Details

sample324.0ms

Algorithm

intervals

Results

42.0ms	96×	body	1280	valid
16.0ms	65×	body	640	valid
4.0ms	68×	body	80	valid
3.0ms	16×	body	320	valid
1.0ms	11×	body	160	valid

simplify17.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	8	9
1	12	9
2	15	9
3	19	9
4	20	9
done	20	9

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.9b

localize12.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
3.4b	(cos (+ a b))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 67

Calls

3 calls:

9.0ms	(* r (/ (sin b) (cos (+ a b))))
3.0ms	(/ (sin b) (cos (+ a b)))
7.0ms	(cos (+ a b))

series165.0ms

Counts

3 → 9

Calls

3 calls:

100.0ms	(* r (/ (sin b) (cos (+ a b))))
39.0ms	(/ (sin b) (cos (+ a b)))
26.0ms	(cos (+ a b))

simplify2.3s

Counts

76 → 76

Iterations

Useful iterations: 3 (424.0ms)

Iter	Nodes	Cost
0	116	909
1	253	883
2	650	793
3	1973	785
done	5000	785

prune215.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (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))

rewrite47.0ms

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:

5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
9.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
25.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
5.0ms	(* (sin a) (sin b))

series468.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
114.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
220.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
50.0ms	(* (sin a) (sin b))

simplify2.0s

Counts

112 → 112

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	170	2072
1	404	2024
2	1177	1856
3	3764	1715
done	5000	1714

prune397.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* r (/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin b) (sin a)) 3)))))
0.2b	(* (sin b) (sin a))
0.3b	(pow (* (sin b) (sin a)) 3)
26.9b	(cbrt (pow (* (sin b) (sin a)) 3))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
19×	`associate-r`
16×	`add-cube-cbrt` `*-un-lft-identity`
14×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
10×	`times-frac`
8×	`cbrt-prod`
6×	`associate-l`
4×	`prod-exp` `cbrt-unprod` `sin-mult` `add-log-exp`
3×	`cube-div` `pow-unpow` `pow-prod-down` `associate-/r/` `unswap-sqr`
2×	`cube-mult` `unpow-prod-down` `cbrt-div` `pow-pow` `unpow3` `cube-prod` `pow-exp` `*-commutative` `rem-cube-cbrt` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `flip3--` `pow1/3` `associate-*r/` `div-exp` `cos-mult` `frac-sub` `flip--` `rem-cbrt-cube` `div-inv`

Counts

4 → 95

Calls

4 calls:

35.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin b) (sin a)) 3)))))
4.0ms	(* (sin b) (sin a))
3.0ms	(pow (* (sin b) (sin a)) 3)
2.0ms	(cbrt (pow (* (sin b) (sin a)) 3))

series380.0ms

Counts

4 → 12

Calls

4 calls:

217.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin b) (sin a)) 3)))))
48.0ms	(* (sin b) (sin a))
65.0ms	(pow (* (sin b) (sin a)) 3)
51.0ms	(cbrt (pow (* (sin b) (sin a)) 3))

simplify785.0ms

Counts

107 → 107

Iterations

Useful iterations: 2 (185.0ms)

Iter	Nodes	Cost
0	188	1602
1	443	1318
2	1418	1190
done	5001	1190

prune429.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0b

localize17.0ms

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

rewrite37.0ms

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:

4.0ms	(* (cos a) (cos b))
10.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
4.0ms	(/ (* (cos a) (cos b)) (sin b))
16.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))

series395.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (cos a) (cos b))
89.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
74.0ms	(/ (* (cos a) (cos b)) (sin b))
190.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))

simplify2.7s

Counts

104 → 104

Iterations

Useful iterations: 3 (1.7s)

Iter	Nodes	Cost
0	174	1613
1	366	1564
2	1069	1436
3	4602	1430
done	5000	1430

prune317.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes167.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	19
1	18	19
done	18	19

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.3s	2916×	body	1280	valid
463.0ms	1853×	body	640	valid
125.0ms	737×	body	320	valid
120.0ms	2155×	body	80	valid
42.0ms	341×	body	160	valid