Details

Time bar (total: 2.3m)

sample120.0ms

Algorithm
intervals
Results
93.0ms256×body80valid

simplify462.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
460.0ms
(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))

prune43.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.7b

localize129.0ms

Local error

Found 4 expressions with local error:

7.1b
(sqrt (+ (* (* l (/ 2 Om)) (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))) 1))
2.3b
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))
0.6b
(* (* l (/ 2 Om)) (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))))
0.3b
(/ 1/2 (sqrt (+ (* (* l (/ 2 Om)) (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))) 1)))

rewrite893.0ms

Algorithm
rewrite-expression-head
Rules
69×add-cbrt-cube add-exp-log
40×prod-exp cbrt-unprod
31×pow1
30×associate-*r/
22×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
18×times-frac pow-prod-down
16×frac-times
15×sqrt-prod
12×sin-mult
10×associate-*l/
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
423.0ms
(sqrt (+ (* (* l (/ 2 Om)) (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))) 1))
225.0ms
(/ 1/2 (sqrt (+ (* (* l (/ 2 Om)) (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))) 1)))
182.0ms
(* (* l (/ 2 Om)) (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))))
57.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
401.0ms
(/ 1/2 (sqrt (+ (* (* l (/ 2 Om)) (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))) 1)))
361.0ms
(sqrt (+ (* (* l (/ 2 Om)) (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))) 1))
221.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))
206.0ms
(* (* l (/ 2 Om)) (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))))

simplify58.8s

Counts
139 → 154
Calls
139 calls:
Slowest
1.4s
(* (* (* (* l l) l) (/ (* (* 2 2) 2) (* (* Om Om) Om))) (* (* (* (+ (* (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)))))
1.2s
(* (* (* (* l l) l) (/ (* (* 2 2) 2) (* (* Om Om) Om))) (* (* (* (+ (* (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)))))
1.1s
(* (* (* (* l l) l) (* (* (/ 2 Om) (/ 2 Om)) (/ 2 Om))) (* (* (* (+ (* (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)))))
1.1s
(* (* (* (* l l) l) (/ (* (* 2 2) 2) (* (* Om Om) Om))) (* (* (* (+ (* (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)))))
1.1s
(* (* l 2) (* (- (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky))) (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx)))) (* l 2)))

prune2.9s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.6b

localize96.0ms

Local error

Found 4 expressions with local error:

46.9b
(posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))))
7.1b
(sqrt (+ (* (* l (/ 2 Om)) (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))))) 1))
2.3b
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))
0.6b
(* (* l (/ 2 Om)) (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))))))

rewrite172.0ms

Algorithm
rewrite-expression-head
Rules
22×add-cbrt-cube add-exp-log
15×pow1
10×prod-exp cbrt-unprod
8×add-sqr-sqrt
7×*-un-lft-identity add-cube-cbrt
6×pow-prod-down associate-*r/
4×associate-*r* associate-*l* associate-*l/ insert-posit16 sin-mult add-log-exp
3×frac-times flip3-+ sqrt-prod flip-+
2×cbrt-undiv sqrt-div div-exp frac-add *-commutative
1×rem-sqrt-square sqrt-pow1 pow1/2 remove-posit16
Counts
4 → 75
Calls
4 calls:
Slowest
69.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))
60.0ms
(sqrt (+ (* (* l (/ 2 Om)) (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))))) 1))
40.0ms
(* (* l (/ 2 Om)) (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))))))
1.0ms
(posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))))

series874.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
297.0ms
(sqrt (+ (* (* l (/ 2 Om)) (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))))) 1))
212.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))
184.0ms
(* (* l (/ 2 Om)) (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))))))
181.0ms
(posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))))

simplify15.8s

Counts
52 → 87
Calls
52 calls:
Slowest
1.0s
(* (* (* (* l l) l) (* (* (/ 2 Om) (/ 2 Om)) (/ 2 Om))) (* (* (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))))) (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))))) (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))))))
731.0ms
(* (* (* (* l l) l) (/ (* (* 2 2) 2) (* (* Om Om) Om))) (* (* (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))))) (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))))) (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))))))
591.0ms
(* (* (* (* l (/ 2 Om)) (* l (/ 2 Om))) (* l (/ 2 Om))) (* (* (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))))) (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))))) (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))))))
566.0ms
(* (* l (/ 2 Om)) (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))))))
528.0ms
(sqrt (sqrt (+ (* (* l (/ 2 Om)) (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))))) 1)))

prune2.7s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.6b

localize95.0ms

Local error

Found 4 expressions with local error:

