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

sample92.0ms

Algorithm

intervals

Results

47.0ms	88×	body	1280	valid
22.0ms	78×	body	640	valid
4.0ms	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

prune8.0ms

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: 14.9b

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)))
2.7b	(cos (+ a b))

rewrite16.0ms

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

series46.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(* r (/ (sin b) (cos (+ a b))))
12.0ms	(/ (sin b) (cos (+ a b)))
6.0ms	(cos (+ a b))

simplify57.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5018	783

prune123.0ms

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	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	11	77

Merged error: 0.2b

Counts

77 → 11

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

rewrite31.0ms

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))))
4.0ms	(* (sin a) (sin b))

series108.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
50.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
29.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
12.0ms	(* (sin a) (sin b))

simplify54.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5901	1692

prune173.0ms

Filtered

87 candidates to 111 candidates (-27.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	100	11	111
Fresh	8	2	10
Picked	1	0	1
Done	0	0	0
Total	109	13	122

Merged error: 0.0b

Counts

122 → 13

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

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 a) (cos b)) (* (sin a) (sin b)))
7.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
5.0ms	(* (sin a) (sin b))
12.0ms	(* (* (sin b) r) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series106.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
24.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
9.0ms	(* (sin a) (sin b))
56.0ms	(* (* (sin b) r) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify55.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5259	1709

prune153.0ms

Filtered

81 candidates to 121 candidates (-49.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	118	3	121
Fresh	4	8	12
Picked	0	1	1
Done	0	0	0
Total	122	12	134

Merged error: 0.0b

Counts

134 → 12

localize16.0ms

Local error

Found 4 expressions with local error:

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

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 b) (sin a)))
9.0ms	(/ r (- (* (cos a) (cos b)) (* (sin b) (sin a))))
4.0ms	(* (sin b) (sin a))
11.0ms	(* (sin b) (/ r (- (* (cos a) (cos b)) (* (sin b) (sin a)))))

series124.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
44.0ms	(/ r (- (* (cos a) (cos b)) (* (sin b) (sin a))))
9.0ms	(* (sin b) (sin a))
54.0ms	(* (sin b) (/ r (- (* (cos a) (cos b)) (* (sin b) (sin a)))))

simplify54.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5575	1726

prune98.0ms

Filtered

87 candidates to 111 candidates (-27.6%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	110	1	111
Fresh	1	9	10
Picked	0	1	1
Done	0	1	1
Total	111	12	123

Merged error: 0.0b

Counts

123 → 12

regimes374.0ms

Accuracy

0% (0.4b 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 (1.0ms)

Iter	Nodes	Cost
0	44	18
1	44	18

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.5s	3009×	body	1280	valid
547.0ms	1886×	body	640	valid
158.0ms	761×	body	320	valid
147.0ms	2027×	body	80	valid
49.0ms	317×	body	160	valid

Details

analyze1.1s

sample92.0ms

simplify3.0ms

prune8.0ms

localize10.0ms

rewrite16.0ms

series46.0ms

simplify57.0ms

prune123.0ms

localize16.0ms

rewrite31.0ms

series108.0ms

simplify54.0ms

prune173.0ms

localize17.0ms

rewrite32.0ms

series106.0ms

simplify55.0ms

prune153.0ms

localize16.0ms

rewrite32.0ms

series124.0ms

simplify54.0ms

prune98.0ms

regimes374.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.6s

Profiling