Details

sample656.0ms

Algorithm

intervals

Results

179.0ms	87×	body	1280	valid
77.0ms	54×	body	640	valid
75.0ms	81×	body	80	valid
29.0ms	24×	body	320	valid
5.0ms	10×	body	160	valid

simplify1.3s

Counts: 1 → 1

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 7.4b

localize30.0ms

Local error

Found 3 expressions with local error:

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

rewrite52.0ms

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:

Slowest

39.0ms	(* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))
11.0ms	(/ (sin ky) (hypot (sin kx) (sin ky)))
0.0ms	(hypot (sin kx) (sin ky))

series767.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

351.0ms	(* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))
225.0ms	(/ (sin ky) (hypot (sin kx) (sin ky)))
190.0ms	(hypot (sin kx) (sin ky))

simplify916.0ms

Counts: 85 → 85

prune1.1s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 7.1b

localize46.0ms

Local error

Found 3 expressions with local error:

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

rewrite33.0ms

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:

Slowest

24.0ms	(* (/ (sin ky) (hypot (sin kx) (sin ky))) (sin th))
8.0ms	(/ (sin ky) (hypot (sin kx) (sin ky)))
0.0ms	(hypot (sin kx) (sin ky))

series733.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

298.0ms	(* (/ (sin ky) (hypot (sin kx) (sin ky))) (sin th))
245.0ms	(/ (sin ky) (hypot (sin kx) (sin ky)))
190.0ms	(hypot (sin kx) (sin ky))

simplify933.0ms

Counts: 85 → 85

prune1.2s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 7.1b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(expm1 (/ (sin ky) (hypot (sin kx) (sin ky))))
0.2b	(* (log1p (expm1 (/ (sin ky) (hypot (sin kx) (sin ky))))) (sin th))
0.2b	(/ (sin ky) (hypot (sin kx) (sin ky)))
0.1b	(log1p (expm1 (/ (sin ky) (hypot (sin kx) (sin ky)))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
8×	`add-cbrt-cube` `add-exp-log`
6×	`pow1`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `insert-posit16` `add-log-exp`
3×	`associate-/r` `associate-r` `associate-l` `associate-/l`
1×	`cbrt-undiv` `log1p-udef` `expm1-log1p` `clear-num` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `log1p-expm1` `*-commutative` `cbrt-unprod` `div-inv` `expm1-udef` `unswap-sqr`

Counts

4 → 75

Calls

4 calls:

Slowest

16.0ms	(/ (sin ky) (hypot (sin kx) (sin ky)))
12.0ms	(* (log1p (expm1 (/ (sin ky) (hypot (sin kx) (sin ky))))) (sin th))
0.0ms	(expm1 (/ (sin ky) (hypot (sin kx) (sin ky))))
0.0ms	(log1p (expm1 (/ (sin ky) (hypot (sin kx) (sin ky)))))

series1.6s

Counts

4 → 12

Calls

4 calls:

Slowest

683.0ms	(log1p (expm1 (/ (sin ky) (hypot (sin kx) (sin ky)))))
351.0ms	(* (log1p (expm1 (/ (sin ky) (hypot (sin kx) (sin ky))))) (sin th))
320.0ms	(expm1 (/ (sin ky) (hypot (sin kx) (sin ky))))
230.0ms	(/ (sin ky) (hypot (sin kx) (sin ky)))

simplify2.0s

Counts: 87 → 87

prune1.4s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 7.1b

localize58.0ms

Local error

Found 4 expressions with local error:

1.1b	(log1p (/ (sin ky) (hypot (sin kx) (sin ky))))
0.2b	(* (expm1 (log1p (/ (sin ky) (hypot (sin kx) (sin ky))))) (sin th))
0.2b	(/ (sin ky) (hypot (sin kx) (sin ky)))
0.1b	(expm1 (log1p (/ (sin ky) (hypot (sin kx) (sin ky)))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
8×	`add-cbrt-cube` `add-exp-log`
6×	`pow1`
5×	`expm1-log1p-u`
4×	`insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-r` `associate-l` `associate-/l`
1×	`cbrt-undiv` `log1p-udef` `expm1-log1p` `clear-num` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `log1p-expm1` `*-commutative` `cbrt-unprod` `div-inv` `expm1-udef` `unswap-sqr`

Counts

4 → 75

Calls

4 calls:

Slowest

8.0ms	(/ (sin ky) (hypot (sin kx) (sin ky)))
8.0ms	(* (expm1 (log1p (/ (sin ky) (hypot (sin kx) (sin ky))))) (sin th))
0.0ms	(log1p (/ (sin ky) (hypot (sin kx) (sin ky))))
0.0ms	(expm1 (log1p (/ (sin ky) (hypot (sin kx) (sin ky)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

Slowest

312.0ms	(log1p (/ (sin ky) (hypot (sin kx) (sin ky))))
287.0ms	(expm1 (log1p (/ (sin ky) (hypot (sin kx) (sin ky)))))
282.0ms	(* (expm1 (log1p (/ (sin ky) (hypot (sin kx) (sin ky))))) (sin th))
255.0ms	(/ (sin ky) (hypot (sin kx) (sin ky)))

simplify2.2s

Counts: 87 → 87

prune1.3s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 7.1b

regimes1.1s

Accuracy

0% (0.2b remaining)

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

bsearch3.0ms

end1.0ms

sample12.7s

Algorithm

intervals

Results

7.3s	2776×	body	1280	valid
3.1s	1795×	body	640	valid
875.0ms	791×	body	320	valid
873.0ms	2292×	body	80	valid
276.0ms	346×	body	160	valid