46.9b
(posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))))
46.9b
(posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))))
46.9b
(posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))))
7.1b
(sqrt (+ (* (* l (/ 2 Om)) (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))))) 1))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt
5×pow1 *-un-lft-identity add-cube-cbrt
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×sqrt-prod remove-posit16
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 43
Calls
4 calls:
Slowest
61.0ms
(sqrt (+ (* (* l (/ 2 Om)) (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))))) 1))
0.0ms
(posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))))
0.0ms
(posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))))
0.0ms
(posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))))

series886.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
284.0ms
(sqrt (+ (* (* l (/ 2 Om)) (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))))) 1))
223.0ms
(posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))))
205.0ms
(posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))))
174.0ms
(posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))))

simplify6.0s

Counts
22 → 55
Calls
22 calls:
Slowest
539.0ms
(sqrt (* (cbrt (+ (* (* l (/ 2 Om)) (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))))) 1)) (cbrt (+ (* (* l (/ 2 Om)) (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))))) 1))))
527.0ms
(sqrt (sqrt (+ (* (* l (/ 2 Om)) (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))))) 1)))
472.0ms
(sqrt (+ (* (* l (/ 2 Om)) (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))))) 1))
469.0ms
(+ (* (* l (/ 2 Om)) (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))))) 1)
386.0ms
(/ (* (+ (* 2 (pow (sin ky) 2)) (* 2 (pow (sin kx) 2))) l) Om)

prune2.1s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.6b

localize108.0ms

Local error

Found 4 expressions with local error:

22.7b
(posit16->real (real->posit16 (sqrt (+ (* (* l (/ 2 Om)) (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))) 1))))
7.1b
(sqrt (+ (* (* l (/ 2 Om)) (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))) 1))
2.3b
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))
0.6b
(* (* l (/ 2 Om)) (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))))

rewrite547.0ms

Algorithm
rewrite-expression-head
Rules
67×add-cbrt-cube add-exp-log
40×prod-exp cbrt-unprod
31×pow1
30×associate-*r/
18×pow-prod-down
16×frac-times
12×sin-mult
10×associate-*l/
8×cbrt-undiv div-exp
7×add-sqr-sqrt flip3-+ flip-+
6×*-un-lft-identity frac-add add-cube-cbrt
4×associate-*l* insert-posit16 add-log-exp
3×sqrt-prod
2×sqrt-div associate-*r* *-commutative
1×rem-sqrt-square sqrt-pow1 pow1/2 remove-posit16
Counts
4 → 109
Calls
4 calls:
Slowest
271.0ms
(sqrt (+ (* (* l (/ 2 Om)) (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))) 1))
200.0ms
(* (* l (/ 2 Om)) (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))))
73.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))
1.0ms
(posit16->real (real->posit16 (sqrt (+ (* (* l (/ 2 Om)) (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))) 1))))

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
319.0ms
(posit16->real (real->posit16 (sqrt (+ (* (* l (/ 2 Om)) (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))) 1))))
262.0ms
(sqrt (+ (* (* l (/ 2 Om)) (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))) 1))
226.0ms
(* (* l (/ 2 Om)) (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om))))
194.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* l (/ 2 Om)))

simplify35.0s

Counts
92 → 121
Calls
92 calls:
Slowest
1.2s
(* (* (* (* l l) l) (/ (* (* 2 2) 2) (* (* Om Om) Om))) (* (* (* (+ (* (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)))))
1.2s
(* (* (* (* l l) l) (/ (* (* 2 2) 2) (* (* Om Om) Om))) (* (* (* (+ (* (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)))))
1.2s
(* (* (* (* l l) l) (* (* (/ 2 Om) (/ 2 Om)) (/ 2 Om))) (* (* (* (+ (* (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)))))
1.1s
(* (* (* (* l l) l) (/ (* (* 2 2) 2) (* (* Om Om) Om))) (* (* (* (+ (* (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)))))
1.1s
(* (* (* (* l (/ 2 Om)) (* l (/ 2 Om))) (* l (/ 2 Om))) (* (* (* (+ (* (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)))))

prune3.9s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.6b

regimes690.0ms

Accuracy

0% (0.7b remaining)

Error of 1.4b against oracle of 0.7b and baseline of 1.4b

bsearch9.0ms

end0.0ms

sample4.0s

Algorithm
intervals
Results
3.7s8000×body80valid