Details

sample104.0ms

Algorithm

intervals

Results

18.0ms	44×	body	1280	valid
16.0ms	260×	body	80	nan
12.0ms	17×	body	2560	valid
12.0ms	171×	body	80	valid
8.0ms	27×	body	640	valid
4.0ms	17×	body	320	valid
1.0ms	7×	body	160	valid

simplify27.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

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: 21.0b

Counts

2 → 1

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ a (* b 3.0))
0.2b	(/ (* z t) 3.0)
0.3b	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
25.7b	(cos (- y (/ (* z t) 3.0)))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

211×	`add-sqr-sqrt`
180×	`times-frac`
165×	`add-cube-cbrt` `*-un-lft-identity`
122×	`cos-sum`
120×	`prod-diff`
70×	`associate-l`
60×	`associate-r`
24×	`unswap-sqr`
19×	`add-exp-log` `*-commutative` `add-cbrt-cube`
15×	`associate-/r` `associate-/l`
9×	`pow1`
5×	`prod-exp` `sqrt-prod` `cbrt-unprod` `div-inv`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff` `pow-prod-down`
2×	`frac-2neg` `clear-num`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in`

Counts

4 → 306

Calls

4 calls:

12.0ms	(/ a (* b 3.0))
8.0ms	(/ (* z t) 3.0)
27.0ms	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
33.0ms	(cos (- y (/ (* z t) 3.0)))

series199.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ a (* b 3.0))
26.0ms	(/ (* z t) 3.0)
112.0ms	(* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0))))
40.0ms	(cos (- y (/ (* z t) 3.0)))

simplify129.0ms

Algorithm

egg-herbie

Counts

318 → 318

Iterations

Useful iterations: 1 (53.0ms)

Iter	Nodes	Cost
0	2212	8598
1	5001	7928

prune1.1s

Filtered

318 candidates to 191 candidates (60.1%)

Pruning

34 alts after pruning (34 fresh and 0 done)

	Pruned	Kept	Total
New	284	34	318
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	285	34	319

Merged error: 16.7b

Counts

319 → 34

localize30.0ms

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)))))
30.2b	(cos (/ (* z t) 3.0))
30.7b	(sin (/ (* z t) 3.0))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

26×	`associate-l`
25×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
16×	`associate-r`
11×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
8×	`unswap-sqr`
5×	`sqrt-prod`
4×	`expm1-log1p-u` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
3×	`associate-r/` `-commutative`
2×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `sin-mult`
1×	`flip3-+` `frac-add` `cos-mult` `flip-+`

Counts

4 → 88

Calls

4 calls:

10.0ms	(* (sin y) (sin (/ (* z t) 3.0)))
42.0ms	(* (* 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))
8.0ms	(sin (/ (* z t) 3.0))

series321.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (sin y) (sin (/ (* z t) 3.0)))
241.0ms	(* (* 2.0 (sqrt x)) (+ (* (cos y) (cos (/ (* z t) 3.0))) (* (sin y) (sin (/ (* z t) 3.0)))))
11.0ms	(cos (/ (* z t) 3.0))
19.0ms	(sin (/ (* z t) 3.0))

simplify83.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	466	1142
1	2126	1032
2	5001	1027

prune614.0ms

Filtered

100 candidates to 75 candidates (75.0%)

Pruning

35 alts after pruning (35 fresh and 0 done)

	Pruned	Kept	Total
New	93	7	100
Fresh	5	28	33
Picked	1	0	1
Done	0	0	0
Total	99	35	134

Merged error: 15.7b

Counts

134 → 35

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* z t) 3.0)
0.3b	(* (* 2.0 (sqrt x)) (+ (* (cos y) (cos (* 0.3333333333333333 (* t z)))) (* (sin y) (sin (/ (* z t) 3.0)))))
30.6b	(cos (* 0.3333333333333333 (* t z)))
30.7b	(sin (/ (* z t) 3.0))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
36×	`times-frac`
35×	`associate-l`
34×	`add-cube-cbrt`
25×	`associate-r`
14×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/l*`
11×	`unswap-sqr`
9×	`pow1`
6×	`*-commutative`
5×	`sqrt-prod`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
3×	`associate-r/` `pow-prod-down` `associate-/r`
2×	`cbrt-undiv` `+-commutative` `distribute-rgt-in` `distribute-lft-in` `div-exp`
1×	`frac-2neg` `flip3-+` `frac-add` `clear-num` `cos-mult` `flip-+` `div-inv` `sin-mult`

Counts

4 → 134

Calls

4 calls:

7.0ms	(/ (* z t) 3.0)
35.0ms	(* (* 2.0 (sqrt x)) (+ (* (cos y) (cos (* 0.3333333333333333 (* t z)))) (* (sin y) (sin (/ (* z t) 3.0)))))
7.0ms	(cos (* 0.3333333333333333 (* t z)))
7.0ms	(sin (/ (* z t) 3.0))

series291.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(/ (* z t) 3.0)
235.0ms	(* (* 2.0 (sqrt x)) (+ (* (cos y) (cos (* 0.3333333333333333 (* t z)))) (* (sin y) (sin (/ (* z t) 3.0)))))
10.0ms	(cos (* 0.3333333333333333 (* t z)))
25.0ms	(sin (/ (* z t) 3.0))

simplify107.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	684	1328
1	3143	1214
2	5001	1209

prune847.0ms

Filtered

146 candidates to 109 candidates (74.7%)

Pruning

37 alts after pruning (37 fresh and 0 done)

	Pruned	Kept	Total
New	140	6	146
Fresh	3	31	34
Picked	1	0	1
Done	0	0	0
Total	144	37	181

Merged error: 15.7b

Counts

181 → 37

localize54.0ms

Local error

Found 4 expressions with local error:

30.7b	(sin (/ (* z t) 3.0))
30.7b	(sin (/ (* z t) 3.0))
30.7b	(sin (/ (* z t) 3.0))
30.7b	(sin (/ (* z t) 3.0))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

4 → 36

Calls

4 calls:

8.0ms	(sin (/ (* z t) 3.0))
8.0ms	(sin (/ (* z t) 3.0))
8.0ms	(sin (/ (* z t) 3.0))
9.0ms	(sin (/ (* z t) 3.0))

series82.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(sin (/ (* z t) 3.0))
18.0ms	(sin (/ (* z t) 3.0))
25.0ms	(sin (/ (* z t) 3.0))
20.0ms	(sin (/ (* z t) 3.0))

simplify124.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	25	224
1	40	196
2	49	196
3	55	196
4	74	196
5	128	196
6	534	196
7	1714	196
8	5001	196

prune343.0ms

Filtered

48 candidates to 44 candidates (91.7%)

Pruning

36 alts after pruning (36 fresh and 0 done)

	Pruned	Kept	Total
New	47	1	48
Fresh	1	35	36
Picked	1	0	1
Done	0	0	0
Total	49	36	85

Merged error: 15.7b

Counts

85 → 36

regimes4.4s

Accuracy

40.6% (3.1b remaining)

Error of 18.6b against oracle of 15.6b and baseline of 20.7b

bsearch7.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	57	46
1	59	46
2	59	46

end0.0ms

sample3.1s

Algorithm

intervals

Results

693.0ms	1594×	body	1280	valid
605.0ms	9050×	body	80	nan
376.0ms	5538×	body	80	valid
285.0ms	966×	body	640	valid
263.0ms	373×	body	2560	valid
99.0ms	434×	body	320	valid
31.0ms	201×	body	160	valid