Details

sample38.0ms

Algorithm

intervals

Results

14.0ms	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

simplify64.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	5
1	22	5
2	30	5
3	52	5
4	114	5
5	322	5
6	1627	5
7	5002	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

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))))
3.6b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
13×	`times-frac`
12×	`add-cube-cbrt`
7×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
4×	`associate-/r*`
3×	`pow1` `associate-/l*`
2×	`flip3-+` `associate-/r/` `flip-+` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `clear-num` `sum-log` `flip--` `div-inv` `distribute-lft-out--`

Counts

3 → 60

Calls

3 calls:

3.0ms	(+ 1.0 (exp (* -2.0 x)))
5.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
11.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series144.0ms

Counts

3 → 9

Calls

3 calls:

17.0ms	(+ 1.0 (exp (* -2.0 x)))
41.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
86.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify95.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	251	494
1	731	465
2	2785	460
3	5001	460

prune132.0ms

Filtered

69 candidates to 50 candidates (72.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	66	3	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	3	70

Merged error: 0.0b

Counts

70 → 3

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
0.0b	(cbrt (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3))
0.0b	(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)
3.6b	(- (cbrt (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)) 1.0)

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

81×	`*-un-lft-identity`
62×	`add-sqr-sqrt` `times-frac`
48×	`cbrt-prod`
47×	`add-cube-cbrt`
38×	`unpow-prod-down` `cube-prod`
16×	`distribute-lft-out`
10×	`associate-/r/`
9×	`add-exp-log` `add-cbrt-cube`
7×	`difference-of-squares`
6×	`add-log-exp`
5×	`pow1` `flip3-+` `flip-+` `div-inv`
4×	`associate-/r*`
3×	`pow-unpow` `associate-/l*` `sqr-pow`
2×	`cbrt-undiv` `cube-div` `cube-mult` `unpow3` `div-exp` `pow-exp` `rem-cube-cbrt`
1×	`pow-to-exp` `sub-neg` `cbrt-div` `flip3--` `pow-pow` `frac-2neg` `pow1/3` `diff-log` `clear-num` `flip--` `rem-cbrt-cube` `distribute-lft-out--`

Counts

4 → 161

Calls

4 calls:

5.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
8.0ms	(cbrt (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3))
10.0ms	(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)
20.0ms	(- (cbrt (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)) 1.0)

series212.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
41.0ms	(cbrt (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3))
52.0ms	(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)
83.0ms	(- (cbrt (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)) 1.0)

simplify76.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	522	1569
1	2157	1433
2	5003	1424

prune240.0ms

Filtered

173 candidates to 86 candidates (49.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	172	1	173
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	173	3	176

Merged error: 0.0b

Counts

176 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (+ (cbrt (sqrt (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3))) (sqrt 1.0)) (- (cbrt (sqrt (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3))) (sqrt 1.0)))
0.3b	(cbrt (sqrt (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)))
0.3b	(cbrt (sqrt (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)))
4.0b	(- (cbrt (sqrt (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3))) (sqrt 1.0))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

124×	`sqrt-prod`
118×	`cbrt-prod`
112×	`add-sqr-sqrt`
72×	`*-un-lft-identity`
56×	`times-frac`
44×	`unpow-prod-down` `cube-prod`
42×	`add-cube-cbrt`
32×	`difference-of-squares`
20×	`associate-r`
13×	`distribute-lft-out`
8×	`associate-/r/`
7×	`flip3-+` `flip-+`
6×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp` `sqr-pow`
4×	`frac-times` `flip3--` `associate-l` `flip--` `div-inv`
3×	`sub-neg`
2×	`cube-div` `distribute-rgt-in` `cube-mult` `cbrt-div` `distribute-lft-in` `pow1/3` `sqrt-div` `unpow3` `associate-r/` `associate-l/` `distribute-lft-out--`
1×	`diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 185

Calls

4 calls:

61.0ms	(* (+ (cbrt (sqrt (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3))) (sqrt 1.0)) (- (cbrt (sqrt (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3))) (sqrt 1.0)))
9.0ms	(cbrt (sqrt (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)))
10.0ms	(cbrt (sqrt (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)))
30.0ms	(- (cbrt (sqrt (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3))) (sqrt 1.0))

series612.0ms

Counts

4 → 12

Calls

4 calls:

