Details

Time bar (total: 2.1m)

sample110.0ms

Algorithm
intervals
Results
88.0ms256×body80valid

simplify182.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
182.0ms
(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.6b

localize45.0ms

Local error

Found 4 expressions with local error:

6.6b
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
1.3b
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
0.3b
(* (sin ky) (sin ky))
0.2b
(* (sin kx) (sin kx))

rewrite532.0ms

Algorithm
rewrite-expression-head
Rules
55×add-cbrt-cube add-exp-log
37×pow1
33×prod-exp cbrt-unprod
23×associate-*r/
20×add-sqr-sqrt
15×pow-prod-down
14×*-un-lft-identity add-cube-cbrt
13×frac-times
10×sin-mult
9×associate-*l*
7×associate-*r* associate-*l/
6×cbrt-undiv swap-sqr div-exp
5×flip3-+ flip-+
4×frac-add insert-posit16 add-log-exp
3×*-commutative sqrt-prod unswap-sqr
2×pow2 pow-plus sqrt-div pow-sqr pow-prod-up sqr-sin
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 126
Calls
4 calls:
Slowest
258.0ms
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
246.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
14.0ms
(* (sin ky) (sin ky))
11.0ms
(* (sin kx) (sin kx))

series813.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
462.0ms
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
286.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
33.0ms
(* (sin kx) (sin kx))
31.0ms
(* (sin ky) (sin ky))

simplify26.1s

Counts
117 → 138
Calls
117 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 l) l) (* (* (/ 2 Om) (/ 2 Om)) (/ 2 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 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 (/ 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 2) 2) (* (* Om Om) Om))) (* (* (* l l) l) (* (* (/ 2 Om) (/ 2 Om)) (/ 2 Om)))))
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 (/ 2 Om)) (* l (/ 2 Om))) (* l (/ 2 Om)))))

prune2.4s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize57.0ms

Local error

Found 4 expressions with local error:

6.6b
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
1.3b
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
0.3b
(* (sin ky) (sin ky))
0.2b
(* (sin kx) (sin kx))

rewrite446.0ms

Algorithm
rewrite-expression-head
Rules
55×add-cbrt-cube add-exp-log
37×pow1
33×prod-exp cbrt-unprod
23×associate-*r/
20×add-sqr-sqrt
15×pow-prod-down
14×*-un-lft-identity add-cube-cbrt
13×frac-times
10×sin-mult
9×associate-*l*
7×associate-*r* associate-*l/
6×cbrt-undiv swap-sqr div-exp
5×flip3-+ flip-+
4×frac-add insert-posit16 add-log-exp
3×*-commutative sqrt-prod unswap-sqr
2×pow2 pow-plus sqrt-div pow-sqr pow-prod-up sqr-sin
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 126
Calls
4 calls:
Slowest
272.0ms
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
128.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
23.0ms
(* (sin kx) (sin kx))
19.0ms
(* (sin ky) (sin ky))

series854.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
454.0ms
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
321.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
41.0ms
(* (sin ky) (sin ky))
38.0ms
(* (sin kx) (sin kx))

simplify26.1s

Counts
117 → 138
Calls
117 calls:
Slowest
1.5s
(* (* (* (+ (* (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)))))
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 (/ 2 Om)) (* l (/ 2 Om))) (* l (/ 2 Om)))))
777.0ms
(* (* (* (+ (* (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)))))

prune2.9s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.3b

localize74.0ms

Local error

Found 4 expressions with local error:

20.3b
(posit16->real (real->posit16 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))))
6.6b
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
1.3b
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
0.3b
(* (sin ky) (sin ky))

rewrite510.0ms

Algorithm
rewrite-expression-head
Rules
53×add-cbrt-cube add-exp-log
32×prod-exp cbrt-unprod
30×pow1
23×associate-*r/
14×add-sqr-sqrt pow-prod-down
13×frac-times
10×*-un-lft-identity add-cube-cbrt
9×sin-mult
7×associate-*l/
6×cbrt-undiv div-exp associate-*l*
5×flip3-+ flip-+
4×associate-*r* frac-add insert-posit16 add-log-exp
3×swap-sqr sqrt-prod
2×sqrt-div *-commutative unswap-sqr
1×pow2 rem-sqrt-square sqrt-pow1 pow-plus pow1/2 pow-sqr pow-prod-up sqr-sin remove-posit16
Counts
4 → 107
Calls
4 calls:
Slowest
292.0ms
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
195.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
19.0ms
(* (sin ky) (sin ky))
0.0ms
(posit16->real (real->posit16 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
458.0ms
(posit16->real (real->posit16 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))))
419.0ms
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
248.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
33.0ms
(* (sin ky) (sin ky))

simplify27.2s

Counts
95 → 119
Calls
95 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 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)))))
1.1s
(* (* (* (+ (* (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 2) 2) (* (* Om Om) Om)))))
866.0ms
(* (* (* (+ (* (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)))))

prune4.4s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.3b

localize103.0ms

Local error

Found 4 expressions with local error:

