Details

sample319.0ms

Algorithm

intervals

Results

93.0ms	97×	body	1280	valid
39.0ms	56×	body	640	valid
33.0ms	19×	body	320	valid
16.0ms	69×	body	80	valid
9.0ms	15×	body	160	valid

simplify30.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	21
5	21
4	20
3	18
2	16
1	12
0	8

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.2b

localize18.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
3.8b	(cos (+ a b))

rewrite75.0ms

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:

42.0ms	(* r (/ (sin b) (cos (+ a b))))
17.0ms	(/ (sin b) (cos (+ a b)))
13.0ms	(cos (+ a b))

series229.0ms

Counts

3 → 9

Calls

3 calls:

152.0ms	(* r (/ (sin b) (cos (+ a b))))
40.0ms	(/ (sin b) (cos (+ a b)))
36.0ms	(cos (+ a b))

simplify778.0ms

Counts

76 → 76

Iterations

Iter	Nodes
3	2203
2	779
1	265
0	117

prune886.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos a) (cos b))
0.2b	(* (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))))

rewrite148.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
24×	`*-un-lft-identity` `add-cube-cbrt`
23×	`associate-r`
19×	`times-frac`
15×	`add-cbrt-cube` `add-exp-log`
10×	`pow1`
9×	`associate-l`
8×	`associate-/r/`
5×	`cos-mult` `sin-mult`
4×	`prod-exp` `cbrt-unprod` `add-log-exp` `unswap-sqr`
3×	`associate-/r` `pow-prod-down` `-commutative` `associate-/l*`
2×	`cbrt-undiv` `flip3--` `div-exp` `frac-sub` `div-inv` `flip--` `sub-div`
1×	`clear-num` `frac-2neg` `associate-*r/`

Counts

4 → 105

Calls

4 calls:

9.0ms	(* (cos a) (cos b))
10.0ms	(* (sin a) (sin b))
100.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
28.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series599.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (cos a) (cos b))
74.0ms	(* (sin a) (sin b))
317.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
162.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify5.6s

Counts

117 → 117

Iterations

Iter	Nodes
3	4386
2	1466
1	457
0	188

prune1.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

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

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`add-cbrt-cube` `add-exp-log`
12×	`*-un-lft-identity` `add-cube-cbrt`
10×	`pow1`
9×	`associate-r` `associate-l`
4×	`prod-exp` `associate-/r/` `cbrt-unprod` `add-log-exp`
3×	`associate-/r` `times-frac` `pow-prod-down` `cos-mult` `-commutative` `sin-mult` `unswap-sqr`
2×	`cbrt-undiv` `div-exp`
1×	`clear-num` `frac-2neg` `flip3--` `frac-sub` `div-inv` `flip--` `associate-/l*` `sub-div`

Counts

4 → 81

Calls

4 calls:

15.0ms	(* (sin b) r)
23.0ms	(* (cos a) (cos b))
19.0ms	(* (sin a) (sin b))
29.0ms	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series532.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (sin b) r)
74.0ms	(* (cos a) (cos b))
56.0ms	(* (sin a) (sin b))
340.0ms	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify23.9s

Counts

93 → 93

Iterations

Iter	Nodes
3	4671
2	1208
1	386
0	157

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize60.0ms

Local error

Found 4 expressions with local error:

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

rewrite186.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
24×	`*-un-lft-identity` `add-cube-cbrt`
23×	`associate-r`
19×	`times-frac`
15×	`add-cbrt-cube` `add-exp-log`
10×	`pow1`
9×	`associate-l`
8×	`associate-/r/`
5×	`cos-mult` `sin-mult`
4×	`prod-exp` `cbrt-unprod` `add-log-exp` `unswap-sqr`
3×	`associate-/r` `pow-prod-down` `-commutative` `associate-/l*`
2×	`cbrt-undiv` `flip3--` `div-exp` `frac-sub` `div-inv` `flip--` `sub-div`
1×	`clear-num` `frac-2neg` `associate-*r/`

Counts

4 → 105

Calls

4 calls:

8.0ms	(* (cos a) (cos b))
115.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
19.0ms	(* (sin b) (sin a))
42.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a))))

series548.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (cos a) (cos b))
297.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
57.0ms	(* (sin b) (sin a))
135.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a))))

simplify8.9s

Counts

117 → 117

Iterations

Iter	Nodes
3	4650
2	1403
1	462
0	193

prune1.4s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes254.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	15
1	15
0	12

end0.0ms

sample7.7s

Algorithm

intervals

Results

4.4s	3000×	body	1280	valid
2.0s	1822×	body	640	valid
470.0ms	729×	body	320	valid
344.0ms	2106×	body	80	valid
151.0ms	343×	body	160	valid