Details

sample315.0ms

Algorithm

intervals

Results

108.0ms	93×	body	1280	valid
53.0ms	26×	body	320	valid
51.0ms	61×	body	640	valid
12.0ms	68×	body	80	valid
3.0ms	8×	body	160	valid

simplify41.0ms

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.6b

localize60.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
4.0b	(cos (+ a b))

rewrite65.0ms

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))))
18.0ms	(/ (sin b) (cos (+ a b)))
19.0ms	(cos (+ a b))

series239.0ms

Counts

3 → 9

Calls

3 calls:

128.0ms	(* r (/ (sin b) (cos (+ a b))))
72.0ms	(/ (sin b) (cos (+ a b)))
39.0ms	(cos (+ a b))

simplify753.0ms

Counts

79 → 79

Iterations

Iter	Nodes
3	2396
2	783
1	267
0	120

prune406.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize60.0ms

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))))

rewrite210.0ms

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:

20.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
113.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
23.0ms	(* (sin a) (sin b))
52.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series705.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
317.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
76.0ms	(* (sin a) (sin b))
165.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify2.8s

Counts

116 → 116

Iterations

Iter	Nodes
3	4180
2	1412
1	435
0	175

prune809.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

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))))

rewrite121.0ms

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:

32.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
20.0ms	(* (sin b) r)
23.0ms	(* (sin b) (sin a))
44.0ms	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin b) (sin a))))

series552.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
40.0ms	(* (sin b) r)
83.0ms	(* (sin b) (sin a))
321.0ms	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin b) (sin a))))

simplify6.9s

Counts

92 → 92

Iterations

Iter	Nodes
3	4548
2	1124
1	363
0	147

prune642.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0b

localize61.0ms

Local error

Found 4 expressions with local error:

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

rewrite160.0ms

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 b) (sin a)))
18.0ms	(* (sin b) (sin a))
39.0ms	(/ r (- (* (cos a) (cos b)) (* (sin b) (sin a))))
83.0ms	(* (sin b) (/ r (- (* (cos a) (cos b)) (* (sin b) (sin a)))))

series813.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
70.0ms	(* (sin b) (sin a))
275.0ms	(/ r (- (* (cos a) (cos b)) (* (sin b) (sin a))))
324.0ms	(* (sin b) (/ r (- (* (cos a) (cos b)) (* (sin b) (sin a)))))

simplify2.6s

Counts

116 → 116

Iterations

Iter	Nodes
3	3494
2	1216
1	437
0	179

prune628.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0b

regimes359.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	15
1	15
0	12

end0.0ms

sample7.2s

Algorithm

intervals

Results

3.2s	2814×	body	1280	valid
2.5s	1909×	body	640	valid
581.0ms	790×	body	320	valid
471.0ms	2107×	body	80	valid
133.0ms	383×	body	160	valid