Details

sample341.0ms

Algorithm

intervals

Results

130.0ms	111×	body	1280	valid
62.0ms	22×	body	320	valid
41.0ms	48×	body	640	valid
12.0ms	67×	body	80	valid
3.0ms	8×	body	160	valid

simplify29.0ms

Counts

1 → 1

Iterations

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.6b

localize19.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.3b	(/ (* r (sin b)) (cos (+ a b)))
2.4b	(cos (+ a b))

rewrite67.0ms

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:

17.0ms	(* r (sin b))
17.0ms	(/ (* r (sin b)) (cos (+ a b)))
28.0ms	(cos (+ a b))

series267.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(* r (sin b))
175.0ms	(/ (* r (sin b)) (cos (+ a b)))
40.0ms	(cos (+ a b))

simplify810.0ms

Counts

59 → 59

Iterations

Iter	Nodes
3	2151
2	565
1	203
0	95

prune534.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize45.0ms

Local error

Found 4 expressions with local error:

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

rewrite100.0ms

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:

35.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
17.0ms	(* r (sin b))
18.0ms	(* (sin a) (sin b))
28.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series555.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
67.0ms	(* r (sin b))
63.0ms	(* (sin a) (sin b))
305.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify2.4s

Counts

92 → 92

Iterations

Iter	Nodes
3	4272
2	1111
1	358
0	145

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

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))
0.3b	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

rewrite194.0ms

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)))
110.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
21.0ms	(* (sin a) (sin b))
25.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series653.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
297.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
85.0ms	(* (sin a) (sin b))
159.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify3.0s

Counts

116 → 116

Iterations

Iter	Nodes
3	4180
2	1412
1	435
0	175

prune1.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize67.0ms

Local error

Found 4 expressions with local error:

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))
0.3b	(* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

rewrite297.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 122

Calls

4 calls:

66.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
94.0ms	(* r (* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
23.0ms	(* (sin a) (sin b))
111.0ms	(* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series720.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
341.0ms	(* r (* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
72.0ms	(* (sin a) (sin b))
157.0ms	(* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify8.8s

Counts

134 → 134

Iterations

Iter	Nodes
3	4331
2	1585
1	487
0	195

prune1.6s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

regimes266.0ms

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

sample6.6s

Algorithm

intervals

Results

3.4s	2950×	body	1280	valid
1.9s	1796×	body	640	valid
487.0ms	744×	body	320	valid
426.0ms	2168×	body	80	valid
108.0ms	343×	body	160	valid