Details

sample51.0ms

Algorithm

intervals

Results

20.0ms	58×	body	1280	valid
11.0ms	45×	body	640	valid
7.0ms	123×	body	80	valid
4.0ms	23×	body	320	valid
1.0ms	7×	body	160	valid

simplify60.0ms

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: 31.4b

localize10.0ms

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)))
2.2b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite55.0ms

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:

6.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
3.0ms	(+ 1.0 (exp (* -2.0 x)))
39.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series135.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
16.0ms	(+ 1.0 (exp (* -2.0 x)))
78.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify50.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (36.0ms)

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

prune251.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b	(* 0.33333333333333337 (pow x 3))
9.2b	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

rewrite8.0ms

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:

6.0ms	(* 0.33333333333333337 (pow x 3))
0.0ms	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

series136.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(* 0.33333333333333337 (pow x 3))
101.0ms	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

simplify185.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 1 (5.0ms)

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

prune123.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (exp (* -2.0 x)))
0.5b	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
0.5b	(/ 1 (sqrt (+ 1.0 (exp (* -2.0 x)))))
32.0b	(fma (/ 1 (sqrt (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

rewrite25.0ms

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)))
10.0ms	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
7.0ms	(/ 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)))
71.0ms	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
50.0ms	(/ 1 (sqrt (+ 1.0 (exp (* -2.0 x)))))
216.0ms	(fma (/ 1 (sqrt (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

simplify42.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (30.0ms)

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

prune291.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1 (sqrt (+ 1.0 (exp (* -2.0 x)))))
32.0b	(fma (/ 1 (sqrt (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))
32.0b	(fma (/ 1 (sqrt (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))
32.0b	(fma (/ 1 (sqrt (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

28×	`*-un-lft-identity`
21×	`times-frac`
20×	`add-sqr-sqrt` `add-cube-cbrt`
16×	`sqrt-prod`
8×	`add-exp-log`
7×	`associate-/r*`
6×	`pow1` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
3×	`pow-flip` `fma-udef` `associate-/l*`
2×	`sqrt-div` `div-exp` `associate-/r/`
1×	`cbrt-undiv` `rec-exp` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `1-exp` `clear-num` `flip-+` `div-inv` `inv-pow`

Counts

4 → 83

Calls

4 calls:

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

series698.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ 1 (sqrt (+ 1.0 (exp (* -2.0 x)))))
217.0ms	(fma (/ 1 (sqrt (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))
221.0ms	(fma (/ 1 (sqrt (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))
215.0ms	(fma (/ 1 (sqrt (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

simplify81.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	230	1035
1	789	886
2	2989	811
3	5002	811

prune274.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes226.0ms

Accuracy

98.1% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 32.4b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	97
1	45	97

end0.0ms

sample1.4s

Algorithm

intervals

Results

572.0ms	1676×	body	1280	valid
310.0ms	1255×	body	640	valid
232.0ms	4143×	body	80	valid
112.0ms	630×	body	320	valid
35.0ms	296×	body	160	valid