Details

sample11.8s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 37.5%

Guaranteed chance to sample good point: 40%

Results

27.0ms	55×	body	1280	valid
14.0ms	17×	body	2560	valid
12.0ms	146×	body	80	valid
8.0ms	25×	body	640	valid
6.0ms	76×	body	80	nan
3.0ms	39×	body	80	invalid
3.0ms	10×	body	320	valid
1.0ms	3×	body	160	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	10
1	55	10
2	76	10
3	89	10
4	92	10
5	92	10

prune5.0ms

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: 21.9b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* z t) 3.0)
0.2b	(/ a (* b 3.0))
0.3b	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
25.8b	(cos (- y (/ (* z t) 3.0)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-exp-log` `add-cbrt-cube`
9×	`pow1` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`times-frac`
5×	`prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `div-exp` `associate-/r` `associate-/l` `add-log-exp`
3×	`cos-diff` `associate-r` `pow-prod-down`
2×	`cos-sum` `frac-2neg` `clear-num` `div-inv`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-l` `*-commutative`

Counts

4 → 72

Calls

4 calls:

4.0ms	(/ (* z t) 3.0)
4.0ms	(/ a (* b 3.0))
6.0ms	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
5.0ms	(cos (- y (/ (* z t) 3.0)))

series50.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(/ (* z t) 3.0)
3.0ms	(/ a (* b 3.0))
33.0ms	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
10.0ms	(cos (- y (/ (* z t) 3.0)))

simplify46.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	419	507
1	1751	432
2	5001	432

prune274.0ms

Filtered

59 candidates to 84 candidates (-42.4%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	62	22	84
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	63	22	85

Merged error: 16.4b

Counts

85 → 22

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 (sqrt x)) (cos (- y (* (/ z (* (cbrt 3.0) (cbrt 3.0))) (/ t (cbrt 3.0))))))
0.3b	(* (/ z (* (cbrt 3.0) (cbrt 3.0))) (/ t (cbrt 3.0)))
0.3b	(/ t (cbrt 3.0))
25.9b	(cos (- y (* (/ z (* (cbrt 3.0) (cbrt 3.0))) (/ t (cbrt 3.0)))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
46×	`times-frac`
35×	`add-cube-cbrt` `*-un-lft-identity`
32×	`add-exp-log`
25×	`associate-r`
24×	`add-cbrt-cube`
23×	`cbrt-prod`
11×	`pow1` `prod-exp` `cbrt-unprod`
8×	`cbrt-undiv` `div-exp` `associate-l`
6×	`associate-/r*` `unswap-sqr`
4×	`pow-prod-down` `add-log-exp`
3×	`cos-diff` `div-inv` `associate-/l*`
2×	`cos-sum` `*-commutative`
1×	`distribute-rgt-in` `frac-times` `sub-neg` `frac-2neg` `distribute-lft-in` `associate-r/` `associate-l/` `clear-num`

Counts

4 → 128

Calls

4 calls:

6.0ms	(* (* 2.0 (sqrt x)) (cos (- y (* (/ z (* (cbrt 3.0) (cbrt 3.0))) (/ t (cbrt 3.0))))))
15.0ms	(* (/ z (* (cbrt 3.0) (cbrt 3.0))) (/ t (cbrt 3.0)))
4.0ms	(/ t (cbrt 3.0))
3.0ms	(cos (- y (* (/ z (* (cbrt 3.0) (cbrt 3.0))) (/ t (cbrt 3.0)))))

series74.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (* 2.0 (sqrt x)) (cos (- y (* (/ z (* (cbrt 3.0) (cbrt 3.0))) (/ t (cbrt 3.0))))))
13.0ms	(* (/ z (* (cbrt 3.0) (cbrt 3.0))) (/ t (cbrt 3.0)))
5.0ms	(/ t (cbrt 3.0))
17.0ms	(cos (- y (* (/ z (* (cbrt 3.0) (cbrt 3.0))) (/ t (cbrt 3.0)))))

simplify78.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	624	1376
1	3063	1203
2	5001	1167

prune521.0ms

Filtered

104 candidates to 140 candidates (-34.6%)

Pruning

29 alts after pruning (29 fresh and 0 done)

	Pruned	Kept	Total
New	127	13	140
Fresh	5	16	21
Picked	1	0	1
Done	0	0	0
Total	133	29	162

Merged error: 16.3b

Counts

162 → 29

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ z (* (cbrt 3.0) (cbrt 3.0))) (* t (/ 1 (cbrt 3.0))))
0.4b	(* t (/ 1 (cbrt 3.0)))
1.0b	(/ 1 (cbrt 3.0))
25.8b	(cos (- y (* (/ z (* (cbrt 3.0) (cbrt 3.0))) (* t (/ 1 (cbrt 3.0))))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

