Details

sample93.0ms

Algorithm

intervals

Results

63.0ms	181×	body	1280	valid
8.0ms	270×	body	80	valid
7.0ms	36×	body	640	valid
3.0ms	27×	body	320	valid
0.0ms	4×	body	160	valid

simplify218.0ms

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: 28.7b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
3.8b	(+ (- (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)))

simplify94.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 2 (21.0ms)

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

prune87.0ms

Filtered

41 candidates to 29 candidates (70.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	37	4	41
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	38	4	42

Merged error: 0.0b

Counts

42 → 4

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 64

Calls

3 calls:

8.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
5.0ms	(* 1/360 (pow x 6))
5.0ms	(* 1/12 (pow x 4))

series141.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
49.0ms	(* 1/360 (pow x 6))
39.0ms	(* 1/12 (pow x 4))

simplify46.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	283	367
1	1255	340
2	5001	327

prune149.0ms

Filtered

73 candidates to 45 candidates (61.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	72	1	73
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	72	5	77

Merged error: 0.0b

Counts

77 → 5

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (exp x) (+ (* 2.0 (+ 2.0 (exp x))) (exp (+ x x))))
0.0b	(/ (+ (* 2.0 2.0) (+ (exp (+ x x)) (* (exp x) (+ 2.0 (- (pow (exp x) 3) (pow 2.0 3)))))) (* (exp x) (+ (* 2.0 (+ 2.0 (exp x))) (exp (+ x x)))))
0.0b	(pow (exp x) 3)
3.7b	(+ (* 2.0 2.0) (+ (exp (+ x x)) (* (exp x) (+ 2.0 (- (pow (exp x) 3) (pow 2.0 3))))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
9×	`add-exp-log` `add-log-exp`
7×	`pow1`
4×	`pow-pow` `flip3-+` `associate-*r/` `flip-+`
3×	`unpow-prod-down` `pow-unpow` `exp-prod` `times-frac` `cube-prod` `associate-r` `associate-l` `sum-log` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `associate-/l/`
1×	`+-commutative` `distribute-rgt-in` `cube-mult` `pow-to-exp` `associate-+r+` `frac-2neg` `distribute-lft-in` `unpow3` `pow-prod-down` `pow-exp` `clear-num` `associate-/r` `-commutative` `div-inv` `rem-cube-cbrt` `unswap-sqr` `sqr-pow`

Counts

4 → 86

Calls

4 calls:

13.0ms	(* (exp x) (+ (* 2.0 (+ 2.0 (exp x))) (exp (+ x x))))
23.0ms	(/ (+ (* 2.0 2.0) (+ (exp (+ x x)) (* (exp x) (+ 2.0 (- (pow (exp x) 3) (pow 2.0 3)))))) (* (exp x) (+ (* 2.0 (+ 2.0 (exp x))) (exp (+ x x)))))
4.0ms	(pow (exp x) 3)
9.0ms	(+ (* 2.0 2.0) (+ (exp (+ x x)) (* (exp x) (+ 2.0 (- (pow (exp x) 3) (pow 2.0 3))))))

series414.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (exp x) (+ (* 2.0 (+ 2.0 (exp x))) (exp (+ x x))))
249.0ms	(/ (+ (* 2.0 2.0) (+ (exp (+ x x)) (* (exp x) (+ 2.0 (- (pow (exp x) 3) (pow 2.0 3)))))) (* (exp x) (+ (* 2.0 (+ 2.0 (exp x))) (exp (+ x x)))))
24.0ms	(pow (exp x) 3)
89.0ms	(+ (* 2.0 2.0) (+ (exp (+ x x)) (* (exp x) (+ 2.0 (- (pow (exp x) 3) (pow 2.0 3))))))

simplify114.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (102.0ms)

Iter	Nodes	Cost
0	522	1373
1	3142	1189
2	5002	1182

prune289.0ms

Filtered

98 candidates to 69 candidates (70.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	96	2	98
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	98	5	103

