Details

sample32.0ms

Algorithm

intervals

Results

13.0ms	58×	body	1280	valid
4.0ms	30×	body	640	valid
4.0ms	141×	body	80	valid
2.0ms	21×	body	320	valid
0.0ms	6×	body	160	valid

simplify61.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 27.0b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
1.8b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 124

Calls

2 calls:

9.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
14.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series117.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
81.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify50.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	376	1556
1	1170	1155
2	5001	1121

prune177.0ms

Filtered

130 candidates to 69 candidates (53.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	128	2	130
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	129	2	131

Merged error: 0.0b

Counts

131 → 2

localize10.0ms

Local error

Found 3 expressions with local error:

0.4b	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
0.4b	(/ 1 (sqrt (+ 1.0 (exp (* -2.0 x)))))
27.7b	(fma (/ 1 (sqrt (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 110

Calls

3 calls:

6.0ms	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
7.0ms	(/ 1 (sqrt (+ 1.0 (exp (* -2.0 x)))))
1.0ms	(fma (/ 1 (sqrt (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

series327.0ms

Counts

3 → 9

Calls

3 calls:

65.0ms	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
49.0ms	(/ 1 (sqrt (+ 1.0 (exp (* -2.0 x)))))
213.0ms	(fma (/ 1 (sqrt (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

simplify139.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	328	1133
1	1147	1003
2	4595	952
3	5001	952

prune204.0ms

Filtered

119 candidates to 69 candidates (58.0%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	119	2	121

Merged error: 0.0b

Counts

121 → 2

localize11.0ms

Local error

Found 2 expressions with local error:

0.1b	(* 0.33333333333333337 (pow x 3))
12.1b	(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))
1.0ms	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

series137.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(* 0.33333333333333337 (pow x 3))
96.0ms	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

simplify186.0ms

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

prune100.0ms

Filtered

49 candidates to 33 candidates (67.3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	49	0	49
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	49	2	51

Merged error: 0.0b

Counts

51 → 2

regimes123.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 30.3b

bsearch2.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	20
1	37	20

end0.0ms

sample883.0ms

Algorithm

intervals

Results

363.0ms	1705×	body	1280	valid
181.0ms	1273×	body	640	valid
107.0ms	4024×	body	80	valid
67.0ms	668×	body	320	valid
20.0ms	330×	body	160	valid