Details

sample282.0ms

Algorithm

intervals

Results

115.0ms	111×	body	1280	valid
62.0ms	22×	body	320	valid
36.0ms	48×	body	640	valid
10.0ms	67×	body	80	valid
3.0ms	8×	body	160	valid

simplify68.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	21
5	21
4	20
3	18
2	16
1	12
0	8

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.6b

localize24.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.3b	(/ (sin b) (cos (+ a b)))
2.4b	(cos (+ a b))

rewrite48.0ms

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:

25.0ms	(* r (/ (sin b) (cos (+ a b))))
10.0ms	(/ (sin b) (cos (+ a b)))
9.0ms	(cos (+ a b))

series232.0ms

Counts

3 → 9

Calls

3 calls:

124.0ms	(* r (/ (sin b) (cos (+ a b))))
56.0ms	(/ (sin b) (cos (+ a b)))
51.0ms	(cos (+ a b))

simplify903.0ms

Counts

85 → 85

Iterations

Iter	Nodes
3	2409
2	802
1	276
0	126

prune796.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize51.0ms

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

rewrite193.0ms

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:

36.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
107.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
11.0ms	(* (sin a) (sin b))
37.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series690.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
317.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
84.0ms	(* (sin a) (sin b))
174.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify3.6s

Counts

126 → 126

Iterations

Iter	Nodes
3	4651
2	1491
1	464
0	186

prune1.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0b

localize63.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (sin b) (/ (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b)))))
0.3b	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
0.3b	(/ (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))
0.4b	(* (* (cos a) (cos b)) (* (cos a) (cos b)))

rewrite392.0ms

Algorithm

rewrite-expression-head

Rules

117×	`times-frac`
82×	`pow1`
65×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
35×	`add-cbrt-cube` `add-exp-log`
34×	`pow-prod-down`
27×	`cos-mult` `sin-mult`
22×	`associate-/r*`
16×	`prod-exp` `associate-/r/` `cbrt-unprod` `difference-of-squares` `associate-/l/`
12×	`associate-l/` `associate-r/`
10×	`frac-times`
9×	`frac-sub`
8×	`pow-sqr` `pow-prod-up`
7×	`associate-/l*`
6×	`div-inv`
5×	`flip3-+` `frac-add` `flip-+` `sub-div`
4×	`expm1-log1p-u` `cbrt-undiv` `pow-plus` `div-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow2` `clear-num` `frac-2neg` `swap-sqr` `associate-r` `associate-l` `*-commutative`
1×	`flip3--` `div-sub` `flip--`

Counts

4 → 231

Calls

4 calls:

78.0ms	(/ (sin b) (/ (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b)))))
65.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
192.0ms	(/ (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))
50.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))

series779.0ms

Counts

4 → 12

Calls

4 calls:

383.0ms	(/ (sin b) (/ (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b)))))
65.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
233.0ms	(/ (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))
97.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))

simplify2.3s

Counts

243 → 243

Iterations

Iter	Nodes
2	3810
1	1020
0	366

prune3.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize63.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin a) (sin b))
0.2b	(* (sin a) (sin b))
0.2b	(* (sin a) (sin b))
0.3b	(* (/ 1 (/ (+ (* (cos a) (cos b)) (* (sin a) (sin b))) 1)) (/ (sin b) (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))))

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

192×	`times-frac`
167×	`add-sqr-sqrt`
118×	`add-exp-log`
98×	`*-un-lft-identity`
83×	`add-cube-cbrt`
66×	`div-exp`
62×	`associate-r`
53×	`associate-l`
46×	`add-cbrt-cube`
33×	`prod-exp`
24×	`unswap-sqr`
18×	`cbrt-undiv` `1-exp`
12×	`pow1` `cbrt-unprod`
11×	`associate-/r/`
9×	`rec-exp`
8×	`div-inv`
6×	`sin-mult`
4×	`expm1-log1p-u` `pow-prod-down` `*-commutative` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `frac-add` `cos-mult` `flip-+`
1×	`frac-times` `associate-l/` `associate-r/`

Counts

4 → 238

Calls

4 calls:

11.0ms	(* (sin a) (sin b))
12.0ms	(* (sin a) (sin b))
22.0ms	(* (sin a) (sin b))
125.0ms	(* (/ 1 (/ (+ (* (cos a) (cos b)) (* (sin a) (sin b))) 1)) (/ (sin b) (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))))

series377.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (sin a) (sin b))
66.0ms	(* (sin a) (sin b))
61.0ms	(* (sin a) (sin b))
189.0ms	(* (/ 1 (/ (+ (* (cos a) (cos b)) (* (sin a) (sin b))) 1)) (/ (sin b) (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))))

simplify6.0s

Counts

250 → 250

Iterations

Iter	Nodes
2	4354
1	1346
0	398

prune3.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes290.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
2	23
1	23
0	18

end0.0ms

sample7.2s

Algorithm

intervals

Results

3.8s	2950×	body	1280	valid
1.9s	1796×	body	640	valid
535.0ms	744×	body	320	valid
446.0ms	2168×	body	80	valid
159.0ms	343×	body	160	valid