Details

sample468.0ms

Algorithm

intervals

Results

73.0ms	94×	body	1280	valid
32.0ms	69×	body	640	valid
9.0ms	26×	body	320	valid
7.0ms	57×	body	80	valid
2.0ms	10×	body	160	valid

simplify70.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	21
5	21
4	20
3	18
2	16
1	12
0	8

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.3b

localize74.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.3b	(/ (sin b) (cos (+ a b)))
2.4b	(cos (+ a b))

rewrite194.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
13×	`associate-r`
10×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
3×	`associate-/r` `associate-l` `insert-posit16` `associate-/l` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`cos-sum` `clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `-commutative`

Counts

3 → 70

Calls

3 calls:

79.0ms	(* r (/ (sin b) (cos (+ a b))))
58.0ms	(/ (sin b) (cos (+ a b)))
37.0ms	(cos (+ a b))

series221.0ms

Counts

3 → 9

Calls

3 calls:

121.0ms	(* r (/ (sin b) (cos (+ a b))))
56.0ms	(/ (sin b) (cos (+ a b)))
44.0ms	(cos (+ a b))

simplify2.0s

Counts

79 → 79

Iterations

Iter	Nodes
done	5004
3	3136
2	844
1	271
0	120

prune391.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize61.0ms

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))))

rewrite203.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`*-un-lft-identity` `add-cube-cbrt`
20×	`associate-r`
19×	`times-frac`
13×	`add-cbrt-cube` `add-exp-log`
8×	`pow1` `associate-/r/`
7×	`sin-mult`
6×	`associate-l` `cos-mult` `add-log-exp`
4×	`insert-posit16`
3×	`associate-/r` `flip3--` `prod-exp` `frac-sub` `cbrt-unprod` `flip--` `associate-/l` `sub-div` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`clear-num` `sub-neg` `frac-2neg` `diff-log` `associate-*r/`

Counts

4 → 104

Calls

4 calls:

36.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
107.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
23.0ms	(* (sin a) (sin b))
32.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series684.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
337.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
87.0ms	(* (sin a) (sin b))
161.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.8s

Counts

116 → 116

Iterations

Iter	Nodes
done	5000
2	1468
1	439
0	175

prune779.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

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

rewrite246.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
20×	`add-cbrt-cube` `associate-r`
18×	`times-frac`
13×	`prod-exp`
12×	`pow1`
8×	`associate-/r/`
7×	`cbrt-unprod` `sin-mult`
6×	`div-exp` `cos-mult` `add-log-exp`
4×	`associate-l` `pow-prod-down` `insert-posit16`
3×	`cbrt-undiv` `rec-exp` `associate-/r` `flip3--` `1-exp` `frac-sub` `flip--` `associate-/l` `sub-div`
2×	`*-commutative` `div-inv`
1×	`clear-num` `sub-neg` `frac-2neg` `diff-log` `associate-*r/` `un-div-inv` `pow-flip` `inv-pow` `unswap-sqr`

Counts

4 → 114

Calls

4 calls:

39.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
52.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
20.0ms	(* (sin a) (sin b))
130.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series680.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
176.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
73.0ms	(* (sin a) (sin b))
305.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify2.9s

Counts

126 → 126

Iterations

Iter	Nodes
done	5013
3	4710
2	1572
1	511
0	186

prune665.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize60.0ms

Local error

Found 4 expressions with local error:

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

rewrite229.0ms

Algorithm

rewrite-expression-head

Rules

120×	`times-frac`
111×	`add-sqr-sqrt`
76×	`*-un-lft-identity`
66×	`add-cube-cbrt`
23×	`associate-/r*`
15×	`difference-of-squares`
13×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/l*`
7×	`div-inv`
6×	`add-log-exp`
5×	`cbrt-undiv` `div-exp` `distribute-lft-out--`
4×	`pow1` `insert-posit16`
3×	`clear-num` `frac-2neg` `associate-/r/`
2×	`flip3--` `flip--`
1×	`sub-neg` `diff-log`

Counts

4 → 162

Calls

4 calls:

91.0ms	(- (/ (cos b) (/ (sin b) (cos a))) (sin a))
10.0ms	(/ (sin b) (cos a))
101.0ms	(/ r (- (/ (cos b) (/ (sin b) (cos a))) (sin a)))
16.0ms	(/ (cos b) (/ (sin b) (cos a)))

series501.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(- (/ (cos b) (/ (sin b) (cos a))) (sin a))
59.0ms	(/ (sin b) (cos a))
242.0ms	(/ r (- (/ (cos b) (/ (sin b) (cos a))) (sin a)))
77.0ms	(/ (cos b) (/ (sin b) (cos a)))

simplify1.6s

Counts

174 → 174

Iterations

Iter	Nodes
done	5001
2	1909
1	643
0	285

prune1.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0b

regimes372.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	17
1	17
0	13

end0.0ms

sample5.7s

Algorithm

intervals

Results

2.5s	2824×	body	1280	valid
1.3s	1836×	body	640	valid
794.0ms	2216×	body	80	valid
712.0ms	785×	body	320	valid
82.0ms	341×	body	160	valid