Details

analyze1.2s

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	92×	body	1280	valid
16.0ms	57×	body	640	valid
10.0ms	29×	body	320	valid
4.0ms	67×	body	80	valid
2.0ms	11×	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: 16.4b

Counts

2 → 2

localize10.0ms

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))

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:

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

series43.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(* r (/ (sin b) (cos (+ b a))))
11.0ms	(/ (sin b) (cos (+ b a)))
6.0ms	(cos (+ b a))

simplify60.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5130	783

prune107.0ms

Filtered

60 candidates to 76 candidates (-26.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	67	9	76
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	68	10	78

Merged error: 0.2b

Counts

78 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

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)))
4.0ms	(* (sin b) (sin a))
11.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a)))))
8.0ms	(/ (sin b) (- (* (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)))
9.0ms	(* (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))))

simplify57.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5375	1650

prune178.0ms

Filtered

87 candidates to 111 candidates (-27.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	97	14	111
Fresh	9	0	9
Picked	1	0	1
Done	0	0	0
Total	107	14	121

Merged error: 0.0b

Counts

121 → 14

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* r (/ (sin b) (- (* (cos b) (cos a)) (cbrt (pow (* (sin b) (sin a)) 3)))))
0.2b	(/ (sin b) (- (* (cos b) (cos a)) (cbrt (pow (* (sin b) (sin a)) 3))))
0.3b	(pow (* (sin b) (sin a)) 3)
22.5b	(cbrt (pow (* (sin b) (sin a)) 3))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
16×	`associate-r`
14×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
8×	`cbrt-prod`
6×	`associate-/r/`
4×	`cube-div` `sin-mult` `add-log-exp`
3×	`pow-unpow` `cbrt-div` `associate-l` `prod-exp` `associate-/r` `cbrt-unprod` `associate-/l`
2×	`cbrt-undiv` `cube-mult` `unpow-prod-down` `flip3--` `pow-pow` `unpow3` `cube-prod` `div-exp` `pow-prod-down` `pow-exp` `cos-mult` `frac-sub` `flip--` `div-inv` `rem-cube-cbrt` `unswap-sqr` `sqr-pow`
1×	`pow-to-exp` `frac-2neg` `pow1/3` `associate-r/` `clear-num` `-commutative` `rem-cbrt-cube`

Counts

4 → 106

Calls

4 calls:

12.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (cbrt (pow (* (sin b) (sin a)) 3)))))
10.0ms	(/ (sin b) (- (* (cos b) (cos a)) (cbrt (pow (* (sin b) (sin a)) 3))))
4.0ms	(pow (* (sin b) (sin a)) 3)
3.0ms	(cbrt (pow (* (sin b) (sin a)) 3))

series101.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (cbrt (pow (* (sin b) (sin a)) 3)))))
27.0ms	(/ (sin b) (- (* (cos b) (cos a)) (cbrt (pow (* (sin b) (sin a)) 3))))
18.0ms	(pow (* (sin b) (sin a)) 3)
9.0ms	(cbrt (pow (* (sin b) (sin a)) 3))

simplify51.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5003	1662

prune179.0ms

Filtered

84 candidates to 118 candidates (-40.5%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	114	4	118
Fresh	3	10	13
Picked	0	1	1
Done	0	0	0
Total	117	15	132

Merged error: 0.0b

Counts

132 → 15

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)))))

rewrite30.0ms

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)))
6.0ms	(/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a))))
4.0ms	(* (sin b) (sin a))
12.0ms	(* (* (sin b) r) (/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a)))))

series99.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (* (cos b) (cos a)) (* (sin b) (sin a)))
23.0ms	(/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a))))
9.0ms	(* (sin b) (sin a))
53.0ms	(* (* (sin b) r) (/ 1 (- (* (cos b) (cos a)) (* (sin b) (sin a)))))

simplify58.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5428	1686

prune96.0ms

Filtered

77 candidates to 121 candidates (-57.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	118	3	121
Fresh	4	9	13
Picked	1	0	1
Done	0	1	1
Total	123	13	136

Merged error: 0.0b

Counts

136 → 13

regimes278.0ms

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	18	19
1	18	19

end0.0ms

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

sample2.5s

Algorithm

intervals

Results

1.4s	2952×	body	1280	valid
501.0ms	1790×	body	640	valid
160.0ms	767×	body	320	valid
141.0ms	2168×	body	80	valid
55.0ms	323×	body	160	valid
0.0ms	1×	body	640	invalid

Details

analyze1.2s

sample85.0ms

simplify3.0ms

prune11.0ms

localize10.0ms

rewrite16.0ms

series43.0ms

simplify60.0ms

prune107.0ms

localize15.0ms

rewrite30.0ms

series101.0ms

simplify57.0ms

prune178.0ms

localize18.0ms

rewrite32.0ms

series101.0ms

simplify51.0ms

prune179.0ms

localize17.0ms

rewrite30.0ms

series99.0ms

simplify58.0ms

prune96.0ms

regimes278.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze1.0s

sample2.5s

Profiling