Details

sample304.0ms

Algorithm

intervals

Results

77.0ms	83×	body	1280	valid
66.0ms	24×	body	320	valid
43.0ms	72×	body	640	valid
11.0ms	61×	body	80	valid
5.0ms	16×	body	160	valid

simplify37.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (6.0ms)

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.8b

localize34.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
3.4b	(cos (+ a b))

rewrite95.0ms

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:

37.0ms	(* r (sin b))
25.0ms	(/ (* r (sin b)) (cos (+ a b)))
28.0ms	(cos (+ a b))

series278.0ms

Counts

3 → 9

Calls

3 calls:

66.0ms	(* r (sin b))
172.0ms	(/ (* r (sin b)) (cos (+ a b)))
40.0ms	(cos (+ a b))

simplify965.0ms

Counts

56 → 56

Iterations

Useful iterations: done (962.0ms)

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

prune379.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize61.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos a) (cos 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))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

24.0ms	(* (cos a) (cos b))
17.0ms	(* r (sin b))
54.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
22.0ms	(* (sin a) (sin b))

series580.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* (cos a) (cos b))
63.0ms	(* r (sin b))
376.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
73.0ms	(* (sin a) (sin b))

simplify1.5s

Counts

93 → 93

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	157	1121
1	387	1083
2	1718	957
done	5001	915

prune793.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos a) (cos 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))

rewrite236.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 105

Calls

4 calls:

22.0ms	(* (cos a) (cos b))
135.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
51.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
23.0ms	(* (sin a) (sin b))

series747.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* (cos a) (cos b))
395.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
200.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
84.0ms	(* (sin a) (sin b))

simplify1.5s

Counts

117 → 117

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	187	1937
1	462	1887
2	1970	1715
done	5001	1657

prune1.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b	(* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
0.2b	(/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
0.2b	(* (sin a) (sin b))
3.2b	(log (exp (* (sin a) (sin b))))

rewrite189.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 96

Calls

4 calls:

108.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
46.0ms	(/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
22.0ms	(* (sin a) (sin b))
8.0ms	(log (exp (* (sin a) (sin b))))

series761.0ms

Counts

4 → 12

Calls

4 calls:

381.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
220.0ms	(/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
76.0ms	(* (sin a) (sin b))
84.0ms	(log (exp (* (sin a) (sin b))))

simplify1.6s

Counts

108 → 108

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	164	1992
1	390	1748
2	1693	1584
done	5001	1568

prune951.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes479.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	13	15
1	16	13
done	16	13

end0.0ms

sample7.1s

Algorithm

intervals

Results

3.7s	2921×	body	1280	valid
1.8s	1832×	body	640	valid
523.0ms	2130×	body	80	valid
443.0ms	780×	body	320	valid
98.0ms	341×	body	160	valid