Details

sample365.0ms

Algorithm

intervals

Results

114.0ms	73×	body	80	valid
65.0ms	97×	body	1280	valid
59.0ms	56×	body	640	valid
5.0ms	21×	body	320	valid
2.0ms	9×	body	160	valid

simplify21.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	8	9
1	12	9
2	16	9
3	19	9
4	20	9
done	20	9

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.1b

localize60.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
1.9b	(cos (+ a b))

rewrite228.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 47

Calls

3 calls:

115.0ms	(* r (sin b))
78.0ms	(/ (* r (sin b)) (cos (+ a b)))
30.0ms	(cos (+ a b))

series435.0ms

Counts

3 → 9

Calls

3 calls:

70.0ms	(* r (sin b))
267.0ms	(/ (* r (sin b)) (cos (+ a b)))
97.0ms	(cos (+ a b))

simplify3.6s

Counts

56 → 56

Iterations

Useful iterations: done (3.6s)

Iter	Nodes	Cost
0	90	535
1	198	525
2	550	447
3	2112	443
done	5001	439

prune209.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize25.0ms

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))))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

9.0ms	(* r (sin b))
28.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
23.0ms	(* (sin a) (sin b))
58.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series538.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(* r (sin b))
113.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
70.0ms	(* (sin a) (sin b))
282.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify2.8s

Counts

88 → 88

Iterations

Useful iterations: 3 (1.5s)

Iter	Nodes	Cost
0	140	1256
1	345	1224
2	1091	1076
3	3874	989
done	5000	989

prune409.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* (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))))

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

28.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
91.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
12.0ms	(* (sin a) (sin b))
35.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series687.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
346.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
69.0ms	(* (sin a) (sin b))
164.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify2.4s

Counts

112 → 112

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	170	2072
1	403	2024
2	1162	1856
3	3369	1715
done	5001	1715

prune555.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (pow (* (cos a) (cos b)) 3) (pow (* (sin b) (sin a)) 3)) (+ (* (* (sin b) (sin a)) (+ (* (cos a) (cos b)) (* (sin a) (sin b)))) (* (* (cos a) (cos b)) (* (cos a) (cos b)))))
0.3b	(pow (* (sin b) (sin a)) 3)
0.4b	(* (* (cos a) (cos b)) (* (cos a) (cos b)))
0.5b	(pow (* (cos a) (cos b)) 3)

rewrite272.0ms

Algorithm

rewrite-expression-head

Rules

49×	`pow1`
41×	`cos-mult`
36×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
27×	`times-frac` `frac-add`
24×	`add-exp-log` `add-cbrt-cube`
23×	`associate-/r/`
21×	`sin-mult`
20×	`add-cube-cbrt`
19×	`pow-prod-down`
18×	`sqr-pow`
17×	`frac-times` `associate-*r/`
16×	`difference-of-squares`
11×	`associate-*l/`
10×	`prod-exp` `cbrt-unprod`
9×	`associate-/l*`
7×	`flip3-+` `flip-+`
6×	`cube-div` `pow-unpow`
4×	`difference-cubes` `pow-pow` `pow-exp` `pow-sqr` `pow-prod-up` `associate-/l/` `distribute-lft-out--` `add-log-exp` `rem-cube-cbrt`
3×	`associate-/r*`
2×	`cube-mult` `pow-to-exp` `unpow-prod-down` `pow-plus` `unpow3` `cube-prod`
1×	`cbrt-undiv` `pow2` `flip3--` `frac-2neg` `div-sub` `swap-sqr` `div-exp` `associate-r` `associate-l` `clear-num` `*-commutative` `frac-sub` `flip--` `div-inv` `sub-div`

Counts

4 → 162

Calls

4 calls:

165.0ms	(/ (- (pow (* (cos a) (cos b)) 3) (pow (* (sin b) (sin a)) 3)) (+ (* (* (sin b) (sin a)) (+ (* (cos a) (cos b)) (* (sin a) (sin b)))) (* (* (cos a) (cos b)) (* (cos a) (cos b)))))
15.0ms	(pow (* (sin b) (sin a)) 3)
66.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))
17.0ms	(pow (* (cos a) (cos b)) 3)

series808.0ms

Counts

4 → 12

Calls

4 calls:

513.0ms	(/ (- (pow (* (cos a) (cos b)) 3) (pow (* (sin b) (sin a)) 3)) (+ (* (* (sin b) (sin a)) (+ (* (cos a) (cos b)) (* (sin a) (sin b)))) (* (* (cos a) (cos b)) (* (cos a) (cos b)))))
89.0ms	(pow (* (sin b) (sin a)) 3)
105.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))
101.0ms	(pow (* (cos a) (cos b)) 3)

simplify3.0s

Counts

174 → 174

Iterations

Useful iterations: 2 (913.0ms)

Iter	Nodes	Cost
0	364	7066
1	1044	6329
2	4985	5863
done	5001	5863

prune1.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes441.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	68
1	26	68
done	26	68

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.8s	2947×	body	1280	valid
690.0ms	1827×	body	640	valid
207.0ms	756×	body	320	valid
186.0ms	2147×	body	80	valid
61.0ms	324×	body	160	valid