Details

sample78.0ms

Algorithm

intervals

Results

41.0ms	91×	body	1280	valid
14.0ms	51×	body	640	valid
6.0ms	31×	body	320	valid
5.0ms	75×	body	80	valid
1.0ms	8×	body	160	valid

simplify12.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	9
1	12	9
2	16	9
3	19	9
4	20	9
done	20	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.0b

localize17.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.3b	(/ (* r (sin b)) (cos (+ a b)))
4.3b	(cos (+ a b))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
5×	`pow1`
3×	`expm1-log1p-u` `times-frac` `associate-r` `associate-l` `associate-/r*` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
1×	`cos-sum` `frac-2neg` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l` `unswap-sqr`

Counts

3 → 53

Calls

3 calls:

3.0ms	(* r (sin b))
4.0ms	(/ (* r (sin b)) (cos (+ a b)))
7.0ms	(cos (+ a b))

series161.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(* r (sin b))
99.0ms	(/ (* r (sin b)) (cos (+ a b)))
24.0ms	(cos (+ a b))

simplify1.8s

Counts

62 → 62

Iterations

Useful iterations: 3 (433.0ms)

Iter	Nodes	Cost
0	96	575
1	208	562
2	577	484
3	2292	482
done	5000	482

prune162.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos a) (cos b))
0.1b	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.2b	(* (sin a) (sin b))
0.3b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

rewrite25.0ms

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×	`cos-mult` `sin-mult`
4×	`expm1-log1p-u` `associate-/r/` `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 → 87

Calls

4 calls:

4.0ms	(* (cos a) (cos b))
5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
4.0ms	(* (sin a) (sin b))
9.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series380.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (cos a) (cos b))
81.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
44.0ms	(* (sin a) (sin b))
213.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify2.0s

Counts

99 → 99

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	167	1410
1	394	1358
2	1280	1213
3	4796	1119
done	5000	1119

prune358.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(* r (sin b))
0.1b	(fma (cos b) (cos a) (- (* (sin b) (sin a))))
0.2b	(* (sin b) (sin a))
0.3b	(/ (* r (sin b)) (fma (cos b) (cos a) (- (* (sin b) (sin a)))))

rewrite14.0ms

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`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `prod-exp` `associate-/r*` `cbrt-unprod`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `unswap-sqr`
1×	`frac-2neg` `clear-num` `fma-udef` `div-inv` `sin-mult` `associate-/l*`

Counts

4 → 74

Calls

4 calls:

4.0ms	(* r (sin b))
0.0ms	(fma (cos b) (cos a) (- (* (sin b) (sin a))))
4.0ms	(* (sin b) (sin a))
4.0ms	(/ (* r (sin b)) (fma (cos b) (cos a) (- (* (sin b) (sin a)))))

series378.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* r (sin b))
82.0ms	(fma (cos b) (cos a) (- (* (sin b) (sin a))))
46.0ms	(* (sin b) (sin a))
213.0ms	(/ (* r (sin b)) (fma (cos b) (cos a) (- (* (sin b) (sin a)))))

simplify1.6s

Counts

86 → 86

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	126	1087
1	269	1071
2	824	917
3	3381	915
done	5000	914

prune312.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (cos b) (cos a) (- (* (sin b) (sin a))))
0.2b	(* (sin b) (sin a))
0.2b	(/ (fma (cos b) (cos a) (- (* (sin b) (sin a)))) (sin b))
0.3b	(/ r (/ (fma (cos b) (cos a) (- (* (sin b) (sin a)))) (sin b)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
58×	`add-sqr-sqrt`
56×	`add-cube-cbrt` `*-un-lft-identity`
16×	`associate-/r*`
13×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `div-inv` `associate-/l*`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l`
2×	`frac-2neg` `clear-num`
1×	`pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `fma-udef` `sin-mult` `unswap-sqr`

Counts

4 → 132

Calls

4 calls:

0.0ms	(fma (cos b) (cos a) (- (* (sin b) (sin a))))
4.0ms	(* (sin b) (sin a))
2.0ms	(/ (fma (cos b) (cos a) (- (* (sin b) (sin a)))) (sin b))
5.0ms	(/ r (/ (fma (cos b) (cos a) (- (* (sin b) (sin a)))) (sin b)))

series449.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(fma (cos b) (cos a) (- (* (sin b) (sin a))))
45.0ms	(* (sin b) (sin a))
105.0ms	(/ (fma (cos b) (cos a) (- (* (sin b) (sin a)))) (sin b))
217.0ms	(/ r (/ (fma (cos b) (cos a) (- (* (sin b) (sin a)))) (sin b)))

simplify829.0ms

Counts

144 → 144

Iterations

Useful iterations: done (825.0ms)

Iter	Nodes	Cost
0	225	3242
1	478	3160
2	1472	2953
done	5000	2952

prune499.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes162.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	16
1	18	16
2	20	16
done	20	16

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.4s	2913×	body	1280	valid
483.0ms	1767×	body	640	valid
146.0ms	773×	body	320	valid
134.0ms	2210×	body	80	valid
50.0ms	337×	body	160	valid