Details

sample80.0ms

Algorithm

intervals

Results

50.0ms	171×	body	1280	valid
9.0ms	217×	body	80	valid
8.0ms	48×	body	640	valid
2.0ms	17×	body	320	valid
1.0ms	13×	body	160	valid

simplify139.0ms

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	65	5
5	96	5
6	140	5
7	285	5
8	1642	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: 32.0b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
4.3b	(+ (- (exp x) 2.0) (exp (neg 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 (neg x)))

series68.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(- (exp x) 2.0)
56.0ms	(+ (- (exp x) 2.0) (exp (neg x)))

simplify88.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	209	282
1	694	269
2	3196	260
3	5001	260

prune90.0ms

Filtered

41 candidates to 29 candidates (70.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	38	3	41
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	39	3	42

Merged error: 0.0b

Counts

42 → 3

localize9.0ms

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))

rewrite24.0ms

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:

4.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
7.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
6.0ms	(* 1/360 (pow x 6))
5.0ms	(* 1/12 (pow x 4))

series261.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
55.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
49.0ms	(* 1/360 (pow x 6))
34.0ms	(* 1/12 (pow x 4))

simplify50.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	329	464
1	1456	438
2	5001	422

prune168.0ms

Filtered

87 candidates to 55 candidates (63.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	85	2	87
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	85	5	90

Merged error: 0.0b

Counts

90 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/360 (pow x 6))
0.1b	(* 1/12 (pow x 4))
0.1b	(pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) 3)
22.6b	(cbrt (pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) 3))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
16×	`add-cube-cbrt` `unpow-prod-down`
15×	`add-exp-log`
14×	`cbrt-prod` `associate-r`
9×	`add-cbrt-cube`
8×	`cube-prod`
6×	`associate-l` `prod-exp` `unswap-sqr` `sqr-pow`
5×	`pow1`
4×	`cube-div` `distribute-lft-out` `add-log-exp`
3×	`pow-to-exp` `pow-unpow` `pow-exp`
2×	`cube-mult` `cbrt-div` `flip3-+` `unpow3` `*-commutative` `cbrt-unprod` `flip-+`
1×	`pow-pow` `pow1/3` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 102

Calls

4 calls:

5.0ms	(* 1/360 (pow x 6))
5.0ms	(* 1/12 (pow x 4))
8.0ms	(pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) 3)
8.0ms	(cbrt (pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) 3))

series212.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* 1/360 (pow x 6))
34.0ms	(* 1/12 (pow x 4))
72.0ms	(pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) 3)
55.0ms	(cbrt (pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) 3))

simplify63.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	419	910
1	1865	843
2	5003	830

prune221.0ms

Filtered

114 candidates to 61 candidates (53.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	114	5	119

Merged error: 0.0b

Counts

119 → 5

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/12 (pow x 4))
1.1b	(pow (pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) (sqrt 3)) (sqrt 3))
2.2b	(pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) (sqrt 3))
22.6b	(cbrt (pow (pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) (sqrt 3)) (sqrt 3)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

32×	`unpow-prod-down`
23×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
17×	`add-cube-cbrt`
12×	`add-exp-log` `cbrt-prod` `pow-unpow`
7×	`associate-r` `sqr-pow`
6×	`pow-exp` `sqrt-prod` `add-cbrt-cube`
5×	`pow1`
4×	`pow-to-exp` `add-log-exp`
3×	`associate-l` `prod-exp` `distribute-lft-out` `unswap-sqr`
2×	`pow-pow`
1×	`pow1/3` `*-commutative` `cbrt-unprod`

Counts

4 → 93

Calls

4 calls:

5.0ms	(* 1/12 (pow x 4))
10.0ms	(pow (pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) (sqrt 3)) (sqrt 3))
8.0ms	(pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) (sqrt 3))
9.0ms	(cbrt (pow (pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) (sqrt 3)) (sqrt 3)))

series1.2s

Counts

4 → 12

Calls

4 calls:

34.0ms	(* 1/12 (pow x 4))
376.0ms	(pow (pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) (sqrt 3)) (sqrt 3))
200.0ms	(pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) (sqrt 3))
554.0ms	(cbrt (pow (pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) (sqrt 3)) (sqrt 3)))

simplify96.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	679	1661
1	3002	1538
2	5001	1535

prune323.0ms

Filtered

105 candidates to 71 candidates (67.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	104	1	105
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	105	5	110

Merged error: 0.0b

Counts

110 → 5

regimes33.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	7
1	17	7

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.8s	5707×	body	1280	valid
216.0ms	7996×	body	80	valid
209.0ms	1211×	body	640	valid
70.0ms	621×	body	320	valid
22.0ms	317×	body	160	valid

Details

sample80.0ms

simplify139.0ms

prune2.0ms

localize6.0ms

rewrite13.0ms

series68.0ms

simplify88.0ms

prune90.0ms

localize9.0ms

rewrite24.0ms

series261.0ms

simplify50.0ms

prune168.0ms

localize12.0ms

rewrite29.0ms

series212.0ms

simplify63.0ms

prune221.0ms

localize28.0ms

rewrite34.0ms

series1.2s

simplify96.0ms

prune323.0ms

regimes33.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.5s

Profiling