Details

sample33.0ms

Algorithm

intervals

Results

11.0ms	47×	body	1280	valid
7.0ms	50×	body	640	valid
3.0ms	125×	body	80	valid
2.0ms	25×	body	320	valid
1.0ms	9×	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: 30.8b

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)))
3.3b	(- (/ 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:

8.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
3.0ms	(+ 1.0 (exp (* -2.0 x)))
13.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series128.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
15.0ms	(+ 1.0 (exp (* -2.0 x)))
78.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify52.0ms

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: 0b

Counts

151 → 3

localize11.0ms

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))
7.8b	(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)))))
6.0ms	(* 0.33333333333333337 (pow x 3))
1.0ms	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

series177.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(fma 1.0 x (- (fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))))
37.0ms	(* 0.33333333333333337 (pow x 3))
95.0ms	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

simplify196.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 1 (6.0ms)

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

prune136.0ms

Filtered

62 candidates to 43 candidates (69.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

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

Merged error: 0b

Counts

65 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1.0 (exp (* -2.0 x))))
0.0b	(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
0.5b	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
3.3b	(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

rewrite233.0ms

Algorithm

rewrite-expression-head

Rules

1732×	`times-frac`
1496×	`*-un-lft-identity`
1023×	`add-sqr-sqrt`
1001×	`sqrt-prod`
996×	`add-cube-cbrt`
585×	`prod-diff`
249×	`distribute-lft-out`
195×	`fma-neg`
86×	`sqrt-div`
84×	`associate-/r/`
43×	`flip3-+` `flip-+`
42×	`div-inv`
30×	`associate-/l*`
14×	`associate-/r*`
11×	`add-exp-log` `add-cbrt-cube`
7×	`difference-of-squares`
6×	`add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
2×	`frac-2neg` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `diff-log` `flip--` `hypot-def` `associate-/l/` `distribute-lft-out--`

Counts

4 → 1110

Calls

4 calls:

4.0ms	(sqrt (+ 1.0 (exp (* -2.0 x))))
17.0ms	(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
6.0ms	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
92.0ms	(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

series225.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(sqrt (+ 1.0 (exp (* -2.0 x))))
35.0ms	(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
67.0ms	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
81.0ms	(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

simplify227.0ms

Algorithm

egg-herbie

Counts

1122 → 1122

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	1613	25952
1	5001	17156

prune1.0s

Filtered

1122 candidates to 310 candidates (27.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	1122	0	1122
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	1122	3	1125

Merged error: 0b

Counts

1125 → 3

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (exp (* -2.0 x)))
0.0b	(/ (sqrt 2.0) (+ 1.0 (exp (* -2.0 x))))
31.6b	(fma (/ (sqrt 2.0) 1) (/ (sqrt 2.0) (+ 1.0 (exp (* -2.0 x)))) (- 1.0))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 77

Calls

3 calls:

3.0ms	(+ 1.0 (exp (* -2.0 x)))
6.0ms	(/ (sqrt 2.0) (+ 1.0 (exp (* -2.0 x))))
1.0ms	(fma (/ (sqrt 2.0) 1) (/ (sqrt 2.0) (+ 1.0 (exp (* -2.0 x)))) (- 1.0))

series214.0ms

Counts

3 → 9

Calls

3 calls:

16.0ms	(+ 1.0 (exp (* -2.0 x)))
67.0ms	(/ (sqrt 2.0) (+ 1.0 (exp (* -2.0 x))))
130.0ms	(fma (/ (sqrt 2.0) 1) (/ (sqrt 2.0) (+ 1.0 (exp (* -2.0 x)))) (- 1.0))

simplify113.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 3 (105.0ms)

Iter	Nodes	Cost
0	276	726
1	879	664
2	3543	652
3	5001	651

prune173.0ms

Filtered

86 candidates to 61 candidates (70.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	86	3	89

Merged error: 0b

Counts

89 → 3

regimes200.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 31.8b

bsearch2.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	19
1	33	19

end0.0ms

sample862.0ms

Algorithm

intervals

Results

346.0ms	1671×	body	1280	valid
178.0ms	1300×	body	640	valid
112.0ms	4075×	body	80	valid
57.0ms	601×	body	320	valid
21.0ms	353×	body	160	valid