Details

sample265.0ms

Algorithm

intervals

Results

83.0ms	89×	body	1280	valid
32.0ms	50×	body	640	valid
14.0ms	34×	body	320	valid
9.0ms	73×	body	80	valid
3.0ms	10×	body	160	valid

simplify101.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	8	9
1	12	9
2	16	9
3	20	9
4	21	9
done	21	9

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.4b

localize14.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
2.8b	(cos (+ a b))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
13×	`associate-r`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
3×	`expm1-log1p-u` `associate-l` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`cos-sum` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

3 → 73

Calls

3 calls:

20.0ms	(* r (/ (sin b) (cos (+ a b))))
16.0ms	(/ (sin b) (cos (+ a b)))
15.0ms	(cos (+ a b))

series205.0ms

Counts

3 → 9

Calls

3 calls:

118.0ms	(* r (/ (sin b) (cos (+ a b))))
47.0ms	(/ (sin b) (cos (+ a b)))
40.0ms	(cos (+ a b))

simplify770.0ms

Counts

82 → 82

Iterations

Useful iterations: done (766.0ms)

Iter	Nodes	Cost
0	122	955
1	283	928
2	1071	842
done	5000	836

prune389.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite240.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`associate-r`
19×	`times-frac`
13×	`add-exp-log` `add-cbrt-cube`
8×	`pow1` `associate-/r/`
7×	`sin-mult`
6×	`associate-l` `cos-mult` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `prod-exp` `associate-/r` `frac-sub` `flip--` `cbrt-unprod` `associate-/l` `sub-div` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`sub-neg` `frac-2neg` `fma-neg` `diff-log` `associate-*r/` `prod-diff` `clear-num`

Counts

4 → 110

Calls

4 calls:

39.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
55.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
126.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
13.0ms	(* (sin b) (sin a))

series725.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
152.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
348.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
90.0ms	(* (sin b) (sin a))

simplify1.3s

Counts

122 → 122

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	187	2200
1	466	2145
2	2145	1957
done	5000	1955

prune615.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite126.0ms

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:

15.0ms	(* r (sin b))
38.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
39.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
32.0ms	(* (sin b) (sin a))

series592.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* r (sin b))
117.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
334.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
70.0ms	(* (sin b) (sin a))

simplify1.2s

Counts

98 → 98

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	157	1364
1	396	1324
2	2010	1182
done	5000	1174

prune571.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(* r (/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin b) (sin a)) 3)))))
0.2b	(* (sin b) (sin a))
0.3b	(pow (* (sin b) (sin a)) 3)
29.7b	(cbrt (pow (* (sin b) (sin a)) 3))

rewrite192.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
19×	`associate-r`
16×	`add-cube-cbrt` `*-un-lft-identity`
14×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
10×	`times-frac`
8×	`cbrt-prod`
6×	`associate-l`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `sin-mult` `add-log-exp`
3×	`cube-div` `pow-unpow` `pow-prod-down` `associate-/r/` `unswap-sqr`
2×	`cube-mult` `unpow-prod-down` `cbrt-div` `pow-pow` `unpow3` `cube-prod` `pow-exp` `*-commutative` `rem-cube-cbrt` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `flip3--` `pow1/3` `associate-*r/` `div-exp` `cos-mult` `frac-sub` `flip--` `rem-cbrt-cube` `div-inv`

Counts

4 → 103

Calls

4 calls:

146.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin b) (sin a)) 3)))))
25.0ms	(* (sin b) (sin a))
12.0ms	(pow (* (sin b) (sin a)) 3)
5.0ms	(cbrt (pow (* (sin b) (sin a)) 3))

series657.0ms

Counts

4 → 12

Calls

4 calls:

369.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin b) (sin a)) 3)))))
85.0ms	(* (sin b) (sin a))
115.0ms	(pow (* (sin b) (sin a)) 3)
88.0ms	(cbrt (pow (* (sin b) (sin a)) 3))

simplify1.8s

Counts

115 → 115

Iterations

Useful iterations: 2 (548.0ms)

Iter	Nodes	Cost
0	196	1688
1	534	1394
2	2620	1266
done	5000	1266

prune684.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes297.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	19
1	18	19
done	18	19

end0.0ms

sample6.0s

Algorithm

intervals

Results

3.4s	2913×	body	1280	valid
1.2s	1797×	body	640	valid
475.0ms	2129×	body	80	valid
322.0ms	788×	body	320	valid
90.0ms	374×	body	160	valid