Details

sample90.0ms

Algorithm

intervals

Results

63.0ms	192×	body	1280	valid
7.0ms	236×	body	80	valid
6.0ms	32×	body	640	valid
2.0ms	18×	body	320	valid
1.0ms	13×	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: 28.8b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
4.4b	(+ (- (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)))

series72.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(- (exp x) 2.0)
59.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify95.0ms

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

prune82.0ms

Filtered

41 candidates to 29 candidates (70.7%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 0.0b

Counts

42 → 1

localize10.0ms

Local error

Found 4 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)) (* 1/12 (pow x 4)))
0.1b	(* 1/360 (pow x 6))
0.1b	(* 1/12 (pow x 4))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 75

Calls

4 calls:

10.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
4.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
5.0ms	(* 1/360 (pow x 6))
5.0ms	(* 1/12 (pow x 4))

series275.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
130.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
52.0ms	(* 1/360 (pow x 6))
36.0ms	(* 1/12 (pow x 4))

simplify52.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	329	464
1	1456	439
2	5001	423

prune161.0ms

Filtered

87 candidates to 55 candidates (63.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	86	1	87
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	86	2	88

Merged error: 0b

Counts

88 → 2

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/12 (pow x 4))
0.1b	(* 1/12 (pow x 4))
0.1b	(* 1/12 (pow x 4))
47.0b	(/ (+ (pow x 4) (- (* (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))) (- (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt`
55×	`*-un-lft-identity`
32×	`times-frac`
27×	`add-cube-cbrt`
21×	`add-exp-log` `associate-r`
20×	`difference-of-squares`
17×	`unpow-prod-down`
12×	`add-cbrt-cube`
11×	`sqr-pow`
9×	`associate-l` `prod-exp` `distribute-lft-out` `unswap-sqr`
8×	`associate-/r*`
5×	`distribute-lft-out--` `unpow2`
4×	`pow1` `associate-/l*` `add-log-exp`
3×	`pow-to-exp` `div-sub` `pow-exp` `*-commutative` `cbrt-unprod`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `neg-sub0` `associate-+r-` `flip3--` `frac-2neg` `flip3-+` `div-exp` `unsub-neg` `clear-num` `flip--` `flip-+` `div-inv`

Counts

4 → 138

Calls

4 calls:

6.0ms	(* 1/12 (pow x 4))
6.0ms	(* 1/12 (pow x 4))
5.0ms	(* 1/12 (pow x 4))
14.0ms	(/ (+ (pow x 4) (- (* (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))) (- (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

series266.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* 1/12 (pow x 4))
42.0ms	(* 1/12 (pow x 4))
36.0ms	(* 1/12 (pow x 4))
153.0ms	(/ (+ (pow x 4) (- (* (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))) (- (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

simplify75.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	359	2510
1	1638	2337
2	5003	2205

prune328.0ms

Filtered

150 candidates to 89 candidates (59.3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	150	0	150
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	150	2	152

Merged error: 0b

Counts

152 → 2

regimes12.0ms

Accuracy

0% (0.0b remaining)

Error of 0.6b against oracle of 0.6b 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

sample2.6s

Algorithm

intervals

Results

1.8s	5675×	body	1280	valid
229.0ms	8028×	body	80	valid
225.0ms	1267×	body	640	valid
67.0ms	580×	body	320	valid
24.0ms	331×	body	160	valid