Details

sample340.0ms

Algorithm

intervals

Results

55.0ms	108×	body	1280	valid
15.0ms	51×	body	640	valid
6.0ms	73×	body	80	valid
4.0ms	17×	body	320	valid
1.0ms	7×	body	160	valid

simplify12.0ms

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: 15.0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (sin b) (cos (+ a b)))
0.2b	(* r (/ (sin b) (cos (+ a b))))
3.7b	(cos (+ a b))

rewrite33.0ms

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:

4.0ms	(/ (sin b) (cos (+ a b)))
9.0ms	(* r (/ (sin b) (cos (+ a b))))
7.0ms	(cos (+ a b))

series157.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(/ (sin b) (cos (+ a b)))
97.0ms	(* r (/ (sin b) (cos (+ a b))))
23.0ms	(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

prune193.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite47.0ms

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)))
4.0ms	(* (sin a) (sin b))
9.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
26.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series445.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
43.0ms	(* (sin a) (sin b))
109.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
213.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify58.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	405	1307
1	1761	1182
2	5002	1173

prune358.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin a) (sin b)) 3))))
0.2b	(* r (/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin a) (sin b)) 3)))))
0.3b	(pow (* (sin a) (sin b)) 3)
26.0b	(cbrt (pow (* (sin a) (sin b)) 3))

rewrite59.0ms

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:

15.0ms	(/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin a) (sin b)) 3))))
35.0ms	(* r (/ (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))

series425.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin a) (sin b)) 3))))
208.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin a) (sin b)) 3)))))
64.0ms	(pow (* (sin a) (sin b)) 3)
44.0ms	(cbrt (pow (* (sin a) (sin b)) 3))

simplify65.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (51.0ms)

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

prune436.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

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:

5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
4.0ms	(* r (sin b))
4.0ms	(* (sin a) (sin b))
10.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series388.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
42.0ms	(* r (sin b))
44.0ms	(* (sin a) (sin b))
219.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify47.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	344	770
1	1513	673
2	5002	663

prune245.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes144.0ms

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	18	12
1	18	12

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.5s	2944×	body	1280	valid
550.0ms	1795×	body	640	valid
201.0ms	2175×	body	80	valid
170.0ms	742×	body	320	valid
62.0ms	345×	body	160	valid