Details

Time bar (total: 1.1m)

sample91.0ms

Algorithm
intervals
Results
64.0ms256×body80valid

simplify293.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
292.0ms
(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))

prune30.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.8b

localize61.0ms

Local error

Found 4 expressions with local error:

7.1b
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
2.8b
(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
(* (/ (* l 2) Om) (/ (* l 2) Om))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
42×add-cbrt-cube add-exp-log
31×add-sqr-sqrt
30×times-frac
28×*-un-lft-identity add-cube-cbrt
15×prod-exp sqrt-prod cbrt-unprod
13×cbrt-undiv div-exp
12×pow1
7×swap-sqr associate-*r* associate-*l*
6×associate-/r*
5×div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-/l*
1×pow2 frac-times rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow-plus pow1/2 pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up fma-udef unswap-sqr
Counts
4 → 128
Calls
4 calls:
Slowest
27.0ms
(* (/ (* l 2) Om) (/ (* l 2) Om))
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)

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
431.0ms
(/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
331.0ms
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
208.0ms
(fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
58.0ms
(* (/ (* l 2) Om) (/ (* l 2) Om))

simplify26.9s

Counts
119 → 140
Calls
119 calls:
Slowest
850.0ms
(/ (cbrt 1/2) (sqrt (cbrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))))
752.0ms
(* (/ (* (* (* l 2) (* l 2)) (* l 2)) (* (* Om Om) Om)) (/ (* (* (* l l) l) (* (* 2 2) 2)) (* (* Om Om) Om)))
629.0ms
(* (/ (* (* (* l l) l) (* (* 2 2) 2)) (* (* Om Om) Om)) (/ (* (* (* l 2) (* l 2)) (* l 2)) (* (* Om Om) Om)))
563.0ms
(* (* (* (/ (* l 2) Om) (/ (* l 2) Om)) (/ (* l 2) Om)) (/ (* (* (* l l) l) (* (* 2 2) 2)) (* (* Om Om) Om)))
554.0ms
(* (/ (* l 2) Om) (/ (* l 2) Om))

prune2.8s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize80.0ms

Local error

Found 4 expressions with local error:

7.1b
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
7.1b
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
7.1b
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
5.7b
(cbrt (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
9×*-un-lft-identity add-cube-cbrt
7×pow1
6×cbrt-prod
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×pow1/3
Counts
4 → 65
Calls
4 calls:
Slowest
1.0ms
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
1.0ms
(cbrt (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))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
410.0ms
(cbrt (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
328.0ms
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
304.0ms
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
303.0ms
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))

simplify8.0s

Counts
33 → 77
Calls
33 calls:
Slowest
439.0ms
(exp (* 1/6 (- (+ (* 2 (log (/ 1 Om))) (log (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2))))) (* 2 (log (/ 1 l))))))
436.0ms
(sqrt (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
434.0ms
(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))))
414.0ms
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
407.0ms
(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))))

prune1.7s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.5b

localize65.0ms

Local error

Found 4 expressions with local error:

2.8b
(fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
0.5b
(log (exp (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
0.3b
(* (/ (* l 2) Om) (/ (* l 2) Om))
0.2b
(fma (sin ky) (sin ky) (* (sin kx) (sin kx)))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
40×add-cbrt-cube add-exp-log
16×add-sqr-sqrt
15×prod-exp cbrt-unprod
14×*-un-lft-identity add-cube-cbrt
12×pow1 cbrt-undiv times-frac div-exp
7×swap-sqr associate-*r* associate-*l*
4×expm1-log1p-u log-prod log-pow insert-posit16 log1p-expm1-u div-inv add-log-exp
3×exp-prod fma-udef
1×pow2 frac-times pow-plus rem-log-exp exp-sum pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up unswap-sqr
Counts
4 → 100
Calls
4 calls:
Slowest
43.0ms
(* (/ (* l 2) Om) (/ (* l 2) Om))
5.0ms
(log (exp (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
1.0ms
(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)))

series519.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
195.0ms
(fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
179.0ms
(log (exp (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
97.0ms
(fma (sin ky) (sin ky) (* (sin kx) (sin kx)))
47.0ms
(* (/ (* l 2) Om) (/ (* l 2) Om))

simplify13.0s

Counts
76 → 112
Calls
76 calls:
Slowest
673.0ms
(* (/ (* (* (* l 2) (* l 2)) (* l 2)) (* (* Om Om) Om)) (/ (* (* (* l l) l) (* (* 2 2) 2)) (* (* Om Om) Om)))
663.0ms
(log (exp (* (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))))))
596.0ms
(* (/ (* (* (* l l) l) (* (* 2 2) 2)) (* (* Om Om) Om)) (/ (* (* (* l 2) (* l 2)) (* l 2)) (* (* Om Om) Om)))
523.0ms
(* (* (* (/ (* l 2) Om) (/ (* l 2) Om)) (/ (* l 2) Om)) (/ (* (* (* l l) l) (* (* 2 2) 2)) (* (* Om Om) Om)))
513.0ms
(* (/ (* (* (* l 2) (* l 2)) (* l 2)) (* (* Om Om) Om)) (* (* (/ (* l 2) Om) (/ (* l 2) Om)) (/ (* l 2) Om)))

prune2.2s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize77.0ms

Local error

Found 4 expressions with local error:

2.1b
(/ (* (sin ky) l) Om)
2.1b
(/ (* (sin ky) l) Om)
1.5b
(/ (* l (sin kx)) Om)
1.5b
(/ (* l (sin kx)) Om)

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
24×add-cbrt-cube add-exp-log
12×add-sqr-sqrt associate-/r* *-un-lft-identity times-frac add-cube-cbrt
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 associate-/l* add-log-exp
Counts
4 → 96
Calls
4 calls:
Slowest
27.0ms
(/ (* l (sin kx)) Om)
21.0ms
(/ (* l (sin kx)) Om)
11.0ms
(/ (* (sin ky) l) Om)
11.0ms
(/ (* (sin ky) l) Om)

series303.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
81.0ms
(/ (* l (sin kx)) Om)
75.0ms
(/ (* (sin ky) l) Om)
74.0ms
(/ (* (sin ky) l) Om)
73.0ms
(/ (* l (sin kx)) Om)

simplify3.1s

Counts
62 → 108
Calls
62 calls:
Slowest
261.0ms
(- (/ (* kx l) Om) (* 1/6 (/ (* (pow kx 3) l) Om)))
248.0ms
(- (/ (* kx l) Om) (* 1/6 (/ (* (pow kx 3) l) Om)))
247.0ms
(- (/ (* ky l) Om) (* 1/6 (/ (* (pow ky 3) l) Om)))
208.0ms
(- (/ (* ky l) Om) (* 1/6 (/ (* (pow ky 3) l) Om)))
205.0ms
(/ (* (* (* (sin ky) l) (* (sin ky) l)) (* (sin ky) l)) (* (* Om Om) Om))

prune2.4s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.5b

regimes619.0ms

Accuracy

0% (0.1b remaining)

Error of 0.9b against oracle of 0.7b and baseline of 0.9b

bsearch6.0ms

end0.0ms

sample3.9s

Algorithm
intervals
Results
3.6s8000×body80valid