Details

sample454.0ms

Algorithm

intervals

Results

202.0ms	75×	body	1280	valid
74.0ms	71×	body	640	valid
18.0ms	25×	body	320	valid
15.0ms	73×	body	80	valid
5.0ms	12×	body	160	valid

simplify205.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

205.0ms

(* (/ (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: 8.3b

localize27.0ms

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))

rewrite24.0ms

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))

series765.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

296.0ms	(* (sin th) (/ (sin ky) (hypot (sin kx) (sin ky))))
267.0ms	(/ (sin ky) (hypot (sin kx) (sin ky)))
201.0ms	(hypot (sin kx) (sin ky))

simplify3.7s

Counts

59 → 85

Calls

59 calls:

Slowest

476.0ms	(/ (* (* (sin ky) (sin ky)) (sin ky)) (* (* (hypot (sin kx) (sin ky)) (hypot (sin kx) (sin ky))) (hypot (sin kx) (sin ky))))
362.0ms	(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
355.0ms	(* (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 ky))
265.0ms	(* (* (* (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)))))

prune1.1s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 8.2b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite42.0ms

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

31.0ms	(* (sin th) (/ (sin ky) (log1p (expm1 (hypot (sin kx) (sin ky))))))
8.0ms	(/ (sin ky) (log1p (expm1 (hypot (sin kx) (sin ky)))))
1.0ms	(expm1 (hypot (sin kx) (sin ky)))
0.0ms	(log1p (expm1 (hypot (sin kx) (sin ky))))

series1.1s

Counts

4 → 12

Calls

4 calls:

Slowest

409.0ms	(* (sin th) (/ (sin ky) (log1p (expm1 (hypot (sin kx) (sin ky))))))
266.0ms	(/ (sin ky) (log1p (expm1 (hypot (sin kx) (sin ky)))))
232.0ms	(log1p (expm1 (hypot (sin kx) (sin ky))))
209.0ms	(expm1 (hypot (sin kx) (sin ky)))

simplify4.7s

Counts

64 → 101

Calls

64 calls:

Slowest

577.0ms	(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
448.0ms	(/ (* (* (sin ky) (sin ky)) (sin ky)) (* (* (log1p (expm1 (hypot (sin kx) (sin ky)))) (log1p (expm1 (hypot (sin kx) (sin ky))))) (log1p (expm1 (hypot (sin kx) (sin ky))))))
382.0ms	(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
311.0ms	(* (* (* (sin th) (sin th)) (sin th)) (* (* (/ (sin ky) (log1p (expm1 (hypot (sin kx) (sin ky))))) (/ (sin ky) (log1p (expm1 (hypot (sin kx) (sin ky)))))) (/ (sin ky) (log1p (expm1 (hypot (sin kx) (sin ky)))))))
290.0ms	(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky))

prune1.6s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 8.2b

localize62.0ms

Local error

Found 4 expressions with local error:

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

rewrite44.0ms

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

25.0ms	(* (sin th) (/ (sin ky) (log1p (expm1 (hypot (sin kx) (sin ky))))))
15.0ms	(/ (sin ky) (log1p (expm1 (hypot (sin kx) (sin ky)))))
1.0ms	(expm1 (hypot (sin kx) (sin ky)))
1.0ms	(log1p (expm1 (hypot (sin kx) (sin ky))))

series1.1s

Counts

4 → 12

Calls

4 calls:

Slowest

387.0ms	(* (sin th) (/ (sin ky) (log1p (expm1 (hypot (sin kx) (sin ky))))))
261.0ms	(/ (sin ky) (log1p (expm1 (hypot (sin kx) (sin ky)))))
240.0ms	(log1p (expm1 (hypot (sin kx) (sin ky))))
237.0ms	(expm1 (hypot (sin kx) (sin ky)))

simplify4.4s

Counts

64 → 101

Calls

64 calls:

