* associate-*l*
2×cbrt-undiv expm1-log1p-u div-exp prod-exp cbrt-unprod fma-udef log1p-expm1-u add-log-exp
1×distribute-rgt-in frac-2neg distribute-lft-in pow-prod-down clear-num *-commutative div-inv associate-/l* unswap-sqr
Counts
2 → 51
Calls
2 calls:
11.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
16.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

series401.0ms

Counts
2 → 6
Calls
2 calls:
148.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
252.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify1.2s

Counts
57 → 57
Iterations

Useful iterations: done (1.2s)

IterNodesCost
0100839
1213806
21313696
done5001690

prune233.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 2 expressions with local error:

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

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
38×times-frac
31×add-cube-cbrt *-un-lft-identity
22×associate-*r* sqrt-prod
9×add-exp-log add-cbrt-cube
6×associate-/r*
4×pow1
3×associate-*l* associate-/l* unswap-sqr
2×cbrt-undiv expm1-log1p-u div-exp prod-exp cbrt-unprod log1p-expm1-u div-inv add-log-exp
1×frac-2neg associate-*r/ pow-prod-down clear-num *-commutative
Counts
2 → 85
Calls
2 calls:
51.0ms
(* (cos th) (/ (fma a1 a1 (* a2 a2)) (sqrt 2.0)))
11.0ms
(/ (fma a1 a1 (* a2 a2)) (sqrt 2.0))

series437.0ms

Counts
2 → 6
Calls
2 calls:
288.0ms
(* (cos th) (/ (fma a1 a1 (* a2 a2)) (sqrt 2.0)))
149.0ms
(/ (fma a1 a1 (* a2 a2)) (sqrt 2.0))

simplify2.4s

Counts
91 → 91
Iterations

Useful iterations: done (2.4s)

IterNodesCost
01261508
12721432
219901240
done50001238

prune384.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 3 expressions with local error:

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

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
56×times-frac
36×cbrt-prod
35×add-exp-log add-sqr-sqrt
33×add-cube-cbrt *-un-lft-identity
22×add-cbrt-cube
18×sqrt-prod
13×cbrt-undiv div-exp
12×div-inv
10×associate-/r*
9×prod-exp cbrt-unprod
6×associate-/l*
5×pow1
3×expm1-log1p-u associate-*r* associate-*l* log1p-expm1-u add-log-exp
2×frac-2neg clear-num fma-udef
1×distribute-rgt-in distribute-lft-in pow-prod-down *-commutative associate-/l/ unswap-sqr
Counts
3 → 127
Calls
3 calls:
17.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
40.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
49.0ms
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

series1.5s

Counts
3 → 9
Calls
3 calls:
160.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
926.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
369.0ms
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

simplify1.9s

Counts
136 → 136
Iterations

Useful iterations: done (1.9s)

IterNodesCost
02123744
14993405
227542971
done50002934

prune667.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite132.0ms

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt
38×times-frac
34×add-cube-cbrt *-un-lft-identity
23×associate-*r*
22×sqrt-prod
20×add-exp-log add-cbrt-cube
11×pow1
7×prod-exp cbrt-unprod
6×associate-*l* associate-/r*
4×expm1-log1p-u hypot-udef pow-prod-down log1p-expm1-u add-log-exp
3×cbrt-undiv associate-*r/ div-exp associate-/l* unswap-sqr
2×sqrt-undiv *-commutative div-inv
1×frac-2neg sqrt-unprod clear-num
Counts
4 → 120
Calls
4 calls:
1.0ms
(hypot a1 a2)
69.0ms
(* (cos th) (* (hypot a2 a1) (/ (hypot a1 a2) (sqrt 2.0))))
47.0ms
(* (hypot a2 a1) (/ (hypot a1 a2) (sqrt 2.0)))
8.0ms
(/ (hypot a1 a2) (sqrt 2.0))

series912.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(hypot a1 a2)
408.0ms
(* (cos th) (* (hypot a2 a1) (/ (hypot a1 a2) (sqrt 2.0))))
259.0ms
(* (hypot a2 a1) (/ (hypot a1 a2) (sqrt 2.0)))
187.0ms
(/ (hypot a1 a2) (sqrt 2.0))

simplify2.7s

Counts
132 → 132
Iterations

Useful iterations: done (2.7s)

IterNodesCost
01651735
13661641
224861467
done50011465

prune654.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes277.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01321
11421
done1421

end0.0ms

sample6.0s

Algorithm
intervals
Results
1.8s2377×body1280valid
1.7s8068×body80valid
1.2s2165×body640valid
400.0ms1084×body320valid
155.0ms524×body160valid