Details

Time bar (total: 17.9s)

sample159.0ms

Algorithm
intervals
Results
89.0ms120×body1280valid
26.0ms65×body640valid
9.0ms256×pre80true
7.0ms23×body320valid
4.0ms42×body80valid
1.0ms6×body160valid

simplify77.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
099
1159
2229
3339
4389
5459
6519
7619
8749
9869
10959
done959

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.7b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b
(- (tan (+ y z)) (tan a))
0.2b
(+ x (- (tan (+ y z)) (tan a)))
4.1b
(tan (+ y z))

rewrite42.0ms

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:
17.0ms
(- (tan (+ y z)) (tan a))
17.0ms
(+ x (- (tan (+ y z)) (tan a)))
6.0ms
(tan (+ y z))

series305.0ms

Counts
3 → 9
Calls
3 calls:
120.0ms
(- (tan (+ y z)) (tan a))
132.0ms
(+ x (- (tan (+ y z)) (tan a)))
52.0ms
(tan (+ y z))

simplify2.0s

Counts
51 → 51
Iterations

Useful iterations: 3 (192.0ms)

IterNodesCost
091627
1196590
2453572
31241570
44651570
done5000570

prune147.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite132.0ms

Algorithm
rewrite-expression-head
Rules
16×associate-*l/
14×add-sqr-sqrt
13×add-exp-log add-cbrt-cube
12×tan-quot *-un-lft-identity
10×add-cube-cbrt
8×pow1 associate-/l/
6×associate-*r* associate-*l* frac-sub add-log-exp
5×flip3-- flip--
3×flip3-+ times-frac prod-exp cbrt-unprod flip-+ associate-/l*
2×cbrt-undiv frac-times div-sub associate-*r/ div-exp pow-prod-down frac-add associate-/r/ *-commutative unswap-sqr
1×+-commutative associate-+r- frac-2neg clear-num associate-/r* sum-log div-inv distribute-lft-out
Counts
4 → 87
Calls
4 calls:
16.0ms
(* (tan y) (tan z))
16.0ms
(* (tan y) (tan z))
60.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
37.0ms
(+ x (/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a))))

series1.5s

Counts
4 → 12
Calls
4 calls:
100.0ms
(* (tan y) (tan z))
101.0ms
(* (tan y) (tan z))
523.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
793.0ms
(+ x (/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a))))

simplify1.1s

Counts
99 → 99
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01942683
16002517
223652064
done50001933

prune473.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
13×*-un-lft-identity
11×add-log-exp
10×tan-quot
8×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
6×associate-+r+ associate-*r* associate-*l*
3×distribute-rgt-in sub-neg distribute-lft-in associate--l+ frac-sub
2×frac-times flip3-+ diff-log associate-*r/ pow-prod-down associate-*l/ prod-exp sum-log *-commutative cbrt-unprod flip-+ distribute-lft-out-- unswap-sqr
1×+-commutative flip3-- frac-add flip-- distribute-lft-out difference-of-squares
Counts
4 → 79
Calls
4 calls:
45.0ms
(- (+ (tan y) (tan z)) (/ (* (- 1 (* (tan y) (tan z))) (sin a)) (cos a)))
15.0ms
(* (tan y) (tan z))
18.0ms
(* (tan y) (tan z))
20.0ms
(+ x (* (/ 1 (- 1 (* (tan y) (tan z)))) (- (+ (tan y) (tan z)) (/ (* (- 1 (* (tan y) (tan z))) (sin a)) (cos a)))))

series1.3s

Counts
4 → 12
Calls
4 calls:
339.0ms
(- (+ (tan y) (tan z)) (/ (* (- 1 (* (tan y) (tan z))) (sin a)) (cos a)))
90.0ms
(* (tan y) (tan z))
104.0ms
(* (tan y) (tan z))
785.0ms
(+ x (* (/ 1 (- 1 (* (tan y) (tan z)))) (- (+ (tan y) (tan z)) (/ (* (- 1 (* (tan y) (tan z))) (sin a)) (cos a)))))

simplify677.0ms

Counts
91 → 91
Iterations

Useful iterations: done (674.0ms)

IterNodesCost
01741987
14651907
216811741
done50011727

prune373.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (cos y) (cos z)) (* (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z)))) (sin a)))
0.2b
(* (* (tan y) (tan z)) (* (tan y) (tan z)))
0.2b
(* (* (tan y) (tan z)) (* (tan y) (tan z)))
0.3b
(/ (- (* (* (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (cos a)) (+ 1 (* (tan y) (tan z)))) (* (* (cos y) (cos z)) (* (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z)))) (sin a)))) (* (* (cos y) (cos z)) (* (cos a) (- 1 (* (* (tan y) (tan z)) (* (tan y) (tan z)))))))

rewrite500.0ms

Algorithm
rewrite-expression-head
Rules
108×associate-*l/
94×pow1
74×frac-times
64×tan-quot
58×add-exp-log add-cbrt-cube
56×associate-*r/
42×pow-prod-down associate-/l/
40×frac-sub
32×prod-exp cbrt-unprod
30×flip3-+ cos-mult flip-+
21×flip3-- flip--
8×pow-sqr pow-prod-up
6×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
5×cbrt-undiv div-exp associate-/r/
4×pow-plus add-log-exp
3×times-frac associate-*r* associate-*l* *-commutative associate-/l*
2×pow2 swap-sqr
1×frac-2neg div-sub clear-num associate-/r* div-inv
Counts
4 → 200
Calls
4 calls:
113.0ms
(* (* (cos y) (cos z)) (* (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z)))) (sin a)))
67.0ms
(* (* (tan y) (tan z)) (* (tan y) (tan z)))
67.0ms
(* (* (tan y) (tan z)) (* (tan y) (tan z)))
239.0ms
(/ (- (* (* (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (cos a)) (+ 1 (* (tan y) (tan z)))) (* (* (cos y) (cos z)) (* (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z)))) (sin a)))) (* (* (cos y) (cos z)) (* (cos a) (- 1 (* (* (tan y) (tan z)) (* (tan y) (tan z)))))))

series1.6s

Counts
4 → 12
Calls
4 calls:
228.0ms
(* (* (cos y) (cos z)) (* (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z)))) (sin a)))
123.0ms
(* (* (tan y) (tan z)) (* (tan y) (tan z)))
132.0ms
(* (* (tan y) (tan z)) (* (tan y) (tan z)))
1.1s
(/ (- (* (* (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (cos a)) (+ 1 (* (tan y) (tan z)))) (* (* (cos y) (cos z)) (* (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z)))) (sin a)))) (* (* (cos y) (cos z)) (* (cos a) (- 1 (* (* (tan y) (tan z)) (* (tan y) (tan z)))))))

simplify546.0ms

Counts
212 → 212
Iterations

Useful iterations: done (537.0ms)

IterNodesCost
03699526
113168418
done50007088

prune1.6s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes241.0ms

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
01831
12531
done2531

end0.0ms

sample4.9s

Algorithm
intervals
Results
2.9s3856×body1280valid
873.0ms2018×body640valid
305.0ms8000×pre80true
212.0ms697×body320valid
100.0ms1145×body80valid
55.0ms284×body160valid