Details

sample312.0ms

Algorithm

intervals

Results

37.0ms	88×	body	1280	valid
16.0ms	56×	body	640	valid
4.0ms	25×	body	320	valid
4.0ms	73×	body	80	valid
2.0ms	14×	body	160	valid

simplify17.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	8	9
1	12	9
2	15	9
3	19	9
4	20	9
done	20	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.9b

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)))
1.8b	(cos (+ a b))

rewrite32.0ms

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×	`expm1-log1p-u` `associate-l` `associate-/r` `log1p-expm1-u` `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 → 73

Calls

3 calls:

10.0ms	(* r (/ (sin b) (cos (+ a b))))
3.0ms	(/ (sin b) (cos (+ a b)))
7.0ms	(cos (+ a b))

series161.0ms

Counts

3 → 9

Calls

3 calls:

98.0ms	(* r (/ (sin b) (cos (+ a b))))
37.0ms	(/ (sin b) (cos (+ a b)))
25.0ms	(cos (+ a b))

simplify476.0ms

Counts

82 → 82

Iterations

Useful iterations: done (473.0ms)

Iter	Nodes	Cost
0	122	955
1	269	924
2	1033	834
done	5000	831

prune227.0ms

Pruning

8 alts after pruning (8 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	(* 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))

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`
4×	`expm1-log1p-u` `log1p-expm1-u`
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` `fma-neg` `diff-log` `associate-*r/` `prod-diff` `clear-num`

Counts

4 → 110

Calls

4 calls:

5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
25.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
9.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
5.0ms	(* (sin a) (sin b))

series460.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
216.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
112.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
49.0ms	(* (sin a) (sin b))

simplify633.0ms

Counts

122 → 122

Iterations

Useful iterations: 2 (143.0ms)

Iter	Nodes	Cost
0	181	2200
1	448	2141
2	1729	1949
done	5000	1949

prune430.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos b) (cos a)) (* (sin a) (sin b)))
0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b))))
0.2b	(* (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×	`expm1-log1p-u` `associate-/r/` `cos-mult` `log1p-expm1-u`
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` `fma-neg` `diff-log` `prod-diff` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 86

Calls

4 calls:

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

series384.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(- (* (cos b) (cos a)) (* (sin a) (sin b)))
38.0ms	(* r (sin b))
219.0ms	(/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b))))
45.0ms	(* (sin a) (sin b))

simplify506.0ms

Counts

98 → 98

Iterations

Useful iterations: 2 (112.0ms)

Iter	Nodes	Cost
0	152	1364
1	375	1324
2	1491	1174
done	5001	1174

prune339.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite46.0ms

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×	`expm1-log1p-u` `rec-exp` `1-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r/` `*-commutative`
1×	`pow-flip` `associate-*r/` `un-div-inv` `sin-mult` `inv-pow`

Counts

4 → 203

Calls

4 calls:

22.0ms	(* r (/ 1 (/ (fma (cos a) (cos b) (- (* (sin b) (sin a)))) (sin b))))
5.0ms	(/ (fma (cos a) (cos b) (- (* (sin b) (sin a)))) (sin b))
6.0ms	(/ 1 (/ (fma (cos a) (cos b) (- (* (sin b) (sin a)))) (sin b)))
4.0ms	(* (sin b) (sin a))

series515.0ms

Counts

4 → 12

Calls

4 calls:

227.0ms	(* r (/ 1 (/ (fma (cos a) (cos b) (- (* (sin b) (sin a)))) (sin b))))
115.0ms	(/ (fma (cos a) (cos b) (- (* (sin b) (sin a)))) (sin b))
124.0ms	(/ 1 (/ (fma (cos a) (cos b) (- (* (sin b) (sin a)))) (sin b)))
49.0ms	(* (sin b) (sin a))

simplify1.5s

Counts

215 → 215

Iterations

Useful iterations: 2 (266.0ms)

Iter	Nodes	Cost
0	289	4943
1	691	4587
2	2626	4026
done	5000	4026

prune596.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes119.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	16
1	18	16
2	20	16
done	20	16

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.2s	2856×	body	1280	valid
467.0ms	1780×	body	640	valid
152.0ms	808×	body	320	valid
127.0ms	2181×	body	80	valid
49.0ms	375×	body	160	valid