Details

Time bar (total: 2.8m)

sample153.0ms

Algorithm
intervals
Results
106.0ms256×body80valid

simplify209.0ms

Calls
1 calls:
Slowest
208.0ms
(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.4b

localize74.0ms

Local error

Found 4 expressions with local error:

6.8b
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
1.7b
(fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
0.3b
(* (sin kx) (sin kx))
0.2b
(* (/ (* l 2) Om) (/ (* l 2) Om))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
458×associate-/l*
392×add-sqr-sqrt
324×frac-times
267×*-un-lft-identity
253×add-cube-cbrt
200×associate-*l*
193×associate-*r*
168×times-frac
114×associate-/r*
66×unswap-sqr
52×*-commutative
49×swap-sqr
42×add-cbrt-cube add-exp-log
39×clear-num
38×frac-2neg
19×pow1
18×associate-*l/ associate-*r/
16×prod-exp cbrt-unprod
12×cbrt-undiv div-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u div-inv add-log-exp
3×un-div-inv sqrt-prod
2×pow2 pow-plus pow-prod-down pow-sqr pow-prod-up
1×rem-sqrt-square sqrt-pow1 pow1/2 fma-udef sqr-sin sin-mult
Calls
4 calls:
Slowest
66.0ms
(* (/ (* l 2) Om) (/ (* l 2) Om))
13.0ms
(* (sin kx) (sin kx))
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)

series628.0ms

Calls
4 calls:
Slowest
340.0ms
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
204.0ms
(fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
50.0ms
(* (/ (* l 2) Om) (/ (* l 2) Om))
34.0ms
(* (sin kx) (sin kx))

simplify1.7m

Calls
938 calls:
Slowest
839.0ms
(* (/ (* l 2) (cbrt Om)) (/ (* l 2) (cbrt Om)))
693.0ms
(sqrt (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
673.0ms
(* (* (cbrt (* l 2)) (cbrt (* l 2))) (/ (* l 2) (sqrt Om)))
665.0ms
(* (/ (* (* (* l 2) (* l 2)) (* l 2)) (* (* Om Om) Om)) (/ (* (* (* l l) l) (* (* 2 2) 2)) (* (* Om Om) Om)))
640.0ms
(* (/ (* (* (* l l) l) (* (* 2 2) 2)) (* (* Om Om) Om)) (/ (* (* (* l 2) (* l 2)) (* l 2)) (* (* Om Om) Om)))

prune11.4s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize93.0ms

Local error

Found 4 expressions with local error:

6.8b
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
3.5b
(/ (* l (sin kx)) Om)
3.5b
(/ (* l (sin kx)) Om)
2.8b
(/ (* (sin ky) l) Om)

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
108×times-frac
105×add-sqr-sqrt
80×*-un-lft-identity add-cube-cbrt
36×associate-*r* associate-*l* associate-/l*
19×add-cbrt-cube add-exp-log
12×*-commutative unswap-sqr
9×associate-/r*
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
1×rem-sqrt-square sqrt-pow1 pow1/2
Calls
4 calls:
Slowest
35.0ms
(/ (* (sin ky) l) Om)
33.0ms
(/ (* l (sin kx)) Om)
32.0ms
(/ (* l (sin kx)) Om)
3.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))

series587.0ms

Calls
4 calls:
Slowest
339.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
99.0ms
(/ (* l (sin kx)) Om)
83.0ms
(/ (* (sin ky) l) Om)
65.0ms
(/ (* l (sin kx)) Om)

simplify10.1s

Calls
278 calls:
Slowest
708.0ms
(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))))
456.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
400.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
301.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
269.0ms
(fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1)

prune4.2s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize72.0ms

Local error

Found 4 expressions with local error:

6.8b
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (* 1 (/ (* l (sin kx)) Om)) (/ (* l (sin kx)) Om))) 1))
3.5b
(/ (* l (sin kx)) Om)
3.5b
(/ (* l (sin kx)) Om)
2.8b
(/ (* (sin ky) l) Om)

