Details

sample279.0ms

Algorithm

intervals

Results

103.0ms	59×	body	640	valid
85.0ms	95×	body	1280	valid
14.0ms	32×	body	320	valid
7.0ms	61×	body	80	valid
3.0ms	9×	body	160	valid

simplify38.0ms

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.2b

localize26.0ms

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))

rewrite105.0ms

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:

50.0ms	(* r (sin b))
26.0ms	(/ (* r (sin b)) (cos (+ a b)))
23.0ms	(cos (+ a b))

series254.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(* r (sin b))
167.0ms	(/ (* r (sin b)) (cos (+ a b)))
44.0ms	(cos (+ a b))

simplify2.6s

Counts

62 → 62

Iterations

Useful iterations: done (2.6s)

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

prune261.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

localize27.0ms

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))))

rewrite120.0ms

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:

20.0ms	(* r (sin b))
44.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
14.0ms	(* (sin a) (sin b))
38.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series641.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* r (sin b))
118.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
79.0ms	(* (sin a) (sin b))
394.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify3.8s

Counts

98 → 98

Iterations

Useful iterations: done (3.8s)

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

prune534.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

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)))))

rewrite49.0ms

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` `*-commutative` `unswap-sqr`
1×	`frac-2neg` `clear-num` `fma-udef` `div-inv` `sin-mult` `associate-/l*`

Counts

4 → 74

Calls

4 calls:

16.0ms	(* r (sin b))
0.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
12.0ms	(* (sin a) (sin b))
17.0ms	(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))

series593.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* r (sin b))
106.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
75.0ms	(* (sin a) (sin b))
351.0ms	(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))

simplify2.3s

Counts

86 → 86

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	127	1087
1	273	1071
2	775	921
3	2734	915
done	5000	912

prune509.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
8×	`pow1`
6×	`associate-r` `associate-l` `associate-/l*`
4×	`distribute-lft-neg-in` `expm1-log1p-u` `neg-mul-1` `distribute-rgt-neg-in` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `neg-sub0` `frac-2neg` `div-sub` `distribute-frac-neg` `div-exp` `clear-num` `cos-mult` `fma-udef` `div-inv`

Counts

4 → 94

Calls

4 calls:

22.0ms	(* (cos b) (cos a))
29.0ms	(* r (sin b))
1.0ms	(fma (sin a) (sin b) (- (* (cos b) (cos a))))
17.0ms	(/ (- (* r (sin b))) (fma (sin a) (sin b) (- (* (cos b) (cos a)))))

series586.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (cos b) (cos a))
54.0ms	(* r (sin b))
131.0ms	(fma (sin a) (sin b) (- (* (cos b) (cos a))))
342.0ms	(/ (- (* r (sin b))) (fma (sin a) (sin b) (- (* (cos b) (cos a)))))

simplify3.8s

Counts

106 → 106

Iterations

Useful iterations: done (3.8s)

Iter	Nodes	Cost
0	176	1718
1	351	1674
2	1003	1548
3	4456	1546
done	5001	1542

prune542.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes287.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	17
1	23	17
2	29	17
done	29	17

end0.0ms

sample5.8s

Algorithm

intervals

Results

3.3s	2939×	body	1280	valid
1.4s	1778×	body	640	valid
327.0ms	811×	body	320	valid
246.0ms	2138×	body	80	valid
192.0ms	335×	body	160	valid