Details

Time bar (total: 34.2s)

sample271.0ms

Algorithm
intervals
Results
168.0ms112×body2560valid
69.0ms83×body1280valid
12.0ms30×body640valid
5.0ms22×body320valid
4.0ms256×pre80true
1.0ms6×body160valid
0.0ms3×body80valid

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: 59.7b

localize6.0ms

Local error

Found 1 expressions with local error:

2.2b
(- (/ 1.0 x) (/ 1.0 (tan x)))

rewrite80.0ms

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:
63.0ms
(- (/ 1.0 x) (/ 1.0 (tan x)))

series114.0ms

Counts
1 → 3
Calls
1 calls:
114.0ms
(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify2.0s

Counts
222 → 222
Iterations

Useful iterations: done (2.0s)

IterNodesCost
03469367
17888269
223596116
done50014410

prune279.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize15.0ms

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))
1.0ms
(fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))

series227.0ms

Counts
2 → 6
Calls
2 calls:
164.0ms
(fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))
63.0ms
(fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))

simplify1.5s

Counts
26 → 26
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
036358
168349
2264307
31651307
done5000307

prune102.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize26.0ms

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)))

rewrite28.0ms

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))))
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)))

series5.4s

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

simplify892.0ms

Counts
93 → 93
Iterations

Useful iterations: done (887.0ms)

IterNodesCost
01692370
14282227
215812081
done50001720

prune617.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.2b

localize65.0ms

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)))

rewrite5.0ms

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)))

series6.6s

Counts
4 → 12
Calls
4 calls:
1.7s
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
1.6s
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
1.5s
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
1.9s
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))

simplify2.1s

Counts
64 → 64
Iterations

Useful iterations: done (2.1s)

IterNodesCost
0871552
12021520
26461436
332941192
done50021096

prune652.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 0.2b

regimes90.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01113
11213
done1213

end0.0ms

sample13.1s

Algorithm
intervals
Results
8.3s3247×body2560valid
3.2s2485×body1280valid
754.0ms1246×body640valid
274.0ms647×body320valid
167.0ms8000×pre80true
153.0ms327×body160valid
6.0ms48×body80valid