Details

Time bar (total: 2.5m)

sample172.0ms

Algorithm
intervals
Results
140.0ms256×body80valid

simplify244.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
243.0ms
(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))

prune34.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize51.0ms

Local error

Found 4 expressions with local error:

10.0b
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
2.0b
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
0.4b
(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1)))
0.3b
(* (sin ky) (sin ky))

rewrite711.0ms

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
302.0ms
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
209.0ms
(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1)))
183.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
12.0ms
(* (sin ky) (sin ky))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
460.0ms
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
432.0ms
(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1)))
245.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
35.0ms
(* (sin ky) (sin ky))

simplify44.9s

Counts
142 → 152
Calls
142 calls:
Slowest
1.3s
(* (* (* (+ (* (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)))))
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 (/ 2 Om)) (* l (/ 2 Om))) (* l (/ 2 Om)))))
1.1s
(* (* (* (+ (* (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)))))
1.1s
(* (* (* (+ (* (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)))))
1.1s
(* (* (* (+ (* (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)))))

prune2.6s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize62.0ms

Local error

Found 4 expressions with local error:

10.0b
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
3.3b
(log (exp (/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1)))))
2.0b
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
0.4b
(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1)))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
53×add-cbrt-cube add-exp-log
37×add-sqr-sqrt
36×times-frac
35×*-un-lft-identity add-cube-cbrt
31×prod-exp cbrt-unprod
25×log-pow
24×pow1 exp-prod sqrt-prod
23×associate-*r/
13×frac-times pow-prod-down
8×sin-mult
7×cbrt-undiv flip3-+ div-exp associate-*l/ flip-+
6×associate-/r* sqrt-div
4×frac-add associate-/r/ insert-posit16 add-log-exp
3×log-prod associate-*l* associate-/l*
2×div-inv
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 rem-log-exp associate-*r* *-commutative unswap-sqr
Counts
4 → 149
Calls
4 calls:
Slowest
575.0ms
(log (exp (/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1)))))
224.0ms
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
220.0ms
(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1)))
198.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))

series1.5s

Counts
4 → 12
Calls
4 calls:
Slowest
445.0ms
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
395.0ms
(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1)))
391.0ms
(log (exp (/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1)))))
267.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))

simplify56.3s

Counts
146 → 161
Calls
146 calls:
Slowest
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)))))
1.1s
(* (* (* (+ (* (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)))))
1.1s
(* (- (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky))) (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx)))) (* (* l 2) (* l 2)))
1.0s
(* (* (* (+ (* (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)))))
989.0ms
(* (* (* (+ (* (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 l) l) (/ (* (* 2 2) 2) (* (* Om Om) Om))) (* (* (* l (/ 2 Om)) (* l (/ 2 Om))) (* l (/ 2 Om)))))

prune3.1s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize89.0ms

Local error

Found 4 expressions with local error:

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

rewrite897.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
9×*-un-lft-identity add-cube-cbrt sqrt-prod
8×pow1
6×log-prod sqrt-div
5×add-exp-log
4×add-cbrt-cube insert-posit16 add-log-exp
3×cbrt-prod rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
2×log-pow
1×pow1/3 rem-log-exp
Counts
4 → 65
Calls
4 calls:
Slowest
251.0ms
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
241.0ms
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
231.0ms
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
172.0ms
(log (cbrt (exp (/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))))))

series1.9s

Counts
4 → 12
Calls
4 calls:
Slowest
500.0ms
(log (cbrt (exp (/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))))))
499.0ms
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
449.0ms
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
433.0ms
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))

simplify13.2s

Counts
40 → 77
Calls
40 calls:
Slowest
614.0ms
(log (cbrt (* (cbrt (exp (/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))))) (cbrt (exp (/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))))))))
591.0ms
(log (* (cbrt (cbrt (exp (/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1)))))) (cbrt (cbrt (exp (/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))))))))
566.0ms
(sqrt (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1)))
514.0ms
(sqrt (* (cbrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1)) (cbrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))))
507.0ms
(+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1)

prune2.4s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize131.0ms

Local error

Found 4 expressions with local error:

10.0b
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
10.0b
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
10.0b
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
3.4b
(log (* (cbrt (exp (/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))))) (cbrt (exp (/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1)))))))

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
15×pow1
10×add-sqr-sqrt
9×log-pow sqrt-prod
7×*-un-lft-identity add-exp-log add-cube-cbrt
6×pow1/3 sqrt-div
4×add-cbrt-cube insert-posit16 add-log-exp
3×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
2×rem-log-exp pow-prod-down pow-sqr pow-prod-up
1×pow2 log-prod pow-plus prod-exp
Counts
4 → 68
Calls
4 calls:
Slowest
323.0ms
(log (* (cbrt (exp (/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))))) (cbrt (exp (/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1)))))))
248.0ms
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
244.0ms
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
206.0ms
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))

series2.0s

Counts
4 → 12
Calls
4 calls:
Slowest
688.0ms
(log (* (cbrt (exp (/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))))) (cbrt (exp (/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1)))))))
487.0ms
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
425.0ms
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
418.0ms
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))

simplify12.1s

Counts
41 → 80
Calls
41 calls:
Slowest
532.0ms
(sqrt (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1)))
518.0ms
(log (cbrt (exp (/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))))))
501.0ms
(sqrt (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1)))
485.0ms
(+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1)
484.0ms
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))

prune2.4s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.1b

regimes544.0ms

Accuracy

0% (0.7b remaining)

Error of 1.6b against oracle of 0.9b and baseline of 1.6b

bsearch6.0ms

end0.0ms

sample3.9s

Algorithm
intervals
Results
3.6s7999×body80valid
1.0ms1×body160valid