Details

Time bar (total: 1.1m)

sample106.0ms

Algorithm
intervals
Results
87.0ms256×body80valid

simplify214.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
213.0ms
(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: 1.6b

localize47.0ms

Local error

Found 4 expressions with local error:

10.4b
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
2.1b
(fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
0.4b
(/ 1/2 (sqrt (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))

rewrite32.0ms

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
22.0ms
(* (/ (* 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
481.0ms
(/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
340.0ms
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
187.0ms
(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))

simplify25.7s

Counts
119 → 140
Calls
119 calls:
Slowest
801.0ms
(/ (cbrt 1/2) (sqrt (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))))
645.0ms
(* (/ (* (* (* l 2) (* l 2)) (* l 2)) (* (* Om Om) Om)) (/ (* (* (* l l) l) (* (* 2 2) 2)) (* (* Om Om) Om)))
570.0ms
(* (/ (* (* (* l l) l) (* (* 2 2) 2)) (* (* Om Om) Om)) (/ (* (* (* l 2) (* l 2)) (* l 2)) (* (* Om Om) Om)))
545.0ms
(* (* (* (/ (* l 2) Om) (/ (* l 2) Om)) (/ (* l 2) Om)) (/ (* (* (* l l) l) (* (* 2 2) 2)) (* (* Om Om) Om)))
512.0ms
(* (/ (* (* (* l l) l) (* (* 2 2) 2)) (* (* Om Om) Om)) (* (* (/ (* l 2) Om) (/ (* l 2) Om)) (/ (* l 2) Om)))

prune2.4s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.4b

localize61.0ms

Local error

Found 4 expressions with local error:

10.4b
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
2.4b
(/ (* l (sin kx)) Om)
2.4b
(/ (* l (sin kx)) Om)
2.0b
(/ (* (sin ky) l) Om)

rewrite52.0ms

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
19.0ms
(/ (* l (sin kx)) Om)
17.0ms
(/ (* (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))

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
772.0ms
(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)
82.0ms
(/ (* l (sin kx)) Om)
56.0ms
(/ (* (sin ky) l) Om)

simplify4.2s

Counts
54 → 100
Calls
54 calls:
Slowest
406.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
387.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
314.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
300.0ms
(sqrt (sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1)))
277.0ms
(fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1)

prune1.7s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize131.0ms

Local error

Found 4 expressions with local error:

10.4b
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
10.4b
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
10.4b
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
6.7b
(cbrt (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
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
2.0ms
(cbrt (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))
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
380.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
363.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
351.0ms
(cbrt (sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1)))
351.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))

simplify7.8s

Counts
33 → 77
Calls
33 calls:
Slowest
435.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
415.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
397.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
395.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
386.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))

prune1.7s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize152.0ms

Local error

Found 4 expressions with local error:

10.4b
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
10.4b
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
10.4b
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
10.4b
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u rem-sqrt-square sqrt-pow1 add-cbrt-cube pow1/2 add-exp-log insert-posit16 log1p-expm1-u add-log-exp
Counts
4 → 64
Calls
4 calls:
Slowest
1.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
1.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
1.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
1.0ms
(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
368.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
354.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
324.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
317.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))

simplify8.6s

Counts
32 → 76
Calls
32 calls:
Slowest
674.0ms
(fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1)
503.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
483.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
467.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
414.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))

prune2.0s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

regimes445.0ms

Accuracy

0% (0.0b remaining)

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

bsearch17.0ms

end0.0ms

sample3.8s

Algorithm
intervals
Results
3.5s8000×body80valid