Details

Time bar (total: 17.9s)

sample165.0ms

Algorithm
intervals
Results
97.0ms126×body1280valid
25.0ms60×body640valid
10.0ms256×pre80true
6.0ms23×body320valid
3.0ms37×body80valid
2.0ms10×body160valid

simplify104.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
099
1159
2229
3319
4379
5479
6619
7849
81079
91379
101649
done1649

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.7b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b
(+ x (- (tan (+ y z)) (tan a)))
0.1b
(- (tan (+ y z)) (tan a))
3.8b
(tan (+ y z))

rewrite19.0ms

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:
7.0ms
(+ x (- (tan (+ y z)) (tan a)))
8.0ms
(- (tan (+ y z)) (tan a))
3.0ms
(tan (+ y z))

series279.0ms

Counts
3 → 9
Calls
3 calls:
117.0ms
(+ x (- (tan (+ y z)) (tan a)))
111.0ms
(- (tan (+ y z)) (tan a))
51.0ms
(tan (+ y z))

simplify1.5s

Counts
51 → 51
Iterations

Useful iterations: 3 (130.0ms)

IterNodesCost
091627
1197590
2434572
31076570
43991570
done5000570

prune152.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

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))

rewrite127.0ms

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:
3.0ms
(+ (tan y) (tan z))
74.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
43.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
5.0ms
(* (tan y) (tan z))

series892.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(+ (tan y) (tan z))
335.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
377.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
90.0ms
(* (tan y) (tan z))

simplify1.0s

Counts
79 → 79
Iterations

Useful iterations: 3 (344.0ms)

IterNodesCost
01541433
13771362
29871302
325291291
done50001291

prune278.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (tan y) (tan z))
0.3b
(* (tan a) (tan a))
0.4b
(* (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))))
1.4b
(/ (- (* (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (* (tan a) (tan a))) (+ (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))

rewrite140.0ms

Algorithm
rewrite-expression-head
Rules
108×*-un-lft-identity
80×times-frac
72×add-sqr-sqrt
56×add-cube-cbrt
27×swap-sqr
24×associate-*r* associate-*l*
23×distribute-lft-out
22×add-exp-log add-cbrt-cube
21×tan-quot
20×pow1
11×associate-/r/ associate-/l/
9×frac-times associate-*r/ associate-*l/ frac-sub
6×prod-exp cbrt-unprod unswap-sqr
5×cbrt-undiv flip3-- div-exp flip-- div-inv difference-of-squares
4×associate-/r* associate-/l* add-log-exp
3×pow-prod-down *-commutative
2×pow2 pow-plus pow-sqr pow-prod-up
1×frac-2neg flip3-+ div-sub frac-add clear-num flip-+
Counts
4 → 188
Calls
4 calls:
5.0ms
(* (tan y) (tan z))
5.0ms
(* (tan a) (tan a))
40.0ms
(* (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))))
80.0ms
(/ (- (* (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (* (tan a) (tan a))) (+ (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))

series1.6s

Counts
4 → 12
Calls
4 calls:
94.0ms
(* (tan y) (tan z))
38.0ms
(* (tan a) (tan a))
222.0ms
(* (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))))
1.2s
(/ (- (* (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (* (tan a) (tan a))) (+ (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))

simplify2.6s

Counts
200 → 200
Iterations

Useful iterations: 2 (393.0ms)

IterNodesCost
03447613
19927005
247666440
done50006440

prune715.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (tan y) (tan z))
0.3b
(* (tan a) (tan a))
0.4b
(* (+ (tan y) (tan z)) (/ (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (- 1 (* (tan y) (tan z)))))
1.4b
(/ (- (* (+ (tan y) (tan z)) (/ (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (- 1 (* (tan y) (tan z))))) (* (tan a) (tan a))) (+ (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))

rewrite218.0ms

Algorithm
rewrite-expression-head
Rules
105×times-frac
91×*-un-lft-identity
76×add-sqr-sqrt
66×associate-*r*
63×add-cube-cbrt
53×tan-quot
23×associate-/l/
21×frac-times associate-*l/ frac-sub
19×add-exp-log add-cbrt-cube
15×pow1
14×distribute-lft-out
13×associate-*r/
11×associate-/r/
10×associate-*l*
9×flip3-+ frac-add flip-+
5×flip3-- prod-exp flip-- cbrt-unprod div-inv unswap-sqr
4×cbrt-undiv div-exp associate-/r* add-log-exp
3×swap-sqr pow-prod-down *-commutative associate-/l*
1×pow2 frac-2neg pow-plus div-sub clear-num pow-sqr pow-prod-up
Counts
4 → 196
Calls
4 calls:
5.0ms
(* (tan y) (tan z))
5.0ms
(* (tan a) (tan a))
85.0ms
(* (+ (tan y) (tan z)) (/ (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (- 1 (* (tan y) (tan z)))))
113.0ms
(/ (- (* (+ (tan y) (tan z)) (/ (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (- 1 (* (tan y) (tan z))))) (* (tan a) (tan a))) (+ (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))

series1.6s

Counts
4 → 12
Calls
4 calls:
95.0ms
(* (tan y) (tan z))
32.0ms
(* (tan a) (tan a))
232.0ms
(* (+ (tan y) (tan z)) (/ (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (- 1 (* (tan y) (tan z)))))
1.2s
(/ (- (* (+ (tan y) (tan z)) (/ (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (- 1 (* (tan y) (tan z))))) (* (tan a) (tan a))) (+ (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))

simplify435.0ms

Counts
208 → 208
Iterations

Useful iterations: done (427.0ms)

IterNodesCost
04207271
111726988
done50006863

prune905.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes267.0ms

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: 0 (0.0ms)

IterNodesCost
01952
12652
done2652

end0.0ms

sample4.8s

Algorithm
intervals
Results
3.0s3961×body1280valid
832.0ms1922×body640valid
323.0ms8000×pre80true
214.0ms682×body320valid
104.0ms1154×body80valid
55.0ms281×body160valid