Details

sample294.0ms

Algorithm

intervals

Results

150.0ms	91×	body	1280	valid
34.0ms	60×	body	640	valid
12.0ms	31×	body	320	valid
9.0ms	65×	body	80	valid
3.0ms	9×	body	160	valid

simplify37.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	21
5	21
4	20
3	18
2	16
1	12
0	8

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize36.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
2.3b	(cos (+ a b))

rewrite351.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 67

Calls

3 calls:

311.0ms	(* r (/ (sin b) (cos (+ a b))))
15.0ms	(/ (sin b) (cos (+ a b)))
18.0ms	(cos (+ a b))

series294.0ms

Counts

3 → 9

Calls

3 calls:

181.0ms	(* r (/ (sin b) (cos (+ a b))))
72.0ms	(/ (sin b) (cos (+ a b)))
41.0ms	(cos (+ a b))

simplify2.1s

Counts

76 → 76

Iterations

Iter	Nodes
done	5001
3	3075
2	838
1	269
0	117

prune493.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

localize33.0ms

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))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`*-un-lft-identity` `add-cube-cbrt`
20×	`associate-r`
19×	`times-frac`
13×	`add-cbrt-cube` `add-exp-log`
8×	`pow1` `associate-/r/`
7×	`sin-mult`
6×	`associate-l` `cos-mult` `add-log-exp`
3×	`associate-/r` `flip3--` `prod-exp` `frac-sub` `cbrt-unprod` `flip--` `associate-/l` `sub-div` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`clear-num` `sub-neg` `frac-2neg` `diff-log` `associate-*r/`

Counts

4 → 100

Calls

4 calls:

15.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
82.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
24.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
18.0ms	(* (sin a) (sin b))

series735.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
353.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
178.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
62.0ms	(* (sin a) (sin b))

simplify1.9s

Counts

112 → 112

Iterations

Iter	Nodes
done	5002
2	1483
1	437
0	171

prune1.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

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

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
18×	`times-frac` `add-cube-cbrt`
13×	`add-cbrt-cube` `add-exp-log`
8×	`associate-/r*`
6×	`pow1` `add-log-exp`
5×	`distribute-lft-out--` `difference-of-squares`
4×	`associate-/l*`
3×	`cbrt-undiv` `div-exp` `associate-r` `associate-l`
2×	`clear-num` `frac-2neg` `flip3--` `prod-exp` `associate-/r/` `cos-mult` `cbrt-unprod` `div-inv` `flip--`
1×	`sub-neg` `diff-log` `pow-prod-down` `*-commutative` `unswap-sqr` `associate-/l/`

Counts

4 → 92

Calls

4 calls:

8.0ms	(* (cos b) (cos a))
18.0ms	(- (/ (* (cos b) (cos a)) (sin b)) (sin a))
54.0ms	(/ r (- (/ (* (cos b) (cos a)) (sin b)) (sin a)))
20.0ms	(/ (* (cos b) (cos a)) (sin b))

series589.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(* (cos b) (cos a))
143.0ms	(- (/ (* (cos b) (cos a)) (sin b)) (sin a))
286.0ms	(/ r (- (/ (* (cos b) (cos a)) (sin b)) (sin a)))
83.0ms	(/ (* (cos b) (cos a)) (sin b))

simplify2.7s

Counts

104 → 104

Iterations

Iter	Nodes
done	5067
3	4500
2	1137
1	386
0	175

prune816.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
28×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
13×	`add-cbrt-cube` `associate-r` `add-exp-log`
6×	`pow1` `associate-/r` `associate-/l` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-l` `div-inv`
2×	`clear-num` `frac-2neg` `flip3--` `prod-exp` `associate-/r/` `cbrt-unprod` `flip--` `unswap-sqr`
1×	`sub-neg` `diff-log` `pow-prod-down` `associate-r/` `-commutative`

Counts

4 → 100

Calls

4 calls:

23.0ms	(- (* (cos b) (/ (cos a) (sin b))) (sin a))
20.0ms	(* (cos b) (/ (cos a) (sin b)))
7.0ms	(/ (cos a) (sin b))
21.0ms	(/ r (- (* (cos b) (/ (cos a) (sin b))) (sin a)))

series533.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(- (* (cos b) (/ (cos a) (sin b))) (sin a))
84.0ms	(* (cos b) (/ (cos a) (sin b)))
58.0ms	(/ (cos a) (sin b))
256.0ms	(/ r (- (* (cos b) (/ (cos a) (sin b))) (sin a)))

simplify2.3s

Counts

112 → 112

Iterations

Iter	Nodes
done	5056
3	4210
2	1303
1	409
0	179

prune765.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes408.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	17
1	17
0	13

end0.0ms

sample5.4s

Algorithm

intervals

Results

3.2s	2868×	body	1280	valid
1.2s	1875×	body	640	valid
278.0ms	768×	body	320	valid
209.0ms	2150×	body	80	valid
83.0ms	339×	body	160	valid