Details

Time bar (total: 1.7m)

sample125.0ms

Algorithm
intervals
Results
99.0ms256×body80valid

simplify273.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
272.0ms
(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))

prune40.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.6b

localize63.0ms

Local error

Found 4 expressions with local error:

8.5b
(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))
0.3b
(* (sin kx) (sin kx))

rewrite465.0ms

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
252.0ms
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
168.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
21.0ms
(* (sin kx) (sin kx))
18.0ms
(* (sin ky) (sin ky))

series807.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
505.0ms
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
254.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
29.0ms
(* (sin ky) (sin ky))
18.0ms
(* (sin kx) (sin kx))

simplify25.8s

Counts
117 → 138
Calls
117 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 2) 2) (* (* Om Om) Om)))))
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)))))
1.1s
(* (* (* (+ (* (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 Om) (/ 2 Om)) (/ 2 Om))) (* (* (* l l) l) (/ (* (* 2 2) 2) (* (* Om Om) Om)))))
933.0ms
(* (* (* (+ (* (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 Om) (/ 2 Om)) (/ 2 Om))) (* (* (* l (/ 2 Om)) (* l (/ 2 Om))) (* l (/ 2 Om)))))

prune2.3s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.3b

localize82.0ms

Local error

Found 4 expressions with local error:

35.9b
(posit16->real (real->posit16 (* (sin ky) (sin ky))))
8.5b
(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))

rewrite386.0ms

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
246.0ms
(sqrt (+ (* (+ (posit16->real (real->posit16 (* (sin ky) (sin ky)))) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
120.0ms
(* (+ (posit16->real (real->posit16 (* (sin ky) (sin ky)))) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
16.0ms
(* (sin ky) (sin ky))
1.0ms
(posit16->real (real->posit16 (* (sin ky) (sin ky))))

series771.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
435.0ms
(sqrt (+ (* (+ (posit16->real (real->posit16 (* (sin ky) (sin ky)))) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
281.0ms
(* (+ (posit16->real (real->posit16 (* (sin ky) (sin ky)))) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
35.0ms
(posit16->real (real->posit16 (* (sin ky) (sin ky))))
20.0ms
(* (sin ky) (sin ky))

simplify21.6s

Counts
88 → 115
Calls
88 calls:
Slowest
1.2s
(* (* (* (+ (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)))))
958.0ms
(* (* (* (+ (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)))))
893.0ms
(* (* (* (+ (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)))))
884.0ms
(* (* (* (+ (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)))))
873.0ms
(+ (log (+ (posit16->real (real->posit16 (* (sin ky) (sin ky)))) (* (sin kx) (sin kx)))) (+ (+ (log l) (- (log 2) (log Om))) (+ (log l) (- (log 2) (log Om)))))

prune3.1s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.3b

localize68.0ms

Local error

Found 4 expressions with local error:

27.0b
(posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))))
8.5b
(sqrt (+ (posit16->real (real->posit16 (* (+ (* (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))

rewrite225.0ms

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
12×*-un-lft-identity
10×add-cube-cbrt
9×sin-mult
7×associate-*l/
6×cbrt-undiv div-exp associate-*l*
5×flip3-+ flip-+
4×associate-*r* frac-add sqrt-prod insert-posit16 add-log-exp
3×swap-sqr
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 distribute-lft-out
Counts
4 → 108
Calls
4 calls:
Slowest
192.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
21.0ms
(* (sin ky) (sin ky))
4.0ms
(sqrt (+ (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))))) 1))
0.0ms
(posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
444.0ms
(sqrt (+ (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))))) 1))
324.0ms
(posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))))
278.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
37.0ms
(* (sin ky) (sin ky))

simplify25.4s

Counts
96 → 120
Calls
96 calls:
Slowest
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)))))
1.0s
(* (* (* (+ (* (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 Om) (/ 2 Om)) (/ 2 Om)))))
990.0ms
(* (* (* (+ (* (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 l) l) (/ (* (* 2 2) 2) (* (* Om Om) Om)))))
935.0ms
(* (* (* (+ (* (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 Om) (/ 2 Om)) (/ 2 Om))) (* (* (* l l) l) (/ (* (* 2 2) 2) (* (* Om Om) Om)))))
890.0ms
(+ (log (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (+ (+ (log l) (- (log 2) (log Om))) (+ (log l) (log (/ 2 Om)))))

prune3.7s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.3b

localize100.0ms

Local error

Found 4 expressions with local error:

27.0b
(posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))))
27.0b
(posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))))
27.0b
(posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))))
8.5b
(sqrt (+ (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))))) 1))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
7×*-un-lft-identity
6×add-sqr-sqrt
5×pow1 add-cube-cbrt
4×add-cbrt-cube add-exp-log sqrt-prod insert-posit16 add-log-exp
3×remove-posit16
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+ distribute-lft-out
Counts
4 → 44
Calls
4 calls:
Slowest
4.0ms
(sqrt (+ (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))))) 1))
0.0ms
(posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))))
0.0ms
(posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))))
0.0ms
(posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
456.0ms
(sqrt (+ (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))))) 1))
297.0ms
(posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))))
279.0ms
(posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))))
232.0ms
(posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))))

simplify6.3s

Counts
23 → 56
Calls
23 calls:
Slowest
808.0ms
(sqrt (* (cbrt (+ (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))))) 1)) (cbrt (+ (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))))) 1))))
568.0ms
(sqrt (+ (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))))) 1))
491.0ms
(sqrt (sqrt (+ (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))))) 1)))
472.0ms
(+ (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))))) 1)
413.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))

prune2.0s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.3b

regimes439.0ms

Accuracy

0% (0.8b remaining)

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

bsearch8.0ms

end0.0ms

sample3.5s

Algorithm
intervals
Results
3.3s7999×body80valid
1.0ms1×body160valid