Details

sample100.0ms

Algorithm

intervals

Results

22.0ms	282×	body	80	nan
18.0ms	42×	body	1280	valid
13.0ms	186×	body	80	valid
10.0ms	31×	body	640	valid
5.0ms	7×	body	2560	valid
4.0ms	16×	body	320	valid
1.0ms	5×	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

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: 18.5b

Counts

2 → 1

localize20.0ms

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))))
23.7b	(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)))

series163.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(/ (* z t) 3.0)
18.0ms	(/ a (* b 3.0))
91.0ms	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
32.0ms	(cos (- y (/ (* z t) 3.0)))

simplify47.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (39.0ms)

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

prune317.0ms

Filtered

84 candidates to 58 candidates (69.0%)

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: 15.2b

Counts

85 → 19

localize27.0ms

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))
28.0b	(sin (/ (* z t) 3.0))

rewrite20.0ms

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))

series260.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (sin y) (sin (/ (* z t) 3.0)))
190.0ms	(* (* 2.0 (sqrt x)) (+ (* (cos y) (cos (/ (* z t) 3.0))) (* (sin y) (sin (/ (* z t) 3.0)))))
9.0ms	(cos (/ (* z t) 3.0))
15.0ms	(sin (/ (* z t) 3.0))

simplify60.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	365	754
1	1772	643
2	5001	640

prune386.0ms

Filtered

68 candidates to 50 candidates (73.5%)

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	57	11	68
Fresh	1	17	18
Picked	1	0	1
Done	0	0	0
Total	59	28	87

Merged error: 15.0b

Counts

87 → 28

localize28.0ms

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)
27.7b	(cos (/ (* z t) 3.0))
28.0b	(sin (/ (* 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	(cos (/ (* z t) 3.0))
2.0ms	(sin (/ (* z t) 3.0))

series60.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(cbrt (pow (cos (/ (* z t) 3.0)) 3))
25.0ms	(pow (cos (/ (* z t) 3.0)) 3)
9.0ms	(cos (/ (* z t) 3.0))
16.0ms	(sin (/ (* z t) 3.0))

simplify129.0ms

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

prune352.0ms

Filtered

70 candidates to 43 candidates (61.4%)

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	66	4	70
Fresh	3	24	27
Picked	1	0	1
Done	0	0	0
Total	70	28	98

Merged error: 15.0b

Counts

98 → 28

localize29.0ms

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)
27.8b	(cos (* 0.3333333333333333 (* t z)))
28.0b	(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))
3.0ms	(pow (cos (* 0.3333333333333333 (* t z))) 3)
3.0ms	(cos (* 0.3333333333333333 (* t z)))
2.0ms	(sin (/ (* z t) 3.0))

series58.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(cbrt (pow (cos (* 0.3333333333333333 (* t z))) 3))
24.0ms	(pow (cos (* 0.3333333333333333 (* t z))) 3)
9.0ms	(cos (* 0.3333333333333333 (* t z)))
15.0ms	(sin (/ (* z t) 3.0))

simplify128.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (17.0ms)

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

prune248.0ms

Filtered

70 candidates to 41 candidates (58.6%)

Pruning

27 alts after pruning (27 fresh and 0 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	1	26	27
Picked	1	0	1
Done	0	0	0
Total	71	27	98

Merged error: 15.0b

Counts

98 → 27

regimes2.7s

Accuracy

58.4% (1.6b remaining)

Error of 18.1b against oracle of 16.5b and baseline of 20.3b

bsearch3.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	32
1	55	32
2	55	32

end0.0ms

sample3.2s

Algorithm

intervals

Results

710.0ms	1555×	body	1280	valid
669.0ms	9285×	body	80	nan
423.0ms	5631×	body	80	valid
294.0ms	922×	body	640	valid
268.0ms	373×	body	2560	valid
108.0ms	455×	body	320	valid
31.0ms	194×	body	160	valid