Details

sample364.0ms

Algorithm

intervals

Results

42.0ms	91×	body	1280	valid
18.0ms	56×	body	640	valid
6.0ms	29×	body	320	valid
4.0ms	70×	body	80	valid
2.0ms	10×	body	160	valid

simplify35.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 14.4b

Counts

2 → 1

localize13.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
3.2b	(cos (+ a b))

rewrite20.0ms

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:

6.0ms	(* 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))))
37.0ms	(/ (sin b) (cos (+ a b)))
24.0ms	(cos (+ a b))

simplify43.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (34.0ms)

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

prune188.0ms

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

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* (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))))

rewrite31.0ms

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)))))
4.0ms	(* (sin a) (sin b))
8.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series443.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(- (* (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))))

simplify54.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	405	1307
1	1761	1182
2	5001	1173

prune345.0ms

Filtered

112 candidates to 86 candidates (76.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	101	11	112
Fresh	7	1	8
Picked	1	0	1
Done	0	0	0
Total	109	12	121

Merged error: 0.0b

Counts

121 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

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:

4.0ms	(* r (sin b))
5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
4.0ms	(* (sin a) (sin b))
8.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series378.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* r (sin b))
83.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
43.0ms	(* (sin a) (sin b))
215.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify52.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	344	770
1	1513	673
2	5001	663

prune245.0ms

Filtered

88 candidates to 63 candidates (71.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	86	2	88
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	88	12	100

Merged error: 0.0b

Counts

100 → 12

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

84×	`pow1`
42×	`cos-mult` `sin-mult`
35×	`add-exp-log` `pow-prod-down` `add-cbrt-cube`
34×	`associate-l`
32×	`associate-/r/`
27×	`add-sqr-sqrt`
25×	`times-frac` `associate-*r/`
23×	`associate-*l/`
22×	`add-cube-cbrt` `*-un-lft-identity`
21×	`frac-times`
18×	`prod-exp` `frac-sub` `cbrt-unprod`
10×	`sub-div`
8×	`pow-sqr` `pow-prod-up`
7×	`difference-of-squares`
5×	`associate-r`
4×	`pow-plus` `associate-/r*` `add-log-exp`
3×	`-commutative` `associate-/l`
2×	`cbrt-undiv` `pow2` `flip3--` `flip3-+` `swap-sqr` `div-exp` `frac-add` `flip--` `flip-+` `div-inv` `unswap-sqr`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num`

Counts

4 → 180

Calls

4 calls:

23.0ms	(* (/ (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))))
14.0ms	(/ (sin b) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))))
9.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
12.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))

series501.0ms

Counts

4 → 12

Calls

4 calls:

244.0ms	(* (/ (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))))
149.0ms	(/ (sin b) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))))
51.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
57.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))

simplify151.0ms

Algorithm

egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	939	3187
1	4978	2741
2	5001	2741

prune530.0ms

Filtered

192 candidates to 122 candidates (63.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	189	3	192
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	191	13	204

Merged error: 0.0b

Counts

204 → 13

regimes195.0ms

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	21	26
1	21	26

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.3s	2928×	body	1280	valid
476.0ms	1817×	body	640	valid
158.0ms	804×	body	320	valid
131.0ms	2126×	body	80	valid
43.0ms	327×	body	160	valid

Details

sample364.0ms

simplify35.0ms

prune4.0ms

localize13.0ms

rewrite20.0ms

series157.0ms

simplify43.0ms

prune188.0ms

localize15.0ms

rewrite31.0ms

series443.0ms

simplify54.0ms

prune345.0ms

localize15.0ms

rewrite23.0ms

series378.0ms

simplify52.0ms

prune245.0ms

localize20.0ms

rewrite67.0ms

series501.0ms

simplify151.0ms

prune530.0ms

regimes195.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.3s

Profiling