Details

sample314.0ms

Algorithm

intervals

Results

42.0ms	95×	body	1280	valid
18.0ms	68×	body	640	valid
4.0ms	22×	body	320	valid
3.0ms	58×	body	80	valid
2.0ms	13×	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: 12.6b

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)))
3.6b	(cos (+ a b))

rewrite36.0ms

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×	`expm1-log1p-u` `associate-l` `associate-/r` `log1p-expm1-u` `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 → 73

Calls

3 calls:

22.0ms	(* r (/ (sin b) (cos (+ a b))))
4.0ms	(/ (sin b) (cos (+ a b)))
6.0ms	(cos (+ a b))

series162.0ms

Counts

3 → 9

Calls

3 calls:

100.0ms	(* r (/ (sin b) (cos (+ a b))))
38.0ms	(/ (sin b) (cos (+ a b)))
23.0ms	(cos (+ a b))

simplify43.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	263	560
1	1093	504
2	5002	504

prune215.0ms

Filtered

82 candidates to 63 candidates (76.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	70	12	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	12	83

Merged error: 0.2b

Counts

83 → 12

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos a) (cos 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))))

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×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `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 → 113

Calls

4 calls:

4.0ms	(* (cos a) (cos b))
12.0ms	(* 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))))

series408.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (cos a) (cos b))
211.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
43.0ms	(* (sin a) (sin b))
113.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify57.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	445	1273
1	1910	1154
2	5001	1152

prune385.0ms

Filtered

125 candidates to 95 candidates (76.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	113	12	125
Fresh	10	1	11
Picked	1	0	1
Done	0	0	0
Total	124	13	137

Merged error: 0.0b

Counts

137 → 13

localize19.0ms

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))

rewrite25.0ms

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×	`expm1-log1p-u` `prod-exp` `associate-/r/` `cbrt-unprod` `log1p-expm1-u` `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 → 89

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))

series348.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (cos a) (cos b))
37.0ms	(* r (sin b))
223.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
43.0ms	(* (sin a) (sin b))

simplify51.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	382	724
1	1662	634
2	5001	633

prune269.0ms

Filtered

101 candidates to 70 candidates (69.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	98	3	101
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	101	13	114

Merged error: 0b

Counts

114 → 13

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
99×	`add-sqr-sqrt`
86×	`add-cube-cbrt` `*-un-lft-identity`
53×	`associate-l`
22×	`add-exp-log` `add-cbrt-cube`
13×	`associate-/l*`
10×	`pow1`
9×	`associate-r` `div-inv`
8×	`associate-/r/` `sin-mult`
6×	`cbrt-undiv` `div-exp` `cos-mult`
5×	`prod-exp` `cbrt-unprod` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-times` `associate-r/` `pow-prod-down` `associate-/r` `*-commutative`
2×	`flip3--` `flip3-+` `frac-add` `frac-sub` `flip--` `flip-+` `sub-div`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `associate-*l/` `clear-num` `associate-/l/`

Counts

4 → 197

Calls

4 calls:

5.0ms	(* (sin a) (sin b))
5.0ms	(* (sin a) (sin b))
21.0ms	(* (/ (/ (sin b) (fma (cos b) (cos a) (* (sin a) (sin b)))) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))
11.0ms	(/ (/ (sin b) (fma (cos b) (cos a) (* (sin a) (sin b)))) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

series562.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (sin a) (sin b))
43.0ms	(* (sin a) (sin b))
257.0ms	(* (/ (/ (sin b) (fma (cos b) (cos a) (* (sin a) (sin b)))) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))
215.0ms	(/ (/ (sin b) (fma (cos b) (cos a) (* (sin a) (sin b)))) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

simplify61.0ms

Algorithm

egg-herbie

Counts

209 → 209

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1182	4668
1	5001	4307

prune765.0ms

Filtered

209 candidates to 173 candidates (82.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	209	0	209
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	209	13	222

Merged error: 0b

Counts

222 → 13

regimes179.0ms

Accuracy

0% (0.3b 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	25
1	23	25
2	23	25

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.2s	2843×	body	1280	valid
492.0ms	1872×	body	640	valid
130.0ms	734×	body	320	valid
121.0ms	2212×	body	80	valid
43.0ms	339×	body	160	valid