Details

sample376.0ms

Algorithm

intervals

Results

152.0ms	92×	body	1280	valid
36.0ms	53×	body	640	valid
14.0ms	72×	body	80	valid
10.0ms	25×	body	320	valid
5.0ms	15×	body	160	valid

simplify38.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.8b

localize31.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
2.9b	(cos (+ a b))

rewrite101.0ms

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:

43.0ms	(* r (sin b))
27.0ms	(/ (* r (sin b)) (cos (+ a b)))
25.0ms	(cos (+ a b))

series300.0ms

Counts

3 → 9

Calls

3 calls:

70.0ms	(* r (sin b))
180.0ms	(/ (* r (sin b)) (cos (+ a b)))
50.0ms	(cos (+ a b))

simplify3.6s

Counts

56 → 56

Iterations

Useful iterations: done (3.6s)

Iter	Nodes	Cost
0	90	535
1	198	525
2	550	447
3	2112	443
done	5001	439

prune212.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`add-exp-log` `add-cbrt-cube`
12×	`add-cube-cbrt` `*-un-lft-identity`
10×	`pow1`
9×	`associate-r` `associate-l`
4×	`prod-exp` `associate-/r/` `cbrt-unprod` `add-log-exp`
3×	`times-frac` `pow-prod-down` `associate-/r` `cos-mult` `-commutative` `sin-mult` `unswap-sqr`
2×	`cbrt-undiv` `div-exp`
1×	`flip3--` `frac-2neg` `clear-num` `frac-sub` `flip--` `div-inv` `associate-/l*` `sub-div`

Counts

4 → 81

Calls

4 calls:

12.0ms	(* (cos a) (cos b))
11.0ms	(* r (sin b))
38.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
23.0ms	(* (sin a) (sin b))

series612.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(* (cos a) (cos b))
55.0ms	(* r (sin b))
403.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
70.0ms	(* (sin a) (sin b))

simplify3.4s

Counts

93 → 93

Iterations

Useful iterations: 3 (1.9s)

Iter	Nodes	Cost
0	157	1121
1	367	1083
2	1142	949
3	3948	880
done	5000	880

prune459.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

28.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
12.0ms	(* (cos a) (cos b))
42.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))
32.0ms	(/ (* (cos a) (cos b)) (sin b))

series625.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
62.0ms	(* (cos a) (cos b))
306.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))
118.0ms	(/ (* (cos a) (cos b)) (sin b))

simplify3.2s

Counts

104 → 104

Iterations

Useful iterations: 3 (1.6s)

Iter	Nodes	Cost
0	174	1613
1	365	1564
2	1051	1436
3	4001	1430
done	5000	1430

prune891.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

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

11.0ms	(* r (sin b))
53.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
14.0ms	(* (sin a) (sin b))
123.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series664.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* r (sin b))
188.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
89.0ms	(* (sin a) (sin b))
335.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify3.9s

Counts

126 → 126

Iterations

Useful iterations: 3 (2.2s)

Iter	Nodes	Cost
0	182	2093
1	451	1915
2	1373	1669
3	4597	1621
done	5000	1621

prune459.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes210.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	16
1	15	16
done	15	16

end0.0ms

sample5.9s

Algorithm

intervals

Results

3.1s	2929×	body	1280	valid
1.6s	1872×	body	640	valid
393.0ms	2086×	body	80	valid
319.0ms	788×	body	320	valid
79.0ms	328×	body	160	valid