Details

sample32.0ms

Algorithm

intervals

Results

11.0ms	49×	body	1280	valid
5.0ms	37×	body	640	valid
4.0ms	141×	body	80	valid
2.0ms	16×	body	320	valid
1.0ms	13×	body	160	valid

simplify62.0ms

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: 26.9b

Counts

2 → 1

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)))
3.8b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite30.0ms

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:

8.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
3.0ms	(+ 1.0 (exp (* -2.0 x)))
12.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series134.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
16.0ms	(+ 1.0 (exp (* -2.0 x)))
81.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify51.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (36.0ms)

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

prune218.0ms

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: 0.0b

Counts

151 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
0.0b	(+ 1.0 (exp (* -2.0 x)))
3.8b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
3.8b	(log (exp (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

164×	`*-un-lft-identity`
118×	`add-sqr-sqrt`
108×	`add-cube-cbrt` `prod-diff`
98×	`times-frac`
59×	`log-prod`
56×	`exp-sum`
26×	`distribute-lft-out`
18×	`fma-neg`
16×	`associate-/r/`
9×	`flip3-+` `flip-+`
8×	`div-inv` `add-log-exp`
7×	`log-pow`
6×	`add-exp-log` `exp-prod` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `difference-of-squares`
3×	`fma-def` `associate-/l*`
2×	`sub-neg` `distribute-lft-out--`
1×	`cbrt-undiv` `+-commutative` `log-div` `flip3--` `frac-2neg` `exp-diff` `diff-log` `div-exp` `rem-log-exp` `clear-num` `sum-log` `flip--`

Counts

4 → 218

Calls

4 calls:

8.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
3.0ms	(+ 1.0 (exp (* -2.0 x)))
12.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
16.0ms	(log (exp (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))

series211.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify68.0ms

Algorithm

egg-herbie

Counts

230 → 230

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	537	2939
1	1513	2129
2	5001	1740

prune318.0ms

Filtered

230 candidates to 113 candidates (49.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	229	1	230
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	231	2	233

Merged error: 0.0b

Counts

233 → 2

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
0.0b	(+ 1.0 (exp (* -2.0 x)))
3.8b	(- (log (exp (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))) 1.0)
3.8b	(log (exp (- (log (exp (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))) 1.0)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

180×	`*-un-lft-identity`
150×	`exp-prod`
142×	`log-pow`
132×	`prod-diff`
128×	`add-sqr-sqrt`
124×	`add-cube-cbrt`
96×	`times-frac`
80×	`log-prod`
71×	`exp-sum`
25×	`distribute-lft-out`
22×	`fma-neg`
16×	`associate-/r/`
14×	`pow1`
9×	`flip3-+` `flip-+`
8×	`div-inv` `add-log-exp`
6×	`associate--l+`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--`
3×	`fma-def`
2×	`sub-neg` `difference-of-squares`
1×	`+-commutative` `log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `sum-log` `flip--` `rem-exp-log`

Counts

4 → 245

Calls

4 calls:

6.0ms	(exp (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
3.0ms	(+ 1.0 (exp (* -2.0 x)))
16.0ms	(- (log (exp (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))) 1.0)
20.0ms	(log (exp (- (log (exp (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))) 1.0)))

series229.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(exp (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
19.0ms	(+ 1.0 (exp (* -2.0 x)))
81.0ms	(- (log (exp (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))) 1.0)
77.0ms	(log (exp (- (log (exp (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))) 1.0)))

simplify75.0ms

Algorithm

egg-herbie

Counts

257 → 257

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	615	3725
1	1559	2188
2	5002	1853

prune379.0ms

Filtered

257 candidates to 116 candidates (45.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	257	0	257
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	257	2	259

Merged error: 0.0b

Counts

259 → 2

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))
10.6b	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

rewrite9.0ms

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)))

series197.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(fma 1.0 x (- (fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))))
37.0ms	(* 0.33333333333333337 (pow x 3))
107.0ms	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

simplify199.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 1 (6.0ms)

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

prune137.0ms

Filtered

62 candidates to 43 candidates (69.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	61	1	62
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	61	3	64

Merged error: 0.0b

Counts

64 → 3

regimes177.0ms

Accuracy

94.7% (1.6b remaining)

Error of 1.6b against oracle of 0.0b and baseline of 29.3b

bsearch2.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	17
1	35	17

end0.0ms

sample872.0ms

Algorithm

intervals

Results

365.0ms	1702×	body	1280	valid
171.0ms	1238×	body	640	valid
106.0ms	4101×	body	80	valid
60.0ms	661×	body	320	valid
20.0ms	298×	body	160	valid