Details

Time bar (total: 16.0s)

sample195.0ms

Algorithm
intervals
Results
100.0ms43×body1280valid
17.0ms38×body640valid
14.0ms140×body80valid
9.0ms26×body320valid
3.0ms9×body160valid

simplify60.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0715
11315
22115
32615
43415
53715
done3715

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite140.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity
18×pow1
12×times-frac
10×add-exp-log add-cbrt-cube
8×tan-quot
6×swap-sqr associate-*r* associate-*l* add-log-exp
5×difference-of-squares
4×associate-/l*
3×associate-/r*
2×pow2 frac-times flip3-- pow-plus associate-*r/ pow-prod-down associate-*l/ prod-exp associate-/r/ pow-sqr *-commutative pow-prod-up flip-- cbrt-unprod associate-/l/ unswap-sqr
1×cbrt-undiv sub-neg frac-2neg flip3-+ diff-log div-sub div-exp clear-num flip-+ div-inv
Counts
4 → 105
Calls
4 calls:
10.0ms
(- 1.0 (* (tan x) (tan x)))
36.0ms
(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
52.0ms
(* (tan x) (tan x))
35.0ms
(* (tan x) (tan x))

series311.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(- 1.0 (* (tan x) (tan x)))
138.0ms
(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
38.0ms
(* (tan x) (tan x))
73.0ms
(* (tan x) (tan x))

simplify1.1s

Counts
117 → 117
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01381632
13511506
215431368
done50001360

prune396.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (+ 1.0 (* (tan x) (tan x))))
0.2b
(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
0.3b
(* (tan x) (tan x))
0.3b
(* (tan x) (tan x))

rewrite124.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
29×*-un-lft-identity
28×add-cube-cbrt
21×pow1 add-exp-log associate-*r*
20×times-frac
15×add-cbrt-cube
10×associate-*l*
8×tan-quot
6×swap-sqr prod-exp
5×unswap-sqr
4×frac-times div-exp associate-*l/ associate-/r/ cbrt-unprod add-log-exp
3×associate-*r/ pow-prod-down associate-/r* *-commutative associate-/l*
2×cbrt-undiv pow2 rec-exp flip3-- flip3-+ pow-plus 1-exp pow-sqr pow-prod-up flip-- flip-+ div-inv
1×pow-flip frac-2neg clear-num un-div-inv inv-pow difference-of-squares
Counts
4 → 132
Calls
4 calls:
19.0ms
(/ 1 (+ 1.0 (* (tan x) (tan x))))
59.0ms
(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
18.0ms
(* (tan x) (tan x))
21.0ms
(* (tan x) (tan x))

series310.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(/ 1 (+ 1.0 (* (tan x) (tan x))))
146.0ms
(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
49.0ms
(* (tan x) (tan x))
46.0ms
(* (tan x) (tan x))

simplify3.7s

Counts
144 → 144
Iterations

Useful iterations: done (3.7s)

IterNodesCost
01692062
14421853
231051591
done50011577

prune434.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.3b
(* (tan x) (tan x))
0.3b
(* (tan x) (tan x))
0.3b
(log (exp (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))))

rewrite154.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
30×add-cube-cbrt *-un-lft-identity
24×times-frac
19×pow1 log-pow
18×exp-prod
10×add-exp-log add-cbrt-cube
8×tan-quot
7×difference-of-squares
6×swap-sqr associate-*r* associate-*l*
4×associate-/r/ associate-/l* add-log-exp
3×log-prod associate-/r*
2×pow2 frac-times flip3-+ pow-plus div-sub associate-*r/ pow-prod-down associate-*l/ prod-exp pow-sqr *-commutative pow-prod-up cbrt-unprod flip-+ div-inv associate-/l/ unswap-sqr
1×cbrt-undiv log-div flip3-- frac-2neg exp-diff div-exp rem-log-exp clear-num flip--
Counts
4 → 123
Calls
4 calls:
27.0ms
(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
32.0ms
(* (tan x) (tan x))
38.0ms
(* (tan x) (tan x))
53.0ms
(log (exp (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))))

series352.0ms

Counts
4 → 12
Calls
4 calls:
118.0ms
(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
59.0ms
(* (tan x) (tan x))
37.0ms
(* (tan x) (tan x))
138.0ms
(log (exp (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))))

simplify1.5s

Counts
135 → 135
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01862167
14031975
218131808
done50011798

prune561.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (tan x) (tan x))
0.3b
(* (tan x) (tan x))
0.3b
(* (tan x) (tan x))
0.3b
(- (/ 1.0 (+ 1.0 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1.0 (* (tan x) (tan x)))))

rewrite133.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
25×pow1
18×*-un-lft-identity
16×add-cube-cbrt
12×tan-quot
10×add-exp-log add-cbrt-cube
9×swap-sqr associate-*r* associate-*l*
6×add-log-exp
4×times-frac associate-/r/ difference-of-squares
3×pow2 frac-times distribute-rgt-out-- pow-plus associate-*r/ pow-prod-down associate-*l/ prod-exp pow-sqr *-commutative pow-prod-up cbrt-unprod unswap-sqr
2×flip3-+ flip-+ div-inv
1×sub-neg flip3-- diff-log frac-sub flip-- distribute-lft-out-- sub-div
Counts
4 → 106
Calls
4 calls:
23.0ms
(* (tan x) (tan x))
24.0ms
(* (tan x) (tan x))
16.0ms
(* (tan x) (tan x))
66.0ms
(- (/ 1.0 (+ 1.0 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1.0 (* (tan x) (tan x)))))

series377.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(* (tan x) (tan x))
39.0ms
(* (tan x) (tan x))
60.0ms
(* (tan x) (tan x))
238.0ms
(- (/ 1.0 (+ 1.0 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1.0 (* (tan x) (tan x)))))

simplify936.0ms

Counts
118 → 118
Iterations

Useful iterations: done (930.0ms)

IterNodesCost
01181623
12951455
212361306
done50001295

prune349.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes202.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01018
11118
done1118

end0.0ms

sample4.6s

Algorithm
intervals
Results
2.0s1481×body1280valid
1.4s1243×body640valid
649.0ms4361×body80valid
271.0ms602×body320valid
88.0ms313×body160valid