Slowest

534.0ms	(/ (* (* (sin ky) (sin ky)) (sin ky)) (* (* (log1p (expm1 (hypot (sin kx) (sin ky)))) (log1p (expm1 (hypot (sin kx) (sin ky))))) (log1p (expm1 (hypot (sin kx) (sin ky))))))
380.0ms	(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))
305.0ms	(* (* (* (sin th) (sin th)) (sin th)) (* (* (/ (sin ky) (log1p (expm1 (hypot (sin kx) (sin ky))))) (/ (sin ky) (log1p (expm1 (hypot (sin kx) (sin ky)))))) (/ (sin ky) (log1p (expm1 (hypot (sin kx) (sin ky)))))))
283.0ms	(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky))
283.0ms	(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))

prune1.6s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 8.2b

localize48.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (sin ky) (sqrt (hypot (sin kx) (sin ky))))
0.2b	(/ (/ (sin ky) (sqrt (hypot (sin kx) (sin ky)))) (sqrt (hypot (sin kx) (sin ky))))
0.2b	(* (sin th) (/ (/ (sin ky) (sqrt (hypot (sin kx) (sin ky)))) (sqrt (hypot (sin kx) (sin ky)))))
0.1b	(sqrt (hypot (sin kx) (sin ky)))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

526×	`times-frac`
306×	`add-sqr-sqrt`
281×	`*-un-lft-identity` `add-cube-cbrt`
272×	`sqrt-prod`
136×	`associate-r`
25×	`associate-/l*`
20×	`add-cbrt-cube` `add-exp-log`
16×	`div-inv`
12×	`associate-/r*`
7×	`pow1` `cbrt-undiv` `div-exp` `unswap-sqr`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `prod-exp` `cbrt-unprod`
2×	`clear-num` `frac-2neg`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-r/` `-commutative` `associate-/l/`

Counts

4 → 401

Calls

4 calls:

Slowest

44.0ms	(* (sin th) (/ (/ (sin ky) (sqrt (hypot (sin kx) (sin ky)))) (sqrt (hypot (sin kx) (sin ky)))))
33.0ms	(/ (/ (sin ky) (sqrt (hypot (sin kx) (sin ky)))) (sqrt (hypot (sin kx) (sin ky))))
16.0ms	(/ (sin ky) (sqrt (hypot (sin kx) (sin ky))))
2.0ms	(sqrt (hypot (sin kx) (sin ky)))

series1.1s

Counts

4 → 12

Calls

4 calls:

Slowest

367.0ms	(* (sin th) (/ (/ (sin ky) (sqrt (hypot (sin kx) (sin ky)))) (sqrt (hypot (sin kx) (sin ky)))))
291.0ms	(/ (sin ky) (sqrt (hypot (sin kx) (sin ky))))
267.0ms	(/ (/ (sin ky) (sqrt (hypot (sin kx) (sin ky)))) (sqrt (hypot (sin kx) (sin ky))))
169.0ms	(sqrt (hypot (sin kx) (sin ky)))

simplify20.5s

Counts

519 → 413

Calls

519 calls:

Slowest

591.0ms	(* (* (* (sin th) (sin th)) (sin th)) (* (* (/ (/ (sin ky) (sqrt (hypot (sin kx) (sin ky)))) (sqrt (hypot (sin kx) (sin ky)))) (/ (/ (sin ky) (sqrt (hypot (sin kx) (sin ky)))) (sqrt (hypot (sin kx) (sin ky))))) (/ (/ (sin ky) (sqrt (hypot (sin kx) (sin ky)))) (sqrt (hypot (sin kx) (sin ky))))))
499.0ms	(/ (* (* (sin ky) (sin ky)) (sin ky)) (* (* (sqrt (hypot (sin kx) (sin ky))) (sqrt (hypot (sin kx) (sin ky)))) (sqrt (hypot (sin kx) (sin ky)))))
362.0ms	(/ (/ (* (* (sin ky) (sin ky)) (sin ky)) (* (* (sqrt (hypot (sin kx) (sin ky))) (sqrt (hypot (sin kx) (sin ky)))) (sqrt (hypot (sin kx) (sin ky))))) (* (* (sqrt (hypot (sin kx) (sin ky))) (sqrt (hypot (sin kx) (sin ky)))) (sqrt (hypot (sin kx) (sin ky)))))
360.0ms	(* (pow (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2))) 1/4) (sin ky))
354.0ms	(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (* (sin th) (sin ky)))

prune5.9s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 8.1b

regimes1.1s

Accuracy

0% (0.4b remaining)

Error of 9.1b against oracle of 8.7b and baseline of 9.1b

bsearch2.0ms

end0.0ms

sample12.1s

Algorithm

intervals

Results

6.5s	2704×	body	1280	valid
3.3s	1869×	body	640	valid
1.0s	2246×	body	80	valid
773.0ms	810×	body	320	valid
227.0ms	371×	body	160	valid