Details

sample184.0ms

Algorithm

intervals

Results

154.0ms

256×

body

valid

simplify303.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

302.0ms

(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))

prune34.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.1b

localize64.0ms

Local error

Found 4 expressions with local error:

9.6b	(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
2.4b	(fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
0.2b	(/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
0.2b	(fma (sin ky) (sin ky) (* (sin kx) (sin kx)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac`
15×	`sqrt-prod`
6×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l*`
2×	`fma-udef`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `div-inv`

Counts

4 → 80

Calls

4 calls:

Slowest

8.0ms	(/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
5.0ms	(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
0.0ms	(fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
0.0ms	(fma (sin ky) (sin ky) (* (sin kx) (sin kx)))

series1.1s

Counts

4 → 12

Calls

4 calls:

Slowest

427.0ms	(/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
379.0ms	(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
185.0ms	(fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
74.0ms	(fma (sin ky) (sin ky) (* (sin kx) (sin kx)))

simplify17.4s

Counts

63 → 92

Calls

63 calls:

Slowest

720.0ms	(sqrt (* (cbrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)) (cbrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))))
458.0ms	(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
450.0ms	(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
434.0ms	(/ (sqrt 1/2) (sqrt (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))))
428.0ms	(/ (cbrt 1/2) (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))

prune1.7s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize88.0ms

Local error

Found 4 expressions with local error:

9.6b	(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
2.1b	(/ (* (sin ky) l) Om)
2.1b	(/ (* (sin ky) l) Om)
1.7b	(/ (* l (sin kx)) Om)

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-cbrt-cube` `add-exp-log`
12×	`add-sqr-sqrt`
11×	`*-un-lft-identity` `add-cube-cbrt`
9×	`associate-/r*` `times-frac`
6×	`cbrt-undiv` `div-exp`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `prod-exp` `sqrt-prod` `cbrt-unprod` `div-inv` `associate-/l*`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 88

Calls

4 calls:

Slowest

19.0ms	(/ (* l (sin kx)) Om)
11.0ms	(/ (* (sin ky) l) Om)
11.0ms	(/ (* (sin ky) l) Om)
1.0ms	(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))

series596.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

365.0ms	(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
86.0ms	(/ (* (sin ky) l) Om)
76.0ms	(/ (* l (sin kx)) Om)
69.0ms	(/ (* (sin ky) l) Om)

simplify4.4s

Counts

55 → 100

Calls

55 calls:

Slowest

575.0ms	(- (/ (* ky l) Om) (* 1/6 (/ (* (pow ky 3) l) Om)))
386.0ms	(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
361.0ms	(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
308.0ms	(sqrt (sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1)))
263.0ms	(sqrt (* (cbrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1)) (cbrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))))

prune1.7s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize51.0ms

Local error

Found 4 expressions with local error:

2.3b	(log (exp (/ (* l (sin kx)) Om)))
2.1b	(/ (* (sin ky) l) Om)
2.1b	(/ (* (sin ky) l) Om)
1.7b	(/ (* l (sin kx)) Om)

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-cbrt-cube` `add-exp-log`
13×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
12×	`times-frac`
9×	`associate-/r*`
8×	`log-pow`
7×	`exp-prod`
6×	`cbrt-undiv` `div-exp`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`log-prod` `clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `associate-/l*`
1×	`rem-log-exp`

Counts

4 → 94

Calls

4 calls:

Slowest

22.0ms	(/ (* l (sin kx)) Om)
19.0ms	(/ (* (sin ky) l) Om)
11.0ms	(/ (* (sin ky) l) Om)
5.0ms	(log (exp (/ (* l (sin kx)) Om)))

series315.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

81.0ms	(/ (* l (sin kx)) Om)
80.0ms	(/ (* (sin ky) l) Om)
79.0ms	(log (exp (/ (* l (sin kx)) Om)))
75.0ms	(/ (* (sin ky) l) Om)

simplify3.0s

Counts

61 → 106

Calls

61 calls:

Slowest

253.0ms	(- (/ (* ky l) Om) (* 1/6 (/ (* (pow ky 3) l) Om)))
250.0ms	(- (/ (* ky l) Om) (* 1/6 (/ (* (pow ky 3) l) Om)))
229.0ms	(- (/ (* kx l) Om) (* 1/6 (/ (* (pow kx 3) l) Om)))
210.0ms	(/ (* (* (* l (sin kx)) (* l (sin kx))) (* l (sin kx))) (* (* Om Om) Om))
200.0ms	(/ (* (* (* (sin ky) l) (* (sin ky) l)) (* (sin ky) l)) (* (* Om Om) Om))

prune2.4s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize86.0ms

Local error

Found 4 expressions with local error:

9.6b	(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
9.6b	(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
9.6b	(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
6.9b	(cbrt (/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
22×	`cbrt-prod`
20×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
7×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`cbrt-div` `pow1/3` `div-inv`

Counts

4 → 82

Calls

4 calls:

Slowest

2.0ms	(cbrt (/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))))
1.0ms	(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
1.0ms	(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
1.0ms	(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))

series1.6s

Counts

4 → 12

Calls

4 calls:

Slowest

600.0ms	(cbrt (/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))))
358.0ms	(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
346.0ms	(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
340.0ms	(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))

simplify13.1s

Counts

50 → 94

Calls

50 calls:

Slowest

470.0ms	(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
466.0ms	(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
466.0ms	(sqrt (* (cbrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)) (cbrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))))
459.0ms	(* (cbrt 1/2) (exp (* 1/6 (- (+ (log (/ 1 (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2))))) (* 2 (log (/ -1 l)))) (* 2 (log (/ -1 Om)))))))
441.0ms	(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))

prune1.9s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

regimes441.0ms

Accuracy

0% (1.0b remaining)

Error of 1.7b against oracle of 0.6b and baseline of 1.7b

bsearch13.0ms

end0.0ms

sample4.3s

Algorithm

intervals

Results

4.0s

8000×

body

valid