Details

Time bar (total: 1.9m)

sample276.0ms

Algorithm
intervals
Results
198.0ms256×body80valid

simplify447.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
446.0ms
(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))

prune33.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.3b

localize82.0ms

Local error

Found 4 expressions with local error:

7.5b
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
2.7b
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
0.5b
(* l (/ 2 Om))
0.5b
(* l (/ 2 Om))

rewrite686.0ms

Algorithm
rewrite-expression-head
Rules
61×add-cbrt-cube add-exp-log
35×prod-exp cbrt-unprod
34×add-sqr-sqrt
27×pow1 associate-*r*
25×associate-*r/
22×*-un-lft-identity add-cube-cbrt
20×times-frac
15×pow-prod-down
13×frac-times
9×associate-*l*
8×cbrt-undiv div-exp sin-mult
7×associate-*l/
5×flip3-+ flip-+ unswap-sqr
4×frac-add insert-posit16 add-log-exp
3×*-commutative sqrt-prod
2×sqrt-div div-inv
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 136
Calls
4 calls:
Slowest
454.0ms
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
210.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
9.0ms
(* l (/ 2 Om))
9.0ms
(* l (/ 2 Om))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
782.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
393.0ms
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
35.0ms
(* l (/ 2 Om))
28.0ms
(* l (/ 2 Om))

simplify27.9s

Counts
119 → 148
Calls
119 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 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)))))
1.2s
(* (* (* (+ (* (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 2) 2) (* (* Om Om) Om)))))
888.0ms
(* (* (* (+ (* (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)))))

prune2.6s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize73.0ms

Local error

Found 4 expressions with local error:

7.5b
(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om))) 1))
2.8b
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))
0.5b
(* l (/ 2 Om))
0.5b
(* l (/ 2 Om))

rewrite341.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
27×associate-*r*
23×add-cbrt-cube add-exp-log
22×*-un-lft-identity add-cube-cbrt
20×times-frac
14×pow1
9×associate-*l* prod-exp cbrt-unprod
7×associate-*r/
5×pow-prod-down
4×insert-posit16 sin-mult add-log-exp unswap-sqr
3×frac-times cbrt-undiv flip3-+ div-exp associate-*l/ *-commutative sqrt-prod flip-+
2×sqrt-div frac-add div-inv
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 110
Calls
4 calls:
Slowest
249.0ms
(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om))) 1))
66.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))
14.0ms
(* l (/ 2 Om))
9.0ms
(* l (/ 2 Om))

series705.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
478.0ms
(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)))
24.0ms
(* l (/ 2 Om))
20.0ms
(* l (/ 2 Om))

simplify11.6s

Counts
87 → 122
Calls
87 calls:
Slowest
634.0ms
(sqrt (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om))) 1)))
539.0ms
(+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om))) 1)
538.0ms
(sqrt (+ (pow (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om))) 3) (pow 1 3)))
520.0ms
(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))))
509.0ms
(* (* (* (+ (* (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))))

prune2.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize68.0ms

Local error

Found 4 expressions with local error:

7.5b
(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om))) 1))
7.5b
(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om))) 1))
5.5b
(sqrt (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om))) 1)))
5.5b
(sqrt (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om))) 1)))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
26×sqrt-prod
16×add-sqr-sqrt
12×sqrt-div
10×pow1 *-un-lft-identity sqrt-pow1 add-cube-cbrt
6×rem-sqrt-square pow1/2
4×flip3-+ add-cbrt-cube add-exp-log flip-+ insert-posit16 add-log-exp
Counts
4 → 76
Calls
4 calls:
Slowest
298.0ms
(sqrt (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om))) 1)))
298.0ms
(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om))) 1))
277.0ms
(sqrt (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om))) 1)))
253.0ms
(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om))) 1))

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
414.0ms
(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om))) 1))
405.0ms
(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om))) 1))
314.0ms
(sqrt (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om))) 1)))
305.0ms
(sqrt (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om))) 1)))

simplify20.9s

Counts
52 → 88
Calls
52 calls:
Slowest
964.0ms
(+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om))) 1)
608.0ms
(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om))) 1))
601.0ms
(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))))
587.0ms
(+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om))) 1)
578.0ms
(sqrt (* (cbrt (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om))) 1))) (cbrt (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om))) 1)))))

prune1.9s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize74.0ms

Local error

Found 4 expressions with local error:

21.8b
(posit16->real (real->posit16 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))))
7.5b
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
2.7b
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
0.5b
(* l (/ 2 Om))

rewrite558.0ms

Algorithm
rewrite-expression-head
Rules
56×add-cbrt-cube add-exp-log
33×prod-exp cbrt-unprod
25×pow1
24×associate-*r/
21×add-sqr-sqrt
14×*-un-lft-identity associate-*r* pow-prod-down add-cube-cbrt
13×frac-times
10×times-frac
8×sin-mult
7×cbrt-undiv div-exp associate-*l/
6×associate-*l*
5×flip3-+ flip-+
4×frac-add insert-posit16 add-log-exp
3×sqrt-prod unswap-sqr
2×sqrt-div *-commutative
1×rem-sqrt-square sqrt-pow1 pow1/2 div-inv remove-posit16
Counts
4 → 112
Calls
4 calls:
Slowest
296.0ms
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
240.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
17.0ms
(* l (/ 2 Om))
0.0ms
(posit16->real (real->posit16 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
502.0ms
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
452.0ms
(posit16->real (real->posit16 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))))
285.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
32.0ms
(* l (/ 2 Om))

simplify27.6s

Counts
96 → 124
Calls
96 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 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 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 (/ 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 2) 2) (* (* Om Om) Om)))))
907.0ms
(* (* (* (+ (* (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)))))

prune4.2s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.3b

regimes561.0ms

Accuracy

0% (0.6b remaining)

Error of 1.3b against oracle of 0.8b and baseline of 1.3b

bsearch6.0ms

end0.0ms

sample4.0s

Algorithm
intervals
Results
3.7s8000×body80valid