Details

Time bar (total: 10.9s)

sample137.0ms

Algorithm
intervals
Results
64.0ms127×body1280valid
19.0ms256×pre80true
17.0ms67×body640valid
5.0ms26×body320valid
2.0ms29×body80valid
1.0ms7×body160valid

simplify1.3s

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
099
1159
2229
3319
4379
5479
6559
7659
8839
91159
101549
111889
122279
132749
143259
153749
164259
174749
185219
195649
206099
216519
226959
237399
247879
258329
268799
279279
289779
2910259
3010739
3111169
3211609
3312029
3412439
3512869
3613309
3713749
3814189
3914619
4015079
4115529
4215999
4316459
4416889
4517339
4617769
4718189
4818629
4919049
5019499
5119949
5220399
5320839
5421259
5521679
5622119
5722559
5823009
5923419
6023869
6124359
6224879
6325369
6425849
6526299
6626759
6727219
6827669
6928099
7028549
7128989
7229399
7329819
7430269
7530749
7631239
7731669
7832109
7932589
8033059
8133479
8233889
8334299
8434749
8535219
8635689
8736159
8836649
8937199
9037779
9138269
9238779
9339269
9439729
9540209
9640699
9741169
9841649
9942129
10042609
10143029
10243459
10343889
10444309
10544739
10645209
10745669
10846139
10946579
11047029
11147469
11247949
11348429
11448919
11549369
11649799
done50019

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 14.8b

Counts
2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b
(+ x (- (tan (+ y z)) (tan a)))
0.1b
(- (tan (+ y z)) (tan a))
4.3b
(tan (+ y z))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity add-log-exp
5×add-sqr-sqrt
4×tan-quot
3×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
2×sub-neg tan-sum associate-+r+ diff-log sum-log frac-sub distribute-lft-out distribute-lft-out--
1×+-commutative associate-+r- flip3-- flip3-+ flip-- flip-+ difference-of-squares
Counts
3 → 42
Calls
3 calls:
6.0ms
(+ x (- (tan (+ y z)) (tan a)))
7.0ms
(- (tan (+ y z)) (tan a))
6.0ms
(tan (+ y z))

series116.0ms

Counts
3 → 9
Calls
3 calls:
45.0ms
(+ x (- (tan (+ y z)) (tan a)))
37.0ms
(- (tan (+ y z)) (tan a))
33.0ms
(tan (+ y z))

simplify1.1s

Counts
51 → 51
Iterations

Useful iterations: 3 (121.0ms)

IterNodesCost
092627
1199591
2442572
31078570
44015570
done5000570

prune99.0ms

Filtered
41 candidates to 51 candidates (-24.4%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New45651
Fresh000
Picked101
Done000
Total46652

Merged error: 0.1b

Counts
52 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ (tan y) (tan z))
0.1b
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
0.1b
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
0.2b
(* (tan y) (tan z))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
13×add-sqr-sqrt add-log-exp
7×tan-quot
6×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
3×associate-*r* associate-*l* sum-log distribute-lft-out
2×+-commutative sub-neg associate-+r+ flip3-+ diff-log flip-+ distribute-lft-out-- difference-of-squares
1×frac-times associate-+r- flip3-- times-frac associate-*r/ pow-prod-down associate-*l/ frac-add prod-exp *-commutative frac-sub flip-- cbrt-unprod unswap-sqr
Counts
4 → 67
Calls
4 calls:
5.0ms
(+ (tan y) (tan z))
14.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
16.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
6.0ms
(* (tan y) (tan z))

series331.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(+ (tan y) (tan z))
145.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
137.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
25.0ms
(* (tan y) (tan z))

simplify710.0ms

Counts
79 → 79
Iterations

Useful iterations: 3 (279.0ms)

IterNodesCost
01551433
13771368
210021303
325431291
done50011291

prune168.0ms

Filtered
59 candidates to 79 candidates (-33.9%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New70979
Fresh235
Picked101
Done000
Total731285