385.0ms	(* (+ (cbrt (sqrt (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3))) (sqrt 1.0)) (- (cbrt (sqrt (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3))) (sqrt 1.0)))
55.0ms	(cbrt (sqrt (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)))
54.0ms	(cbrt (sqrt (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)))
117.0ms	(- (cbrt (sqrt (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3))) (sqrt 1.0))

simplify97.0ms

Algorithm

egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	685	3534
1	2765	3357
2	5001	3353

prune476.0ms

Filtered

197 candidates to 98 candidates (49.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	195	2	197
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	196	4	200

Merged error: 0.0b

Counts

200 → 4

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (+ (* (sqrt 2.0) (sqrt (/ 1 (+ (exp (* -2.0 x)) 1.0)))) (sqrt 1.0)) (- (cbrt (sqrt (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3))) (sqrt 1.0)))
0.3b	(cbrt (sqrt (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)))
0.5b	(* (sqrt 2.0) (sqrt (/ 1 (+ (exp (* -2.0 x)) 1.0))))
4.0b	(- (cbrt (sqrt (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3))) (sqrt 1.0))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

123×	`add-sqr-sqrt`
113×	`sqrt-prod`
73×	`cbrt-prod`
59×	`*-un-lft-identity`
48×	`times-frac`
41×	`associate-r`
35×	`add-cube-cbrt`
32×	`difference-of-squares`
26×	`unpow-prod-down` `cube-prod`
10×	`pow1`
9×	`associate-l` `distribute-lft-out` `unswap-sqr`
8×	`add-exp-log` `add-cbrt-cube`
6×	`flip3-+` `associate-/r/` `flip-+` `add-log-exp`
5×	`sqr-pow`
4×	`frac-times` `flip3--` `pow-prod-down` `flip--`
3×	`sub-neg` `associate-*r/` `div-inv`
2×	`distribute-rgt-in` `distribute-lft-in` `sqrt-pow1` `pow1/2` `sqrt-div` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod` `distribute-lft-out--`
1×	`cube-div` `cube-mult` `cbrt-div` `pow1/3` `sqrt-unprod` `diff-log` `unpow3`

Counts

4 → 180

Calls

4 calls:

47.0ms	(* (+ (* (sqrt 2.0) (sqrt (/ 1 (+ (exp (* -2.0 x)) 1.0)))) (sqrt 1.0)) (- (cbrt (sqrt (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3))) (sqrt 1.0)))
10.0ms	(cbrt (sqrt (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)))
14.0ms	(* (sqrt 2.0) (sqrt (/ 1 (+ (exp (* -2.0 x)) 1.0))))
27.0ms	(- (cbrt (sqrt (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3))) (sqrt 1.0))

series673.0ms

Counts

4 → 12

Calls

4 calls:

405.0ms	(* (+ (* (sqrt 2.0) (sqrt (/ 1 (+ (exp (* -2.0 x)) 1.0)))) (sqrt 1.0)) (- (cbrt (sqrt (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3))) (sqrt 1.0)))
57.0ms	(cbrt (sqrt (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)))
88.0ms	(* (sqrt 2.0) (sqrt (/ 1 (+ (exp (* -2.0 x)) 1.0))))
121.0ms	(- (cbrt (sqrt (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3))) (sqrt 1.0))

simplify127.0ms

Algorithm

egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1000	3224
1	4516	3027
2	5001	3027

prune544.0ms

Filtered

192 candidates to 103 candidates (53.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	192	0	192
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	192	4	196

Merged error: 0.0b

Counts

196 → 4

regimes348.0ms

Accuracy

98.9% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 30.1b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	35
1	51	35

end0.0ms

sample1.0s

Algorithm

intervals

Results

422.0ms	1678×	body	1280	valid
221.0ms	1296×	body	640	valid
134.0ms	4069×	body	80	valid
74.0ms	643×	body	320	valid
26.0ms	314×	body	160	valid