Details

sample314.0ms

Algorithm

intervals

Results

40.0ms	96×	body	1280	valid
17.0ms	62×	body	640	valid
4.0ms	23×	body	320	valid
4.0ms	62×	body	80	valid
2.0ms	13×	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: 17.7b

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)))
4.1b	(cos (+ a b))

rewrite31.0ms

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)))
6.0ms	(cos (+ a b))

series160.0ms

Counts

3 → 9

Calls

3 calls:

96.0ms	(* r (/ (sin b) (cos (+ a b))))
38.0ms	(/ (sin b) (cos (+ a b)))
25.0ms	(cos (+ a b))

simplify2.1s

Counts

76 → 76

Iterations

Useful iterations: 3 (412.0ms)

Iter	Nodes	Cost
0	116	909
1	253	883
2	648	793
3	1972	785
done	5001	785

prune212.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

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))

rewrite46.0ms

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)))
8.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
25.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
4.0ms	(* (sin a) (sin b))

series464.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
112.0ms	(/ (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))

simplify1.9s

Counts

112 → 112

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	170	2072
1	404	2024
2	1174	1904
3	3762	1715
done	5001	1714

prune384.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

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))
13.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))
4.0ms	(/ (* (cos a) (cos b)) (sin b))

series388.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (cos a) (cos b))
88.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
188.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))
73.0ms	(/ (* (cos a) (cos b)) (sin b))

simplify2.6s

Counts

104 → 104

Iterations

Useful iterations: 3 (1.7s)

Iter	Nodes	Cost
0	174	1613
1	365	1564
2	1068	1436
3	4619	1430
done	5000	1430

prune341.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

88×	`pow1`
36×	`pow-prod-down`
34×	`add-exp-log` `add-cbrt-cube`
18×	`prod-exp` `cbrt-unprod`
8×	`pow-sqr` `pow-prod-up`
6×	`add-sqr-sqrt` `add-cube-cbrt` `pow-unpow` `*-un-lft-identity`
5×	`cos-mult` `sin-mult`
4×	`pow-pow` `pow-plus` `pow-exp` `add-log-exp` `rem-cube-cbrt`
2×	`cube-div` `pow2` `cube-mult` `frac-times` `pow-to-exp` `unpow-prod-down` `unpow3` `cube-prod` `associate-r/` `swap-sqr` `associate-r` `associate-l` `associate-l/` `*-commutative` `sqr-pow`

Counts

4 → 120

Calls

4 calls:

14.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
3.0ms	(pow (* (sin a) (sin b)) 3)
13.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))
3.0ms	(pow (* (cos a) (cos b)) 3)

series238.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
63.0ms	(pow (* (sin a) (sin b)) 3)
57.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))
62.0ms	(pow (* (cos a) (cos b)) 3)

simplify803.0ms

Counts

132 → 132

Iterations

Useful iterations: 2 (188.0ms)

Iter	Nodes	Cost
0	163	1498
1	434	972
2	1807	900
done	5000	900

prune380.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes153.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

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

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.3s	2940×	body	1280	valid
451.0ms	1823×	body	640	valid
136.0ms	761×	body	320	valid
129.0ms	2119×	body	80	valid
45.0ms	359×	body	160	valid