Details

sample3.0s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 37.5%

Guaranteed chance to sample good point: 30%

Results

24.0ms	49×	body	1280	valid
12.0ms	24×	body	640	valid
12.0ms	15×	body	2560	valid
11.0ms	143×	body	80	valid
6.0ms	74×	body	80	nan
4.0ms	17×	body	320	valid
3.0ms	37×	body	80	invalid
2.0ms	8×	body	160	valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune6.0ms

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: 22.7b

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))))
23.6b	(cos (- y (/ (* z t) 3.0)))

rewrite26.0ms

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)
8.0ms	(/ a (* b 3.0))
6.0ms	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
6.0ms	(cos (- y (/ (* z t) 3.0)))

series49.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(/ (* z t) 3.0)
3.0ms	(/ a (* b 3.0))
32.0ms	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
11.0ms	(cos (- y (/ (* z t) 3.0)))

simplify60.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 1 (14.0ms)

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

prune261.0ms

Filtered

59 candidates to 84 candidates (-42.4%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	65	19	84
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	19	85

Merged error: 17.7b

Counts

85 → 19

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin y) (sin (/ (* z t) 3.0)))
0.3b	(* (* 2.0 (sqrt x)) (+ (* (cos y) (cos (/ (* z t) 3.0))) (* (sin y) (sin (/ (* z t) 3.0)))))
27.7b	(cos (/ (* z t) 3.0))
28.3b	(sin (/ (* z t) 3.0))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`associate-*r/`
2×	`*-commutative` `sin-mult`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `frac-add` `cos-mult` `flip-+` `unswap-sqr`

Counts

4 → 56

Calls

4 calls:

5.0ms	(* (sin y) (sin (/ (* z t) 3.0)))
9.0ms	(* (* 2.0 (sqrt x)) (+ (* (cos y) (cos (/ (* z t) 3.0))) (* (sin y) (sin (/ (* z t) 3.0)))))
2.0ms	(cos (/ (* z t) 3.0))
2.0ms	(sin (/ (* z t) 3.0))

series79.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(* (sin y) (sin (/ (* z t) 3.0)))
60.0ms	(* (* 2.0 (sqrt x)) (+ (* (cos y) (cos (/ (* z t) 3.0))) (* (sin y) (sin (/ (* z t) 3.0)))))
3.0ms	(cos (/ (* z t) 3.0))
4.0ms	(sin (/ (* z t) 3.0))

simplify67.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	392	756
1	1908	649
2	5002	648

prune270.0ms

Filtered

52 candidates to 68 candidates (-30.8%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	60	8	68
Fresh	4	14	18
Picked	1	0	1
Done	0	0	0
Total	65	22	87

Merged error: 17.5b

Counts

87 → 22

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin y) (sin (/ (* z t) 3.0)))
0.2b	(* (* 2.0 (sqrt x)) (+ (* (cos y) (cos (* 0.3333333333333333 (* t z)))) (* (sin y) (sin (/ (* z t) 3.0)))))
28.3b	(sin (/ (* z t) 3.0))
28.7b	(cos (* 0.3333333333333333 (* t z)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`associate-*r/`
2×	`*-commutative` `sin-mult`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `frac-add` `cos-mult` `flip-+` `unswap-sqr`

Counts

4 → 56

Calls

4 calls:

5.0ms	(* (sin y) (sin (/ (* z t) 3.0)))
10.0ms	(* (* 2.0 (sqrt x)) (+ (* (cos y) (cos (* 0.3333333333333333 (* t z)))) (* (sin y) (sin (/ (* z t) 3.0)))))
2.0ms	(sin (/ (* z t) 3.0))
2.0ms	(cos (* 0.3333333333333333 (* t z)))

series90.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (sin y) (sin (/ (* z t) 3.0)))
62.0ms	(* (* 2.0 (sqrt x)) (+ (* (cos y) (cos (* 0.3333333333333333 (* t z)))) (* (sin y) (sin (/ (* z t) 3.0)))))
4.0ms	(sin (/ (* z t) 3.0))
3.0ms	(cos (* 0.3333333333333333 (* t z)))

simplify89.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	398	756
1	1920	649
2	5002	648

prune293.0ms

Filtered

50 candidates to 68 candidates (-36.0%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	61	7	68
Fresh	2	19	21
Picked	1	0	1
Done	0	0	0
Total	64	26	90

Merged error: 17.5b

Counts

90 → 26

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (pow (cos (* 0.3333333333333333 (* t z))) 3))
0.3b	(pow (cos (* 0.3333333333333333 (* t z))) 3)
28.3b	(sin (/ (* z t) 3.0))
28.7b	(cos (* 0.3333333333333333 (* t z)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`unpow-prod-down` `cube-prod`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
3×	`pow-unpow`
2×	`cube-mult` `unpow3` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-exp` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 58

Calls

4 calls:

3.0ms	(cbrt (pow (cos (* 0.3333333333333333 (* t z))) 3))
3.0ms	(pow (cos (* 0.3333333333333333 (* t z))) 3)
2.0ms	(sin (/ (* z t) 3.0))
3.0ms	(cos (* 0.3333333333333333 (* t z)))

series19.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(cbrt (pow (cos (* 0.3333333333333333 (* t z))) 3))
8.0ms	(pow (cos (* 0.3333333333333333 (* t z))) 3)
4.0ms	(sin (/ (* z t) 3.0))
3.0ms	(cos (* 0.3333333333333333 (* t z)))

simplify156.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	113	373
1	396	347
2	2796	341
3	5002	341

prune112.0ms

Filtered

41 candidates to 70 candidates (-70.7%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	1	24	25
Picked	1	0	1
Done	0	0	0
Total	71	25	96

Merged error: 17.5b

Counts

96 → 25

regimes4.1s

Accuracy

63.4% (1.4b remaining)

Error of 17.8b against oracle of 16.4b and baseline of 20.2b

bsearch2.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	59	39
1	61	39
2	61	39

end0.0ms

sample5.7s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 37.5%

Guaranteed chance to sample good point: 30%

Results

749.0ms	1548×	body	1280	valid
365.0ms	4488×	body	80	valid
319.0ms	920×	body	640	valid
316.0ms	410×	body	2560	valid
187.0ms	2245×	body	80	nan
103.0ms	414×	body	320	valid
84.0ms	1057×	body	80	invalid
39.0ms	220×	body	160	valid

Details

sample3.0s

simplify14.0ms

prune6.0ms

localize17.0ms

rewrite26.0ms

series49.0ms

simplify60.0ms

prune261.0ms

localize26.0ms

rewrite19.0ms

series79.0ms

simplify67.0ms

prune270.0ms

localize27.0ms

rewrite21.0ms

series90.0ms

simplify89.0ms

prune293.0ms

localize34.0ms

rewrite13.0ms

series19.0ms

simplify156.0ms

prune112.0ms

regimes4.1s

bsearch2.0ms

simplify3.0ms

end0.0ms

sample5.7s

Profiling