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

sample82.0ms

Algorithm

intervals

Results

40.0ms	84×	body	1280	valid
17.0ms	61×	body	640	valid
6.0ms	29×	body	320	valid
5.0ms	68×	body	80	valid
2.0ms	14×	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

prune16.0ms

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: 14.4b

Counts

2 → 2

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
3.1b	(cos (+ a b))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
5×	`pow1`
3×	`times-frac` `associate-r` `associate-l` `associate-/r*` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
1×	`cos-sum` `frac-2neg` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l` `unswap-sqr`

Counts

3 → 47

Calls

3 calls:

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

series37.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(* r (sin b))
24.0ms	(/ (* r (sin b)) (cos (+ a b)))
6.0ms	(cos (+ a b))

simplify56.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5357	439

prune95.0ms

Filtered

43 candidates to 56 candidates (-30.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	49	7	56
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	50	8	58

Merged error: 0.2b

Counts

58 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* r (sin b))
0.2b	(- (* (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))))

rewrite23.0ms

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

series84.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* r (sin b))
16.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
9.0ms	(* (sin a) (sin b))
51.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify37.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4979	974
1	4979	974

prune144.0ms

Filtered

65 candidates to 87 candidates (-33.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	78	9	87
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	84	11	95

Merged error: 0.0b

Counts

95 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite27.0ms

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

series85.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(- (* (/ (cos b) (sin b)) (cos a)) (sin a))
6.0ms	(/ (cos b) (sin b))
14.0ms	(* (/ (cos b) (sin b)) (cos a))
46.0ms	(/ r (- (* (/ (cos b) (sin b)) (cos a)) (sin a)))

simplify46.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4939	1437
1	4939	1437

prune153.0ms

Filtered

84 candidates to 111 candidates (-32.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	108	3	111
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	111	11	122

Merged error: 0.0b

Counts

122 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos b) (/ (cos a) (sin b))) (sin a))
0.2b	(* (cos b) (/ (cos a) (sin b)))
0.2b	(/ r (- (* (cos b) (/ (cos a) (sin 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-r` `add-cbrt-cube`
6×	`pow1` `associate-/r` `associate-/l` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-l` `div-inv`
2×	`flip3--` `frac-2neg` `prod-exp` `clear-num` `associate-/r/` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `diff-log` `associate-r/` `pow-prod-down` `-commutative`

Counts

4 → 99

Calls

4 calls:

6.0ms	(- (* (cos b) (/ (cos a) (sin b))) (sin a))
7.0ms	(* (cos b) (/ (cos a) (sin b)))
8.0ms	(/ r (- (* (cos b) (/ (cos a) (sin b))) (sin a)))
4.0ms	(/ (cos a) (sin b))

series90.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(- (* (cos b) (/ (cos a) (sin b))) (sin a))
14.0ms	(* (cos b) (/ (cos a) (sin b)))
46.0ms	(/ r (- (* (cos b) (/ (cos a) (sin b))) (sin a)))
10.0ms	(/ (cos a) (sin b))

simplify60.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5144	1445

prune101.0ms

Filtered

88 candidates to 111 candidates (-26.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	110	1	111
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	111	11	122

Merged error: 0.0b

Counts

122 → 11

regimes301.0ms

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	22	13
1	22	13

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.5s	2964×	body	1280	valid
563.0ms	1862×	body	640	valid
157.0ms	736×	body	320	valid
144.0ms	2087×	body	80	valid
54.0ms	351×	body	160	valid
0.0ms	1×	body	1280	invalid
0.0ms	1×	body	640	invalid

Details

analyze1.1s

sample82.0ms

simplify3.0ms

prune16.0ms

localize10.0ms

rewrite14.0ms

series37.0ms

simplify56.0ms

prune95.0ms

localize16.0ms

rewrite23.0ms

series84.0ms

simplify37.0ms

prune144.0ms

localize15.0ms

rewrite27.0ms

series85.0ms

simplify46.0ms

prune153.0ms

localize15.0ms

rewrite28.0ms

series90.0ms

simplify60.0ms

prune101.0ms

regimes301.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.6s

Profiling