Details

sample38.0ms

Algorithm

intervals

Results

16.0ms	59×	body	1280	valid
7.0ms	42×	body	640	valid
3.0ms	124×	body	80	valid
2.0ms	22×	body	320	valid
1.0ms	9×	body	160	valid

simplify64.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	15	5
1	22	5
2	30	5
3	52	5
4	114	5
5	322	5
6	1627	5
7	5002	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
0.0b	(+ 1.0 (exp (* -2.0 x)))
2.7b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
13×	`times-frac`
12×	`add-cube-cbrt`
7×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
4×	`associate-/r*`
3×	`pow1` `associate-/l*`
2×	`flip3-+` `associate-/r/` `flip-+` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `clear-num` `sum-log` `flip--` `div-inv` `distribute-lft-out--`

Counts

3 → 60

Calls

3 calls:

6.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
3.0ms	(+ 1.0 (exp (* -2.0 x)))
33.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series135.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
16.0ms	(+ 1.0 (exp (* -2.0 x)))
80.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify93.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	251	494
1	731	465
2	2785	460
3	5002	460

prune152.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 2 expressions with local error:

0.1b	(* 0.33333333333333337 (pow x 3))
8.2b	(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 42

Calls

2 calls:

7.0ms	(* 0.33333333333333337 (pow x 3))
3.0ms	(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))

series142.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(* 0.33333333333333337 (pow x 3))
107.0ms	(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))

simplify36.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	199	228
1	849	205
2	5001	204

prune106.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (exp (* -2.0 x)))
0.0b	(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
0.5b	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
2.7b	(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

rewrite220.0ms

Algorithm

rewrite-expression-head

Rules

388×	`times-frac`
304×	`*-un-lft-identity`
229×	`sqrt-prod`
212×	`add-sqr-sqrt`
188×	`add-cube-cbrt`
57×	`distribute-lft-out`
30×	`associate-/l*`
20×	`sqrt-div` `associate-/r/`
14×	`associate-/r*`
11×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
10×	`div-inv`
8×	`add-log-exp`
7×	`difference-of-squares`
4×	`pow1` `cbrt-undiv` `div-exp`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `sub-neg` `flip3--` `diff-log` `sum-log` `flip--` `associate-/l/` `distribute-lft-out--`

Counts

4 → 317

Calls

4 calls:

3.0ms	(+ 1.0 (exp (* -2.0 x)))
23.0ms	(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
7.0ms	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
167.0ms	(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

series205.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(+ 1.0 (exp (* -2.0 x)))
39.0ms	(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
68.0ms	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
81.0ms	(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

simplify90.0ms

Algorithm

egg-herbie

Counts

329 → 329

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	787	5699
1	2791	5067
2	5002	4914

prune476.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes119.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 32.5b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	20
1	37	20

end0.0ms

sample912.0ms

Algorithm

intervals

Results

383.0ms	1697×	body	1280	valid
182.0ms	1207×	body	640	valid
116.0ms	4178×	body	80	valid
59.0ms	621×	body	320	valid
19.0ms	297×	body	160	valid