Details

sample322.0ms

Algorithm

intervals

Results

45.0ms	97×	body	1280	valid
14.0ms	54×	body	640	valid
4.0ms	24×	body	320	valid
4.0ms	73×	body	80	valid
1.0ms	8×	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: 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)))
4.1b	(cos (+ a b))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 78

Calls

3 calls:

8.0ms	(* r (/ (sin b) (cos (+ a b))))
5.0ms	(/ (sin b) (cos (+ a b)))
6.0ms	(cos (+ a b))

series167.0ms

Counts

3 → 9

Calls

3 calls:

102.0ms	(* r (/ (sin b) (cos (+ a b))))
40.0ms	(/ (sin b) (cos (+ a b)))
25.0ms	(cos (+ a b))

simplify42.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	267	572
1	1143	516
2	5001	513

prune168.0ms

Filtered

87 candidates to 63 candidates (72.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	78	9	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	79	9	88

Merged error: 0.2b

Counts

88 → 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))
0.2b	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

155×	`add-sqr-sqrt`
113×	`*-un-lft-identity`
67×	`times-frac`
44×	`associate-r`
42×	`associate-l`
40×	`add-cube-cbrt`
39×	`unswap-sqr`
36×	`distribute-lft-out--` `difference-of-squares`
22×	`associate-/r*`
17×	`associate-*r/`
13×	`add-exp-log` `add-cbrt-cube`
8×	`pow1` `associate-/r/`
7×	`sin-mult` `associate-/l*`
6×	`cos-mult` `add-log-exp`
3×	`flip3--` `prod-exp` `clear-num` `frac-sub` `flip--` `cbrt-unprod` `sub-div`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `pow-prod-down` `un-div-inv` `*-commutative` `div-inv`
1×	`sub-neg` `diff-log`

Counts

4 → 182

Calls

4 calls:

16.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
28.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
5.0ms	(* (sin a) (sin b))
20.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series473.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
226.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
46.0ms	(* (sin a) (sin b))
116.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify72.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	520	2232
1	2247	2107
2	5001	2106

prune458.0ms

Filtered

194 candidates to 129 candidates (66.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	182	12	194
Fresh	8	0	8
Picked	1	0	1
Done	0	0	0
Total	191	12	203

Merged error: 0.0b

Counts

203 → 12

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

340×	`add-sqr-sqrt`
276×	`times-frac`
266×	`*-un-lft-identity`
122×	`add-cube-cbrt`
75×	`associate-l`
73×	`unswap-sqr`
72×	`distribute-lft-out--` `difference-of-squares`
43×	`associate-/r*`
25×	`associate-/l*`
21×	`associate-/r/`
13×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/l/`
7×	`sin-mult`
6×	`pow1` `cos-mult` `div-inv` `add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`flip3--` `frac-2neg` `associate-r` `clear-num` `frac-sub` `flip--` `sub-div`
1×	`sub-neg` `diff-log` `div-sub` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 291

Calls

4 calls:

18.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
20.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
25.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))
5.0ms	(* (sin a) (sin b))

series487.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
120.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
235.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))
46.0ms	(* (sin a) (sin b))

simplify114.0ms

Algorithm

egg-herbie

Counts

303 → 303

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	876	4790
1	3710	4642
2	5001	4627

prune713.0ms

Filtered

303 candidates to 200 candidates (66.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	298	5	303
Fresh	6	5	11
Picked	1	0	1
Done	0	0	0
Total	305	10	315

Merged error: 0.0b

Counts

315 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

155×	`add-sqr-sqrt`
112×	`*-un-lft-identity`
80×	`associate-l`
67×	`times-frac`
40×	`add-cube-cbrt`
39×	`unswap-sqr`
36×	`distribute-lft-out--` `difference-of-squares`
22×	`associate-/r*`
17×	`associate-*l/`
13×	`add-exp-log` `add-cbrt-cube`
8×	`pow1` `associate-/r/`
7×	`sin-mult`
6×	`associate-r` `cos-mult` `associate-/l*` `add-log-exp`
3×	`flip3--` `prod-exp` `frac-sub` `flip--` `cbrt-unprod` `sub-div`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `pow-prod-down` `clear-num` `*-commutative` `div-inv`
1×	`sub-neg` `diff-log`

Counts

4 → 180

Calls

4 calls:

18.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
5.0ms	(* (sin a) (sin b))
18.0ms	(/ r (- (* (cos a) (cos b)) (* (sin a) (sin b))))
26.0ms	(* (/ r (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (sin b))

series559.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
47.0ms	(* (sin a) (sin b))
192.0ms	(/ r (- (* (cos a) (cos b)) (* (sin a) (sin b))))
235.0ms	(* (/ r (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (sin b))

simplify65.0ms

Algorithm

egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	518	2196
1	2221	2076
2	5001	2065

prune406.0ms

Filtered

192 candidates to 129 candidates (67.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	191	1	192
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	192	10	202

Merged error: 0.0b

Counts

202 → 10

regimes162.0ms

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	2871×	body	1280	valid
464.0ms	1810×	body	640	valid
142.0ms	791×	body	320	valid
116.0ms	2160×	body	80	valid
47.0ms	368×	body	160	valid