Details

sample309.0ms

Algorithm

intervals

Results

90.0ms	91×	body	1280	valid
75.0ms	23×	body	320	valid
39.0ms	67×	body	640	valid
11.0ms	60×	body	80	valid
5.0ms	15×	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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.2b

localize40.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
5.5b	(cos (+ a b))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 47

Calls

3 calls:

41.0ms	(* r (sin b))
29.0ms	(/ (* r (sin b)) (cos (+ a b)))
23.0ms	(cos (+ a b))

series382.0ms

Counts

3 → 9

Calls

3 calls:

114.0ms	(* r (sin b))
223.0ms	(/ (* r (sin b)) (cos (+ a b)))
45.0ms	(cos (+ a b))

simplify3.6s

Counts

56 → 56

Iterations

Iter	Nodes
done	5001
3	2369
2	586
1	206
0	90

prune499.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize64.0ms

Local error

Found 4 expressions with local error:

0.1b	(* r (sin b))
0.1b	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.2b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.3b	(* (sin a) (sin b))

rewrite171.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`add-exp-log` `add-cbrt-cube`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1`
6×	`associate-r` `associate-l` `add-log-exp`
5×	`sin-mult`
4×	`associate-/r/` `cos-mult`
3×	`times-frac` `prod-exp` `associate-/r*` `cbrt-unprod`
2×	`cbrt-undiv` `flip3--` `div-exp` `pow-prod-down` `*-commutative` `frac-sub` `flip--` `sub-div` `unswap-sqr`
1×	`sub-neg` `frac-2neg` `diff-log` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 76

Calls

4 calls:

26.0ms	(* r (sin b))
39.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
65.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
37.0ms	(* (sin a) (sin b))

series763.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* r (sin b))
174.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
434.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
89.0ms	(* (sin a) (sin b))

simplify5.4s

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
3	4589
2	1147
1	360
0	140

prune973.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize96.0ms

Local error

Found 4 expressions with local error:

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

rewrite498.0ms

Algorithm

rewrite-expression-head

Rules

29×	`sin-mult`
27×	`cos-mult`
24×	`frac-times`
19×	`associate-/l/`
18×	`add-sqr-sqrt`
15×	`add-exp-log` `add-cbrt-cube`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`flip3-+` `frac-add` `flip-+`
10×	`pow1`
9×	`associate-r` `associate-l`
8×	`flip3--` `associate-*r/` `frac-sub` `flip--` `sub-div`
6×	`associate-*l/`
4×	`prod-exp` `cbrt-unprod` `add-log-exp`
3×	`times-frac` `pow-prod-down` `associate-/r` `associate-/r/` `-commutative` `unswap-sqr`
2×	`cbrt-undiv` `distribute-rgt-in` `sub-neg` `distribute-lft-in` `div-exp`
1×	`frac-2neg` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 122

Calls

4 calls:

25.0ms	(* (sin a) (sin b))
32.0ms	(* (sin a) (sin b))
203.0ms	(* (+ (* (cos a) (cos b)) (* (sin a) (sin b))) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
184.0ms	(/ (* (+ (* (cos a) (cos b)) (* (sin a) (sin b))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))

series678.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(* (sin a) (sin b))
88.0ms	(* (sin a) (sin b))
310.0ms	(* (+ (* (cos a) (cos b)) (* (sin a) (sin b))) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
187.0ms	(/ (* (+ (* (cos a) (cos b)) (* (sin a) (sin b))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify4.5s

Counts

134 → 134

Iterations

Iter	Nodes
done	5000
2	3336
1	571
0	185

prune1.8s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize108.0ms

Local error

Found 4 expressions with local error:

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

rewrite184.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-exp-log` `add-cbrt-cube`
18×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity`
10×	`pow1`
9×	`associate-r` `associate-l`
5×	`prod-exp` `cbrt-unprod` `sin-mult`
4×	`cbrt-undiv` `div-exp` `associate-/r/` `add-log-exp`
3×	`times-frac` `pow-prod-down` `associate-/r` `-commutative` `unswap-sqr`
2×	`cos-mult`
1×	`flip3--` `frac-2neg` `associate-l/` `clear-num` `frac-sub` `flip--` `div-inv` `associate-/l/` `associate-/l` `sub-div`

Counts

4 → 85

Calls

4 calls:

26.0ms	(* (sin a) (sin b))
27.0ms	(* (sin a) (sin b))
29.0ms	(* (sin a) (sin b))
99.0ms	(/ (* (/ (sin b) (+ (* (cos a) (cos b)) (* (sin a) (sin b)))) r) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series1.3s

Counts

4 → 12

Calls

4 calls:

94.0ms	(* (sin a) (sin b))
91.0ms	(* (sin a) (sin b))
95.0ms	(* (sin a) (sin b))
981.0ms	(/ (* (/ (sin b) (+ (* (cos a) (cos b)) (* (sin a) (sin b)))) r) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify3.3s

Counts

97 → 97

Iterations

Iter	Nodes
done	5000
2	1706
1	442
0	150

prune1.0s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes597.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	20
1	20
0	15

end0.0ms

sample7.1s

Algorithm

intervals

Results

4.2s	2850×	body	1280	valid
1.5s	1867×	body	640	valid
417.0ms	2196×	body	80	valid
386.0ms	747×	body	320	valid
178.0ms	340×	body	160	valid