Details

sample323.0ms

Algorithm

intervals

Results

81.0ms	85×	body	1280	valid
39.0ms	64×	body	640	valid
14.0ms	23×	body	320	valid
11.0ms	76×	body	80	valid
3.0ms	8×	body	160	valid

simplify89.0ms

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

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

localize33.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
2.4b	(cos (+ a b))

rewrite70.0ms

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:

17.0ms	(* r (sin b))
28.0ms	(/ (* r (sin b)) (cos (+ a b)))
23.0ms	(cos (+ a b))

series285.0ms

Counts

3 → 9

Calls

3 calls:

65.0ms	(* r (sin b))
169.0ms	(/ (* r (sin b)) (cos (+ a b)))
51.0ms	(cos (+ a b))

simplify853.0ms

Counts

62 → 62

Iterations

Useful iterations: done (851.0ms)

Iter	Nodes	Cost
0	96	575
1	215	562
2	880	492
done	5001	482

prune354.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize43.0ms

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

rewrite106.0ms

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:

19.0ms	(* r (sin b))
23.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
18.0ms	(* (sin a) (sin b))
41.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series616.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* r (sin b))
117.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
74.0ms	(* (sin a) (sin b))
369.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.3s

Counts

98 → 98

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	152	1364
1	386	1324
2	1625	1178
done	5000	1122

prune767.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

13.0ms	(* r (sin b))
1.0ms	(fma (cos a) (cos b) (* (- (sin b)) (sin a)))
25.0ms	(* (- (sin b)) (sin a))
13.0ms	(/ (* r (sin b)) (fma (cos a) (cos b) (* (- (sin b)) (sin a))))

series608.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* r (sin b))
141.0ms	(fma (cos a) (cos b) (* (- (sin b)) (sin a)))
79.0ms	(* (- (sin b)) (sin a))
338.0ms	(/ (* r (sin b)) (fma (cos a) (cos b) (* (- (sin b)) (sin a))))

simplify1.2s

Counts

93 → 93

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	138	1156
1	316	1135
2	1557	987
done	5001	985

prune771.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
24×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
16×	`associate-r`
13×	`add-exp-log` `associate-l` `add-cbrt-cube`
8×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `prod-exp` `associate-/r` `cbrt-unprod` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`distribute-lft-neg-out` `neg-mul-1` `frac-2neg` `associate-*r/` `clear-num` `fma-udef`

Counts

4 → 101

Calls

4 calls:

1.0ms	(fma (cos a) (cos b) (* (- (sin b)) (sin a)))
25.0ms	(* (- (sin b)) (sin a))
15.0ms	(* r (/ (sin b) (fma (cos a) (cos b) (* (- (sin b)) (sin a)))))
10.0ms	(/ (sin b) (fma (cos a) (cos b) (* (- (sin b)) (sin a))))

series676.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(fma (cos a) (cos b) (* (- (sin b)) (sin a)))
75.0ms	(* (- (sin b)) (sin a))
281.0ms	(* r (/ (sin b) (fma (cos a) (cos b) (* (- (sin b)) (sin a)))))
191.0ms	(/ (sin b) (fma (cos a) (cos b) (* (- (sin b)) (sin a))))

simplify1.2s

Counts

113 → 113

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	163	1900
1	386	1865
2	1720	1675
done	5001	1673

prune760.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes293.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	18
1	21	18
2	25	18
3	26	18
done	26	18

end0.0ms

sample5.7s

Algorithm

intervals

Results

3.1s	2921×	body	1280	valid
1.4s	1818×	body	640	valid
352.0ms	744×	body	320	valid
327.0ms	2198×	body	80	valid
79.0ms	322×	body	160	valid