Details

sample37.0ms

Algorithm

intervals

Results

13.0ms	55×	body	1280	valid
7.0ms	43×	body	640	valid
4.0ms	132×	body	80	valid
2.0ms	15×	body	320	valid
1.0ms	11×	body	160	valid

simplify50.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4800	10
1	4800	10

prune11.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 29.1b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (exp (* -2.0 x)))
0.0b	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
3.6b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite19.0ms

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:

3.0ms	(+ 1.0 (exp (* -2.0 x)))
5.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
9.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series16.0ms

Counts

3 → 9

Calls

3 calls:

2.0ms	(+ 1.0 (exp (* -2.0 x)))
6.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
8.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify50.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4972	836
1	4972	836

prune140.0ms

Filtered

53 candidates to 69 candidates (-30.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	65	4	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	4	70

Merged error: 0.1b

Counts

70 → 4

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ 1.0 (/ 2.0 (+ 1.0 (pow (exp -2.0) x)))) (+ 1.0 (pow (exp -2.0) x)))
0.0b	(/ (- (pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3) (pow 1.0 3)) (+ (* 1.0 1.0) (* 2.0 (/ (+ 1.0 (/ 2.0 (+ 1.0 (pow (exp -2.0) x)))) (+ 1.0 (pow (exp -2.0) x))))))
0.0b	(pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3)
3.5b	(- (pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3) (pow 1.0 3))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

299×	`add-sqr-sqrt`
179×	`times-frac`
151×	`*-un-lft-identity`
120×	`difference-of-squares`
108×	`unpow-prod-down` `cube-prod`
69×	`add-cube-cbrt`
51×	`sqr-pow`
37×	`associate-/l*`
25×	`distribute-lft-out--`
16×	`distribute-lft-out`
11×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/r/`
7×	`associate-/r*`
6×	`add-log-exp`
5×	`pow1` `difference-cubes` `flip3-+` `flip-+`
4×	`div-inv` `associate-/l/`
3×	`cbrt-undiv` `pow-unpow` `div-exp`
2×	`flip3--` `frac-2neg` `pow-exp` `clear-num` `flip--` `rem-cube-cbrt`
1×	`cube-div` `cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `diff-log` `unpow3` `div-sub`

Counts

4 → 290

Calls

4 calls:

15.0ms	(/ (+ 1.0 (/ 2.0 (+ 1.0 (pow (exp -2.0) x)))) (+ 1.0 (pow (exp -2.0) x)))
41.0ms	(/ (- (pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3) (pow 1.0 3)) (+ (* 1.0 1.0) (* 2.0 (/ (+ 1.0 (/ 2.0 (+ 1.0 (pow (exp -2.0) x)))) (+ 1.0 (pow (exp -2.0) x))))))
8.0ms	(pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3)
30.0ms	(- (pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3) (pow 1.0 3))

series103.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(/ (+ 1.0 (/ 2.0 (+ 1.0 (pow (exp -2.0) x)))) (+ 1.0 (pow (exp -2.0) x)))
58.0ms	(/ (- (pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3) (pow 1.0 3)) (+ (* 1.0 1.0) (* 2.0 (/ (+ 1.0 (/ 2.0 (+ 1.0 (pow (exp -2.0) x)))) (+ 1.0 (pow (exp -2.0) x))))))
11.0ms	(pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3)
19.0ms	(- (pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3) (pow 1.0 3))

simplify140.0ms

Algorithm

egg-herbie

Counts

302 → 302

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4984	12987
1	4984	12987

prune1.1s

Filtered

150 candidates to 302 candidates (-101.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	300	2	302
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	302	4	306

Merged error: 0.0b

Counts

306 → 4

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3)
0.0b	(pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3)
0.0b	(pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 6)
3.4b	(- (pow (pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3) 3) (pow (pow 1.0 3) 3))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

