Details

sample103.0ms

Algorithm

intervals

Results

23.0ms	48×	body	1280	valid
19.0ms	318×	body	80	nan
11.0ms	186×	body	80	valid
10.0ms	35×	body	640	valid
5.0ms	7×	body	2560	valid
3.0ms	14×	body	320	valid
1.0ms	5×	body	160	valid

simplify19.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	33	10
1	58	10
2	82	10
3	99	10
4	107	10
5	109	10
6	109	10

prune4.0ms

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: 19.1b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

23×	`cos-sum`
22×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
21×	`prod-diff`
19×	`add-exp-log` `add-cbrt-cube`
15×	`times-frac`
9×	`pow1`
5×	`prod-exp` `cbrt-unprod` `div-inv`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
3×	`cos-diff` `associate-r` `pow-prod-down`
2×	`frac-2neg` `clear-num`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-l` `*-commutative`

Counts

4 → 101

Calls

4 calls:

4.0ms	(/ a (* b 3.0))
5.0ms	(/ (* z t) 3.0)
10.0ms	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
9.0ms	(cos (- y (/ (* z t) 3.0)))

series182.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(/ a (* b 3.0))
19.0ms	(/ (* z t) 3.0)
102.0ms	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
41.0ms	(cos (- y (/ (* z t) 3.0)))

simplify76.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	685	1511
1	2361	1261
2	5001	1258

prune449.0ms

Filtered

113 candidates to 72 candidates (63.7%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	91	22	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	92	22	114

Merged error: 14.5b

Counts

114 → 22

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* z t) 3.0)
0.3b	(* (sin y) (sin (/ (* z t) 3.0)))
27.6b	(sin (/ (* z t) 3.0))
27.7b	(cos (/ (* z t) 3.0))

rewrite16.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `associate-r` `associate-l` `associate-/r*`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
1×	`frac-2neg` `pow-prod-down` `clear-num` `-commutative` `div-inv` `sin-mult` `associate-/l` `unswap-sqr`

Counts

4 → 62

Calls

4 calls:

5.0ms	(/ (* z t) 3.0)
5.0ms	(* (sin y) (sin (/ (* z t) 3.0)))
2.0ms	(sin (/ (* z t) 3.0))
3.0ms	(cos (/ (* z t) 3.0))

series94.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(/ (* z t) 3.0)
48.0ms	(* (sin y) (sin (/ (* z t) 3.0)))
16.0ms	(sin (/ (* z t) 3.0))
11.0ms	(cos (/ (* z t) 3.0))

simplify80.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	205	369
1	792	318
2	3097	318
3	5001	318

prune428.0ms

Filtered

74 candidates to 58 candidates (78.4%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	69	5	74
Fresh	2	19	21
Picked	1	0	1
Done	0	0	0
Total	72	24	96

Merged error: 14.5b

Counts

96 → 24

localize34.0ms

Local error

Found 4 expressions with local error:

16.1b	(cbrt (/ (* z t) 3.0))
16.1b	(cbrt (/ (* z t) 3.0))
27.3b	(sin (* (* (cbrt (/ (* z t) 3.0)) (cbrt (/ (* z t) 3.0))) (cbrt (/ (* z t) 3.0))))
27.7b	(cos (/ (* z t) 3.0))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

14×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`times-frac`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-div` `pow1/3` `div-inv`

Counts

4 → 54

Calls

4 calls:

3.0ms	(cbrt (/ (* z t) 3.0))
3.0ms	(cbrt (/ (* z t) 3.0))
4.0ms	(sin (* (* (cbrt (/ (* z t) 3.0)) (cbrt (/ (* z t) 3.0))) (cbrt (/ (* z t) 3.0))))
2.0ms	(cos (/ (* z t) 3.0))

series299.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(cbrt (/ (* z t) 3.0))
106.0ms	(cbrt (/ (* z t) 3.0))
76.0ms	(sin (* (* (cbrt (/ (* z t) 3.0)) (cbrt (/ (* z t) 3.0))) (cbrt (/ (* z t) 3.0))))
11.0ms	(cos (/ (* z t) 3.0))

simplify197.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 4 (52.0ms)

Iter	Nodes	Cost
0	141	462
1	265	416
2	579	400
3	1464	396
4	4795	384
5	5001	384

prune482.0ms

Filtered

66 candidates to 58 candidates (87.9%)

Pruning

26 alts after pruning (25 fresh and 1 done)

	Pruned	Kept	Total
New	62	4	66
Fresh	2	21	23
Picked	0	1	1
Done	0	0	0
Total	64	26	90

Merged error: 14.4b

Counts

90 → 26

localize40.0ms

Local error

Found 4 expressions with local error:

16.1b	(cbrt (/ (* z t) 3.0))
16.1b	(cbrt (/ (* z t) 3.0))
27.4b	(sin (* (* (cbrt (/ (* z t) 3.0)) (cbrt (/ (* z t) 3.0))) (* (* (cbrt (cbrt (/ (* z t) 3.0))) (cbrt (cbrt (/ (* z t) 3.0)))) (cbrt (cbrt (/ (* z t) 3.0))))))
27.7b	(cos (/ (* z t) 3.0))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

14×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`times-frac`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-div` `pow1/3` `div-inv`

Counts

4 → 54

Calls

4 calls:

3.0ms	(cbrt (/ (* z t) 3.0))
3.0ms	(cbrt (/ (* z t) 3.0))
8.0ms	(sin (* (* (cbrt (/ (* z t) 3.0)) (cbrt (/ (* z t) 3.0))) (* (* (cbrt (cbrt (/ (* z t) 3.0))) (cbrt (cbrt (/ (* z t) 3.0)))) (cbrt (cbrt (/ (* z t) 3.0))))))
2.0ms	(cos (/ (* z t) 3.0))

series300.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(cbrt (/ (* z t) 3.0))
107.0ms	(cbrt (/ (* z t) 3.0))
76.0ms	(sin (* (* (cbrt (/ (* z t) 3.0)) (cbrt (/ (* z t) 3.0))) (* (* (cbrt (cbrt (/ (* z t) 3.0))) (cbrt (cbrt (/ (* z t) 3.0)))) (cbrt (cbrt (/ (* z t) 3.0))))))
12.0ms	(cos (/ (* z t) 3.0))

simplify62.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (23.0ms)

Iter	Nodes	Cost
0	149	594
1	291	526
2	636	510
3	1679	506
4	5001	506

prune433.0ms

Filtered

66 candidates to 58 candidates (87.9%)

Pruning

28 alts after pruning (27 fresh and 1 done)

	Pruned	Kept	Total
New	62	4	66
Fresh	1	23	24
Picked	1	0	1
Done	0	1	1
Total	64	28	92

Merged error: 14.4b

Counts

92 → 28

regimes2.8s

Accuracy

38.8% (2.4b remaining)

Error of 19.1b against oracle of 16.7b and baseline of 20.6b

bsearch3.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	41
1	56	41

end0.0ms

sample2.9s

Algorithm

intervals

Results

660.0ms	1619×	body	1280	valid
548.0ms	9053×	body	80	nan
360.0ms	5517×	body	80	valid
269.0ms	956×	body	640	valid
263.0ms	379×	body	2560	valid
98.0ms	469×	body	320	valid
31.0ms	192×	body	160	valid