Details

sample99.0ms

Algorithm

intervals

Results

24.0ms	51×	body	1280	valid
17.0ms	290×	body	80	nan
12.0ms	185×	body	80	valid
7.0ms	11×	body	2560	valid
6.0ms	24×	body	640	valid
3.0ms	16×	body	320	valid
1.0ms	6×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 21.6b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ a (* b 3.0))
0.3b	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
0.4b	(/ (* z t) 3.0)
24.4b	(cos (- y (/ (* z t) 3.0)))

rewrite22.0ms

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

series169.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(/ a (* b 3.0))
95.0ms	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
18.0ms	(/ (* z t) 3.0)
37.0ms	(cos (- y (/ (* z t) 3.0)))

simplify46.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (40.0ms)

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

prune323.0ms

Filtered

84 candidates to 58 candidates (69.0%)

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: 16.2b

Counts

85 → 20

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ z (sqrt 3.0)) (/ t (sqrt 3.0)))
0.4b	(/ z (sqrt 3.0))
0.4b	(/ t (sqrt 3.0))
24.3b	(cos (- y (* (/ z (sqrt 3.0)) (/ t (sqrt 3.0)))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

90×	`add-sqr-sqrt`
84×	`times-frac`
60×	`add-cube-cbrt` `*-un-lft-identity`
48×	`sqrt-prod`
22×	`associate-r` `associate-l`
20×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/r*`
9×	`unswap-sqr`
6×	`pow1` `cbrt-undiv` `div-exp` `associate-/l*`
4×	`prod-exp` `cbrt-unprod` `div-inv` `add-log-exp`
2×	`cos-sum` `frac-2neg` `clear-num`
1×	`cos-diff` `frac-times` `sub-neg` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 161

Calls

4 calls:

20.0ms	(* (/ z (sqrt 3.0)) (/ t (sqrt 3.0)))
4.0ms	(/ z (sqrt 3.0))
4.0ms	(/ t (sqrt 3.0))
3.0ms	(cos (- y (* (/ z (sqrt 3.0)) (/ t (sqrt 3.0)))))

series408.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(* (/ z (sqrt 3.0)) (/ t (sqrt 3.0)))
57.0ms	(/ z (sqrt 3.0))
53.0ms	(/ t (sqrt 3.0))
170.0ms	(cos (- y (* (/ z (sqrt 3.0)) (/ t (sqrt 3.0)))))

simplify63.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	478	1167
1	2151	1077
2	5002	1023

prune588.0ms

Filtered

173 candidates to 111 candidates (64.2%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	158	15	173
Fresh	8	11	19
Picked	1	0	1
Done	0	0	0
Total	167	26	193

Merged error: 15.9b

Counts

193 → 26

localize28.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ t (sqrt 3.0))
0.4b	(/ t (sqrt 3.0))
30.3b	(sin (* (/ z (sqrt 3.0)) (/ t (sqrt 3.0))))
30.9b	(cos (* (/ z (sqrt 3.0)) (/ t (sqrt 3.0))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
34×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
24×	`sqrt-prod`
12×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
4×	`pow1` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 92

Calls

4 calls:

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

series279.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(/ t (sqrt 3.0))
56.0ms	(/ t (sqrt 3.0))
93.0ms	(sin (* (/ z (sqrt 3.0)) (/ t (sqrt 3.0))))
77.0ms	(cos (* (/ z (sqrt 3.0)) (/ t (sqrt 3.0))))

simplify59.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	142	596
1	393	550
2	1626	528
3	5001	528

prune606.0ms

Filtered

104 candidates to 70 candidates (67.3%)

Pruning

34 alts after pruning (34 fresh and 0 done)

	Pruned	Kept	Total
New	93	11	104
Fresh	2	23	25
Picked	1	0	1
Done	0	0	0
Total	96	34	130

Merged error: 15.7b

Counts

130 → 34

localize36.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (/ t (sqrt 3.0)))
0.6b	(cbrt (/ t (sqrt 3.0)))
30.8b	(sin (* (/ z (sqrt 3.0)) (* (* (cbrt (/ t (sqrt 3.0))) (cbrt (/ t (sqrt 3.0)))) (cbrt (/ t (sqrt 3.0))))))
30.9b	(cos (* (/ z (sqrt 3.0)) (/ t (sqrt 3.0))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

44×	`cbrt-prod`
36×	`times-frac`
30×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`sqrt-prod`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
2×	`cbrt-div` `pow1/3` `div-inv`

Counts

4 → 76

Calls

4 calls:

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

series862.0ms

Counts

4 → 12

Calls

4 calls:

337.0ms	(cbrt (/ t (sqrt 3.0)))
339.0ms	(cbrt (/ t (sqrt 3.0)))
108.0ms	(sin (* (/ z (sqrt 3.0)) (* (* (cbrt (/ t (sqrt 3.0))) (cbrt (/ t (sqrt 3.0)))) (cbrt (/ t (sqrt 3.0))))))
78.0ms	(cos (* (/ z (sqrt 3.0)) (/ t (sqrt 3.0))))

simplify45.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 3 (36.0ms)

Iter	Nodes	Cost
0	191	804
1	398	742
2	1387	721
3	5001	697

prune462.0ms

Filtered

88 candidates to 64 candidates (72.7%)

Pruning

37 alts after pruning (37 fresh and 0 done)

	Pruned	Kept	Total
New	83	5	88
Fresh	1	32	33
Picked	1	0	1
Done	0	0	0
Total	85	37	122

Merged error: 15.6b

Counts

122 → 37

regimes3.6s

Accuracy

58.8% (1.7b remaining)

Error of 17.6b against oracle of 15.9b and baseline of 20.0b

bsearch3.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	45
1	63	45

end0.0ms

sample2.8s

Algorithm

intervals

Results

601.0ms	1560×	body	1280	valid
532.0ms	9139×	body	80	nan
355.0ms	5614×	body	80	valid
260.0ms	388×	body	2560	valid
244.0ms	899×	body	640	valid
90.0ms	463×	body	320	valid
25.0ms	182×	body	160	valid