35.0b
(posit16->real (real->posit16 (* (sin ky) (sin ky))))
6.6b
(sqrt (+ (* (+ (posit16->real (real->posit16 (* (sin ky) (sin ky)))) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
1.3b
(* (+ (posit16->real (real->posit16 (* (sin ky) (sin ky)))) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
0.3b
(* (sin ky) (sin ky))

rewrite401.0ms

Algorithm
rewrite-expression-head
Rules
53×add-cbrt-cube add-exp-log
32×prod-exp cbrt-unprod
30×pow1
18×associate-*r/
14×add-sqr-sqrt pow-prod-down
10×*-un-lft-identity add-cube-cbrt
9×frac-times
6×cbrt-undiv div-exp associate-*l*
5×flip3-+ associate-*l/ flip-+
4×associate-*r* insert-posit16 add-log-exp
3×swap-sqr sqrt-prod
2×sqrt-div *-commutative unswap-sqr
1×pow2 rem-sqrt-square sqrt-pow1 pow-plus pow1/2 pow-sqr pow-prod-up sqr-sin remove-posit16 sin-mult
Counts
4 → 103
Calls
4 calls:
Slowest
245.0ms
(sqrt (+ (* (+ (posit16->real (real->posit16 (* (sin ky) (sin ky)))) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
134.0ms
(* (+ (posit16->real (real->posit16 (* (sin ky) (sin ky)))) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
20.0ms
(* (sin ky) (sin ky))
0.0ms
(posit16->real (real->posit16 (* (sin ky) (sin ky))))

series822.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
497.0ms
(sqrt (+ (* (+ (posit16->real (real->posit16 (* (sin ky) (sin ky)))) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
284.0ms
(* (+ (posit16->real (real->posit16 (* (sin ky) (sin ky)))) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
21.0ms
(posit16->real (real->posit16 (* (sin ky) (sin ky))))
20.0ms
(* (sin ky) (sin ky))

simplify20.9s

Counts
88 → 115
Calls
88 calls:
Slowest
1.3s
(* (* (* (+ (posit16->real (real->posit16 (* (sin ky) (sin ky)))) (* (sin kx) (sin kx))) (+ (posit16->real (real->posit16 (* (sin ky) (sin ky)))) (* (sin kx) (sin kx)))) (+ (posit16->real (real->posit16 (* (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)))))
914.0ms
(* (* (* (+ (posit16->real (real->posit16 (* (sin ky) (sin ky)))) (* (sin kx) (sin kx))) (+ (posit16->real (real->posit16 (* (sin ky) (sin ky)))) (* (sin kx) (sin kx)))) (+ (posit16->real (real->posit16 (* (sin ky) (sin ky)))) (* (sin kx) (sin kx)))) (* (* (* (* l l) l) (* (* (/ 2 Om) (/ 2 Om)) (/ 2 Om))) (* (* (* l (/ 2 Om)) (* l (/ 2 Om))) (* l (/ 2 Om)))))
890.0ms
(* (* (* (+ (posit16->real (real->posit16 (* (sin ky) (sin ky)))) (* (sin kx) (sin kx))) (+ (posit16->real (real->posit16 (* (sin ky) (sin ky)))) (* (sin kx) (sin kx)))) (+ (posit16->real (real->posit16 (* (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)))))
830.0ms
(* (* (* (+ (posit16->real (real->posit16 (* (sin ky) (sin ky)))) (* (sin kx) (sin kx))) (+ (posit16->real (real->posit16 (* (sin ky) (sin ky)))) (* (sin kx) (sin kx)))) (+ (posit16->real (real->posit16 (* (sin ky) (sin ky)))) (* (sin kx) (sin kx)))) (* (* (* (* l l) l) (* (* (/ 2 Om) (/ 2 Om)) (/ 2 Om))) (* (* (* l l) l) (* (* (/ 2 Om) (/ 2 Om)) (/ 2 Om)))))
823.0ms
(* (* (* (+ (posit16->real (real->posit16 (* (sin ky) (sin ky)))) (* (sin kx) (sin kx))) (+ (posit16->real (real->posit16 (* (sin ky) (sin ky)))) (* (sin kx) (sin kx)))) (+ (posit16->real (real->posit16 (* (sin ky) (sin ky)))) (* (sin kx) (sin kx)))) (* (* (* (* l (/ 2 Om)) (* l (/ 2 Om))) (* l (/ 2 Om))) (* (* (* l (/ 2 Om)) (* l (/ 2 Om))) (* l (/ 2 Om)))))

prune3.4s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.3b

regimes472.0ms

Accuracy

0% (0.2b remaining)

Error of 1.1b against oracle of 0.9b and baseline of 1.1b

bsearch8.0ms

end0.0ms

sample3.9s

Algorithm
intervals
Results
3.6s8000×body80valid