Details

sample29.0ms

Algorithm

intervals

Results

8.0ms	42×	body	1280	valid
5.0ms	41×	body	640	valid
4.0ms	151×	body	80	valid
1.0ms	13×	body	320	valid
1.0ms	9×	body	160	valid

simplify64.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	5
1	22	5
2	31	5
3	54	5
4	119	5
5	333	5
6	1646	5
7	5001	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.7b

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)))
3.1b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

99×	`*-un-lft-identity`
68×	`add-sqr-sqrt`
63×	`add-cube-cbrt`
61×	`times-frac`
54×	`prod-diff`
18×	`fma-neg`
17×	`distribute-lft-out`
10×	`associate-/r/`
7×	`add-log-exp`
6×	`flip3-+` `flip-+`
5×	`add-exp-log` `add-cbrt-cube` `div-inv`
4×	`associate-/r*`
3×	`pow1` `expm1-log1p-u` `fma-def` `log1p-expm1-u` `associate-/l*`
2×	`difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `clear-num` `sum-log` `flip--` `distribute-lft-out--`

Counts

3 → 141

Calls

3 calls:

10.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
3.0ms	(+ 1.0 (exp (* -2.0 x)))
44.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series133.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(/ 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)

simplify56.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	398	1645
1	1287	1235
2	5001	1212

prune269.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (exp (* -2.0 x)))
0.4b	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
0.4b	(/ 1 (sqrt (+ 1.0 (exp (* -2.0 x)))))
25.2b	(fma (/ 1 (sqrt (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

55×	`*-un-lft-identity`
42×	`times-frac`
37×	`add-sqr-sqrt` `add-cube-cbrt`
32×	`sqrt-prod`
14×	`associate-/r*`
10×	`add-exp-log`
9×	`distribute-lft-out`
8×	`add-cbrt-cube`
6×	`pow1` `associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `sqrt-div` `associate-/r/` `log1p-expm1-u`
3×	`pow-flip` `fma-def` `flip3-+` `div-exp` `flip-+`
2×	`cbrt-undiv` `frac-2neg` `clear-num` `div-inv`
1×	`+-commutative` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `sum-log` `fma-udef` `inv-pow`

Counts

4 → 127

Calls

4 calls:

3.0ms	(+ 1.0 (exp (* -2.0 x)))
7.0ms	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
8.0ms	(/ 1 (sqrt (+ 1.0 (exp (* -2.0 x)))))
0.0ms	(fma (/ 1 (sqrt (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

series353.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(+ 1.0 (exp (* -2.0 x)))
70.0ms	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
46.0ms	(/ 1 (sqrt (+ 1.0 (exp (* -2.0 x)))))
220.0ms	(fma (/ 1 (sqrt (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

simplify45.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	378	1222
1	1335	1083
2	5001	1031

prune334.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 2 expressions with local error:

0.1b	(* 0.33333333333333337 (pow x 3))
10.2b	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

rewrite9.0ms

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` `unswap-sqr`
3×	`associate-l` `prod-exp`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `sqr-pow`
1×	`cube-mult` `pow-to-exp` `unpow3` `pow-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

2 → 43

Calls

2 calls:

7.0ms	(* 0.33333333333333337 (pow x 3))
0.0ms	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

series144.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(* 0.33333333333333337 (pow x 3))
100.0ms	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

simplify191.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	142	195
1	582	172
2	3698	172
3	5002	172

prune132.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes138.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 29.4b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	20
1	37	20

end0.0ms

sample848.0ms

Algorithm

intervals

Results

336.0ms	1596×	body	1280	valid
179.0ms	1307×	body	640	valid
107.0ms	4140×	body	80	valid
57.0ms	636×	body	320	valid
19.0ms	321×	body	160	valid