Details

sample62.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 99.996948%

Results

26.0ms	53×	body	2560	valid
9.0ms	35×	body	1280	valid
8.0ms	48×	body	640	valid
4.0ms	35×	body	320	valid
2.0ms	68×	body	80	valid
1.0ms	17×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	4
1	21	4
2	26	4
3	28	4
4	28	4

prune2.0ms

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:

3.4b	(- 1.0 (cos x))
15.3b	(/ (- 1.0 (cos x)) (* x x))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-exp-log` `add-cbrt-cube`
5×	`times-frac` `associate-/l*`
4×	`add-cube-cbrt` `add-log-exp`
3×	`distribute-lft-out--` `difference-of-squares`
2×	`pow1` `cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

2 → 42

Calls

2 calls:

3.0ms	(- 1.0 (cos x))
7.0ms	(/ (- 1.0 (cos x)) (* x x))

series15.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(- 1.0 (cos x))
11.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify59.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	221	271
1	735	239
2	2396	239
3	5002	239

prune89.0ms

Filtered

34 candidates to 48 candidates (-41.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	40	8	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	41	8	49

Merged error: 0.1b

Counts

49 → 8

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
0.1b	(/ (- 1.0 (cos x)) x)
3.4b	(- 1.0 (cos x))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
46×	`times-frac`
29×	`add-cube-cbrt`
27×	`add-exp-log`
19×	`associate-r`
17×	`add-cbrt-cube`
13×	`associate-l`
9×	`div-exp`
8×	`prod-exp` `distribute-lft-out--` `difference-of-squares`
6×	`unswap-sqr`
5×	`pow1` `cbrt-undiv` `associate-/l*` `add-log-exp`
4×	`cbrt-unprod`
3×	`associate-/r*` `div-inv`
2×	`rec-exp` `flip3--` `1-exp` `flip--` `associate-/l/`
1×	`frac-times` `sub-neg` `frac-2neg` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

3 → 114

Calls

3 calls:

14.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
8.0ms	(/ (- 1.0 (cos x)) x)
4.0ms	(- 1.0 (cos x))

series15.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
6.0ms	(/ (- 1.0 (cos x)) x)
3.0ms	(- 1.0 (cos x))

simplify60.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	521	814
1	2334	726
2	5001	690

prune144.0ms

Filtered

82 candidates to 123 candidates (-50.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	120	3	123
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	121	10	131

Merged error: 0.1b

Counts

131 → 10

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (/ 1 x) (* (- 1.0 (cos x)) (/ 1 x)))
0.2b	(* (- 1.0 (cos x)) (/ 1 x))
3.4b	(- 1.0 (cos x))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

77×	`add-exp-log`
40×	`prod-exp`
29×	`add-sqr-sqrt` `add-cbrt-cube`
23×	`*-un-lft-identity`
20×	`times-frac` `div-exp`
18×	`add-cube-cbrt` `associate-l`
14×	`associate-r`
12×	`frac-times` `cbrt-unprod`
10×	`pow1` `rec-exp` `1-exp`
9×	`associate-*r/`
7×	`flip3--` `associate-*l/` `flip--`
6×	`cbrt-undiv`
5×	`add-log-exp`
4×	`pow-prod-down`
3×	`un-div-inv` `unswap-sqr`
2×	`*-commutative` `div-inv` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `diff-log`

Counts

3 → 119

Calls

3 calls:

13.0ms	(* (/ 1 x) (* (- 1.0 (cos x)) (/ 1 x)))
10.0ms	(* (- 1.0 (cos x)) (/ 1 x))
4.0ms	(- 1.0 (cos x))

series15.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(* (/ 1 x) (* (- 1.0 (cos x)) (/ 1 x)))
6.0ms	(* (- 1.0 (cos x)) (/ 1 x))
3.0ms	(- 1.0 (cos x))

simplify58.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	548	852
1	2382	685
2	5001	663

prune263.0ms

Filtered

76 candidates to 128 candidates (-68.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	128	10	138

Merged error: 0.1b

Counts

138 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos x) (+ (cos x) 1.0))
0.3b	(+ (cos x) 1.0)
0.4b	(pow (cos x) 3)
3.2b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
16×	`difference-of-squares`
15×	`unpow-prod-down` `cube-prod`
9×	`add-cube-cbrt` `sqr-pow`
8×	`add-log-exp`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`distribute-lft-out--`
4×	`associate-r`
3×	`pow-unpow` `associate-l`
2×	`flip3-+` `associate-*r/` `flip-+` `distribute-lft-out`
1×	`difference-cubes` `+-commutative` `distribute-rgt-in` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `distribute-lft-in` `diff-log` `unpow3` `pow-prod-down` `pow-exp` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 92

Calls

4 calls:

6.0ms	(* (cos x) (+ (cos x) 1.0))
4.0ms	(+ (cos x) 1.0)
2.0ms	(pow (cos x) 3)
11.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series21.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(* (cos x) (+ (cos x) 1.0))
2.0ms	(+ (cos x) 1.0)
5.0ms	(pow (cos x) 3)
8.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify68.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	353	593
1	1734	555
2	5001	535

prune141.0ms

Filtered

61 candidates to 104 candidates (-70.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	100	4	104
Fresh	3	5	8
Picked	1	0	1
Done	0	1	1
Total	104	10	114

Merged error: 0.0b

Counts

114 → 10

regimes131.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.0b

bsearch35.0ms

Steps

Iters	Range		Point
9	3.9520027896654484e-05	11806.685469302465	0.03461561865294332
10	-21869.37453130546	-1.302763117677963e-06	-0.030915338542040083

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	22
1	48	22

end0.0ms

sample1.8s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 99.996948%

Results

799.0ms	1576×	body	2560	valid
348.0ms	1279×	body	1280	valid
262.0ms	1501×	body	640	valid
118.0ms	969×	body	320	valid
78.0ms	2200×	body	80	valid
44.0ms	475×	body	160	valid

Details

sample62.0ms

simplify6.0ms

prune2.0ms

localize6.0ms

rewrite11.0ms

series15.0ms

simplify59.0ms

prune89.0ms

localize7.0ms

rewrite30.0ms

series15.0ms

simplify60.0ms

prune144.0ms

localize8.0ms

rewrite32.0ms

series15.0ms

simplify58.0ms

prune263.0ms

localize18.0ms

rewrite27.0ms

series21.0ms

simplify68.0ms

prune141.0ms

regimes131.0ms

bsearch35.0ms

simplify1.0ms

end0.0ms

sample1.8s

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