Details

sample270.0ms

Algorithm

intervals

Results

78.0ms	93×	body	1280	valid
30.0ms	57×	body	640	valid
12.0ms	22×	body	320	valid
8.0ms	70×	body	80	valid
4.0ms	14×	body	160	valid

simplify90.0ms

Counts

1 → 1

Iterations

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.8b

localize30.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
4.4b	(cos (+ a b))

rewrite96.0ms

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:

37.0ms	(* r (/ (sin b) (cos (+ a b))))
14.0ms	(/ (sin b) (cos (+ a b)))
34.0ms	(cos (+ a b))

series370.0ms

Counts

3 → 9

Calls

3 calls:

231.0ms	(* r (/ (sin b) (cos (+ a b))))
79.0ms	(/ (sin b) (cos (+ a b)))
59.0ms	(cos (+ a b))

simplify5.1s

Counts

79 → 79

Iterations

Iter	Nodes
done	5002
3	3110
2	844
1	272
0	120

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize61.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.1b	(* 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))))

rewrite259.0ms

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:

28.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
157.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
17.0ms	(* (sin a) (sin b))
47.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series1.3s

Counts

4 → 12

Calls

4 calls:

196.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
579.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
126.0ms	(* (sin a) (sin b))
353.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify3.3s

Counts

116 → 116

Iterations

Iter	Nodes
done	5002
2	1465
1	443
0	175

prune1.7s

Pruning

9 alts after pruning (9 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 b) (sin a)))
0.1b	(* (sin b) r)
0.2b	(* (sin b) (sin a))
0.2b	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin b) (sin a))))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

24.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
17.0ms	(* (sin b) r)
25.0ms	(* (sin b) (sin a))
46.0ms	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin b) (sin a))))

series1.1s

Counts

4 → 12

Calls

4 calls:

216.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
86.0ms	(* (sin b) r)
96.0ms	(* (sin b) (sin a))
670.0ms	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin b) (sin a))))

simplify2.9s

Counts

92 → 92

Iterations

Iter	Nodes
done	5001
2	1140
1	365
0	147

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize118.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin a) (sin b))
0.2b	(/ (sin b) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))))
0.2b	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
23.5b	(cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))

rewrite608.0ms

Algorithm

rewrite-expression-head

Rules

45×	`pow1`
29×	`sin-mult`
20×	`add-cbrt-cube` `add-exp-log`
18×	`pow-prod-down`
16×	`add-sqr-sqrt`
14×	`cbrt-div` `*-un-lft-identity` `add-cube-cbrt`
11×	`frac-times` `associate-*l/`
9×	`times-frac` `prod-exp` `associate-/r/` `cbrt-unprod`
7×	`associate-*r/` `cos-mult` `frac-sub`
4×	`associate-r` `associate-l` `pow-sqr` `pow-prod-up` `insert-posit16` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`pow-plus` `*-commutative`
1×	`cbrt-prod` `pow2` `cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `pow1/3` `swap-sqr` `div-exp` `pow3` `rem-cbrt-cube` `div-inv` `flip--` `unswap-sqr`

Counts

4 → 113

Calls

4 calls:

17.0ms	(* (sin a) (sin b))
271.0ms	(/ (sin b) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))))
73.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
238.0ms	(cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))

series771.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(* (sin a) (sin b))
358.0ms	(/ (sin b) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))))
174.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
121.0ms	(cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))

simplify7.2s

Counts

125 → 125

Iterations

Iter	Nodes
done	5018
3	4290
2	1500
1	452
0	196

prune1.7s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes837.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	15
1	15
0	12

end0.0ms

sample5.5s

Algorithm

intervals

Results

2.9s	2902×	body	1280	valid
1.1s	1902×	body	640	valid
741.0ms	2112×	body	80	valid
314.0ms	724×	body	320	valid
135.0ms	361×	body	160	valid