Details

Time bar (total: 1.2m)

sample113.0ms

Algorithm
intervals
Results
92.0ms256×body80valid

simplify245.0ms

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)))))))))

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize38.0ms

Local error

Found 4 expressions with local error:

10.0b
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
1.2b
(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)))
0.3b
(* (sin kx) (sin kx))

rewrite30.0ms

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
11.0ms
(* (sin kx) (sin kx))
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)

series859.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
342.0ms
(/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
327.0ms
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
160.0ms
(fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
29.0ms
(* (sin kx) (sin kx))

simplify17.5s

Counts
86 → 111
Calls
86 calls:
Slowest
732.0ms
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
440.0ms
(/ (sqrt 1/2) (cbrt (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))))
429.0ms
(/ (* (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))))
428.0ms
(/ (cbrt 1/2) (sqrt (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))))
419.0ms
(/ (* (cbrt 1/2) (cbrt 1/2)) (* (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)))))

prune1.9s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize44.0ms

Local error

Found 4 expressions with local error:

10.0b
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
1.6b
(/ (* l (sin kx)) Om)
1.6b
(/ (* l (sin kx)) Om)
1.1b
(/ (* (sin ky) l) Om)

rewrite42.0ms

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
11.0ms
(/ (* l (sin kx)) Om)
11.0ms
(/ (* l (sin kx)) Om)
11.0ms
(/ (* (sin ky) l) Om)
8.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))

series577.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
335.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
97.0ms
(/ (* (sin ky) l) Om)
76.0ms
(/ (* l (sin kx)) Om)
69.0ms
(/ (* l (sin kx)) Om)

simplify4.2s

Counts
54 → 100
Calls
54 calls:
Slowest
395.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
393.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
328.0ms
(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))))
295.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
288.0ms
(sqrt (sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1)))

prune1.8s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.1b

localize57.0ms

Local error

Found 4 expressions with local error:

10.0b
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
3.3b
(log (exp (/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))))
1.2b
(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)))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
35×add-sqr-sqrt
34×*-un-lft-identity add-cube-cbrt
24×sqrt-prod
23×log-pow
22×exp-prod
6×pow1 associate-/r* add-cbrt-cube add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×log-prod associate-/l*
2×div-inv
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-exp rem-log-exp fma-udef
Counts
4 → 106
Calls
4 calls:
Slowest
12.0ms
(log (exp (/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))))
5.0ms
(/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
2.0ms
(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)

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
384.0ms
(/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
376.0ms
(log (exp (/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))))
300.0ms
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
167.0ms
(fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)

simplify25.9s

Counts
88 → 118
Calls
88 calls:
Slowest
739.0ms
(/ (* (cbrt 1/2) (cbrt 1/2)) (* (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)))))
458.0ms
(sqrt (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
449.0ms
(/ (cbrt 1/2) (sqrt (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))))
448.0ms
(/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
438.0ms
(/ (cbrt 1/2) (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))

prune2.3s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.1b

localize117.0ms

Local error

Found 4 expressions with local error:

10.0b
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
10.0b
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
10.0b
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
4.4b
(log (cbrt (exp (/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))))))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
9×*-un-lft-identity add-cube-cbrt sqrt-prod
8×pow1
6×log-prod
5×add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-prod rem-sqrt-square sqrt-pow1 pow1/2
2×log-pow
1×pow1/3 rem-log-exp
Counts
4 → 67
Calls
4 calls:
Slowest
4.0ms
(log (cbrt (exp (/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))))))
2.0ms
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
1.0ms
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
1.0ms
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
340.0ms
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
327.0ms
(log (cbrt (exp (/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))))))
302.0ms
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
283.0ms
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))

simplify9.1s

Counts
34 → 79
Calls
34 calls:
Slowest
844.0ms
(log (cbrt (* (cbrt (exp (/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))))) (cbrt (exp (/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))))))))
472.0ms
(log (cbrt (sqrt (exp (/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))))))
452.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
442.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
438.0ms
(log (sqrt (cbrt (exp (/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))))))

prune1.9s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.1b

regimes544.0ms

Accuracy

0% (0.0b remaining)

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

bsearch6.0ms

end0.0ms

sample3.7s

Algorithm
intervals
Results
3.4s7999×body80valid
0.0ms1×body160valid