Details

sample325.0ms

Algorithm

intervals

Results

112.0ms	90×	body	1280	valid
58.0ms	67×	body	640	valid
44.0ms	19×	body	320	valid
12.0ms	68×	body	80	valid
4.0ms	12×	body	160	valid

simplify1.6s

Counts: 1 → 1

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 8.6b

localize38.0ms

Local error

Found 3 expressions with local error:

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

rewrite25.0ms

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

13.0ms	(* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))
10.0ms	(/ (sin ky) (hypot (sin kx) (sin ky)))
0.0ms	(hypot (sin kx) (sin ky))

series776.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

366.0ms	(* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))
258.0ms	(/ (sin ky) (hypot (sin kx) (sin ky)))
152.0ms	(hypot (sin kx) (sin ky))

simplify1.1s

Counts: 85 → 85

prune1.2s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 8.5b

localize37.0ms

Local error

Found 3 expressions with local error:

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

rewrite23.0ms

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

14.0ms	(* (/ (sin ky) (hypot (sin kx) (sin ky))) (sin th))
7.0ms	(/ (sin ky) (hypot (sin kx) (sin ky)))
0.0ms	(hypot (sin kx) (sin ky))

series756.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

344.0ms	(* (/ (sin ky) (hypot (sin kx) (sin ky))) (sin th))
237.0ms	(/ (sin ky) (hypot (sin kx) (sin ky)))
175.0ms	(hypot (sin kx) (sin ky))

simplify1.5s

Counts: 85 → 85

prune1.1s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 8.5b

localize26.0ms

Local error

Found 3 expressions with local error:

0.3b	(* (sin ky) (/ (sin th) (hypot (sin kx) (sin ky))))
0.2b	(/ (sin th) (hypot (sin kx) (sin ky)))
0.1b	(hypot (sin kx) (sin ky))

rewrite26.0ms

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

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

series725.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

310.0ms	(* (sin ky) (/ (sin th) (hypot (sin kx) (sin ky))))
277.0ms	(/ (sin th) (hypot (sin kx) (sin ky)))
138.0ms	(hypot (sin kx) (sin ky))

simplify1.0s

Counts: 85 → 85

prune1.2s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 8.5b

localize31.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin ky) (/ (sin th) (log1p (expm1 (hypot (sin kx) (sin ky))))))
0.3b	(expm1 (hypot (sin kx) (sin ky)))
0.2b	(/ (sin th) (log1p (expm1 (hypot (sin kx) (sin ky)))))
0.1b	(log1p (expm1 (hypot (sin kx) (sin ky))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `add-cube-cbrt`
19×	`times-frac`
13×	`associate-r`
11×	`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-l` `associate-/l`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`log1p-udef` `expm1-log1p` `clear-num` `frac-2neg` `pow-prod-down` `log1p-expm1` `associate-r/` `-commutative` `expm1-udef`

Counts

4 → 89

Calls

4 calls:

Slowest

21.0ms	(* (sin ky) (/ (sin th) (log1p (expm1 (hypot (sin kx) (sin ky))))))
16.0ms	(/ (sin th) (log1p (expm1 (hypot (sin kx) (sin ky)))))
1.0ms	(expm1 (hypot (sin kx) (sin ky)))
0.0ms	(log1p (expm1 (hypot (sin kx) (sin ky))))

series1.0s

Counts

4 → 12

Calls

4 calls:

Slowest

352.0ms	(* (sin ky) (/ (sin th) (log1p (expm1 (hypot (sin kx) (sin ky))))))
316.0ms	(/ (sin th) (log1p (expm1 (hypot (sin kx) (sin ky)))))
195.0ms	(log1p (expm1 (hypot (sin kx) (sin ky))))
184.0ms	(expm1 (hypot (sin kx) (sin ky)))

simplify1.2s

Counts: 101 → 101

prune1.5s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 8.5b

regimes969.0ms

Accuracy

0% (0.2b remaining)

Error of 8.5b against oracle of 8.3b and baseline of 8.5b

bsearch4.0ms

end0.0ms

sample12.2s

Algorithm

intervals

Results

7.2s	2727×	body	1280	valid
3.2s	1908×	body	640	valid
657.0ms	2251×	body	80	valid
625.0ms	772×	body	320	valid
261.0ms	342×	body	160	valid