Details

sample258.0ms

Algorithm

intervals

Results

172.0ms	106×	body	2560	valid
54.0ms	85×	body	1280	valid
13.0ms	41×	body	640	valid
4.0ms	256×	pre	80	true
3.0ms	15×	body	320	valid
1.0ms	8×	body	160	valid
0.0ms	1×	body	80	valid

simplify2.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.0b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1.0 (tan x))
2.6b	(- (/ 1.0 x) (/ 1.0 (tan x)))

rewrite50.0ms

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:

6.0ms	(/ 1.0 (tan x))
28.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

series148.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(/ 1.0 (tan x))
110.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify46.0ms

Counts: 56 → 56

prune120.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize15.0ms

Local error

Found 3 expressions with local error:

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

rewrite49.0ms

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` `add-log-exp`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`cube-prod` `sqr-pow`
3×	`pow1` `sum-log`
2×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod`
1×	`+-commutative` `cube-mult` `associate-+r+` `flip3-+` `unpow3` `flip-+`

Counts

3 → 69

Calls

3 calls:

22.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
12.0ms	(* 0.0021164021164021165 (pow x 5))
13.0ms	(* 0.022222222222222223 (pow x 3))

series155.0ms

Counts

3 → 9

Calls

3 calls:

63.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
50.0ms	(* 0.0021164021164021165 (pow x 5))
42.0ms	(* 0.022222222222222223 (pow x 3))

simplify40.0ms

Counts: 78 → 78

prune178.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))) (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))))
0.5b	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
0.5b	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
0.5b	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))

rewrite193.0ms

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:

137.0ms	(* (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))) (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))))
20.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
16.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
16.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))

series1.4s

Counts

4 → 12

Calls

4 calls:

305.0ms	(* (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))) (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))))
563.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
286.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
290.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))

simplify61.0ms

Counts: 99 → 99

prune422.0ms

Pruning

18 alts after pruning (16 fresh and 2 done)

Merged error: 0.2b

localize43.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
0.5b	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
0.6b	(cbrt (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))))
0.6b	(cbrt (* (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))) (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))))

rewrite98.0ms

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:

16.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
17.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
17.0ms	(cbrt (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))))
46.0ms	(cbrt (* (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))) (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))))

series1.2s

Counts

4 → 12

Calls

4 calls:

292.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
285.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
310.0ms	(cbrt (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))))
347.0ms	(cbrt (* (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))) (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))))

simplify67.0ms

Counts: 71 → 71

prune406.0ms

Pruning

20 alts after pruning (18 fresh and 2 done)

Merged error: 0.1b

regimes138.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

end0.0ms

sample9.4s

Algorithm

intervals

Results

5.5s	3271×	body	2560	valid
2.1s	2481×	body	1280	valid
542.0ms	1256×	body	640	valid
523.0ms	8000×	pre	80	true
471.0ms	641×	body	320	valid
47.0ms	303×	body	160	valid
4.0ms	48×	body	80	valid