Details

analyze1.0s

Algorithm: search

sample83.0ms

Algorithm

intervals

Results

45.0ms	95×	body	1280	valid
16.0ms	58×	body	640	valid
5.0ms	76×	body	80	valid
5.0ms	22×	body	320	valid
1.0ms	5×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	5
1	16	5
2	20	5
3	21	5
4	21	5

prune4.0ms

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: 16.2b

Counts

2 → 1

localize14.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
2.8b	(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)))
5.0ms	(cos (+ a b))

simplify36.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	252	536
1	1064	480
2	5001	477

prune106.0ms

Filtered

57 candidates to 76 candidates (-33.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	68	8	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	8	77

Merged error: 0.1b

Counts

77 → 8

localize15.0ms

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

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 → 100

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

series102.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
50.0ms	(* 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))))

simplify54.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	405	1307
1	1761	1182
2	5001	1173

prune163.0ms

Filtered

86 candidates to 112 candidates (-30.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	103	9	112
Fresh	6	1	7
Picked	1	0	1
Done	0	0	0
Total	110	10	120

Merged error: 0.0b

Counts

120 → 10

localize16.0ms

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

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 → 110

Calls

4 calls:

5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
6.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
5.0ms	(* (sin a) (sin b))
14.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series97.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
25.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
9.0ms	(* (sin a) (sin b))
48.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify62.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	483	1379
1	2301	1192
2	5001	1164

prune132.0ms

Filtered

75 candidates to 122 candidates (-62.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	121	1	122
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	121	11	132

Merged error: 0b

Counts

132 → 11

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
0.3b	(pow (* (sin a) (sin b)) 3)
0.4b	(* (* (cos a) (cos b)) (* (cos a) (cos b)))
0.5b	(pow (* (cos a) (cos b)) 3)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

88×	`pow1`
36×	`pow-prod-down`
34×	`add-exp-log` `add-cbrt-cube`
18×	`prod-exp` `cbrt-unprod`
8×	`pow-sqr` `pow-prod-up`
6×	`add-sqr-sqrt` `add-cube-cbrt` `pow-unpow` `*-un-lft-identity`
5×	`cos-mult` `sin-mult`
4×	`pow-pow` `pow-plus` `pow-exp` `add-log-exp` `rem-cube-cbrt`
2×	`cube-div` `pow2` `cube-mult` `frac-times` `pow-to-exp` `unpow-prod-down` `unpow3` `cube-prod` `associate-r/` `swap-sqr` `associate-r` `associate-l` `associate-l/` `*-commutative` `sqr-pow`

Counts

4 → 120

Calls

4 calls:

9.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
5.0ms	(pow (* (sin a) (sin b)) 3)
8.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))
4.0ms	(pow (* (cos a) (cos b)) 3)

series57.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
15.0ms	(pow (* (sin a) (sin b)) 3)
12.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))
15.0ms	(pow (* (cos a) (cos b)) 3)

simplify72.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	450	568
1	2270	531
2	5001	531

prune119.0ms

Filtered

62 candidates to 132 candidates (-112.9%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	132	11	143

Merged error: 0b

Counts

143 → 11

regimes249.0ms

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	20	11
1	20	11

end0.0ms

analyze1.0s

Algorithm: search

sample2.5s

Algorithm

intervals

Results

1.4s	2869×	body	1280	valid
547.0ms	1841×	body	640	valid
161.0ms	755×	body	320	valid
144.0ms	2175×	body	80	valid
59.0ms	360×	body	160	valid

Details

analyze1.0s

sample83.0ms

simplify6.0ms

prune4.0ms

localize14.0ms

rewrite16.0ms

series40.0ms

simplify36.0ms

prune106.0ms

localize15.0ms

rewrite33.0ms

series102.0ms

simplify54.0ms

prune163.0ms

localize16.0ms

rewrite33.0ms

series97.0ms

simplify62.0ms

prune132.0ms

localize30.0ms

rewrite30.0ms

series57.0ms

simplify72.0ms

prune119.0ms

regimes249.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze1.0s

sample2.5s

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