Details

sample1.3s

Algorithm

intervals

Results

996.0ms	105×	body	1280	valid
69.0ms	59×	body	640	valid
18.0ms	24×	body	320	valid
13.0ms	60×	body	80	valid
4.0ms	8×	body	160	valid

simplify49.0ms

Counts

1 → 1

Iterations

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

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.7b

localize72.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
2.8b	(cos (+ a b))

rewrite40.0ms

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:

13.0ms	(* r (sin b))
12.0ms	(/ (* r (sin b)) (cos (+ a b)))
12.0ms	(cos (+ a b))

series262.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(* r (sin b))
153.0ms	(/ (* r (sin b)) (cos (+ a b)))
54.0ms	(cos (+ a b))

simplify1.1s

Counts

65 → 65

Iterations

Iter	Nodes
done	2000
3	2000
2	611
1	223
0	101

prune676.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize26.0ms

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

rewrite104.0ms

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:

34.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
17.0ms	(* r (sin b))
21.0ms	(* (sin a) (sin b))
30.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series569.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
57.0ms	(* r (sin b))
68.0ms	(* (sin a) (sin b))
314.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.2s

Counts

102 → 102

Iterations

Iter	Nodes
done	2126
3	2126
2	1177
1	391
0	157

prune1.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

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

rewrite354.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 195

Calls

4 calls:

63.0ms	(/ (* r (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)))))
59.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
38.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))
191.0ms	(/ (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))

series1.0s

Counts

4 → 12

Calls

4 calls:

569.0ms	(/ (* r (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)))))
66.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
97.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))
277.0ms	(/ (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.4s

Counts

207 → 207

Iterations

Iter	Nodes
done	2000
2	2000
1	963
0	313

prune3.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0b

localize60.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin a) (sin b))
0.2b	(* (sin a) (sin b))
0.2b	(/ r (/ (+ (* (cos a) (cos b)) (* (sin a) (sin b))) 1))
0.2b	(* (/ r (/ (+ (* (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))))))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

243×	`times-frac`
175×	`add-sqr-sqrt`
126×	`*-un-lft-identity`
123×	`add-cube-cbrt`
63×	`add-exp-log`
59×	`associate-r`
50×	`associate-l`
49×	`add-cbrt-cube`
32×	`div-exp`
21×	`cbrt-undiv`
14×	`prod-exp` `unswap-sqr`
13×	`associate-/r*` `div-inv`
12×	`associate-/r/`
11×	`cbrt-unprod`
10×	`pow1`
5×	`sin-mult`
4×	`expm1-log1p-u` `1-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `pow-prod-down` `frac-add` `cos-mult` `-commutative` `flip-+` `associate-/l`
1×	`frac-times` `clear-num` `frac-2neg` `associate-l/` `associate-r/`

Counts

4 → 263

Calls

4 calls:

11.0ms	(* (sin a) (sin b))
11.0ms	(* (sin a) (sin b))
10.0ms	(/ r (/ (+ (* (cos a) (cos b)) (* (sin a) (sin b))) 1))
93.0ms	(* (/ r (/ (+ (* (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))))))

series829.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* (sin a) (sin b))
80.0ms	(* (sin a) (sin b))
320.0ms	(/ r (/ (+ (* (cos a) (cos b)) (* (sin a) (sin b))) 1))
358.0ms	(* (/ r (/ (+ (* (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))))))

simplify1.7s

Counts

275 → 275

Iterations

Iter	Nodes
done	2000
2	2000
1	1497
0	449

prune4.4s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

regimes350.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	23
1	23
0	17

end0.0ms

sample7.4s

Algorithm

intervals

Results

4.0s	2947×	body	1280	valid
2.2s	1870×	body	640	valid
449.0ms	742×	body	320	valid
446.0ms	2117×	body	80	valid
113.0ms	325×	body	160	valid