Details

sample271.0ms

Algorithm

intervals

Results

119.0ms	92×	body	1280	valid
26.0ms	60×	body	640	valid
7.0ms	25×	body	320	valid
7.0ms	72×	body	80	valid
1.0ms	7×	body	160	valid

simplify18.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.5b

localize17.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
2.4b	(cos (+ a b))

rewrite93.0ms

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×	`times-frac` `associate-r` `associate-l` `associate-/r*` `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 → 47

Calls

3 calls:

22.0ms	(* r (sin b))
29.0ms	(/ (* r (sin b)) (cos (+ a b)))
24.0ms	(cos (+ a b))

series255.0ms

Counts

3 → 9

Calls

3 calls:

68.0ms	(* r (sin b))
159.0ms	(/ (* r (sin b)) (cos (+ a b)))
28.0ms	(cos (+ a b))

simplify754.0ms

Counts

56 → 56

Iterations

Useful iterations: done (752.0ms)

Iter	Nodes	Cost
0	90	535
1	206	525
2	855	455
done	5000	443

prune226.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize35.0ms

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))))

rewrite107.0ms

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×	`sin-mult`
4×	`associate-/r/` `cos-mult`
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` `diff-log` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 76

Calls

4 calls:

27.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
10.0ms	(* r (sin b))
26.0ms	(* (sin a) (sin b))
40.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series656.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
78.0ms	(* r (sin b))
80.0ms	(* (sin a) (sin b))
372.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.2s

Counts

88 → 88

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	140	1256
1	359	1224
2	1561	1084
done	5000	1024

prune393.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.2b	(* (sin a) (sin b))
0.3b	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

rewrite206.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-exp-log`
27×	`add-sqr-sqrt`
23×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
22×	`add-cbrt-cube`
18×	`times-frac`
14×	`pow1` `prod-exp`
8×	`associate-/r/` `cbrt-unprod`
7×	`associate-l`
6×	`div-exp`
5×	`pow-prod-down` `sin-mult`
4×	`cos-mult` `add-log-exp`
3×	`cbrt-undiv` `rec-exp` `1-exp` `associate-/r` `-commutative` `associate-/l*`
2×	`flip3--` `frac-sub` `flip--` `div-inv` `sub-div` `unswap-sqr`
1×	`pow-flip` `frac-2neg` `associate-*r/` `clear-num` `un-div-inv` `inv-pow`

Counts

4 → 114

Calls

4 calls:

20.0ms	(* r (sin b))
52.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
18.0ms	(* (sin a) (sin b))
107.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series573.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* r (sin b))
130.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
73.0ms	(* (sin a) (sin b))
328.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify3.1s

Counts

126 → 126

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	182	2093
1	505	1960
2	3138	1677
done	5001	1659

prune686.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos b) (cos a))
0.1b	(- (/ (* (cos b) (cos a)) (sin b)) (/ (sin a) 1))
0.2b	(/ (* (cos b) (cos a)) (sin b))
0.3b	(/ r (- (/ (* (cos b) (cos a)) (sin b)) (/ (sin a) 1)))

rewrite209.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
34×	`times-frac`
20×	`add-cube-cbrt`
15×	`difference-of-squares`
13×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r*`
6×	`pow1` `add-log-exp`
5×	`distribute-lft-out--`
4×	`associate-/l*`
3×	`cbrt-undiv` `div-exp` `associate-r` `associate-l` `associate-/r/`
2×	`flip3--` `frac-2neg` `prod-exp` `clear-num` `cos-mult` `frac-sub` `flip--` `cbrt-unprod` `div-inv`
1×	`sub-neg` `diff-log` `pow-prod-down` `*-commutative` `associate-/l/` `unswap-sqr`

Counts

4 → 104

Calls

4 calls:

23.0ms	(* (cos b) (cos a))
64.0ms	(- (/ (* (cos b) (cos a)) (sin b)) (/ (sin a) 1))
29.0ms	(/ (* (cos b) (cos a)) (sin b))
85.0ms	(/ r (- (/ (* (cos b) (cos a)) (sin b)) (/ (sin a) 1)))

series568.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* (cos b) (cos a))
138.0ms	(- (/ (* (cos b) (cos a)) (sin b)) (/ (sin a) 1))
82.0ms	(/ (* (cos b) (cos a)) (sin b))
280.0ms	(/ r (- (/ (* (cos b) (cos a)) (sin b)) (/ (sin a) 1)))

simplify1.6s

Counts

116 → 116

Iterations

Useful iterations: 2 (352.0ms)

Iter	Nodes	Cost
0	201	2114
1	438	1860
2	2246	1736
done	5000	1736

prune509.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

regimes255.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	18
1	20	18
done	20	18

end0.0ms

sample5.8s

Algorithm

intervals

Results

3.0s	2868×	body	1280	valid
1.3s	1851×	body	640	valid
785.0ms	733×	body	320	valid
236.0ms	2198×	body	80	valid
86.0ms	350×	body	160	valid