Details

sample33.0ms

Algorithm

intervals

Results

12.0ms	59×	body	1280	valid
6.0ms	43×	body	640	valid
3.0ms	129×	body	80	valid
2.0ms	18×	body	320	valid
0.0ms	7×	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	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: 30.1b

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)))
2.4b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite23.0ms

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:

8.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
3.0ms	(+ 1.0 (exp (* -2.0 x)))
10.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series130.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
19.0ms	(+ 1.0 (exp (* -2.0 x)))
76.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify90.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	251	494
1	731	465
2	2785	460
3	5002	460

prune141.0ms

Filtered

69 candidates to 50 candidates (72.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	64	5	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	5	70

Merged error: 0.1b

Counts

70 → 5

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (/ 2.0 (+ (exp (* -2.0 x)) 1.0)))
0.0b	(/ (- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3)) (+ (* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ 1.0 (/ 2.0 (+ (exp (* -2.0 x)) 1.0)))) (* 1.0 1.0)))
0.0b	(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)
2.4b	(- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

289×	`add-sqr-sqrt`
163×	`times-frac`
123×	`*-un-lft-identity`
120×	`difference-of-squares`
108×	`unpow-prod-down` `cube-prod`
59×	`add-cube-cbrt`
51×	`sqr-pow`
33×	`associate-/l*`
25×	`distribute-lft-out--`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`distribute-lft-out`
6×	`associate-/r/`
5×	`pow1` `difference-cubes`
4×	`flip3-+` `flip-+`
3×	`pow-unpow` `associate-/r*` `div-inv`
2×	`cbrt-undiv` `flip3--` `div-exp` `pow-exp` `flip--` `associate-/l/` `rem-cube-cbrt`
1×	`+-commutative` `cube-div` `cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `unpow3` `div-sub` `clear-num` `sum-log`

Counts

4 → 262

Calls

4 calls:

9.0ms	(+ 1.0 (/ 2.0 (+ (exp (* -2.0 x)) 1.0)))
57.0ms	(/ (- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3)) (+ (* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ 1.0 (/ 2.0 (+ (exp (* -2.0 x)) 1.0)))) (* 1.0 1.0)))
7.0ms	(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)
30.0ms	(- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3))

series544.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(+ 1.0 (/ 2.0 (+ (exp (* -2.0 x)) 1.0)))
303.0ms	(/ (- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3)) (+ (* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ 1.0 (/ 2.0 (+ (exp (* -2.0 x)) 1.0)))) (* 1.0 1.0)))
53.0ms	(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)
133.0ms	(- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3))

simplify162.0ms

Algorithm

egg-herbie

Counts

274 → 274

Iterations

Useful iterations: 2 (100.0ms)

Iter	Nodes	Cost
0	954	6948
1	3943	6728
2	5001	6646

prune521.0ms

Filtered

274 candidates to 134 candidates (48.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	270	4	274
Fresh	3	1	4
Picked	1	0	1
Done	0	0	0
Total	274	5	279

Merged error: 0.1b

Counts

279 → 5

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ 1.0 (/ 2.0 (+ (exp (* -2.0 x)) 1.0))))
0.5b	(cbrt (+ 1.0 (/ 2.0 (+ (exp (* -2.0 x)) 1.0))))
0.5b	(cbrt (+ 1.0 (/ 2.0 (+ (exp (* -2.0 x)) 1.0))))
2.4b	(- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

53×	`add-sqr-sqrt`
24×	`difference-of-squares`
23×	`*-un-lft-identity`
18×	`unpow-prod-down` `cube-prod`
12×	`cbrt-prod`
10×	`sqr-pow`
8×	`times-frac`
7×	`add-cube-cbrt`
6×	`cbrt-div` `add-log-exp`
5×	`distribute-lft-out--`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
1×	`difference-cubes` `sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 84

Calls

4 calls:

9.0ms	(cbrt (+ 1.0 (/ 2.0 (+ (exp (* -2.0 x)) 1.0))))
9.0ms	(cbrt (+ 1.0 (/ 2.0 (+ (exp (* -2.0 x)) 1.0))))
9.0ms	(cbrt (+ 1.0 (/ 2.0 (+ (exp (* -2.0 x)) 1.0))))
31.0ms	(- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3))

series594.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(cbrt (+ 1.0 (/ 2.0 (+ (exp (* -2.0 x)) 1.0))))
152.0ms	(cbrt (+ 1.0 (/ 2.0 (+ (exp (* -2.0 x)) 1.0))))
157.0ms	(cbrt (+ 1.0 (/ 2.0 (+ (exp (* -2.0 x)) 1.0))))
133.0ms	(- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3))

simplify44.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	334	1238
1	1023	1175
2	5001	1162

prune294.0ms

Filtered

96 candidates to 65 candidates (67.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	96	5	101

Merged error: 0.1b

Counts

101 → 5

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)
0.0b	(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)
0.0b	(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)
2.4b	(- (* (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)) (* (pow 1.0 3) (pow 1.0 3)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

91×	`*-un-lft-identity`
72×	`times-frac`
55×	`add-sqr-sqrt` `add-cube-cbrt`
54×	`unpow-prod-down` `cube-prod`
18×	`distribute-lft-out`
13×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/r/`
9×	`pow-unpow`
7×	`pow1`
6×	`flip3-+` `pow-exp` `flip-+` `div-inv` `add-log-exp` `rem-cube-cbrt`
3×	`cbrt-undiv` `cube-div` `cube-mult` `pow-to-exp` `pow-pow` `unpow3` `div-exp` `sqr-pow`
2×	`pow-prod-down`
1×	`difference-cubes` `sub-neg` `flip3--` `diff-log` `flip--` `difference-of-squares`

Counts

4 → 182

Calls

4 calls:

10.0ms	(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)
7.0ms	(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)
7.0ms	(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)
20.0ms	(- (* (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)) (* (pow 1.0 3) (pow 1.0 3)))

series274.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)
49.0ms	(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)
51.0ms	(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)
122.0ms	(- (* (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)) (* (pow 1.0 3) (pow 1.0 3)))

simplify87.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	490	2003
1	2216	1672
2	5002	1642

prune419.0ms

Filtered

194 candidates to 92 candidates (47.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	193	1	194
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	193	6	199

Merged error: 0.1b

Counts

199 → 6

regimes289.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.4b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	69
1	57	69

end0.0ms

sample862.0ms

Algorithm

intervals

Results

358.0ms	1722×	body	1280	valid
178.0ms	1278×	body	640	valid
106.0ms	4079×	body	80	valid
53.0ms	592×	body	320	valid
22.0ms	329×	body	160	valid