Details

sample416.0ms

Algorithm

intervals

Results

229.0ms	65×	body	80	valid
70.0ms	94×	body	1280	valid
27.0ms	60×	body	640	valid
9.0ms	30×	body	320	valid
1.0ms	7×	body	160	valid

simplify44.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.7b

localize30.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (sin b) (cos (+ a b)))
0.2b	(* r (/ (sin b) (cos (+ a b))))
3.9b	(cos (+ a b))

rewrite100.0ms

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:

28.0ms	(/ (sin b) (cos (+ a b)))
43.0ms	(* r (/ (sin b) (cos (+ a b))))
25.0ms	(cos (+ a b))

series276.0ms

Counts

3 → 9

Calls

3 calls:

96.0ms	(/ (sin b) (cos (+ a b)))
151.0ms	(* r (/ (sin b) (cos (+ a b))))
29.0ms	(cos (+ a b))

simplify3.9s

Counts

82 → 82

Iterations

Useful iterations: done (3.9s)

Iter	Nodes	Cost
0	122	955
1	260	924
2	666	834
3	1809	830
done	5001	824

prune331.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.3b

localize39.0ms

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

rewrite214.0ms

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:

22.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
47.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
12.0ms	(* (sin a) (sin b))
129.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series718.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
174.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
80.0ms	(* (sin a) (sin b))
359.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify2.8s

Counts

122 → 122

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	181	2200
1	430	2141
2	1247	1971
3	3712	1826
done	5000	1821

prune637.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

0.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
23.0ms	(/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
24.0ms	(* (sin a) (sin b))
30.0ms	(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))

series679.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
162.0ms	(/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
68.0ms	(* (sin a) (sin b))
293.0ms	(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))

simplify2.4s

Counts

106 → 106

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	153	1831
1	326	1797
2	888	1607
3	2448	1599
done	5000	1572

prune564.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b	(* r (sin b))
0.2b	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
0.2b	(* (sin a) (sin b))
0.3b	(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))

rewrite83.0ms

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`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `prod-exp` `associate-/r*` `cbrt-unprod`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `unswap-sqr`
1×	`frac-2neg` `clear-num` `fma-udef` `div-inv` `sin-mult` `associate-/l*`

Counts

4 → 74

Calls

4 calls:

21.0ms	(* r (sin b))
1.0ms	(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)))))

series669.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* r (sin b))
115.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
88.0ms	(* (sin a) (sin b))
402.0ms	(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))

simplify2.2s

Counts

86 → 86

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	127	1087
1	273	1071
2	775	921
3	2734	915
done	5000	912

prune413.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes234.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	18
1	16	18
done	16	18

end0.0ms

sample5.6s

Algorithm

intervals

Results

3.2s	2916×	body	1280	valid
1.3s	1826×	body	640	valid
296.0ms	2134×	body	80	valid
291.0ms	784×	body	320	valid
82.0ms	341×	body	160	valid