Details

sample321.0ms

Algorithm

intervals

Results

85.0ms	85×	body	1280	valid
79.0ms	61×	body	640	valid
11.0ms	73×	body	80	valid
9.0ms	20×	body	320	valid
6.0ms	17×	body	160	valid

simplify39.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	20
5	20
4	19
3	17
2	14
1	12
0	8

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.8b

localize32.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
5.4b	(cos (+ a b))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-cbrt-cube` `add-exp-log`
9×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
3×	`associate-/r` `times-frac` `associate-r` `associate-l*` `insert-posit16` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
1×	`cos-sum` `clear-num` `frac-2neg` `pow-prod-down` `-commutative` `div-inv` `associate-/l` `unswap-sqr`

Counts

3 → 50

Calls

3 calls:

19.0ms	(* r (sin b))
12.0ms	(/ (* r (sin b)) (cos (+ a b)))
11.0ms	(cos (+ a b))

series233.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(* r (sin b))
160.0ms	(/ (* r (sin b)) (cos (+ a b)))
25.0ms	(cos (+ a b))

simplify613.0ms

Counts

59 → 59

Iterations

Iter	Nodes
3	2161
2	566
1	205
0	95

prune643.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize30.0ms

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))))

rewrite70.0ms

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:

17.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
15.0ms	(* r (sin b))
11.0ms	(* (sin a) (sin b))
26.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series547.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
52.0ms	(* r (sin b))
67.0ms	(* (sin a) (sin b))
284.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify2.0s

Counts

92 → 92

Iterations

Iter	Nodes
3	4460
2	1144
1	360
0	145

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize47.0ms

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))))

rewrite604.0ms

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:

23.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
509.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
22.0ms	(* (sin a) (sin b))
47.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series596.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
287.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
52.0ms	(* (sin a) (sin b))
156.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.3s

Counts

116 → 116

Iterations

Iter	Nodes
3	3772
2	1354
1	435
0	175

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize57.0ms

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))))

rewrite112.0ms

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:

31.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
14.0ms	(* r (sin b))
20.0ms	(* (sin a) (sin b))
46.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series515.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
45.0ms	(* r (sin b))
66.0ms	(* (sin a) (sin b))
294.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.9s

Counts

92 → 92

Iterations

Iter	Nodes
3	4460
2	1144
1	360
0	145

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes298.0ms

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
2	15
1	15
0	12

end0.0ms

sample7.4s

Algorithm

intervals

Results

4.6s	2891×	body	1280	valid
1.5s	1855×	body	640	valid
465.0ms	762×	body	320	valid
410.0ms	2148×	body	80	valid
157.0ms	344×	body	160	valid