Details

Time bar (total: 2.7m)

sample156.0ms

Algorithm
intervals
Results
88.0ms256×body80valid

simplify433.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
432.0ms
(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.2b

localize46.0ms

Local error

Found 4 expressions with local error:

9.2b
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
2.2b
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
0.5b
(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1)))
0.3b
(* (sin kx) (sin kx))

rewrite1000.0ms

Algorithm
rewrite-expression-head
Rules
55×add-cbrt-cube add-exp-log
32×prod-exp cbrt-unprod
30×pow1
29×add-sqr-sqrt
25×*-un-lft-identity add-cube-cbrt
23×associate-*r/
18×times-frac
15×sqrt-prod
14×pow-prod-down
13×frac-times
9×sin-mult
7×cbrt-undiv div-exp associate-*l/
6×associate-/r* flip3-+ associate-*l* flip-+
4×sqrt-div associate-*r* frac-add insert-posit16 add-log-exp
3×swap-sqr associate-/l*
2×associate-/r/ *-commutative unswap-sqr
1×pow2 rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow-plus pow1/2 pow-sqr pow-prod-up sqr-sin div-inv
Counts
4 → 140
Calls
4 calls:
Slowest
498.0ms
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
238.0ms
(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1)))
235.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
22.0ms
(* (sin kx) (sin kx))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
495.0ms
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
392.0ms
(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1)))
269.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
29.0ms
(* (sin kx) (sin kx))

simplify47.2s

Counts
142 → 152
Calls
142 calls:
Slowest
1.4s
(* (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (* (* (* (* l l) l) (/ (* (* 2 2) 2) (* (* Om Om) Om))) (* (* (* l (/ 2 Om)) (* l (/ 2 Om))) (* l (/ 2 Om)))))
1.2s
(* (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (* (* (* (* l l) l) (/ (* (* 2 2) 2) (* (* Om Om) Om))) (* (* (* l l) l) (* (* (/ 2 Om) (/ 2 Om)) (/ 2 Om)))))
1.2s
(* (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (* (* (* (* l l) l) (/ (* (* 2 2) 2) (* (* Om Om) Om))) (* (* (* l l) l) (/ (* (* 2 2) 2) (* (* Om Om) Om)))))
1.2s
(* (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (* (* (* (* l l) l) (* (* (/ 2 Om) (/ 2 Om)) (/ 2 Om))) (* (* (* l l) l) (/ (* (* 2 2) 2) (* (* Om Om) Om)))))
981.0ms
(* (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (* (* (* (* l (/ 2 Om)) (* l (/ 2 Om))) (* l (/ 2 Om))) (* (* (* l l) l) (* (* (/ 2 Om) (/ 2 Om)) (/ 2 Om)))))

prune2.7s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize78.0ms

Local error

Found 4 expressions with local error:

9.2b
(sqrt (+ (* 4 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (* (/ Om l) (/ Om l)))) 1))
2.1b
(/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (* (/ Om l) (/ Om l)))
0.5b
(/ 1/2 (sqrt (+ (* 4 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (* (/ Om l) (/ Om l)))) 1)))
0.3b
(* (sin kx) (sin kx))

rewrite217.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
26×*-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
21×times-frac
15×sqrt-prod
12×pow1
10×cbrt-undiv div-exp
7×associate-/r*
6×associate-/l*
5×prod-exp associate-/r/ cbrt-unprod
4×sqrt-div insert-posit16 add-log-exp
3×flip3-+ swap-sqr associate-*r* associate-*l* flip-+ sqr-sin sin-mult associate-/l/
2×clear-num frac-2neg div-sub div-inv
1×pow2 frac-times rem-sqrt-square associate-+r- sqrt-pow1 pow-plus pow1/2 pow-prod-down associate-*l/ frac-add associate-*r/ pow-sqr *-commutative pow-prod-up associate-+l- unswap-sqr
Counts
4 → 122
Calls
4 calls:
Slowest
73.0ms
(sqrt (+ (* 4 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (* (/ Om l) (/ Om l)))) 1))
66.0ms
(/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (* (/ Om l) (/ Om l)))
65.0ms
(/ 1/2 (sqrt (+ (* 4 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (* (/ Om l) (/ Om l)))) 1)))
11.0ms
(* (sin kx) (sin kx))

