Details

analyze1.1s

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

sample88.0ms

Algorithm

intervals

Results

42.0ms	88×	body	1280	valid
23.0ms	78×	body	640	valid
5.0ms	21×	body	320	valid
4.0ms	56×	body	80	valid
2.0ms	13×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	9
1	20	9

prune11.0ms

Filtered

1 candidates to 1 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: 14.8b

Counts

2 → 2

localize11.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ b a))))
0.2b	(/ (sin b) (cos (+ b a)))
2.7b	(cos (+ b a))

rewrite21.0ms

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:

6.0ms	(* r (/ (sin b) (cos (+ b a))))
4.0ms	(/ (sin b) (cos (+ b a)))
8.0ms	(cos (+ b a))

series41.0ms

Counts

3 → 9

Calls

3 calls:

23.0ms	(* r (/ (sin b) (cos (+ b a))))
11.0ms	(/ (sin b) (cos (+ b a)))
6.0ms	(cos (+ b a))

simplify57.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4966	783
1	4966	783

prune120.0ms

Filtered

60 candidates to 76 candidates (-26.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	65	11	76
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	67	11	78

Merged error: 0.2b

Counts

78 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

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

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 → 99

Calls

4 calls:

5.0ms	(- (* (cos b) (cos a)) (* (sin b) (sin a)))
13.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a)))))
8.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a))))
4.0ms	(* (sin b) (sin a))

series101.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (* (cos b) (cos a)) (* (sin b) (sin a)))
50.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a)))))
27.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a))))
9.0ms	(* (sin b) (sin a))

simplify67.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4927	1675
1	4927	1675

prune178.0ms

Filtered

88 candidates to 111 candidates (-26.1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	100	11	111
Fresh	7	3	10
Picked	1	0	1
Done	0	0	0
Total	108	14	122

Merged error: 0.0b

Counts

122 → 14

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos b) (cos a)) (* (sin b) (sin a)))
0.2b	(/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a))))
0.2b	(* (sin b) (sin a))
0.3b	(* (* (sin b) r) (/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a)))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
20×	`associate-r` `add-cbrt-cube`
18×	`times-frac`
13×	`prod-exp`
12×	`pow1`
8×	`associate-/r/`
7×	`cbrt-unprod` `sin-mult`
6×	`div-exp` `cos-mult` `add-log-exp`
4×	`associate-l` `pow-prod-down`
3×	`cbrt-undiv` `rec-exp` `flip3--` `1-exp` `associate-/r` `frac-sub` `flip--` `associate-/l` `sub-div`
2×	`*-commutative` `div-inv`
1×	`sub-neg` `pow-flip` `frac-2neg` `diff-log` `associate-*r/` `clear-num` `un-div-inv` `inv-pow` `unswap-sqr`

Counts

4 → 109

Calls

4 calls:

5.0ms	(- (* (cos b) (cos a)) (* (sin b) (sin a)))
7.0ms	(/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a))))
4.0ms	(* (sin b) (sin a))
14.0ms	(* (* (sin b) r) (/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a)))))

series101.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (* (cos b) (cos a)) (* (sin b) (sin a)))
25.0ms	(/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a))))
9.0ms	(* (sin b) (sin a))
51.0ms	(* (* (sin b) r) (/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a)))))

simplify65.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4927	1709
1	4927	1709

prune155.0ms

Filtered

76 candidates to 121 candidates (-59.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	118	3	121
Fresh	3	10	13
Picked	1	0	1
Done	0	0	0
Total	122	13	135

Merged error: 0.0b

Counts

135 → 13

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a))))
0.2b	(* r (* (sin b) (/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a))))))
0.2b	(* (sin b) (sin a))
0.3b	(* (sin b) (/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a)))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-exp-log`
32×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
23×	`add-cube-cbrt`
22×	`add-cbrt-cube`
21×	`associate-r`
20×	`times-frac`
14×	`pow1` `prod-exp`
9×	`associate-l`
8×	`associate-/r/` `cbrt-unprod`
6×	`div-exp`
5×	`pow-prod-down` `sin-mult`
4×	`associate-*r/` `cos-mult` `add-log-exp` `unswap-sqr`
3×	`cbrt-undiv` `rec-exp` `1-exp` `associate-/r` `-commutative` `associate-/l*`
2×	`flip3--` `un-div-inv` `frac-sub` `flip--` `div-inv` `sub-div`
1×	`pow-flip` `frac-2neg` `clear-num` `inv-pow`

Counts

4 → 118

Calls

4 calls:

7.0ms	(/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a))))
11.0ms	(* r (* (sin b) (/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a))))))
4.0ms	(* (sin b) (sin a))
12.0ms	(* (sin b) (/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a)))))

series110.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a))))
47.0ms	(* r (* (sin b) (/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a))))))
9.0ms	(* (sin b) (sin a))
29.0ms	(* (sin b) (/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a)))))

simplify55.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	6130	1782

prune100.0ms

Filtered

80 candidates to 130 candidates (-62.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	130	13	143

Merged error: 0.0b

Counts

143 → 13

regimes290.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	44	18
1	44	18

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.5s	3009×	body	1280	valid
574.0ms	1886×	body	640	valid
177.0ms	761×	body	320	valid
146.0ms	2027×	body	80	valid
54.0ms	317×	body	160	valid

Details

analyze1.1s

sample88.0ms

simplify3.0ms

prune11.0ms

localize11.0ms

rewrite21.0ms

series41.0ms

simplify57.0ms

prune120.0ms

localize16.0ms

rewrite33.0ms

series101.0ms

simplify67.0ms

prune178.0ms

localize17.0ms

rewrite33.0ms

series101.0ms

simplify65.0ms

prune155.0ms

localize17.0ms

rewrite38.0ms

series110.0ms

simplify55.0ms

prune100.0ms

regimes290.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.7s

Profiling