Merged error: 0.1b

Counts
85 → 12

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (+ (tan y) (tan z)) (cos a))
0.2b
(* (tan y) (tan z))
0.2b
(* (tan y) (tan z))
0.2b
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
19×associate-*l/
18×add-sqr-sqrt
15×add-exp-log add-cbrt-cube
14×tan-quot *-un-lft-identity
12×add-cube-cbrt
10×pow1 associate-*l*
9×associate-*r*
8×associate-/l/
6×frac-sub
5×flip3-- flip--
4×prod-exp cbrt-unprod add-log-exp
3×flip3-+ times-frac pow-prod-down frac-add *-commutative flip-+ associate-/l* unswap-sqr
2×cbrt-undiv frac-times associate-*r/ div-exp associate-/r/
1×frac-2neg div-sub clear-num associate-/r* div-inv distribute-lft-out
Counts
4 → 96
Calls
4 calls:
9.0ms
(* (+ (tan y) (tan z)) (cos a))
6.0ms
(* (tan y) (tan z))
6.0ms
(* (tan y) (tan z))
17.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

series260.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(* (+ (tan y) (tan z)) (cos a))
27.0ms
(* (tan y) (tan z))
25.0ms
(* (tan y) (tan z))
169.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

simplify657.0ms

Counts
108 → 108
Iterations

Useful iterations: done (653.0ms)

IterNodesCost
02012138
16192077
224451711
done50001653

prune192.0ms

Filtered
84 candidates to 108 candidates (-28.6%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New1071108
Fresh11011
Picked011
Done000
Total10812120

Merged error: 0.1b

Counts
120 → 12

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (/ (* (+ (tan y) (tan z)) (cos a)) (- 1 (* (tan y) (tan z)))) (/ (sin a) 1))
0.2b
(* (+ (tan y) (tan z)) (cos a))
0.2b
(/ (- (/ (* (+ (tan y) (tan z)) (cos a)) (- 1 (* (tan y) (tan z)))) (/ (sin a) 1)) (cos a))
0.2b
(* (tan y) (tan z))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
59×add-sqr-sqrt
37×*-un-lft-identity
31×times-frac
20×add-cube-cbrt
15×difference-of-squares
10×add-exp-log add-cbrt-cube
8×pow1
7×associate-*l* associate-/l*
6×tan-quot associate-*r* add-log-exp
5×distribute-lft-out--
4×associate-*l/
3×associate-/r* associate-/l/
2×flip3-- pow-prod-down prod-exp *-commutative frac-sub flip-- cbrt-unprod unswap-sqr
1×cbrt-undiv frac-times sub-neg frac-2neg flip3-+ diff-log div-sub associate-*r/ div-exp frac-add clear-num flip-+ div-inv distribute-lft-out
Counts
4 → 107
Calls
4 calls:
16.0ms
(- (/ (* (+ (tan y) (tan z)) (cos a)) (- 1 (* (tan y) (tan z)))) (/ (sin a) 1))
9.0ms
(* (+ (tan y) (tan z)) (cos a))
23.0ms
(/ (- (/ (* (+ (tan y) (tan z)) (cos a)) (- 1 (* (tan y) (tan z)))) (/ (sin a) 1)) (cos a))
6.0ms
(* (tan y) (tan z))

series391.0ms

Counts
4 → 12
Calls
4 calls:
147.0ms
(- (/ (* (+ (tan y) (tan z)) (cos a)) (- 1 (* (tan y) (tan z)))) (/ (sin a) 1))
39.0ms
(* (+ (tan y) (tan z)) (cos a))
179.0ms
(/ (- (/ (* (+ (tan y) (tan z)) (cos a)) (- 1 (* (tan y) (tan z)))) (/ (sin a) 1)) (cos a))
25.0ms
(* (tan y) (tan z))

simplify516.0ms

Counts
119 → 119
Iterations

Useful iterations: done (512.0ms)

IterNodesCost
02133148
15292925
216922733
done50022633

prune148.0ms

Filtered
89 candidates to 119 candidates (-33.7%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1181119
Fresh1910
Picked101
Done101
Total12110131

Merged error: 0.1b

Counts
131 → 10

regimes971.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
02129
12727
done2727

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.6s3963×body1280valid
557.0ms8000×pre80true
501.0ms2013×body640valid
117.0ms666×body320valid
58.0ms1056×body80valid
35.0ms302×body160valid

Profiling

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