Details

sample316.0ms

Algorithm

intervals

Results

141.0ms	92×	body	1280	valid
35.0ms	60×	body	640	valid
11.0ms	25×	body	320	valid
10.0ms	72×	body	80	valid
2.0ms	7×	body	160	valid

simplify19.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	8	9
1	12	9
2	16	9
3	20	9
4	21	9
done	21	9

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.4b

localize15.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (sin b) (cos (+ a b)))
0.2b	(* r (/ (sin b) (cos (+ a b))))
2.4b	(cos (+ a b))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 67

Calls

3 calls:

27.0ms	(/ (sin b) (cos (+ a b)))
21.0ms	(* r (/ (sin b) (cos (+ a b))))
14.0ms	(cos (+ a b))

series381.0ms

Counts

3 → 9

Calls

3 calls:

124.0ms	(/ (sin b) (cos (+ a b)))
228.0ms	(* r (/ (sin b) (cos (+ a b))))
28.0ms	(cos (+ a b))

simplify781.0ms

Counts

76 → 76

Iterations

Useful iterations: done (776.0ms)

Iter	Nodes	Cost
0	116	909
1	271	887
2	1040	801
done	5001	791

prune249.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite232.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

19.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
132.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
51.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
26.0ms	(* (sin b) (sin a))

series681.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
327.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
187.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
55.0ms	(* (sin b) (sin a))

simplify1.7s

Counts

112 → 112

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	175	2072
1	439	2028
2	1991	1842
done	5001	1761

prune693.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite131.0ms

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:

19.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
27.0ms	(* r (sin b))
27.0ms	(* (sin b) (sin a))
56.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin b) (sin a))))

series581.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
50.0ms	(* r (sin b))
56.0ms	(* (sin b) (sin a))
348.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin b) (sin a))))

simplify1.1s

Counts

88 → 88

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	145	1256
1	370	1224
2	1883	1084
done	5001	1080

prune447.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite907.0ms

Algorithm

rewrite-expression-head

Rules

86×	`pow1`
39×	`add-exp-log` `add-cbrt-cube`
36×	`pow-prod-down`
29×	`associate-l`
25×	`sin-mult`
24×	`cos-mult`
21×	`prod-exp` `cbrt-unprod`
16×	`associate-/r/`
15×	`associate-*r/`
13×	`add-sqr-sqrt` `frac-times` `associate-*l/`
9×	`add-cube-cbrt` `*-un-lft-identity` `frac-sub`
8×	`associate-r` `pow-sqr` `pow-prod-up`
5×	`sub-div`
4×	`times-frac` `pow-plus` `*-commutative` `add-log-exp`
2×	`cbrt-undiv` `pow2` `flip3-+` `swap-sqr` `div-exp` `frac-add` `flip-+` `unswap-sqr`
1×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `flip--` `div-inv` `difference-of-squares`

Counts

4 → 145

Calls

4 calls:

26.0ms	(* (sin b) (sin a))
79.0ms	(* (* (sin b) (sin a)) (* (sin b) (sin a)))
744.0ms	(* (/ (* r (sin b)) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin b) (sin a)) (* (sin b) (sin a))))) (+ (* (cos a) (cos b)) (* (sin b) (sin a))))
48.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))

series933.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(* (sin b) (sin a))
88.0ms	(* (* (sin b) (sin a)) (* (sin b) (sin a)))
667.0ms	(* (/ (* r (sin b)) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin b) (sin a)) (* (sin b) (sin a))))) (+ (* (cos a) (cos b)) (* (sin b) (sin a))))
93.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))

simplify579.0ms

Counts

157 → 157

Iterations

Useful iterations: done (568.0ms)

Iter	Nodes	Cost
0	240	3545
1	846	3021
done	5000	2594

prune776.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes221.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	40
1	24	40
done	24	40

end0.0ms

sample5.7s

Algorithm

intervals

Results

3.5s	2868×	body	1280	valid
1.0s	1851×	body	640	valid
347.0ms	2198×	body	80	valid
254.0ms	733×	body	320	valid
145.0ms	350×	body	160	valid