Details

sample1.1s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 30.853271%

Guaranteed chance to sample good point: 79.08465%

Results

23.0ms	42×	body	1280	valid
12.0ms	37×	body	640	valid
11.0ms	141×	body	80	valid
7.0ms	19×	body	320	valid
5.0ms	64×	body	80	overflowed
3.0ms	17×	body	160	valid
2.0ms	25×	body	80	invalid
1.0ms	2×	body	1280	invalid
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

prune7.0ms

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: 25.8b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (/ 1.0 eps))
0.0b	(* (- 1.0 eps) x)
0.0b	(* (+ 1.0 eps) x)
2.4b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

rewrite44.0ms

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--` `flip3-+` `flip--` `flip-+`
18×	`un-div-inv`
14×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`associate-l`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube` `add-log-exp`
6×	`associate-r`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `unswap-sqr`
1×	`+-commutative` `sub-neg` `diff-log` `sum-log` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 148

Calls

4 calls:

5.0ms	(+ 1.0 (/ 1.0 eps))
6.0ms	(* (- 1.0 eps) x)
6.0ms	(* (+ 1.0 eps) x)
16.0ms	(- (* (+ 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

4 → 12

Calls

4 calls:

3.0ms	(+ 1.0 (/ 1.0 eps))
5.0ms	(* (- 1.0 eps) x)
4.0ms	(* (+ 1.0 eps) x)
45.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

simplify143.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (108.0ms)

Iter	Nodes	Cost
0	1203	3643
1	4629	3381
2	5001	3372

prune272.0ms

Filtered

78 candidates to 160 candidates (-105.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	158	2	160
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	159	2	161

Merged error: 0.0b

Counts

161 → 2

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b	(* 0.6666666666666667 (pow x 3))
5.4b	(- (+ (* 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)))

simplify33.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (28.0ms)

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

prune76.0ms

Filtered

31 candidates to 51 candidates (-64.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	50	1	51
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	50	3	53

Merged error: 0.0b

Counts

53 → 3

localize17.0ms

Local error

Found 4 expressions with local error:

5.4b	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
10.0b	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
10.0b	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
10.0b	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-log-exp`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
3×	`pow1/3`
2×	`diff-log`
1×	`sub-neg` `associate--l+` `sum-log`

Counts

4 → 53

Calls

4 calls:

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

series34.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
10.0ms	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
9.0ms	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
10.0ms	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))

simplify131.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	252	983
1	905	918
2	4255	839
3	5002	839

prune336.0ms

Filtered

59 candidates to 65 candidates (-10.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	64	1	65
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	65	3	68

Merged error: 0.0b

Counts

68 → 3

localize23.0ms

Local error

Found 4 expressions with local error:

9.4b	(- (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ (* 0.6666666666666667 (pow x 3)) 2.0)) (* (* 1.0 (pow x 2)) (* 1.0 (pow x 2))))
10.0b	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
10.0b	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
10.0b	(cbrt (+ (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-div` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`flip3--` `pow1/3` `flip--`
2×	`associate--l+`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3-+` `diff-log` `flip-+` `difference-of-squares`

Counts

4 → 54

Calls

4 calls:

13.0ms	(- (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ (* 0.6666666666666667 (pow x 3)) 2.0)) (* (* 1.0 (pow x 2)) (* 1.0 (pow x 2))))
6.0ms	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
6.0ms	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
6.0ms	(cbrt (+ (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))

series36.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(- (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ (* 0.6666666666666667 (pow x 3)) 2.0)) (* (* 1.0 (pow x 2)) (* 1.0 (pow x 2))))
9.0ms	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
11.0ms	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
10.0ms	(cbrt (+ (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))

simplify50.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	374	1120
1	1484	1022
2	5001	950

prune519.0ms

Filtered

63 candidates to 66 candidates (-4.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	66	3	69

Merged error: 0.0b

Counts

69 → 3

regimes106.0ms

Accuracy

97% (0.5b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 16.5b

bsearch92.0ms

Steps

Iters	Range		Point
9	0.001080383412879609	2694116.5863935	69.84336347903472

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	25
1	49	25
2	49	25

end0.0ms

sample3.5s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 30.853271%

Guaranteed chance to sample good point: 79.08465%

Results

900.0ms	1658×	body	1280	valid
440.0ms	1298×	body	640	valid
322.0ms	4113×	body	80	valid
148.0ms	1934×	body	80	overflowed
146.0ms	612×	body	320	valid
82.0ms	1036×	body	80	invalid
49.0ms	319×	body	160	valid
10.0ms	18×	body	1280	invalid
4.0ms	13×	body	320	invalid
3.0ms	9×	body	640	invalid
1.0ms	3×	body	160	invalid

Details

sample1.1s

simplify36.0ms

prune7.0ms

localize17.0ms

rewrite44.0ms

series57.0ms

simplify143.0ms

prune272.0ms

localize10.0ms

rewrite14.0ms

series8.0ms

simplify33.0ms

prune76.0ms

localize17.0ms

rewrite27.0ms

series34.0ms

simplify131.0ms

prune336.0ms

localize23.0ms

rewrite32.0ms

series36.0ms

simplify50.0ms

prune519.0ms

regimes106.0ms

bsearch92.0ms

simplify2.0ms

end0.0ms

sample3.5s

Profiling