Details

sample489.0ms

Algorithm

intervals

Results

171.0ms	81×	body	1280	valid
121.0ms	56×	body	640	valid
29.0ms	84×	body	80	valid
22.0ms	23×	body	320	valid
7.0ms	12×	body	160	valid

simplify243.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

242.0ms

(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.3b

localize21.0ms

Local error

Found 3 expressions with local error:

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

rewrite32.0ms

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

14.0ms	(* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))
8.0ms	(/ (sin ky) (hypot (sin kx) (sin ky)))
0.0ms	(hypot (sin kx) (sin ky))

series745.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

343.0ms	(* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))
233.0ms	(/ (sin ky) (hypot (sin kx) (sin ky)))
169.0ms	(hypot (sin kx) (sin ky))

simplify3.5s

Counts

59 → 85

Calls

59 calls:

Slowest

469.0ms	(/ (* (* (sin ky) (sin ky)) (sin ky)) (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky))))
334.0ms	(* (* (* (sin th) (sin th)) (sin th)) (* (* (/ (sin ky) (hypot (sin kx) (sin ky))) (/ (sin ky) (hypot (sin kx) (sin ky)))) (/ (sin ky) (hypot (sin kx) (sin ky)))))
330.0ms	(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
325.0ms	(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
275.0ms	(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky))

prune1.2s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 9.1b

localize41.0ms

Local error

Found 4 expressions with local error:

0.4b	(log1p (/ (sin ky) (hypot (sin kx) (sin ky))))
0.1b	(* (sin th) (expm1 (log1p (/ (sin ky) (hypot (sin kx) (sin ky))))))
0.1b	(/ (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

9.0ms	(* (sin th) (expm1 (log1p (/ (sin ky) (hypot (sin kx) (sin ky))))))
7.0ms	(/ (sin ky) (hypot (sin kx) (sin ky)))
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

334.0ms	(log1p (/ (sin ky) (hypot (sin kx) (sin ky))))
305.0ms	(* (sin th) (expm1 (log1p (/ (sin ky) (hypot (sin kx) (sin ky))))))
276.0ms	(expm1 (log1p (/ (sin ky) (hypot (sin kx) (sin ky)))))
198.0ms	(/ (sin ky) (hypot (sin kx) (sin ky)))

simplify3.8s

Counts

49 → 87

Calls

49 calls:

Slowest

467.0ms	(/ (* (* (sin ky) (sin ky)) (sin ky)) (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky))))
360.0ms	(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
326.0ms	(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
285.0ms	(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky))
283.0ms	(log (+ (* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky)) 1))

prune1.3s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 9.1b

localize58.0ms

Local error

Found 4 expressions with local error:

0.4b	(log1p (/ (sin ky) (hypot (sin kx) (sin ky))))
0.1b	(* (sin th) (expm1 (log1p (/ (sin ky) (hypot (sin kx) (sin ky))))))
0.1b	(log1p (expm1 (* (sin th) (expm1 (log1p (/ (sin ky) (hypot (sin kx) (sin ky))))))))
0.1b	(/ (sin ky) (hypot (sin kx) (sin ky)))

rewrite23.0ms

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`
2×	`log1p-udef` `log1p-expm1`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 75

Calls

4 calls:

Slowest

14.0ms	(* (sin th) (expm1 (log1p (/ (sin ky) (hypot (sin kx) (sin ky))))))
8.0ms	(/ (sin ky) (hypot (sin kx) (sin ky)))
0.0ms	(log1p (/ (sin ky) (hypot (sin kx) (sin ky))))
0.0ms	(log1p (expm1 (* (sin th) (expm1 (log1p (/ (sin ky) (hypot (sin kx) (sin ky))))))))

series1.3s

Counts

4 → 12

Calls

4 calls:

Slowest

436.0ms	(log1p (expm1 (* (sin th) (expm1 (log1p (/ (sin ky) (hypot (sin kx) (sin ky))))))))
325.0ms	(log1p (/ (sin ky) (hypot (sin kx) (sin ky))))
313.0ms	(* (sin th) (expm1 (log1p (/ (sin ky) (hypot (sin kx) (sin ky))))))
196.0ms	(/ (sin ky) (hypot (sin kx) (sin ky)))

simplify3.9s

Counts

49 → 87

Calls

49 calls:

