Details

sample112.0ms

Algorithm

intervals

Results

24.0ms	287×	body	80	nan
20.0ms	44×	body	1280	valid
14.0ms	182×	body	80	valid
10.0ms	14×	body	2560	valid
10.0ms	29×	body	640	valid
3.0ms	14×	body	320	valid
1.0ms	7×	body	160	valid

simplify15.0ms

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: 20.1b

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))
0.2b	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
25.5b	(cos (- y (/ (* z t) 3.0)))

rewrite34.0ms

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:

5.0ms	(/ (* z t) 3.0)
4.0ms	(/ a (* b 3.0))
10.0ms	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
12.0ms	(cos (- y (/ (* z t) 3.0)))

series160.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(/ (* z t) 3.0)
18.0ms	(/ a (* b 3.0))
90.0ms	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
32.0ms	(cos (- y (/ (* z t) 3.0)))

simplify70.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (56.0ms)

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

prune416.0ms

Filtered

113 candidates to 72 candidates (63.7%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	92	21	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	93	21	114

Merged error: 16.1b

Counts

114 → 21

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin y) (sin (/ (* z t) 3.0)))
1.5b	(* (* 2.0 (sqrt x)) (* (sin y) (sin (/ (* z t) 3.0))))
28.4b	(cos (/ (* z t) 3.0))
28.5b	(sin (/ (* z t) 3.0))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

18×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `*-un-lft-identity`
4×	`expm1-log1p-u` `associate-r` `associate-l` `log1p-expm1-u` `add-log-exp`
2×	`*-commutative` `sin-mult`
1×	`associate-*r/` `unswap-sqr`

Counts

4 → 64

Calls

4 calls:

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

series156.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (sin y) (sin (/ (* z t) 3.0)))
89.0ms	(* (* 2.0 (sqrt x)) (* (sin y) (sin (/ (* z t) 3.0))))
9.0ms	(cos (/ (* z t) 3.0))
17.0ms	(sin (/ (* z t) 3.0))

simplify155.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	233	598
1	961	490
2	4991	488
3	5001	488

prune395.0ms

Filtered

76 candidates to 55 candidates (72.4%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	70	6	76
Fresh	1	19	20
Picked	1	0	1
Done	0	0	0
Total	72	25	97

Merged error: 16.0b

Counts

97 → 25

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (pow (cos (/ (* z t) 3.0)) 3))
1.5b	(* (* 2.0 (sqrt x)) (* (sin y) (sin (/ (* z t) 3.0))))
28.4b	(cos (/ (* z t) 3.0))
28.5b	(sin (/ (* z t) 3.0))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`cbrt-prod`
8×	`pow-prod-down` `prod-exp` `cbrt-unprod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down` `cube-prod`
1×	`cube-mult` `pow1/3` `unpow3` `associate-r/` `associate-r` `associate-l` `-commutative` `rem-cbrt-cube` `sin-mult` `sqr-pow`

Counts

4 → 66

Calls

4 calls:

2.0ms	(cbrt (pow (cos (/ (* z t) 3.0)) 3))
9.0ms	(* (* 2.0 (sqrt x)) (* (sin y) (sin (/ (* z t) 3.0))))
2.0ms	(cos (/ (* z t) 3.0))
2.0ms	(sin (/ (* z t) 3.0))

series130.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(cbrt (pow (cos (/ (* z t) 3.0)) 3))
93.0ms	(* (* 2.0 (sqrt x)) (* (sin y) (sin (/ (* z t) 3.0))))
9.0ms	(cos (/ (* z t) 3.0))
15.0ms	(sin (/ (* z t) 3.0))

simplify133.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	263	575
1	994	496
2	4670	494
3	5001	494

prune400.0ms

Filtered

78 candidates to 52 candidates (66.7%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	75	3	78
Fresh	2	22	24
Picked	1	0	1
Done	0	0	0
Total	78	25	103

Merged error: 16.0b

Counts

103 → 25

localize33.0ms

Local error

Found 4 expressions with local error:

0.4b	(log (exp (cos (/ (* z t) 3.0))))
1.5b	(* (* 2.0 (sqrt x)) (* (sin y) (sin (/ (* z t) 3.0))))
28.4b	(cos (/ (* z t) 3.0))
28.5b	(sin (/ (* z t) 3.0))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

17×	`pow1`
16×	`add-exp-log` `add-cbrt-cube`
8×	`pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`expm1-log1p-u` `log-pow` `log1p-expm1-u` `add-log-exp`
3×	`log-prod` `exp-prod`
1×	`associate-r/` `rem-log-exp` `associate-r` `associate-l` `-commutative` `sin-mult`

Counts

4 → 60

Calls

4 calls:

4.0ms	(log (exp (cos (/ (* z t) 3.0))))
9.0ms	(* (* 2.0 (sqrt x)) (* (sin y) (sin (/ (* z t) 3.0))))
2.0ms	(cos (/ (* z t) 3.0))
4.0ms	(sin (/ (* z t) 3.0))

series125.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(log (exp (cos (/ (* z t) 3.0))))
90.0ms	(* (* 2.0 (sqrt x)) (* (sin y) (sin (/ (* z t) 3.0))))
9.0ms	(cos (/ (* z t) 3.0))
16.0ms	(sin (/ (* z t) 3.0))

simplify117.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (110.0ms)

Iter	Nodes	Cost
0	237	534
1	835	435
2	4108	433
3	5001	421

prune360.0ms

Filtered

72 candidates to 54 candidates (75.0%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	69	3	72
Fresh	1	23	24
Picked	1	0	1
Done	0	0	0
Total	71	26	97

Merged error: 16.0b

Counts

97 → 26

regimes2.3s

Accuracy

49.5% (1.9b remaining)

Error of 18.1b against oracle of 16.2b and baseline of 19.9b

bsearch5.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	30
1	47	30

end0.0ms

sample3.3s

Algorithm

intervals

Results

771.0ms	1617×	body	1280	valid
682.0ms	8969×	body	80	nan
436.0ms	5565×	body	80	valid
319.0ms	936×	body	640	valid
293.0ms	381×	body	2560	valid
107.0ms	428×	body	320	valid
35.0ms	189×	body	160	valid