Details

sample295.0ms

Algorithm

intervals

Results

100.0ms	100×	body	1280	valid
71.0ms	14×	body	160	valid
31.0ms	53×	body	640	valid
12.0ms	27×	body	320	valid
8.0ms	62×	body	80	valid

simplify35.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	8	9
1	12	9
2	16	9
3	20	9
4	21	9
done	21	9

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.9b

localize27.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
2.2b	(cos (+ a b))

rewrite96.0ms

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:

48.0ms	(* r (/ (sin b) (cos (+ a b))))
19.0ms	(/ (sin b) (cos (+ a b)))
24.0ms	(cos (+ a b))

series227.0ms

Counts

3 → 9

Calls

3 calls:

145.0ms	(* r (/ (sin b) (cos (+ a b))))
55.0ms	(/ (sin b) (cos (+ a b)))
27.0ms	(cos (+ a b))

simplify729.0ms

Counts

82 → 82

Iterations

Useful iterations: done (725.0ms)

Iter	Nodes	Cost
0	122	955
1	283	928
2	1071	842
done	5000	836

prune293.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite218.0ms

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:

27.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
25.0ms	(* (sin b) (sin a))
133.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
29.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a))))

series715.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
83.0ms	(* (sin b) (sin a))
333.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
176.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a))))

simplify2.0s

Counts

122 → 122

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	187	2200
1	467	2145
2	2138	1957
done	5001	1870

prune726.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

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

rewrite115.0ms

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:

10.0ms	(* r (sin b))
39.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
46.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
18.0ms	(* (sin b) (sin a))

series590.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* r (sin b))
121.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
333.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
70.0ms	(* (sin b) (sin a))

simplify1.2s

Counts

98 → 98

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	157	1364
1	396	1324
2	2010	1182
done	5000	1174

prune475.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
24×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
16×	`associate-r`
13×	`add-exp-log` `associate-l` `add-cbrt-cube`
8×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `prod-exp` `associate-/r` `cbrt-unprod` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`distribute-lft-neg-out` `neg-mul-1` `frac-2neg` `associate-*r/` `clear-num` `fma-udef`

Counts

4 → 101

Calls

4 calls:

0.0ms	(fma (cos a) (cos b) (* (- (sin a)) (sin b)))
17.0ms	(* (- (sin a)) (sin b))
15.0ms	(* r (/ (sin b) (fma (cos a) (cos b) (* (- (sin a)) (sin b)))))
15.0ms	(/ (sin b) (fma (cos a) (cos b) (* (- (sin a)) (sin b))))

series781.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(fma (cos a) (cos b) (* (- (sin a)) (sin b)))
96.0ms	(* (- (sin a)) (sin b))
336.0ms	(* r (/ (sin b) (fma (cos a) (cos b) (* (- (sin a)) (sin b)))))
212.0ms	(/ (sin b) (fma (cos a) (cos b) (* (- (sin a)) (sin b))))

simplify1.1s

Counts

113 → 113

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	159	1900
1	382	1865
2	1695	1671
done	5000	1669

prune738.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes257.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify15.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	18
1	21	18
2	25	18
3	26	18
done	26	18

end0.0ms

sample5.7s

Algorithm

intervals

Results

3.5s	2983×	body	1280	valid
1.1s	1826×	body	640	valid
332.0ms	2093×	body	80	valid
228.0ms	738×	body	320	valid
121.0ms	360×	body	160	valid