Details

sample341.0ms

Algorithm

intervals

Results

56.0ms	85×	body	1280	valid
30.0ms	64×	body	640	valid
11.0ms	23×	body	320	valid
8.0ms	76×	body	80	valid
2.0ms	8×	body	160	valid

simplify65.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

localize18.0ms

Local error

Found 3 expressions with local error:

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

rewrite61.0ms

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:

22.0ms	(* r (/ (sin b) (cos (+ a b))))
12.0ms	(/ (sin b) (cos (+ a b)))
14.0ms	(cos (+ a b))

series207.0ms

Counts

3 → 9

Calls

3 calls:

133.0ms	(* r (/ (sin b) (cos (+ a b))))
46.0ms	(/ (sin b) (cos (+ a b)))
28.0ms	(cos (+ a b))

simplify824.0ms

Counts

82 → 82

Iterations

Useful iterations: done (820.0ms)

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

prune552.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite228.0ms

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:

27.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
24.0ms	(* (sin b) (sin a))
131.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
43.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a))))

series741.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
63.0ms	(* (sin b) (sin a))
351.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
173.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a))))

simplify2.0s

Counts

122 → 122

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	187	2200
1	467	2145
2	2138	1957
done	5001	1870

prune932.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite69.0ms

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 a)) (sin b)))
34.0ms	(* (- (sin a)) (sin b))
17.0ms	(* r (/ (sin b) (fma (cos a) (cos b) (* (- (sin a)) (sin b)))))
10.0ms	(/ (sin b) (fma (cos a) (cos b) (* (- (sin a)) (sin b))))

series833.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(fma (cos a) (cos b) (* (- (sin a)) (sin b)))
94.0ms	(* (- (sin a)) (sin b))
385.0ms	(* r (/ (sin b) (fma (cos a) (cos b) (* (- (sin a)) (sin b)))))
233.0ms	(/ (sin b) (fma (cos a) (cos b) (* (- (sin a)) (sin b))))

simplify1.3s

Counts

113 → 113

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	159	1900
1	382	1865
2	1695	1671
done	5000	1669

prune931.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize51.0ms

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

rewrite73.0ms

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:

11.0ms	(* r (sin b))
0.0ms	(fma (cos a) (cos b) (* (- (sin a)) (sin b)))
25.0ms	(* (- (sin a)) (sin b))
34.0ms	(/ (* r (sin b)) (fma (cos a) (cos b) (* (- (sin a)) (sin b))))

series661.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(* r (sin b))
147.0ms	(fma (cos a) (cos b) (* (- (sin a)) (sin b)))
95.0ms	(* (- (sin a)) (sin b))
340.0ms	(/ (* r (sin b)) (fma (cos a) (cos b) (* (- (sin a)) (sin b))))

simplify1.3s

Counts

93 → 93

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	133	1156
1	317	1135
2	1574	983
done	5001	979

prune566.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes384.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample5.8s

Algorithm

intervals

Results

3.4s	2921×	body	1280	valid
1.2s	1818×	body	640	valid
337.0ms	2198×	body	80	valid
295.0ms	744×	body	320	valid
84.0ms	322×	body	160	valid