Details

sample35.0ms

Algorithm

intervals

Results

13.0ms	57×	body	1280	valid
7.0ms	39×	body	640	valid
4.0ms	133×	body	80	valid
2.0ms	16×	body	320	valid
1.0ms	11×	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: 28.8b

Counts

2 → 1

localize6.0ms

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))))
3.6b	(- (/ 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:

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

series128.0ms

Counts

3 → 9

Calls

3 calls:

15.0ms	(+ 1.0 (exp (* -2.0 x)))
35.0ms	(/ 2.0 (+ 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 (37.0ms)

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

prune233.0ms

Filtered

150 candidates to 86 candidates (57.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	146	4	150
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	147	4	151

Merged error: 0.0b

Counts

151 → 4

localize9.0ms

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)))))
3.6b	(- (/ (/ 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:

3.0ms	(sqrt (+ 1.0 (exp (* -2.0 x))))
16.0ms	(/ (/ 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)))))
91.0ms	(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

series218.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(sqrt (+ 1.0 (exp (* -2.0 x))))
38.0ms	(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
63.0ms	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
76.0ms	(- (/ (/ 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 (39.0ms)

Iter	Nodes	Cost
0	1613	25952
1	5001	17156

prune1.1s

Filtered

1122 candidates to 310 candidates (27.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	1120	2	1122
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	1123	3	1126

Merged error: 0.0b

Counts

1126 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (sqrt (+ 1.0 (exp (* -2.0 x)))))
0.5b	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
0.5b	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
3.8b	(fma (/ (sqrt (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))) (sqrt (sqrt (+ 1.0 (exp (* -2.0 x)))))) (/ (sqrt (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))) (sqrt (sqrt (+ 1.0 (exp (* -2.0 x)))))) (- 1.0))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

56×	`*-un-lft-identity`
44×	`sqrt-prod`
42×	`times-frac`
40×	`add-sqr-sqrt`
38×	`add-cube-cbrt`
14×	`associate-/r*`
9×	`distribute-lft-out`
8×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
6×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `sqrt-pow1` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `pow1/2` `div-exp` `clear-num` `div-inv`
1×	`fma-udef`

Counts

4 → 128

Calls

4 calls:

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

series579.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(sqrt (sqrt (+ 1.0 (exp (* -2.0 x)))))
71.0ms	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
69.0ms	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
309.0ms	(fma (/ (sqrt (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))) (sqrt (sqrt (+ 1.0 (exp (* -2.0 x)))))) (/ (sqrt (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))) (sqrt (sqrt (+ 1.0 (exp (* -2.0 x)))))) (- 1.0))

simplify151.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	335	1519
1	1070	1403
2	4777	1330
3	5001	1330

prune402.0ms

Filtered

140 candidates to 94 candidates (67.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	140	3	143

Merged error: 0.0b

Counts

143 → 3

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ 1.0 (exp (* -2.0 x))))
0.5b	(cbrt (+ 1.0 (exp (* -2.0 x))))
0.5b	(cbrt (+ 1.0 (exp (* -2.0 x))))
29.4b	(fma (/ 1 (sqrt (* (cbrt (+ 1.0 (exp (* -2.0 x)))) (cbrt (+ 1.0 (exp (* -2.0 x))))))) (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (cbrt (+ 1.0 (exp (* -2.0 x)))))) (- 1.0))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
12×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
1×	`fma-udef`

Counts

4 → 58

Calls

4 calls:

3.0ms	(cbrt (+ 1.0 (exp (* -2.0 x))))
7.0ms	(cbrt (+ 1.0 (exp (* -2.0 x))))
3.0ms	(cbrt (+ 1.0 (exp (* -2.0 x))))
1.0ms	(fma (/ 1 (sqrt (* (cbrt (+ 1.0 (exp (* -2.0 x)))) (cbrt (+ 1.0 (exp (* -2.0 x))))))) (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (cbrt (+ 1.0 (exp (* -2.0 x)))))) (- 1.0))

series765.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(cbrt (+ 1.0 (exp (* -2.0 x))))
137.0ms	(cbrt (+ 1.0 (exp (* -2.0 x))))
131.0ms	(cbrt (+ 1.0 (exp (* -2.0 x))))
359.0ms	(fma (/ 1 (sqrt (* (cbrt (+ 1.0 (exp (* -2.0 x)))) (cbrt (+ 1.0 (exp (* -2.0 x))))))) (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (cbrt (+ 1.0 (exp (* -2.0 x)))))) (- 1.0))

simplify81.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (72.0ms)

Iter	Nodes	Cost
0	221	794
1	648	713
2	2505	693
3	5001	689

prune269.0ms

Filtered

70 candidates to 60 candidates (85.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	70	3	73

Merged error: 0.0b

Counts

73 → 3

regimes218.0ms

Accuracy

98.9% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 29.8b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	58
1	43	58

end0.0ms

sample975.0ms

Algorithm

intervals

Results

396.0ms	1678×	body	1280	valid
211.0ms	1296×	body	640	valid
127.0ms	4069×	body	80	valid
71.0ms	643×	body	320	valid
22.0ms	314×	body	160	valid