Details

sample89.0ms

Algorithm

intervals

Results

56.0ms	172×	body	1280	valid
7.0ms	262×	body	80	valid
7.0ms	40×	body	640	valid
3.0ms	33×	body	320	valid
0.0ms	6×	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

prune3.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 31.2b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
4.5b	(+ (- (exp x) 2.0) (exp (neg x)))

rewrite12.0ms

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)
7.0ms	(+ (- (exp x) 2.0) (exp (neg x)))

series84.0ms

Counts

2 → 6

Calls

2 calls:

16.0ms	(- (exp x) 2.0)
68.0ms	(+ (- (exp x) 2.0) (exp (neg x)))

simplify86.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 2 (18.0ms)

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

prune107.0ms

Filtered

41 candidates to 29 candidates (29.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	39	2	41
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	39	3	42

Merged error: 0.0b

Counts

42 → 3

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

rewrite25.0ms

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:

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

series379.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
68.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
62.0ms	(* 1/360 (pow x 6))
43.0ms	(* 1/12 (pow x 4))

simplify53.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (46.0ms)

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

prune289.0ms

Filtered

87 candidates to 55 candidates (36.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	86	1	87
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	86	4	90

Merged error: 0.0b

Counts

90 → 4

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (exp x) 2.0)
4.5b	(log (exp (+ (- (exp x) 2.0) (exp (neg x)))))
4.5b	(+ (- (exp x) 2.0) (exp (neg x)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
10×	`add-log-exp`
7×	`add-sqr-sqrt`
6×	`log-pow`
5×	`add-cube-cbrt` `exp-prod`
4×	`pow1` `log-prod` `frac-add` `distribute-lft-out`
3×	`add-exp-log` `flip3--` `exp-diff` `add-cbrt-cube` `flip--` `distribute-lft-out--`
2×	`neg-sub0` `exp-neg` `associate-+l-` `sub-neg` `associate-+l+` `diff-log` `sum-log`
1×	`+-commutative` `log-div` `flip3-+` `rem-log-exp` `exp-sum` `flip-+` `difference-of-squares`

Counts

3 → 54

Calls

3 calls:

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

series163.0ms

Counts

3 → 9

Calls

3 calls:

16.0ms	(- (exp x) 2.0)
72.0ms	(log (exp (+ (- (exp x) 2.0) (exp (neg x)))))
75.0ms	(+ (- (exp x) 2.0) (exp (neg x)))

simplify93.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	242	437
1	778	405
2	3360	396
3	5001	396

prune176.0ms

Filtered

63 candidates to 40 candidates (36.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	63	0	63
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	63	4	67

Merged error: 0.0b

Counts

67 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/12 (pow x 4))
0.1b	(* 1/12 (pow x 4))
0.1b	(* (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
43.8b	(/ (+ (pow x 4) (neg (* (+ (* 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)))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-sqr-sqrt`
56×	`*-un-lft-identity`
32×	`times-frac`
28×	`add-cube-cbrt`
20×	`difference-of-squares`
18×	`add-exp-log`
17×	`associate-r`
13×	`unpow-prod-down`
12×	`add-cbrt-cube`
11×	`pow1`
9×	`associate-l` `distribute-lft-out` `sqr-pow`
8×	`associate-/r*`
7×	`flip3-+` `prod-exp` `flip-+` `unswap-sqr`
5×	`distribute-lft-out--` `unpow2`
4×	`frac-times` `associate-/l*` `add-log-exp`
3×	`div-sub` `swap-sqr` `*-commutative` `cbrt-unprod`
2×	`pow-to-exp` `associate-r/` `associate-l/` `pow-exp` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `pow2` `neg-sub0` `distribute-rgt-in` `associate-+r-` `flip3--` `frac-2neg` `distribute-lft-in` `pow-plus` `div-exp` `unsub-neg` `pow-prod-down` `clear-num` `pow-sqr` `pow-prod-up` `flip--` `div-inv`

Counts

4 → 148

Calls

4 calls:

5.0ms	(* 1/12 (pow x 4))
5.0ms	(* 1/12 (pow x 4))
10.0ms	(* (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
14.0ms	(/ (+ (pow x 4) (neg (* (+ (* 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)))))

series370.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* 1/12 (pow x 4))
50.0ms	(* 1/12 (pow x 4))
82.0ms	(* (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
194.0ms	(/ (+ (pow x 4) (neg (* (+ (* 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)))))

simplify130.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (94.0ms)

Iter	Nodes	Cost
0	570	2943
1	2922	2738
2	5001	2670

prune896.0ms

Filtered

160 candidates to 95 candidates (40.6%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	160	0	160
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	160	4	164

Merged error: 0.0b

Counts

164 → 4

regimes98.0ms

Accuracy

0% (0.6b remaining)

Error of 0.6b against oracle of 0.0b 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

sample2.5s

Algorithm

intervals

Results

1.7s	5620×	body	1280	valid
223.0ms	1298×	body	640	valid
205.0ms	7998×	body	80	valid
63.0ms	610×	body	320	valid
20.0ms	304×	body	160	valid

Details

sample89.0ms

simplify139.0ms

prune3.0ms

localize6.0ms

rewrite12.0ms

series84.0ms

simplify86.0ms

prune107.0ms

localize10.0ms

rewrite25.0ms

series379.0ms

simplify53.0ms

prune289.0ms

localize9.0ms

rewrite21.0ms

series163.0ms

simplify93.0ms

prune176.0ms

localize14.0ms

rewrite40.0ms

series370.0ms

simplify130.0ms

prune896.0ms

regimes98.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.5s

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