Details

Time bar (total: 34.8s)

sample399.0ms

Algorithm
intervals
Results
238.0ms109×body2560valid
78.0ms83×body1280valid
41.0ms256×pre80true
15.0ms32×body640valid
8.0ms24×body320valid
2.0ms8×body160valid

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
188
2118
done118

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.0b

localize8.0ms

Local error

Found 1 expressions with local error:

2.0b
(- (/ 1.0 x) (/ 1.0 (tan x)))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
262×times-frac
211×add-sqr-sqrt
207×*-un-lft-identity
199×add-cube-cbrt
182×prod-diff
30×div-inv
13×tan-quot fma-neg associate-/r/
5×distribute-lft-out--
4×difference-of-squares
3×add-log-exp
1×pow1 add-exp-log expm1-log1p-u sub-neg flip3-- diff-log frac-sub add-cbrt-cube flip-- log1p-expm1-u
Counts
1 → 219
Calls
1 calls:
64.0ms
(- (/ 1.0 x) (/ 1.0 (tan x)))

series133.0ms

Counts
1 → 3
Calls
1 calls:
133.0ms
(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify2.7s

Counts
222 → 222
Iterations

Useful iterations: done (2.6s)

IterNodesCost
03469367
17888269
223596116
done50014410

prune459.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
2×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube fma-udef log1p-expm1-u add-log-exp
Counts
2 → 20
Calls
2 calls:
0.0ms
(fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))
0.0ms
(fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))

series271.0ms

Counts
2 → 6
Calls
2 calls:
182.0ms
(fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))
90.0ms
(fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))

simplify1.6s

Counts
26 → 26
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
036358
168349
2264307
31651307
done5000307

prune135.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize42.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))) (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
0.7b
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
0.7b
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
0.7b
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 81
Calls
4 calls:
22.0ms
(* (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))) (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
2.0ms
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
2.0ms
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
2.0ms
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))

series6.0s

Counts
4 → 12
Calls
4 calls:
1.5s
(* (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))) (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
1.4s
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
1.4s
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
1.7s
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))

simplify833.0ms

Counts
93 → 93
Iterations

Useful iterations: done (828.0ms)

IterNodesCost
01692370
14282227
215812081
done50001720

prune720.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.2b

localize54.0ms

Local error

Found 4 expressions with local error:

0.7b
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
0.7b
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
0.7b
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
0.7b
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u pow1/3 add-cbrt-cube log1p-expm1-u add-log-exp
Counts
4 → 52
Calls
4 calls:
1.0ms
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
1.0ms
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
1.0ms
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
1.0ms
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))

series5.2s

Counts
4 → 12
Calls
4 calls:
1.3s
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
1.3s
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
1.3s
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
1.4s
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))

simplify1.6s

Counts
64 → 64
Iterations

Useful iterations: done (1.6s)

IterNodesCost
0871552
12021520
26461436
332941192
done50021096

prune520.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 0.2b

regimes179.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01113
11213
done1213

end0.0ms

sample13.8s

Algorithm
intervals
Results
8.9s3252×body2560valid
3.2s2554×body1280valid
786.0ms1252×body640valid
301.0ms602×body320valid
211.0ms8000×pre80true
75.0ms304×body160valid
4.0ms36×body80valid