Details

Time bar (total: 31.0s)

sample291.0ms

Algorithm
intervals
Results
197.0ms106×body2560valid
56.0ms81×body1280valid
13.0ms38×body640valid
5.0ms18×body320valid
4.0ms256×pre80true
2.0ms12×body160valid
0.0ms1×body80valid

simplify23.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
188
2118
done118

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ 1.0 (tan x))
3.4b
(- (/ 1.0 x) (/ 1.0 (tan x)))

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
271×times-frac
220×add-sqr-sqrt
216×*-un-lft-identity
208×add-cube-cbrt
182×prod-diff
31×div-inv
14×tan-quot associate-/r/
13×fma-neg
5×distribute-lft-out--
4×add-exp-log add-cbrt-cube add-log-exp difference-of-squares
3×associate-/r* associate-/l*
2×pow1 expm1-log1p-u log1p-expm1-u
1×cbrt-undiv sub-neg flip3-- frac-2neg diff-log div-exp clear-num frac-sub flip--
Counts
2 → 249
Calls
2 calls:
8.0ms
(/ 1.0 (tan x))
69.0ms
(- (/ 1.0 x) (/ 1.0 (tan x)))

series207.0ms

Counts
2 → 6
Calls
2 calls:
40.0ms
(/ 1.0 (tan x))
167.0ms
(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify2.1s

Counts
255 → 255
Iterations

Useful iterations: done (2.1s)

IterNodesCost
03699638
18068496
216936110
done50004346

prune663.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize9.0ms

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)))

series254.0ms

Counts
2 → 6
Calls
2 calls:
177.0ms
(fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))
77.0ms
(fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))

simplify1.2s

Counts
26 → 26
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
036358
161349
2176307
3971307
done5000307

prune100.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize14.0ms

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))))
0.6b
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
0.6b
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
0.6b
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))

rewrite18.0ms

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:
12.0ms
(* (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)))

series5.3s

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)))

simplify2.6s

Counts
93 → 93
Iterations

Useful iterations: done (2.6s)

IterNodesCost
01692370
13962227
211652081
344631663
done50001656

prune474.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.2b

localize37.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
0.6b
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
0.6b
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
0.6b
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))

rewrite16.0ms

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:
2.0ms
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
2.0ms
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
8.0ms
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
2.0ms
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))

series5.9s

Counts
4 → 12
Calls
4 calls:
1.7s
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
1.5s
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
1.5s
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
1.3s
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))

simplify1.5s

Counts
64 → 64
Iterations

Useful iterations: done (1.5s)

IterNodesCost
0871552
12021520
25581436
321601192
done50001096

prune428.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.2b

regimes52.0ms

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

sample9.9s

Algorithm
intervals
Results
6.5s3168×body2560valid
2.2s2582×body1280valid
510.0ms1270×body640valid
164.0ms610×body320valid
148.0ms8000×pre80true
63.0ms335×body160valid
3.0ms35×body80valid