Slowest

444.0ms	(/ (* (* (sin ky) (sin ky)) (sin ky)) (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky))))
359.0ms	(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
338.0ms	(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
320.0ms	(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
316.0ms	(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))

prune1.5s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 9.1b

localize53.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (sin ky) (sqrt (hypot (sin kx) (sin ky))))
0.3b	(* (* (sin th) (/ 1 (sqrt (hypot (sin kx) (sin ky))))) (/ (sin ky) (sqrt (hypot (sin kx) (sin ky)))))
0.3b	(* (sin th) (/ 1 (sqrt (hypot (sin kx) (sin ky)))))
0.2b	(/ 1 (sqrt (hypot (sin kx) (sin ky))))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
73×	`add-sqr-sqrt`
63×	`*-un-lft-identity`
61×	`add-cube-cbrt`
54×	`add-exp-log`
44×	`associate-r` `sqrt-prod`
34×	`add-cbrt-cube`
22×	`prod-exp`
14×	`div-exp`
13×	`pow1`
12×	`associate-/r*` `cbrt-unprod`
8×	`cbrt-undiv`
6×	`associate-/l*`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `associate-l` `pow-prod-down` `associate-*r/` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`un-div-inv` `pow-flip`
2×	`frac-times` `clear-num` `frac-2neg` `associate-l/` `-commutative`
1×	`sqrt-pow1` `pow1/2` `inv-pow`

Counts

4 → 197

Calls

4 calls:

Slowest

45.0ms	(* (* (sin th) (/ 1 (sqrt (hypot (sin kx) (sin ky))))) (/ (sin ky) (sqrt (hypot (sin kx) (sin ky)))))
29.0ms	(* (sin th) (/ 1 (sqrt (hypot (sin kx) (sin ky)))))
10.0ms	(/ 1 (sqrt (hypot (sin kx) (sin ky))))
8.0ms	(/ (sin ky) (sqrt (hypot (sin kx) (sin ky))))

series1.0s

Counts

4 → 12

Calls

4 calls:

Slowest

294.0ms	(* (* (sin th) (/ 1 (sqrt (hypot (sin kx) (sin ky))))) (/ (sin ky) (sqrt (hypot (sin kx) (sin ky)))))
286.0ms	(* (sin th) (/ 1 (sqrt (hypot (sin kx) (sin ky)))))
241.0ms	(/ (sin ky) (sqrt (hypot (sin kx) (sin ky))))
183.0ms	(/ 1 (sqrt (hypot (sin kx) (sin ky))))

simplify13.4s

Counts

199 → 209

Calls

199 calls:

Slowest

707.0ms	(+ (+ (log (sin th)) (log (/ 1 (sqrt (hypot (sin kx) (sin ky)))))) (- (log (sin ky)) (log (sqrt (hypot (sin kx) (sin ky))))))
541.0ms	(+ (+ (log (sin th)) (- 0 (log (sqrt (hypot (sin kx) (sin ky)))))) (log (/ (sin ky) (sqrt (hypot (sin kx) (sin ky))))))
474.0ms	(* (* (* (* (sin th) (sin th)) (sin th)) (/ (* (* 1 1) 1) (* (* (sqrt (hypot (sin kx) (sin ky))) (sqrt (hypot (sin kx) (sin ky)))) (sqrt (hypot (sin kx) (sin ky)))))) (/ (* (* (sin ky) (sin ky)) (sin ky)) (* (* (sqrt (hypot (sin kx) (sin ky))) (sqrt (hypot (sin kx) (sin ky)))) (sqrt (hypot (sin kx) (sin ky))))))
465.0ms	(+ (+ (log (sin th)) (- 0 (log (sqrt (hypot (sin kx) (sin ky)))))) (- (log (sin ky)) (log (sqrt (hypot (sin kx) (sin ky))))))
455.0ms	(+ (+ (log (sin th)) (- (log 1) (log (sqrt (hypot (sin kx) (sin ky)))))) (- (log (sin ky)) (log (sqrt (hypot (sin kx) (sin ky))))))

prune2.9s

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 9.1b

regimes1.2s

Accuracy

0% (0.3b remaining)

Error of 9.0b against oracle of 8.7b and baseline of 9.0b

bsearch2.0ms

end0.0ms

sample11.6s

Algorithm

intervals

Results

6.5s	2668×	body	1280	valid
2.6s	1848×	body	640	valid
1.2s	2349×	body	80	valid
757.0ms	758×	body	320	valid
252.0ms	377×	body	160	valid