Details

sample201.0ms

Algorithm

intervals

Results

69.0ms	59×	body	640	valid
48.0ms	95×	body	1280	valid
11.0ms	32×	body	320	valid
5.0ms	61×	body	80	valid
1.0ms	9×	body	160	valid

simplify19.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.2b

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.3b	(/ (* r (sin b)) (cos (+ a b)))
4.9b	(cos (+ a b))

rewrite59.0ms

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

Calls

3 calls:

29.0ms	(* r (sin b))
15.0ms	(/ (* r (sin b)) (cos (+ a b)))
13.0ms	(cos (+ a b))

series185.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(* r (sin b))
115.0ms	(/ (* r (sin b)) (cos (+ a b)))
27.0ms	(cos (+ a b))

simplify2.7s

Counts

62 → 62

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	96	575
1	207	562
2	572	484
3	2172	482
done	5000	480

prune280.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

localize26.0ms

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

rewrite127.0ms

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×	`expm1-log1p-u` `associate-/r/` `cos-mult` `log1p-expm1-u`
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` `fma-neg` `diff-log` `prod-diff` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 86

Calls

4 calls:

17.0ms	(* r (sin b))
46.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
24.0ms	(* (sin a) (sin b))
37.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series609.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* r (sin b))
129.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
56.0ms	(* (sin a) (sin b))
372.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify3.5s

Counts

98 → 98

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	152	1364
1	370	1324
2	1162	1174
3	4193	1081
done	5000	1078

prune507.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b	(* r (sin b))
0.1b	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
0.2b	(* (sin a) (sin b))
0.3b	(/ (* r (sin b)) (+ (fma (cos a) (cos b) (- (* (sin a) (sin b)))) (* (sin b) (* (sin a) 0))))

rewrite64.0ms

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`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `prod-exp` `associate-/r*` `cbrt-unprod`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-/r/` `*-commutative` `unswap-sqr`
1×	`frac-2neg` `flip3-+` `clear-num` `flip-+` `fma-udef` `div-inv` `sin-mult` `associate-/l*`

Counts

4 → 76

Calls

4 calls:

10.0ms	(* r (sin b))
0.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
14.0ms	(* (sin a) (sin b))
38.0ms	(/ (* r (sin b)) (+ (fma (cos a) (cos b) (- (* (sin a) (sin b)))) (* (sin b) (* (sin a) 0))))

series541.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* r (sin b))
98.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
83.0ms	(* (sin a) (sin b))
295.0ms	(/ (* r (sin b)) (+ (fma (cos a) (cos b) (- (* (sin a) (sin b)))) (* (sin b) (* (sin a) 0))))

simplify2.7s

Counts

88 → 88

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	144	1423
1	334	1275
2	992	1024
3	3227	961
done	5000	958

prune515.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite201.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
43×	`*-un-lft-identity`
33×	`add-cube-cbrt`
30×	`times-frac`
21×	`prod-diff`
13×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/r*`
7×	`fma-neg`
6×	`pow1` `div-inv` `add-log-exp`
5×	`distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `log1p-expm1-u` `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`
1×	`sub-neg` `diff-log` `pow-prod-down` `*-commutative` `associate-/l/` `unswap-sqr`

Counts

4 → 128

Calls

4 calls:

23.0ms	(* (cos b) (cos a))
62.0ms	(- (/ (* (cos b) (cos a)) (sin b)) (sin a))
31.0ms	(/ (* (cos b) (cos a)) (sin b))
76.0ms	(/ r (- (/ (* (cos b) (cos a)) (sin b)) (sin a)))

series635.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (cos b) (cos a))
173.0ms	(- (/ (* (cos b) (cos a)) (sin b)) (sin a))
106.0ms	(/ (* (cos b) (cos a)) (sin b))
303.0ms	(/ r (- (/ (* (cos b) (cos a)) (sin b)) (sin a)))

simplify1.7s

Counts

140 → 140

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	213	2538
1	455	2227
2	1268	1949
done	5001	1820

prune461.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes214.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	15
1	16	15
done	16	15

end0.0ms

sample5.9s

Algorithm

intervals

Results

2.7s	2939×	body	1280	valid
1.6s	1778×	body	640	valid
713.0ms	811×	body	320	valid
236.0ms	2138×	body	80	valid
136.0ms	335×	body	160	valid