Details

sample293.0ms

Algorithm

intervals

Results

101.0ms	100×	body	1280	valid
34.0ms	54×	body	640	valid
13.0ms	28×	body	320	valid
9.0ms	67×	body	80	valid
2.0ms	7×	body	160	valid

simplify76.0ms

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: 16.0b

localize27.0ms

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))

rewrite47.0ms

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))))
12.0ms	(/ (sin b) (cos (+ a b)))
9.0ms	(cos (+ a b))

series213.0ms

Counts

3 → 9

Calls

3 calls:

127.0ms	(* r (/ (sin b) (cos (+ a b))))
51.0ms	(/ (sin b) (cos (+ a b)))
34.0ms	(cos (+ a b))

simplify2.2s

Counts

85 → 85

Iterations

Iter	Nodes
done	5001
3	3116
2	877
1	280
0	126

prune473.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

localize31.0ms

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))))

rewrite223.0ms

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)))
105.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
30.0ms	(* (sin a) (sin b))
50.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series677.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
364.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
61.0ms	(* (sin a) (sin b))
137.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.6s

Counts

126 → 126

Iterations

Iter	Nodes
done	5001
2	1557
1	468
0	186

prune936.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(* r (sin b))
0.1b	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.2b	(* (sin a) (sin b))
0.2b	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-exp-log`
27×	`add-sqr-sqrt`
23×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
22×	`add-cbrt-cube`
18×	`times-frac`
14×	`pow1` `prod-exp`
8×	`associate-/r/` `cbrt-unprod`
7×	`associate-l`
6×	`div-exp`
5×	`pow-prod-down` `sin-mult`
4×	`expm1-log1p-u` `cos-mult` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `rec-exp` `associate-/r` `1-exp` `-commutative` `associate-/l*`
2×	`flip3--` `frac-sub` `div-inv` `flip--` `sub-div` `unswap-sqr`
1×	`clear-num` `frac-2neg` `associate-*r/` `un-div-inv` `pow-flip` `inv-pow`

Counts

4 → 126

Calls

4 calls:

17.0ms	(* r (sin b))
64.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
11.0ms	(* (sin a) (sin b))
66.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series586.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* r (sin b))
144.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
53.0ms	(* (sin a) (sin b))
330.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify3.0s

Counts

138 → 138

Iterations

Iter	Nodes
done	5000
3	4659
2	1522
1	509
0	195

prune875.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize56.0ms

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))

rewrite113.0ms

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:

30.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
10.0ms	(* (cos a) (cos b))
39.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))
31.0ms	(/ (* (cos a) (cos b)) (sin b))

series549.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
61.0ms	(* (cos a) (cos b))
274.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))
87.0ms	(/ (* (cos a) (cos b)) (sin b))

simplify1.4s

Counts

144 → 144

Iterations

Iter	Nodes
done	5000
2	1296
1	476
0	216

prune749.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes307.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	17
1	17
0	14

end0.0ms

sample5.5s

Algorithm

intervals

Results

3.1s	2928×	body	1280	valid
1.2s	1854×	body	640	valid
659.0ms	787×	body	320	valid
219.0ms	2083×	body	80	valid
82.0ms	352×	body	160	valid