Details

sample339.0ms

Algorithm

intervals

Results

52.0ms	112×	body	1280	valid
16.0ms	58×	body	640	valid
5.0ms	52×	body	80	valid
5.0ms	24×	body	320	valid
1.0ms	10×	body	160	valid

simplify13.0ms

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: 16.2b

Counts

2 → 1

localize13.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.3b	(/ (sin b) (cos (+ a b)))
3.0b	(cos (+ a b))

rewrite37.0ms

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:

8.0ms	(* r (/ (sin b) (cos (+ a b))))
20.0ms	(/ (sin b) (cos (+ a b)))
6.0ms	(cos (+ a b))

series156.0ms

Counts

3 → 9

Calls

3 calls:

95.0ms	(* r (/ (sin b) (cos (+ a b))))
37.0ms	(/ (sin b) (cos (+ a b)))
23.0ms	(cos (+ a b))

simplify41.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (34.0ms)

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

prune192.0ms

Filtered

76 candidates to 57 candidates (75.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	67	9	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	9	77

Merged error: 0.2b

Counts

77 → 9

localize19.0ms

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))
0.3b	(/ (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))))

series445.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
208.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
45.0ms	(* (sin a) (sin b))
112.0ms	(/ (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	1307
1	1761	1182
2	5001	1173

prune355.0ms

Filtered

112 candidates to 86 candidates (76.8%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	96	16	112
Fresh	8	0	8
Picked	1	0	1
Done	0	0	0
Total	105	16	121

Merged error: 0.0b

Counts

121 → 16

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos a) (cos b)) (* (sin a) (sin 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

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

series381.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
41.0ms	(* 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

88 → 88

Iterations

Useful iterations: 2 (40.0ms)

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

prune260.0ms

Filtered

88 candidates to 63 candidates (71.6%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	84	4	88
Fresh	4	11	15
Picked	1	0	1
Done	0	0	0
Total	89	15	104

Merged error: 0.0b

Counts

104 → 15

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (pow (* (cos a) (cos b)) 3) (pow (* (sin a) (sin b)) 3)) (+ (* (* (sin a) (sin b)) (+ (* (sin a) (sin b)) (* (cos a) (cos b)))) (* (* (cos a) (cos b)) (* (cos a) (cos b)))))
0.3b	(pow (* (sin a) (sin b)) 3)
0.5b	(* (* (cos a) (cos b)) (* (cos a) (cos b)))
0.6b	(pow (* (cos a) (cos b)) 3)

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

49×	`pow1`
41×	`cos-mult`
36×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
27×	`times-frac` `frac-add`
24×	`add-exp-log` `add-cbrt-cube`
23×	`associate-/r/`
21×	`sin-mult`
20×	`add-cube-cbrt`
19×	`pow-prod-down`
18×	`sqr-pow`
17×	`frac-times` `associate-*r/`
16×	`difference-of-squares`
11×	`associate-*l/`
10×	`prod-exp` `cbrt-unprod`
9×	`associate-/l*`
7×	`flip3-+` `flip-+`
6×	`cube-div` `pow-unpow`
4×	`difference-cubes` `pow-pow` `pow-exp` `pow-sqr` `pow-prod-up` `associate-/l/` `distribute-lft-out--` `add-log-exp` `rem-cube-cbrt`
3×	`associate-/r*`
2×	`cube-mult` `pow-to-exp` `unpow-prod-down` `pow-plus` `unpow3` `cube-prod`
1×	`cbrt-undiv` `pow2` `flip3--` `frac-2neg` `div-sub` `swap-sqr` `div-exp` `associate-r` `associate-l` `clear-num` `*-commutative` `frac-sub` `flip--` `div-inv` `sub-div`

Counts

4 → 162

Calls

4 calls:

27.0ms	(/ (- (pow (* (cos a) (cos b)) 3) (pow (* (sin a) (sin b)) 3)) (+ (* (* (sin a) (sin b)) (+ (* (sin a) (sin b)) (* (cos a) (cos b)))) (* (* (cos a) (cos b)) (* (cos a) (cos b)))))
5.0ms	(pow (* (sin a) (sin b)) 3)
9.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))
5.0ms	(pow (* (cos a) (cos b)) 3)

series534.0ms

Counts

4 → 12

Calls

4 calls:

354.0ms	(/ (- (pow (* (cos a) (cos b)) 3) (pow (* (sin a) (sin b)) 3)) (+ (* (* (sin a) (sin b)) (+ (* (sin a) (sin b)) (* (cos a) (cos b)))) (* (* (cos a) (cos b)) (* (cos a) (cos b)))))
61.0ms	(pow (* (sin a) (sin b)) 3)
57.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))
62.0ms	(pow (* (cos a) (cos b)) 3)

simplify61.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1052	4256
1	5002	4091

prune589.0ms

Filtered

174 candidates to 112 candidates (64.4%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	172	2	174
Fresh	1	13	14
Picked	0	1	1
Done	0	0	0
Total	173	16	189

Merged error: 0.0b

Counts

189 → 16

regimes231.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	32
1	26	32

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.3s	2867×	body	1280	valid
494.0ms	1829×	body	640	valid
154.0ms	807×	body	320	valid
141.0ms	2133×	body	80	valid
50.0ms	367×	body	160	valid

Details

sample339.0ms

simplify13.0ms

prune4.0ms

localize13.0ms

rewrite37.0ms

series156.0ms

simplify41.0ms

prune192.0ms

localize19.0ms

rewrite32.0ms

series445.0ms

simplify55.0ms

prune355.0ms

localize16.0ms

rewrite24.0ms

series381.0ms

simplify48.0ms

prune260.0ms

localize25.0ms

rewrite53.0ms

series534.0ms

simplify61.0ms

prune589.0ms

regimes231.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.3s

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