Details

Time bar (total: 3.4m)

sample164.0ms

Algorithm
intervals
Results
131.0ms256×body80valid

simplify199.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
198.0ms
(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.9b

localize93.0ms

Local error

Found 4 expressions with local error:

11.3b
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
2.3b
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
0.6b
(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1)))
0.3b
(* (sin kx) (sin kx))

rewrite613.0ms

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
232.0ms
(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1)))
209.0ms
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
157.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
11.0ms
(* (sin kx) (sin kx))

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
417.0ms
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
345.0ms
(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1)))
265.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
19.0ms
(* (sin kx) (sin kx))

simplify45.9s

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 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 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 Om) (/ 2 Om)) (/ 2 Om)))))
843.0ms
(* (* (* (+ (* (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)))))

prune2.5s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.6b

localize51.0ms

Local error

Found 4 expressions with local error:

11.3b
(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om))) 1))
2.6b
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))
0.8b
(* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om)))
0.6b
(/ 1/2 (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om))) 1)))

rewrite675.0ms

Algorithm
rewrite-expression-head
Rules
69×add-cbrt-cube add-exp-log
40×prod-exp cbrt-unprod
31×pow1
24×associate-*r/
22×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
18×times-frac pow-prod-down
16×frac-times associate-*l/
15×sqrt-prod
12×sin-mult
9×cbrt-undiv div-exp
8×flip3-+ flip-+
6×associate-/r* frac-add
4×sqrt-div associate-*l* insert-posit16 add-log-exp
3×associate-/l*
2×associate-*r* associate-/r/ *-commutative
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-inv
Counts
4 → 142
Calls
4 calls:
Slowest
240.0ms
(/ 1/2 (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om))) 1)))
212.0ms
(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om))) 1))
152.0ms
(* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om)))
68.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
464.0ms
(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om))) 1))
384.0ms
(/ 1/2 (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om))) 1)))
270.0ms
(* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om)))
165.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))

simplify58.2s

Counts
140 → 154
Calls
140 calls:
Slowest
1.6s
(* (* (* (* (+ (* (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))))
1.4s
(* (* (* (* (+ (* (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))))
1.2s
(* (* (* (* (+ (* (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))))
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 2) 2) (* (* Om Om) Om))))

prune2.8s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.6b

localize58.0ms

Local error

Found 4 expressions with local error:

2.6b
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))
1.8b
(log (exp (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om)))))
0.8b
(* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om)))
0.3b
(* (sin kx) (sin kx))

rewrite268.0ms

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×sin-mult
12×add-sqr-sqrt
10×*-un-lft-identity add-cube-cbrt
8×cbrt-undiv div-exp
7×associate-*l*
6×flip3-+ frac-add flip-+
5×associate-*r* add-log-exp
4×insert-posit16
3×log-prod swap-sqr log-pow *-commutative
1×pow2 exp-prod pow-plus exp-to-pow rem-log-exp pow-sqr pow-prod-up sqr-sin unswap-sqr
Counts
4 → 127
Calls
4 calls:
Slowest
167.0ms
(* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om)))
66.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))
21.0ms
(* (sin kx) (sin kx))
9.0ms
(log (exp (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om)))))

series687.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
261.0ms
(log (exp (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om)))))
238.0ms
(* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))) (* l (/ 2 Om)))
168.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))
20.0ms
(* (sin kx) (sin kx))

simplify34.4s

Counts
114 → 139
Calls
114 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))))
1.4s
(* (* (* (* (+ (* (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 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 (/ 2 Om)) (* l (/ 2 Om))) (* l (/ 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 Om) (/ 2 Om)) (/ 2 Om)))) (* (* (* l (/ 2 Om)) (* l (/ 2 Om))) (* l (/ 2 Om))))

prune2.7s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.6b

localize76.0ms

Local error

Found 4 expressions with local error:

