Details

sample494.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 48.260498%

Guaranteed chance to sample good point: 93.234635%

Results

31.0ms	56×	body	1280	valid
16.0ms	49×	body	640	valid
9.0ms	122×	body	80	valid
5.0ms	22×	body	320	valid
1.0ms	7×	body	160	valid
1.0ms	1×	body	1280	invalid
0.0ms	1×	body	640	invalid
0.0ms	4×	body	80	invalid
0.0ms	4×	body	80	overflowed
0.0ms	1×	body	320	invalid

simplify36.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (34.0ms)

Iter	Nodes	Cost
0	46	16
1	122	16
2	347	16
3	1295	16
4	5001	15

prune9.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 32.1b

Counts

2 → 1

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (+ 1.0 eps) x)
0.0b	(* (- 1.0 eps) x)
1.9b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub`
72×	`exp-neg` `frac-times`
54×	`neg-sub0` `exp-diff`
40×	`associate-*l/`
36×	`associate-*r/`
29×	`flip3--` `flip--`
28×	`flip3-+` `flip-+`
18×	`un-div-inv`
13×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
9×	`associate-l`
7×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
6×	`associate-r`
5×	`add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `diff-log` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 136

Calls

3 calls:

6.0ms	(* (+ 1.0 eps) x)
6.0ms	(* (- 1.0 eps) x)
17.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

series57.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(* (+ 1.0 eps) x)
4.0ms	(* (- 1.0 eps) x)
48.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

simplify138.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (107.0ms)

Iter	Nodes	Cost
0	1178	3582
1	4531	3328
2	5001	3319

prune242.0ms

Filtered

68 candidates to 145 candidates (-113.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	143	2	145
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	143	3	146

Merged error: 0b

Counts

146 → 3

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b	(* 0.6666666666666667 (pow x 3))
6.8b	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`associate-r`
7×	`add-exp-log` `add-log-exp`
6×	`add-cube-cbrt` `*-un-lft-identity`
4×	`unpow-prod-down` `cube-prod` `add-cbrt-cube` `unswap-sqr`
3×	`associate-l` `prod-exp`
2×	`pow1` `diff-log` `sqr-pow`
1×	`cube-mult` `pow-to-exp` `sub-neg` `flip3--` `unpow3` `pow-exp` `associate--l+` `sum-log` `*-commutative` `flip--` `cbrt-unprod`

Counts

2 → 45

Calls

2 calls:

6.0ms	(* 0.6666666666666667 (pow x 3))
7.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

series8.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(* 0.6666666666666667 (pow x 3))
4.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

simplify35.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	207	270
1	894	242
2	5002	238

prune72.0ms

Filtered

31 candidates to 51 candidates (-64.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	51	0	51
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	51	3	54

Merged error: 0b

Counts

54 → 3

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1.0 eps) (/ 1.0 eps))
0.7b	(/ (- (* (* (- (* 1.0 1.0) (* (/ 1.0 eps) (/ 1.0 eps))) (exp (neg (* (- 1.0 eps) x)))) (exp (* (+ 1.0 eps) x))) (* (- 1.0 (/ 1.0 eps)) (- (/ 1.0 eps) 1.0))) (* (- 1.0 (/ 1.0 eps)) (exp (* (+ 1.0 eps) x))))
8.9b	(* (- (* 1.0 1.0) (* (/ 1.0 eps) (/ 1.0 eps))) (exp (neg (* (- 1.0 eps) x))))
20.4b	(- (* (* (- (* 1.0 1.0) (* (/ 1.0 eps) (/ 1.0 eps))) (exp (neg (* (- 1.0 eps) x)))) (exp (* (+ 1.0 eps) x))) (* (- 1.0 (/ 1.0 eps)) (- (/ 1.0 eps) 1.0)))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

