Details

sample314.0ms

Algorithm

intervals

Results

38.0ms	89×	body	1280	valid
19.0ms	76×	body	640	valid
5.0ms	57×	body	80	valid
5.0ms	23×	body	320	valid
1.0ms	11×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	5
1	16	5
2	20	5
3	21	5
4	21	5

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: 16.6b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
4.9b	(cos (+ a b))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 67

Calls

3 calls:

7.0ms	(* r (/ (sin b) (cos (+ a b))))
4.0ms	(/ (sin b) (cos (+ a b)))
6.0ms	(cos (+ a b))

series157.0ms

Counts

3 → 9

Calls

3 calls:

96.0ms	(* r (/ (sin b) (cos (+ a b))))
36.0ms	(/ (sin b) (cos (+ a b)))
24.0ms	(cos (+ a b))

simplify40.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	252	536
1	1064	480
2	5001	477

prune204.0ms

Filtered

76 candidates to 57 candidates (75.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	65	11	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	11	77

Merged error: 0.2b

Counts

77 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`associate-r`
19×	`times-frac`
13×	`add-exp-log` `add-cbrt-cube`
8×	`pow1` `associate-/r/`
7×	`sin-mult`
6×	`associate-l` `cos-mult` `add-log-exp`
3×	`flip3--` `prod-exp` `associate-/r` `frac-sub` `flip--` `cbrt-unprod` `associate-/l` `sub-div` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`sub-neg` `frac-2neg` `diff-log` `associate-*r/` `clear-num`

Counts

4 → 100

Calls

4 calls:

5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
11.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
5.0ms	(* (sin a) (sin b))
8.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series442.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
209.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
46.0ms	(* (sin a) (sin b))
109.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify55.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	405	1308
1	1761	1183
2	5001	1173

prune378.0ms

Filtered

112 candidates to 86 candidates (76.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	99	13	112
Fresh	10	0	10
Picked	1	0	1
Done	0	0	0
Total	110	13	123

Merged error: 0.0b

Counts

123 → 13

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.2b	(* r (sin b))
0.2b	(* (sin a) (sin b))
0.3b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

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

series378.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
41.0ms	(* r (sin b))
43.0ms	(* (sin a) (sin b))
211.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify48.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	344	770
1	1513	673
2	5002	663

prune292.0ms

Filtered

88 candidates to 64 candidates (72.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	80	8	88
Fresh	8	4	12
Picked	1	0	1
Done	0	0	0
Total	89	12	101

Merged error: 0.0b

Counts

101 → 12

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin a) (sin b))
0.3b	(* (/ (sin b) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b))))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))
0.3b	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
0.4b	(* (* (cos a) (cos b)) (* (cos a) (cos b)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

86×	`pow1`
37×	`associate-l`
36×	`pow-prod-down`
35×	`add-exp-log` `add-cbrt-cube`
25×	`sin-mult`
24×	`cos-mult`
22×	`add-sqr-sqrt`
19×	`prod-exp` `cbrt-unprod`
16×	`associate-/r/`
15×	`add-cube-cbrt` `-un-lft-identity` `associate-r/`
13×	`frac-times` `times-frac` `associate-*l/`
9×	`frac-sub`
8×	`associate-r` `pow-sqr` `pow-prod-up`
5×	`sub-div`
4×	`pow-plus` `*-commutative` `add-log-exp`
3×	`difference-of-squares` `unswap-sqr`
2×	`pow2` `flip3-+` `swap-sqr` `frac-add` `flip-+`
1×	`cbrt-undiv` `distribute-rgt-in` `flip3--` `distribute-lft-in` `div-exp` `flip--` `div-inv`

Counts

4 → 152

Calls

4 calls:

5.0ms	(* (sin a) (sin b))
24.0ms	(* (/ (sin b) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b))))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))
9.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
9.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))

series404.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (sin a) (sin b))
251.0ms	(* (/ (sin b) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b))))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))
50.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
56.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))

simplify115.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (100.0ms)

Iter	Nodes	Cost
0	790	2073
1	4144	1731
2	5001	1727

prune519.0ms

Filtered

164 candidates to 101 candidates (61.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	160	4	164
Fresh	4	7	11
Picked	0	1	1
Done	0	0	0
Total	164	12	176

Merged error: 0b

Counts

176 → 12

regimes191.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	26
1	21	26

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.2s	2763×	body	1280	valid
471.0ms	1820×	body	640	valid
147.0ms	828×	body	320	valid
129.0ms	2251×	body	80	valid
49.0ms	339×	body	160	valid