Details

sample260.0ms

Algorithm

intervals

Results

79.0ms	92×	body	1280	valid
68.0ms	53×	body	640	valid
11.0ms	72×	body	80	valid
9.0ms	25×	body	320	valid
4.0ms	15×	body	160	valid

simplify37.0ms

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.8b

localize29.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
2.9b	(cos (+ a b))

rewrite96.0ms

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:

42.0ms	(* r (sin b))
26.0ms	(/ (* r (sin b)) (cos (+ a b)))
23.0ms	(cos (+ a b))

series286.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(* r (sin b))
175.0ms	(/ (* r (sin b)) (cos (+ a b)))
47.0ms	(cos (+ a b))

simplify2.8s

Counts

62 → 62

Iterations

Useful iterations: done (2.8s)

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

prune292.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

22.0ms	(* (cos a) (cos b))
18.0ms	(* r (sin b))
38.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
28.0ms	(* (sin a) (sin b))

series554.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (cos a) (cos b))
47.0ms	(* r (sin b))
375.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
84.0ms	(* (sin a) (sin b))

simplify3.2s

Counts

101 → 101

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	165	1189
1	382	1149
2	1182	1085
3	4098	938
done	5001	936

prune491.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite189.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
24×	`add-cube-cbrt` `*-un-lft-identity`
23×	`associate-r`
19×	`times-frac`
15×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
9×	`associate-l`
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×	`pow-prod-down` `associate-/r` `-commutative` `associate-/l*`
2×	`cbrt-undiv` `flip3--` `div-exp` `frac-sub` `flip--` `div-inv` `sub-div`
1×	`frac-2neg` `associate-*r/` `clear-num`

Counts

4 → 113

Calls

4 calls:

11.0ms	(* (cos a) (cos b))
125.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
12.0ms	(* (sin a) (sin b))
37.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series671.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (cos a) (cos b))
327.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
93.0ms	(* (sin a) (sin b))
193.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify2.7s

Counts

125 → 125

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	195	2025
1	442	1967
2	1261	1788
3	3587	1683
done	5000	1679

prune676.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 146

Calls

4 calls:

0.0ms	(fma (- (cos b)) (cos a) (* (sin a) (sin b)))
23.0ms	(* r (/ (- (sin b)) (fma (- (cos b)) (cos a) (* (sin a) (sin b)))))
19.0ms	(* (sin a) (sin b))
19.0ms	(/ (- (sin b)) (fma (- (cos b)) (cos a) (* (sin a) (sin b))))

series736.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(fma (- (cos b)) (cos a) (* (sin a) (sin b)))
312.0ms	(* r (/ (- (sin b)) (fma (- (cos b)) (cos a) (* (sin a) (sin b)))))
81.0ms	(* (sin a) (sin b))
205.0ms	(/ (- (sin b)) (fma (- (cos b)) (cos a) (* (sin a) (sin b))))

simplify3.5s

Counts

158 → 158

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	224	3187
1	483	3091
2	1330	2884
3	4363	2880
done	5002	2875

prune773.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

regimes183.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify9.0ms

Iterations

Useful iterations: 3 (7.0ms)

Iter	Nodes	Cost
0	15	19
1	26	19
2	32	19
3	36	18
done	36	18

end0.0ms

sample5.4s

Algorithm

intervals

Results

3.1s	2929×	body	1280	valid
1.2s	1872×	body	640	valid
330.0ms	788×	body	320	valid
281.0ms	2086×	body	80	valid
81.0ms	328×	body	160	valid