Details

sample395.0ms

Algorithm

intervals

Results

218.0ms	104×	body	1280	valid
46.0ms	29×	body	320	valid
25.0ms	50×	body	640	valid
6.0ms	62×	body	80	valid
2.0ms	11×	body	160	valid

simplify26.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.3b

localize18.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (sin b))
0.3b	(/ (* r (sin b)) (cos (+ a b)))
3.6b	(cos (+ a b))

rewrite90.0ms

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:

43.0ms	(* r (sin b))
24.0ms	(/ (* r (sin b)) (cos (+ a b)))
17.0ms	(cos (+ a b))

series282.0ms

Counts

3 → 9

Calls

3 calls:

74.0ms	(* r (sin b))
161.0ms	(/ (* r (sin b)) (cos (+ a b)))
48.0ms	(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

prune192.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite148.0ms

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:

34.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
18.0ms	(* r (sin b))
26.0ms	(* (sin a) (sin b))
66.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series637.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
63.0ms	(* r (sin b))
89.0ms	(* (sin a) (sin b))
354.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify3.4s

Counts

98 → 98

Iterations

Useful iterations: done (3.4s)

Iter	Nodes	Cost
0	152	1364
1	370	1324
2	1166	1174
3	4192	1081
done	5002	1078

prune577.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

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

rewrite72.0ms

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` `fma-udef` `div-inv` `sin-mult`

Counts

4 → 94

Calls

4 calls:

0.0ms	(fma (- (cos b)) (cos a) (* (sin b) (sin a)))
16.0ms	(* r (sin b))
34.0ms	(* (sin b) (sin a))
18.0ms	(/ (- (* r (sin b))) (fma (- (cos b)) (cos a) (* (sin b) (sin a))))

series646.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(fma (- (cos b)) (cos a) (* (sin b) (sin a)))
49.0ms	(* r (sin b))
72.0ms	(* (sin b) (sin a))
388.0ms	(/ (- (* r (sin b))) (fma (- (cos b)) (cos a) (* (sin b) (sin a))))

simplify3.6s

Counts

106 → 106

Iterations

Useful iterations: done (3.6s)

Iter	Nodes	Cost
0	169	1709
1	334	1667
2	954	1542
3	4366	1540
done	5002	1537

prune603.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

238×	`times-frac`
135×	`add-sqr-sqrt`
133×	`add-cube-cbrt` `*-un-lft-identity`
42×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
16×	`associate-/r*`
14×	`neg-mul-1`
13×	`add-exp-log` `add-cbrt-cube` `div-inv` `associate-/l*`
6×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l`
2×	`frac-2neg` `clear-num`
1×	`neg-sub0` `div-sub` `distribute-frac-neg` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `fma-udef` `sin-mult` `unswap-sqr`

Counts

4 → 232

Calls

4 calls:

1.0ms	(fma (- (cos b)) (cos a) (* (sin b) (sin a)))
25.0ms	(* (sin b) (sin a))
30.0ms	(/ (- r) (/ (fma (- (cos b)) (cos a) (* (sin b) (sin a))) (sin b)))
12.0ms	(/ (fma (- (cos b)) (cos a) (* (sin b) (sin a))) (sin b))

series743.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(fma (- (cos b)) (cos a) (* (sin b) (sin a)))
72.0ms	(* (sin b) (sin a))
348.0ms	(/ (- r) (/ (fma (- (cos b)) (cos a) (* (sin b) (sin a))) (sin b)))
173.0ms	(/ (fma (- (cos b)) (cos a) (* (sin b) (sin a))) (sin b))

simplify2.7s

Counts

244 → 244

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	377	6955
1	873	6725
2	2688	6491
done	5000	6134

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes241.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	17
1	17	17
2	21	17
3	24	17
done	24	17

end0.0ms

sample5.7s

Algorithm

intervals

Results

3.1s	2904×	body	1280	valid
1.4s	1843×	body	640	valid
351.0ms	770×	body	320	valid
302.0ms	2146×	body	80	valid
75.0ms	339×	body	160	valid