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
389.0ms
(sqrt (+ (* 4 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (* (/ Om l) (/ Om l)))) 1))
314.0ms
(/ 1/2 (sqrt (+ (* 4 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (* (/ Om l) (/ Om l)))) 1)))
311.0ms
(/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (* (/ Om l) (/ Om l)))
33.0ms
(* (sin kx) (sin kx))

simplify25.6s

Counts
115 → 134
Calls
115 calls:
Slowest
744.0ms
(cbrt (sqrt (+ (* 4 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (* (/ Om l) (/ Om l)))) 1)))
635.0ms
(/ (* (* (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (* (/ (* (* Om Om) Om) (* (* l l) l)) (/ (* (* Om Om) Om) (* (* l l) l))))
590.0ms
(/ (* (* (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (* (/ (* (* Om Om) Om) (* (* l l) l)) (* (* (/ Om l) (/ Om l)) (/ Om l))))
539.0ms
(/ (* (* (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (* (* (* (/ Om l) (/ Om l)) (/ Om l)) (/ (* (* Om Om) Om) (* (* l l) l))))
500.0ms
(/ 1/2 (sqrt (sqrt (+ (* 4 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (* (/ Om l) (/ Om l)))) 1))))

prune2.4s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize59.0ms

Local error

Found 4 expressions with local error:

9.2b
(sqrt (+ (* 4 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (* (/ Om l) (/ Om l)))) 1))
2.1b
(/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (* (/ Om l) (/ Om l)))
2.1b
(log (exp (/ 1/2 (sqrt (+ (* 4 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (* (/ Om l) (/ Om l)))) 1)))))
0.5b
(/ 1/2 (sqrt (+ (* 4 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (* (/ Om l) (/ Om l)))) 1)))

rewrite340.0ms

Algorithm
rewrite-expression-head
Rules
39×times-frac
37×add-sqr-sqrt
36×*-un-lft-identity add-cube-cbrt
25×log-pow
24×exp-prod add-cbrt-cube add-exp-log sqrt-prod
10×cbrt-undiv div-exp
7×associate-/r* associate-/r/
6×pow1 sqrt-div associate-/l*
4×flip3-+ prod-exp cbrt-unprod flip-+ insert-posit16 add-log-exp
3×log-prod div-inv associate-/l/
2×clear-num frac-2neg div-sub sqr-sin sin-mult
1×frac-times rem-sqrt-square associate-+r- sqrt-pow1 pow1/2 rem-log-exp associate-*l/ frac-add associate-*r/ associate-+l-
Counts
4 → 131
Calls
4 calls:
Slowest
112.0ms
(log (exp (/ 1/2 (sqrt (+ (* 4 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (* (/ Om l) (/ Om l)))) 1)))))
92.0ms
(/ 1/2 (sqrt (+ (* 4 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (* (/ Om l) (/ Om l)))) 1)))
78.0ms
(sqrt (+ (* 4 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (* (/ Om l) (/ Om l)))) 1))
53.0ms
(/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (* (/ Om l) (/ Om l)))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
358.0ms
(/ 1/2 (sqrt (+ (* 4 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (* (/ Om l) (/ Om l)))) 1)))
345.0ms
(sqrt (+ (* 4 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (* (/ Om l) (/ Om l)))) 1))
338.0ms
(log (exp (/ 1/2 (sqrt (+ (* 4 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (* (/ Om l) (/ Om l)))) 1)))))
265.0ms
(/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (* (/ Om l) (/ Om l)))

simplify35.3s

Counts
119 → 143
Calls
119 calls:
Slowest
780.0ms
(/ (* (* 1/2 1/2) 1/2) (* (* (sqrt (+ (* 4 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (* (/ Om l) (/ Om l)))) 1)) (sqrt (+ (* 4 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (* (/ Om l) (/ Om l)))) 1))) (sqrt (+ (* 4 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (* (/ Om l) (/ Om l)))) 1))))
733.0ms
(/ (* (* (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (* (/ (* (* Om Om) Om) (* (* l l) l)) (/ (* (* Om Om) Om) (* (* l l) l))))
589.0ms
(/ (* (* (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (* (/ (* (* Om Om) Om) (* (* l l) l)) (* (* (/ Om l) (/ Om l)) (/ Om l))))
528.0ms
(/ (* (* (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (* (* (* (/ Om l) (/ Om l)) (/ Om l)) (/ (* (* Om Om) Om) (* (* l l) l))))
524.0ms
(/ (sqrt 1/2) (* (cbrt (sqrt (+ (* 4 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (* (/ Om l) (/ Om l)))) 1))) (cbrt (sqrt (+ (* 4 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (* (/ Om l) (/ Om l)))) 1)))))