77×	`add-exp-log`
47×	`add-sqr-sqrt`
43×	`times-frac`
37×	`*-un-lft-identity`
36×	`prod-exp` `add-cbrt-cube`
35×	`add-cube-cbrt`
23×	`cbrt-prod` `associate-r`
20×	`div-exp` `cbrt-unprod`
12×	`pow1`
11×	`cbrt-undiv`
10×	`associate-l`
6×	`associate-/r*`
5×	`rec-exp` `1-exp` `associate-*r/` `unswap-sqr`
4×	`pow-prod-down` `add-log-exp`
3×	`un-div-inv` `div-inv` `associate-/l*`
2×	`frac-times` `cos-sum` `pow-flip` `*-commutative`
1×	`cos-diff` `sub-neg` `frac-2neg` `pow1/3` `associate-*l/` `clear-num` `inv-pow`

Counts

4 → 148

Calls

4 calls:

14.0ms	(* (/ z (* (cbrt 3.0) (cbrt 3.0))) (* t (/ 1 (cbrt 3.0))))
10.0ms	(* t (/ 1 (cbrt 3.0)))
4.0ms	(/ 1 (cbrt 3.0))
3.0ms	(cos (- y (* (/ z (* (cbrt 3.0) (cbrt 3.0))) (* t (/ 1 (cbrt 3.0))))))

series33.0ms

Counts

4 → 10

Calls

4 calls:

11.0ms	(* (/ z (* (cbrt 3.0) (cbrt 3.0))) (* t (/ 1 (cbrt 3.0))))
5.0ms	(* t (/ 1 (cbrt 3.0)))
0.0ms	(/ 1 (cbrt 3.0))
17.0ms	(cos (- y (* (/ z (* (cbrt 3.0) (cbrt 3.0))) (* t (/ 1 (cbrt 3.0))))))

simplify67.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	527	1156
1	2396	916
2	5001	830

prune432.0ms

Filtered

81 candidates to 158 candidates (-95.1%)

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	153	5	158
Fresh	5	23	28
Picked	1	0	1
Done	0	0	0
Total	159	28	187

Merged error: 16.2b

Counts

187 → 28

localize23.0ms

Local error

Found 4 expressions with local error:

16.9b	(cbrt (/ (* z t) 3.0))
16.9b	(cbrt (/ (* z t) 3.0))
16.9b	(cbrt (/ (* z t) 3.0))
25.7b	(cos (- y (* (* (cbrt (/ (* z t) 3.0)) (cbrt (/ (* z t) 3.0))) (cbrt (/ (* z t) 3.0)))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

21×	`cbrt-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-div` `pow1/3` `div-inv`
2×	`cos-sum`
1×	`cos-diff` `sub-neg`

Counts

4 → 58

Calls

4 calls:

3.0ms	(cbrt (/ (* z t) 3.0))
3.0ms	(cbrt (/ (* z t) 3.0))
3.0ms	(cbrt (/ (* z t) 3.0))
3.0ms	(cos (- y (* (* (cbrt (/ (* z t) 3.0)) (cbrt (/ (* z t) 3.0))) (cbrt (/ (* z t) 3.0)))))

series67.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(cbrt (/ (* z t) 3.0))
17.0ms	(cbrt (/ (* z t) 3.0))
17.0ms	(cbrt (/ (* z t) 3.0))
16.0ms	(cos (- y (* (* (cbrt (/ (* z t) 3.0)) (cbrt (/ (* z t) 3.0))) (cbrt (/ (* z t) 3.0)))))

simplify43.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (32.0ms)

Iter	Nodes	Cost
0	163	597
1	358	549
2	1149	531
3	5001	507

prune177.0ms

Filtered

58 candidates to 70 candidates (-20.7%)

Pruning

33 alts after pruning (32 fresh and 1 done)

	Pruned	Kept	Total
New	64	6	70
Fresh	1	26	27
Picked	0	1	1
Done	0	0	0
Total	65	33	98

Merged error: 16.2b

Counts

98 → 33

regimes5.4s

Accuracy

55.5% (1.8b remaining)

Error of 17.8b against oracle of 16.0b and baseline of 20.0b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	46
1	55	46

end0.0ms

sample15.1s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 37.5%

Guaranteed chance to sample good point: 40%

Results

802.0ms	1619×	body	1280	valid
373.0ms	4529×	body	80	valid
315.0ms	923×	body	640	valid
267.0ms	334×	body	2560	valid
174.0ms	2171×	body	80	nan
111.0ms	419×	body	320	valid
91.0ms	1131×	body	80	invalid
34.0ms	176×	body	160	valid

Details

sample11.8s

simplify10.0ms

prune5.0ms

localize17.0ms

rewrite21.0ms

series50.0ms

simplify46.0ms

prune274.0ms

localize20.0ms

rewrite34.0ms

series74.0ms

simplify78.0ms

prune521.0ms

localize22.0ms

rewrite40.0ms

series33.0ms

simplify67.0ms

prune432.0ms

localize23.0ms

rewrite14.0ms

series67.0ms

simplify43.0ms

prune177.0ms

regimes5.4s

bsearch2.0ms

simplify2.0ms

end0.0ms

sample15.1s

Profiling