Details

sample262.0ms

Algorithm

intervals

Results

71.0ms	67×	body	640	valid
69.0ms	83×	body	1280	valid
14.0ms	25×	body	320	valid
12.0ms	75×	body	80	valid
2.0ms	6×	body	160	valid

simplify22.0ms

Counts

1 → 1

Iterations

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.9b

localize38.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
2.8b	(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:

25.0ms	(* r (/ (sin b) (cos (+ a b))))
10.0ms	(/ (sin b) (cos (+ a b)))
10.0ms	(cos (+ a b))

series375.0ms

Counts

3 → 9

Calls

3 calls:

281.0ms	(* r (/ (sin b) (cos (+ a b))))
65.0ms	(/ (sin b) (cos (+ a b)))
28.0ms	(cos (+ a b))

simplify1.2s

Counts

79 → 79

Iterations

Iter	Nodes
done	2008
3	2008
2	844
1	271
0	120

prune409.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize51.0ms

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))

rewrite197.0ms

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:

17.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
107.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
49.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
23.0ms	(* (sin a) (sin b))

series650.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
306.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
147.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
65.0ms	(* (sin a) (sin b))

simplify1.8s

Counts

116 → 116

Iterations

Iter	Nodes
done	2016
3	2016
2	1478
1	439
0	175

prune831.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize63.0ms

Local error

Found 4 expressions with local error:

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

rewrite189.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 114

Calls

4 calls:

24.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
46.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
96.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
22.0ms	(* (sin a) (sin b))

series643.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
136.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
297.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
65.0ms	(* (sin a) (sin b))

simplify1.3s

Counts

126 → 126

Iterations

Iter	Nodes
done	2102
3	2102
2	1561
1	501
0	186

prune869.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize77.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin a) (sin b))
0.2b	(* (sin a) (sin b))
0.3b	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
0.3b	(* (* (cos a) (cos b)) (* (cos a) (cos b)))

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

86×	`pow1`
36×	`pow-prod-down`
32×	`add-cbrt-cube` `add-exp-log`
18×	`prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt`
8×	`-un-lft-identity` `associate-r` `associate-l*` `pow-sqr` `pow-prod-up` `add-cube-cbrt`
6×	`sin-mult`
4×	`pow-plus` `cos-mult` `*-commutative` `insert-posit16` `add-log-exp`
2×	`pow2` `frac-times` `swap-sqr` `associate-l/` `associate-r/` `unswap-sqr`

Counts

4 → 116

Calls

4 calls:

21.0ms	(* (sin a) (sin b))
16.0ms	(* (sin a) (sin b))
71.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
44.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))

series267.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (sin a) (sin b))
59.0ms	(* (sin a) (sin b))
64.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
82.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))

simplify1.2s

Counts

128 → 128

Iterations

Iter	Nodes
done	2004
3	2004
2	1206
1	331
0	123

prune645.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes347.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	24
1	24
0	17

end0.0ms

sample7.0s

Algorithm

intervals

Results

3.7s	2838×	body	1280	valid
2.0s	1884×	body	640	valid
494.0ms	783×	body	320	valid
350.0ms	2134×	body	80	valid
194.0ms	362×	body	160	valid