Details

sample309.0ms

Algorithm

intervals

Results

36.0ms	89×	body	1280	valid
16.0ms	57×	body	640	valid
5.0ms	84×	body	80	valid
3.0ms	18×	body	320	valid
1.0ms	8×	body	160	valid

simplify11.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
3.2b	(cos (+ a b))

rewrite21.0ms

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 (+ a b))))
5.0ms	(/ (sin b) (cos (+ a b)))
6.0ms	(cos (+ a b))

series168.0ms

Counts

3 → 9

Calls

3 calls:

96.0ms	(* r (/ (sin b) (cos (+ a b))))
37.0ms	(/ (sin b) (cos (+ a b)))
36.0ms	(cos (+ a b))

simplify40.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (33.0ms)

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

prune200.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

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

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:

12.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
8.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
5.0ms	(* (sin a) (sin b))

series451.0ms

Counts

4 → 12

Calls

4 calls:

212.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
81.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
109.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
48.0ms	(* (sin a) (sin b))

simplify55.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (44.0ms)

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

prune376.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* r (sin b))
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))

rewrite24.0ms

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 → 76

Calls

4 calls:

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

series381.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* r (sin b))
82.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
214.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
47.0ms	(* (sin a) (sin b))

simplify45.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	344	770
1	1513	673
2	5001	663

prune275.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin a) (sin b))
0.2b	(* (sin a) (sin b))
0.3b	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
0.4b	(* (* (cos a) (cos b)) (* (cos a) (cos b)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

86×	`pow1`
36×	`pow-prod-down`
32×	`add-exp-log` `add-cbrt-cube`
18×	`prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `-un-lft-identity` `associate-r` `associate-l*` `pow-sqr` `pow-prod-up`
6×	`sin-mult`
4×	`pow-plus` `cos-mult` `*-commutative` `add-log-exp`
2×	`pow2` `frac-times` `associate-r/` `swap-sqr` `associate-l/` `unswap-sqr`

Counts

4 → 112

Calls

4 calls:

5.0ms	(* (sin a) (sin b))
5.0ms	(* (sin a) (sin b))
9.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
11.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))

series198.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (sin a) (sin b))
44.0ms	(* (sin a) (sin b))
55.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
54.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))

simplify45.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	313	685
1	1434	524
2	5002	504

prune269.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

regimes169.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	10
1	15	10

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.2s	2870×	body	1280	valid
474.0ms	1886×	body	640	valid
139.0ms	749×	body	320	valid
120.0ms	2149×	body	80	valid
44.0ms	349×	body	160	valid