Details

sample317.0ms

Algorithm

intervals

Results

36.0ms	87×	body	1280	valid
19.0ms	65×	body	640	valid
4.0ms	72×	body	80	valid
4.0ms	22×	body	320	valid
1.0ms	10×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 18.5b

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)))
3.7b	(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))

series169.0ms

Counts

3 → 9

Calls

3 calls:

96.0ms	(* r (/ (sin b) (cos (+ a b))))
38.0ms	(/ (sin b) (cos (+ a b)))
34.0ms	(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

prune208.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite31.0ms

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)))
11.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
5.0ms	(* (sin a) (sin b))
8.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series451.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
210.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
49.0ms	(* (sin a) (sin b))
111.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify56.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (45.0ms)

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

prune391.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin a) (sin b))
0.2b	(/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin a) (sin b)) 3))))
0.3b	(pow (* (sin a) (sin b)) 3)
25.7b	(cbrt (pow (* (sin a) (sin b)) 3))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
11×	`add-exp-log` `add-cbrt-cube`
9×	`pow1` `times-frac`
8×	`cbrt-prod`
4×	`sin-mult` `add-log-exp`
3×	`cube-div` `pow-unpow` `associate-r` `associate-l` `associate-/r` `associate-/r/` `associate-/l`
2×	`cube-mult` `unpow-prod-down` `cbrt-div` `pow-pow` `unpow3` `cube-prod` `pow-prod-down` `pow-exp` `prod-exp` `cbrt-unprod` `rem-cube-cbrt` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `flip3--` `frac-2neg` `pow1/3` `div-exp` `clear-num` `cos-mult` `*-commutative` `frac-sub` `flip--` `rem-cbrt-cube` `div-inv` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

5.0ms	(* (sin a) (sin b))
10.0ms	(/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin a) (sin b)) 3))))
5.0ms	(pow (* (sin a) (sin b)) 3)
3.0ms	(cbrt (pow (* (sin a) (sin b)) 3))

series264.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (sin a) (sin b))
112.0ms	(/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin a) (sin b)) 3))))
61.0ms	(pow (* (sin a) (sin b)) 3)
47.0ms	(cbrt (pow (* (sin a) (sin b)) 3))

simplify50.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	338	899
1	1422	821
2	5001	809

prune383.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite44.0ms

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:

16.0ms	(* r (/ 1 (/ (- (* (cos b) (cos a)) (* (sin a) (sin b))) (sin b))))
5.0ms	(* (sin a) (sin b))
8.0ms	(/ (- (* (cos b) (cos a)) (* (sin a) (sin b))) (sin b))
7.0ms	(/ 1 (/ (- (* (cos b) (cos a)) (* (sin a) (sin b))) (sin b)))

series471.0ms

Counts

4 → 12

Calls

4 calls:

213.0ms	(* r (/ 1 (/ (- (* (cos b) (cos a)) (* (sin a) (sin b))) (sin b))))
42.0ms	(* (sin a) (sin b))
103.0ms	(/ (- (* (cos b) (cos a)) (* (sin a) (sin b))) (sin b))
112.0ms	(/ 1 (/ (- (* (cos b) (cos a)) (* (sin a) (sin b))) (sin b)))

simplify94.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	710	3076
1	3564	2768
2	5001	2632

prune554.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes172.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	13
1	21	13

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.3s	2935×	body	1280	valid
463.0ms	1835×	body	640	valid
131.0ms	748×	body	320	valid
125.0ms	2144×	body	80	valid
48.0ms	342×	body	160	valid