Details

sample123.0ms

Algorithm

intervals

Results

21.0ms	46×	body	1280	valid
19.0ms	271×	body	80	nan
14.0ms	184×	body	80	valid
11.0ms	15×	body	2560	valid
10.0ms	32×	body	640	valid
4.0ms	16×	body	320	valid
1.0ms	6×	body	160	valid

simplify9.0ms

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

prune5.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 19.4b

Counts

2 → 1

localize16.0ms

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))))
23.0b	(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)))

series49.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(/ (* z t) 3.0)
3.0ms	(/ a (* b 3.0))
32.0ms	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
10.0ms	(cos (- y (/ (* z t) 3.0)))

simplify43.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	419	507
1	1751	432
2	5001	432

prune263.0ms

Filtered

84 candidates to 59 candidates (29.8%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	63	21	84
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	64	21	85

Merged error: 16.2b

Counts

85 → 21

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ a (* b 3.0))
0.3b	(* (* 2.0 (sqrt x)) (+ (* (cos y) (cos (/ (* z t) 3.0))) (* (sin y) (sin (/ (* z t) 3.0)))))
26.7b	(cos (/ (* z t) 3.0))
26.8b	(sin (/ (* z t) 3.0))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`prod-exp` `cbrt-unprod` `add-log-exp`
3×	`times-frac` `associate-r/` `associate-r` `pow-prod-down` `associate-/l`
2×	`cbrt-undiv` `div-exp`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `flip3-+` `associate-l` `frac-add` `clear-num` `associate-/r` `cos-mult` `-commutative` `flip-+` `div-inv` `sin-mult`

Counts

4 → 58

Calls

4 calls:

4.0ms	(/ a (* b 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))

series73.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(/ a (* b 3.0))
62.0ms	(* (* 2.0 (sqrt x)) (+ (* (cos y) (cos (/ (* z t) 3.0))) (* (sin y) (sin (/ (* z t) 3.0)))))
3.0ms	(cos (/ (* z t) 3.0))
4.0ms	(sin (/ (* z t) 3.0))

simplify56.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	460	697
1	2089	586
2	5001	585

prune299.0ms

Filtered

70 candidates to 52 candidates (25.7%)

Pruning

27 alts after pruning (27 fresh and 0 done)

	Pruned	Kept	Total
New	61	9	70
Fresh	2	18	20
Picked	1	0	1
Done	0	0	0
Total	64	27	91

Merged error: 16.2b

Counts

91 → 27

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin y) (sin (* 0.3333333333333333 (* t z))))
0.3b	(* (* 2.0 (sqrt x)) (+ (* (cos y) (cos (/ (* z t) 3.0))) (* (sin y) (sin (* 0.3333333333333333 (* t z))))))
26.7b	(cos (/ (* z t) 3.0))
27.1b	(sin (* 0.3333333333333333 (* t z)))

rewrite21.0ms

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 (* 0.3333333333333333 (* t z))))
10.0ms	(* (* 2.0 (sqrt x)) (+ (* (cos y) (cos (/ (* z t) 3.0))) (* (sin y) (sin (* 0.3333333333333333 (* t z))))))
2.0ms	(cos (/ (* z t) 3.0))
3.0ms	(sin (* 0.3333333333333333 (* t z)))

series82.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(* (sin y) (sin (* 0.3333333333333333 (* t z))))
60.0ms	(* (* 2.0 (sqrt x)) (+ (* (cos y) (cos (/ (* z t) 3.0))) (* (sin y) (sin (* 0.3333333333333333 (* t z))))))
3.0ms	(cos (/ (* z t) 3.0))
6.0ms	(sin (* 0.3333333333333333 (* t z)))

simplify56.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	396	756
1	1917	649
2	5002	648

prune281.0ms

Filtered

68 candidates to 50 candidates (26.5%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	65	3	68
Fresh	3	23	26
Picked	1	0	1
Done	0	0	0
Total	69	26	95

Merged error: 16.2b

Counts

95 → 26

localize35.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (sin y))
0.7b	(cbrt (sin y))
26.7b	(cos (/ (* z t) 3.0))
27.1b	(sin (* 0.3333333333333333 (* t z)))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
2×	`pow1/3`

Counts

4 → 36

Calls

4 calls:

1.0ms	(cbrt (sin y))
1.0ms	(cbrt (sin y))
2.0ms	(cos (/ (* z t) 3.0))
3.0ms	(sin (* 0.3333333333333333 (* t z)))

series44.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(cbrt (sin y))
18.0ms	(cbrt (sin y))
3.0ms	(cos (/ (* z t) 3.0))
4.0ms	(sin (* 0.3333333333333333 (* t z)))

simplify197.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 3 (31.0ms)

Iter	Nodes	Cost
0	102	244
1	234	220
2	707	208
3	3969	184
4	5001	184

prune93.0ms

Filtered

48 candidates to 39 candidates (18.8%)

Pruning

26 alts after pruning (25 fresh and 1 done)

	Pruned	Kept	Total
New	47	1	48
Fresh	1	24	25
Picked	0	1	1
Done	0	0	0
Total	48	26	74

Merged error: 16.2b

Counts

74 → 26

regimes4.2s

Accuracy

61.1% (1.5b remaining)

Error of 17.6b against oracle of 16.1b and baseline of 20.0b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	37
1	56	37
2	56	37

end0.0ms

sample3.8s

Algorithm

intervals

Results

765.0ms	1605×	body	1280	valid
678.0ms	9153×	body	80	nan
425.0ms	5561×	body	80	valid
323.0ms	952×	body	640	valid
282.0ms	372×	body	2560	valid
108.0ms	440×	body	320	valid
34.0ms	203×	body	160	valid

Details

sample123.0ms

simplify9.0ms

prune5.0ms

localize16.0ms

rewrite21.0ms

series49.0ms

simplify43.0ms

prune263.0ms

localize24.0ms

rewrite18.0ms

series73.0ms

simplify56.0ms

prune299.0ms

localize26.0ms

rewrite21.0ms

series82.0ms

simplify56.0ms

prune281.0ms

localize35.0ms

rewrite8.0ms

series44.0ms

simplify197.0ms

prune93.0ms

regimes4.2s

bsearch1.0ms

simplify2.0ms

end0.0ms

sample3.8s

Profiling