Details

sample142.0ms

Algorithm

intervals

Results

32.0ms	302×	body	80	nan
29.0ms	46×	body	1280	valid
19.0ms	185×	body	80	valid
14.0ms	32×	body	640	valid
12.0ms	13×	body	2560	valid
3.0ms	10×	body	320	valid
2.0ms	10×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.9b

localize19.0ms

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))))
23.7b	(cos (- y (/ (* z t) 3.0)))

rewrite26.0ms

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:

3.0ms	(/ (* z t) 3.0)
3.0ms	(/ a (* b 3.0))
11.0ms	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
8.0ms	(cos (- y (/ (* z t) 3.0)))

series166.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(/ (* z t) 3.0)
18.0ms	(/ a (* b 3.0))
92.0ms	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
39.0ms	(cos (- y (/ (* z t) 3.0)))

simplify47.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (40.0ms)

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

prune310.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 15.8b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 (sqrt x)) (cos (- y (* (/ z (* (cbrt 3.0) (cbrt 3.0))) (/ t (cbrt 3.0))))))
0.3b	(* (/ z (* (cbrt 3.0) (cbrt 3.0))) (/ t (cbrt 3.0)))
0.4b	(/ t (cbrt 3.0))
23.7b	(cos (- y (* (/ z (* (cbrt 3.0) (cbrt 3.0))) (/ t (cbrt 3.0)))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
46×	`times-frac`
35×	`add-cube-cbrt` `*-un-lft-identity`
32×	`add-exp-log`
25×	`associate-r`
24×	`add-cbrt-cube`
23×	`cbrt-prod`
11×	`pow1` `prod-exp` `cbrt-unprod`
8×	`cbrt-undiv` `div-exp` `associate-l`
6×	`associate-/r*` `unswap-sqr`
4×	`pow-prod-down` `add-log-exp`
3×	`cos-diff` `div-inv` `associate-/l*`
2×	`cos-sum` `*-commutative`
1×	`distribute-rgt-in` `frac-times` `sub-neg` `frac-2neg` `distribute-lft-in` `associate-r/` `associate-l/` `clear-num`

Counts

4 → 128

Calls

4 calls:

11.0ms	(* (* 2.0 (sqrt x)) (cos (- y (* (/ z (* (cbrt 3.0) (cbrt 3.0))) (/ t (cbrt 3.0))))))
25.0ms	(* (/ z (* (cbrt 3.0) (cbrt 3.0))) (/ t (cbrt 3.0)))
3.0ms	(/ t (cbrt 3.0))
4.0ms	(cos (- y (* (/ z (* (cbrt 3.0) (cbrt 3.0))) (/ t (cbrt 3.0)))))

series436.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(* (* 2.0 (sqrt x)) (cos (- y (* (/ z (* (cbrt 3.0) (cbrt 3.0))) (/ t (cbrt 3.0))))))
98.0ms	(* (/ z (* (cbrt 3.0) (cbrt 3.0))) (/ t (cbrt 3.0)))
60.0ms	(/ t (cbrt 3.0))
100.0ms	(cos (- y (* (/ z (* (cbrt 3.0) (cbrt 3.0))) (/ t (cbrt 3.0)))))

simplify76.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	609	1376
1	3001	1200
2	5001	1171

prune619.0ms

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 15.7b

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (/ z (* (cbrt 3.0) (cbrt 3.0))))
0.6b	(cbrt (/ z (* (cbrt 3.0) (cbrt 3.0))))
0.6b	(cbrt (/ z (* (cbrt 3.0) (cbrt 3.0))))
23.8b	(cos (- y (* (* (cbrt (/ z (* (cbrt 3.0) (cbrt 3.0)))) (cbrt (/ z (* (cbrt 3.0) (cbrt 3.0))))) (* (cbrt (/ z (* (cbrt 3.0) (cbrt 3.0)))) (/ t (cbrt 3.0))))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

21×	`cbrt-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-div` `pow1/3` `div-inv`
2×	`cos-sum`
1×	`cos-diff` `sub-neg`

Counts

4 → 58

Calls

4 calls:

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

series1.4s

Counts

4 → 12

Calls

4 calls:

