Details

sample585.0ms

Algorithm

intervals

Results

279.0ms	91×	body	1280	valid
118.0ms	62×	body	640	valid
50.0ms	75×	body	80	valid
16.0ms	21×	body	320	valid
4.0ms	7×	body	160	valid

simplify40.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	21
5	21
4	20
3	18
2	16
1	12
0	8

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.6b

localize60.0ms

Local error

Found 3 expressions with local error:

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

rewrite67.0ms

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:

20.0ms	(/ (sin b) (cos (+ a b)))
27.0ms	(* r (/ (sin b) (cos (+ a b))))
16.0ms	(cos (+ a b))

series304.0ms

Counts

3 → 9

Calls

3 calls:

66.0ms	(/ (sin b) (cos (+ a b)))
193.0ms	(* r (/ (sin b) (cos (+ a b))))
44.0ms	(cos (+ a b))

simplify4.1s

Counts

79 → 79

Iterations

Iter	Nodes
4	8089
3	1977
2	743
1	267
0	120

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

localize56.0ms

Local error

Found 4 expressions with local error:

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

rewrite187.0ms

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:

28.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
29.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
112.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
15.0ms	(* (sin a) (sin b))

series725.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
164.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
365.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
90.0ms	(* (sin a) (sin b))

simplify1.4s

Counts

116 → 116

Iterations

Iter	Nodes
3	3832
2	1364
1	436
0	175

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize70.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin a) (sin b))
0.2b	(* (sin a) (sin b))
0.3b	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
25.6b	(cbrt (* (* (sin a) (sin b)) (* (* (sin a) (sin b)) (* (sin a) (sin b)))))

rewrite216.0ms

Algorithm

rewrite-expression-head

Rules

47×	`pow1`
20×	`add-cbrt-cube` `add-exp-log`
19×	`pow-prod-down`
18×	`sin-mult`
12×	`add-sqr-sqrt`
10×	`prod-exp` `cbrt-unprod`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`cbrt-div` `associate-r` `associate-l`
6×	`frac-times` `associate-*r/`
4×	`associate-*l/` `pow-sqr` `pow-prod-up` `insert-posit16` `add-log-exp`
3×	`*-commutative`
2×	`pow-plus` `unswap-sqr`
1×	`cbrt-prod` `pow2` `pow1/3` `cube-unmult` `swap-sqr` `rem-cbrt-cube`

Counts

4 → 96

Calls

4 calls:

11.0ms	(* (sin a) (sin b))
11.0ms	(* (sin a) (sin b))
71.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
121.0ms	(cbrt (* (* (sin a) (sin b)) (* (* (sin a) (sin b)) (* (sin a) (sin b)))))

series313.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(* (sin a) (sin b))
84.0ms	(* (sin a) (sin b))
78.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
75.0ms	(cbrt (* (* (sin a) (sin b)) (* (* (sin a) (sin b)) (* (sin a) (sin b)))))

simplify1.6s

Counts

108 → 108

Iterations

Iter	Nodes
3	3430
2	855
1	246
0	110

prune1.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize99.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
0.3b	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
10.6b	(cbrt (* (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))))
25.6b	(cbrt (* (* (sin a) (sin b)) (cbrt (* (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))))))

rewrite2.1s

Algorithm

rewrite-expression-head

Rules

648×	`sin-mult`
452×	`frac-times`
316×	`cbrt-div`
254×	`associate-*r/`
228×	`associate-*l/`
82×	`pow1`
34×	`pow-prod-down`
28×	`add-cbrt-cube` `add-exp-log`
16×	`prod-exp` `cbrt-unprod`
8×	`pow-sqr` `pow-prod-up`
4×	`add-sqr-sqrt` `*-un-lft-identity` `pow-plus` `add-cube-cbrt` `insert-posit16` `add-log-exp`
2×	`cbrt-prod` `pow2` `pow1/3` `swap-sqr` `associate-r` `associate-l` `*-commutative`
1×	`pow3` `rem-cbrt-cube`

Counts

4 → 287

Calls

4 calls:

50.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
74.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
1.1s	(cbrt (* (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))))
918.0ms	(cbrt (* (* (sin a) (sin b)) (cbrt (* (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))))))

series305.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
73.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
76.0ms	(cbrt (* (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))))
73.0ms	(cbrt (* (* (sin a) (sin b)) (cbrt (* (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))))))

simplify1.1s

Counts

299 → 299

Iterations

Iter	Nodes
2	2231
1	1009
0	535

prune6.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

regimes284.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
2	23
1	23
0	18

end0.0ms

sample7.0s

Algorithm

intervals

Results

4.3s	2937×	body	1280	valid
1.4s	1855×	body	640	valid
564.0ms	792×	body	320	valid
381.0ms	2099×	body	80	valid
109.0ms	318×	body	160	valid