Details

sample3.7s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 37.5%

Guaranteed chance to sample good point: 15%

Results

25.0ms	51×	body	1280	valid
12.0ms	16×	body	2560	valid
11.0ms	139×	body	80	valid
9.0ms	74×	body	80	nan
8.0ms	24×	body	640	valid
4.0ms	15×	body	320	valid
3.0ms	41×	body	80	invalid
2.0ms	11×	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

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: 22.6b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* z t) 3.0)
0.3b	(/ a (* b 3.0))
0.3b	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
24.9b	(cos (- y (/ (* z t) 3.0)))

rewrite24.0ms

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:

5.0ms	(/ (* z t) 3.0)
4.0ms	(/ a (* b 3.0))
6.0ms	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
8.0ms	(cos (- y (/ (* z t) 3.0)))

series48.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(/ (* z t) 3.0)
3.0ms	(/ a (* b 3.0))
31.0ms	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
10.0ms	(cos (- y (/ (* z t) 3.0)))

simplify45.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 1 (10.0ms)

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

prune259.0ms

Filtered

59 candidates to 84 candidates (-42.4%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	64	20	84
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	20	85

Merged error: 18.1b

Counts

85 → 20

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ a (* b 3.0))
0.3b	(* (* 2.0 (sqrt x)) (+ (* (cos y) (cos (/ (* z t) 3.0))) (* (sin y) (sin (/ (* z t) 3.0)))))
28.6b	(cos (/ (* z t) 3.0))
29.2b	(sin (/ (* z t) 3.0))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`prod-exp` `cbrt-unprod` `add-log-exp`
3×	`times-frac` `associate-r/` `associate-r` `pow-prod-down` `associate-/l`
2×	`cbrt-undiv` `div-exp`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `flip3-+` `associate-l` `frac-add` `clear-num` `associate-/r` `cos-mult` `-commutative` `flip-+` `div-inv` `sin-mult`

Counts

4 → 58

Calls

4 calls:

4.0ms	(/ a (* b 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))

series75.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(/ a (* b 3.0))
64.0ms	(* (* 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))

simplify59.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	460	697
1	2089	586
2	5001	585

prune264.0ms

Filtered

53 candidates to 70 candidates (-32.1%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	63	7	70
Fresh	4	15	19
Picked	1	0	1
Done	0	0	0
Total	68	22	90

Merged error: 17.9b

Counts

90 → 22

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin y) (sin (/ (* z t) 3.0)))
0.3b	(/ a (* b 3.0))
29.2b	(sin (/ (* z t) 3.0))
29.5b	(cos (* 0.3333333333333333 (* t z)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1`
4×	`add-log-exp`
3×	`times-frac` `associate-r` `associate-l` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
1×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `div-inv` `sin-mult` `unswap-sqr`

Counts

4 → 54

Calls

4 calls:

5.0ms	(* (sin y) (sin (/ (* z t) 3.0)))
4.0ms	(/ a (* b 3.0))
2.0ms	(sin (/ (* z t) 3.0))
2.0ms	(cos (* 0.3333333333333333 (* t z)))

series22.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(* (sin y) (sin (/ (* z t) 3.0)))
3.0ms	(/ a (* b 3.0))
4.0ms	(sin (/ (* z t) 3.0))
3.0ms	(cos (* 0.3333333333333333 (* t z)))

simplify51.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	200	336
1	642	285
2	2118	285
3	5001	285

prune276.0ms

Filtered

49 candidates to 66 candidates (-34.7%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	60	6	66
Fresh	2	19	21
Picked	1	0	1
Done	0	0	0
Total	63	25	88

Merged error: 17.9b

Counts

88 → 25

localize35.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin y))
0.6b	(cbrt (sin y))
29.2b	(sin (/ (* z t) 3.0))
29.5b	(cos (* 0.3333333333333333 (* t z)))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
2×	`pow1/3`

Counts

4 → 36

Calls

4 calls:

1.0ms	(cbrt (sin y))
1.0ms	(cbrt (sin y))
2.0ms	(sin (/ (* z t) 3.0))
3.0ms	(cos (* 0.3333333333333333 (* t z)))

series44.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(cbrt (sin y))
19.0ms	(cbrt (sin y))
4.0ms	(sin (/ (* z t) 3.0))
4.0ms	(cos (* 0.3333333333333333 (* t z)))

simplify189.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 3 (29.0ms)

Iter	Nodes	Cost
0	102	244
1	234	220
2	707	208
3	3969	184
4	5001	184

prune84.0ms

Filtered

39 candidates to 48 candidates (-23.1%)

Pruning

25 alts after pruning (24 fresh and 1 done)

	Pruned	Kept	Total
New	48	0	48
Fresh	0	24	24
Picked	0	1	1
Done	0	0	0
Total	48	25	73

Merged error: 17.9b

Counts

73 → 25

regimes4.2s

Accuracy

64.1% (1.4b remaining)

Error of 17.6b against oracle of 16.2b and baseline of 20.1b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	31
1	56	31
2	56	31

end0.0ms

sample6.4s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 37.5%

Guaranteed chance to sample good point: 15%

Results

728.0ms	1537×	body	1280	valid
362.0ms	4516×	body	80	valid
316.0ms	412×	body	2560	valid
313.0ms	910×	body	640	valid
180.0ms	2252×	body	80	nan
101.0ms	405×	body	320	valid
86.0ms	1050×	body	80	invalid
42.0ms	220×	body	160	valid

Details

sample3.7s

simplify10.0ms

prune6.0ms

localize17.0ms

rewrite24.0ms

series48.0ms

simplify45.0ms

prune259.0ms

localize25.0ms

rewrite18.0ms

series75.0ms

simplify59.0ms

prune264.0ms

localize27.0ms

rewrite15.0ms

series22.0ms

simplify51.0ms

prune276.0ms

localize35.0ms

rewrite8.0ms

series44.0ms

simplify189.0ms

prune84.0ms

regimes4.2s

bsearch1.0ms

simplify2.0ms

end0.0ms

sample6.4s

Profiling