Details

sample77.0ms

Algorithm

intervals

Results

52.0ms	185×	body	1280	valid
6.0ms	275×	body	80	valid
6.0ms	38×	body	640	valid
2.0ms	20×	body	320	valid
1.0ms	11×	body	160	valid

simplify219.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	5
1	26	5
2	41	5
3	55	5
4	67	5
5	100	5
6	144	5
7	296	5
8	1321	5
9	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: 30.1b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
3.4b	(+ (- (exp x) 2.0) (exp (- x)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity` `add-log-exp`
4×	`add-sqr-sqrt` `frac-add`
3×	`flip3--` `flip--`
2×	`pow1` `add-exp-log` `neg-sub0` `exp-neg` `add-cube-cbrt` `sub-neg` `associate-+l+` `exp-diff` `diff-log` `sum-log` `add-cbrt-cube` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `associate-+l-` `flip3-+` `flip-+` `difference-of-squares`

Counts

2 → 35

Calls

2 calls:

4.0ms	(- (exp x) 2.0)
8.0ms	(+ (- (exp x) 2.0) (exp (- x)))

series71.0ms

Counts

2 → 6

Calls

2 calls:

13.0ms	(- (exp x) 2.0)
58.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify91.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	211	282
1	715	269
2	3477	260
3	5001	260

prune89.0ms

Filtered

41 candidates to 29 candidates (70.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	39	2	41
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	40	2	42

Merged error: 0.0b

Counts

42 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
0.0b	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
0.1b	(* 1/360 (pow x 6))
0.1b	(* 1/12 (pow x 4))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

32×	`*-un-lft-identity`
20×	`add-sqr-sqrt`
14×	`add-exp-log` `associate-r` `associate-l`
13×	`distribute-lft-out`
11×	`add-log-exp`
10×	`add-cube-cbrt`
8×	`pow1` `unpow-prod-down` `add-cbrt-cube`
6×	`prod-exp` `unswap-sqr`
4×	`sum-log` `sqr-pow`
3×	`+-commutative`
2×	`pow-to-exp` `associate-+r+` `flip3-+` `pow-prod-down` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+`

Counts

4 → 86

Calls

4 calls:

24.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
32.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
7.0ms	(* 1/360 (pow x 6))
7.0ms	(* 1/12 (pow x 4))

series275.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
57.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
51.0ms	(* 1/360 (pow x 6))
36.0ms	(* 1/12 (pow x 4))

simplify54.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	331	520
1	1458	495
2	5002	479

prune198.0ms

Filtered

98 candidates to 56 candidates (57.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	98	2	100

Merged error: 0.0b

Counts

100 → 2

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

76×	`frac-add`
60×	`add-sqr-sqrt`
56×	`-un-lft-identity` `associate-/l`
38×	`neg-sub0` `exp-neg` `exp-diff`
32×	`difference-of-squares`
27×	`unpow-prod-down` `cube-prod`
17×	`sqr-pow`
12×	`add-cube-cbrt`
11×	`pow-unpow`
10×	`associate-/r*` `distribute-lft-out--` `add-log-exp`
8×	`difference-cubes` `distribute-lft-out`
5×	`pow1` `add-exp-log` `+-commutative` `add-cbrt-cube`
4×	`associate-+l+` `pow-pow` `associate-/l/`
3×	`exp-prod` `flip3-+` `associate-l` `sum-log` `flip-+`
2×	`distribute-rgt-in` `flip3--` `frac-2neg` `distribute-lft-in` `pow-exp` `clear-num` `flip--`
1×	`cube-mult` `pow-to-exp` `associate-+l-` `unpow3` `div-sub` `rem-cube-cbrt`

Counts

4 → 145

Calls

4 calls:

