Details

sample862.0ms

Algorithm

intervals

Results

266.0ms	84×	body	1280	valid
136.0ms	66×	body	640	valid
30.0ms	26×	body	320	valid
23.0ms	69×	body	80	valid
8.0ms	11×	body	160	valid

simplify423.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

422.0ms

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

prune33.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.7b

localize21.0ms

Local error

Found 3 expressions with local error:

2.7b	(/ (* (sin th) (sin ky)) (hypot (sin kx) (sin ky)))
0.2b	(* (sin th) (sin ky))
0.1b	(hypot (sin kx) (sin ky))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 58

Calls

3 calls:

Slowest

21.0ms	(/ (* (sin th) (sin ky)) (hypot (sin kx) (sin ky)))
11.0ms	(* (sin th) (sin ky))
0.0ms	(hypot (sin kx) (sin ky))

series1.0s

Counts

3 → 9

Calls

3 calls:

Slowest

794.0ms	(/ (* (sin th) (sin ky)) (hypot (sin kx) (sin ky)))
180.0ms	(hypot (sin kx) (sin ky))
60.0ms	(* (sin th) (sin ky))

simplify2.4s

Counts

35 → 67

Calls

35 calls:

Slowest

446.0ms	(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
415.0ms	(* (* (* (sin th) (sin th)) (sin th)) (* (* (sin ky) (sin ky)) (sin ky)))
405.0ms	(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
206.0ms	(/ (* (* (* (sin th) (sin ky)) (* (sin th) (sin ky))) (* (sin th) (sin ky))) (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky))))
203.0ms	(/ (* (* (* (sin th) (sin th)) (sin th)) (* (* (sin ky) (sin ky)) (sin ky))) (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky))))

prune920.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 9.0b

localize44.0ms

Local error

Found 3 expressions with local error:

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

rewrite22.0ms

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 th) (/ (sin ky) (hypot (sin kx) (sin ky))))
9.0ms	(/ (sin ky) (hypot (sin kx) (sin ky)))
0.0ms	(hypot (sin kx) (sin ky))

series677.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

302.0ms	(* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))
216.0ms	(/ (sin ky) (hypot (sin kx) (sin ky)))
159.0ms	(hypot (sin kx) (sin ky))

simplify4.0s

Counts

59 → 85

Calls

59 calls:

Slowest

445.0ms	(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
443.0ms	(/ (* (* (sin ky) (sin ky)) (sin ky)) (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky))))
383.0ms	(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky))
378.0ms	(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
378.0ms	(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky))

prune1.0s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 9.0b

localize19.0ms

Local error

Found 3 expressions with local error:

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

rewrite40.0ms

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

29.0ms	(* (/ (sin ky) (hypot (sin kx) (sin ky))) (sin th))
9.0ms	(/ (sin ky) (hypot (sin kx) (sin ky)))
0.0ms	(hypot (sin kx) (sin ky))

series724.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

344.0ms	(* (/ (sin ky) (hypot (sin kx) (sin ky))) (sin th))
225.0ms	(/ (sin ky) (hypot (sin kx) (sin ky)))
155.0ms	(hypot (sin kx) (sin ky))

simplify3.9s

Counts

59 → 85

Calls

59 calls:

Slowest

426.0ms	(/ (* (* (sin ky) (sin ky)) (sin ky)) (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky))))
413.0ms	(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
407.0ms	(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky))
396.0ms	(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
347.0ms	(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky))

prune1.0s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 9.0b

localize22.0ms

Local error

Found 3 expressions with local error:

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

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
53×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
16×	`associate-/r*`
10×	`add-cbrt-cube` `add-exp-log`
6×	`div-inv` `associate-/l*`
4×	`cbrt-undiv` `div-exp`
3×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg`
1×	`hypot-udef` `associate-/r/`

Counts

3 → 114

Calls

3 calls:

Slowest

10.0ms	(/ (sin th) (/ (hypot (sin kx) (sin ky)) (sin ky)))
6.0ms	(/ (hypot (sin kx) (sin ky)) (sin ky))
0.0ms	(hypot (sin kx) (sin ky))

series738.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

340.0ms	(/ (sin th) (/ (hypot (sin kx) (sin ky)) (sin ky)))
223.0ms	(/ (hypot (sin kx) (sin ky)) (sin ky))
174.0ms	(hypot (sin kx) (sin ky))

simplify8.4s

Counts

132 → 123

Calls

132 calls:

Slowest

573.0ms	(/ (* (cbrt (sin th)) (cbrt (sin th))) (/ (* (cbrt (hypot (sin kx) (sin ky))) (cbrt (hypot (sin kx) (sin ky)))) (* (cbrt (sin ky)) (cbrt (sin ky)))))
561.0ms	(/ (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky))) (* (* (sin ky) (sin ky)) (sin ky)))
529.0ms	(* (sqrt (+ (pow (sin ky) 2) (pow (sin kx) 2))) (/ 1 (sin ky)))
482.0ms	(/ (* (* (sin th) (sin th)) (sin th)) (* (* (/ (hypot (sin kx) (sin ky)) (sin ky)) (/ (hypot (sin kx) (sin ky)) (sin ky))) (/ (hypot (sin kx) (sin ky)) (sin ky))))
479.0ms	(* (sqrt (+ (pow (sin ky) 2) (pow (sin kx) 2))) (/ 1 (sin ky)))

prune1.6s

Pruning

22 alts after pruning (20 fresh and 2 done)

Merged error: 9.0b

regimes1.3s

Accuracy

0% (0.2b remaining)

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

bsearch3.0ms

end0.0ms

sample12.3s

Algorithm

intervals

Results

6.5s	2766×	body	1280	valid
3.1s	1811×	body	640	valid
1.3s	772×	body	320	valid
879.0ms	2305×	body	80	valid
185.0ms	346×	body	160	valid