Details

sample312.0ms

Algorithm

intervals

Results

40.0ms	96×	body	1280	valid
17.0ms	62×	body	640	valid
4.0ms	23×	body	320	valid
3.0ms	62×	body	80	valid
2.0ms	13×	body	160	valid

simplify18.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.7b

localize12.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
4.1b	(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:

9.0ms	(* r (/ (sin b) (cos (+ a b))))
3.0ms	(/ (sin b) (cos (+ a b)))
6.0ms	(cos (+ a b))

series161.0ms

Counts

3 → 9

Calls

3 calls:

97.0ms	(* r (/ (sin b) (cos (+ a b))))
38.0ms	(/ (sin b) (cos (+ a b)))
25.0ms	(cos (+ a b))

simplify2.1s

Counts

82 → 82

Iterations

Useful iterations: 3 (434.0ms)

Iter	Nodes	Cost
0	122	955
1	264	924
2	675	834
3	2085	830
done	5000	830

prune229.0ms

Pruning

7 alts after pruning (7 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	(/ (sin b) (- (* (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))

rewrite45.0ms

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

series467.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
116.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
219.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
49.0ms	(* (sin a) (sin b))

simplify2.1s

Counts

122 → 122

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	181	2200
1	429	2141
2	1252	1949
3	4078	1826
done	5000	1825

prune432.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
16×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
8×	`pow1`
6×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`prod-exp` `associate-/r` `cbrt-unprod` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`frac-2neg` `associate-*r/` `clear-num` `fma-udef` `sin-mult`

Counts

4 → 94

Calls

4 calls:

0.0ms	(fma (cos a) (cos b) (- (* (sin b) (sin a))))
3.0ms	(/ (sin b) (fma (cos a) (cos b) (- (* (sin b) (sin a)))))
7.0ms	(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin b) (sin a))))))
4.0ms	(* (sin b) (sin a))

series465.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(fma (cos a) (cos b) (- (* (sin b) (sin a))))
115.0ms	(/ (sin b) (fma (cos a) (cos b) (- (* (sin b) (sin a)))))
219.0ms	(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin b) (sin a))))))
48.0ms	(* (sin b) (sin a))

simplify1.9s

Counts

106 → 106

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	154	1831
1	330	1797
2	939	1607
3	3297	1599
done	5001	1598

prune382.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
16×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
8×	`pow1`
6×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`prod-exp` `associate-/r` `cbrt-unprod` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`frac-2neg` `associate-*r/` `clear-num` `cos-mult` `fma-udef`

Counts

4 → 94

Calls

4 calls:

3.0ms	(* (cos a) (cos b))
0.0ms	(fma (sin b) (- (sin a)) (* (cos a) (cos b)))
3.0ms	(/ (sin b) (fma (sin b) (- (sin a)) (* (cos a) (cos b))))
7.0ms	(* r (/ (sin b) (fma (sin b) (- (sin a)) (* (cos a) (cos b)))))

series466.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (cos a) (cos b))
86.0ms	(fma (sin b) (- (sin a)) (* (cos a) (cos b)))
115.0ms	(/ (sin b) (fma (sin b) (- (sin a)) (* (cos a) (cos b))))
220.0ms	(* r (/ (sin b) (fma (sin b) (- (sin a)) (* (cos a) (cos b)))))

simplify1.4s

Counts

106 → 106

Iterations

Useful iterations: 3 (597.0ms)

Iter	Nodes	Cost
0	162	1842
1	348	1806
2	907	1611
3	2670	1605
done	5000	1605

prune363.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes161.0ms

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: 1 (1.0ms)

Iter	Nodes	Cost
0	14	18
1	19	16
done	19	16

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.3s	2940×	body	1280	valid
461.0ms	1823×	body	640	valid
130.0ms	761×	body	320	valid
118.0ms	2119×	body	80	valid
46.0ms	359×	body	160	valid