Details

sample152.0ms

Algorithm

intervals

Results

121.0ms

256×

body

valid

simplify871.0ms

Counts: 1 → 1

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.4b

localize59.0ms

Local error

Found 4 expressions with local error:

8.0b	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))
3.4b	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
0.3b	(* (sin kx) (sin kx))
0.3b	(* (/ (* l 2) Om) (/ (* l 2) Om))

rewrite347.0ms

Algorithm

rewrite-expression-head

Rules

89×	`add-cbrt-cube` `add-exp-log`
41×	`prod-exp` `cbrt-unprod`
24×	`add-sqr-sqrt` `pow1` `cbrt-undiv` `div-exp`
18×	`*-un-lft-identity` `add-cube-cbrt`
14×	`frac-times`
13×	`associate-l`
12×	`times-frac`
11×	`associate-r`
10×	`swap-sqr`
9×	`sin-mult`
8×	`associate-l/` `associate-r/`
5×	`flip3-+` `pow-prod-down` `flip-+`
4×	`frac-add` `insert-posit16` `div-inv` `add-log-exp`
3×	`*-commutative` `sqrt-prod` `unswap-sqr`
2×	`pow2` `pow-plus` `sqrt-div` `pow-sqr` `pow-prod-up`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `sqr-sin`

Counts

4 → 152

Calls

4 calls:

Slowest

177.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))
129.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
24.0ms	(* (/ (* l 2) Om) (/ (* l 2) Om))
10.0ms	(* (sin kx) (sin kx))

series1.3s

Counts

4 → 12

Calls

4 calls:

Slowest

503.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))
440.0ms	(* (/ (* l 2) Om) (/ (* l 2) Om))
323.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
27.0ms	(* (sin kx) (sin kx))

simplify504.0ms

Counts: 185 → 164

prune2.9s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.4b

localize45.0ms

Local error

Found 4 expressions with local error:

8.0b	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))
3.6b	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om))
1.3b	(* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om))
0.3b	(* (sin kx) (sin kx))

rewrite377.0ms

Algorithm

rewrite-expression-head

Rules

69×	`add-cbrt-cube` `add-exp-log`
33×	`prod-exp` `cbrt-unprod`
19×	`add-sqr-sqrt` `pow1`
17×	`associate-r`
16×	`frac-times` `cbrt-undiv` `div-exp` `associate-*l/`
14×	`*-un-lft-identity` `add-cube-cbrt`
13×	`sin-mult`
7×	`flip3-+` `associate-l` `flip-+`
6×	`times-frac` `frac-add`
5×	`pow-prod-down`
4×	`associate-*r/` `insert-posit16` `add-log-exp`
3×	`swap-sqr` `*-commutative` `sqrt-prod`
2×	`sqrt-div` `div-inv` `unswap-sqr`
1×	`pow2` `rem-sqrt-square` `sqrt-pow1` `pow-plus` `pow1/2` `pow-sqr` `pow-prod-up` `sqr-sin`

Counts

4 → 136

Calls

4 calls:

Slowest

168.0ms	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))
101.0ms	(* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om))
83.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om))
21.0ms	(* (sin kx) (sin kx))

series887.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

404.0ms	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))
285.0ms	(* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om))
166.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om))
33.0ms	(* (sin kx) (sin kx))

simplify489.0ms

Counts: 162 → 148

prune2.4s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize76.0ms

Local error

Found 4 expressions with local error:

8.0b	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))
3.6b	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om))
1.3b	(* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om))
0.3b	(* (sin kx) (sin kx))

rewrite345.0ms

Algorithm

rewrite-expression-head

Rules

69×	`add-cbrt-cube` `add-exp-log`
33×	`prod-exp` `cbrt-unprod`
19×	`add-sqr-sqrt` `pow1`
17×	`associate-r`
16×	`frac-times` `cbrt-undiv` `div-exp` `associate-*l/`
14×	`*-un-lft-identity` `add-cube-cbrt`
13×	`sin-mult`
7×	`flip3-+` `associate-l` `flip-+`
6×	`times-frac` `frac-add`
5×	`pow-prod-down`
4×	`associate-*r/` `insert-posit16` `add-log-exp`
3×	`swap-sqr` `*-commutative` `sqrt-prod`
2×	`sqrt-div` `div-inv` `unswap-sqr`
1×	`pow2` `rem-sqrt-square` `sqrt-pow1` `pow-plus` `pow1/2` `pow-sqr` `pow-prod-up` `sqr-sin`

Counts

4 → 136

Calls

4 calls:

Slowest

156.0ms	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))
118.0ms	(* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om))
57.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om))
12.0ms	(* (sin kx) (sin kx))

series919.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

447.0ms	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))
257.0ms	(* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om))
192.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om))
22.0ms	(* (sin kx) (sin kx))

simplify607.0ms

Counts: 162 → 148

prune2.8s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize66.0ms

Local error

Found 4 expressions with local error:

3.6b	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om))
1.3b	(* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om))
1.0b	(log (exp (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om))))
0.3b	(* (sin kx) (sin kx))

rewrite273.0ms

Algorithm

rewrite-expression-head

Rules

69×	`add-cbrt-cube` `add-exp-log`
33×	`prod-exp` `cbrt-unprod`
19×	`pow1`
18×	`add-sqr-sqrt`
17×	`associate-r`
16×	`frac-times` `cbrt-undiv` `div-exp` `associate-*l/`
14×	`*-un-lft-identity` `add-cube-cbrt`
13×	`sin-mult`
7×	`associate-l`
6×	`flip3-+` `times-frac` `frac-add` `flip-+`
5×	`pow-prod-down` `add-log-exp`
4×	`associate-*r/` `insert-posit16`
3×	`log-prod` `swap-sqr` `log-pow` `*-commutative`
2×	`div-inv` `unswap-sqr`
1×	`pow2` `exp-prod` `pow-plus` `exp-to-pow` `rem-log-exp` `pow-sqr` `pow-prod-up` `sqr-sin`

Counts

4 → 135

Calls

4 calls:

Slowest

153.0ms	(* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om))
78.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om))
20.0ms	(* (sin kx) (sin kx))
16.0ms	(log (exp (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om))))

series856.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

289.0ms	(* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om))
282.0ms	(log (exp (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om))))
249.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om))
36.0ms	(* (sin kx) (sin kx))

simplify485.0ms

Counts: 160 → 147

prune2.9s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

regimes490.0ms

Accuracy

0% (0.6b remaining)

Error of 1.2b against oracle of 0.6b and baseline of 1.2b

bsearch5.0ms

end0.0ms

sample3.9s

Algorithm

intervals

Results

3.6s

8000×

body

valid