Details

sample212.0ms

Algorithm

intervals

Results

65.0ms	94×	body	1280	valid
40.0ms	11×	body	160	valid
29.0ms	62×	body	640	valid
7.0ms	21×	body	320	valid
6.0ms	68×	body	80	valid

simplify20.0ms

Counts

1 → 1

Iterations

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

prune39.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.4b

localize22.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (sin b) (cos (+ a b)))
0.2b	(* r (/ (sin b) (cos (+ a b))))
2.2b	(cos (+ a b))

rewrite36.0ms

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:

8.0ms	(/ (sin b) (cos (+ a b)))
15.0ms	(* r (/ (sin b) (cos (+ a b))))
10.0ms	(cos (+ a b))

series341.0ms

Counts

3 → 9

Calls

3 calls:

151.0ms	(/ (sin b) (cos (+ a b)))
151.0ms	(* r (/ (sin b) (cos (+ a b))))
38.0ms	(cos (+ a b))

simplify1.1s

Counts

82 → 82

Iterations

Iter	Nodes
done	5001
2	1075
1	283
0	123

prune587.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite169.0ms

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:

26.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
42.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
88.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
10.0ms	(* (sin a) (sin b))

series706.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
202.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
324.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
66.0ms	(* (sin a) (sin b))

simplify1.4s

Counts

122 → 122

Iterations

Iter	Nodes
done	5001
2	1958
1	467
0	182

prune954.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

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

rewrite60.0ms

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))))
7.0ms	(/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
23.0ms	(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
19.0ms	(* (sin a) (sin b))

series714.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
173.0ms	(/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
321.0ms	(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
62.0ms	(* (sin a) (sin b))

simplify1.4s

Counts

106 → 106

Iterations

Iter	Nodes
done	5000
2	1703
1	374
0	156

prune1.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

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

rewrite42.0ms

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))))
12.0ms	(* r (sin b))
19.0ms	(* (sin a) (sin b))
10.0ms	(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))

series577.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
70.0ms	(* r (sin b))
67.0ms	(* (sin a) (sin b))
320.0ms	(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))

simplify1.5s

Counts

86 → 86

Iterations

Iter	Nodes
done	5000
2	1342
1	301
0	129

prune565.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes309.0ms

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	20
2	20
1	18
0	12

end0.0ms

sample5.9s

Algorithm

intervals

Results

3.1s	2960×	body	1280	valid
1.3s	1897×	body	640	valid
651.0ms	707×	body	320	valid
253.0ms	2060×	body	80	valid
92.0ms	376×	body	160	valid