Details

sample451.0ms

Algorithm

intervals

Results

189.0ms	77×	body	1280	valid
91.0ms	66×	body	640	valid
21.0ms	78×	body	80	valid
16.0ms	20×	body	320	valid
9.0ms	15×	body	160	valid

simplify1.6s

Counts

1 → 1

Iterations

Iter	Nodes
7	3496
6	1008
5	394
4	173
3	82
2	47
1	25
0	13

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.4b

localize69.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
0.2b	(* (sin kx) (sin kx))
0.3b	(* (sin ky) (sin ky))
3.1b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
28×	`*-un-lft-identity` `add-cube-cbrt`
19×	`pow1`
18×	`times-frac`
15×	`sqrt-prod`
10×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r` `sqrt-div` `swap-sqr` `associate-r` `associate-l*` `sin-mult`
4×	`insert-posit16` `add-log-exp`
3×	`associate-/r/` `associate-/l*`
2×	`pow2` `flip3-+` `pow-plus` `pow-prod-down` `frac-add` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `sqr-sin` `unswap-sqr`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `div-inv`

Counts

4 → 116

Calls

4 calls:

19.0ms	(/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
21.0ms	(* (sin kx) (sin kx))
23.0ms	(* (sin ky) (sin ky))
26.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series347.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
24.0ms	(* (sin kx) (sin kx))
34.0ms	(* (sin ky) (sin ky))
133.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify2.1s

Counts

128 → 128

Iterations

Iter	Nodes
3	3803
2	1420
1	431
0	191

prune1.8s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 10.5b

localize58.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (sin kx))
0.7b	(cbrt (sin kx))
0.7b	(cbrt (sin kx))
3.1b	(sqrt (+ (* (* (* (cbrt (sin kx)) (cbrt (sin kx))) (* (cbrt (sin kx)) (cbrt (sin kx)))) (* (cbrt (sin kx)) (cbrt (sin kx)))) (* (sin ky) (sin ky))))

rewrite335.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 52

Calls

4 calls:

2.0ms	(cbrt (sin kx))
2.0ms	(cbrt (sin kx))
2.0ms	(cbrt (sin kx))
327.0ms	(sqrt (+ (* (* (* (cbrt (sin kx)) (cbrt (sin kx))) (* (cbrt (sin kx)) (cbrt (sin kx)))) (* (cbrt (sin kx)) (cbrt (sin kx)))) (* (sin ky) (sin ky))))

series552.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(cbrt (sin kx))
164.0ms	(cbrt (sin kx))
137.0ms	(cbrt (sin kx))
136.0ms	(sqrt (+ (* (* (* (cbrt (sin kx)) (cbrt (sin kx))) (* (cbrt (sin kx)) (cbrt (sin kx)))) (* (cbrt (sin kx)) (cbrt (sin kx)))) (* (sin ky) (sin ky))))

simplify5.6s

Counts

64 → 64

Iterations

Iter	Nodes
4	8159
3	1726
2	522
1	196
0	81

prune1.3s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 10.5b

localize64.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
3.1b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
3.1b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
3.1b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
12×	`sqrt-div`
8×	`sin-mult`
7×	`pow1`
4×	`flip3-+` `add-cbrt-cube` `frac-add` `add-exp-log` `flip-+` `insert-posit16` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/`
1×	`cbrt-div` `pow1/3` `div-inv`

Counts

4 → 86

Calls

4 calls:

17.0ms	(cbrt (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
14.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
12.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
12.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series505.0ms

Counts

4 → 12

Calls

4 calls:

197.0ms	(cbrt (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
109.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
97.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
101.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify3.8s

Counts

98 → 98

Iterations

Iter	Nodes
4	5321
3	1825
2	690
1	311
0	172

prune1.9s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 10.5b

localize46.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin ky) (sin ky))
0.5b	(* (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
3.1b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
3.1b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
56×	`add-sqr-sqrt`
54×	`sqrt-div`
36×	`pow1`
34×	`sqrt-pow1`
22×	`*-un-lft-identity` `add-cube-cbrt`
21×	`sin-mult`
18×	`pow1/2` `swap-sqr`
12×	`associate-r` `associate-l`
10×	`flip3-+` `frac-add` `pow-prod-up` `flip-+` `unswap-sqr`
9×	`frac-times`
8×	`add-cbrt-cube` `add-exp-log`
6×	`pow-prod-down` `pow-sqr`
4×	`insert-posit16` `add-log-exp`
3×	`associate-l/` `associate-r/`
2×	`pow2` `rem-sqrt-square` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`
1×	`rem-square-sqrt` `sqrt-unprod` `sqr-sin`

Counts

4 → 153

Calls

4 calls:

11.0ms	(* (sin ky) (sin ky))
112.0ms	(* (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
11.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
12.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series356.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (sin ky) (sin ky))
108.0ms	(* (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
116.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
97.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify1.4s

Counts

165 → 165

Iterations

Iter	Nodes
3	2279
2	916
1	404
0	192

prune2.8s

Pruning

19 alts after pruning (17 fresh and 2 done)

Merged error: 10.5b

regimes1.2s

Accuracy

0% (1.5b remaining)

Error of 12.3b against oracle of 10.8b and baseline of 12.3b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
2	18
1	18
0	15

end0.0ms

sample11.3s

Algorithm

intervals

Results

6.3s	2775×	body	1280	valid
3.1s	1779×	body	640	valid
771.0ms	796×	body	320	valid
641.0ms	2313×	body	80	valid
173.0ms	337×	body	160	valid