prune2.7s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize75.0ms

Local error

Found 4 expressions with local error:

9.2b
(sqrt (+ (* 4 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (* (/ Om l) (/ Om l)))) 1))
9.2b
(sqrt (+ (* 4 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (* (/ Om l) (/ Om l)))) 1))
2.9b
(log (sqrt (exp (/ 1/2 (sqrt (+ (* 4 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (* (/ Om l) (/ Om l)))) 1))))))
2.9b
(log (sqrt (exp (/ 1/2 (sqrt (+ (* 4 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (* (/ Om l) (/ Om l)))) 1))))))

rewrite370.0ms

Algorithm
rewrite-expression-head
Rules
54×log-pow
52×sqrt-pow1
48×exp-prod
38×add-sqr-sqrt
36×*-un-lft-identity times-frac add-cube-cbrt
30×sqrt-prod
12×log-prod
10×pow1
8×sqrt-div
6×add-exp-log
4×flip3-+ add-cbrt-cube pow1/2 associate-/r/ flip-+ insert-posit16 add-log-exp
2×rem-sqrt-square rem-log-exp div-inv
Counts
4 → 116
Calls
4 calls:
Slowest
129.0ms
(log (sqrt (exp (/ 1/2 (sqrt (+ (* 4 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (* (/ Om l) (/ Om l)))) 1))))))
123.0ms
(log (sqrt (exp (/ 1/2 (sqrt (+ (* 4 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (* (/ Om l) (/ Om l)))) 1))))))
63.0ms
(sqrt (+ (* 4 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (* (/ Om l) (/ Om l)))) 1))
53.0ms
(sqrt (+ (* 4 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (* (/ Om l) (/ Om l)))) 1))

series1.8s

Counts
4 → 12
Calls
4 calls:
Slowest
508.0ms
(log (sqrt (exp (/ 1/2 (sqrt (+ (* 4 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (* (/ Om l) (/ Om l)))) 1))))))
477.0ms
(log (sqrt (exp (/ 1/2 (sqrt (+ (* 4 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (* (/ Om l) (/ Om l)))) 1))))))
409.0ms
(sqrt (+ (* 4 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (* (/ Om l) (/ Om l)))) 1))
401.0ms
(sqrt (+ (* 4 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (* (/ Om l) (/ Om l)))) 1))

simplify28.6s

Counts
90 → 128
Calls
90 calls:
Slowest
825.0ms
(log (sqrt (* (cbrt (exp (/ 1/2 (sqrt (+ (* 4 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (* (/ Om l) (/ Om l)))) 1))))) (cbrt (exp (/ 1/2 (sqrt (+ (* 4 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (* (/ Om l) (/ Om l)))) 1))))))))
515.0ms
(/ (/ (cbrt 1/2) (sqrt (sqrt (+ (* 4 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (* (/ Om l) (/ Om l)))) 1)))) 2)
490.0ms
(/ (/ 1/2 (sqrt (sqrt (+ (* 4 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (* (/ Om l) (/ Om l)))) 1)))) 2)
488.0ms
(/ (/ (cbrt 1/2) (sqrt (cbrt (+ (* 4 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (* (/ Om l) (/ Om l)))) 1)))) 2)
485.0ms
(/ (/ (sqrt 1/2) (sqrt (cbrt (+ (* 4 (/ (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))) (* (/ Om l) (/ Om l)))) 1)))) 2)

prune3.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

regimes473.0ms

Accuracy

0% (0.8b remaining)

Error of 1.6b against oracle of 0.8b and baseline of 1.6b

bsearch9.0ms

end0.0ms

sample4.2s

Algorithm
intervals
Results
3.9s8000×body80valid