Merged error: 0.0b

Counts

103 → 5

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (exp (+ x x)) (exp (+ x x)))
0.0b	(pow (exp x) 3)
0.0b	(* (/ (+ (* 2.0 2.0) (+ (exp (+ x x)) (* (exp x) (+ 2.0 (- (pow (exp x) 3) (pow 2.0 3)))))) (* (exp x) (- (* (* 2.0 (+ 2.0 (exp x))) (* 2.0 (+ 2.0 (exp x)))) (* (exp (+ x x)) (exp (+ x x)))))) (- (* 2.0 (+ 2.0 (exp x))) (exp (+ x x))))
3.7b	(+ (* 2.0 2.0) (+ (exp (+ x x)) (* (exp x) (+ 2.0 (- (pow (exp x) 3) (pow 2.0 3))))))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

119×	`exp-prod`
91×	`*-un-lft-identity`
75×	`add-sqr-sqrt`
45×	`add-cube-cbrt`
30×	`distribute-lft-out`
24×	`distribute-rgt-out` `pow-prod-down`
19×	`pow-sqr` `pow-prod-up`
16×	`add-cbrt-cube`
14×	`pow1` `distribute-lft1-in` `distribute-rgt1-in`
13×	`associate-l`
12×	`add-exp-log`
10×	`count-2`
9×	`add-log-exp`
8×	`exp-sum`
7×	`associate-r`
6×	`distribute-rgt-in` `distribute-lft-in`
5×	`prod-exp` `cbrt-unprod` `unswap-sqr`
4×	`pow-pow` `associate-*r/` `swap-sqr` `associate--l+`
3×	`unpow-prod-down` `pow-unpow` `flip3--` `times-frac` `cube-prod` `sum-log` `flip--`
2×	`cbrt-undiv` `frac-times` `sub-neg` `div-exp` `associate-/r/` `*-commutative`
1×	`+-commutative` `pow2` `cube-mult` `pow-to-exp` `associate-+r+` `flip3-+` `pow-plus` `unpow3` `associate-*l/` `pow-exp` `flip-+` `div-inv` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 169

Calls

4 calls:

21.0ms	(* (exp (+ x x)) (exp (+ x x)))
4.0ms	(pow (exp x) 3)
37.0ms	(* (/ (+ (* 2.0 2.0) (+ (exp (+ x x)) (* (exp x) (+ 2.0 (- (pow (exp x) 3) (pow 2.0 3)))))) (* (exp x) (- (* (* 2.0 (+ 2.0 (exp x))) (* 2.0 (+ 2.0 (exp x)))) (* (exp (+ x x)) (exp (+ x x)))))) (- (* 2.0 (+ 2.0 (exp x))) (exp (+ x x))))
10.0ms	(+ (* 2.0 2.0) (+ (exp (+ x x)) (* (exp x) (+ 2.0 (- (pow (exp x) 3) (pow 2.0 3))))))

series521.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (exp (+ x x)) (exp (+ x x)))
24.0ms	(pow (exp x) 3)
381.0ms	(* (/ (+ (* 2.0 2.0) (+ (exp (+ x x)) (* (exp x) (+ 2.0 (- (pow (exp x) 3) (pow 2.0 3)))))) (* (exp x) (- (* (* 2.0 (+ 2.0 (exp x))) (* 2.0 (+ 2.0 (exp x)))) (* (exp (+ x x)) (exp (+ x x)))))) (- (* 2.0 (+ 2.0 (exp x))) (exp (+ x x))))
95.0ms	(+ (* 2.0 2.0) (+ (exp (+ x x)) (* (exp x) (+ 2.0 (- (pow (exp x) 3) (pow 2.0 3))))))

simplify169.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	807	2700
1	4796	2313
2	5002	2313

prune433.0ms

Filtered

181 candidates to 96 candidates (53.0%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	181	0	181
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	181	5	186

Merged error: 0.0b

Counts

186 → 5

regimes29.0ms

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

sample2.7s

Algorithm

intervals

Results

1.9s	5615×	body	1280	valid
253.0ms	8058×	body	80	valid
243.0ms	1264×	body	640	valid
76.0ms	625×	body	320	valid
25.0ms	319×	body	160	valid