295×	`add-sqr-sqrt`
274×	`unpow-prod-down`
256×	`cube-prod`
140×	`difference-of-squares`
119×	`*-un-lft-identity`
100×	`times-frac`
75×	`sqr-pow`
47×	`add-cube-cbrt`
21×	`distribute-lft-out--`
15×	`distribute-lft-out`
13×	`add-exp-log`
10×	`associate-/r/` `add-cbrt-cube`
9×	`pow-unpow`
7×	`pow1`
6×	`pow-exp` `add-log-exp`
5×	`flip3-+` `flip-+` `div-inv`
4×	`rem-cube-cbrt`
3×	`pow-to-exp` `pow-pow` `div-exp`
2×	`cbrt-undiv` `cube-div` `cube-mult` `unpow3`
1×	`difference-cubes` `sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 319

Calls

4 calls:

8.0ms	(pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3)
8.0ms	(pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3)
8.0ms	(pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 6)
112.0ms	(- (pow (pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3) 3) (pow (pow 1.0 3) 3))

series60.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3)
11.0ms	(pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3)
17.0ms	(pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 6)
21.0ms	(- (pow (pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3) 3) (pow (pow 1.0 3) 3))

simplify110.0ms

Algorithm

egg-herbie

Counts

331 → 331

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5091	8510

prune1.2s

Filtered

115 candidates to 331 candidates (-187.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	331	0	331
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	331	4	335

Merged error: 0.0b

Counts

335 → 4

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3)
0.0b	(/ (- (pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 6) (pow 1.0 6)) (+ (pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3) (pow 1.0 3)))
0.0b	(pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 6)
3.4b	(- (pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 6) (pow 1.0 6))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

300×	`*-un-lft-identity`
278×	`add-sqr-sqrt`
240×	`unpow-prod-down`
222×	`times-frac`
132×	`difference-of-squares`
99×	`distribute-lft-out`
90×	`cube-prod`
79×	`sqr-pow`
58×	`add-cube-cbrt`
22×	`distribute-lft-out--`
18×	`sum-cubes`
17×	`associate-/l*`
12×	`add-exp-log`
9×	`associate-/r*` `add-cbrt-cube`
8×	`associate-/r/`
6×	`pow1` `pow-unpow` `add-log-exp`
4×	`flip3-+` `pow-exp` `flip-+` `div-inv`
3×	`div-exp`
2×	`cbrt-undiv` `pow-to-exp` `flip3--` `pow-pow` `flip--` `associate-/l/` `rem-cube-cbrt`
1×	`cube-div` `cube-mult` `sub-neg` `frac-2neg` `diff-log` `unpow3` `div-sub` `clear-num`

Counts

4 → 311

Calls

4 calls:

8.0ms	(pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3)
52.0ms	(/ (- (pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 6) (pow 1.0 6)) (+ (pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3) (pow 1.0 3)))
8.0ms	(pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 6)
17.0ms	(- (pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 6) (pow 1.0 6))

series91.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3)
48.0ms	(/ (- (pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 6) (pow 1.0 6)) (+ (pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3) (pow 1.0 3)))
13.0ms	(pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 6)
19.0ms	(- (pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 6) (pow 1.0 6))

simplify115.0ms

Algorithm

egg-herbie

Counts

323 → 323

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5022	11165

prune1.3s

Filtered

138 candidates to 323 candidates (-134.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	322	1	323
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	323	4	327

Merged error: 0.0b

Counts

327 → 4

regimes161.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 29.4b

bsearch39.0ms

Steps

Iters	Range		Point
9	6.297138620167189e-13	0.0009073523377833194	0.0008346978469289081
8	-2.244380864214425	-0.0005406173305783882	-0.0007812437886708263

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	59	118
1	59	118

end0.0ms

sample1.1s

Algorithm

intervals

Results

410.0ms	1681×	body	1280	valid
203.0ms	1261×	body	640	valid
132.0ms	4085×	body	80	valid
72.0ms	633×	body	320	valid
24.0ms	340×	body	160	valid

Details

sample37.0ms

simplify50.0ms

prune11.0ms

localize6.0ms

rewrite19.0ms

series16.0ms

simplify50.0ms

prune140.0ms

localize18.0ms

rewrite114.0ms

series103.0ms

simplify140.0ms

prune1.1s

localize30.0ms

rewrite154.0ms

series60.0ms

simplify110.0ms

prune1.2s

localize24.0ms

rewrite107.0ms

series91.0ms

simplify115.0ms

prune1.3s

regimes161.0ms

bsearch39.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling