Details

sample343.0ms

Algorithm

intervals

Results

44.0ms	90×	body	1280	valid
17.0ms	56×	body	640	valid
8.0ms	74×	body	80	valid
5.0ms	21×	body	320	valid
3.0ms	15×	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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
2.7b	(cos (+ a b))

rewrite31.0ms

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:

9.0ms	(* r (/ (sin b) (cos (+ a b))))
3.0ms	(/ (sin b) (cos (+ a b)))
7.0ms	(cos (+ a b))

series159.0ms

Counts

3 → 9

Calls

3 calls:

97.0ms	(* r (/ (sin b) (cos (+ a b))))
37.0ms	(/ (sin b) (cos (+ a b)))
24.0ms	(cos (+ a b))

simplify41.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (34.0ms)

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

prune197.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
24×	`add-cube-cbrt` `*-un-lft-identity`
23×	`associate-r`
19×	`times-frac`
15×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
9×	`associate-l`
8×	`associate-/r/`
5×	`cos-mult` `sin-mult`
4×	`prod-exp` `cbrt-unprod` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `associate-/r` `-commutative` `associate-/l*`
2×	`cbrt-undiv` `flip3--` `div-exp` `frac-sub` `flip--` `div-inv` `sub-div`
1×	`frac-2neg` `associate-*r/` `clear-num`

Counts

4 → 105

Calls

4 calls:

4.0ms	(* (cos a) (cos b))
4.0ms	(* (sin a) (sin b))
24.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
9.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series408.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (cos a) (cos b))
44.0ms	(* (sin a) (sin b))
212.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
110.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify56.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	428	1219
1	1858	1103
2	5001	1098

prune378.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* r (/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin a) (sin b)) 3)))))
0.2b	(/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin a) (sin b)) 3))))
0.3b	(pow (* (sin a) (sin b)) 3)
29.4b	(cbrt (pow (* (sin a) (sin b)) 3))

rewrite54.0ms

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:

34.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin a) (sin b)) 3)))))
13.0ms	(/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin a) (sin b)) 3))))
3.0ms	(pow (* (sin a) (sin b)) 3)
2.0ms	(cbrt (pow (* (sin a) (sin b)) 3))

series435.0ms

Counts

4 → 12

Calls

4 calls:

212.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin a) (sin b)) 3)))))
110.0ms	(/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin a) (sin b)) 3))))
64.0ms	(pow (* (sin a) (sin b)) 3)
48.0ms	(cbrt (pow (* (sin a) (sin b)) 3))

simplify63.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	439	1400
1	1996	1222
2	5001	1212

prune450.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
0.3b	(* (cbrt (* (sin a) (sin b))) (cbrt (* (* (sin a) (sin b)) (* (sin a) (sin b)))))
7.0b	(cbrt (* (sin a) (sin b)))
28.0b	(cbrt (* (* (sin a) (sin b)) (* (sin a) (sin b))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

45×	`pow1`
21×	`sin-mult`
19×	`pow-prod-down`
18×	`add-exp-log`
16×	`add-cbrt-cube`
14×	`cbrt-div`
9×	`add-sqr-sqrt` `prod-exp` `cbrt-unprod`
7×	`frac-times` `associate-*r/`
6×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
5×	`associate-r` `associate-l` `associate-*l/`
4×	`pow1/3` `pow-sqr` `pow-prod-up` `add-log-exp`
2×	`pow-plus` `*-commutative` `unswap-sqr`
1×	`pow2` `cube-unmult` `swap-sqr`

Counts

4 → 89

Calls

4 calls:

14.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
21.0ms	(* (cbrt (* (sin a) (sin b))) (cbrt (* (* (sin a) (sin b)) (* (sin a) (sin b)))))
2.0ms	(cbrt (* (sin a) (sin b)))
12.0ms	(cbrt (* (* (sin a) (sin b)) (* (sin a) (sin b))))

series304.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
45.0ms	(* (cbrt (* (sin a) (sin b))) (cbrt (* (* (sin a) (sin b)) (* (sin a) (sin b)))))
93.0ms	(cbrt (* (sin a) (sin b)))
110.0ms	(cbrt (* (* (sin a) (sin b)) (* (sin a) (sin b))))

simplify45.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	335	953
1	1422	793
2	5001	757

prune342.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes172.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	19
1	26	19

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.4s	2998×	body	1280	valid
568.0ms	1813×	body	640	valid
164.0ms	735×	body	320	valid
161.0ms	2114×	body	80	valid
56.0ms	340×	body	160	valid