Details

sample223.0ms

Algorithm

intervals

Results

144.0ms	98×	body	2560	valid
49.0ms	83×	body	1280	valid
10.0ms	40×	body	640	valid
5.0ms	28×	body	320	valid
3.0ms	256×	pre	80	true
1.0ms	5×	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

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1.0 (tan x))
1.6b	(- (/ 1.0 x) (/ 1.0 (tan x)))

rewrite21.0ms

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:

2.0ms	(/ 1.0 (tan x))
17.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

series141.0ms

Counts

2 → 6

Calls

2 calls:

33.0ms	(/ 1.0 (tan x))
108.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify51.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 3 (47.0ms)

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

prune112.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize13.0ms

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))

rewrite22.0ms

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:

9.0ms	(+ (* 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))

series147.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
50.0ms	(* 0.0021164021164021165 (pow x 5))
35.0ms	(* 0.022222222222222223 (pow x 3))

simplify44.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	301	381
1	1298	348
2	5002	348

prune172.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize10.0ms

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))

rewrite32.0ms

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-+l+` `flip3-+` `unpow3` `flip-+`

Counts

3 → 69

Calls

3 calls:

19.0ms	(+ (+ (* 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))

series150.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(+ (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))) (* 0.3333333333333333 x))
52.0ms	(* 0.0021164021164021165 (pow x 5))
36.0ms	(* 0.022222222222222223 (pow x 3))

simplify43.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	303	388
1	1327	351
2	5001	351

prune166.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.3b

localize14.0ms

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

rewrite108.0ms

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:

78.0ms	(* (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))))
9.0ms	(cbrt (+ (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))) (* 0.3333333333333333 x)))
9.0ms	(cbrt (+ (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))) (* 0.3333333333333333 x)))
9.0ms	(cbrt (+ (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))) (* 0.3333333333333333 x)))

series1.2s

Counts

4 → 12

Calls

4 calls:

303.0ms	(* (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))))
266.0ms	(cbrt (+ (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))) (* 0.3333333333333333 x)))
400.0ms	(cbrt (+ (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))) (* 0.3333333333333333 x)))
266.0ms	(cbrt (+ (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))) (* 0.3333333333333333 x)))

simplify65.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	487	2207
1	1880	2080
2	5002	1862

prune340.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.2b

regimes64.0ms

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

sample6.5s

Algorithm

intervals

Results

4.4s	3202×	body	2560	valid
1.4s	2536×	body	1280	valid
344.0ms	1276×	body	640	valid
115.0ms	617×	body	320	valid
98.0ms	8000×	pre	80	true
37.0ms	318×	body	160	valid
3.0ms	51×	body	80	valid