Details

sample229.0ms

Algorithm

intervals

Results

101.0ms	89×	body	1280	valid
31.0ms	55×	body	640	valid
11.0ms	31×	body	320	valid
7.0ms	67×	body	80	valid
3.0ms	14×	body	160	valid

simplify22.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	20
5	20
4	19
3	17
2	14
1	12
0	8

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize35.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.3b	(/ (* r (sin b)) (cos (+ a b)))
3.6b	(cos (+ a b))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-cbrt-cube` `add-exp-log`
9×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
3×	`expm1-log1p-u` `associate-/r` `times-frac` `associate-r` `associate-l*` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
1×	`cos-sum` `clear-num` `frac-2neg` `pow-prod-down` `-commutative` `div-inv` `associate-/l` `unswap-sqr`

Counts

3 → 56

Calls

3 calls:

15.0ms	(* r (sin b))
24.0ms	(/ (* r (sin b)) (cos (+ a b)))
11.0ms	(cos (+ a b))

series271.0ms

Counts

3 → 9

Calls

3 calls:

65.0ms	(* r (sin b))
168.0ms	(/ (* r (sin b)) (cos (+ a b)))
38.0ms	(cos (+ a b))

simplify1.9s

Counts

65 → 65

Iterations

Iter	Nodes
done	5070
3	2428
2	611
1	223
0	101

prune334.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize60.0ms

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))
0.4b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

rewrite105.0ms

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:

38.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
17.0ms	(* r (sin b))
15.0ms	(* (sin a) (sin b))
33.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series563.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
52.0ms	(* r (sin b))
84.0ms	(* (sin a) (sin b))
317.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.6s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
2	1177
1	391
0	157

prune724.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.0b

localize62.0ms

Local error

Found 4 expressions with local error:

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

rewrite215.0ms

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)))
12.0ms	(* (sin a) (sin b))
114.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
53.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series691.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
70.0ms	(* (sin a) (sin b))
347.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
157.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.8s

Counts

126 → 126

Iterations

Iter	Nodes
done	5000
2	1551
1	469
0	186

prune910.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite78.0ms

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:

10.0ms	(* (cos a) (cos b))
25.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
14.0ms	(/ (* (cos a) (cos b)) (sin b))
27.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))

series684.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (cos a) (cos b))
158.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
142.0ms	(/ (* (cos a) (cos b)) (sin b))
328.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))

simplify2.1s

Counts

144 → 144

Iterations

Iter	Nodes
done	5000
2	1310
1	477
0	216

prune747.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes309.0ms

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

sample7.3s

Algorithm

intervals

Results

4.6s	2893×	body	1280	valid
1.4s	1826×	body	640	valid
483.0ms	2174×	body	80	valid
419.0ms	765×	body	320	valid
148.0ms	343×	body	160	valid