Details

sample299.0ms

Algorithm

intervals

Results

160.0ms	104×	body	1280	valid
29.0ms	50×	body	640	valid
12.0ms	29×	body	320	valid
8.0ms	62×	body	80	valid
3.0ms	11×	body	160	valid

simplify19.0ms

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: 17.3b

localize16.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (sin b))
0.3b	(/ (* r (sin b)) (cos (+ a b)))
3.6b	(cos (+ a b))

rewrite82.0ms

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:

41.0ms	(* r (sin b))
25.0ms	(/ (* r (sin b)) (cos (+ a b)))
12.0ms	(cos (+ a b))

series245.0ms

Counts

3 → 9

Calls

3 calls:

68.0ms	(* r (sin b))
138.0ms	(/ (* r (sin b)) (cos (+ a b)))
39.0ms	(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

prune225.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite104.0ms

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:

19.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
12.0ms	(* r (sin b))
19.0ms	(* (sin a) (sin b))
52.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series702.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
79.0ms	(* r (sin b))
89.0ms	(* (sin a) (sin b))
383.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify3.2s

Counts

88 → 88

Iterations

Useful iterations: 3 (1.6s)

Iter	Nodes	Cost
0	140	1256
1	345	1224
2	1091	1076
3	3873	989
done	5000	989

prune470.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize50.0ms

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))))

rewrite268.0ms

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:

30.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
154.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
25.0ms	(* (sin a) (sin b))
56.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series808.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
368.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
93.0ms	(* (sin a) (sin b))
219.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify2.6s

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

prune636.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

14.0ms	(* (cos a) (cos b))
25.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
63.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))
38.0ms	(/ (* (cos a) (cos b)) (sin b))

series641.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (cos a) (cos b))
124.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
332.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))
132.0ms	(/ (* (cos a) (cos b)) (sin b))

simplify3.5s

Counts

104 → 104

Iterations

Useful iterations: 3 (1.4s)

Iter	Nodes	Cost
0	174	1613
1	365	1564
2	1052	1436
3	4003	1430
done	5000	1430

prune481.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes279.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	13	15
1	17	13
done	17	13

end0.0ms

sample5.5s

Algorithm

intervals

Results

2.7s	2904×	body	1280	valid
1.1s	1843×	body	640	valid
948.0ms	770×	body	320	valid
268.0ms	2146×	body	80	valid
88.0ms	339×	body	160	valid