Details

sample232.0ms

Algorithm

intervals

Results

121.0ms	92×	body	1280	valid
31.0ms	60×	body	640	valid
10.0ms	25×	body	320	valid
9.0ms	72×	body	80	valid
2.0ms	7×	body	160	valid

simplify31.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 13.4b

localize14.0ms

Local error

Found 3 expressions with local error:

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

rewrite98.0ms

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×	`expm1-log1p-u` `associate-l` `associate-/r` `log1p-expm1-u` `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 → 73

Calls

3 calls:

40.0ms	(/ (sin b) (cos (+ a b)))
37.0ms	(* r (/ (sin b) (cos (+ a b))))
17.0ms	(cos (+ a b))

series231.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(/ (sin b) (cos (+ a b)))
153.0ms	(* r (/ (sin b) (cos (+ a b))))
26.0ms	(cos (+ a b))

simplify862.0ms

Counts

82 → 82

Iterations

Useful iterations: done (858.0ms)

Iter	Nodes	Cost
0	122	955
1	282	928
2	1069	842
done	5001	836

prune393.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite269.0ms

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`
4×	`expm1-log1p-u` `log1p-expm1-u`
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` `fma-neg` `diff-log` `associate-*r/` `prod-diff` `clear-num`

Counts

4 → 110

Calls

4 calls:

39.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
155.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
40.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
27.0ms	(* (sin b) (sin a))

series631.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
276.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
149.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
66.0ms	(* (sin b) (sin a))

simplify1.3s

Counts

122 → 122

Iterations

Useful iterations: 2 (362.0ms)

Iter	Nodes	Cost
0	187	2200
1	466	2145
2	2145	1953
done	5000	1953

prune615.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`add-exp-log` `add-cbrt-cube`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1`
6×	`associate-r` `associate-l` `add-log-exp`
5×	`sin-mult`
4×	`expm1-log1p-u` `associate-/r/` `cos-mult` `log1p-expm1-u`
3×	`times-frac` `prod-exp` `associate-/r*` `cbrt-unprod`
2×	`cbrt-undiv` `flip3--` `div-exp` `pow-prod-down` `*-commutative` `frac-sub` `flip--` `sub-div` `unswap-sqr`
1×	`sub-neg` `frac-2neg` `fma-neg` `diff-log` `prod-diff` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 86

Calls

4 calls:

20.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
24.0ms	(* r (sin b))
25.0ms	(* (sin b) (sin a))
37.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin b) (sin a))))

series632.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
58.0ms	(* r (sin b))
81.0ms	(* (sin b) (sin a))
369.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin b) (sin a))))

simplify1.2s

Counts

98 → 98

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	157	1364
1	395	1324
2	1969	1180
done	5001	1174

prune542.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (pow (* (cos a) (cos b)) 3) (pow (* (sin b) (sin a)) 3)) (fma (* (cos a) (cos b)) (* (cos a) (cos b)) (* (* (sin b) (sin a)) (fma (cos a) (cos b) (* (sin b) (sin a))))))
0.3b	(pow (* (sin b) (sin a)) 3)
0.3b	(fma (* (cos a) (cos b)) (* (cos a) (cos b)) (* (* (sin b) (sin a)) (fma (cos a) (cos b) (* (sin b) (sin a)))))
0.5b	(pow (* (cos a) (cos b)) 3)

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
27×	`times-frac`
20×	`add-cube-cbrt`
18×	`sqr-pow`
16×	`difference-of-squares`
12×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
9×	`associate-/l*`
6×	`cube-div` `pow-unpow`
4×	`difference-cubes` `expm1-log1p-u` `pow-pow` `pow-exp` `log1p-expm1-u` `associate-/l/` `distribute-lft-out--` `add-log-exp` `rem-cube-cbrt`
3×	`associate-/r*` `cos-mult` `sin-mult`
2×	`cube-mult` `pow-to-exp` `unpow-prod-down` `unpow3` `cube-prod` `pow-prod-down` `prod-exp` `cbrt-unprod`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-sub` `div-exp` `clear-num` `frac-sub` `flip--` `fma-udef` `div-inv` `sub-div`

Counts

4 → 118

Calls

4 calls:

65.0ms	(/ (- (pow (* (cos a) (cos b)) 3) (pow (* (sin b) (sin a)) 3)) (fma (* (cos a) (cos b)) (* (cos a) (cos b)) (* (* (sin b) (sin a)) (fma (cos a) (cos b) (* (sin b) (sin a))))))
10.0ms	(pow (* (sin b) (sin a)) 3)
0.0ms	(fma (* (cos a) (cos b)) (* (cos a) (cos b)) (* (* (sin b) (sin a)) (fma (cos a) (cos b) (* (sin b) (sin a)))))
26.0ms	(pow (* (cos a) (cos b)) 3)

series1.2s

Counts

4 → 12

Calls

4 calls:

699.0ms	(/ (- (pow (* (cos a) (cos b)) 3) (pow (* (sin b) (sin a)) 3)) (fma (* (cos a) (cos b)) (* (cos a) (cos b)) (* (* (sin b) (sin a)) (fma (cos a) (cos b) (* (sin b) (sin a))))))
80.0ms	(pow (* (sin b) (sin a)) 3)
301.0ms	(fma (* (cos a) (cos b)) (* (cos a) (cos b)) (* (* (sin b) (sin a)) (fma (cos a) (cos b) (* (sin b) (sin a)))))
79.0ms	(pow (* (cos a) (cos b)) 3)

simplify2.6s

Counts

130 → 130

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	237	5142
1	642	4812
2	3067	4239
done	5000	4238

prune828.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes199.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	58
1	30	58
done	30	58

end0.0ms

sample5.8s

Algorithm

intervals

Results

3.4s	2868×	body	1280	valid
1.2s	1851×	body	640	valid
410.0ms	733×	body	320	valid
280.0ms	2198×	body	80	valid
95.0ms	350×	body	160	valid