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

sample88.0ms

Algorithm

intervals

Results

50.0ms	97×	body	1280	valid
17.0ms	62×	body	640	valid
5.0ms	25×	body	320	valid
5.0ms	67×	body	80	valid
1.0ms	5×	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

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: 14.4b

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))

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))

series40.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify61.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5018	783

prune100.0ms

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

localize17.0ms

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))
0.3b	(/ (sin b) (- (* (cos a) (cos b)) (* (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)))))
5.0ms	(* (sin a) (sin b))
8.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series103.0ms

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

simplify55.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5901	1692

prune160.0ms

Filtered

90 candidates to 111 candidates (-23.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	100	11	111
Fresh	6	0	6
Picked	1	0	1
Done	0	0	0
Total	107	11	118

Merged error: 0.0b

Counts

118 → 11

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos a) (cos b)) (log (pow (exp (sin a)) (sin b))))
0.2b	(* r (/ (sin b) (- (* (cos a) (cos b)) (log (pow (exp (sin a)) (sin b))))))
0.3b	(/ (sin b) (- (* (cos a) (cos b)) (log (pow (exp (sin a)) (sin b)))))
2.6b	(log (pow (exp (sin a)) (sin b)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
24×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
15×	`associate-r`
14×	`log-prod`
12×	`add-exp-log`
11×	`add-cbrt-cube`
7×	`associate--r+`
6×	`pow1` `unpow-prod-down`
5×	`add-log-exp`
4×	`associate-/r/`
3×	`flip3--` `rem-log-exp` `associate-l` `associate-/r` `flip--` `associate-/l`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `frac-2neg` `diff-log` `associate-r/` `pow-prod-down` `pow-exp` `clear-num` `log-pow` `-commutative`

Counts

4 → 99

Calls

4 calls:

7.0ms	(- (* (cos a) (cos b)) (log (pow (exp (sin a)) (sin b))))
10.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (log (pow (exp (sin a)) (sin b))))))
8.0ms	(/ (sin b) (- (* (cos a) (cos b)) (log (pow (exp (sin a)) (sin b)))))
5.0ms	(log (pow (exp (sin a)) (sin b)))

series145.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(- (* (cos a) (cos b)) (log (pow (exp (sin a)) (sin b))))
60.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (log (pow (exp (sin a)) (sin b))))))
38.0ms	(/ (sin b) (- (* (cos a) (cos b)) (log (pow (exp (sin a)) (sin b)))))
21.0ms	(log (pow (exp (sin a)) (sin b)))

simplify56.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4946	1765
1	4946	1765

prune137.0ms

Filtered

84 candidates to 111 candidates (-32.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	110	1	111
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	112	10	122

Merged error: 0.0b

Counts

122 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (/ (cos a) (sin b)) (cos b)) (sin a))
0.2b	(/ (cos a) (sin b))
0.2b	(* (/ (cos a) (sin b)) (cos b))
0.2b	(/ r (- (* (/ (cos a) (sin b)) (cos b)) (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 a) (sin b)) (cos b)) (sin a))
4.0ms	(/ (cos a) (sin b))
6.0ms	(* (/ (cos a) (sin b)) (cos b))
8.0ms	(/ r (- (* (/ (cos a) (sin b)) (cos b)) (sin a)))

series89.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(- (* (/ (cos a) (sin b)) (cos b)) (sin a))
10.0ms	(/ (cos a) (sin b))
15.0ms	(* (/ (cos a) (sin b)) (cos b))
45.0ms	(/ r (- (* (/ (cos a) (sin b)) (cos b)) (sin a)))

simplify48.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4937	1443
1	4937	1443

prune105.0ms

Filtered

88 candidates to 111 candidates (-26.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	109	2	111
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	110	11	121

Merged error: 0.0b

Counts

121 → 11

regimes246.0ms

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 (0.0ms)

Iter	Nodes	Cost
0	22	13
1	22	13

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.4s	2914×	body	1280	valid
519.0ms	1822×	body	640	valid
158.0ms	801×	body	320	valid
141.0ms	2150×	body	80	valid
47.0ms	313×	body	160	valid
0.0ms	1×	body	1280	invalid

Details

analyze1.0s

sample88.0ms

simplify3.0ms

prune7.0ms

localize10.0ms

rewrite16.0ms

series40.0ms

simplify61.0ms

prune100.0ms

localize17.0ms

rewrite32.0ms

series103.0ms

simplify55.0ms

prune160.0ms

localize20.0ms

rewrite34.0ms

series145.0ms

simplify56.0ms

prune137.0ms

localize14.0ms

rewrite27.0ms

series89.0ms

simplify48.0ms

prune105.0ms

regimes246.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.5s

Profiling