Details

sample377.0ms

Algorithm

intervals

Results

48.0ms	96×	body	1280	valid
20.0ms	65×	body	640	valid
5.0ms	72×	body	80	valid
4.0ms	19×	body	320	valid
1.0ms	4×	body	160	valid

simplify34.0ms

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: 16.4b

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)))
3.0b	(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:

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

series160.0ms

Counts

3 → 9

Calls

3 calls:

99.0ms	(* r (/ (sin b) (cos (+ a b))))
37.0ms	(/ (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

prune193.0ms

Filtered

76 candidates to 57 candidates (75.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	66	10	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	10	77

Merged error: 0.2b

Counts

77 → 10

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))))

rewrite33.0ms

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))
9.0ms	(/ (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)))
208.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
45.0ms	(* (sin a) (sin b))
110.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify54.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (44.0ms)

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

prune368.0ms

Filtered

112 candidates to 86 candidates (76.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	99	13	112
Fresh	8	1	9
Picked	1	0	1
Done	0	0	0
Total	108	14	122

Merged error: 0.0b

Counts

122 → 14

localize16.0ms

Local error

Found 4 expressions with local error:

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

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

series374.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* r (sin b))
80.0ms	(- (* (cos a) (cos b)) (* (sin a) (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 (40.0ms)

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

prune248.0ms

Filtered

88 candidates to 63 candidates (71.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	85	3	88
Fresh	5	8	13
Picked	1	0	1
Done	0	0	0
Total	91	11	102

Merged error: 0.0b

Counts

102 → 11

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

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 135

Calls

4 calls:

5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
5.0ms	(* (sin a) (sin b))
8.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
7.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))

series450.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
42.0ms	(* (sin a) (sin b))
110.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
219.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))

simplify74.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	570	2147
1	2453	2011
2	5002	1990

prune416.0ms

Filtered

147 candidates to 119 candidates (81.0%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	146	1	147
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	147	11	158

Merged error: 0.0b

Counts

158 → 11

regimes152.0ms

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	14	10
1	14	10

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.3s	2917×	body	1280	valid
498.0ms	1829×	body	640	valid
139.0ms	720×	body	320	valid
130.0ms	2189×	body	80	valid
48.0ms	345×	body	160	valid

Details

sample377.0ms

simplify34.0ms

prune4.0ms

localize12.0ms

rewrite20.0ms

series160.0ms

simplify40.0ms

prune193.0ms

localize16.0ms

rewrite33.0ms

series442.0ms

simplify54.0ms

prune368.0ms

localize16.0ms

rewrite24.0ms

series374.0ms

simplify48.0ms

prune248.0ms

localize16.0ms

rewrite29.0ms

series450.0ms

simplify74.0ms

prune416.0ms

regimes152.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.3s

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