Details

sample308.0ms

Algorithm

intervals

Results

138.0ms	83×	body	1280	valid
44.0ms	72×	body	640	valid
12.0ms	61×	body	80	valid
10.0ms	24×	body	320	valid
5.0ms	16×	body	160	valid

simplify39.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.8b

localize37.0ms

Local error

Found 3 expressions with local error:

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

rewrite113.0ms

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:

61.0ms	(* r (/ (sin b) (cos (+ a b))))
21.0ms	(/ (sin b) (cos (+ a b)))
24.0ms	(cos (+ a b))

series316.0ms

Counts

3 → 9

Calls

3 calls:

197.0ms	(* r (/ (sin b) (cos (+ a b))))
76.0ms	(/ (sin b) (cos (+ a b)))
42.0ms	(cos (+ a b))

simplify1.1s

Counts

76 → 76

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	116	909
1	272	887
2	1040	801
done	5000	791

prune622.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize53.0ms

Local error

Found 4 expressions with local error:

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

rewrite279.0ms

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))
156.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
67.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
28.0ms	(* (sin b) (sin a))

series797.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(* (cos a) (cos b))
413.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
218.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
89.0ms	(* (sin b) (sin a))

simplify2.4s

Counts

117 → 117

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	192	1937
1	466	1887
2	2105	1715
done	5001	1632

prune1.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize50.0ms

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 b) (sin a))))
0.2b	(* (sin b) (sin a))

rewrite140.0ms

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:

22.0ms	(* (cos a) (cos b))
18.0ms	(* r (sin b))
69.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
26.0ms	(* (sin b) (sin a))

series666.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(* (cos a) (cos b))
75.0ms	(* r (sin b))
421.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
88.0ms	(* (sin b) (sin a))

simplify1.7s

Counts

93 → 93

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	162	1121
1	396	1083
2	2015	953
done	5001	949

prune873.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin b) (sin a))))))
0.2b	(* (sin b) (sin a))
3.2b	(log (exp (* (sin b) (sin a))))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

20.0ms	(* r (sin b))
56.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin b) (sin a))))))
37.0ms	(* (sin b) (sin a))
10.0ms	(log (exp (* (sin b) (sin a))))

series720.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* r (sin b))
449.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin b) (sin a))))))
95.0ms	(* (sin b) (sin a))
110.0ms	(log (exp (* (sin b) (sin a))))

simplify1.4s

Counts

86 → 86

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	137	1122
1	324	992
2	1654	872
done	5000	864

prune748.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes525.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

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

end0.0ms

sample7.0s

Algorithm

intervals

Results

3.2s	2921×	body	1280	valid
1.9s	1832×	body	640	valid
840.0ms	780×	body	320	valid
326.0ms	2130×	body	80	valid
94.0ms	341×	body	160	valid