Details

sample387.0ms

Algorithm

intervals

Results

147.0ms	89×	body	1280	valid
35.0ms	61×	body	640	valid
11.0ms	26×	body	320	valid
9.0ms	71×	body	80	valid
2.0ms	9×	body	160	valid

simplify47.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	21
5	21
4	20
3	18
2	16
1	12
0	8

prune58.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.7b

localize40.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
3.8b	(cos (+ a b))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 73

Calls

3 calls:

29.0ms	(* r (/ (sin b) (cos (+ a b))))
16.0ms	(/ (sin b) (cos (+ a b)))
19.0ms	(cos (+ a b))

series432.0ms

Counts

3 → 9

Calls

3 calls:

175.0ms	(* r (/ (sin b) (cos (+ a b))))
164.0ms	(/ (sin b) (cos (+ a b)))
93.0ms	(cos (+ a b))

simplify2.2s

Counts

82 → 82

Iterations

Iter	Nodes
done	5012
3	3284
2	879
1	280
0	123

prune601.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos a) (cos b)) (* (sin a) (sin 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))))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 110

Calls

4 calls:

13.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
109.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
18.0ms	(* (sin a) (sin b))
45.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series721.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
373.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
87.0ms	(* (sin a) (sin b))
147.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.7s

Counts

122 → 122

Iterations

Iter	Nodes
done	5001
2	1514
1	462
0	182

prune966.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

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

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

0.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
11.0ms	(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
18.0ms	(* (sin a) (sin b))
13.0ms	(/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))

series700.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
308.0ms	(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
83.0ms	(* (sin a) (sin b))
176.0ms	(/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))

simplify2.2s

Counts

106 → 106

Iterations

Iter	Nodes
done	5000
2	1288
1	369
0	156

prune883.0ms

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

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

0.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
7.0ms	(* r (sin b))
11.0ms	(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
9.0ms	(* (sin a) (sin b))

series634.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
54.0ms	(* r (sin b))
364.0ms	(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
67.0ms	(* (sin a) (sin b))

simplify1.7s

Counts

86 → 86

Iterations

Iter	Nodes
done	5000
2	933
1	301
0	129

prune664.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes425.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	16
1	16
0	14

end0.0ms

sample5.2s

Algorithm

intervals

Results

2.8s	2890×	body	1280	valid
1.4s	1831×	body	640	valid
282.0ms	2128×	body	80	valid
280.0ms	806×	body	320	valid
174.0ms	346×	body	160	valid