217×	`associate-*l/`
162×	`flip3--` `flip--`
144×	`frac-sub`
141×	`frac-times`
74×	`associate-/l/`
71×	`associate-*r/`
68×	`exp-neg`
51×	`neg-sub0` `exp-diff`
50×	`add-sqr-sqrt`
43×	`times-frac`
36×	`add-cube-cbrt` `*-un-lft-identity`
23×	`add-cbrt-cube`
21×	`add-exp-log`
17×	`associate-l` `un-div-inv`
16×	`associate-r`
13×	`pow1` `swap-sqr`
6×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `add-log-exp`
5×	`div-inv` `unswap-sqr`
4×	`associate--r+`
3×	`sub-neg` `associate-/l*`
2×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `associate-/r/` `*-commutative`
1×	`pow2` `frac-2neg` `pow-plus` `diff-log` `div-sub` `clear-num` `associate-/r*` `pow-sqr` `pow-prod-up` `difference-of-squares`

Counts

4 → 281

Calls

4 calls:

14.0ms	(* (/ 1.0 eps) (/ 1.0 eps))
31.0ms	(/ (- (* (* (- (* 1.0 1.0) (* (/ 1.0 eps) (/ 1.0 eps))) (exp (neg (* (- 1.0 eps) x)))) (exp (* (+ 1.0 eps) x))) (* (- 1.0 (/ 1.0 eps)) (- (/ 1.0 eps) 1.0))) (* (- 1.0 (/ 1.0 eps)) (exp (* (+ 1.0 eps) x))))
10.0ms	(* (- (* 1.0 1.0) (* (/ 1.0 eps) (/ 1.0 eps))) (exp (neg (* (- 1.0 eps) x))))
17.0ms	(- (* (* (- (* 1.0 1.0) (* (/ 1.0 eps) (/ 1.0 eps))) (exp (neg (* (- 1.0 eps) x)))) (exp (* (+ 1.0 eps) x))) (* (- 1.0 (/ 1.0 eps)) (- (/ 1.0 eps) 1.0)))

series122.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (/ 1.0 eps) (/ 1.0 eps))
75.0ms	(/ (- (* (* (- (* 1.0 1.0) (* (/ 1.0 eps) (/ 1.0 eps))) (exp (neg (* (- 1.0 eps) x)))) (exp (* (+ 1.0 eps) x))) (* (- 1.0 (/ 1.0 eps)) (- (/ 1.0 eps) 1.0))) (* (- 1.0 (/ 1.0 eps)) (exp (* (+ 1.0 eps) x))))
11.0ms	(* (- (* 1.0 1.0) (* (/ 1.0 eps) (/ 1.0 eps))) (exp (neg (* (- 1.0 eps) x))))
32.0ms	(- (* (* (- (* 1.0 1.0) (* (/ 1.0 eps) (/ 1.0 eps))) (exp (neg (* (- 1.0 eps) x)))) (exp (* (+ 1.0 eps) x))) (* (- 1.0 (/ 1.0 eps)) (- (/ 1.0 eps) 1.0)))

simplify114.0ms

Algorithm

egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 1 (40.0ms)

Iter	Nodes	Cost
0	2177	8269
1	5003	8036

prune2.3s

Filtered

216 candidates to 293 candidates (-35.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	293	0	293
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	293	3	296

Merged error: 0b

Counts

296 → 3

regimes201.0ms

Accuracy

96.2% (0.6b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 16.1b

bsearch114.0ms

Steps

Iters	Range		Point
10	2.7947671091464944e-11	92069.95548288956	1.2908851057150332

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	23
1	56	23
2	56	23

end0.0ms

sample2.6s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 48.260498%

Guaranteed chance to sample good point: 93.234635%

Results

935.0ms	1709×	body	1280	valid
434.0ms	1302×	body	640	valid
324.0ms	4073×	body	80	valid
142.0ms	609×	body	320	valid
48.0ms	307×	body	160	valid
10.0ms	114×	body	80	invalid
9.0ms	17×	body	1280	invalid
8.0ms	101×	body	80	overflowed
6.0ms	15×	body	640	invalid
2.0ms	8×	body	320	invalid

Details

sample494.0ms

simplify36.0ms

prune9.0ms

localize17.0ms

rewrite38.0ms

series57.0ms

simplify138.0ms

prune242.0ms

localize10.0ms

rewrite14.0ms

series8.0ms

simplify35.0ms

prune72.0ms

localize27.0ms

rewrite94.0ms

series122.0ms

simplify114.0ms

prune2.3s

regimes201.0ms

bsearch114.0ms

simplify2.0ms

end0.0ms

sample2.6s

Profiling