Details

sample442.0ms

Algorithm

intervals

Results

134.0ms	91×	body	1280	valid
59.0ms	21×	body	320	valid
47.0ms	75×	body	80	valid
42.0ms	62×	body	640	valid
5.0ms	7×	body	160	valid

simplify22.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	20
5	20
4	19
3	17
2	14
1	12
0	8

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.7b

localize96.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.3b	(/ (* r (sin b)) (cos (+ a b)))
4.2b	(cos (+ a b))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-cbrt-cube` `add-exp-log`
9×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
3×	`associate-/r` `times-frac` `associate-r` `associate-l*` `insert-posit16` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
1×	`cos-sum` `clear-num` `frac-2neg` `pow-prod-down` `-commutative` `div-inv` `associate-/l` `unswap-sqr`

Counts

3 → 50

Calls

3 calls:

51.0ms	(* r (sin b))
63.0ms	(/ (* r (sin b)) (cos (+ a b)))
25.0ms	(cos (+ a b))

series453.0ms

Counts

3 → 9

Calls

3 calls:

89.0ms	(* r (sin b))
316.0ms	(/ (* r (sin b)) (cos (+ a b)))
47.0ms	(cos (+ a b))

simplify929.0ms

Counts

59 → 59

Iterations

Iter	Nodes
3	2161
2	566
1	205
0	95

prune450.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite102.0ms

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:

14.0ms	(* r (sin b))
19.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
14.0ms	(* (sin a) (sin b))
53.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series645.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* r (sin b))
144.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
83.0ms	(* (sin a) (sin b))
349.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify2.0s

Counts

92 → 92

Iterations

Iter	Nodes
3	4441
2	1145
1	360
0	145

prune1.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 4 expressions with local error:

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

rewrite221.0ms

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:

35.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
52.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
113.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
18.0ms	(* (sin a) (sin b))

series699.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
161.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
331.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
90.0ms	(* (sin a) (sin b))

simplify1.5s

Counts

116 → 116

Iterations

Iter	Nodes
3	3832
2	1364
1	436
0	175

prune1.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

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)))
25.6b	(cbrt (* (* (sin a) (sin b)) (* (* (sin a) (sin b)) (* (sin a) (sin b)))))

rewrite303.0ms

Algorithm

rewrite-expression-head

Rules

47×	`pow1`
20×	`add-cbrt-cube` `add-exp-log`
19×	`pow-prod-down`
18×	`sin-mult`
12×	`add-sqr-sqrt`
10×	`prod-exp` `cbrt-unprod`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`cbrt-div` `associate-r` `associate-l`
6×	`frac-times` `associate-*r/`
4×	`associate-*l/` `pow-sqr` `pow-prod-up` `insert-posit16` `add-log-exp`
3×	`*-commutative`
2×	`pow-plus` `unswap-sqr`
1×	`cbrt-prod` `pow2` `pow1/3` `cube-unmult` `swap-sqr` `rem-cbrt-cube`

Counts

4 → 96

Calls

4 calls:

12.0ms	(* (sin a) (sin b))
22.0ms	(* (sin a) (sin b))
88.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
179.0ms	(cbrt (* (* (sin a) (sin b)) (* (* (sin a) (sin b)) (* (sin a) (sin b)))))

series276.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (sin a) (sin b))
76.0ms	(* (sin a) (sin b))
69.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
64.0ms	(cbrt (* (* (sin a) (sin b)) (* (* (sin a) (sin b)) (* (sin a) (sin b)))))

simplify1.3s

Counts

108 → 108

Iterations

Iter	Nodes
3	3430
2	855
1	246
0	110

prune1.6s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes324.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
2	19
1	19
0	15

end0.0ms

sample7.3s

Algorithm

intervals

Results

3.6s	2937×	body	1280	valid
2.4s	1855×	body	640	valid
523.0ms	792×	body	320	valid
497.0ms	2099×	body	80	valid
121.0ms	318×	body	160	valid