Details

sample305.0ms

Algorithm

intervals

Results

170.0ms	99×	body	1280	valid
39.0ms	61×	body	640	valid
9.0ms	65×	body	80	valid
8.0ms	19×	body	320	valid
4.0ms	12×	body	160	valid

simplify38.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	8	9
1	12	9
2	16	9
3	19	9
4	20	9
done	20	9

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.2b

localize29.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
4.2b	(cos (+ a b))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
5×	`pow1`
3×	`expm1-log1p-u` `times-frac` `associate-r` `associate-l` `associate-/r*` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
1×	`cos-sum` `frac-2neg` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l` `unswap-sqr`

Counts

3 → 53

Calls

3 calls:

36.0ms	(* r (sin b))
14.0ms	(/ (* r (sin b)) (cos (+ a b)))
17.0ms	(cos (+ a b))

series270.0ms

Counts

3 → 9

Calls

3 calls:

76.0ms	(* r (sin b))
152.0ms	(/ (* r (sin b)) (cos (+ a b)))
41.0ms	(cos (+ a b))

simplify915.0ms

Counts

62 → 62

Iterations

Useful iterations: done (911.0ms)

Iter	Nodes	Cost
0	96	575
1	215	562
2	880	492
done	5001	482

prune275.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

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

rewrite125.0ms

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:

20.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
18.0ms	(* r (sin b))
70.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
14.0ms	(* (sin a) (sin b))

series603.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
76.0ms	(* r (sin b))
329.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
67.0ms	(* (sin a) (sin b))

simplify1.1s

Counts

98 → 98

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	152	1364
1	386	1324
2	1797	1182
done	5001	1174

prune464.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

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))

rewrite240.0ms

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:

39.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
128.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
40.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
26.0ms	(* (sin a) (sin b))

series692.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
322.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
167.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
62.0ms	(* (sin a) (sin b))

simplify1.4s

Counts

122 → 122

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	181	2200
1	465	2145
2	1988	1953
done	5000	1883

prune586.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite75.0ms

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:

23.0ms	(* (cos b) (cos a))
1.0ms	(fma (sin b) (- (sin a)) (* (cos b) (cos a)))
32.0ms	(* r (/ (sin b) (fma (sin b) (- (sin a)) (* (cos b) (cos a)))))
14.0ms	(/ (sin b) (fma (sin b) (- (sin a)) (* (cos b) (cos a))))

series719.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(* (cos b) (cos a))
129.0ms	(fma (sin b) (- (sin a)) (* (cos b) (cos a)))
318.0ms	(* r (/ (sin b) (fma (sin b) (- (sin a)) (* (cos b) (cos a)))))
200.0ms	(/ (sin b) (fma (sin b) (- (sin a)) (* (cos b) (cos a))))

simplify1.1s

Counts

106 → 106

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	161	1842
1	370	1810
2	1450	1621
done	5000	1612

prune429.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes218.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	14	17
1	18	13
2	19	13
done	19	13

end0.0ms

sample6.0s

Algorithm

intervals

Results

3.6s	2984×	body	1280	valid
1.1s	1805×	body	640	valid
378.0ms	2162×	body	80	valid
242.0ms	716×	body	320	valid
122.0ms	335×	body	160	valid