Details

sample107.0ms

Algorithm

intervals

Results

23.0ms	295×	body	80	nan
21.0ms	48×	body	1280	valid
13.0ms	189×	body	80	valid
12.0ms	17×	body	2560	valid
7.0ms	24×	body	640	valid
3.0ms	13×	body	320	valid
0.0ms	3×	body	160	valid

simplify11.0ms

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

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 21.5b

Counts

2 → 1

localize19.0ms

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))))
25.9b	(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)))

series159.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(/ (* z t) 3.0)
17.0ms	(/ a (* b 3.0))
89.0ms	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
32.0ms	(cos (- y (/ (* z t) 3.0)))

simplify44.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	404	507
1	1689	429
2	5001	426

prune328.0ms

Filtered

84 candidates to 58 candidates (69.0%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	63	21	84
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	64	21	85

Merged error: 16.7b

Counts

85 → 21

localize29.0ms

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)))))
29.0b	(sin (/ (* z t) 3.0))
29.1b	(cos (/ (* 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	(sin (/ (* z t) 3.0))
2.0ms	(cos (/ (* z t) 3.0))

series239.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ a (* b 3.0))
192.0ms	(* (* 2.0 (sqrt x)) (+ (* (cos y) (cos (/ (* z t) 3.0))) (* (sin y) (sin (/ (* z t) 3.0)))))
15.0ms	(sin (/ (* z t) 3.0))
10.0ms	(cos (/ (* z t) 3.0))

simplify54.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	433	695
1	1951	580
2	5001	577

prune339.0ms

Filtered

70 candidates to 52 candidates (74.3%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	64	6	70
Fresh	1	19	20
Picked	1	0	1
Done	0	0	0
Total	66	25	91

Merged error: 16.7b

Counts

91 → 25

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (pow (cos (/ (* z t) 3.0)) 3))
0.4b	(pow (cos (/ (* z t) 3.0)) 3)
29.0b	(sin (/ (* z t) 3.0))
29.1b	(cos (/ (* z t) 3.0))

rewrite10.0ms

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:

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

series55.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(cbrt (pow (cos (/ (* z t) 3.0)) 3))
21.0ms	(pow (cos (/ (* z t) 3.0)) 3)
15.0ms	(sin (/ (* z t) 3.0))
10.0ms	(cos (/ (* z t) 3.0))

simplify133.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	120	373
1	411	347
2	2822	341
3	5001	341

prune375.0ms

Filtered

70 candidates to 42 candidates (60.0%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	66	4	70
Fresh	2	22	24
Picked	1	0	1
Done	0	0	0
Total	69	26	95

Merged error: 16.7b

Counts

95 → 26

localize31.0ms

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)
28.7b	(cos (* 0.3333333333333333 (* t z)))
29.0b	(sin (/ (* z t) 3.0))

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))
4.0ms	(pow (cos (* 0.3333333333333333 (* t z))) 3)
3.0ms	(cos (* 0.3333333333333333 (* t z)))
2.0ms	(sin (/ (* z t) 3.0))

series59.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(cbrt (pow (cos (* 0.3333333333333333 (* t z))) 3))
21.0ms	(pow (cos (* 0.3333333333333333 (* t z))) 3)
9.0ms	(cos (* 0.3333333333333333 (* t z)))
19.0ms	(sin (/ (* z t) 3.0))

simplify138.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	113	373
1	398	347
2	2797	341
3	5001	341

prune243.0ms

Filtered

70 candidates to 41 candidates (58.6%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	67	3	70
Fresh	2	23	25
Picked	1	0	1
Done	0	0	0
Total	70	26	96

Merged error: 16.7b

Counts

96 → 26

regimes2.5s

Accuracy

53% (1.7b remaining)

Error of 18.4b against oracle of 16.8b and baseline of 20.3b

bsearch3.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	35
1	57	35
2	57	35

end0.0ms

sample3.3s

Algorithm

intervals

Results

700.0ms	1553×	body	1280	valid
635.0ms	9085×	body	80	nan
593.0ms	5545×	body	80	valid
306.0ms	961×	body	640	valid
298.0ms	395×	body	2560	valid
106.0ms	452×	body	320	valid
34.0ms	208×	body	160	valid