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

sample85.0ms

Algorithm

intervals

Results

41.0ms	85×	body	1280	valid
15.0ms	55×	body	640	valid
5.0ms	26×	body	320	valid
5.0ms	74×	body	80	valid
2.0ms	16×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	20	9
1	20	9

prune20.0ms

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: 15.9b

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)))
3.1b	(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))

series43.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(* r (/ (sin b) (cos (+ a b))))
12.0ms	(/ (sin b) (cos (+ a b)))
6.0ms	(cos (+ a b))

simplify58.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5018	783

prune107.0ms

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

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))))

rewrite34.0ms

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)))))
6.0ms	(* (sin a) (sin b))
8.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series108.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
53.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
9.0ms	(* (sin a) (sin b))
29.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify54.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5901	1692

prune179.0ms

Filtered

90 candidates to 111 candidates (-23.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	101	10	111
Fresh	6	0	6
Picked	1	0	1
Done	0	0	0
Total	108	10	118

Merged error: 0.0b

Counts

118 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin b) r)
0.1b	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.2b	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.2b	(* (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 → 75

Calls

4 calls:

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

series90.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* (sin b) r)
19.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
55.0ms	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
9.0ms	(* (sin a) (sin b))

simplify37.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4996	1008
1	4996	1008

prune128.0ms

Filtered

64 candidates to 87 candidates (-35.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	86	1	87
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	86	11	97

Merged error: 0.0b

Counts

97 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* (/ (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))

rewrite28.0ms

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))
7.0ms	(* (/ (cos a) (sin b)) (cos b))
8.0ms	(/ r (- (* (/ (cos a) (sin b)) (cos b)) (sin a)))
4.0ms	(/ (cos a) (sin b))

series96.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(- (* (/ (cos a) (sin b)) (cos b)) (sin a))
17.0ms	(* (/ (cos a) (sin b)) (cos b))
49.0ms	(/ r (- (* (/ (cos a) (sin b)) (cos b)) (sin a)))
11.0ms	(/ (cos a) (sin b))

simplify46.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4937	1443
1	4937	1443

prune108.0ms

Filtered

88 candidates to 111 candidates (-26.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	109	2	111
Fresh	3	6	9
Picked	0	1	1
Done	0	1	1
Total	112	10	122

Merged error: 0.0b

Counts

122 → 10

regimes259.0ms

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 (1.0ms)

Iter	Nodes	Cost
0	41	16
1	41	16

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.5s	2830×	body	1280	valid
535.0ms	1851×	body	640	valid
169.0ms	779×	body	320	valid
151.0ms	2182×	body	80	valid
56.0ms	358×	body	160	valid
0.0ms	1×	body	1280	invalid

Details

analyze1.0s

sample85.0ms

simplify4.0ms

prune20.0ms

localize10.0ms

rewrite17.0ms

series43.0ms

simplify58.0ms

prune107.0ms

localize16.0ms

rewrite34.0ms

series108.0ms

simplify54.0ms

prune179.0ms

localize18.0ms

rewrite24.0ms

series90.0ms

simplify37.0ms

prune128.0ms

localize15.0ms

rewrite28.0ms

series96.0ms

simplify46.0ms

prune108.0ms

regimes259.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.6s

Profiling