Details

sample75.0ms

Algorithm

intervals

Results

37.0ms	91×	body	1280	valid
14.0ms	56×	body	640	valid
5.0ms	29×	body	320	valid
4.0ms	65×	body	80	valid
2.0ms	15×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	5
1	16	5
2	19	5
3	20	5
4	20	5
done	20	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.4b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
4.4b	(cos (+ a b))

rewrite40.0ms

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:

14.0ms	(* r (sin b))
12.0ms	(/ (* r (sin b)) (cos (+ a b)))
11.0ms	(cos (+ a b))

series177.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(* r (sin b))
102.0ms	(/ (* r (sin b)) (cos (+ a b)))
36.0ms	(cos (+ a b))

simplify32.0ms

Counts

56 → 56

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	198	305
1	861	257
2	5001	256
done	5001	256

prune135.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

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))))

rewrite68.0ms

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:

9.0ms	(* r (sin b))
18.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
12.0ms	(* (sin a) (sin b))
27.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series403.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* r (sin b))
88.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
49.0ms	(* (sin a) (sin b))
226.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify46.0ms

Counts

88 → 88

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	344	770
1	1513	673
2	5001	663
done	5001	663

prune284.0ms

Pruning

13 alts after pruning (13 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))
0.2b	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))

rewrite78.0ms

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:

17.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
12.0ms	(* (sin a) (sin b))
29.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
15.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))

series491.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
46.0ms	(* (sin a) (sin b))
120.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
239.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))

simplify71.0ms

Counts

147 → 147

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	570	2145
1	2453	2009
2	5001	1988
done	5001	1988

prune497.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))
0.2b	(* (sin a) (sin b))
0.2b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
4.9b	(log (exp (* (sin a) (sin b))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

14.0ms	(- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))
14.0ms	(* (sin a) (sin b))
25.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
4.0ms	(log (exp (* (sin a) (sin b))))

series413.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))
45.0ms	(* (sin a) (sin b))
235.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
47.0ms	(log (exp (* (sin a) (sin b))))

simplify36.0ms

Counts

83 → 83

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	322	847
1	1257	710
2	5002	703
done	5002	703

prune264.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0b

regimes174.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	12
1	18	12
done	18	12

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.2s	2893×	body	1280	valid
476.0ms	1909×	body	640	valid
136.0ms	766×	body	320	valid
118.0ms	2141×	body	80	valid
36.0ms	292×	body	160	valid