Details

sample240.0ms

Algorithm

intervals

Results

182.0ms	99×	body	2560	valid
36.0ms	78×	body	1280	valid
8.0ms	49×	body	640	valid
3.0ms	256×	pre	80	true
2.0ms	18×	body	320	valid
1.0ms	10×	body	160	valid
0.0ms	2×	body	80	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	4
1	11	4
2	11	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1.0 (tan x))
3.0b	(- (/ 1.0 x) (/ 1.0 (tan x)))

rewrite19.0ms

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:

4.0ms	(/ 1.0 (tan x))
13.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

series141.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(/ 1.0 (tan x))
106.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify57.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 3 (48.0ms)

Iter	Nodes	Cost
0	232	342
1	610	327
2	1894	327
3	5001	326

prune114.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
19×	`associate-r`
14×	`add-exp-log`
11×	`add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
8×	`unpow-prod-down` `add-cbrt-cube`
7×	`unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`pow1` `cube-prod` `sum-log` `sqr-pow`
2×	`+-commutative` `pow-to-exp` `flip3-+` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+`
1×	`cube-mult` `associate-+r+` `unpow3`

Counts

4 → 80

Calls

4 calls:

4.0ms	(+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))
8.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
5.0ms	(* 0.0021164021164021165 (pow x 5))
6.0ms	(* 0.022222222222222223 (pow x 3))

series290.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))
64.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
48.0ms	(* 0.0021164021164021165 (pow x 5))
41.0ms	(* 0.022222222222222223 (pow x 3))

simplify52.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	355	465
1	1532	436
2	5001	436

prune200.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

localize15.0ms

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)))))
0.7b	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
0.7b	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
0.7b	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))

rewrite40.0ms

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:

17.0ms	(* (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)))))
6.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
6.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
7.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))

series1.1s

Counts

4 → 12

Calls

4 calls:

317.0ms	(* (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)))))
275.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
274.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
277.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))

simplify69.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	496	2207
1	1932	2080
2	5001	1862

prune398.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
0.7b	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
0.7b	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
0.7b	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `cbrt-div` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `flip3-+` `pow1/3` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

6.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
7.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
7.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
7.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))

series1.1s

Counts

4 → 12

Calls

4 calls:

268.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
280.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
278.0ms	(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))))

simplify47.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	275	1312
1	1020	1244
2	5001	1104

prune460.0ms

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 0.1b

regimes67.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	7
1	18	7

end0.0ms

sample7.0s

Algorithm

intervals

Results

5.1s	3226×	body	2560	valid
1.3s	2539×	body	1280	valid
224.0ms	1281×	body	640	valid
107.0ms	8000×	pre	80	true
65.0ms	618×	body	320	valid
20.0ms	285×	body	160	valid
4.0ms	51×	body	80	valid