Details

Time bar (total: 10.8s)

sample81.0ms

Algorithm
intervals
Results
34.0ms54×body1280valid
15.0ms44×body640valid
12.0ms151×body80valid
7.0ms29×body320valid
2.0ms15×body160valid

simplify36.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (4.0ms)

IterNodesCost
01012
11812
23211
34411
45511
56011
66211
done6211

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
0.1b
(/ 1.0 (sin B))
0.2b
(/ 1.0 (tan B))
0.3b
(* x (/ 1.0 (tan B)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
31×*-un-lft-identity
29×add-cube-cbrt
28×times-frac
14×associate-*r*
13×add-exp-log add-cbrt-cube
8×add-log-exp
6×pow1 fma-def associate-/r* associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×cbrt-undiv div-exp associate-*l* div-inv
2×tan-quot frac-2neg associate-*r/ prod-exp clear-num sum-log associate-/r/ cbrt-unprod unswap-sqr
1×+-commutative neg-sub0 distribute-lft-neg-in associate-+l- neg-mul-1 distribute-rgt-neg-in flip3-+ pow-prod-down neg-log frac-add *-commutative flip-+ distribute-neg-frac distribute-lft-out
Counts
4 → 117
Calls
4 calls:
9.0ms
(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
2.0ms
(/ 1.0 (sin B))
2.0ms
(/ 1.0 (tan B))
8.0ms
(* x (/ 1.0 (tan B)))

series275.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B)))
18.0ms
(/ 1.0 (sin B))
36.0ms
(/ 1.0 (tan B))
109.0ms
(* x (/ 1.0 (tan B)))

simplify1.7s

Counts
129 → 129
Iterations

Useful iterations: 3 (868.0ms)

IterNodesCost
01881244
14381180
211441075
338371067
done50011067

prune351.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
0.1b
(/ 1.0 (sin B))
0.2b
(/ (* x 1.0) (tan B))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
20×fma-def
18×add-sqr-sqrt add-cube-cbrt times-frac
10×add-exp-log add-cbrt-cube
9×distribute-rgt-neg-in
8×distribute-lft-neg-in
7×add-log-exp
6×associate-/r*
4×div-inv associate-/l*
3×tan-quot pow1 cbrt-undiv expm1-log1p-u div-exp associate-/r/ log1p-expm1-u
2×frac-2neg clear-num sum-log distribute-lft-out
1×+-commutative neg-sub0 associate-+l- neg-mul-1 flip3-+ neg-log frac-add prod-exp cbrt-unprod flip-+ distribute-neg-frac
Counts
3 → 91
Calls
3 calls:
31.0ms
(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
2.0ms
(/ 1.0 (sin B))
4.0ms
(/ (* x 1.0) (tan B))

series243.0ms

Counts
3 → 9
Calls
3 calls:
115.0ms
(+ (- (/ (* x 1.0) (tan B))) (/ 1.0 (sin B)))
18.0ms
(/ 1.0 (sin B))
110.0ms
(/ (* x 1.0) (tan B))

simplify1.8s

Counts
100 → 100
Iterations

Useful iterations: 3 (939.0ms)

IterNodesCost
0150887
1350843
2989755
33983747
done5001747

prune266.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (- (* 1.0 (/ (* x (cos B)) (sin B)))) (/ 1.0 (sin B)))
0.1b
(/ 1.0 (sin B))
0.1b
(* x (cos B))
0.2b
(/ (* x (cos B)) (sin B))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt *-un-lft-identity
17×add-cube-cbrt
13×add-exp-log add-cbrt-cube
12×times-frac
8×add-log-exp
6×pow1 fma-def associate-/r*
4×expm1-log1p-u log1p-expm1-u associate-/l*
3×cbrt-undiv div-exp associate-*r* associate-*l* div-inv
2×distribute-rgt-neg-in frac-2neg prod-exp clear-num sum-log cbrt-unprod distribute-lft-out
1×+-commutative neg-sub0 distribute-lft-neg-in associate-+l- neg-mul-1 flip3-+ associate-*r/ pow-prod-down neg-log frac-add *-commutative flip-+ distribute-neg-frac unswap-sqr
Counts
4 → 96
Calls
4 calls:
9.0ms
(+ (- (* 1.0 (/ (* x (cos B)) (sin B)))) (/ 1.0 (sin B)))
2.0ms
(/ 1.0 (sin B))
3.0ms
(* x (cos B))
6.0ms
(/ (* x (cos B)) (sin B))

series249.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(+ (- (* 1.0 (/ (* x (cos B)) (sin B)))) (/ 1.0 (sin B)))
21.0ms
(/ 1.0 (sin B))
35.0ms
(* x (cos B))
92.0ms
(/ (* x (cos B)) (sin B))

simplify1.1s

Counts
108 → 108
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01621113
13761066
21067948
done5000937

prune282.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (- (/ 1 (/ (tan B) (* x 1.0)))) (/ 1.0 (sin B)))
0.1b
(/ 1.0 (sin B))
0.2b
(/ (tan B) (* x 1.0))
0.2b
(/ 1 (/ (tan B) (* x 1.0)))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
107×times-frac
68×*-un-lft-identity
59×add-sqr-sqrt add-cube-cbrt
56×fma-def
32×add-exp-log
29×distribute-rgt-neg-in
26×distribute-lft-neg-in
20×add-cbrt-cube
16×div-inv
15×div-exp
11×associate-/r*
9×associate-/l*
8×cbrt-undiv add-log-exp
5×pow1
4×expm1-log1p-u prod-exp log1p-expm1-u distribute-lft-out
3×rec-exp frac-2neg 1-exp clear-num associate-/r/
2×sum-log cbrt-unprod
1×tan-quot +-commutative neg-sub0 associate-+l- neg-mul-1 pow-flip flip3-+ neg-log frac-add flip-+ associate-/l/ distribute-neg-frac inv-pow
Counts
4 → 187
Calls
4 calls:
76.0ms
(+ (- (/ 1 (/ (tan B) (* x 1.0)))) (/ 1.0 (sin B)))
2.0ms
(/ 1.0 (sin B))
3.0ms
(/ (tan B) (* x 1.0))
6.0ms
(/ 1 (/ (tan B) (* x 1.0)))

series274.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(+ (- (/ 1 (/ (tan B) (* x 1.0)))) (/ 1.0 (sin B)))
19.0ms
(/ 1.0 (sin B))
52.0ms
(/ (tan B) (* x 1.0))
85.0ms
(/ 1 (/ (tan B) (* x 1.0)))

simplify987.0ms

Counts
199 → 199
Iterations

Useful iterations: done (983.0ms)

IterNodesCost
02351771
15511578
214161329
done50001327

prune478.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes50.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01115
11815
22215
32815
done2815

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.0s1749×body1280valid
529.0ms1427×body640valid
379.0ms4866×body80valid
187.0ms718×body320valid
63.0ms364×body160valid