Details

Time bar (total: 1.7m)

sample141.0ms

Algorithm
intervals
Results
110.0ms256×body80valid

simplify1.2s

Counts
1 → 1

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.7b

localize98.0ms

Local error

Found 4 expressions with local error:

9.4b
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
2.3b
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
0.4b
(/ (/ 1 2) (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1)))
0.3b
(* (sin kx) (sin kx))

rewrite688.0ms

Algorithm
rewrite-expression-head
Rules
141×times-frac
91×add-sqr-sqrt
87×*-un-lft-identity add-cube-cbrt
62×add-exp-log
58×add-cbrt-cube
45×sqrt-prod
32×prod-exp cbrt-unprod
30×pow1
23×associate-*r/
14×pow-prod-down
13×frac-times associate-/l*
12×div-exp
9×cbrt-undiv sin-mult
8×div-inv
7×associate-*l/
6×associate-/r* flip3-+ associate-*l* flip-+
4×sqrt-div associate-*r* frac-add insert-posit16 add-log-exp
3×swap-sqr
2×associate-/r/ *-commutative unswap-sqr
1×pow2 rem-sqrt-square rec-exp clear-num frac-2neg sqrt-pow1 pow-plus pow1/2 1-exp pow-sqr pow-prod-up sqr-sin associate-/l/
Counts
4 → 215
Calls
4 calls:
Slowest
269.0ms
(/ (/ 1 2) (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1)))
222.0ms
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
160.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
21.0ms
(* (sin kx) (sin kx))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
486.0ms
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
337.0ms
(/ (/ 1 2) (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1)))
249.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
32.0ms
(* (sin kx) (sin kx))

simplify2.5s

Counts
227 → 227

prune4.9s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.6b

localize89.0ms

Local error

Found 4 expressions with local error:

9.4b
(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om))) 1))
2.2b
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))
0.4b
(* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om)))
0.4b
(/ (/ 1 2) (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om))) 1)))

rewrite672.0ms

Algorithm
rewrite-expression-head
Rules
141×times-frac
84×add-sqr-sqrt
83×*-un-lft-identity add-cube-cbrt
76×add-exp-log
72×add-cbrt-cube
45×sqrt-prod
40×prod-exp cbrt-unprod
31×pow1
24×associate-*r/
18×pow-prod-down
16×frac-times associate-*l/
14×div-exp
13×associate-/l*
12×sin-mult
11×cbrt-undiv
8×flip3-+ flip-+ div-inv
6×associate-/r* frac-add
4×sqrt-div associate-*l* insert-posit16 add-log-exp
2×associate-*r* associate-/r/ *-commutative
1×rem-sqrt-square rec-exp clear-num frac-2neg sqrt-pow1 pow1/2 1-exp associate-/l/
Counts
4 → 217
Calls
4 calls:
Slowest
253.0ms
(/ (/ 1 2) (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om))) 1)))
185.0ms
(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om))) 1))
172.0ms
(* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om)))
55.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
475.0ms
(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om))) 1))
422.0ms
(/ (/ 1 2) (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om))) 1)))
258.0ms
(* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om)))
246.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))

simplify2.1s

Counts
229 → 229

prune5.4s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.4b

localize74.0ms

Local error

Found 4 expressions with local error:

9.4b
(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om))) 1))
2.2b
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))
0.7b
(/ (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om))) 1)) (sqrt (/ 1 2)))
0.4b
(/ (sqrt (/ 1 2)) (/ (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om))) 1)) (sqrt (/ 1 2))))

rewrite881.0ms

Algorithm
rewrite-expression-head
Rules
5243×times-frac
3613×sqrt-prod
2290×add-sqr-sqrt
2289×*-un-lft-identity add-cube-cbrt
230×div-inv
117×associate-/r*
23×sqrt-div
22×associate-/l*
20×add-cbrt-cube add-exp-log
19×associate-/r/
10×pow1
5×cbrt-undiv div-exp prod-exp associate-*r/ cbrt-unprod
4×flip3-+ flip-+ insert-posit16 sin-mult add-log-exp
3×frac-times sqrt-undiv associate-*l* pow-prod-down associate-*l/ associate-/l/
2×clear-num frac-2neg frac-add
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r* *-commutative
Counts
4 → 1930
Calls
4 calls:
Slowest
289.0ms
(/ (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om))) 1)) (sqrt (/ 1 2)))
216.0ms
(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om))) 1))
168.0ms
(/ (sqrt (/ 1 2)) (/ (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om))) 1)) (sqrt (/ 1 2))))
65.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))

series1.8s

Counts
4 → 12
Calls
4 calls:
Slowest
736.0ms
(/ (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om))) 1)) (sqrt (/ 1 2)))
458.0ms
(/ (sqrt (/ 1 2)) (/ (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om))) 1)) (sqrt (/ 1 2))))
432.0ms
(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om))) 1))
173.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))

simplify6.8s

Counts
1942 → 1942

prune53.4s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.4b

localize126.0ms

Local error

Found 4 expressions with local error:

9.4b
(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om))) 1))
2.2b
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))
0.7b
(* (/ (sqrt (/ 1 2)) (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om))) 1))) (sqrt (/ 1 2)))
0.4b
(/ (sqrt (/ 1 2)) (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om))) 1)))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
384×times-frac
351×sqrt-prod
307×add-sqr-sqrt
202×*-un-lft-identity
185×add-cube-cbrt
105×associate-*l*
36×unswap-sqr
20×add-cbrt-cube add-exp-log
17×associate-*r*
16×div-inv associate-/l*
12×pow1
9×sqrt-div
7×prod-exp cbrt-unprod
6×associate-/r* associate-*r/
5×flip3-+ flip-+
4×frac-times pow-prod-down associate-*l/ associate-/r/ insert-posit16 sin-mult add-log-exp
3×cbrt-undiv div-exp
2×sqrt-undiv frac-add *-commutative
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 sqrt-unprod associate-/l/
Counts
4 → 351
Calls
4 calls:
Slowest
551.0ms
(* (/ (sqrt (/ 1 2)) (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om))) 1))) (sqrt (/ 1 2)))
215.0ms
(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om))) 1))
210.0ms
(/ (sqrt (/ 1 2)) (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om))) 1)))
77.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))

series1.5s

Counts
4 → 12
Calls
4 calls:
Slowest
480.0ms
(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om))) 1))
432.0ms
(* (/ (sqrt (/ 1 2)) (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om))) 1))) (sqrt (/ 1 2)))
406.0ms
(/ (sqrt (/ 1 2)) (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om))) 1)))
205.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))

simplify1.9s

Counts
363 → 363

prune9.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.4b

regimes694.0ms

Accuracy

0% (0.7b remaining)

Error of 1.4b against oracle of 0.6b and baseline of 1.4b

bsearch7.0ms

end0.0ms

sample3.8s

Algorithm
intervals
Results
3.5s7999×body80valid
1.0ms1×body160valid