Details

Time bar (total: 46.9s)

sample167.0ms

Algorithm
intervals
Results
99.0ms256×body80valid

simplify246.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
245.0ms
(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))

prune36.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.6b

localize39.0ms

Local error

Found 4 expressions with local error:

8.5b
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
1.9b
(fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
0.2b
(* (/ (* l 2) Om) (/ (* l 2) Om))
0.2b
(* (sin kx) (sin kx))

rewrite65.0ms

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
Counts
4 → 116
Calls
4 calls:
Slowest
33.0ms
(* (/ (* l 2) Om) (/ (* l 2) Om))
24.0ms
(* (sin kx) (sin kx))
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)

series570.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
318.0ms
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
196.0ms
(fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
37.0ms
(* (/ (* l 2) Om) (/ (* l 2) Om))
19.0ms
(* (sin kx) (sin kx))

simplify12.3s

Counts
96 → 128
Calls
96 calls:
Slowest
643.0ms
(* (/ (* (* (* l 2) (* l 2)) (* l 2)) (* (* Om Om) Om)) (/ (* (* (* l l) l) (* (* 2 2) 2)) (* (* Om Om) Om)))
562.0ms
(* (/ (* (* (* l l) l) (* (* 2 2) 2)) (* (* Om Om) Om)) (/ (* (* (* l 2) (* l 2)) (* l 2)) (* (* Om Om) Om)))
549.0ms
(* (* (* (/ (* l 2) Om) (/ (* l 2) Om)) (/ (* l 2) Om)) (/ (* (* (* l l) l) (* (* 2 2) 2)) (* (* Om Om) Om)))
520.0ms
(* (/ (* (* (* l 2) (* l 2)) (* l 2)) (* (* Om Om) Om)) (/ (* (* (* l 2) (* l 2)) (* l 2)) (* (* Om Om) Om)))
500.0ms
(+ (- (log (* l 2)) (log Om)) (log (/ (* l 2) Om)))

prune2.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.7b

localize50.0ms

Local error

Found 4 expressions with local error:

8.5b
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
3.8b
(/ (* l (sin kx)) Om)
3.8b
(/ (* l (sin kx)) Om)
2.5b
(/ (* (sin ky) l) Om)

rewrite69.0ms

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
22.0ms
(/ (* l (sin kx)) Om)
22.0ms
(/ (* l (sin kx)) Om)
21.0ms
(/ (* (sin ky) l) Om)
3.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))

series499.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
269.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
94.0ms
(/ (* l (sin kx)) Om)
76.0ms
(/ (* l (sin kx)) Om)
59.0ms
(/ (* (sin ky) l) Om)

simplify4.5s

Counts
54 → 100
Calls
54 calls:
Slowest
466.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
455.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
298.0ms
(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))))
261.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
258.0ms
(- (/ (* ky l) Om) (* 1/6 (/ (* (pow ky 3) l) Om)))

prune2.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.7b

localize74.0ms

Local error

Found 4 expressions with local error:

12.5b
(cbrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
12.5b
(cbrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
12.5b
(cbrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
7.1b
(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))))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
12×pow1
9×cbrt-prod sqrt-pow1 pow1/3
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 rem-sqrt-square pow-plus pow1/2 sqrt-prod
Counts
4 → 64
Calls
4 calls:
Slowest
7.0ms
(cbrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
5.0ms
(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))))
1.0ms
(cbrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
1.0ms
(cbrt (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
386.0ms
(cbrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
332.0ms
(cbrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
324.0ms
(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))))
320.0ms
(cbrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))

simplify8.2s

Counts
32 → 76
Calls
32 calls:
Slowest
419.0ms
(exp (* 1/3 (- (+ (log (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (* 2 (log (/ -1 Om)))) (* 2 (log (/ -1 l))))))
406.0ms
(exp (* 1/3 (- (+ (log (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (* 2 (log (/ -1 Om)))) (* 2 (log (/ -1 l))))))
380.0ms
(exp (* 1/3 (- (+ (log (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (* 2 (log (/ -1 Om)))) (* 2 (log (/ -1 l))))))
376.0ms
(exp (* 1/3 (- (+ (log (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (* 2 (log (/ -1 Om)))) (* 2 (log (/ -1 l))))))
369.0ms
(* (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1) (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))

prune1.7s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.7b

localize147.0ms

Local error

Found 4 expressions with local error:

25.6b
(posit16->real (real->posit16 (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))))))
12.5b
(cbrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
12.5b
(cbrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
12.5b
(cbrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3
1×remove-posit16
Counts
4 → 53
Calls
4 calls:
Slowest
2.0ms
(cbrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
1.0ms
(cbrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
1.0ms
(cbrt (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 (* (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))))))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
330.0ms
(cbrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
324.0ms
(cbrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
306.0ms
(posit16->real (real->posit16 (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))))))
284.0ms
(cbrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))

simplify5.2s

Counts
22 → 65
Calls
22 calls:
Slowest
493.0ms
(exp (* 1/3 (- (+ (log (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (* 2 (log (/ -1 Om)))) (* 2 (log (/ -1 l))))))
410.0ms
(exp (* 1/3 (- (+ (log (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (* 2 (log (/ -1 Om)))) (* 2 (log (/ -1 l))))))
397.0ms
(exp (* 1/3 (- (+ (log (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (* 2 (log (/ -1 Om)))) (* 2 (log (/ -1 l))))))
394.0ms
(exp (* 1/3 (- (+ (log (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (* 2 (log (/ -1 Om)))) (* 2 (log (/ -1 l))))))
353.0ms
(cbrt (sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1)))

prune2.2s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.7b

regimes608.0ms

Accuracy

0% (0.0b remaining)

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

bsearch16.0ms

end0.0ms

sample3.4s

Algorithm
intervals
Results
3.1s8000×body80valid