Details

analyze1.0s

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
6.2%	93.6%	0.1%	7
9.4%	90.5%	0.1%	8
14%	85.8%	0.1%	9
19.5%	80.4%	0.1%	10
20.7%	79.2%	0.1%	11
22%	77.8%	0.1%	12
23.5%	76.4%	0.1%	13
23.8%	76%	0.1%	14

sample95.0ms

Algorithm

intervals

Results

57.0ms	121×	body	1280	valid
12.0ms	42×	body	640	valid
7.0ms	14×	body	160	valid
5.0ms	23×	body	320	valid
4.0ms	56×	body	80	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	9
1	20	9

prune7.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 15.8b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
2.0b	(cos (+ a b))

rewrite17.0ms

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)))
4.0ms	(cos (+ a b))

series41.0ms

Counts

3 → 9

Calls

3 calls:

23.0ms	(* r (/ (sin b) (cos (+ a b))))
12.0ms	(/ (sin b) (cos (+ a b)))
6.0ms	(cos (+ a b))

simplify62.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5018	783

prune105.0ms

Filtered

60 candidates to 76 candidates (-26.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	69	7	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	7	77

Merged error: 0.2b

Counts

77 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.1b	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
0.2b	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.2b	(* (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 → 99

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

series104.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
51.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
28.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
9.0ms	(* (sin a) (sin b))

simplify57.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5901	1692

prune166.0ms

Filtered

87 candidates to 111 candidates (-27.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	101	10	111
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	106	12	118

Merged error: 0b

Counts

118 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
28×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
13×	`add-exp-log` `associate-l` `add-cbrt-cube`
6×	`pow1` `associate-/r` `associate-/l` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-r` `div-inv`
2×	`flip3--` `frac-2neg` `prod-exp` `clear-num` `associate-/r/` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `diff-log` `pow-prod-down` `associate-l/` `-commutative`

Counts

4 → 99

Calls

4 calls:

6.0ms	(- (* (/ (cos a) (sin b)) (cos b)) (sin a))
6.0ms	(* (/ (cos a) (sin b)) (cos b))
10.0ms	(/ r (- (* (/ (cos a) (sin b)) (cos b)) (sin a)))
4.0ms	(/ (cos a) (sin b))

series92.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(- (* (/ (cos a) (sin b)) (cos b)) (sin a))
18.0ms	(* (/ (cos a) (sin b)) (cos b))
45.0ms	(/ r (- (* (/ (cos a) (sin b)) (cos b)) (sin a)))
10.0ms	(/ (cos a) (sin b))

simplify49.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4937	1443
1	4937	1443

prune148.0ms

Filtered

88 candidates to 111 candidates (-26.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	108	3	111
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	112	11	123

Merged error: 0b

Counts

123 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin b) (cos a))
0.2b	(* (/ 1 (/ (sin b) (cos a))) (cos b))
0.2b	(/ 1 (/ (sin b) (cos a)))
0.2b	(/ r (- (* (/ 1 (/ (sin b) (cos a))) (cos b)) (sin a)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

165×	`times-frac`
112×	`add-sqr-sqrt`
100×	`*-un-lft-identity`
98×	`add-cube-cbrt`
44×	`associate-l`
38×	`add-exp-log`
22×	`add-cbrt-cube`
19×	`associate-/r*`
16×	`div-exp`
11×	`div-inv`
9×	`associate-/l*`
8×	`cbrt-undiv`
7×	`pow1` `prod-exp`
5×	`unswap-sqr`
4×	`rec-exp` `1-exp` `associate-/r/` `add-log-exp`
3×	`frac-2neg` `associate-r` `clear-num` `cbrt-unprod`
1×	`flip3--` `pow-flip` `pow-prod-down` `associate-l/` `-commutative` `flip--` `inv-pow`

Counts

4 → 204

Calls

4 calls:

4.0ms	(/ (sin b) (cos a))
12.0ms	(* (/ 1 (/ (sin b) (cos a))) (cos b))
6.0ms	(/ 1 (/ (sin b) (cos a)))
12.0ms	(/ r (- (* (/ 1 (/ (sin b) (cos a))) (cos b)) (sin a)))

series81.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ (sin b) (cos a))
14.0ms	(* (/ 1 (/ (sin b) (cos a))) (cos b))
10.0ms	(/ 1 (/ (sin b) (cos a)))
47.0ms	(/ r (- (* (/ 1 (/ (sin b) (cos a))) (cos b)) (sin a)))

simplify64.0ms

Algorithm

egg-herbie

Counts

216 → 216

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4969	2538
1	4969	2538

prune184.0ms

Filtered

154 candidates to 216 candidates (-40.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	215	1	216
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	217	10	227

Merged error: 0b

Counts

227 → 10

regimes314.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	13
1	21	13

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.6s	3035×	body	1280	valid
522.0ms	1813×	body	640	valid
150.0ms	732×	body	320	valid
135.0ms	2069×	body	80	valid
51.0ms	351×	body	160	valid

Details

analyze1.0s

sample95.0ms

simplify3.0ms

prune7.0ms

localize10.0ms

rewrite17.0ms

series41.0ms

simplify62.0ms

prune105.0ms

localize18.0ms

rewrite32.0ms

series104.0ms

simplify57.0ms

prune166.0ms

localize15.0ms

rewrite30.0ms

series92.0ms

simplify49.0ms

prune148.0ms

localize19.0ms

rewrite44.0ms

series81.0ms

simplify64.0ms

prune184.0ms

regimes314.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.7s

Profiling