Details

sample182.0ms

Algorithm

intervals

Results

94.0ms	91×	body	1280	valid
20.0ms	56×	body	640	valid
6.0ms	75×	body	80	valid
6.0ms	25×	body	320	valid
1.0ms	9×	body	160	valid

simplify22.0ms

Counts

1 → 1

Iterations

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

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.6b

localize31.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ r (cos (+ b a)))
0.2b	(* (sin b) (/ r (cos (+ b a))))
2.3b	(cos (+ b a))

rewrite86.0ms

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` `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 → 67

Calls

3 calls:

27.0ms	(/ r (cos (+ b a)))
33.0ms	(* (sin b) (/ r (cos (+ b a))))
19.0ms	(cos (+ b a))

series318.0ms

Counts

3 → 9

Calls

3 calls:

87.0ms	(/ r (cos (+ b a)))
200.0ms	(* (sin b) (/ r (cos (+ b a))))
30.0ms	(cos (+ b a))

simplify883.0ms

Counts

76 → 76

Iterations

Iter	Nodes
done	5000
2	1471
1	277
0	118

prune379.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize46.0ms

Local error

Found 4 expressions with local error:

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

rewrite176.0ms

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`
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 → 100

Calls

4 calls:

14.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
11.0ms	(* (sin a) (sin b))
29.0ms	(/ r (- (* (cos a) (cos b)) (* (sin a) (sin b))))
120.0ms	(* (sin b) (/ r (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series897.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
88.0ms	(* (sin a) (sin b))
347.0ms	(/ r (- (* (cos a) (cos b)) (* (sin a) (sin b))))
358.0ms	(* (sin b) (/ r (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify1.3s

Counts

112 → 112

Iterations

Iter	Nodes
done	5000
2	2319
1	445
0	172

prune845.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

14.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
7.0ms	(* r (sin b))
9.0ms	(* (sin a) (sin b))
33.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series580.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
51.0ms	(* r (sin b))
66.0ms	(* (sin a) (sin b))
336.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify871.0ms

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
2	1577
1	365
0	141

prune584.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

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

rewrite116.0ms

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`
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 → 100

Calls

4 calls:

13.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
9.0ms	(* (sin a) (sin b))
58.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
33.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series703.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
68.0ms	(* (sin a) (sin b))
358.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
143.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.0s

Counts

112 → 112

Iterations

Iter	Nodes
done	5001
2	1858
1	441
0	171

prune718.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes382.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	15
1	15
0	12

end0.0ms

sample5.9s

Algorithm

intervals

Results

3.3s	2928×	body	1280	valid
1.5s	1797×	body	640	valid
370.0ms	758×	body	320	valid
232.0ms	2178×	body	80	valid
81.0ms	339×	body	160	valid