Details

sample234.0ms

Algorithm

intervals

Results

135.0ms	99×	body	1280	valid
26.0ms	61×	body	640	valid
6.0ms	19×	body	320	valid
6.0ms	65×	body	80	valid
3.0ms	12×	body	160	valid

simplify33.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.2b

localize17.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
4.2b	(cos (+ a b))

rewrite65.0ms

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:

30.0ms	(* r (sin b))
20.0ms	(/ (* r (sin b)) (cos (+ a b)))
13.0ms	(cos (+ a b))

series227.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(* r (sin b))
144.0ms	(/ (* r (sin b)) (cos (+ a b)))
31.0ms	(cos (+ a b))

simplify795.0ms

Counts

56 → 56

Iterations

Useful iterations: done (792.0ms)

Iter	Nodes	Cost
0	90	535
1	206	525
2	855	455
done	5000	443

prune212.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize32.0ms

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))

rewrite113.0ms

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:

25.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
11.0ms	(* r (sin b))
49.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
26.0ms	(* (sin a) (sin b))

series567.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
73.0ms	(* r (sin b))
304.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
90.0ms	(* (sin a) (sin b))

simplify1.2s

Counts

88 → 88

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	140	1256
1	361	1224
2	1707	1084
done	5000	1028

prune519.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

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))

rewrite228.0ms

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:

23.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
137.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
42.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
19.0ms	(* (sin a) (sin b))

series745.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
378.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
184.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
70.0ms	(* (sin a) (sin b))

simplify1.2s

Counts

112 → 112

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	170	2072
1	436	2028
2	1980	1842
done	5000	1770

prune592.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos a) (cos b))
0.1b	(- (/ (* (cos a) (cos b)) (sin b)) (/ (sin a) 1))
0.2b	(/ (* (cos a) (cos b)) (sin b))
0.2b	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (/ (sin a) 1)))

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
34×	`times-frac`
20×	`add-cube-cbrt`
15×	`difference-of-squares`
13×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r*`
6×	`pow1` `add-log-exp`
5×	`distribute-lft-out--`
4×	`associate-/l*`
3×	`cbrt-undiv` `div-exp` `associate-r` `associate-l` `associate-/r/`
2×	`flip3--` `frac-2neg` `prod-exp` `clear-num` `cos-mult` `frac-sub` `flip--` `cbrt-unprod` `div-inv`
1×	`sub-neg` `diff-log` `pow-prod-down` `*-commutative` `associate-/l/` `unswap-sqr`

Counts

4 → 104

Calls

4 calls:

22.0ms	(* (cos a) (cos b))
58.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (/ (sin a) 1))
25.0ms	(/ (* (cos a) (cos b)) (sin b))
56.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (/ (sin a) 1)))

series630.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (cos a) (cos b))
148.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (/ (sin a) 1))
123.0ms	(/ (* (cos a) (cos b)) (sin b))
309.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (/ (sin a) 1)))

simplify1.8s

Counts

116 → 116

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	202	2120
1	439	1866
2	2259	1740
done	5001	1738

prune540.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes244.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample5.8s

Algorithm

intervals

Results

3.1s	2984×	body	1280	valid
1.4s	1805×	body	640	valid
354.0ms	716×	body	320	valid
320.0ms	2162×	body	80	valid
107.0ms	335×	body	160	valid