Details

sample355.0ms

Algorithm

intervals

Results

127.0ms	103×	body	1280	valid
73.0ms	43×	body	640	valid
25.0ms	30×	body	320	valid
13.0ms	73×	body	80	valid
2.0ms	7×	body	160	valid

simplify39.0ms

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.4b

localize40.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
2.9b	(cos (+ a b))

rewrite56.0ms

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:

12.0ms	(* r (sin b))
24.0ms	(/ (* r (sin b)) (cos (+ a b)))
19.0ms	(cos (+ a b))

series200.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(* r (sin b))
121.0ms	(/ (* r (sin b)) (cos (+ a b)))
25.0ms	(cos (+ a b))

simplify618.0ms

Counts

65 → 65

Iterations

Iter	Nodes
done	2000
2	611
1	223
0	101

prune331.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize47.0ms

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

rewrite107.0ms

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:

35.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
8.0ms	(* r (sin b))
39.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
23.0ms	(* (sin a) (sin b))

series586.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
73.0ms	(* r (sin b))
334.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
63.0ms	(* (sin a) (sin b))

simplify817.0ms

Counts

102 → 102

Iterations

Iter	Nodes
done	2010
2	1162
1	394
0	157

prune748.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize55.0ms

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 b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.2b	(* (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:

17.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
88.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
31.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
29.0ms	(* (sin a) (sin b))

series701.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
333.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
174.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
68.0ms	(* (sin a) (sin b))

simplify877.0ms

Counts

126 → 126

Iterations

Iter	Nodes
done	2002
2	1536
1	468
0	186

prune804.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize49.0ms

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

rewrite199.0ms

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:

8.0ms	(* r (sin b))
39.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
128.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
22.0ms	(* (sin a) (sin b))

series642.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* r (sin b))
164.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
352.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
63.0ms	(* (sin a) (sin b))

simplify887.0ms

Counts

138 → 138

Iterations

Iter	Nodes
done	2002
2	1554
1	509
0	195

prune853.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

regimes374.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	17
1	17
0	14

end0.0ms

sample7.5s

Algorithm

intervals

Results

3.8s	2956×	body	1280	valid
1.6s	1821×	body	640	valid
1.3s	2115×	body	80	valid
519.0ms	766×	body	320	valid
122.0ms	343×	body	160	valid