Details

Time bar (total: 27.1s)

sample309.0ms

Algorithm
intervals
Results
170.0ms103×body2560valid
64.0ms79×body1280valid
50.0ms42×body640valid
5.0ms17×body320valid
5.0ms256×pre80true
2.0ms11×body160valid
0.0ms4×body80valid

simplify6.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06217
18217
211217
done11217

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.4b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ 1.0 (tan x))
2.9b
(- (/ 1.0 x) (/ 1.0 (tan x)))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
20×*-un-lft-identity
19×times-frac
12×add-cube-cbrt
5×distribute-lft-out--
4×add-cbrt-cube add-exp-log add-log-exp difference-of-squares
3×associate-/r* div-inv associate-/l*
2×pow1
1×cbrt-undiv clear-num sub-neg frac-2neg flip3-- diff-log div-exp tan-quot associate-/r/ frac-sub flip--
Counts
2 → 50
Calls
2 calls:
21.0ms
(/ 1.0 (tan x))
26.0ms
(- (/ 1.0 x) (/ 1.0 (tan x)))

series232.0ms

Counts
2 → 6
Calls
2 calls:
61.0ms
(/ 1.0 (tan x))
172.0ms
(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify1.9s

Counts
56 → 56
Iterations

Useful iterations: 3 (1.0s)

IterNodesCost
011518018
124217032
268516909
3398216789
done500116789

prune176.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* x (+ 0.3333333333333333 (* (* x x) 0.022222222222222223))) (* 0.0021164021164021165 (pow x 5)))
0.1b
(* 0.0021164021164021165 (pow x 5))
0.1b
(* (* x x) 0.022222222222222223)

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt add-exp-log
10×add-cbrt-cube associate-*r*
8×pow1
7×*-un-lft-identity add-cube-cbrt
6×prod-exp
5×add-log-exp
4×unpow-prod-down associate-*l* cbrt-unprod unswap-sqr
3×pow-prod-down
2×associate-+l+ *-commutative sqr-pow
1×distribute-rgt-in pow-to-exp +-commutative sum-log distribute-lft-in flip3-+ pow-exp flip-+
Counts
3 → 57
Calls
3 calls:
18.0ms
(+ (* x (+ 0.3333333333333333 (* (* x x) 0.022222222222222223))) (* 0.0021164021164021165 (pow x 5)))
13.0ms
(* 0.0021164021164021165 (pow x 5))
22.0ms
(* (* x x) 0.022222222222222223)

series152.0ms

Counts
3 → 9
Calls
3 calls:
65.0ms
(+ (* x (+ 0.3333333333333333 (* (* x x) 0.022222222222222223))) (* 0.0021164021164021165 (pow x 5)))
55.0ms
(* 0.0021164021164021165 (pow x 5))
32.0ms
(* (* x x) 0.022222222222222223)

simplify1.5s

Counts
66 → 66
Iterations

Useful iterations: 2 (328.0ms)

IterNodesCost
011522086
130919782
2176519662
done500019662

prune277.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.3b

localize48.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (+ (* x (+ 0.3333333333333333 (* (* x x) 0.022222222222222223))) (* 0.0021164021164021165 (pow x 5)))) (cbrt (+ (* x (+ 0.3333333333333333 (* (* x x) 0.022222222222222223))) (* 0.0021164021164021165 (pow x 5)))))
0.6b
(cbrt (+ (* x (+ 0.3333333333333333 (* (* x x) 0.022222222222222223))) (* 0.0021164021164021165 (pow x 5))))
0.6b
(cbrt (+ (* x (+ 0.3333333333333333 (* (* x x) 0.022222222222222223))) (* 0.0021164021164021165 (pow x 5))))
0.6b
(cbrt (+ (* x (+ 0.3333333333333333 (* (* x x) 0.022222222222222223))) (* 0.0021164021164021165 (pow x 5))))

rewrite134.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
18×cbrt-div
15×*-un-lft-identity add-cube-cbrt
11×pow1
9×flip3-+ pow1/3 flip-+
6×swap-sqr associate-*r* associate-*l* add-exp-log
4×frac-times add-cbrt-cube add-log-exp unswap-sqr
2×pow-prod-down associate-*l/ associate-*r/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 87
Calls
4 calls:
101.0ms
(* (cbrt (+ (* x (+ 0.3333333333333333 (* (* x x) 0.022222222222222223))) (* 0.0021164021164021165 (pow x 5)))) (cbrt (+ (* x (+ 0.3333333333333333 (* (* x x) 0.022222222222222223))) (* 0.0021164021164021165 (pow x 5)))))
10.0ms
(cbrt (+ (* x (+ 0.3333333333333333 (* (* x x) 0.022222222222222223))) (* 0.0021164021164021165 (pow x 5))))
7.0ms
(cbrt (+ (* x (+ 0.3333333333333333 (* (* x x) 0.022222222222222223))) (* 0.0021164021164021165 (pow x 5))))
11.0ms
(cbrt (+ (* x (+ 0.3333333333333333 (* (* x x) 0.022222222222222223))) (* 0.0021164021164021165 (pow x 5))))