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
108×times-frac
105×add-sqr-sqrt
80×*-un-lft-identity add-cube-cbrt
36×associate-*r* associate-*l* associate-/l*
19×add-cbrt-cube add-exp-log
12×*-commutative unswap-sqr
9×associate-/r*
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
1×rem-sqrt-square sqrt-pow1 pow1/2
Calls
4 calls:
Slowest
26.0ms
(/ (* l (sin kx)) Om)
22.0ms
(/ (* (sin ky) l) Om)
16.0ms
(/ (* l (sin kx)) Om)
1.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (* 1 (/ (* l (sin kx)) Om)) (/ (* l (sin kx)) Om))) 1))

series581.0ms

Calls
4 calls:
Slowest
329.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (* 1 (/ (* l (sin kx)) Om)) (/ (* l (sin kx)) Om))) 1))
99.0ms
(/ (* l (sin kx)) Om)
86.0ms
(/ (* l (sin kx)) Om)
65.0ms
(/ (* (sin ky) l) Om)

simplify10.0s

Calls
278 calls:
Slowest
531.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
438.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
352.0ms
(sqrt (* (cbrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (* 1 (/ (* l (sin kx)) Om)) (/ (* l (sin kx)) Om))) 1)) (cbrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (* 1 (/ (* l (sin kx)) Om)) (/ (* l (sin kx)) Om))) 1))))
340.0ms
(sqrt (sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (* 1 (/ (* l (sin kx)) Om)) (/ (* l (sin kx)) Om))) 1)))
297.0ms
(fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (* 1 (/ (* l (sin kx)) Om)) (/ (* l (sin kx)) Om))) 1)

prune4.7s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize62.0ms

Local error

Found 4 expressions with local error:

3.5b
(/ (* l (sin kx)) Om)
3.5b
(/ (* l (sin kx)) Om)
2.8b
(/ (* (sin ky) l) Om)
2.8b
(/ (* (sin ky) l) Om)

rewrite134.0ms

Algorithm
rewrite-expression-head
Rules
144×times-frac
136×add-sqr-sqrt
104×*-un-lft-identity add-cube-cbrt
48×associate-*r* associate-*l* associate-/l*
24×add-cbrt-cube add-exp-log
16×*-commutative unswap-sqr
12×associate-/r*
8×cbrt-undiv div-exp
4×expm1-log1p-u pow1 clear-num frac-2neg prod-exp cbrt-unprod insert-posit16 log1p-expm1-u div-inv add-log-exp
Calls
4 calls:
Slowest
39.0ms
(/ (* (sin ky) l) Om)
37.0ms
(/ (* (sin ky) l) Om)
32.0ms
(/ (* l (sin kx)) Om)
19.0ms
(/ (* l (sin kx)) Om)

series370.0ms

Calls
4 calls:
Slowest
101.0ms
(/ (* (sin ky) l) Om)
95.0ms
(/ (* l (sin kx)) Om)
94.0ms
(/ (* (sin ky) l) Om)
80.0ms
(/ (* l (sin kx)) Om)

simplify10.9s

Calls
360 calls:
Slowest
668.0ms
(- (/ (* kx l) Om) (* 1/6 (/ (* (pow kx 3) l) Om)))
239.0ms
(- (/ (* ky l) Om) (* 1/6 (/ (* (pow ky 3) l) Om)))
236.0ms
(/ (* (* (* l (sin kx)) (* l (sin kx))) (* l (sin kx))) (* (* Om Om) Om))
227.0ms
(/ (* (* (* l (sin kx)) (* l (sin kx))) (* l (sin kx))) (* (* Om Om) Om))
214.0ms
(- (/ (* kx l) Om) (* 1/6 (/ (* (pow kx 3) l) Om)))

prune5.8s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.4b

regimes372.0ms

Accuracy

0% (0.0b remaining)

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

bsearch10.0ms

end0.0ms

sample3.9s

Algorithm
intervals
Results
3.7s8000×body80valid