Details

Time bar (total: 34.9s)

sample301.0ms

Algorithm
intervals
Results
189.0ms105×body2560valid
63.0ms77×body1280valid
17.0ms37×body640valid
8.0ms26×body320valid
6.0ms256×pre80true
2.0ms9×body160valid
0.0ms2×body80valid

simplify21.0ms

Counts
1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.9b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ 1.0 (tan x))
3.2b
(- (/ 1.0 x) (/ 1.0 (tan x)))

rewrite122.0ms

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-exp-log add-cbrt-cube add-log-exp difference-of-squares
3×associate-/r* div-inv associate-/l*
2×pow1
1×tan-quot cbrt-undiv sub-neg flip3-- frac-2neg diff-log div-exp clear-num associate-/r/ frac-sub flip--
Counts
2 → 50
Calls
2 calls:
12.0ms
(/ 1.0 (tan x))
107.0ms
(- (/ 1.0 x) (/ 1.0 (tan x)))

series216.0ms

Counts
2 → 6
Calls
2 calls:
50.0ms
(/ 1.0 (tan x))
166.0ms
(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify901.0ms

Counts
56 → 56

prune220.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))
0.0b
(* 0.0021164021164021165 (pow x 5))
0.1b
(* 0.022222222222222223 (pow x 3))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
19×associate-*r*
13×add-exp-log
10×add-cube-cbrt *-un-lft-identity
8×unpow-prod-down
7×add-cbrt-cube unswap-sqr
6×associate-*l* prod-exp
5×add-log-exp
4×cube-prod sqr-pow
3×pow1
2×pow-to-exp pow-exp *-commutative cbrt-unprod
1×+-commutative cube-mult flip3-+ unpow3 sum-log flip-+
Counts
3 → 67
Calls
3 calls:
26.0ms
(+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))
22.0ms
(* 0.0021164021164021165 (pow x 5))
25.0ms
(* 0.022222222222222223 (pow x 3))

series293.0ms

Counts
3 → 9
Calls
3 calls:
149.0ms
(+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))
95.0ms
(* 0.0021164021164021165 (pow x 5))
49.0ms
(* 0.022222222222222223 (pow x 3))

simplify799.0ms

Counts
76 → 76

prune229.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.3b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite121.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
18×cbrt-div
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×flip3-+ pow1/3 flip-+
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×frac-times add-cbrt-cube add-log-exp unswap-sqr
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 87
Calls
4 calls:
88.0ms
(* (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))) (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
12.0ms
(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
9.0ms
(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
7.0ms
(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))

series6.3s

Counts
4 → 12
Calls
4 calls:
1.6s
(* (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))) (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
1.6s
(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
1.3s
(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
1.8s
(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))

simplify921.0ms

Counts
99 → 99

prune582.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 0.2b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
28×cbrt-div
16×cbrt-prod
9×flip3-+ flip-+
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log frac-times pow1/3 add-cbrt-cube add-log-exp
2×associate-*r/ associate-*l/
Counts
4 → 59
Calls
4 calls:
13.0ms
(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
13.0ms
(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
41.0ms
(cbrt (* (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))) (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))))
7.0ms
(cbrt (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))

series6.1s

Counts
4 → 12
Calls
4 calls:
1.4s
(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
1.4s
(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
1.8s
(cbrt (* (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))) (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))))
1.5s
(cbrt (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))

simplify874.0ms

Counts
71 → 71

prune550.0ms

Pruning

20 alts after pruning (17 fresh and 3 done)

Merged error: 0.1b

regimes167.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 0.3b

bsearch0.0ms

simplify1.8s

end0.0ms

sample14.1s

Algorithm
intervals
Results
8.7s3317×body2560valid
3.7s2456×body1280valid
749.0ms1215×body640valid
309.0ms647×body320valid
216.0ms8000×pre80true
141.0ms314×body160valid
6.0ms51×body80valid