Details

sample79.0ms

Algorithm

intervals

Results

42.0ms	95×	body	1280	valid
17.0ms	68×	body	640	valid
4.0ms	22×	body	320	valid
3.0ms	58×	body	80	valid
2.0ms	13×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	5
1	16	5
2	19	5
3	20	5
4	20	5

prune2.0ms

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: 12.6b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
3.6b	(cos (+ a b))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
5×	`pow1`
3×	`times-frac` `associate-r` `associate-l` `associate-/r*` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
1×	`cos-sum` `frac-2neg` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l` `unswap-sqr`

Counts

3 → 47

Calls

3 calls:

4.0ms	(* r (sin b))
5.0ms	(/ (* r (sin b)) (cos (+ a b)))
6.0ms	(cos (+ a b))

series157.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(* r (sin b))
95.0ms	(/ (* r (sin b)) (cos (+ a b)))
23.0ms	(cos (+ a b))

simplify32.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	198	305
1	861	257
2	5001	256

prune130.0ms

Filtered

56 candidates to 40 candidates (71.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	48	8	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	49	8	57

Merged error: 0.2b

Counts

57 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos a) (cos b))
0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.2b	(* (sin a) (sin b))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`add-exp-log` `add-cbrt-cube`
12×	`add-cube-cbrt` `*-un-lft-identity`
10×	`pow1`
9×	`associate-r` `associate-l`
4×	`prod-exp` `associate-/r/` `cbrt-unprod` `add-log-exp`
3×	`times-frac` `pow-prod-down` `associate-/r` `cos-mult` `-commutative` `sin-mult` `unswap-sqr`
2×	`cbrt-undiv` `div-exp`
1×	`flip3--` `frac-2neg` `clear-num` `frac-sub` `flip--` `div-inv` `associate-/l*` `sub-div`

Counts

4 → 81

Calls

4 calls:

4.0ms	(* (cos a) (cos b))
4.0ms	(* r (sin b))
9.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
5.0ms	(* (sin a) (sin b))

series334.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (cos a) (cos b))
39.0ms	(* r (sin b))
211.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
46.0ms	(* (sin a) (sin b))

simplify48.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	367	682
1	1616	594
2	5001	593

prune273.0ms

Filtered

93 candidates to 65 candidates (69.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	82	11	93
Fresh	6	1	7
Picked	1	0	1
Done	0	0	0
Total	89	12	101

Merged error: 0.0b

Counts

101 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos b) (cos a))
0.2b	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
0.2b	(* (sin a) (sin b))
0.2b	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
24×	`add-cube-cbrt` `*-un-lft-identity`
23×	`associate-r`
19×	`times-frac`
15×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
9×	`associate-l`
8×	`associate-/r/`
5×	`cos-mult` `sin-mult`
4×	`prod-exp` `cbrt-unprod` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `associate-/r` `-commutative` `associate-/l*`
2×	`cbrt-undiv` `flip3--` `div-exp` `frac-sub` `flip--` `div-inv` `sub-div`
1×	`frac-2neg` `associate-*r/` `clear-num`

Counts

4 → 105

Calls

4 calls:

5.0ms	(* (cos b) (cos a))
12.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
5.0ms	(* (sin a) (sin b))
8.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

series403.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (cos b) (cos a))
205.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
45.0ms	(* (sin a) (sin b))
111.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

simplify55.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	428	1219
1	1840	1103
2	5001	1098

prune320.0ms

Filtered

117 candidates to 86 candidates (73.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	114	3	117
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	116	13	129

Merged error: 0b

Counts

129 → 13

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (sin a)) (cbrt (sin a)))
0.6b	(cbrt (sin a))
0.6b	(cbrt (sin a))
0.6b	(cbrt (sin a))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

7.0ms	(* (cbrt (sin a)) (cbrt (sin a)))
2.0ms	(cbrt (sin a))
1.0ms	(cbrt (sin a))
2.0ms	(cbrt (sin a))

series399.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(* (cbrt (sin a)) (cbrt (sin a)))
94.0ms	(cbrt (sin a))
96.0ms	(cbrt (sin a))
97.0ms	(cbrt (sin a))

simplify94.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (88.0ms)

Iter	Nodes	Cost
0	154	453
1	551	401
2	3082	369
3	5002	363

prune244.0ms

Filtered

85 candidates to 60 candidates (70.6%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	85	13	98

Merged error: 0b

Counts

98 → 13

regimes171.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	10
1	15	10

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.2s	2843×	body	1280	valid
477.0ms	1872×	body	640	valid
147.0ms	734×	body	320	valid
125.0ms	2212×	body	80	valid
43.0ms	339×	body	160	valid