Details

sample80.0ms

Algorithm

intervals

Results

44.0ms	99×	body	1280	valid
16.0ms	64×	body	640	valid
4.0ms	24×	body	320	valid
3.0ms	59×	body	80	valid
1.0ms	10×	body	160	valid

simplify12.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	9
1	12	9
2	16	9
3	19	9
4	20	9
done	20	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.2b

localize17.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
3.3b	(cos (+ a b))

rewrite16.0ms

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:

3.0ms	(* r (sin b))
4.0ms	(/ (* r (sin b)) (cos (+ a b)))
7.0ms	(cos (+ a b))

series164.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(* r (sin b))
101.0ms	(/ (* r (sin b)) (cos (+ a b)))
24.0ms	(cos (+ a b))

simplify2.0s

Counts

56 → 56

Iterations

Useful iterations: 3 (688.0ms)

Iter	Nodes	Cost
0	90	535
1	199	525
2	706	447
3	4402	443
done	5000	443

prune152.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

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

rewrite23.0ms

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:

4.0ms	(* r (sin b))
5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
4.0ms	(* (sin a) (sin b))
9.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series387.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* r (sin b))
83.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
45.0ms	(* (sin a) (sin b))
219.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify588.0ms

Counts

88 → 88

Iterations

Useful iterations: 2 (116.0ms)

Iter	Nodes	Cost
0	140	1256
1	343	1224
2	1259	1170
done	5000	1170

prune286.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

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

rewrite48.0ms

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:

5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
25.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
6.0ms	(* (sin a) (sin b))
9.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series463.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
218.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
48.0ms	(* (sin a) (sin b))
114.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify673.0ms

Counts

112 → 112

Iterations

Useful iterations: 2 (138.0ms)

Iter	Nodes	Cost
0	170	2072
1	404	2024
2	1389	1834
done	5000	1834

prune393.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

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

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 135

Calls

4 calls:

5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
4.0ms	(* (sin a) (sin b))
10.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
10.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))

series471.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
45.0ms	(* (sin a) (sin b))
118.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
224.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))

simplify812.0ms

Counts

147 → 147

Iterations

Useful iterations: done (807.0ms)

Iter	Nodes	Cost
0	240	3375
1	568	3269
2	2015	2904
done	5001	2902

prune452.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes158.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	16
1	15	16
done	15	16

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.3s	2963×	body	1280	valid
487.0ms	1882×	body	640	valid
130.0ms	733×	body	320	valid
120.0ms	2086×	body	80	valid
43.0ms	339×	body	160	valid