Details

sample299.0ms

Algorithm

intervals

Results

100.0ms	105×	body	1280	valid
82.0ms	59×	body	640	valid
11.0ms	24×	body	320	valid
9.0ms	60×	body	80	valid
3.0ms	8×	body	160	valid

simplify42.0ms

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.7b

localize61.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
2.8b	(cos (+ a b))

rewrite52.0ms

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` `insert-posit16` `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 → 76

Calls

3 calls:

28.0ms	(* r (/ (sin b) (cos (+ a b))))
11.0ms	(/ (sin b) (cos (+ a b)))
10.0ms	(cos (+ a b))

series383.0ms

Counts

3 → 9

Calls

3 calls:

249.0ms	(* r (/ (sin b) (cos (+ a b))))
101.0ms	(/ (sin b) (cos (+ a b)))
33.0ms	(cos (+ a b))

simplify1.6s

Counts

85 → 85

Iterations

Iter	Nodes
done	2000
3	2000
2	877
1	280
0	126

prune435.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize33.0ms

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

rewrite202.0ms

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` `insert-posit16` `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 → 114

Calls

4 calls:

39.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
102.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
46.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
13.0ms	(* (sin a) (sin b))

series796.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
395.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
176.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
86.0ms	(* (sin a) (sin b))

simplify1.4s

Counts

126 → 126

Iterations

Iter	Nodes
done	2002
3	2002
2	1536
1	468
0	186

prune825.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin b) (+ (- (* (cos a) (cos b)) (* (sin b) (sin a))) (fma (- (sin b)) (sin a) (* (sin b) (sin a)))))
0.2b	(* (sin b) (sin a))
0.2b	(* (sin b) (sin a))
52.3b	(fma (- (sin b)) (sin a) (* (sin b) (sin a)))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
21×	`add-sqr-sqrt`
17×	`add-cube-cbrt`
12×	`times-frac`
10×	`add-cbrt-cube` `add-exp-log`
8×	`pow1`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `associate-/r*` `insert-posit16` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
3×	`associate-/l*`
2×	`pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `sin-mult` `unswap-sqr`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `flip-+` `fma-udef` `div-inv`

Counts

4 → 91

Calls

4 calls:

73.0ms	(/ (sin b) (+ (- (* (cos a) (cos b)) (* (sin b) (sin a))) (fma (- (sin b)) (sin a) (* (sin b) (sin a)))))
12.0ms	(* (sin b) (sin a))
16.0ms	(* (sin b) (sin a))
1.0ms	(fma (- (sin b)) (sin a) (* (sin b) (sin a)))

series490.0ms

Counts

4 → 12

Calls

4 calls:

258.0ms	(/ (sin b) (+ (- (* (cos a) (cos b)) (* (sin b) (sin a))) (fma (- (sin b)) (sin a) (* (sin b) (sin a)))))
59.0ms	(* (sin b) (sin a))
91.0ms	(* (sin b) (sin a))
81.0ms	(fma (- (sin b)) (sin a) (* (sin b) (sin a)))

simplify1.4s

Counts

103 → 103

Iterations

Iter	Nodes
done	2001
3	2001
2	756
1	252
0	123

prune765.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite127.0ms

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` `add-log-exp`
5×	`sin-mult`
4×	`expm1-log1p-u` `associate-/r/` `cos-mult` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*` `times-frac` `prod-exp` `cbrt-unprod`
2×	`cbrt-undiv` `flip3--` `div-exp` `pow-prod-down` `*-commutative` `frac-sub` `flip--` `sub-div` `unswap-sqr`
1×	`clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `prod-diff` `div-inv` `associate-/l*`

Counts

4 → 90

Calls

4 calls:

21.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
19.0ms	(* (sin b) r)
24.0ms	(* (sin a) (sin b))
61.0ms	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series534.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
43.0ms	(* (sin b) r)
70.0ms	(* (sin a) (sin b))
306.0ms	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.4s

Counts

102 → 102

Iterations

Iter	Nodes
done	2072
3	2072
2	1243
1	393
0	156

prune676.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0b

regimes318.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	15
1	15
0	12

end0.0ms

sample7.7s

Algorithm

intervals

Results

4.0s	2947×	body	1280	valid
2.0s	1870×	body	640	valid
791.0ms	2117×	body	80	valid
436.0ms	742×	body	320	valid
153.0ms	325×	body	160	valid