Details

sample189.0ms

Algorithm

intervals

Results

151.0ms

256×

body

valid

simplify350.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

349.0ms

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

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize40.0ms

Local error

Found 4 expressions with local error:

7.5b	(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
1.2b	(fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
0.3b	(/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
0.3b	(* (sin kx) (sin kx))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
24×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac`
15×	`sqrt-prod`
12×	`pow1`
8×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`swap-sqr` `associate-r` `associate-l` `associate-/l*`
1×	`pow2` `cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow-plus` `pow1/2` `div-exp` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `fma-udef` `sqr-sin` `div-inv` `sin-mult` `unswap-sqr`

Counts

4 → 99

Calls

4 calls:

Slowest

19.0ms	(* (sin kx) (sin kx))
4.0ms	(/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
3.0ms	(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)

series992.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

460.0ms	(/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
305.0ms	(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
193.0ms	(fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
34.0ms	(* (sin kx) (sin kx))

simplify32.6s

Counts

133 → 111

Calls

133 calls:

Slowest

984.0ms	(* (* (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1) (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)) (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
760.0ms	(/ 1 (sqrt (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))))
731.0ms	(sqrt (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
557.0ms	(* (* (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)) (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))) (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
472.0ms	(* (* (/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))) (/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))) (/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))))

prune2.0s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.5b

localize89.0ms

Local error

Found 4 expressions with local error:

7.5b	(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
2.6b	(/ (* (sin ky) l) Om)
2.6b	(/ (* (sin ky) l) Om)
1.7b	(/ (* l (sin kx)) Om)

rewrite57.0ms

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

25.0ms	(/ (* (sin ky) l) Om)
16.0ms	(/ (* l (sin kx)) Om)
12.0ms	(/ (* (sin ky) l) Om)
2.0ms	(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))

series633.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

413.0ms	(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
81.0ms	(/ (* (sin ky) l) Om)
76.0ms	(/ (* l (sin kx)) Om)
63.0ms	(/ (* (sin ky) l) Om)

simplify10.1s

Counts

113 → 100

Calls

113 calls:

Slowest

417.0ms	(* (* (sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1)) (sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))) (sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1)))
363.0ms	(sqrt (cbrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1)))
351.0ms	(exp (sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1)))
336.0ms	(sqrt (sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1)))
332.0ms	(* (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (/ (* (sin ky) l) Om))

prune1.9s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.5b

localize54.0ms

Local error

Found 4 expressions with local error:

7.5b	(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* l (sin ky)) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
2.6b	(/ (* l (sin ky)) Om)
2.6b	(/ (* (sin ky) l) Om)
1.7b	(/ (* l (sin kx)) Om)

rewrite67.0ms

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

23.0ms	(/ (* l (sin kx)) Om)
23.0ms	(/ (* (sin ky) l) Om)
18.0ms	(/ (* l (sin ky)) Om)
2.0ms	(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* l (sin ky)) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))

series625.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

369.0ms	(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* l (sin ky)) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
100.0ms	(/ (* l (sin kx)) Om)
78.0ms	(/ (* l (sin ky)) Om)
77.0ms	(/ (* (sin ky) l) Om)

simplify11.5s

Counts

113 → 100

Calls

113 calls:

Slowest

784.0ms	(sqrt (sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* l (sin ky)) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1)))
505.0ms	(* (* (sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* l (sin ky)) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1)) (sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* l (sin ky)) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))) (sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* l (sin ky)) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1)))
454.0ms	(* (cbrt (sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* l (sin ky)) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))) (cbrt (sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* l (sin ky)) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))))
433.0ms	(sqrt (sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* l (sin ky)) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1)))
431.0ms	(sqrt (sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* l (sin ky)) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1)))

prune1.8s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.5b

localize75.0ms

Local error

Found 4 expressions with local error:

2.8b	(log (exp (/ (* (sin ky) l) Om)))
2.6b	(/ (* (sin ky) l) Om)
2.6b	(/ (* (sin ky) l) Om)
1.7b	(/ (* l (sin kx)) Om)

rewrite81.0ms

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

27.0ms	(/ (* (sin ky) l) Om)
23.0ms	(/ (* l (sin kx)) Om)
23.0ms	(/ (* (sin ky) l) Om)
6.0ms	(log (exp (/ (* (sin ky) l) Om)))

series377.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

101.0ms	(/ (* (sin ky) l) Om)
96.0ms	(/ (* (sin ky) l) Om)
96.0ms	(/ (* l (sin kx)) Om)
83.0ms	(log (exp (/ (* (sin ky) l) Om)))

simplify6.8s

Counts

120 → 106

Calls

120 calls:

Slowest

348.0ms	(* (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om)) (/ (* l (sin kx)) Om))
329.0ms	(* (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (/ (* (sin ky) l) Om))
301.0ms	(* (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (/ (* (sin ky) l) Om))
249.0ms	(- (/ (* ky l) Om) (* 1/6 (/ (* (pow ky 3) l) Om)))
236.0ms	(- (/ (* kx l) Om) (* 1/6 (/ (* (pow kx 3) l) Om)))

prune2.3s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

regimes579.0ms

Accuracy

0% (0.0b remaining)

Error of 0.7b against oracle of 0.7b and baseline of 0.7b

bsearch9.0ms

end0.0ms

sample3.7s

Algorithm

intervals

Results

3.4s

8000×

body

valid