Details

Time bar (total: 5.4s)

sample249.0ms

Algorithm
intervals
Results
75.0ms94×body1280valid
31.0ms61×body640valid
12.0ms73×body80valid
6.0ms16×body320valid
3.0ms12×body160valid

simplify86.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
08243
112243
216243
318243
420243
521243
done21243

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.2b

localize22.0ms

Local error

Found 3 expressions with local error:

0.2b
(* r (/ (sin b) (cos (+ a b))))
0.3b
(/ (sin b) (cos (+ a b)))
3.1b
(cos (+ a b))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
19×*-un-lft-identity times-frac add-cube-cbrt
13×associate-*r*
10×add-cbrt-cube add-exp-log
5×pow1
3×associate-/r* associate-*l* associate-/l* add-log-exp
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
1×cos-sum clear-num frac-2neg pow-prod-down associate-*r/ *-commutative
Counts
3 → 67
Calls
3 calls:
29.0ms
(* r (/ (sin b) (cos (+ a b))))
15.0ms
(/ (sin b) (cos (+ a b)))
18.0ms
(cos (+ a b))

series195.0ms

Counts
3 → 9
Calls
3 calls:
105.0ms
(* r (/ (sin b) (cos (+ a b))))
51.0ms
(/ (sin b) (cos (+ a b)))
38.0ms
(cos (+ a b))

simplify3.1s

Counts
76 → 76
Iterations

Useful iterations: 3 (1.2s)

IterNodesCost
011723680
126922057
283821856
3307521536
done500121536

prune557.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.3b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.2b
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
0.2b
(* (sin a) (sin b))
0.2b
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

rewrite170.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
22×*-un-lft-identity add-cube-cbrt
20×associate-*r*
19×times-frac
13×add-cbrt-cube add-exp-log
8×pow1 associate-/r/
7×sin-mult
6×associate-*l* cos-mult add-log-exp
3×associate-/r* flip3-- prod-exp frac-sub cbrt-unprod flip-- associate-/l* sub-div unswap-sqr
2×cbrt-undiv div-exp pow-prod-down *-commutative div-inv
1×clear-num sub-neg frac-2neg diff-log associate-*r/
Counts
4 → 100
Calls
4 calls:
27.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
96.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
9.0ms
(* (sin a) (sin b))
33.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series663.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
310.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
79.0ms
(* (sin a) (sin b))
169.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify159.0ms

Iterations

Useful iterations: 0 (23.0ms)

IterNodesCost
017151765