Details

Time bar (total: 46.9s)

sample142.0ms

Algorithm
intervals
Results
113.0ms256×body80valid

simplify301.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
300.0ms
(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.5b

localize139.0ms

Local error

Found 4 expressions with local error:

10.5b
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
2.4b
(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
(* (sin kx) (sin kx))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
24×*-un-lft-identity add-cube-cbrt
18×times-frac
15×sqrt-prod
12×pow1
8×add-cbrt-cube add-exp-log
6×associate-/r*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×swap-sqr associate-*r* associate-*l* associate-/l*
1×pow2 cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow-plus pow1/2 div-exp pow-prod-down prod-exp pow-sqr *-commutative pow-prod-up cbrt-unprod fma-udef sqr-sin div-inv sin-mult unswap-sqr
Counts
4 → 99
Calls
4 calls:
Slowest
24.0ms
(* (sin kx) (sin kx))
9.0ms
(/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
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)

series893.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
404.0ms
(/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
316.0ms
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
150.0ms
(fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
22.0ms
(* (sin kx) (sin kx))

simplify17.5s

Counts
86 → 111
Calls
86 calls:
Slowest
757.0ms
(/ 1 (* (cbrt (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))) (cbrt (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))))
479.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
478.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
446.0ms
(/ (sqrt 1/2) (sqrt (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))))
441.0ms
(/ (sqrt 1/2) (cbrt (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))))

prune2.2s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize62.0ms

Local error

Found 4 expressions with local error:

10.5b
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
2.7b
(/ (* (sin ky) l) Om)
2.7b
(/ (* (sin ky) l) Om)
2.0b
(/ (* l (sin kx)) Om)

rewrite47.0ms

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
21.0ms
(/ (* l (sin kx)) Om)
12.0ms
(/ (* (sin ky) l) Om)
11.0ms
(/ (* (sin ky) l) Om)
1.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))

series561.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
329.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
82.0ms
(/ (* (sin ky) l) Om)
76.0ms
(/ (* l (sin kx)) Om)
73.0ms
(/ (* (sin ky) l) Om)

simplify4.4s

Counts
55 → 100
Calls
55 calls:
Slowest
479.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
410.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
339.0ms
(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))))
318.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
280.0ms
(sqrt (sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1)))

prune2.0s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize128.0ms

Local error

Found 4 expressions with local error:

47.8b
(posit16->real (real->posit16 (/ (* (sin ky) l) Om)))
10.5b
(sqrt (fma 4 (+ (* (posit16->real (real->posit16 (/ (* (sin ky) l) Om))) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
2.7b
(/ (* (sin ky) l) Om)
2.7b
(/ (* (sin ky) l) Om)

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
14×add-cbrt-cube add-exp-log
10×add-sqr-sqrt
9×*-un-lft-identity add-cube-cbrt
6×associate-/r* times-frac
5×pow1
4×expm1-log1p-u cbrt-undiv div-exp insert-posit16 log1p-expm1-u add-log-exp
3×sqrt-prod
2×clear-num frac-2neg prod-exp cbrt-unprod div-inv associate-/l*
1×rem-sqrt-square sqrt-pow1 pow1/2 remove-posit16
Counts
4 → 75
Calls
4 calls:
Slowest
18.0ms
(/ (* (sin ky) l) Om)
11.0ms
(/ (* (sin ky) l) Om)
1.0ms
(sqrt (fma 4 (+ (* (posit16->real (real->posit16 (/ (* (sin ky) l) Om))) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
0.0ms
(posit16->real (real->posit16 (/ (* (sin ky) l) Om)))

series606.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
358.0ms
(sqrt (fma 4 (+ (* (posit16->real (real->posit16 (/ (* (sin ky) l) Om))) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
102.0ms
(posit16->real (real->posit16 (/ (* (sin ky) l) Om)))
75.0ms
(/ (* (sin ky) l) Om)
71.0ms
(/ (* (sin ky) l) Om)

simplify3.7s

Counts
44 → 87
Calls
44 calls:
Slowest
454.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
377.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
301.0ms
(sqrt (fma 4 (+ (* (posit16->real (real->posit16 (/ (* (sin ky) l) Om))) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
273.0ms
(sqrt (* (cbrt (fma 4 (+ (* (posit16->real (real->posit16 (/ (* (sin ky) l) Om))) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1)) (cbrt (fma 4 (+ (* (posit16->real (real->posit16 (/ (* (sin ky) l) Om))) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))))
267.0ms
(- (/ (* ky l) Om) (* 1/6 (/ (* (pow ky 3) l) Om)))

prune2.7s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize84.0ms

Local error

Found 4 expressions with local error:

47.8b
(posit16->real (real->posit16 (/ (* (sin ky) l) Om)))
47.8b
(posit16->real (real->posit16 (/ (* (sin ky) l) Om)))
10.5b
(sqrt (fma 4 (+ (* (posit16->real (real->posit16 (/ (* (sin ky) l) Om))) (posit16->real (real->posit16 (/ (* (sin ky) l) Om)))) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
2.7b
(/ (* (sin ky) l) Om)

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
9×add-cbrt-cube add-exp-log
8×add-sqr-sqrt
7×*-un-lft-identity add-cube-cbrt
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* times-frac sqrt-prod
2×cbrt-undiv div-exp remove-posit16
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 prod-exp cbrt-unprod div-inv associate-/l*
Counts
4 → 62
Calls
4 calls:
Slowest
17.0ms
(/ (* (sin ky) l) Om)
1.0ms
(sqrt (fma 4 (+ (* (posit16->real (real->posit16 (/ (* (sin ky) l) Om))) (posit16->real (real->posit16 (/ (* (sin ky) l) Om)))) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
0.0ms
(posit16->real (real->posit16 (/ (* (sin ky) l) Om)))
0.0ms
(posit16->real (real->posit16 (/ (* (sin ky) l) Om)))

series613.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
353.0ms
(sqrt (fma 4 (+ (* (posit16->real (real->posit16 (/ (* (sin ky) l) Om))) (posit16->real (real->posit16 (/ (* (sin ky) l) Om)))) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
98.0ms
(/ (* (sin ky) l) Om)
85.0ms
(posit16->real (real->posit16 (/ (* (sin ky) l) Om)))
76.0ms
(posit16->real (real->posit16 (/ (* (sin ky) l) Om)))

simplify3.8s

Counts
32 → 74
Calls
32 calls:
Slowest
898.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
471.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
282.0ms
(sqrt (fma 4 (+ (* (posit16->real (real->posit16 (/ (* (sin ky) l) Om))) (posit16->real (real->posit16 (/ (* (sin ky) l) Om)))) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
255.0ms
(sqrt (sqrt (fma 4 (+ (* (posit16->real (real->posit16 (/ (* (sin ky) l) Om))) (posit16->real (real->posit16 (/ (* (sin ky) l) Om)))) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1)))
250.0ms
(fma 4 (+ (* (posit16->real (real->posit16 (/ (* (sin ky) l) Om))) (posit16->real (real->posit16 (/ (* (sin ky) l) Om)))) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1)

prune2.7s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.2b

regimes365.0ms

Accuracy

0% (0.0b remaining)

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

bsearch5.0ms

end0.0ms

sample3.9s

Algorithm
intervals
Results
3.7s8000×body80valid