Details

sample291.0ms

Algorithm

intervals

Results

92.0ms	67×	body	640	valid
91.0ms	83×	body	1280	valid
18.0ms	25×	body	320	valid
13.0ms	75×	body	80	valid
2.0ms	6×	body	160	valid

simplify32.0ms

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.9b

localize68.0ms

Local error

Found 3 expressions with local error:

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

rewrite63.0ms

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:

17.0ms	(* r (sin b))
25.0ms	(/ (* r (sin b)) (cos (+ a b)))
18.0ms	(cos (+ a b))

series216.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(* r (sin b))
129.0ms	(/ (* r (sin b)) (cos (+ a b)))
30.0ms	(cos (+ a b))

simplify970.0ms

Counts

59 → 59

Iterations

Iter	Nodes
done	2023
3	2023
2	671
1	212
0	95

prune272.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize34.0ms

Local error

Found 4 expressions with local error:

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

11.0ms	(* r (sin b))
18.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
58.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
22.0ms	(* (sin a) (sin b))

series577.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* r (sin b))
146.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
320.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
63.0ms	(* (sin a) (sin b))

simplify1.1s

Counts

92 → 92

Iterations

Iter	Nodes
done	2001
3	2001
2	1132
1	367
0	145

prune600.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite218.0ms

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)))
111.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
47.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
22.0ms	(* (sin a) (sin b))

series737.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
353.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
200.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
72.0ms	(* (sin a) (sin b))

simplify1.1s

Counts

116 → 116

Iterations

Iter	Nodes
done	2016
3	2016
2	1478
1	439
0	175

prune657.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize56.0ms

Local error

Found 4 expressions with local error:

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

rewrite224.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`*-un-lft-identity` `add-cube-cbrt`
20×	`associate-l`
19×	`times-frac`
13×	`add-cbrt-cube` `add-exp-log`
8×	`pow1` `associate-/r/`
7×	`sin-mult`
6×	`associate-r` `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-*l/`

Counts

4 → 104

Calls

4 calls:

29.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
119.0ms	(* (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) r)
51.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
23.0ms	(* (sin a) (sin b))

series754.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
369.0ms	(* (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) r)
169.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
87.0ms	(* (sin a) (sin b))

simplify1.5s

Counts

116 → 116

Iterations

Iter	Nodes
done	2006
3	2006
2	1449
1	436
0	175

prune721.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes288.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	20
1	20
0	14

end0.0ms

sample7.6s

Algorithm

intervals

Results

4.3s	2838×	body	1280	valid
2.0s	1884×	body	640	valid
485.0ms	783×	body	320	valid
419.0ms	2134×	body	80	valid
134.0ms	362×	body	160	valid