36.6b
(posit16->real (real->posit16 (* (sin kx) (sin kx))))
11.3b
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (posit16->real (real->posit16 (* (sin kx) (sin kx))))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
2.3b
(* (+ (* (sin ky) (sin ky)) (posit16->real (real->posit16 (* (sin kx) (sin kx))))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
0.6b
(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (posit16->real (real->posit16 (* (sin kx) (sin kx))))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1)))

rewrite628.0ms

Algorithm
rewrite-expression-head
Rules
53×add-cbrt-cube add-exp-log
31×prod-exp cbrt-unprod
23×add-sqr-sqrt pow1
21×*-un-lft-identity add-cube-cbrt
18×times-frac associate-*r/
15×sqrt-prod
13×pow-prod-down
9×frac-times
7×cbrt-undiv div-exp
6×associate-/r* flip3-+ flip-+
5×associate-*l/
4×sqrt-div insert-posit16 add-log-exp
3×associate-*l* associate-/l*
2×associate-/r/
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 associate-*r* *-commutative div-inv remove-posit16 unswap-sqr
Counts
4 → 117
Calls
4 calls:
Slowest
237.0ms
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (posit16->real (real->posit16 (* (sin kx) (sin kx))))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
223.0ms
(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (posit16->real (real->posit16 (* (sin kx) (sin kx))))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1)))
165.0ms
(* (+ (* (sin ky) (sin ky)) (posit16->real (real->posit16 (* (sin kx) (sin kx))))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
1.0ms
(posit16->real (real->posit16 (* (sin kx) (sin kx))))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
402.0ms
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (posit16->real (real->posit16 (* (sin kx) (sin kx))))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
388.0ms
(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (posit16->real (real->posit16 (* (sin kx) (sin kx))))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1)))
254.0ms
(* (+ (* (sin ky) (sin ky)) (posit16->real (real->posit16 (* (sin kx) (sin kx))))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
27.0ms
(posit16->real (real->posit16 (* (sin kx) (sin kx))))

simplify43.9s

Counts
113 → 129
Calls
113 calls:
Slowest
1.2s
(* (* (* (+ (* (sin ky) (sin ky)) (posit16->real (real->posit16 (* (sin kx) (sin kx))))) (+ (* (sin ky) (sin ky)) (posit16->real (real->posit16 (* (sin kx) (sin kx)))))) (+ (* (sin ky) (sin ky)) (posit16->real (real->posit16 (* (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)) (posit16->real (real->posit16 (* (sin kx) (sin kx))))) (+ (* (sin ky) (sin ky)) (posit16->real (real->posit16 (* (sin kx) (sin kx)))))) (+ (* (sin ky) (sin ky)) (posit16->real (real->posit16 (* (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)) (posit16->real (real->posit16 (* (sin kx) (sin kx))))) (+ (* (sin ky) (sin ky)) (posit16->real (real->posit16 (* (sin kx) (sin kx)))))) (+ (* (sin ky) (sin ky)) (posit16->real (real->posit16 (* (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)) (posit16->real (real->posit16 (* (sin kx) (sin kx))))) (+ (* (sin ky) (sin ky)) (posit16->real (real->posit16 (* (sin kx) (sin kx)))))) (+ (* (sin ky) (sin ky)) (posit16->real (real->posit16 (* (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)) (posit16->real (real->posit16 (* (sin kx) (sin kx))))) (+ (* (sin ky) (sin ky)) (posit16->real (real->posit16 (* (sin kx) (sin kx)))))) (+ (* (sin ky) (sin ky)) (posit16->real (real->posit16 (* (sin kx) (sin kx)))))) (* (* (* (* l l) l) (/ (* (* 2 2) 2) (* (* Om Om) Om))) (* (* (* l l) l) (/ (* (* 2 2) 2) (* (* Om Om) Om)))))

prune3.5s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.6b

regimes630.0ms

Accuracy

0% (0.7b remaining)

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

bsearch12.0ms

end0.0ms

sample3.8s

Algorithm
intervals
Results
3.5s8000×body80valid