Details

Time bar (total: 2.7m)

sample79.0ms

Algorithm
intervals
Results
61.0ms256×body80valid

simplify232.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
231.0ms
(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))

prune30.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.1b

localize68.0ms

Local error

Found 4 expressions with local error:

9.6b
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
3.0b
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
0.3b
(* (sin ky) (sin ky))
0.2b
(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1)))

rewrite1.1s

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
690.0ms
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
269.0ms
(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1)))
149.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
11.0ms
(* (sin ky) (sin ky))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
473.0ms
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
410.0ms
(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1)))
283.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
21.0ms
(* (sin ky) (sin ky))

simplify46.5s

Counts
142 → 152
Calls
142 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)))))
1.2s
(* (* (* (+ (* (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 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)))))
949.0ms
(sqrt (- (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))

prune2.5s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize69.0ms

Local error

Found 4 expressions with local error:

9.6b
(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)))
0.3b
(* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om)))
0.3b
(* (sin ky) (sin ky))

rewrite561.0ms

Algorithm
rewrite-expression-head
Rules
69×add-cbrt-cube add-exp-log
41×prod-exp cbrt-unprod
38×pow1
24×associate-*r/
19×pow-prod-down
16×frac-times associate-*l/
13×add-sqr-sqrt sin-mult
10×*-un-lft-identity add-cube-cbrt
8×cbrt-undiv div-exp
7×flip3-+ associate-*l* flip-+
6×frac-add
5×associate-*r*
4×insert-posit16 add-log-exp
3×swap-sqr *-commutative sqrt-prod
2×sqrt-div
1×pow2 rem-sqrt-square sqrt-pow1 pow-plus pow1/2 pow-sqr pow-prod-up sqr-sin unswap-sqr
Counts
4 → 128
Calls
4 calls:
Slowest
237.0ms
(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om))) 1))
202.0ms
(* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om)))
95.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))
22.0ms
(* (sin ky) (sin ky))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
513.0ms
(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om))) 1))
302.0ms
(* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om)))
216.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))
33.0ms
(* (sin ky) (sin ky))

simplify36.4s

Counts
115 → 140
Calls
115 calls:
Slowest
1.7s
(* (* (* (* (+ (* (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))))
1.3s
(* (* (* (* (+ (* (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))))
1.3s
(* (* (* (* (+ (* (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 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))))
1.1s
(* (* (* (* (+ (* (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 (/ 2 Om)) (* l (/ 2 Om))) (* l (/ 2 Om)))) (* (* (* l l) l) (* (* (/ 2 Om) (/ 2 Om)) (/ 2 Om))))

prune2.5s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize101.0ms

Local error

Found 4 expressions with local error:

9.6b
(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)))
0.3b
(* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om)))
0.3b
(* (sin ky) (sin ky))

rewrite561.0ms

Algorithm
rewrite-expression-head
Rules
69×add-cbrt-cube add-exp-log
41×prod-exp cbrt-unprod
38×pow1
24×associate-*r/
19×pow-prod-down
16×frac-times associate-*l/
13×add-sqr-sqrt sin-mult
10×*-un-lft-identity add-cube-cbrt
8×cbrt-undiv div-exp
7×flip3-+ associate-*l* flip-+
6×frac-add
5×associate-*r*
4×insert-posit16 add-log-exp
3×swap-sqr *-commutative sqrt-prod
2×sqrt-div
1×pow2 rem-sqrt-square sqrt-pow1 pow-plus pow1/2 pow-sqr pow-prod-up sqr-sin unswap-sqr
Counts
4 → 128
Calls
4 calls:
Slowest
255.0ms
(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om))) 1))
196.0ms
(* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om)))
85.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))
21.0ms
(* (sin ky) (sin ky))

series927.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
423.0ms
(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)))
199.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))
21.0ms
(* (sin ky) (sin ky))

simplify36.9s

Counts
115 → 140
Calls
115 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))))
1.3s
(* (* (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))) (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))) (* (* (* l (/ 2 Om)) (* l (/ 2 Om))) (* l (/ 2 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))))
1.3s
(* (* (* (* (+ (* (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))) (* l (/ 2 Om))) (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))) (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))) (* (* (* l l) l) (/ (* (* 2 2) 2) (* (* Om Om) Om))))

prune2.7s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize108.0ms

Local error

Found 4 expressions with local error:

9.6b
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
9.6b
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
9.6b
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
6.9b
(cbrt (/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))))

rewrite888.0ms

Algorithm
rewrite-expression-head
Rules
24×cbrt-prod
23×add-sqr-sqrt
20×*-un-lft-identity add-cube-cbrt
18×times-frac sqrt-prod
8×sqrt-div
7×pow1
4×flip3-+ add-cbrt-cube add-exp-log flip-+ insert-posit16 add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×associate-/r/
1×cbrt-div pow1/3 div-inv
Counts
4 → 82
Calls
4 calls:
Slowest
262.0ms
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
254.0ms
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
228.0ms
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
142.0ms
(cbrt (/ 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
496.0ms
(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))
477.0ms
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
466.0ms
(cbrt (/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))))

simplify20.1s

Counts
58 → 94
Calls
58 calls:
Slowest
839.0ms
(cbrt (/ (sqrt 1/2) (sqrt (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1)))))
595.0ms
(cbrt (/ (* (cbrt 1/2) (cbrt 1/2)) (* (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))))))
571.0ms
(cbrt (/ (* (cbrt 1/2) (cbrt 1/2)) (sqrt (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1)))))
553.0ms
(sqrt (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1)))
551.0ms
(cbrt (/ 1 (sqrt (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: 0.4b

regimes573.0ms

Accuracy

0% (0.8b remaining)

Error of 1.5b against oracle of 0.7b and baseline of 1.5b

bsearch11.0ms

end0.0ms

sample3.7s

Algorithm
intervals
Results
3.4s8000×body80valid