Details

Time bar (total: 1.1m)

sample136.0ms

Algorithm
intervals
Results
101.0ms256×body80valid

simplify284.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
283.0ms
(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: 1.3b

localize52.0ms

Local error

Found 4 expressions with local error:

7.5b
(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
(/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
0.2b
(fma (sin ky) (sin ky) (* (sin kx) (sin kx)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
20×*-un-lft-identity add-cube-cbrt
18×times-frac
15×sqrt-prod
6×associate-/r* add-cbrt-cube add-exp-log
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-/l*
2×fma-udef
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-exp div-inv
Counts
4 → 80
Calls
4 calls:
Slowest
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 (sin ky) (sin ky) (* (sin kx) (sin kx)))
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
416.0ms
(/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
321.0ms
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
176.0ms
(fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
98.0ms
(fma (sin ky) (sin ky) (* (sin kx) (sin kx)))

simplify17.3s

Counts
63 → 92
Calls
63 calls:
Slowest
830.0ms
(/ (cbrt 1/2) (sqrt (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))))
429.0ms
(/ (sqrt 1/2) (sqrt (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))))
423.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
423.0ms
(/ (* (cbrt 1/2) (cbrt 1/2)) (sqrt (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))))
419.0ms
(/ (sqrt 1/2) (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))

prune1.7s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize76.0ms

Local error

Found 4 expressions with local error:

7.5b
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
3.1b
(/ (* (sin ky) l) Om)
3.1b
(/ (* (sin ky) l) Om)
3.0b
(/ (* l (sin kx)) Om)

rewrite41.0ms

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
Counts
4 → 88
Calls
4 calls:
Slowest
18.0ms
(/ (* (sin ky) l) Om)
11.0ms
(/ (* (sin ky) l) Om)
11.0ms
(/ (* l (sin kx)) Om)
1.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))

series616.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
382.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
86.0ms
(/ (* l (sin kx)) Om)
78.0ms
(/ (* (sin ky) l) Om)
71.0ms
(/ (* (sin ky) l) Om)

simplify4.6s

Counts
55 → 100
Calls
55 calls:
Slowest
450.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
412.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
372.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
339.0ms
(fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1)
335.0ms
(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))))

prune1.9s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize86.0ms

Local error

Found 4 expressions with local error:

7.5b
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
7.5b
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
5.5b
(sqrt (sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1)))
5.5b
(sqrt (sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1)))

rewrite23.0ms

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
Counts
4 → 76
Calls
4 calls:
Slowest
13.0ms
(sqrt (sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1)))
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))

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
383.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
369.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
339.0ms
(sqrt (sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1)))
335.0ms
(sqrt (sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1)))

simplify11.5s

Counts
44 → 88
Calls
44 calls:
Slowest
720.0ms
(fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1)
480.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
420.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
417.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
415.0ms
(exp (* 1/4 (- (+ (log (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (* 2 (log (/ -1 Om)))) (* 2 (log (/ -1 l))))))

prune2.0s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize101.0ms

Local error

Found 4 expressions with local error:

40.0b
(posit16->real (real->posit16 (fma (sin ky) (sin ky) (* (sin kx) (sin kx)))))
7.5b
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (posit16->real (real->posit16 (fma (sin ky) (sin ky) (* (sin kx) (sin kx))))) 1))
1.7b
(fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (posit16->real (real->posit16 (fma (sin ky) (sin ky) (* (sin kx) (sin kx))))) 1)
0.3b
(/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (posit16->real (real->posit16 (fma (sin ky) (sin ky) (* (sin kx) (sin kx))))) 1)))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
20×*-un-lft-identity add-cube-cbrt
18×times-frac
15×sqrt-prod
6×associate-/r* add-cbrt-cube add-exp-log
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-/l*
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-exp fma-udef div-inv remove-posit16
Counts
4 → 80
Calls
4 calls:
Slowest
4.0ms
(/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (posit16->real (real->posit16 (fma (sin ky) (sin ky) (* (sin kx) (sin kx))))) 1)))
2.0ms
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (posit16->real (real->posit16 (fma (sin ky) (sin ky) (* (sin kx) (sin kx))))) 1))
1.0ms
(posit16->real (real->posit16 (fma (sin ky) (sin ky) (* (sin kx) (sin kx)))))
0.0ms
(fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (posit16->real (real->posit16 (fma (sin ky) (sin ky) (* (sin kx) (sin kx))))) 1)

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
433.0ms
(/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (posit16->real (real->posit16 (fma (sin ky) (sin ky) (* (sin kx) (sin kx))))) 1)))
333.0ms
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (posit16->real (real->posit16 (fma (sin ky) (sin ky) (* (sin kx) (sin kx))))) 1))
203.0ms
(fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (posit16->real (real->posit16 (fma (sin ky) (sin ky) (* (sin kx) (sin kx))))) 1)
102.0ms
(posit16->real (real->posit16 (fma (sin ky) (sin ky) (* (sin kx) (sin kx)))))

simplify16.8s

Counts
64 → 92
Calls
64 calls:
Slowest
744.0ms
(cbrt (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (posit16->real (real->posit16 (fma (sin ky) (sin ky) (* (sin kx) (sin kx))))) 1)))
432.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
421.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
405.0ms
(/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (posit16->real (real->posit16 (fma (sin ky) (sin ky) (* (sin kx) (sin kx))))) 1)))
401.0ms
(/ (* (cbrt 1/2) (cbrt 1/2)) (sqrt (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (posit16->real (real->posit16 (fma (sin ky) (sin ky) (* (sin kx) (sin kx))))) 1))))

prune2.9s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.3b

regimes507.0ms

Accuracy

0% (0.0b remaining)

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

bsearch12.0ms

end0.0ms

sample4.2s

Algorithm
intervals
Results
3.9s8000×body80valid