15.0ms	(+ (* 2.0 (+ 2.0 (exp x))) (exp (+ x x)))
3.0ms	(+ 2.0 (exp x))
4.0ms	(pow (exp x) 3)
77.0ms	(+ (/ (- (pow (exp x) 3) (pow 2.0 3)) (+ (* 2.0 (+ 2.0 (exp x))) (exp (+ x x)))) (exp (- x)))

series262.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ (* 2.0 (+ 2.0 (exp x))) (exp (+ x x)))
8.0ms	(+ 2.0 (exp x))
28.0ms	(pow (exp x) 3)
194.0ms	(+ (/ (- (pow (exp x) 3) (pow 2.0 3)) (+ (* 2.0 (+ 2.0 (exp x))) (exp (+ x x)))) (exp (- x)))

simplify161.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 2 (132.0ms)

Iter	Nodes	Cost
0	915	3051
1	4599	2981
2	5002	2881

prune273.0ms

Filtered

157 candidates to 69 candidates (43.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	156	1	157
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	156	3	159

Merged error: 0.0b

Counts

159 → 3

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite4.5s

Algorithm

rewrite-expression-head

Rules

19674×	`associate-/l*`
19088×	`frac-times`
18408×	`add-sqr-sqrt`
14095×	`*-un-lft-identity`
13707×	`frac-sub`
11277×	`difference-of-squares`
10661×	`exp-neg`
9138×	`neg-sub0` `exp-diff`
8433×	`unpow-prod-down` `cube-prod`
5619×	`sqr-pow`
3524×	`distribute-lft-out--`
3510×	`associate-/r*`
3388×	`associate-r/` `associate-l/`
2817×	`pow-unpow`
2808×	`difference-cubes`
1550×	`un-div-inv`
1420×	`add-cube-cbrt`
1404×	`associate-/l/` `distribute-lft-out`
711×	`clear-num`
706×	`associate-l`
703×	`flip3--` `flip--`
702×	`frac-2neg`
30×	`times-frac`
29×	`unswap-sqr`
21×	`swap-sqr`
14×	`*-commutative`
12×	`pow-pow`
9×	`exp-prod`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`pow-exp` `add-log-exp`
3×	`cube-mult` `pow-to-exp` `unpow3` `rem-cube-cbrt`
1×	`sub-neg` `diff-log`

Counts

4 → 13850

Calls

4 calls:

4.0ms	(pow (exp x) 3)
4.0ms	(pow (exp x) 3)
4.0ms	(pow (exp x) 3)
1.6s	(- (* (/ (- (pow (exp x) 3) (pow 2.0 3)) (+ (* 2.0 (+ 2.0 (exp x))) (exp (+ x x)))) (/ (- (pow (exp x) 3) (pow 2.0 3)) (+ (* 2.0 (+ 2.0 (exp x))) (exp (+ x x))))) (* (exp (- x)) (exp (- x))))

series467.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(pow (exp x) 3)
24.0ms	(pow (exp x) 3)
23.0ms	(pow (exp x) 3)
394.0ms	(- (* (/ (- (pow (exp x) 3) (pow 2.0 3)) (+ (* 2.0 (+ 2.0 (exp x))) (exp (+ x x)))) (/ (- (pow (exp x) 3) (pow 2.0 3)) (+ (* 2.0 (+ 2.0 (exp x))) (exp (+ x x))))) (* (exp (- x)) (exp (- x))))

simplify7.9s

Algorithm

egg-herbie

Counts

13862 → 13862

Iterations

Useful iterations: 0 (180.0ms)

Iter	Nodes	Cost
0	13794	933527

prune37.9s

Filtered

13862 candidates to 5280 candidates (38.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	13862	0	13862
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	13862	3	13865

Merged error: 0.0b

Counts

13865 → 3

regimes17.0ms

Accuracy

0% (0.5b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	7
1	17	7

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.6s	5626×	body	1280	valid
184.0ms	1238×	body	640	valid
164.0ms	7748×	body	80	valid
59.0ms	646×	body	320	valid
19.0ms	334×	body	160	valid