Details

sample492.0ms

Algorithm

intervals

Results

183.0ms	103×	body	1280	valid
179.0ms	43×	body	640	valid
23.0ms	30×	body	320	valid
16.0ms	73×	body	80	valid
4.0ms	7×	body	160	valid

simplify35.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	21
5	21
4	20
3	18
2	16
1	12
0	8

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.4b

localize122.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
2.9b	(cos (+ a b))

rewrite158.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
13×	`associate-r`
10×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
3×	`associate-/r` `associate-l` `insert-posit16` `associate-/l` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`cos-sum` `clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `-commutative`

Counts

3 → 70

Calls

3 calls:

32.0ms	(* r (/ (sin b) (cos (+ a b))))
105.0ms	(/ (sin b) (cos (+ a b)))
16.0ms	(cos (+ a b))

series464.0ms

Counts

3 → 9

Calls

3 calls:

283.0ms	(* r (/ (sin b) (cos (+ a b))))
108.0ms	(/ (sin b) (cos (+ a b)))
72.0ms	(cos (+ a b))

simplify753.0ms

Counts

79 → 79

Iterations

Iter	Nodes
done	2002
2	844
1	271
0	120

prune404.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

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))

rewrite222.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`*-un-lft-identity` `add-cube-cbrt`
20×	`associate-r`
19×	`times-frac`
13×	`add-cbrt-cube` `add-exp-log`
8×	`pow1` `associate-/r/`
7×	`sin-mult`
6×	`associate-l` `cos-mult` `add-log-exp`
4×	`insert-posit16`
3×	`associate-/r` `flip3--` `prod-exp` `frac-sub` `cbrt-unprod` `flip--` `associate-/l` `sub-div` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`clear-num` `sub-neg` `frac-2neg` `diff-log` `associate-*r/`

Counts

4 → 104

Calls

4 calls:

16.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
128.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
54.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
19.0ms	(* (sin a) (sin b))

series684.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
298.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
193.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
91.0ms	(* (sin a) (sin b))

simplify907.0ms

Counts

116 → 116

Iterations

Iter	Nodes
done	2016
2	1478
1	439
0	175

prune745.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0b

localize60.0ms

Local error

Found 4 expressions with local error:

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

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`add-cbrt-cube` `add-exp-log`
10×	`*-un-lft-identity` `add-cube-cbrt`
8×	`pow1`
6×	`associate-r` `associate-l` `add-log-exp`
5×	`sin-mult`
4×	`associate-/r/` `cos-mult` `insert-posit16`
3×	`associate-/r*` `times-frac` `prod-exp` `cbrt-unprod`
2×	`cbrt-undiv` `flip3--` `div-exp` `pow-prod-down` `*-commutative` `frac-sub` `flip--` `sub-div` `unswap-sqr`
1×	`clear-num` `sub-neg` `frac-2neg` `diff-log` `div-inv` `associate-/l*`

Counts

4 → 80

Calls

4 calls:

18.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
9.0ms	(* (sin b) r)
42.0ms	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
22.0ms	(* (sin b) (sin a))

series627.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
60.0ms	(* (sin b) r)
362.0ms	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
84.0ms	(* (sin b) (sin a))

simplify780.0ms

Counts

92 → 92

Iterations

Iter	Nodes
done	2007
2	1148
1	365
0	147

prune737.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin b) r)
0.2b	(/ (* (sin b) r) (- (* (cos a) (cos b)) (log (exp (* (sin b) (sin a))))))
0.2b	(* (sin b) (sin a))
3.1b	(log (exp (* (sin b) (sin a))))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`add-cbrt-cube` `add-exp-log`
11×	`*-un-lft-identity` `add-cube-cbrt`
9×	`pow1`
6×	`associate-r` `associate-l`
5×	`add-log-exp`
4×	`insert-posit16`
3×	`log-prod` `associate-/r*` `times-frac` `prod-exp` `log-pow` `cbrt-unprod`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-/r/` `*-commutative` `unswap-sqr`
1×	`exp-prod` `clear-num` `frac-2neg` `flip3--` `exp-to-pow` `rem-log-exp` `div-inv` `flip--` `sin-mult` `associate-/l*`

Counts

4 → 78

Calls

4 calls:

8.0ms	(* (sin b) r)
26.0ms	(/ (* (sin b) r) (- (* (cos a) (cos b)) (log (exp (* (sin b) (sin a))))))
19.0ms	(* (sin b) (sin a))
10.0ms	(log (exp (* (sin b) (sin a))))

series524.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (sin b) r)
336.0ms	(/ (* (sin b) r) (- (* (cos a) (cos b)) (log (exp (* (sin b) (sin a))))))
77.0ms	(* (sin b) (sin a))
51.0ms	(log (exp (* (sin b) (sin a))))

simplify1.3s

Counts

90 → 90

Iterations

Iter	Nodes
done	2000
2	944
1	321
0	141

prune470.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0b

regimes318.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	15
1	15
0	12

end0.0ms

sample7.7s

Algorithm

intervals

Results

4.5s	2956×	body	1280	valid
1.9s	1821×	body	640	valid
536.0ms	766×	body	320	valid
365.0ms	2115×	body	80	valid
161.0ms	343×	body	160	valid