Details

sample223.0ms

Algorithm

intervals

Results

61.0ms	90×	body	1280	valid
58.0ms	66×	body	80	valid
29.0ms	63×	body	640	valid
8.0ms	27×	body	320	valid
2.0ms	10×	body	160	valid

simplify18.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	8	9
1	12	9
2	16	9
3	20	9
4	21	9
done	21	9

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.2b

localize16.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
5.5b	(cos (+ a b))

rewrite92.0ms

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:

60.0ms	(* r (/ (sin b) (cos (+ a b))))
11.0ms	(/ (sin b) (cos (+ a b)))
13.0ms	(cos (+ a b))

series248.0ms

Counts

3 → 9

Calls

3 calls:

146.0ms	(* r (/ (sin b) (cos (+ a b))))
57.0ms	(/ (sin b) (cos (+ a b)))
44.0ms	(cos (+ a b))

simplify5.7s

Counts

76 → 76

Iterations

Useful iterations: 4 (4.1s)

Iter	Nodes	Cost
0	116	909
1	249	883
2	638	793
3	1727	785
4	4912	783
done	5000	783

prune276.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize29.0ms

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 b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.2b	(* (sin a) (sin b))

rewrite196.0ms

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:

33.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
98.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
44.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
14.0ms	(* (sin a) (sin b))

series765.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
375.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
199.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
63.0ms	(* (sin a) (sin b))

simplify2.4s

Counts

112 → 112

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	170	2072
1	403	2024
2	1160	1838
3	3364	1715
done	5000	1715

prune555.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
0.2b	(* r (/ 1 (- (/ (* (cos a) (cos b)) (sin b)) (sin a))))
0.2b	(/ (* (cos a) (cos b)) (sin b))
0.2b	(/ 1 (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt`
43×	`*-un-lft-identity`
35×	`times-frac`
26×	`add-cube-cbrt`
22×	`add-exp-log`
21×	`associate-r`
16×	`add-cbrt-cube`
8×	`associate-/r*` `distribute-lft-out--` `difference-of-squares`
7×	`pow1`
6×	`div-exp` `add-log-exp`
5×	`prod-exp`
4×	`cbrt-undiv` `associate-/r/` `associate-/l*`
3×	`flip3--` `associate-l` `flip--` `cbrt-unprod` `div-inv` `unswap-sqr`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num`
1×	`sub-neg` `pow-flip` `diff-log` `associate-r/` `pow-prod-down` `un-div-inv` `cos-mult` `-commutative` `associate-/l/` `inv-pow`

Counts

4 → 121

Calls

4 calls:

27.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
78.0ms	(* r (/ 1 (- (/ (* (cos a) (cos b)) (sin b)) (sin a))))
15.0ms	(/ (* (cos a) (cos b)) (sin b))
49.0ms	(/ 1 (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))

series783.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
316.0ms	(* r (/ 1 (- (/ (* (cos a) (cos b)) (sin b)) (sin a))))
141.0ms	(/ (* (cos a) (cos b)) (sin b))
195.0ms	(/ 1 (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))

simplify3.0s

Counts

133 → 133

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	195	2342
1	441	2125
2	1076	1923
3	3314	1913
done	5000	1913

prune552.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b	(* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
0.2b	(/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
0.2b	(* (sin a) (sin b))
3.7b	(log (exp (* (sin a) (sin b))))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
23×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
18×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
6×	`associate-l`
5×	`add-log-exp`
4×	`associate-/r/`
3×	`log-prod` `prod-exp` `associate-/r` `log-pow` `cbrt-unprod` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `flip3--` `div-exp` `pow-prod-down` `*-commutative` `flip--` `div-inv`
1×	`exp-prod` `exp-to-pow` `frac-2neg` `associate-*r/` `rem-log-exp` `clear-num` `sin-mult`

Counts

4 → 96

Calls

4 calls:

77.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
36.0ms	(/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
22.0ms	(* (sin a) (sin b))
9.0ms	(log (exp (* (sin a) (sin b))))

series675.0ms

Counts

4 → 12

Calls

4 calls:

356.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
166.0ms	(/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
63.0ms	(* (sin a) (sin b))
90.0ms	(log (exp (* (sin a) (sin b))))

simplify2.3s

Counts

108 → 108

Iterations

Useful iterations: 3 (954.0ms)

Iter	Nodes	Cost
0	164	1992
1	355	1744
2	993	1576
3	2780	1507
done	5002	1507

prune640.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes269.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	18
1	17	18
done	17	18

end0.0ms

sample5.9s

Algorithm

intervals

Results

3.4s	2814×	body	1280	valid
1.3s	1927×	body	640	valid
380.0ms	2165×	body	80	valid
346.0ms	769×	body	320	valid
82.0ms	327×	body	160	valid