Details

sample36.0ms

Algorithm

intervals

Results

13.0ms	53×	body	1280	valid
6.0ms	35×	body	640	valid
5.0ms	142×	body	80	valid
2.0ms	17×	body	320	valid
1.0ms	9×	body	160	valid

simplify63.0ms

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: 26.7b

Counts

2 → 1

localize7.0ms

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))))
2.6b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite31.0ms

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:

3.0ms	(+ 1.0 (exp (* -2.0 x)))
5.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
16.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series136.0ms

Counts

3 → 9

Calls

3 calls:

17.0ms	(+ 1.0 (exp (* -2.0 x)))
36.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
83.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify58.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (42.0ms)

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

prune222.0ms

Filtered

150 candidates to 86 candidates (57.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	147	3	150
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	148	3	151

Merged error: 0b

Counts

151 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (/ 2.0 (+ (exp (* -2.0 x)) 1.0)))
0.0b	(log (exp (/ 2.0 (+ (exp (* -2.0 x)) 1.0))))
0.0b	(/ 2.0 (+ (exp (* -2.0 x)) 1.0))
2.6b	(- (log (exp (/ 2.0 (+ (exp (* -2.0 x)) 1.0)))) 1.0)

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

136×	`*-un-lft-identity`
108×	`exp-prod`
96×	`log-pow`
91×	`add-sqr-sqrt`
89×	`add-cube-cbrt`
84×	`times-frac`
66×	`prod-diff`
22×	`fma-neg` `distribute-lft-out`
14×	`associate-/r/`
10×	`pow1`
7×	`flip3-+` `flip-+` `div-inv`
6×	`add-exp-log` `log-prod` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u`
3×	`associate--l+` `associate-/l*`
2×	`distribute-lft-out--`
1×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `flip--` `rem-exp-log` `difference-of-squares`

Counts

4 → 203

Calls

4 calls:

6.0ms	(exp (/ 2.0 (+ (exp (* -2.0 x)) 1.0)))
7.0ms	(log (exp (/ 2.0 (+ (exp (* -2.0 x)) 1.0))))
9.0ms	(/ 2.0 (+ (exp (* -2.0 x)) 1.0))
17.0ms	(- (log (exp (/ 2.0 (+ (exp (* -2.0 x)) 1.0)))) 1.0)

series213.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(exp (/ 2.0 (+ (exp (* -2.0 x)) 1.0)))
41.0ms	(log (exp (/ 2.0 (+ (exp (* -2.0 x)) 1.0))))
36.0ms	(/ 2.0 (+ (exp (* -2.0 x)) 1.0))
84.0ms	(- (log (exp (/ 2.0 (+ (exp (* -2.0 x)) 1.0)))) 1.0)

simplify67.0ms

Algorithm

egg-herbie

Counts

215 → 215

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	476	2370
1	1408	1585
2	5002	1539

prune334.0ms

Filtered

215 candidates to 122 candidates (56.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	215	0	215
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	215	3	218

Merged error: 0b

Counts

218 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (log1p (/ 2.0 (+ 1.0 (exp (* -2.0 x))))))
0.0b	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
0.3b	(log1p (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
27.3b	(- (expm1 (log1p (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))) 1.0)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

30×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
20×	`add-cube-cbrt`
12×	`times-frac`
9×	`prod-diff`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`expm1-log1p-u`
4×	`pow1` `associate-/r*` `log1p-expm1-u` `distribute-lft-out`
3×	`fma-neg` `associate-/l*`
2×	`associate-/r/` `expm1-udef`
1×	`cbrt-undiv` `associate--l-` `sub-neg` `log1p-udef` `expm1-log1p` `flip3--` `frac-2neg` `flip3-+` `diff-log` `log1p-expm1` `div-exp` `clear-num` `flip--` `flip-+` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 86

Calls

4 calls:

1.0ms	(expm1 (log1p (/ 2.0 (+ 1.0 (exp (* -2.0 x))))))
5.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
1.0ms	(log1p (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
4.0ms	(- (expm1 (log1p (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))) 1.0)

series470.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(expm1 (log1p (/ 2.0 (+ 1.0 (exp (* -2.0 x))))))
42.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
89.0ms	(log1p (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
208.0ms	(- (expm1 (log1p (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))) 1.0)

simplify46.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	362	854
1	1342	684
2	5002	677

prune182.0ms

Filtered

98 candidates to 68 candidates (69.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	98	3	101

Merged error: 0b

Counts

101 → 3

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 1.0 x (- (fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))))
0.1b	(* 0.33333333333333337 (pow x 3))
10.3b	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`associate-r`
8×	`add-exp-log`
7×	`add-cube-cbrt` `*-un-lft-identity`
5×	`add-cbrt-cube`
4×	`unpow-prod-down` `cube-prod` `unswap-sqr`
3×	`pow1` `expm1-log1p-u` `associate-l` `prod-exp` `log1p-expm1-u` `add-log-exp`
2×	`fma-udef` `sqr-pow`
1×	`cube-mult` `pow-to-exp` `unpow3` `pow-exp` `*-commutative` `cbrt-unprod`

Counts

3 → 53

Calls

3 calls:

1.0ms	(fma 1.0 x (- (fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))))
7.0ms	(* 0.33333333333333337 (pow x 3))
1.0ms	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

series199.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(fma 1.0 x (- (fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))))
37.0ms	(* 0.33333333333333337 (pow x 3))
108.0ms	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

simplify196.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	170	298
1	655	262
2	4021	262
3	5002	262

prune129.0ms

Filtered

62 candidates to 43 candidates (69.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	62	0	62
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	62	3	65

Merged error: 0b

Counts

65 → 3

regimes193.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 28.9b

bsearch2.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	22
1	34	22

end0.0ms

sample996.0ms

Algorithm

intervals

Results

423.0ms	1763×	body	1280	valid
195.0ms	1161×	body	640	valid
132.0ms	4131×	body	80	valid
69.0ms	608×	body	320	valid
24.0ms	337×	body	160	valid