Details

Time bar (total: 55.6s)

sample141.0ms

Algorithm
intervals
Results
115.0ms256×body80valid

simplify259.0ms

Calls
1 calls:
Slowest
258.0ms
(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.6b

localize47.0ms

Local error

Found 4 expressions with local error:

9.2b
(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
(* (/ (* l 2) Om) (/ (* l 2) Om))
0.2b
(* (sin kx) (sin kx))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
42×add-cbrt-cube add-exp-log
22×add-sqr-sqrt
19×pow1
17×*-un-lft-identity add-cube-cbrt
16×prod-exp cbrt-unprod
12×cbrt-undiv times-frac div-exp
10×swap-sqr associate-*r* associate-*l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u div-inv add-log-exp
3×sqrt-prod
2×pow2 pow-plus pow-prod-down pow-sqr *-commutative pow-prod-up unswap-sqr
1×frac-times rem-sqrt-square sqrt-pow1 pow1/2 associate-*l/ associate-*r/ fma-udef sqr-sin sin-mult
Calls
4 calls:
Slowest
22.0ms
(* (sin kx) (sin kx))
22.0ms
(* (/ (* l 2) Om) (/ (* l 2) Om))
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)

series601.0ms

Calls
4 calls:
Slowest
318.0ms
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
206.0ms
(fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
42.0ms
(* (/ (* l 2) Om) (/ (* l 2) Om))
34.0ms
(* (sin kx) (sin kx))

simplify13.1s

Calls
96 calls:
Slowest
1.0s
(* (/ (* (* (* l l) l) (* (* 2 2) 2)) (* (* Om Om) Om)) (/ (* (* (* l 2) (* l 2)) (* l 2)) (* (* Om Om) Om)))
697.0ms
(* (/ (* (* (* l 2) (* l 2)) (* l 2)) (* (* Om Om) Om)) (/ (* (* (* l l) l) (* (* 2 2) 2)) (* (* Om Om) Om)))
565.0ms
(* (/ (* (* (* l l) l) (* (* 2 2) 2)) (* (* Om Om) Om)) (* (* (/ (* l 2) Om) (/ (* l 2) Om)) (/ (* l 2) Om)))
525.0ms
(* (* (* (/ (* l 2) Om) (/ (* l 2) Om)) (/ (* l 2) Om)) (/ (* (* (* l l) l) (* (* 2 2) 2)) (* (* Om Om) Om)))
523.0ms
(* (/ (* (* (* l 2) (* l 2)) (* l 2)) (* (* Om Om) Om)) (* (* (/ (* l 2) Om) (/ (* l 2) Om)) (/ (* l 2) Om)))

prune2.5s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize91.0ms

Local error

Found 4 expressions with local error:

9.2b
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
3.4b
(/ (* (sin ky) l) Om)
3.4b
(/ (* (sin ky) l) Om)
2.3b
(/ (* l (sin kx)) Om)

rewrite48.0ms

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
Calls
4 calls:
Slowest
22.0ms
(/ (* (sin ky) l) Om)
11.0ms
(/ (* (sin ky) l) Om)
11.0ms
(/ (* 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))

series596.0ms

Calls
4 calls:
Slowest
369.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
101.0ms
(/ (* l (sin kx)) Om)
71.0ms
(/ (* (sin ky) l) Om)
55.0ms
(/ (* (sin ky) l) Om)

simplify4.4s

Calls
55 calls:
Slowest
513.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
418.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
375.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
325.0ms
(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))))
314.0ms
(- (/ (* ky l) Om) (* 1/6 (/ (* (pow ky 3) l) Om)))

prune1.8s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize69.0ms

Local error

Found 4 expressions with local error:

9.2b
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
9.2b
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
7.4b
(sqrt (sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1)))
7.4b
(sqrt (sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
26×sqrt-prod
16×add-sqr-sqrt
10×pow1 *-un-lft-identity sqrt-pow1 add-cube-cbrt
6×rem-sqrt-square pow1/2
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
Calls
4 calls:
Slowest
3.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
3.0ms
(sqrt (sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1)))
2.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
2.0ms
(sqrt (sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1)))

series1.4s

Calls
4 calls:
Slowest
364.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
358.0ms
(sqrt (sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1)))
332.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
320.0ms
(sqrt (sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1)))

simplify11.6s

Calls
44 calls:
Slowest
710.0ms
(sqrt (sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1)))
445.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
437.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
436.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
405.0ms
(sqrt (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)))))

prune1.7s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize131.0ms

Local error

Found 4 expressions with local error:

27.1b
(posit16->real (real->posit16 (sqrt (sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1)))))
9.2b
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
9.2b
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
7.4b
(sqrt (sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
16×sqrt-prod
12×add-sqr-sqrt
8×pow1 *-un-lft-identity add-cube-cbrt
6×sqrt-pow1
4×expm1-log1p-u rem-sqrt-square add-cbrt-cube pow1/2 add-exp-log insert-posit16 log1p-expm1-u add-log-exp
1×remove-posit16
Calls
4 calls:
Slowest
4.0ms
(sqrt (sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1)))
2.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
2.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
1.0ms
(posit16->real (real->posit16 (sqrt (sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1)))))

series1.4s

Calls
4 calls:
Slowest
389.0ms
(posit16->real (real->posit16 (sqrt (sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1)))))
381.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
339.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
338.0ms
(sqrt (sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1)))

simplify8.7s

Calls
34 calls:
Slowest
477.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
459.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
428.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
426.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
420.0ms
(exp (* 1/4 (- (+ (* 2 (log (/ 1 Om))) (log (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2))))) (* 2 (log (/ 1 l))))))

prune2.6s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.1b

regimes477.0ms

Accuracy

0% (0.0b remaining)

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

bsearch6.0ms

end0.0ms

sample3.9s

Algorithm
intervals
Results
3.7s8000×body80valid