Details

sample793.0ms

Algorithm

intervals

Results

536.0ms	69×	body	80	valid
111.0ms	89×	body	1280	valid
56.0ms	52×	body	640	valid
10.0ms	33×	body	320	valid
4.0ms	13×	body	160	valid

simplify43.0ms

Counts

1 → 1

Iterations

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

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.8b

localize42.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
2.8b	(cos (+ a b))

rewrite103.0ms

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

Calls

3 calls:

54.0ms	(* r (/ (sin b) (cos (+ a b))))
18.0ms	(/ (sin b) (cos (+ a b)))
24.0ms	(cos (+ a b))

series248.0ms

Counts

3 → 9

Calls

3 calls:

139.0ms	(* r (/ (sin b) (cos (+ a b))))
63.0ms	(/ (sin b) (cos (+ a b)))
45.0ms	(cos (+ a b))

simplify2.1s

Counts

82 → 82

Iterations

Iter	Nodes
done	5012
3	3284
2	879
1	280
0	123

prune585.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

localize53.0ms

Local error

Found 4 expressions with local error:

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

rewrite167.0ms

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

Counts

4 → 110

Calls

4 calls:

71.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
34.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
18.0ms	(* (sin a) (sin b))
40.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series727.0ms

Counts

4 → 12

Calls

4 calls:

343.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
127.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
82.0ms	(* (sin a) (sin b))
174.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.8s

Counts

122 → 122

Iterations

Iter	Nodes
done	5000
2	1563
1	462
0	182

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

12.0ms	(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
0.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
14.0ms	(* (sin a) (sin b))
7.0ms	(/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))

series729.0ms

Counts

4 → 12

Calls

4 calls:

332.0ms	(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
130.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
72.0ms	(* (sin a) (sin b))
194.0ms	(/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))

simplify2.1s

Counts

106 → 106

Iterations

Iter	Nodes
done	5000
2	1283
1	368
0	156

prune880.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize122.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
0.3b	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
0.4b	(* (* (cos a) (cos b)) (* (cos a) (cos b)))
0.4b	(* (* (cos a) (cos b)) (* (cos a) (cos b)))

rewrite198.0ms

Algorithm

rewrite-expression-head

Rules

160×	`pow1`
68×	`pow-prod-down`
52×	`add-cbrt-cube` `add-exp-log`
32×	`prod-exp` `cbrt-unprod`
16×	`pow-sqr` `pow-prod-up`
8×	`pow-plus` `cos-mult` `sin-mult`
4×	`pow2` `add-sqr-sqrt` `expm1-log1p-u` `frac-times` `-un-lft-identity` `swap-sqr` `associate-r` `associate-l` `associate-l/` `associate-r/` `-commutative` `add-cube-cbrt` `log1p-expm1-u` `add-log-exp`

Counts

4 → 156

Calls

4 calls:

73.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
44.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
33.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))
37.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))

series344.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
99.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
88.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))
78.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))

simplify2.9s

Counts

168 → 168

Iterations

Iter	Nodes
done	5001
3	3836
2	1129
1	295
0	107

prune805.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes373.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	33
1	33
0	23

end0.0ms

sample5.1s

Algorithm

intervals

Results

2.8s	2858×	body	1280	valid
1.2s	1820×	body	640	valid
529.0ms	2173×	body	80	valid
292.0ms	797×	body	320	valid
78.0ms	352×	body	160	valid