Details

Time bar (total: 2.8m)

sample536.0ms

Algorithm
intervals
Results
503.0ms256×body80valid

simplify225.0ms

Calls
1 calls:
Slowest
224.0ms
(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: 2.6b

localize51.0ms

Local error

Found 4 expressions with local error:

11.7b
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
3.4b
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
0.5b
(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1)))
0.3b
(* (sin ky) (sin ky))

rewrite627.0ms

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
Calls
4 calls:
Slowest
259.0ms
(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1)))
202.0ms
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
134.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
19.0ms
(* (sin ky) (sin ky))

series1.3s

Calls
4 calls:
Slowest
488.0ms
(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
414.0ms
(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1)))
316.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
33.0ms
(* (sin ky) (sin ky))

simplify45.7s

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 (/ 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 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)))))
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)))))
847.0ms
(* (* (* (+ (* (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)))))

prune2.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 1.0b

localize77.0ms

Local error

Found 4 expressions with local error:

3.4b
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
2.7b
(log (exp (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))))
0.3b
(* (sin ky) (sin ky))
0.2b
(* (sin kx) (sin kx))

rewrite289.0ms

Algorithm
rewrite-expression-head
Rules
55×add-cbrt-cube add-exp-log
37×pow1
33×prod-exp cbrt-unprod
23×associate-*r/
19×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/ add-log-exp
6×cbrt-undiv swap-sqr div-exp
4×flip3-+ frac-add log-pow flip-+ insert-posit16
3×log-prod *-commutative unswap-sqr
2×pow2 pow-plus exp-to-pow pow-sqr pow-prod-up sqr-sin
1×exp-prod sum-log rem-log-exp
Calls
4 calls:
Slowest
236.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
23.0ms
(log (exp (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))))
18.0ms
(* (sin ky) (sin ky))
10.0ms
(* (sin kx) (sin kx))

series618.0ms

Calls
4 calls:
Slowest
288.0ms
(log (exp (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))))
281.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
32.0ms
(* (sin kx) (sin kx))
18.0ms
(* (sin ky) (sin ky))

simplify24.8s

Calls
117 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 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)))))
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)))))
986.0ms
(* (- (* (* (sin ky) (sin ky)) (* (sin ky) (sin ky))) (* (* (sin kx) (sin kx)) (* (sin kx) (sin kx)))) (* (* l 2) (* l 2)))
976.0ms
(* (* (* (+ (* (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)))))

prune2.9s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.0b

localize133.0ms

Local error

Found 4 expressions with local error:

7.8b
(real->posit16 (log (exp (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))))))
3.4b
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
2.9b
(posit16->real (real->posit16 (log (exp (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))))))
2.7b
(log (exp (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))))

rewrite204.0ms

Algorithm
rewrite-expression-head
Rules
50×add-cbrt-cube add-exp-log
31×prod-exp cbrt-unprod
23×associate-*r/
22×pow1
13×frac-times pow-prod-down
8×sin-mult
7×associate-*l/
6×add-sqr-sqrt cbrt-undiv div-exp add-log-exp
5×*-un-lft-identity add-cube-cbrt
4×flip3-+ frac-add log-pow flip-+
3×log-prod associate-*l* insert-posit16
2×exp-to-pow
1×exp-prod sum-log rem-log-exp associate-*r* *-commutative remove-posit16 unswap-sqr
Calls
4 calls:
Slowest
178.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
22.0ms
(log (exp (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))))
1.0ms
(real->posit16 (log (exp (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))))))
0.0ms
(posit16->real (real->posit16 (log (exp (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))))))

series809.0ms

Calls
4 calls:
Slowest
284.0ms
(log (exp (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))))
274.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
250.0ms
(posit16->real (real->posit16 (log (exp (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))))))
0.0ms
(real->posit16 (log (exp (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))))))

simplify25.7s

Calls
69 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 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 (/ 2 Om)) (* l (/ 2 Om))) (* (* l (/ 2 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)))))
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)))))
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)))))

prune2.9s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.0b

localize85.0ms

Local error

Found 4 expressions with local error:

3.4b
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
3.4b
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
2.7b
(log (sqrt (exp (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))))))
2.7b
(log (sqrt (exp (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))))))

rewrite365.0ms

Algorithm
rewrite-expression-head
Rules
100×add-exp-log
98×add-cbrt-cube
62×prod-exp cbrt-unprod
46×associate-*r/
44×pow1
26×frac-times pow-prod-down
16×sin-mult
14×associate-*l/
12×add-sqr-sqrt cbrt-undiv log-prod div-exp log-pow
10×*-un-lft-identity add-cube-cbrt add-log-exp
8×sqrt-pow1 flip3-+ frac-add flip-+
6×associate-*l* sqrt-prod
4×exp-to-pow insert-posit16
2×exp-prod sum-log pow1/2 rem-log-exp associate-*r* *-commutative unswap-sqr
Calls
4 calls:
Slowest
184.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
140.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
23.0ms
(log (sqrt (exp (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))))))
13.0ms
(log (sqrt (exp (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))))))

series1.0s

Calls
4 calls:
Slowest
289.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
271.0ms
(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
228.0ms
(log (sqrt (exp (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))))))
222.0ms
(log (sqrt (exp (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))))))

simplify46.4s

Calls
138 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 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 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 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)))))

prune4.2s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 1.0b

regimes735.0ms

Accuracy

0% (0.5b remaining)

Error of 1.2b against oracle of 0.7b and baseline of 1.2b

bsearch15.0ms

end0.0ms

sample3.8s

Algorithm
intervals
Results
3.6s8000×body80valid