Details

sample697.0ms

Algorithm

intervals

Results

243.0ms	88×	body	1280	valid
66.0ms	68×	body	640	valid
17.0ms	25×	body	320	valid
14.0ms	65×	body	80	valid
4.0ms	10×	body	160	valid

simplify2.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
7	3205
6	911
5	367
4	177
3	95
2	61
1	25
0	13

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 8.1b

localize29.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot (sin ky) (sin kx))
0.1b	(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))
0.2b	(/ (sin ky) (hypot (sin ky) (sin kx)))

rewrite79.0ms

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×	`expm1-log1p-u` `associate-/r` `associate-l` `insert-posit16` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`hypot-udef` `clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `-commutative`

Counts

3 → 76

Calls

3 calls:

0.0ms	(hypot (sin ky) (sin kx))
36.0ms	(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))
24.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))

series851.0ms

Counts

3 → 9

Calls

3 calls:

190.0ms	(hypot (sin ky) (sin kx))
365.0ms	(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))
297.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))

simplify2.0s

Counts

85 → 85

Iterations

Iter	Nodes
done	5003
3	2946
2	1013
1	306
0	133

prune647.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 8.0b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot (sin ky) (sin kx))
0.1b	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))
0.2b	(/ (sin ky) (hypot (sin ky) (sin kx)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
13×	`associate-l`
10×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
3×	`expm1-log1p-u` `associate-/r` `associate-r` `insert-posit16` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`hypot-udef` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `-commutative`

Counts

3 → 76

Calls

3 calls:

0.0ms	(hypot (sin ky) (sin kx))
27.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))
12.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))

series775.0ms

Counts

3 → 9

Calls

3 calls:

191.0ms	(hypot (sin ky) (sin kx))
357.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))
227.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))

simplify2.5s

Counts

85 → 85

Iterations

Iter	Nodes
done	5002
3	2864
2	914
1	308
0	135

prune673.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 8.0b

localize40.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot (sin kx) (sin ky))
0.2b	(/ (sin th) (hypot (sin kx) (sin ky)))
0.2b	(* (sin ky) (/ (sin th) (hypot (sin kx) (sin ky))))

rewrite65.0ms

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×	`expm1-log1p-u` `associate-/r` `associate-l` `insert-posit16` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`hypot-udef` `clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `-commutative`

Counts

3 → 76

Calls

3 calls:

0.0ms	(hypot (sin kx) (sin ky))
25.0ms	(/ (sin th) (hypot (sin kx) (sin ky)))
36.0ms	(* (sin ky) (/ (sin th) (hypot (sin kx) (sin ky))))

series735.0ms

Counts

3 → 9

Calls

3 calls:

193.0ms	(hypot (sin kx) (sin ky))
238.0ms	(/ (sin th) (hypot (sin kx) (sin ky)))
303.0ms	(* (sin ky) (/ (sin th) (hypot (sin kx) (sin ky))))

simplify1.8s

Counts

85 → 85

Iterations

Iter	Nodes
done	5001
3	2686
2	893
1	279
0	124

prune622.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 8.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))) (cbrt (* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))))
7.0b	(cbrt (* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th)))
7.0b	(cbrt (* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th)))
7.0b	(cbrt (* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th)))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1`
10×	`add-sqr-sqrt`
9×	`pow1/3`
8×	`-un-lft-identity` `associate-l/` `add-cube-cbrt`
7×	`cbrt-prod` `cbrt-div`
6×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `swap-sqr` `associate-r` `associate-l` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `prod-exp` `associate-r/` `-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 76

Calls

4 calls:

26.0ms	(* (cbrt (* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))) (cbrt (* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))))
13.0ms	(cbrt (* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th)))
16.0ms	(cbrt (* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th)))
24.0ms	(cbrt (* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th)))

series1.7s

Counts

4 → 12

Calls

4 calls:

434.0ms	(* (cbrt (* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))) (cbrt (* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))))
457.0ms	(cbrt (* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th)))
421.0ms	(cbrt (* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th)))
407.0ms	(cbrt (* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th)))

simplify1.6s

Counts

88 → 88

Iterations

Iter	Nodes
done	5001
3	1682
2	615
1	244
0	104

prune570.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 8.0b

regimes1.1s

Accuracy

0% (0.2b remaining)

Error of 9.0b against oracle of 8.8b and baseline of 9.0b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	10
1	10
0	9

end0.0ms

sample9.6s

Algorithm

intervals

Results

5.0s	2646×	body	1280	valid
2.9s	1814×	body	640	valid
633.0ms	772×	body	320	valid
550.0ms	2393×	body	80	valid
192.0ms	375×	body	160	valid