Details

sample335.0ms

Algorithm

intervals

Results

142.0ms	97×	body	1280	valid
44.0ms	56×	body	640	valid
15.0ms	69×	body	80	valid
11.0ms	19×	body	320	valid
5.0ms	15×	body	160	valid

simplify22.0ms

Counts

1 → 1

Iterations

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.2b

localize19.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
3.8b	(cos (+ a b))

rewrite74.0ms

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×	`expm1-log1p-u` `associate-/r` `times-frac` `associate-r` `associate-l*` `log1p-expm1-u` `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 → 53

Calls

3 calls:

15.0ms	(* r (sin b))
23.0ms	(/ (* r (sin b)) (cos (+ a b)))
33.0ms	(cos (+ a b))

series282.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(* r (sin b))
182.0ms	(/ (* r (sin b)) (cos (+ a b)))
42.0ms	(cos (+ a b))

simplify805.0ms

Counts

62 → 62

Iterations

Iter	Nodes
3	2232
2	588
1	209
0	98

prune671.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize57.0ms

Local error

Found 4 expressions with local error:

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

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`add-cbrt-cube` `add-exp-log`
12×	`*-un-lft-identity` `add-cube-cbrt`
10×	`pow1`
9×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `prod-exp` `associate-/r/` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `times-frac` `pow-prod-down` `cos-mult` `-commutative` `sin-mult` `unswap-sqr`
2×	`cbrt-undiv` `div-exp`
1×	`clear-num` `frac-2neg` `flip3--` `frac-sub` `div-inv` `flip--` `associate-/l*` `sub-div`

Counts

4 → 89

Calls

4 calls:

7.0ms	(* r (sin b))
8.0ms	(* (cos a) (cos b))
13.0ms	(* (sin a) (sin b))
44.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series532.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* r (sin b))
71.0ms	(* (cos a) (cos b))
56.0ms	(* (sin a) (sin b))
347.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify4.3s

Counts

101 → 101

Iterations

Iter	Nodes
3	4487
2	1181
1	395
0	166

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize57.0ms

Local error

Found 4 expressions with local error:

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

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
62×	`add-sqr-sqrt`
58×	`*-un-lft-identity` `add-cube-cbrt`
16×	`associate-/r*`
15×	`add-cbrt-cube` `add-exp-log`
8×	`pow1`
6×	`associate-r` `associate-l` `div-inv` `associate-/l*`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `log1p-expm1-u` `add-log-exp` `associate-/l/`
3×	`cos-mult` `sin-mult`
2×	`clear-num` `frac-2neg` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`flip3--` `div-sub` `associate-/r/` `frac-sub` `flip--` `sub-div`

Counts

4 → 148

Calls

4 calls:

8.0ms	(* (cos a) (cos b))
10.0ms	(* (sin a) (sin b))
47.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
21.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))

series585.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (cos a) (cos b))
71.0ms	(* (sin a) (sin b))
144.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
309.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))

simplify1.6s

Counts

160 → 160

Iterations

Iter	Nodes
2	2028
1	639
0	261

prune2.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize55.0ms

Local error

Found 4 expressions with local error:

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

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
24×	`*-un-lft-identity` `add-cube-cbrt`
23×	`associate-l`
19×	`times-frac`
15×	`add-cbrt-cube` `add-exp-log`
10×	`pow1`
9×	`associate-r`
8×	`associate-/r/`
5×	`cos-mult` `sin-mult`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`associate-/r` `pow-prod-down` `-commutative` `associate-/l*`
2×	`cbrt-undiv` `flip3--` `div-exp` `frac-sub` `div-inv` `flip--` `sub-div`
1×	`clear-num` `frac-2neg` `associate-*l/`

Counts

4 → 113

Calls

4 calls:

8.0ms	(* (cos a) (cos b))
30.0ms	(/ r (- (* (cos a) (cos b)) (* (sin a) (sin b))))
11.0ms	(* (sin a) (sin b))
91.0ms	(* (/ r (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (sin b))

series677.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (cos a) (cos b))
253.0ms	(/ r (- (* (cos a) (cos b)) (* (sin a) (sin b))))
55.0ms	(* (sin a) (sin b))
320.0ms	(* (/ r (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (sin b))

simplify6.3s

Counts

125 → 125

Iterations

Iter	Nodes
3	4197
2	1460
1	479
0	201

prune1.5s

Pruning

11 alts after pruning (9 fresh and 2 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

simplify2.0ms

Iterations

Iter	Nodes
2	15
1	15
0	12

end0.0ms

sample7.4s

Algorithm

intervals

Results

4.1s	3000×	body	1280	valid
2.1s	1822×	body	640	valid
413.0ms	729×	body	320	valid
378.0ms	2106×	body	80	valid
125.0ms	343×	body	160	valid