Details

sample426.0ms

Algorithm

intervals

Results

104.0ms	100×	body	1280	valid
73.0ms	54×	body	640	valid
14.0ms	28×	body	320	valid
9.0ms	67×	body	80	valid
2.0ms	7×	body	160	valid

simplify35.0ms

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.0b

localize37.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
2.3b	(cos (+ a b))

rewrite86.0ms

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:

49.0ms	(* r (/ (sin b) (cos (+ a b))))
17.0ms	(/ (sin b) (cos (+ a b)))
16.0ms	(cos (+ a b))

series290.0ms

Counts

3 → 9

Calls

3 calls:

170.0ms	(* r (/ (sin b) (cos (+ a b))))
72.0ms	(/ (sin b) (cos (+ a b)))
47.0ms	(cos (+ a b))

simplify2.7s

Counts

85 → 85

Iterations

Iter	Nodes
done	5010
3	4437
2	849
1	280
0	126

prune489.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

localize27.0ms

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))))

rewrite166.0ms

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:

33.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
82.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
19.0ms	(* (sin a) (sin b))
29.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series600.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
302.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
48.0ms	(* (sin a) (sin b))
140.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.6s

Counts

126 → 126

Iterations

Iter	Nodes
done	5000
2	1538
1	468
0	186

prune782.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite112.0ms

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:

36.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
16.0ms	(* r (sin b))
22.0ms	(* (sin a) (sin b))
36.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series577.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
50.0ms	(* r (sin b))
76.0ms	(* (sin a) (sin b))
322.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify2.0s

Counts

102 → 102

Iterations

Iter	Nodes
done	5003
2	1269
1	391
0	157

prune661.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
43×	`*-un-lft-identity`
33×	`add-cube-cbrt`
30×	`times-frac`
21×	`prod-diff`
13×	`add-cbrt-cube` `add-exp-log`
8×	`associate-/r*`
7×	`fma-neg`
6×	`pow1` `div-inv` `add-log-exp`
5×	`distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `associate-/l*`
3×	`cbrt-undiv` `div-exp` `associate-r` `associate-l`
2×	`clear-num` `frac-2neg` `flip3--` `prod-exp` `associate-/r/` `cos-mult` `cbrt-unprod` `flip--`
1×	`sub-neg` `diff-log` `pow-prod-down` `*-commutative` `unswap-sqr` `associate-/l/`

Counts

4 → 132

Calls

4 calls:

23.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
16.0ms	(* (cos a) (cos b))
49.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))
28.0ms	(/ (* (cos a) (cos b)) (sin b))

series585.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
61.0ms	(* (cos a) (cos b))
269.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))
99.0ms	(/ (* (cos a) (cos b)) (sin b))

simplify1.5s

Counts

144 → 144

Iterations

Iter	Nodes
done	5000
2	1321
1	476
0	216

prune726.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes234.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	11
0	11

end0.0ms

sample7.3s

Algorithm

intervals

Results

4.2s	2928×	body	1280	valid
1.6s	1854×	body	640	valid
694.0ms	2083×	body	80	valid
495.0ms	787×	body	320	valid
123.0ms	352×	body	160	valid