Details

sample356.0ms

Algorithm

intervals

Results

101.0ms	63×	body	640	valid
94.0ms	90×	body	1280	valid
13.0ms	27×	body	320	valid
12.0ms	66×	body	80	valid
3.0ms	10×	body	160	valid

simplify37.0ms

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.3b

localize26.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
5.5b	(cos (+ a b))

rewrite100.0ms

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:

44.0ms	(* r (sin b))
27.0ms	(/ (* r (sin b)) (cos (+ a b)))
24.0ms	(cos (+ a b))

series208.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(* r (sin b))
119.0ms	(/ (* r (sin b)) (cos (+ a b)))
46.0ms	(cos (+ a b))

simplify3.7s

Counts

56 → 56

Iterations

Useful iterations: done (3.7s)

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

prune194.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* r (sin b))
0.2b	(- (* (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))

rewrite113.0ms

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:

11.0ms	(* r (sin b))
36.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
44.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
20.0ms	(* (sin a) (sin b))

series1.0s

Counts

4 → 12

Calls

4 calls:

63.0ms	(* r (sin b))
110.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
757.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
81.0ms	(* (sin a) (sin b))

simplify3.1s

Counts

88 → 88

Iterations

Useful iterations: 3 (1.6s)

Iter	Nodes	Cost
0	140	1256
1	345	1224
2	1088	1098
3	3884	989
done	5001	989

prune474.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite161.0ms

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:

19.0ms	(* (cos a) (cos b))
52.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
27.0ms	(/ (* (cos a) (cos b)) (sin b))
58.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))

series677.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (cos a) (cos b))
171.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
141.0ms	(/ (* (cos a) (cos b)) (sin b))
305.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))

simplify3.4s

Counts

104 → 104

Iterations

Useful iterations: 3 (1.5s)

Iter	Nodes	Cost
0	174	1613
1	365	1564
2	1055	1436
3	4014	1430
done	5000	1430

prune481.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite257.0ms

Algorithm

rewrite-expression-head

Rules

120×	`times-frac`
111×	`add-sqr-sqrt`
76×	`*-un-lft-identity`
66×	`add-cube-cbrt`
23×	`associate-/r*`
15×	`difference-of-squares`
13×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/l*`
7×	`div-inv`
6×	`add-log-exp`
5×	`cbrt-undiv` `div-exp` `distribute-lft-out--`
4×	`pow1`
3×	`frac-2neg` `clear-num` `associate-/r/`
2×	`flip3--` `flip--`
1×	`sub-neg` `quot-tan` `diff-log`

Counts

4 → 159

Calls

4 calls:

110.0ms	(- (/ (cos a) (/ (sin b) (cos b))) (sin a))
24.0ms	(/ (sin b) (cos b))
32.0ms	(/ (cos a) (/ (sin b) (cos b)))
74.0ms	(/ r (- (/ (cos a) (/ (sin b) (cos b))) (sin a)))

series534.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(- (/ (cos a) (/ (sin b) (cos b))) (sin a))
27.0ms	(/ (sin b) (cos b))
85.0ms	(/ (cos a) (/ (sin b) (cos b)))
256.0ms	(/ r (- (/ (cos a) (/ (sin b) (cos b))) (sin a)))

simplify3.4s

Counts

171 → 171

Iterations

Useful iterations: 3 (1.8s)

Iter	Nodes	Cost
0	282	2980
1	573	2867
2	1592	2729
3	4604	2721
done	5000	2721

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes293.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	15
1	15	15
done	15	15

end0.0ms

sample5.9s

Algorithm

intervals

Results

2.4s	2814×	body	1280	valid
1.8s	1927×	body	640	valid
526.0ms	327×	body	160	valid
390.0ms	2165×	body	80	valid
254.0ms	769×	body	320	valid