Details

sample75.0ms

Algorithm

intervals

Results

41.0ms	99×	body	1280	valid
15.0ms	54×	body	640	valid
4.0ms	75×	body	80	valid
3.0ms	17×	body	320	valid
1.0ms	11×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	5
1	16	5
2	19	5
3	20	5
4	20	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.1b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
4.3b	(cos (+ a b))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
5×	`pow1`
3×	`times-frac` `associate-r` `associate-l` `associate-/r*` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
1×	`cos-sum` `frac-2neg` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l` `unswap-sqr`

Counts

3 → 47

Calls

3 calls:

3.0ms	(* r (sin b))
4.0ms	(/ (* r (sin b)) (cos (+ a b)))
7.0ms	(cos (+ a b))

series157.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(* r (sin b))
96.0ms	(/ (* r (sin b)) (cos (+ a b)))
25.0ms	(cos (+ a b))

simplify34.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	198	305
1	861	257
2	5001	256

prune143.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos a) (cos b))
0.1b	(* r (sin b))
0.2b	(* (sin a) (sin b))
0.3b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

4.0ms	(* (cos a) (cos b))
3.0ms	(* r (sin b))
4.0ms	(* (sin a) (sin b))
9.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series334.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (cos a) (cos b))
37.0ms	(* r (sin b))
45.0ms	(* (sin a) (sin b))
211.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify47.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	367	682
1	1616	594
2	5001	593

prune279.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos b) (cos a))
0.1b	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
0.2b	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))
0.2b	(* (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 b) (cos a))
24.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
8.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))
4.0ms	(* (sin a) (sin b))

series408.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (cos b) (cos a))
213.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
109.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))
46.0ms	(* (sin a) (sin b))

simplify56.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	428	1219
1	1841	1103
2	5001	1098

prune378.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* r (/ 1 (/ (- (* (cos b) (cos a)) (* (sin a) (sin b))) (sin b))))
0.2b	(* (sin a) (sin b))
0.3b	(/ (- (* (cos b) (cos a)) (* (sin a) (sin b))) (sin b))
0.3b	(/ 1 (/ (- (* (cos b) (cos a)) (* (sin a) (sin b))) (sin b)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

156×	`times-frac`
108×	`add-sqr-sqrt`
94×	`*-un-lft-identity`
92×	`add-cube-cbrt`
47×	`associate-r`
38×	`add-exp-log`
22×	`add-cbrt-cube`
16×	`associate-/r*`
15×	`div-exp`
10×	`div-inv`
9×	`pow1`
8×	`prod-exp`
7×	`cbrt-undiv`
6×	`associate-l` `associate-/l*` `unswap-sqr`
4×	`rec-exp` `1-exp` `cbrt-unprod` `associate-/l/` `add-log-exp`
3×	`sin-mult`
2×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r/` `cos-mult` `*-commutative`
1×	`flip3--` `pow-flip` `div-sub` `associate-*r/` `un-div-inv` `frac-sub` `flip--` `inv-pow` `sub-div`

Counts

4 → 200

Calls

4 calls:

26.0ms	(* r (/ 1 (/ (- (* (cos b) (cos a)) (* (sin a) (sin b))) (sin b))))
4.0ms	(* (sin a) (sin b))
10.0ms	(/ (- (* (cos b) (cos a)) (* (sin a) (sin b))) (sin b))
8.0ms	(/ 1 (/ (- (* (cos b) (cos a)) (* (sin a) (sin b))) (sin b)))

series482.0ms

Counts

4 → 12

Calls

4 calls:

222.0ms	(* r (/ 1 (/ (- (* (cos b) (cos a)) (* (sin a) (sin b))) (sin b))))
43.0ms	(* (sin a) (sin b))
104.0ms	(/ (- (* (cos b) (cos a)) (* (sin a) (sin b))) (sin b))
113.0ms	(/ 1 (/ (- (* (cos b) (cos a)) (* (sin a) (sin b))) (sin b)))

simplify91.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	710	3077
1	3595	2769
2	5001	2633

prune548.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes136.0ms

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	19	11
1	19	11

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.2s	2911×	body	1280	valid
493.0ms	1901×	body	640	valid
144.0ms	760×	body	320	valid
120.0ms	2097×	body	80	valid
42.0ms	335×	body	160	valid