Details

sample315.0ms

Algorithm

intervals

Results

38.0ms	84×	body	1280	valid
14.0ms	56×	body	640	valid
5.0ms	29×	body	320	valid
4.0ms	76×	body	80	valid
1.0ms	11×	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: 16.7b

localize13.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
5.5b	(cos (+ a b))

rewrite52.0ms

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:

27.0ms	(* r (/ (sin b) (cos (+ a b))))
10.0ms	(/ (sin b) (cos (+ a b)))
12.0ms	(cos (+ a b))

series143.0ms

Counts

3 → 9

Calls

3 calls:

87.0ms	(* r (/ (sin b) (cos (+ a b))))
34.0ms	(/ (sin b) (cos (+ a b)))
22.0ms	(cos (+ a b))

simplify39.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (33.0ms)

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

prune291.0ms

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)) (* (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))))
0.2b	(* (sin a) (sin b))

rewrite137.0ms

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:

19.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
74.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
26.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
15.0ms	(* (sin a) (sin b))

series408.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
194.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
101.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
39.0ms	(* (sin a) (sin b))

simplify53.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (43.0ms)

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

prune737.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

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

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-exp-log`
23×	`associate-r`
20×	`add-cbrt-cube`
19×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
14×	`prod-exp`
13×	`pow1`
9×	`times-frac`
8×	`cbrt-unprod`
7×	`associate-l`
6×	`add-log-exp`
5×	`pow-prod-down` `sin-mult`
4×	`div-exp` `associate-/r/` `cos-mult`
3×	`*-commutative`
2×	`cbrt-undiv` `rec-exp` `flip3--` `1-exp` `frac-sub` `flip--` `sub-div` `unswap-sqr`
1×	`sub-neg` `diff-log` `associate-*r/` `un-div-inv` `div-inv`

Counts

4 → 93

Calls

4 calls:

9.0ms	(* r (sin b))
19.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
12.0ms	(* (sin a) (sin b))
73.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series347.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* r (sin b))
74.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
39.0ms	(* (sin a) (sin b))
195.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify62.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	480	986
1	2365	829
2	5003	816

prune568.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin a) (sin b))
0.3b	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
0.3b	(/ (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))
0.4b	(* (* (cos a) (cos b)) (* (cos a) (cos b)))

rewrite240.0ms

Algorithm

rewrite-expression-head

Rules

84×	`pow1`
35×	`pow-prod-down`
32×	`add-exp-log` `add-cbrt-cube`
24×	`sin-mult`
23×	`cos-mult`
17×	`add-sqr-sqrt` `prod-exp` `cbrt-unprod`
16×	`associate-/l/`
15×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac` `associate-r/` `associate-l/`
10×	`frac-times`
9×	`frac-sub`
8×	`pow-sqr` `pow-prod-up`
5×	`associate-r` `associate-l` `sub-div`
4×	`pow-plus` `associate-/l*` `add-log-exp` `difference-of-squares`
3×	`associate-/r` `associate-/r/` `-commutative`
2×	`pow2` `swap-sqr`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `flip3-+` `div-sub` `div-exp` `frac-add` `clear-num` `flip--` `flip-+` `div-inv` `unswap-sqr`

Counts

4 → 144

Calls

4 calls:

13.0ms	(* (sin a) (sin b))
46.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
135.0ms	(/ (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))
41.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))

series324.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (sin a) (sin b))
51.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
186.0ms	(/ (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))
48.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))

simplify90.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	559	1889
1	3034	1639
2	5002	1629

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes460.0ms

Accuracy

0% (0.4b 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	28	36
1	28	36

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.3s	2915×	body	1280	valid
487.0ms	1880×	body	640	valid
140.0ms	755×	body	320	valid
119.0ms	2121×	body	80	valid
48.0ms	330×	body	160	valid