437.0ms	(cbrt (/ z (* (cbrt 3.0) (cbrt 3.0))))
415.0ms	(cbrt (/ z (* (cbrt 3.0) (cbrt 3.0))))
428.0ms	(cbrt (/ z (* (cbrt 3.0) (cbrt 3.0))))
136.0ms	(cos (- y (* (* (cbrt (/ z (* (cbrt 3.0) (cbrt 3.0)))) (cbrt (/ z (* (cbrt 3.0) (cbrt 3.0))))) (* (cbrt (/ z (* (cbrt 3.0) (cbrt 3.0)))) (/ t (cbrt 3.0))))))

simplify112.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 4 (103.0ms)

Iter	Nodes	Cost
0	157	858
1	333	777
2	906	756
3	3548	747
4	5002	726

prune529.0ms

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 15.5b

localize43.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (/ z (* (cbrt 3.0) (cbrt 3.0))))
0.6b	(cbrt (/ z (* (cbrt 3.0) (cbrt 3.0))))
28.5b	(sin (- (* (* (cbrt (/ z (* (cbrt 3.0) (cbrt 3.0)))) (cbrt (/ z (* (cbrt 3.0) (cbrt 3.0))))) (* (cbrt (/ z (* (cbrt 3.0) (cbrt 3.0)))) (/ t (cbrt 3.0))))))
28.7b	(cos (* (* (cbrt (/ z (* (cbrt 3.0) (cbrt 3.0)))) (cbrt (/ z (* (cbrt 3.0) (cbrt 3.0))))) (* (cbrt (/ z (* (cbrt 3.0) (cbrt 3.0)))) (/ t (cbrt 3.0)))))

rewrite50.0ms

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` `add-cbrt-cube` `add-log-exp`
2×	`cbrt-div` `pow1/3` `div-inv`
1×	`neg-sub0` `sin-neg` `sin-diff`

Counts

4 → 48

Calls

4 calls:

3.0ms	(cbrt (/ z (* (cbrt 3.0) (cbrt 3.0))))
3.0ms	(cbrt (/ z (* (cbrt 3.0) (cbrt 3.0))))
16.0ms	(sin (- (* (* (cbrt (/ z (* (cbrt 3.0) (cbrt 3.0)))) (cbrt (/ z (* (cbrt 3.0) (cbrt 3.0))))) (* (cbrt (/ z (* (cbrt 3.0) (cbrt 3.0)))) (/ t (cbrt 3.0))))))
26.0ms	(cos (* (* (cbrt (/ z (* (cbrt 3.0) (cbrt 3.0)))) (cbrt (/ z (* (cbrt 3.0) (cbrt 3.0))))) (* (cbrt (/ z (* (cbrt 3.0) (cbrt 3.0)))) (/ t (cbrt 3.0)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

452.0ms	(cbrt (/ z (* (cbrt 3.0) (cbrt 3.0))))
444.0ms	(cbrt (/ z (* (cbrt 3.0) (cbrt 3.0))))
100.0ms	(sin (- (* (* (cbrt (/ z (* (cbrt 3.0) (cbrt 3.0)))) (cbrt (/ z (* (cbrt 3.0) (cbrt 3.0))))) (* (cbrt (/ z (* (cbrt 3.0) (cbrt 3.0)))) (/ t (cbrt 3.0))))))
86.0ms	(cos (* (* (cbrt (/ z (* (cbrt 3.0) (cbrt 3.0)))) (cbrt (/ z (* (cbrt 3.0) (cbrt 3.0))))) (* (cbrt (/ z (* (cbrt 3.0) (cbrt 3.0)))) (/ t (cbrt 3.0)))))

simplify206.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 4 (199.0ms)

Iter	Nodes	Cost
0	157	826
1	348	713
2	1007	699
3	4245	693
4	5002	679

prune665.0ms

Pruning

32 alts after pruning (32 fresh and 0 done)

Merged error: 15.4b

regimes3.5s

Accuracy

57.2% (1.7b remaining)

Error of 17.3b against oracle of 15.6b and baseline of 19.5b

bsearch4.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	73	73
1	84	73
2	92	73
3	92	73

end0.0ms

sample4.1s

Algorithm

intervals

Results

951.0ms	9328×	body	80	nan
920.0ms	1542×	body	1280	valid
625.0ms	5739×	body	80	valid
429.0ms	969×	body	640	valid
313.0ms	338×	body	2560	valid
142.0ms	432×	body	320	valid
52.0ms	215×	body	160	valid