Details

sample285.0ms

Algorithm

intervals

Results

79.0ms	93×	body	1280	valid
31.0ms	57×	body	640	valid
12.0ms	22×	body	320	valid
8.0ms	70×	body	80	valid
4.0ms	14×	body	160	valid

simplify24.0ms

Counts

1 → 1

Iterations

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.8b

localize34.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
4.4b	(cos (+ a b))

rewrite80.0ms

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:

40.0ms	(* r (/ (sin b) (cos (+ a b))))
17.0ms	(/ (sin b) (cos (+ a b)))
19.0ms	(cos (+ a b))

series225.0ms

Counts

3 → 9

Calls

3 calls:

137.0ms	(* r (/ (sin b) (cos (+ a b))))
62.0ms	(/ (sin b) (cos (+ a b)))
26.0ms	(cos (+ a b))

simplify2.2s

Counts

79 → 79

Iterations

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

prune446.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize50.0ms

Local error

Found 4 expressions with local error:

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

rewrite190.0ms

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:

34.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
98.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
25.0ms	(* (sin a) (sin b))
30.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series755.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
359.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
62.0ms	(* (sin a) (sin b))
189.0ms	(/ (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

prune895.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize54.0ms

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))))

rewrite93.0ms

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` `insert-posit16`
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 → 80

Calls

4 calls:

23.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
9.0ms	(* r (sin b))
18.0ms	(* (sin a) (sin b))
40.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series579.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
59.0ms	(* r (sin b))
90.0ms	(* (sin a) (sin b))
315.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.6s

Counts

92 → 92

Iterations

Iter	Nodes
done	5000
2	1237
1	365
0	145

prune709.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin b) (sin a))
0.2b	(/ (sin b) (- (* (cos a) (cos b)) (cbrt (* (* (sin b) (sin a)) (* (* (sin b) (sin a)) (* (sin b) (sin a)))))))
0.2b	(* (* (sin b) (sin a)) (* (sin b) (sin a)))
23.5b	(cbrt (* (* (sin b) (sin a)) (* (* (sin b) (sin a)) (* (sin b) (sin a)))))

rewrite480.0ms

Algorithm

rewrite-expression-head

Rules

45×	`pow1`
29×	`sin-mult`
20×	`add-cbrt-cube` `add-exp-log`
18×	`pow-prod-down`
16×	`add-sqr-sqrt`
14×	`cbrt-div` `*-un-lft-identity` `add-cube-cbrt`
11×	`frac-times` `associate-*r/`
9×	`times-frac` `prod-exp` `associate-/r/` `cbrt-unprod`
7×	`associate-*l/` `cos-mult` `frac-sub`
4×	`associate-r` `associate-l` `pow-sqr` `pow-prod-up` `insert-posit16` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`pow-plus` `*-commutative`
1×	`cbrt-prod` `pow2` `cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `pow1/3` `cube-unmult` `swap-sqr` `div-exp` `rem-cbrt-cube` `div-inv` `flip--` `unswap-sqr`

Counts

4 → 113

Calls

4 calls:

17.0ms	(* (sin b) (sin a))
199.0ms	(/ (sin b) (- (* (cos a) (cos b)) (cbrt (* (* (sin b) (sin a)) (* (* (sin b) (sin a)) (* (sin b) (sin a)))))))
58.0ms	(* (* (sin b) (sin a)) (* (sin b) (sin a)))
200.0ms	(cbrt (* (* (sin b) (sin a)) (* (* (sin b) (sin a)) (* (sin b) (sin a)))))

series402.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(* (sin b) (sin a))
178.0ms	(/ (sin b) (- (* (cos a) (cos b)) (cbrt (* (* (sin b) (sin a)) (* (* (sin b) (sin a)) (* (sin b) (sin a)))))))
66.0ms	(* (* (sin b) (sin a)) (* (sin b) (sin a)))
84.0ms	(cbrt (* (* (sin b) (sin a)) (* (* (sin b) (sin a)) (* (sin b) (sin a)))))

simplify3.7s

Counts

125 → 125

Iterations

Iter	Nodes
done	5000
3	4761
2	1333
1	458
0	202

prune689.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes259.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	15
1	15
0	12

end0.0ms

sample5.8s

Algorithm

intervals

Results

3.2s	2902×	body	1280	valid
1.2s	1902×	body	640	valid
669.0ms	2112×	body	80	valid
388.0ms	724×	body	320	valid
94.0ms	361×	body	160	valid