Details

sample367.0ms

Algorithm

intervals

Results

166.0ms	100×	body	1280	valid
46.0ms	56×	body	640	valid
19.0ms	23×	body	320	valid
11.0ms	62×	body	80	valid
7.0ms	15×	body	160	valid

simplify33.0ms

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: 16.5b

localize51.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
3.2b	(cos (+ a b))

rewrite49.0ms

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` `insert-posit16` `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 → 70

Calls

3 calls:

27.0ms	(* r (/ (sin b) (cos (+ a b))))
9.0ms	(/ (sin b) (cos (+ a b)))
9.0ms	(cos (+ a b))

series274.0ms

Counts

3 → 9

Calls

3 calls:

160.0ms	(* r (/ (sin b) (cos (+ a b))))
72.0ms	(/ (sin b) (cos (+ a b)))
42.0ms	(cos (+ a b))

simplify978.0ms

Counts

79 → 79

Iterations

Iter	Nodes
3	2396
2	783
1	267
0	120

prune845.0ms

Pruning

10 alts after pruning (10 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 a) (sin b))
0.2b	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

rewrite168.0ms

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`
4×	`insert-posit16`
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 → 104

Calls

4 calls:

36.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
90.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
11.0ms	(* (sin a) (sin b))
27.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series716.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
362.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
70.0ms	(* (sin a) (sin b))
167.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify3.2s

Counts

116 → 116

Iterations

Iter	Nodes
3	4180
2	1412
1	435
0	175

prune1.6s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.2b	(* (sin a) (sin b))
0.3b	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

rewrite170.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-exp-log`
27×	`add-sqr-sqrt`
23×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
22×	`add-cbrt-cube`
18×	`times-frac`
14×	`pow1` `prod-exp`
8×	`associate-/r/` `cbrt-unprod`
7×	`associate-l`
6×	`div-exp`
5×	`pow-prod-down` `sin-mult`
4×	`cos-mult` `insert-posit16` `add-log-exp`
3×	`cbrt-undiv` `rec-exp` `associate-/r` `1-exp` `-commutative` `associate-/l*`
2×	`flip3--` `frac-sub` `div-inv` `flip--` `sub-div` `unswap-sqr`
1×	`clear-num` `frac-2neg` `associate-*r/` `un-div-inv` `pow-flip` `inv-pow`

Counts

4 → 118

Calls

4 calls:

9.0ms	(* r (sin b))
44.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
12.0ms	(* (sin a) (sin b))
103.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series628.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* r (sin b))
143.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
69.0ms	(* (sin a) (sin b))
348.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify8.5s

Counts

130 → 130

Iterations

Iter	Nodes
3	4621
2	1533
1	497
0	187

prune1.9s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize93.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
0.3b	(* (* (cos a) (cos b)) (* (sin a) (sin b)))
0.4b	(* (* (cos a) (cos b)) (* (cos a) (cos b)))
0.4b	(* (* (cos a) (cos b)) (* (cos a) (cos b)))

rewrite305.0ms

Algorithm

rewrite-expression-head

Rules

133×	`pow1`
59×	`pow-prod-down`
52×	`add-cbrt-cube` `add-exp-log`
32×	`prod-exp` `cbrt-unprod`
12×	`pow-sqr` `pow-prod-up`
10×	`cos-mult`
6×	`pow-plus` `sin-mult`
4×	`add-sqr-sqrt` `frac-times` `-un-lft-identity` `associate-r` `associate-l` `associate-l/` `associate-r/` `-commutative` `add-cube-cbrt` `insert-posit16` `add-log-exp`
3×	`pow2` `swap-sqr`

Counts

4 → 140

Calls

4 calls:

86.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
69.0ms	(* (* (cos a) (cos b)) (* (sin a) (sin b)))
71.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))
73.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))

series387.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
144.0ms	(* (* (cos a) (cos b)) (* (sin a) (sin b)))
87.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))
73.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))

simplify7.6s

Counts

152 → 152

Iterations

Iter	Nodes
3	9949
2	1605
1	357
0	131

prune2.7s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes373.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
2	18
1	18
0	14

end0.0ms

sample7.1s

Algorithm

intervals

Results

3.8s	2885×	body	1280	valid
2.0s	1883×	body	640	valid
569.0ms	732×	body	320	valid
336.0ms	2174×	body	80	valid
117.0ms	328×	body	160	valid