series1.6s

Counts
4 → 12
Calls
4 calls:
441.0ms
(* (cbrt (+ (* x (+ 0.3333333333333333 (* (* x x) 0.022222222222222223))) (* 0.0021164021164021165 (pow x 5)))) (cbrt (+ (* x (+ 0.3333333333333333 (* (* x x) 0.022222222222222223))) (* 0.0021164021164021165 (pow x 5)))))
395.0ms
(cbrt (+ (* x (+ 0.3333333333333333 (* (* x x) 0.022222222222222223))) (* 0.0021164021164021165 (pow x 5))))
383.0ms
(cbrt (+ (* x (+ 0.3333333333333333 (* (* x x) 0.022222222222222223))) (* 0.0021164021164021165 (pow x 5))))
341.0ms
(cbrt (+ (* x (+ 0.3333333333333333 (* (* x x) 0.022222222222222223))) (* 0.0021164021164021165 (pow x 5))))

simplify2.1s

Counts
99 → 99
Iterations

Useful iterations: done (2.1s)

IterNodesCost
019684769
153175000
2235074880
done500074200

prune703.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 0.2b

localize370.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (+ (* x (+ 0.3333333333333333 (* (* x x) 0.022222222222222223))) (* 0.0021164021164021165 (pow x 5))))
0.7b
(cbrt (cbrt (+ (* x (+ 0.3333333333333333 (* (* x x) 0.022222222222222223))) (* 0.0021164021164021165 (pow x 5)))))
0.7b
(cbrt (cbrt (+ (* x (+ 0.3333333333333333 (* (* x x) 0.022222222222222223))) (* 0.0021164021164021165 (pow x 5)))))
0.7b
(cbrt (cbrt (+ (* x (+ 0.3333333333333333 (* (* x x) 0.022222222222222223))) (* 0.0021164021164021165 (pow x 5)))))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
30×cbrt-prod
14×cbrt-div
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×pow1 flip3-+ add-cbrt-cube pow1/3 add-exp-log flip-+ add-log-exp
Counts
4 → 61
Calls
4 calls:
12.0ms
(cbrt (+ (* x (+ 0.3333333333333333 (* (* x x) 0.022222222222222223))) (* 0.0021164021164021165 (pow x 5))))
13.0ms
(cbrt (cbrt (+ (* x (+ 0.3333333333333333 (* (* x x) 0.022222222222222223))) (* 0.0021164021164021165 (pow x 5)))))
12.0ms
(cbrt (cbrt (+ (* x (+ 0.3333333333333333 (* (* x x) 0.022222222222222223))) (* 0.0021164021164021165 (pow x 5)))))
17.0ms
(cbrt (cbrt (+ (* x (+ 0.3333333333333333 (* (* x x) 0.022222222222222223))) (* 0.0021164021164021165 (pow x 5)))))

series1.5s

Counts
4 → 12
Calls
4 calls:
309.0ms
(cbrt (+ (* x (+ 0.3333333333333333 (* (* x x) 0.022222222222222223))) (* 0.0021164021164021165 (pow x 5))))
375.0ms
(cbrt (cbrt (+ (* x (+ 0.3333333333333333 (* (* x x) 0.022222222222222223))) (* 0.0021164021164021165 (pow x 5)))))
382.0ms
(cbrt (cbrt (+ (* x (+ 0.3333333333333333 (* (* x x) 0.022222222222222223))) (* 0.0021164021164021165 (pow x 5)))))
443.0ms
(cbrt (cbrt (+ (* x (+ 0.3333333333333333 (* (* x x) 0.022222222222222223))) (* 0.0021164021164021165 (pow x 5)))))

simplify2.0s

Counts
73 → 73
Iterations

Useful iterations: done (1.9s)

IterNodesCost
016072621
141463836
2164063796
done500063156

prune599.0ms

Pruning

19 alts after pruning (16 fresh and 3 done)

Merged error: 0.1b

regimes204.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
012455
117455
done17455

end0.0ms

sample13.2s

Algorithm
intervals
Results
7.9s3279×body2560valid
3.7s2515×body1280valid
718.0ms1225×body640valid
319.0ms632×body320valid
192.0ms8000×pre80true
67.0ms300×body160valid
5.0ms49×body80valid